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AFFTAC 3 - Scott Runnels Consulting

1. Lemon Figure 3 2 Illustration of the four step editing process for setting up AFFTAC simulations 27 Running an Analysis There are two ways to initiate the execution of an analysis One is to highlight the analysis in the Analysis Database of the Main Window and then click the dark blue panel in the upper right portion of the Main Window The other is to click the Run Now button in any of the four editing windows In this latter option the changes you have made during the editing sequence are automatically made part of the current highlighted analysis However those changes are not saved permanently to the Analysis Database until you choose the menu option File Save Analyses Database The analysis is carried out by AFFTAC s Computational Module which is a stand alone executable invoked by the GUI When you request the simulation to be run the GUI writes the necessary input files for the Computational Module It then runs the Computational Module which executes in an DOS window that opens to display the simulation s progress Once the simulation is completed the GUI reads the Computational Module s output files and displays them in the two panels on the right hand side of the Main Window Viewing and Using Results After a simulation is completed the results are displayed on the right hand side of the Main Window The top right panel of the Main Window displays a par
2. Figure 3 1 AFFTAC s Main Window in which the Analysis Database is displayed in the left most Manage Legacy TPS Model Fraction covered by TPS not valid for bare tarka 1 r r A Edit Analysis Conditions 3 Edit Tank Car Properties Tank Geometry Tank Material Fre Conditions 20000 Nominal Capacty gal ASTM 537 80 Class 1 Tensile Strength 70 Kps m iyu Diameter in 500 Meum Bunt Pressure Sardar Torch os Wal Thickness 81000 Ta dpecil Conditions of Tank to Strength Model Database Fre Emast s ll 08 Enissivty 4 Tank s inner Surface Used by old TPS model mupersceded TPS model a used si i Safety Relief Device Angie cl Rotover degree Trang Device 25800 Rated Eden Baseine Case 17 Flow Capacty SCFM of ar n 255 Pressure ips 9 25 SattoDacharge Pressure pug Vert with Rupture Disc gt ne os Vapor Discharge decima traction 06 Liquid Discharge Coefficient decimal fraction e Such to PRO Database Setup Ladis eo Previous Select Lading Defaut Ua Low H20 Content z f m H H20 Content PL Water SetchioGenemued TPS Mods
3. 0 128 At this point the surface integral can be simplified in two ways 1 In the present application the surface area is comprised of only one inlet and one outlet The areas for the inlet and outlet are A and A respectively 2 An approximation is made concerning the direction of the flow at the inlet and outlet It is assumed that the flow is normal to the control volume A and A which means that the dot product between velocity and the surface normal vector is simply the magnitude of the velocity V Under these assumptions 2 2 B 40 h e 44 h The products of density area and velocity that appear on both sides of the above equation are expressions of mass flow rate Conservation of mass therefore means that these two products must be equal and therefore cancel And so the First Law becomes 2 2 B 41 V h aM h 2 2 1 The control volume for this application is chosen to be such that the velocity at the inlet is very small such that V is negligible Under that assumption the First Law is 1 B 42 B 43 is a constant With c being a constant the above equation may be integrated such that h h c T T 44 is an arbitrary datum Substituting this expression into the First Law produces y B 45 2 tc T T c T T The 7 terms cancel and thus 129 y B 46 5 eT e Dividing by To y T B 47 c
4. eae ae enean 123 APPLICATIONS OF THE FIRST LAW OF 5 1 00 123 Application to Ouasi Static Process iiie set exer rne eerta e 123 Application to a Control Volume dd eed adt dd geadt ados 126 MASS FLOW FOR AN IDEAL 131 AFFTAC S SUB SONIC VAPOR FLOW 133 APPENDIX C THERMODYNAMIC IDENTITIES FOR AN IDEAL GAS 135 APPENDIX D DERIVATION OF PRD AREA ESTIMATION FORMULA 137 APPENDIX E DERIVATION OF SHELL FULL LIQUID EXPULSION PRESSURE 24 2 2 26 eden ora rae cana ne sani o ione bras ac Ue ME 141 APPENDIX F GOVERNING EQUATIONS FOR THE GENERALIZED TPS Tr RR 145 CONVECTION AND RADIATION COMMUNICATION 5 0 0 100 145 CONDUCTION COMMUNICATION AREAS 1 0 80000000 146 HEAT BALANCE 8 0081808 800800 148 Area Int ve eee e deep 148 Right Side s Exposed ALOT ete a Pelias bashie qe teli Revue t PHAR Ie
5. ap 79 and then by V T B 48 26 0 T k In Appendix C it is shown that for an ideal gas e Using that fact the First Law becomes V so B 49 2 T Also for ideal gas and this term appears in the above equation Therefore the ratio M where M is the Mach number the ratio of speed to the speed of sound The First Law terms of M is xps qe B 50 Inverting the above equation _ 1 51 ir aym 2 Using Equation B 22 the First Law may be written as k 1 7 52 1 020 2 M or 130 Mass Flow for an Ideal Gas The mass flow rate is pVA where p density V average velocity A area of flow For an ideal gas where p pressure R gas constant By substitution of the ideal gas law into the mass flow rate equation G VA RT B 53 B 54 B 55 B 56 B 57 B 58 The following step is simple algebra The RT term is split into two square roots and a form of unity k k is introduced The value k is the ratio of the vapor s specific heats as was described in the previous sub section Equations B 13 B14 fk G pA NRT For an ideal gas the speed of sound c is c AKkRT For an ideal gas the Mach number is B 59 B 60 131 The Mach number can therefore be used in
6. c 1 c Ac 1 lt c F 8b p c l c 1 F 8c Table F 1 Computing Areas of Contact and Exposure Using a Joint Probability Approach To determine the communication areas between two areas one multiplies the two joint probabilities together because doing so represents the probability of overlap Table F 2 summarizes the results of this approach The left column describes the two areas that are overlapping the third column is the area of overlap Nomenclature column establishes a simpler notation that is used in subsequent equations There are some subtleties to the notation First the area connecting T and is reversible e g Using this fact the variable can be used to represent other 2 the i index L and R in is omitted since that conduction must occur on layer i combinations Substituting i for i A Another subtlety is that 1 Ql Likewise the i subscript is omitted on R in since it that conduction must be i And note that if the area connecting and is needed i can be substituted for i giving the quantity A r 1 6 Finally the subscript on L is omitted in A since that conduction must be on i 147 Conduction Joint Probability at Path a Point of Overlap Scaled to Obtain Connecting Occuring Area Nomenclature Ci 4C Ci Ci 9
7. 108 00 Baseline Case 4 TPS version of Case 1 Scott Runnels 09 26 2010 Narr Hines cope yt 0 9000 T Tank Material Type carbon steel TPS Test Metal MetalwPartialCoverage Gap Metal FirstName LastName 10 02 2012 Tensile Strength of Tank Material psi 7 0e 004 PRV Fullcircle test A 1400 FirstName LastName 11 12 2012 Nominal Burst Strength psig 500 0 PRV Fullcircle test A 37000 FirstName LastName 11 12 2012 Calculated Horst NbresgER sa Model Results for Baseline Case 1 PRODUCT Hydrochloric Acid Version TIME TEMPERATURES PRESSURES MASS FILLED RATE OF j min deg F WITHIN BURST FRACT FRACT PRODUCT uj Create and Delete Edit LIQ TANK TANK STR IN RELEASE Analyses Analyses Plotting PROD VAPOR psi psi TANK TANK 1bs min Plot Di New Edit Analysis Dipin OUTSIDE CONCENTRATION RANGE OF THERMAL PROPERTY DATA TUNER 0 00 70 0 70 0 0 0 6 5 002 1 000 0 980 0 0 3 00 71 1 120 7 0 2 6 5e 002 1 000 0 980 0 0 6 00 74 4 246 7 0 7 6 5 002 1 000 0 981 0 0 3 aste Release 4 00 T mue 122 m S L j Figure 3 3 AFFTAC s Main Window displaying the results of an analysis on the right Temperatures deg F Fraction eo d 8 200 9 20 40 Time min 0 995 0 99 0 985 0 98 50 Time min 100 100 Pressures psi 0 20 40 60 Tim
8. Sulfuric Acid Figure 13 1 Ladings Database 113 Click New When you do a new lading is added to the list and is displayed as the last entry This new lading is merely a placeholder It does not yet have any real data associated with it To provide the necessary data highlight it and click the Edit button Doing so displays the window shown in Figure 13 2 In this window the various properties required by the AFFTAC Computational Module are displayed First type in the name Lading in the Name entry box Next make sure that the Substance button is selected Note that if Solution is selected try it there are some properties that require values for both the solvent and solute and some values are required at two concentration levels Now it will be demonstrated how to provide the data for one of the properties Click on the Edit Table button next to the Specific Heat label When you do the window shown in Figure 13 3 appears Edit Lading Properties EI Name Myladng Type of Lading Molecular Weight E Lading has a critical temperature Solution 0 0 9090909 Emissi Substance Depends on Temp Edit Table Specific Heat BTU b 7 Edit Table Specific Volume ft 3 Ib 2 Edit Table Heat of Vaporization BTU Ib 7 Edit Table Vapor Pressure psia 7 Edit Table Compressibility Factor 7 Edit Table Figure 13
9. 2 W k n n Diagonal entry gt Grr gt Ps Ww ik ik k i 1 i k i 1 Diagonal entry 1 Diagonal entry A A 4 T Ww J J i 1 R i One entry before the diagonal l lt i lt n i 1 R Ww k One entry before the diagonal A i n W Third row of blocks k Diagonal entry A 6 lt lt W 1 0 i n Diagonal entry 1 if c 0 One after the diagonal EC l lt i lt n Wi lt Diagonal entry 1 i n Diagonal entry 1 if c 0 158 F 39 c 0 i n F 40 l lt i lt n c 0 i n F 41 F 42 F 43 F 44 Diagonal entry t 4 t Ap One before E Oneafter W i 1 1 1 1 l lt i lt n 1 33 j if 0 i norif c 0 Diagonal entry 1 or if c 0 159
10. 60 144 gk 2 32 2 1 4 2 which is what is used in the code i e the line originally presented in this appendix rewritten as 0 e D 15 Ato 140 Appendix E Derivation of Shell Full Liquid Expulsion Pressure In the ShellFull routine the discharge coefficient is used to compute the pressure required to discharge the required amount of liquid where the required amount is computed using a volume comparison The line of code to compute the required pressure is shown below pcom pmin pow reql 720 0 DischargeCoef Liq areq 2 64 4 splq The volume to be expelled is computed as follows reql 0 9 reql40 1 TotalMass splq TankVolume cufeet delt Ignoring for the moment the 0 9 0 1 relxation factors this equation may be rewritten as 141 TotalM ass v Vank reql m reql 15 the required liquid volumetric flow rate in a shell full condition Renaming 3 ft that variable to EM the pcom equation from the line of code above may be written min as 2 720 64 4 Vig Pom P min T The derivation of this equation starts with the Bernoulli equation 1 Prom z Prin tu I It 1 Ibm of ft Peom ft Puis ft z a ft sec With units it 1s The fact that 2 1 Ibm 2 5 g ft may be substituted to produce lbf Ibf Pia lbf sec y ft 2 Pain 27 ft sec C
11. An indication of a representative value to use for this parameter can be inferred from the results of the full scale fire test on a tank car filled with propane 6 The results of this test indicated that the average conductance over the surface of the car was 300 BTU hr ft deg F The conductance of the 5 8 in thick steel wall can be estimated at approximately 500 BTU hr ft deg F which implies that the conductance for the film would be about 750 BTU hr ft deg F A value of 1000 BTU hr f deg F is recommended as conservative representative value When only vapor is present the convection coefficient is set to 1 0 BTU hr ft deg F 44 In both the legacy and new generalized TPS model the convective heat transfer is modeled as an additional virtual layer of resistance because it has exactly the same mathematical form as a heat conductance model linear in the temperature difference Temperature Change in the Tank Wall Adjacent to the Vapor In both of the het flux terms in the preceding two sub sections the value for T is wall vapor considered known But as discussed at the beginning of this chapter and shown in Figure 5 2 it is determined by considering the heat balance on that part of the tank wall The net heat flux 15 the heat entering the wall from the outside minus the heat leaving the wall and going into the lading The difference in those fluxes is used to evolve wall vapor over time as follows dT 5 10
12. Ibf D 4 Pad Lg Pap Making these substitutions Qa tom ES ee k 1 lbf k zum 144 Coy Pexp 4 ft Ibf eden exp Ibm R or D 6 A ft k l ee oe k 2 pz Dv p ft 2 ft Ibf 41 Ibm R Now the remaining units may be considered First inside the radical the fact that ibe ft D 7 2 1 Ibm sec 138 is used Making that substitution 2d 1 Alf exp 60 144 Ibf k ft p Af 4 ft 22 R exp 2 sec The Rankine units cancel leaving ft sec the denominator inside the radical Bringing those units outside the radical results in Ibm D 9 tm sec 60 144 lbf sec k 2 Ka Cos Pexp 2 f A ft Kk Simplifying produces fe D 10 F 2 c a 6014 k 2 p 287 k 1 Using again that ldbm _ 1 sec g ft results in 2 25 1 Y sec fe D 12 S mY Leh ft ay k 2 ca n zc J vl exp Pulling inside the radical and coelescing units produces 139 amp 0 rt o k l cos 160344 gk 2 t AGERE ecl exp The term in curly braces evaluates as follows D 14 ZRT k 1 0 0763 1 53 3533 60 459 1 4 1 exp
13. Users Manual For AFFTAC 4 00 Beta 06 Prepared by Dr Scott Runnels Scott Runnels Consulting For The RSI AAR Railroad Tank Car Safety Research amp Test Project January 24 2013 Copyright 2001 2013 The RSI AAR Tank Car Safety Research amp Test Project LICENSE AGREEMENT FOR USE OF AFFTAC FOR WINDOWS SOFTWARE LICENSE AGREEMENT FOR USE OF AFFTAC FOR WINDOWS SOFTWARE The purpose of this License Agreement Agreement is to set forth the terms and conditions that shall govern the use of the AFFTAC 4 00 software AFFTAC by the licensee the Licensee to whom AFFTAC has been distributed without charge through The RPI AAR Tank Car Safety and Research Project comprised of The Railway Progress Institute and the Association of American Railroads collectively Licensor The parties agree as follows TERMS 1 LIMITED LICENSE Licensor hereby grants to the Licensee and the Licensee hereby accepts a non transferable non exclusive limited license to use AFFTAC and any licensed supporting materials Licensed Materials Notwithstanding the foregoing the Licensee s right to use AFFTAC is subject to the restrictions set forth in Sections 1 a 1 e below a The Licensee may not disassemble decompile or otherwise reverse engineer AFFTAC b The Licensee shall not remove or alter any copyright notices and other proprietary rights legends of Licensor or of any other entity contained in or on AFFTAC c The Licensee
14. ccsssccceccescececcsccececcsceceasesceccansecceaaesceceaseseceeaneneeees 51 Bare Tank or Non Jacketed Tank with Partial Insulation Coverage 22 Partial Insulation Coverage Inside Jacket 54 HEAT FLUX INTO LADING AND THE TANK WALL OVER VAPOR 57 CONDUCTANCES FOR MULTI LAYER 55 22 20000000 00 57 THE GENERALIZED TPS MODEL AND n aeneae au 61 USING THE GENERALIZED TPS MODEL eeeeeeeeeeeen nn ne nnnm nnn nnn nnn nnn nnn nna 63 GENERAL TPS MODEL THEORY 64 E ZEILE 66 Right Side B EXPOSED 66 Left 51 8 Exposed Area ee tes eb med idus 67 Tp CODD OM side tuque adde da De 67 STRENGTH ae pese beoe acu 69 LEGACY STRENGTH MODBL 3 2 etc tese Paces ba ive det det Ee Pee iude 69 THE STRENGTH MODEL 70 Validated Entries in the Failure Model Database eee 75 LARSON MILLER MODEL 75 Burst Pressure for the Larson Miller Failure Model sss 80 Interactions wit
15. 1 layer which are specified in the middle of the window A component consists of a bulk material the specification of the layer s thickness and the emissivity on each surface Also the coverage of the component can be specified as a function of angle around the tank in the lower middle portion of the window Finally a TPS is constructed on the far right by assembling layers In Figure 7 4 several TPSs are shown The layers of the highlighted TPS SteelJacketedTrend50 are shown in the rightmost list box 63 A Generalized TPS Model Setup aa x Define Bulk Materials Define Components using Bulk Materials Build a TPS from Components Material Name Conductivity Tables i What s this What s this What s this e die et Insulator Composed of RawMatName Bare Tank Wall Conductor OneLayer Insulator Coverage50 Imaginary Interior Emmissivity TwoLayer Void Perf Imaginary_TPS Jacket Void ar ade Exterior Emmissivity Liner Wall 4Segment Width inches 4Segment ConductorForJacket Te Void Add BareJacketed Damagedinsulator 65 Before InsulatedJacketed Wall 55 5 pus pon deecte So sly InsulatedJacketed_SSCase5 Delete iacket 55Lase What s this BareTank2Layer ALIM Bare Tank3l BareJacketed3LayerWall Very Thin Wall BareJacketed2LayerWith ThinW d iner
16. 84 Table 9 1 Parameters used in modeling PRDs Specifying a PRD Directly during the Editing Sequence To specify the parameters describing a PRD directly in an analysis click the Switch to Legacy PRD Setup button in the Edit Tank Car Properties window which is the second of the four window editing sequence for an analysis When you click that button the lower part of the Edit Tank Car Properties window will take on the appearance like that shown in Figure 9 1 left As can be seen from the figure there are two types of PRDs a valve and a vent with rupture disk The values specifying their performance were described in Table 9 1 and can be more fully understood by reading the theory section later in this chapter A Edit Tank Car Proper pum MM eee oes Tank Geometry Tank Material Tank Geometry Tank Material 20000 Nominal Capacity gal TC 1288 20000 Nominal Capacity 1288 Non Nomalized n Normalized Inside Diameter Inside Diameter n TC 1288 Non Nomalized No UTS mali n 1288 Non 05 Wall Thickness ASTM A516 1288 yrs 1968 2002 05 Wall Thickness Switch to Legacy Strength Model Edt Database Switch to Legacy Strength Model Edit Database I 08 Emissivity of Tank s Inner Surface Used by old TPS model only 08 Emissivity of Tank s Inner Surface Used by old TPS model only supersceded if new TPS model
17. ACC Ta c 1 A similar exercise can be performed for the left side of Layer i and the right side of Layer i 2 Their communication area is Acl eis F 5 Likewise for i and i 3 1 1 6 And for Layer i 4 it is 1 1 1 So in general the communication area between the left side of Layer i and the right side of Layer j is i F 8 A m 1 mo 1 Conduction Communication Areas areas including the area in contact and the areas exposed to radiation and convective heat transfer experience conduction The areas over which each of the three temperatures exist may be computed by considering the fractional coverages as 146 probabilities For example the probability at any point in the i interface of Layers i and 1 1 being in contact is the product of the probability of there being material present on Layer i with the probability of there being material present on Layer i cj 7 Scaling this product by the total area considered yeilds the area of the region in contact a similar fashion the area over which T exists is the product of the probability that material in Layer i is present with the probability that material in Layer i is not present c In summary the areas as follows Temperature Joint Probability at a Point Scaled to Obtain Area T a F 8a
18. Due y j Q E tol 2 g Jes F outer noIns f tof ii Psp outer Ins OT outer Ins 56 of Ao amp 6 16 2 ar Su tof om gt OT serons 2 6 EC CN 6 17 oT 2 6 E Wm OP icis of 40 RR 2 E An initial guess is required to start the Newton Raphson iterations For all but the first time step the solution from the previous time step is sufficient But for the first time step the initial guess is provided using an approximation The geometric view factor for the flame tank exchange is assumed to be unity except in the case of a torch fire where it is assumed to be 0 536 The geometric view factor for the jacket wall exchange is unity Heat Flux Into Lading and the Tank Wall over Vapor Space Once the nonlinear system is solved to determine the temperatures on the outer surfaces those values can be used to compute the flux as follows C gt 41 Qrps liquid Fel Tian C 1 1089 Y NI T ain C 6 18 Qrps vapor Fp CT aioe pee apr Lie 1 Fp vapor Cw 6 19 Here C and C represent the conductivities for the regions with and without insulation Conductances for Multi Layer TPSs The thermal transport models described in the previous section rely heavily on composite conductances Considering one dimensional heat conduction through several layers it is 5
19. coverage in Layer i Heat conduction still occurs to the left but radiative and convective heat transfer occurs to the right Again a heat balance on the interface states that the heat flowing into it must equal the heat flowing out of it That requirement is embodied in the following equation where heat conduction to the left is represented in the first terms and radiative plus convective heat flow is represented in the last terms 6 2 E Te d T Tri T W 1 olr T 2 4 h T T 2 44 Ep 1 Fi Again while not all of the nomenclature is defined here it is in Appendix F the above equation can still give you a feel for this part of the theory Part of the heat leaving a surface that is exposed is due to conduction through its own layer those are the first two terms The third term represents the convective heat transfer between the exposed area and all of the other exposed areas it sees Keep in mind that there are an arbitrary number of layers which explains why the summation sign is needed The last term is the radiative exchange between the exposed area and all the other exposed areas it sees 66 Left Side s Exposed Area The equation for the left side s exposed area is exactly analogous to that for the right k 6 3 S Ar A Ads w W ge olf 71 i l A h W T J A 2 LR vel L j e LR 1 Ep 1 Again the theory is
20. that m p 0 1 227 10 8 In terms of diameter d the result 15 dp 10 9 At Wall has c thickness 1 PA 2 AQ Figure 10 1 Circumferential stress in the tank wall and its relationship to the pressure differential PN Wall has thickness 7 Oa Figure 10 2 Axial stress in the tank wall 102 Elastic Strain The axial and circumferential stresses derived above are related to the corresponding strains through Hooke s law of elasticity o Cy a E E E where E is Young s modulus and vis Poisson s ratio Plastic Strain 10 10 The plastic strain that occurs and is modeled using the Larson Miller model is not yet implemented in the volume change calculation Combined Strain The thermal strain circumferential strain and axial strain all contribute to a change in volume of the tank car The thermal strain acts in all three directions and so the change in volume depends on it to the third power The circumferential strain will act only on the circular cross section and so the change in volume depends on it to the second power The axial strain only acts in one direction Therefore the new volume is due to these effects is modeled as 1 oT V 1 a il 17 oT 10 11 103 104 Numerics Some of the core conservation models in AFFTAC manifest themselves as first order ordinary differential equations For example Equ
21. wall vapor TH dt vapor E nad wall liquid d conv wall vapor where each term is a per area basis including which is the mass of the tank wall vapor wall over the vapor space on a per area basis It is the product of its density and specific heat Clearly the last two heat flux terms are the very ones in the preceding sub sections that depend on T This is not surprising because all of these variables are in fact all vapor linked simultaneously in time But as has been mentioned multiple times at this point in the manual these linked governing equations are split and solved in pieces Thus using T soper and other values from the previous time step q T and ipo Ale computed Those values are then used to update and other variables as well such as T In Figure 5 2 and the above equation q is the heat conducted from the outer part of the TPS into the tank wall Along with its counterpart in the liquid region q it is a principle output of the TPS models and its computation is described in detail in those chapters Temperature Change of the Lading and Tank Wall Adjacent to the Liquid As already mentioned AFFTAC assumes the vapor and liquid temperatures are equal and the tank wall adjacent to the liquid is at the same temperature as the liquid The liquid phase of the lading and the part of the tank wall adjacent to it are lumped into one
22. ASTM A 537 80 70 000 Class 1 Min 14 ASTM 302 69 60 000 Gr B Min 15 ASTMA302 70a 60 000 Gr B Min Table 8 1 For carbon steels hard coded room temperature tensile strength column 3 and multiplicative adjustment factor that reduces that strength due to higher temperatures column 4 Here temperature T is in thousandths of Rankines See 15 71 ID Description S AdjustmentFactor d 16 ASTM A 240 70 75 000 1 0 45 T 0 860 0 90 8 60 T 1 760 Type 304 Min 17 ASTM A 240 70 70 000 f 240 55 0 55 T 1 760 0 40 1 76 T 2 16 Type 304L Min 0 T 2 160 18 ASTM A 240 70 75 000 1 0 55 T 0 860 0 90 8 60 T 1 760 Type 316 Min 19 ASTM A 240 70 70 000 f 240 45 0 45 T 1 760 0 40 1 76 T 2 16 Type 316L Min 0 T 2 160 Table 8 2 For stainless steels hard coded room temperature tensile strength column 3 and multiplicative adjustment factor that reduces that strength due to higher temperatures column 4 Here temperature T is in thousandths of Rankines See 16 and 17 Alloy 6061 Min ID Descripiion 5 Adjustment Factor 20 ASTM B 209 70 75 000 1 0 55 T 0 860 0 90 0 610 T 1 260 Alloy 5052 Min f 21 ASTM 209 70 38 000 0 gt 2 6 5083 22 ASTM B 209 70 35 000 Alloy 5086 Min Here it is noted
23. BT EC B 18 a For an ideal gas pv RT so that the above equation may be written as Ty _ v k B 19 T v I 1 T v k l B 20 T Vi 125 The ideal gas law RT be applied again to produce T RT p e u T p pel T RT Pi Manipulation of the above equation results in k l pof K B 22 T Application to a Control Volume The differential form of the First Law of Thermodynamics for a system First Law is as follows dQ dW dE B 23 where Q heat transferred in to the sy stem B 24 W work done by thesystem E energy in the sy stem The right hand side has to do with the state of the fluid in the system Since fluid can move through the system it is helpful to highlight that fact when writing the First Law as time derivatives In particular the energy time derivative must be a substantial derivative 1 follows the substance which is the fluid Capital D is used for that purpose and the time derivative form of the First Law may be written as dQ 2 dW DE B 25 dt dt Dt It is necessary at this point to more firmly establish the notion of a control volume which will be denoted here by Reynolds Transport Theorem accounts for the fact that the substance fluid flows through the control volume In taking the flow into account the First Law which is meant to apply to a system can be made to handle the situation where fluid flows through
24. Non Nomalized TC 128B yrs 1968 2002 A212B yr 1964 tht 1 Done write to file Done dont write yet Figure 8 3 Failure Model Database management window 74 r A Strength Model Editor e Name 128B Non Nommalized V Larson Miller Edit Larson Miller Parameter V Ultimate Tensile Strength Edit Ultimate Tensile Stress mm Figure 8 4 Editing window for new failure models Larson Miller and Ultimate Tensile Strength models are two of a set of future options Validated Entries in the Failure Model Database AFFTAC comes shipped with a handful of steels that have been successfully validated against the Larson Miller failure model in recent small scale experiments The validation procedure is described in 21 In that report the fits to the experimental data are shown Also verification tests that are part of the AFFTAC Regression Test Database are described in the Verification and Validation Testing document Larson Miller Model Theory High stress at an elevated temperature creates damage in materials that accumulates over time The damage is due to the migration and production of microscopic defects both of which occur at higher rates as stress and temperature is increased As the damage accumulates the material becomes weaker and it creeps under loading Eventually the damage can accumulate to such a high level that th
25. OK This same process may be repeated for all of the properties listed Note that the current version of the Computational Module has certain requirements regarding the number of data points that should be provided for each property If those requirements are not met the AFFTAC GUI will inform you when you click OK in the Edit Lading window 115 Switch to algebraic input method 40 60 Temperature deg F Figure 13 4 Specific volume for Tutorial 2 116 Bibliography 1 Johnson Milton IIT Research Institute Chicago IL 60616 Tank Car Thermal Analysis Volume I User s Manual for Analysis Program final report for the U S Department of Transportation Federal Railroad Administration Office of Research and Development Washington D C 20590 DOT FRA ORD 98 09A November 1998 2 Johnson Milton IIT Research Institute Chicago IL 60616 Tank Car Thermal Analysis Volume II Technical Documentation Report for Analysis Program final report for the U S Department of Transportation Federal Railroad Administration Office of Research and Development Washington D C 20590 DOT FRA ORD 98 09B November 1998 3 Johnson M R Temperatures Pressures and Liquid Levels of Tank Cars Engulfed in Fires Volume 1 Results of Parameteric Analyses and Volume II Description of Analytic Procedure Federal Railroad Administration Report No DOT FRA OR amp D 84 08 IL June 1984 4 Specificatio
26. Original Mass Of Tank Filled Fraction wo wo Rate of Release Ibs min LIE ud lub lu 0 50 100 0 20 40 60 80 100 Time min Time min Plot Controls Pressure fraction filled Log Fraction of Life Depleted 0 50 100 Time min Click plot to copy ctrl v to paste in MS Office Figure 8 6 New plotting capability that shows Fraction of Life Depleted when the Larson Miller failure model is used The second stage is truly much larger than the other two on the order of a thousand times greater Thus it is often the exclusive focus of phenomenological failure modeling for engineering applications The strain rate during that second stage 15 referred to using different terms including the secondary strain rate the steady state strain rate and the minimum strain rate All of these terms are correct and appropriate Here the term secondary strain rate will be used and the variable will be denoted as In deriving the Larson Miller phenomenological failure model it is assumed that the phenomena giving rise to the secondary strain can be modeled using the Arrhenius equation The Arrhenius equation is empirical but has been found to accurately model several phenomena such as diffusion and reactions where temperature plays a key role Insofar as the accumulation of damage that leads to ductile failure is like a diffusion process
27. The heat of vaporization decreases with increasing temperature The following default values are suggested although they may not be conservative in all cases Temperature 60 240 If the product is a solution containing at least 50 percent water as the solvent the Heat of Vaporization BTU Ib 300 100 following values are suggested Temperature Heat of Vaporization BTU Ib 60 800 240 300 Compressibility Factor This parameter does not have a major influence on the calculations A default value of 0 9 16 suggested for the compressibility factor of product vapor It would be entered into the program at two values for temperature e g 60 and 300 P Ratio of Specific Heats This parameter does not have a major influence on the calculations A default value of 1 1 is suggested for the ratio of specific heats of product vapor It would be entered into the program at two values for temperature e g 60 and 300 P 122 Appendix B Choked Vapor Flow Derivation and Area Estimation Method The primary reference for these derivations is given in 19 Applications of the First Law of Thermodynamics Application to Quasi Static Process In this section thermodynamic relationships are derived that describe intrinsic responses of the fluid without consideration of a system To derive these relationships consider fluid in a quasi static process where pressure p is uniform The differential form of the First Law of Thermo
28. Typical Simulation Heat is added to the system on the outside of the tank car through heat exchange with the fire This heat is transported to the inside of the tank through the tank wall and thermal protection system eventually reaching the lading The heat is transported to the lading by contact with the wall and by radiation to and from its interior surfaces The lading responds by heating up the liquid thermally expands and evaporates causing the vapor pressure to increase If the tank is in a shell full condition i e when it is completely full of liquid the liquid s thermal expansion results in an increase in pressure inside the tank When vapor is present the pressure also increases but is due instead to the vapor 17 pressure Either way when the pressure inside the tank reaches a sufficient level the tank s pressure relief device opens and allows lading to be released A supporting model for the pressure relief device is provided as part of the AFFTAC simulator Flow of vapor liquid or a mixture depending on the rollover condition and the amount of liquid present is accommodated by these models The simulation is carried out starting at time 0 and under normal circumstances ending at a user specified time However as the simulation proceeds the lading could eventually be completely expelled causing the simulation to end earlier Another possibility for early termination occurs when the pressure relief device is not able
29. When solving for the part of the tank wall adjacent to the liquid the inner temperature of the tank wall is set to Tiading When solving for the part of the tank wall adjacent to the vapor the inner temperature of the tank wall is set to Twall vapor When solving for the liquid region the solution obtained for Touter ms is used for Touter ms liquia and the solution obtained for Touter noIns 18 used for exact analogy is used for the vapor region The following equation represents the heat balance on the jacket E E E 6 5 4 2 Je F of innl Fyp 42 0 This is the heat balance on the bare tank surface E E 6 6 4 2 _ 4 2 on ae T 0 And this is the heat balance on the insulation surface M 6 7 o 2 C 0 2 6 2 6 54 outer noIns eee T outer nsulation LM Wall Insulation a Insulation Between Jacket b Partial Insulation Between and Tank Wall Jacket and Tank Wall Figure 6 4 Heat exchange diagram for jacketed systems showing relevant nomenclature In the above equations o is the Stefan Boltzmann constant and the f parameters are the surface configuration factors surface configuration factors rely upon the emissivities geometric view factors and areas of the surfaces involved see Equations 5 2 5 5 The and C are thermal con
30. calculation forward At the end of each time step all variables will have been updated This method is often referred to as nonlinear lagging or operator splitting This aspect of the calculations is very important to understand when delving into the theoretical descriptions in the chapters that follow In all of the chapters you will notice that some values which you know to be transient and part of the overall solution will be assumed known for that part of the theory By considering all parts of the theory in the same context you will see how all values are eventually updated 18 Heat Transfer and Mass Flow Computations Shell Full a Update lading temperature a Compute mass flow Liquid and Vapor Venting Liquid a Compute mass flow a Update liquid temperature Vapor Only a Update lading temperature a Compute mass flow Liquid and Vapor Venting Vapor a Compute mass flow a Update padding gas pressure a Update liquid temperature Figure 2 1 Conceptual flow chart of the AFFTAC model computations Heat Transfer Assumptions Heat transfer is a primary driver in AFFTAC and so in a sense the heat transfer model is the core driving model It has multiple aspects that are addressed in multiple places in this manual Here some of the key overarching assumptions and approaches are described First the fire is modeled as a fixed temperature surface some
31. is constant in time value of the conductance is 5 4 BTU hr ft deg F r A Edit Analysis Conditions Fire Conditions Standard Pool Fire Sandard Torch Fire Special Conditions 0 8 Fire Emissivity 8 Length of Simulation minutes Editing Baseline Case 1 Run Now Figure 12 1 Analysis conditions for Tutorial 1 108 Edit Tank Car Properties maa Tank Geometry Tank Material 33000 Nominal Capacity gal AAR TC128 70 Grs A amp B Min Tensile Strength 81 Kpsi X 112 Inside Diameter in 500 Minimum Bursting Pressure psig 0 5625 Wall Thickness in 81000 Tenslie Strength of Tank Material psi Switch to Strength Model Database 08 Emissivity of Tank s Inner Surface Used by old TPS model only supersceded if new TPS model is used Safety Relief Device Device Type 32000 Rated Flow Capacity SCFM of air 270 Pressure psig Valve I a 247 5 StarttoDischarge Pressure psig 7 Vent with Rupture Disc 08 Vapor Discharge Coefficient decimal fraction 06 Liquid Discharge Coefficient decimal fraction Switch to PRD Database Previous Cancel Run Now Figure 12 2 Tank car properties for Tutorial 1 r 3 Legacy TPS Mode Setup E mo Type of Insulation 7 Bare Temperature independent FRA
32. is used supersceded if new TPS model is used Safety Relief Device Safety Relief Device Device Type 25800 Rated Flow Capacty SCFM of air Midland A 1075 Midland A 1225 2855 Rating Pressure psig Midiand A 1280 Midang ATUS 25 Start 4oDischarge Pressure psig Midland A 14225 Vent with Rupture Disc Midland A 14375 24 Midland A 2165 Midland A 2085 Midiand 37225 37280 08 Vapor Discharge Coefficient decimal fraction Default PRV Mode NEW ACDL Verfication 06 Liquid Discharge Coefficient decimal fraction Midand A 1400 NoRelease Midland 37225 No Release Switch to PRD Database Switch to Legacy PRD Setup Edi Database Previous Net FunNow Previous Net Run Now Figure 9 1 The Edit Tank Car Properties window shown in two modes in the bottom portion of the window On the left is the traditional direct entry of PRD values On the right is the PRD Database mode Specifying a PRD using the PRD Database The PRD Database provides pre calibrated pressure relief valves PRVs listed by name This database can also be expanded to include other PRVs and vents with rupture disks To use the PRD database click the Switch to PRD Database button in the Edit Tank Car Properties window which is the second in the four window editing sequence for an analysis When you click that button the lower part of the Edit Tank Ca
33. may have different values for each layer i see Figure F 1 Therefore in the implemented algorithm the coverage array has two subscripts the first for the angle region and the second for the layer c is the coverage for Layer i in angle region The angular dependence of the TPS does not affect the assumption that the inner tank wall temperature adjacent to the liquid lading which is equal to the liquid temperature is uniform However it does affect the assumption that the inner tank wall temperature adjacent to the vapor lading is uniform Rather an array of innermost temperatures is introduced in AFFTAC these values are determined using the procedure described in the first paragraph of this section Likewise an array of outermost temperatures for this region are introduced these are determined using the procedure described in that same paragraph A0 na Figure F 1 Illustration of how the coverage values c can vary based on a user specified number of angle bins 151 Nonlinear Solver Equation F 9 F 11 with boundary conditions F 12 F 13 constitute simultaneous nonlinear equations for the 3n temperatures Tri and Tri i 1 2 3 where n is the number of layers As is currently done in AFFTAC these temperatures are determined using the Newton Raphson iterative method To formulate the solver functions are defined using the heat balance and boundary conditions described earlier In other
34. on the macroscopic scale e g the diffusion of voids it is reasonable to assert that the Arrhenius equation may be a good candidate for a phenomenological model Experimental data has proven that this assertion is valid Therefore proceeding along those lines of reasoning it is suggested that the secondary strain rate is governed by the following Arrhenius type equation 77 S 8 3 where A a material constant AH the activation energy of the phenomenon which here is creep R the Universal Gas Constant and T absolute temperature Since is considered to be a constant it can equally well be expressed as a change in strain over a discrete time Ar so that the Arrhenius relation becomes Ae Aeg SHIRT 8 4 At Equation 8 4 can be solved for AH R through straightforward algebraic manipulation Doing so produces 8 5 A x 4 In Ar R A amp R is a constant and it is asserted that the activation energy is a function of stress alone Thus the ratio on the left hand side of the equation is thought to be a function of stress alone As will be seen shortly it is related to the Larson Miller parameter which is often abbreviated as LMP and will be introduced shortly Equation 8 5 applies for each incremental strain occurring over a time step However given that the strain rate is assumed constant during this second phase the above relationship can be used to predict the time increment required for failure to oc
35. prove interesting and are therefore shipped with the release Installation System Requirements and Technical Assistance AFFTAC 4 00 is designed for systems running MS Windows XP Vista and 7 operating systems It should be compatible with Windows 8 but it has not yet been tested on that operating system The AFFTAC 4 00 graphical user interface was developed in Microsoft Visual Studio 2008 version 9 0 30729 1 SP Microsoft NET Framework Version 3 5 SP1 Assistance can be obtained from Dr Scott R Runnels Scott Runnels Consulting 630 Camino Encantado Los Alamos NM 87544 505 695 9241 SRunnels srconsult com www srconsult com 14 Acknowledgements Special thanks go to John Sbragia whose careful testing of AFFTAC has revealed multiple deficiencies that once fixed improved the reliability and robustness of the code Also thanks go to Todd Treichel for his skillful management of the AFFTAC project The original development of AFFTAC for Windows and the initial three databases were funded by the RPI AAR Railroad Tank Car Safety Research amp Test Project and was performed under Southwest Research Institute project number 18 6965 Development past 2000 was continued by Scott Runnels Consulting under the same funding source Thanks go to Tom Dalrymple for his advice during the designing of the graphical user interface and suggesting the use of databases in the original AFFTAC for Windows as well as the overall project manageme
36. shall not misrepresent to a third party that the Licensee or any party other than Licensor i has title to AFFTAC or ii is in any way responsible for the creation of the content of AFFTAC d Licensor shall have the right at its sole discretion and without incurring any liability to the Licensee to modify AFFTAC or discontinue its development sale or support e The Licensee shall not modify AFFTAC or combine AFFTAC with any other software 2 OWNERSHIP OF INTELLECTUAL PROPERTY Licensors own all intellectual property rights including but not limited to all patents trademarks copyrights trade secrets and data rights pertaining to AFFTAC including translations compilations partial copies and derivative works thereof and such rights shall remain in Licensor or its licensors The Licensee agrees that except for the limited license granted herein this Agreement does not grant the Licensee any rights to patents copyrights trade secrets trademarks whether registered or unregistered data rights or any other rights or licenses with respect to AFFTAC AFFTAC may not be sold leased or sublicensed in whole or in part by the Licensee except with Licensor s prior written consent The Licensee acknowledges Licensor s intellectual property rights in AFFTAC and agrees that it will not challenge such rights in any way a Derivative Works The Licensee may not create any derivative works of AFFTAC In the event that the Licensee create
37. simpler Therefore it is recommended that you also use these legacy strength models to provide results that you check against the results produced when using the Strength Model Database Mistakes in units or errors in the code can be much more easily detected that way To use an entry in the Strength Model Database when editing an analysis click the Switch to the Strength Model Database button in the Edit Tank Car Properties window which is the second in the four window editing sequence When you do that the list of current entries in the Strength Model Database appears and you may select one for the current analysis That editing window displaying the Strength Model Database is shown in Figure 8 2 To edit or expand the entries in the database click the Edit Database button which appears when you click the Switch to Strength Model Database When you click the Edit Database button the Strength Model Database manager window appears like that shown in Figure 8 3 From that window you may create new or delete existing database entries If you choose to edit an entry the window in Figure 8 4 appears which shows that each strength model can implement either the Larson Miller strength model the ultimate tensile strength data or both The ultimate tensile strength model is described by the ultimate tensile strength entered as a function of temperature The Larson Miller model is described by the Larson Miller parameter entered as a function
38. that the Bernoulli equation can be applied along any streamline streamline that flows through the middle of the relief device is chosen for the analysis For any two points 1 and 2 on the streamline the Bernoulli equation states that d 9 5 Vy p V 24 ze p where V is the speed at those points and p is the pressure Since the pressure is a function of temperature the above integral may be rewritten as m di Va RUDEE sS For this analysis Point 1 is assumed to be located far from the opening so that when there is no padding gas present V can be assumed to be zero When padding gas is present the saturated condition of the liquid flow through the valve will be reached after the fluid has been given some velocity In this circumstance the initial velocity is approximated as 9 7 V 28 p In either case V is known and so is 1 the bulk pressure inside the tank For any value 75 which corresponds to some unknown position along the streamline the above integral can therefore be used to compute the speed V2 p2 at a second point The 91 objective is to find the temperature Tz that corresponds to the point along the streamline where the cross sectional area of the flow is a minimum When that point is found it is used to compute the mass flow rate Point 2 is found using the above integral with the help of an additional constraint which is that the entropy of the liquid v
39. the arrows that point towards the right Once the Start to Discharge pressure P is reached the valve begins to open in proportion to the amount that pressure is exceeded If the pressure continues to increase the valve will eventually be fully open There are two paths that the valve can follow when closing If the valve is fully open and the pressure drops below the full open pressure opes times the valve will begin to close an amount that is proportional to the difference between the full open pressure and a reference closing pressure Febow times The fraction open at 15 fapow Once is reached the valve will become more sensitive the rate of closure with respect to the pressure increases until it is fully closed at times That path is marked other path marked is followed if the pressure begins to drop before the valve is fully open Prior to AFFTAC 4 00 the values open and feibow Were hard coded When you choose to specify a PRV by typing values directly into the Edit Tank Car Properties window which is the second in the four window sequence encountered when 95 editing an analysis it is those same hard coded values that are used They are shown in the table below Hard Coded PRV Open Close Modeling Values used in Old Setup Method full open 1 03 F closure 0 82 F elbow 0 88 elbow 0 8
40. the vapor space and liquid each as having a uniform temperature is based on the assumption that the conditions are uniform on the respective inside surfaces of the tank This assumption is not strictly without consequence because the temperature of the inner wall surface could be colder for regions close to the liquid s surface The temperature would depend on the length of time the wall has been exposed to the vapor and also the amount of radiant energy that has been received from the hotter part of the wall Uniform conditions will be closely approached when the liquid level is near the top of the tank because a slight drop in the liquid level will expose a large area of the inner surface of the tank Uniform conditions will also be approached when the level of the liquid is low Although the transient difference in temperature may be larger when the liquid level is near the center of the tank calculations show that the difference would only have a small effect on the total heat transfer 46 The Legacy TPS Model and Database There are two separate models for thermal protection systems TPSs in AFFTAC You are required to choose one of them when setting up an analysis even if the tank is bare that part is still accommodated as part of the TPS model The TPS model described in this chapter is the legacy model which has been in AFFTAC for decades It provides important capabilities and also provides an important reference point for calculation
41. then terminated Ultimate Tensile Strength Data As mentioned earlier in this chapter the ultimate tensile strength UTS model is implemented in a way very similar to the legacy AFFTAC failure model In the new UTS model the input data is queried to determine the UTS of the tank at the highest temperature in the tank wall Using that value the internal pressure sustainable by the tank wall is computed If the actual pressure inside the tank exceeds that computed pressure failure occurs The only difference between this model and the legacy version is that you can specify the UTS using polynomial or tabular entry whereas the legacy version uses hard coded equations The legacy model is retained in AFFTAC to maintain backward compatibility and for providing benchmark calculations against which the more general failure models can be compared Both the new UTS model and the Larson Miller failure model which are contained in the Strength Model Database can be run simultaneously during a simulation 82 Pressure Relief Devices and the PRD Database There two ways of specifying the pressure relief device PRD in an AFFTAC simulation One is to enter the appropriate values in the Edit Tank Car Properties window which is the second of the four windows encountered when editing an analysis Those values relate to the valve s flow capacity pressure at which it will open and certain coefficients that make the flow models more accurate i
42. thermal mass denoted here as wa mass of the vapor is negligible by comparison and although it could be included in principle it is neglected here The net flux into the lading is 45 A att liquid rPS liquid 2 Fraction Engulfed Rad walt liquid Ed 2 E The first term the right hand side is the conductive exchange between the tank wall and the liquid which is scaled by the area of contact between the liquid and tank wall It is one of the primary outputs of the TPS model If you refer to the theory sections for both the legacy and new generalized TPS models you will see sections where the computation of that quantity is described Keeping in mind that the thermal model is one dimensional the Fraction Engulfed term is used to represent the fact that some of the tank may not be engulfed in the flame It changes depending upon whether a pool fire or a torch fire is being considered During times when the pressure relief device is open and lading is being expelled the amount of work W performed by pushing part of itself through the device is OW subtracted from Also the latent heat of vaporization for the expelled lading is net subtracted Thus the temperature change is given by dT 5 12 lading __ m Wm mH liquid adjacentwall d t Here is the latent heat of vaporization Aside Modeling the tank wall over
43. thoroughly developed in Appendix F and you are encouraged to explore that material Flux Computation The key output of the TPS model is the flux into and through the innermost surface of the TPS which may be a liner or the tank wall itself Once all of the temperatures in Figure 7 6 and Equations 6 1 6 3 are known the flux through and into the innermost surface is computed using the conduction term 1 k 6 5 QTPs liquid T Tdi k nho Arps vapor T T 1 67 68 Strength Models There are two separate methods for modeling strength in AFFTAC Both are described in this chapter starting with the legacy strength model Legacy Strength Model The legacy strength model is relatively straightforward to explain and use You make the choice regarding which strength model to use in the Edit Tank Car Properties window which is the second of the four window editing sequence for any analysis The upper right part of that window has two modes one of which is displayed when using the legacy strength model and the other when using the Strength Model Database The modes are toggled by clicking the button that says either Switch to Strength Model Database Or Switch to Legacy Strength Model Figure 8 1 shows the window with the legacy models displayed The legacy failure model is based on an estimate of the material s room temperature ultimate tensile strength which is a constant multiplied by a factor that decrease
44. through the valve Therefore no mass exchange of the padding gas between the vapor and liquid phases would on the one hand delay the time at which the relief device opens but on the other hand increase the pressure after the lading begins to flow through it To some extent these effects would probably counteract each other Regardless when the space occupied by the vapor reaches approximately 10 the effect of the padding gas becomes insignificant on the prediction of flow through the relief device As mentioned above since the amount of liquid is small the pressure of the padding gas is computed using the ideal gas law still holding to the assumption of no mass exchange between the liquid and vapor phases The user s inputs for the padding gas initial pressure initial volume occupied by the vapor and initial temperature are used in conjunction with the current volume and current temperature to compute the current pressure The embodiment of this law is expressed in 100 1 0 Tuan 0 10 1 1 E f t Trading Wpaa 0 P paalt P paa 0 X where ppa4 t is the pressure of the padding gas at time t f t is the fraction of the tank filled with liquid at time t and w t is the weight of the padding gas at time t In all cases the pad gas pressure is never allowed to be negative Modeling Tank Deformation Thermal Expansion When the tank heats up its volume increases due to thermal expansion of the tank wall Al
45. to as P Start The valve begins to open at P Start and is fully open at a value greater than P Start That value is 1 01 in the upper window in Figure 9 3 but you are free to enter whatever value is appropriate for the valve you are modeling If the pressure decreases at any time after the PRV is open the closing path is different than the opening path If it is fully open when the pressure decreases it follows the upper curve shown in Figure 9 3 If it is not yet fully open it follows the lower curve The control points that define the closing paths are all inputs that you are free to specify Again this is discussed more fully in the section entitled Modeling the Opening and Closing of PRDs later in this chapter Specifics for a Vent with Rupture Disk For a vent with a rupture disk the graph of open close behavior is not present Instead the only value of relevance is the start to discharge value which is when the rupture vent bursts Theory for Modeling flow through a PRD There are four different scenarios in which the tank car can lose lading through the PRD They are illustrated in Figure 9 4 In the two cases where vapor alone is being ejected the classical model for choked vapor flow described in a subsequent section is used In the two cases where liquid is being ejected it is assumed that some of the liquid might evaporate during the process resulting in two phase flow Therefore a two phase isentropic inviscid fl
46. used to determine whether or not liquid or vapor is adjacent to the pressure relief device Liquid Surface Tank U Figure 5 4 Geometry used to derive the equation relating the angle to the liquid surface endpoint to the fraction of tank filled with liquid 43 Temperatures of the Lading and the Tank Wall Radiative Heat Exchange with the Tank Wall As discussed above a classical gray body radiative exchange model is used between the innermost tank wall surface adjacent to the vapor and the surface of the liquid That net flux on a per area basis is eT 5 8 naa wall liquid LIS is The value of f 1s the surface configuration factor for the liquid lading surface and the tank wall above it as captured in Equation 5 4 Convective Heat Exchange with Tank Wall A standard engineering model is used for the convective heat exchange between the vapor and the innermost tank wall surface adjacent to it For heat flux on a per area basis that model is 5 9 WE vies T ss where is the film coefficient Aside The h film coefficient is difficult to estimate since it represents fluid flow that can take on a variety of forms Film coefficients spanning an order of magnitude are reported in the literature depending on the properties of the liquid whether or not boiling is present at the interface and the geometry of the interface e g see 5
47. user specifically the rated flow capacity rating pressure and coefficient of vapor discharge as described in Table 9 1 It is assumed that the experimental data was obtained using air at room temperature For air under those conditions Z 1 0 y 1 4 R 53 3 ft Ibf Ibm deg R T 519 7 deg R 60 deg F In those conditions the density of air is 0 0763 Ibm ft which is required because the rated flow capacity is given in cubic feet per minute Substituting those values into the above equation produces the following estimate for the valve area which appears in this form in the Computational Module m 9 4 m Coy p 2644 90 However there is a non trival amount of units conversion embedded in this equation How this equation is arrived at is described in detail in Appendix D Low Speed Vapor Flow If the total pressure within the tank is greater than atmospheric pressure 14 7 psia but less than 12 3 psig the flow can no longer be considered choked In these cases the amount of vapor flow produced during a choked condition is computed and then scaled downward accordingly Two Phase Flow When liquid escapes through the pressure relief device its pressure and temperature drops leading to the creation of some vapor from the liquid state The resulting situation is known as two phase flow and can occur any time liquid is being ejected The model for two phase flow assumes that the flow is inviscid which means
48. was undertaken to use AFFTAC to validate model parameters for liquid two phase flow through pressure relief devices More recently a new creep and failure model was added Significant advances in testing and software quality assurance have been made in this third phase as well A regression test system and database of over 50 regression tests have been established many of those tests are carefully designed verification tests of the regression tests and the recent validation work are described in a separate companion document entitled AFFTAC Verification and Validation Testing As of this release that document along with this manual are updated and released as part of each AFFTAC formal release 11 Analyses Database Ladings Database Legacy TPS Database GUI manages the databases Generalized TPS Database Failure Model Database PRD Database User i AFFTAC GUI User specifies inputs and views outputs in the GUI Computational Input Files temporary Computational Module J Computational Output Files Figure 1 1 Overview of AFFTAC operations and components Software Components GUI Computational Module and Databases An overview of how the AFFTAC software package components interact is shown in Figure 1 1 user interacts with the GUI which writes an ASCII file that the Computational Module reads The GUI manages the execution of the Computational Module and the displaying of t
49. windows In this first window select the Standard Pool Fire option and enter 100 for the Length of the Simulation entry Leave zero as the entry for the rollover angle When you are finished making those adjustments the window should look like that shown in Figure 12 1 When it does click Next Doing so displays the Edit Tank Car Properties window Enter the following information Nominal Capacity 33000 Inside Diameter 112 Wall Thickness 0 5625 Then select AAR TC128 70 Grs A amp B Min Tensile Strength 81 Kpsi from the pull down arrow Enter the following data for the material Nominal Burst Strength 750 Tensile Strength 81000 Emissivity 0 8 107 In the lower half of the window select the Valve option under Device Type for the Safety Relief Device option and enter the following information Rated Flow Capacity 32000 Rating Pressure 270 Start to Discharge Pressure 247 5 Vapor Discharge Coefficient 0 8 Liquid Discharge Coefficient 0 6 When you have finished making these entries the window should look like that shown in Figure 12 2 When it does click Next Doing so will leave you in the Select TPS Model window For this tutorial highlight Example 1 which is a pre loaded TPS type To see the data describing the insulation named Example 1 double click on it Doing so displays the window shown in Figure 12 3 Example 1 insulation type is temperature independent thermal protection system that
50. yu 149 Side s Exposed Arel I INO Ban I gd ON Melo kate 149 DOHHdary Conditi ns epa ertet icd 149 ANGULAR DEPENDENGE ee cvs nde Ie ERE ee EC 150 NONLINEAR SOEVER 2 3 0 e ecce t enit rete bte ve redit iDe a de etn 152 10 Introduction History The AFFTAC computer program was originally developed by Dr Milton Johnson at IITRI circa 1984 under funding from the United States Federal Railroad Administration to predict the effects of fire on railroad tank cars It makes predictions of key state variables such as the lading temperature temperature of the tank wall pressure inside the tank flow through the pressure relief device and failure if relevant of the tank wall In the years following its initial development AFFTAC was expanded to provide more information and handle more types of vents as well as be more accessible to users Eventually in 1992 it was ported to the PC Beginning in 2000 AFFTAC entered a new phase of development with Dr Scott Runnels as its custodian The first task undertaken in this new phase was the development of a graphical user interface GUI to assist the user in managing data and analysis A third phase of development began circa 2008 with three new efforts The first was a new more general thermal protection system model After that an effort
51. 011 Inside Diameter ins 112 00 Baseline Case 4 TPS version of Case 1 Scott Runnels 09 26 2010 quus pe ee Tank Material Type carbon steel TPS Test Metal MetalwPartialCoverage Gap Metal FirstName LastName 10 02 2012 Tensile Strength of Tank Material psi 8 1e4004 PRV Full circle test A 1400 FirstName LastName 11 12 2012 Nominal Burst Strength psig 750 0 PRV Full circle test A 37000 FirstName LastName 11 12 2012 BUS Model Results for Sample PRODUCT Butane Version TIME TEMPERATURES PRESSURES MASS FILLED RATE OF min deg F WITHIN BURST FRACT FRACT PRODUCT Create and Delete Edit LIQ TANK TANK STR IN RELEASE Analyses Analyses Plotting PROD VAPOR psi psi TANK lbs min 60 0 60 0 11 2 8 1 002 1 000 0 960 60 1 63 5 11 2 8 1 002 1 000 0 960 60 2 67 0 11 3 8 1 002 1 000 0 960 60 3 70 5 11 3 8 1 002 1 000 0 960 60 4 74 0 11 4 8 1 002 1 000 0 960 60 5 77 5 11 4 8 1 002 1 000 0 960 Displayed Edit Analysis Edit Admin Data Release 4 00 Figure 1 2 Example of AFFTAC s Main Window where in the left most pane the Analysis Database is displayed Although they are read automatically they are not saved automatically You should use caution to ensure changes you make to the database files are saved when you want to keep them In general the management of the various d
52. 2 Configuration of Edit Lading Properties window for Tutorial 2 114 A Property Entry Wii Specific Volume as a function of Temperature Temperature deg F T T T T 4 1 Cw ft 3 Ib m T7 T 7 Lacs 1 1 L 1 9 20 40 1 60 100 120 Temperature deg F Figure 13 3 Property Entry Window Although there are values supplied in that window they are not to be taken as legitimate but rather placeholders to demonstrate how the window should look once data is entered For now click Clear Table which will remove these entries and prepare the table for fresh data After you have cleared the placeholder data click on the left cell in the temperature column Using the numeric keypad on your keyboard type the value 30 and press ENTER Next type 120 and press ENTER Repeat this process to enter 210 and 260 do not press ENTER after 260 Now click on the top right cell under the Cp column Type 0 5546 and press ENTER Type 0 5946 and press ENTER again Continue entering 0 7141 and 0 9619 do not press ENTER after 0 9619 Click Refresh to view the updated graph You may edit the data by clicking directly over the cell you wish to change You can also copy cut and paste rows using the buttons provided When you are finished the window should look like that shown in Figure 13 4 Once the data has been entered correctly click
53. 5 Table 9 2 Default parameters for valve opening and closing model However if you choose to use the PRD Database you have the freedom to change these values In a recent experimental and validation exercise described in the AFFTAC Verification and Validation Testing document values for these key parameters as well as areas and coefficients of liquid discharge were determined and used to establish a database of PRVs manufactured by Midland Manufacturing Those values are shown in the Table 9 3 AFFAC is shipped with these entries However you can edit and expand this database as needed Very important details regarding how these values were obtained are documented thoroughly in AFFTAC Verification and Validation Testing a companion document to this User s Manual You are encouraged to refer to that document to understand more Fraction Opened 1 00 f ebow B i piternate closing p T T P PF xP Pressure s full_open 5 full close 5 elbow Start to Discharge Pressure Figure 9 6 Model for the spring loaded pressure relief valve 96 Table 9 3 Results of the model calibration exercise for the valve opening and closing model Frangible Disk The model for the frangible disk is straightforward If the pressure differential across the disk is less than the user specified disk burst pressure there is no opening However onc
54. 7 well known that the effective conductance C of the composite layer is related to the conductance C of each layer as follows 1 Yl 6 20 cA i l i where n is the number of layers Here each represents a layer in a composite system Those layers include the tank wall itself but also insulation and tank linings Although not shown explicitly in Figure 6 4 other layers may exist such as a lining Their conductance is used to modify the C using the equation above AFFTAC s legacy TPS model accommodates different behaviors for the insulation layers and linings For example you can specify an amount of time during which some layers deteriorate Also you can specify a temperature dependent conductivity In that case a nonlinear system must be solved to determine the effective conductance of the entire layer As discussed earlier in this chapter the conductivity may be expressed by the user as follows K K T KT 6 21 To solve the heat conduction equation when the conductance is of this form the algorithm divides the insulation layer into 50 elements It then starts at the inside of the layer and using the previous value for the effective conductance and the heat flux that it allows marches through the 50 elements computing the temperature distribution as it proceeds When it arrives at the outside of the insulation it checks to see if the temperature matches that predicted by using the previous effective cond
55. ATIONAL MODULE AND DATABASES 12 INSTALLATION SYSTEM REQUIREMENTS AND TECHNICAL ASSISTANCE 14 9 1 1 theses etes eset esse esee te 15 THE SCOPE AND INTERACTION OF AFFTAC S MODELS nnns 17 PHYSICS ASPECTS OF A TYPICAL 5 00000 1 0060 17 HEAT TRANSFER 5 8 0040 000000000000 19 PRESSURE RELIEF DEVICE 2 0 00 00 20 TANK FAILURE MODELING EEANN NEEESE TAA 22 MATERIAL EXPANSION 04040 0 0 0 0 0 23 CREATING AND RUNNING AFFTAC SIMULATIONS ccccccccsscosscossccsssessoes 25 SETTING UP AN 515 1 1 6 6 eae sees aua 25 RUNNING AN 515 1 etie set eset esse esaet etes stesse 28 VIEWING AND USING 5 4 28 ADMINISTRATIVE 2 0000000 30 TABLE OF CAPABILITY SETUP 6 2 040000 00000000000 30 THE LADI
56. Aft SteelJacketedTest Add Delete Delete ConductorForJacketTe I 1 Insulator_CoverageO Copy Pase odi Steellacketed Trend 100 SteeWacketedTrend50 n Add Delete Delete Done fil Paste copy 1 E e M Done dont write yet Cancel OOS Figure 7 4 Main management and editing window for the Generalized TPS Model Database General TPS Model Theory Before attempting to understand the theory for the generalized TPS model it is highly recommended that you read the chapter entitled Details of the Overall Thermal Model The material there will help you understand how the calculations of the TPS model fit in to the overall solution process and also some of the parameters used in the model development Consider Figure 7 5 which shows each layer of a five layer system as if the system had been disassembled and each layer laid out side by side As the figure shows each of the inner layers may have a coverage value c less than unity The voids in these layers affect how heat is transferred through the system as illustrated in Figure 7 6 which shows that there are three temperatures at each material interface One temperature is that of the area where the two adjacent layers are in contact Specifically is
57. Following the same methodology that is currently in AFFTAC the following two boundary conditions are applied to the above equations 1 Inner Boundary Known Temperature Condition This condition is applied by setting T nown Note that a requirement of the model is that the innermost and 149 outermost layers have 100 converage The value of Tnown is taken as the inner layer s inner temperature from the previous time step The process of using this old value is part of the current nonlinear lagging methodology in AFFTAC So for Layer 1 Equations F 11 is replaced with T F 12 nown 2 Outer Boundary Flux Condition This condition replaces the conduction radiation and convection occuring towards the right for Layer n with a heat flux that is based on the flame temperature and outermost layer temperature Thus Equation F 10 fori 2 n is replaced with k F 13 LL Aral T Aole EER jt 0 i i The factor f is a shape configuration factor as discussed in the chapter entitled Details of the Overall Thermal Model Also it is noted that because there is 100 coverage on this outer surface T T This equation replaces Equation F 11 for i 2 n 3 Zero Coverage Because no lateral conduction is built into the model the model breaks down for small coverage values However the model recovers its accuracy in the limit of zero coverage by setting the conduction region temp
58. NGS 1 sese sese sese sese sese sese sese aun 33 Using Defa lt rU 33 ERES 36 DETAILS OF THE OVERALL THERMAL MODEL 39 ESSENTIAL CONSTRUCTS 200004 000000 seres essen nana 39 CONSTRUCTS OF RADIATIVE HEAT EXCHANGE 4040000 00000000 tres senis 41 TEMPERATURES THE LADING AND THE 0005 44 Radiative Heat Exchange with the Tank Wall essere 44 Convective Heat Exchange with Tank Wallace estas nth QU 44 Temperature Change in the Tank Wall Adjacent to the Vapor sess 45 Temperature Change of the Lading and Tank Wall Adjacent to the Liquid 45 THE LEGACY TPS MODEL AND 47 MANAGING THE LEGACY TPS MODEL 5 47 SETTING UP TPS IN THE LEGACY MODEL eene eene 48 ppm EEE H 46 ERA Stand rd dei nsi d e 50 Temperatire Independent 1 50 Temperature Dependent Tsulafiola oo t 50 Steel Jacketed 2 component Insulation cesses 50 LEGACY TPS MODEL THEORY
59. S model include 1 The ability to accommodate an arbitrary number of material layers in the TPS 2 Each layer of the TPS can have an arbitrary coverage defects that varies as a function of position around the tank 3 Each layer of the TPS may have its thermal conductivity specified using tabular data 4 Each layer of the TPS may undergo a change of phase at a certain temperature wherein the thermal conductivity becomes described by a different table Various aspects of the requirements are represented in Figures 7 1 7 3 on the pages that follow 61 a An arbitrary number of layers is accommodated a Jacket tank wall and liners are also treated as layers a Any layer may exhibit partial coverage Arbitrary number of layers Figure 7 1 Composite thermal protection system model a Layers are named separately and saved in the database a Composite systems are assembled from named layers and also saved in the database EHI For jacketed systems the outermost layer Material G would be the jacket and that would be part of the database Material F Material E Material D Material C Material B MaterialA Innermost layer may be tank wall or liner Figure 7 2 Summary of how materials can be named and then combined to form a composite thermal protection system Material Database Conductivity heat capacit
60. Standard Temperature Dependent 7 Steel Jacketed 5 Steel Jacketed 2 component Conductivity s change with time 7 Linear Decay Constant 54 qdcmcaeeUIU casn 3 16 inch thick rubber liner Figure 12 3 Legacy TPS Model for Tutorial 1 Now click OK to return to the Select TPS Model window To add or delete TPS types in the database the Legacy TPS Database can be accessed by clicking the Manage Legacy TPS Database button in the Select TPS Model window It can also be accessed through the Main Window under the Edit Databases Legacy TPS Model menu option 109 Highlight Example 1 in the Select TPS Model window and click Next which will display the fourth in the series of four editing windows Select the lading named Butane and enter the following data Fraction of Tank Filled 0 96 Initial Temperature 60 The Ladings Database can be accessed through the Manage Ladings Database button or the menu option Edit Databases Ladings in the Main Window The inputs you have provided in the past three windows may be reviewed using the Previous and Next buttons that are shown at the bottom of each of the four editing windows Clicking Cancel would erase these changes and return you to the Main Window At this point the Setup Lading window should look like that shown in Figure 12 4 When it does click Run Now which will execute the analysis and return you to the Main Window To review the input as echoed by th
61. Thermal TD ON SION 101 JO KT LEE 103 PlastiG FOIE s ith doe Tees 103 GOMDINEE SIFIlW s e 103 5 OL UE CEDE DE Ve Gra On 105 oi is Qu d 105 OvershO0tt aoi e 106 TUTORIAL 1 A SIMPLE ANALYSIS eee eee e eee eee e e e e e e ee 107 TUTORIAL 2 ADDING sese sese 113 50458 4 4415 6 6 664606 ees oodo aseo sodes orna deos oco 117 APPENDIX 5 119 9 5 ut eite tero 119 SPECIFIC HEAT 120 SPECIFIC VOLUME 22 idee eise iode 120 HEAT OF 121 COMPRESSIBILTEY PAC TOR Tie 122 RATIO OF SPECIFIC esee tease seen ne 122 APPENDIX B CHOKED VAPOR FLOW DERIVATION AND AREA ESTIMATION METHOD c esee no Sena nen oae nana nona
62. Value Let AFFTAC estimate area Input area manually 1 Valve Area sq in Select type of Safety Relief Device 9 Valve Vent with Rupture Disk 294 Startto Discharge Pressure Pstart below psi Rated Flow Capacity SCFM of air 270 7 Fating Pressure psig 08 77 VaporDischarge Coefficient decimal fraction Options for Liquid Discharge Coefficient Liquid Discharge Coefficient 9 Liquid Discharge Coefficient X Area 00034 Discharge Coef X Area sq ft Options for Area Value Let AFFTAC estimate area Input area manually 1 Vent Area sq in Select type of Safety Relief Device Valve Vent with Rupture Disk 294 Rupture Pressure psi Figure 9 3 Window for editing a specific entry in the PRD Database The mode shown in the upper window is for a valve The mode shown in the lower window is for a vent 87 Specifics for a PRV When you select the type of PRD to be a pressure relief valve PRV the window displays a chart showing the nonlinear and hysteresis open close behavior of the PRV This behavior is discussed in more detail in Modeling the Opening and Closing of PRDs later in this chapter and the process for finding the parameters are in the AFFTAC Verification and Validation Testing document The primary quantity of interest for the open close behavior is the start to discharge pressure which is entered on the left hand side of the window In the plot that value is referred
63. abase is central to AFFTAC and is displayed in AFFTAC s Main Window as in Figure 3 1 To create a new analysis from scratch using default values click on the New button in the Main Window To create a new analysis that is based on an existing one highlight the existing one click Copy and then click Paste When you do a new analysis will be created that is identical to the one you copied except for its title and its administration information which you will eventually specify You may edit that analysis by highlighting it and clicking Edit Analysis It is valuable to understand that each analysis you create in the Analysis Database will contain two kinds of entries 1 Numerical and Logical Data These are straightforward entries having to do with direct data about the simulation For example the length of the simulation is a numerical entry that is part of an analysis 2 References to the Other Database Entries These are names of components such as ladings thermal protection systems and pressure relief devices PRDs that contribute to the simulation setup example is the lading name If you select Butane for the lading that name is used to pull thermodynamic properties from the Ladings Database under the name Butane and provide them to the Computational Module for the simulation Thus the single entry Butane in the analysis specification contains a great deal of information including multiple 25 tables
64. adjustment factor f T is not a function of time meaning that it does not accommodate the widely observed phenomenon of creep The Strength Model Database The other way to model strength of the tank wall is to use the Strength Model Database by selecting the button Switch to Strength Model Database in the same Edit Tank Car Properties Window The Strength Model Database is like the other databases used in AFFTAC in that by choosing a particular name you are drawing upon potentially several pieces of data that are transmitted to the Computational Module for a simulation The Strength Model Database accommodates two types of strength models which may be used individually or in combination One is the Larson Miller creep and failure model the other is ultimate tensile strength data that you can enter as a function of temperature 70 ID Description 5 Adjustment Factor 1 ASTM A 515 70 55 000 Gr 55 Min 2 ASTM A 515 70 60 000 Gr 60 Min 3 ASTM A 515 70 65 000 Gr 65 Min 4 ASTM A 515 70 70 000 Gr 70 Min IE C 1 0 54 T 0460 T 1260 6 AS 285 70a 50 000 7 41 74 1 17 07 0 460 T 1 260 r In 7 ASTM A 286 70a 55 000 0 T gt 1 947 Gr C Min 8 ASTM A 516 70a 55 000 Gr 55 Min 9 ASTM A 516 70a 60 000 Gr 60 Min 10 ASTM A 516 70a 65 000 Gr 65 Min 11 ASTM A 516 70a 70 000 Gr 70 Min 12 128 70 81 000 Grs A amp B Min 13
65. ampening Typically 0 25 lt lt 0 5 In addition to the thermal solution values dampening is also used for the auxiliary models For example in computing the change in volume due to thermal expansion and the pressure differential the new value for the volume is dampened using 1 3 Overshoot A problem similar to the instability problem discussed above is that of overshoot For example during the choked flow computations if the resulting pressure after discharge during the time step would be less than atmospheric in the case of a vent or less than the valve closing pressure in the case of a safety relief valve the out flows are arbitrarily reduced This compensation is required because of the consequences due to the finite time step which may not be sufficiently accurate for rapidly changing conditions The effect is significant only as the shell full condition is approached 106 Tutorial 1 A Simple Analysis To begin this tutorial start the AFFTAC GUI When you do the Main Window should appear where the Analysis Database is displayed In its distributed version AFFTAC s Analysis Database comes preloaded with several regression tests including the example problems in 1 For this tutorial one of these example problems Example 1 1 will be recreated from scratch Click New in AFFTAC s Main Window Doing so will create a new entry at the bottom of the Analysis Database and will also display the first of the four editing
66. and T y e ACC 1 F 8e T and 1 nd E Ac 1 OR Xt T Arr 8180 e Cia 1 Ac 1 n F 5g Table F 2 Computing Conduction Communication Areas Using a Joint Probability Approach It is worthwhile to make special notation for how these values change at endpoints Specifically and c represent the coverage of the non existent layers adjacent to the innermost and outermost layers respectively Hence c 20 Thus the above area values for these endpoints are Area Value 1 lt lt i i n AC 0 0 F 8h n Ace 2 1 0 81 Arr Ac ee 20 Acl 5i F 8j Au 6 Acte 0 8 Table F 3 Endpoint values for area Heat Balance Equations Area in Contact For generality consider interface i which is the interface between Layer i and Layer i Since this area is in contact conduction is the only mechanism for heat transfer A heat balance on the interface states that the heat flowing into it must equal the heat flowing out of it That requirement is embodied in the following equation 148 k A i T 2 A T T W JD a A r r z Tri F 9 Right Side s Exposed Area Consider again interface i but this time the part of that interface that is exposed due to a lack of coverage in Layer i Heat condu
67. anges with time but is constant in space The part of the tank wall adjacent to the liquid phase is also assumed to be at that same temperature The innermost surface of the tank wall adjacent to the vapor is at a temperature that may be different from the lading temperature Its temperature is denoted as 7 As shown in Figure 5 1 heat is transferred to the lading by three mechanisms 1 Conduction to the liquid through the TPS tank wall ii Convection to the vapor by contact with the inner tank wall and i Radiation to the liquid surface from the inner tank wall that is adjacent to the vapor The tank is heated through radiative exchange with the flame only Convection with the surrounding air is not included in the model 39 Computing 4 and 3 i is the responsibility of the TPS model of which there are two kinds in AFFTAC They are each discussed in their own subsequent chapters Those models take as a given the innermost surface temperature and the flame temperature Using those two boundary conditions they compute the heat flux conducted through the innermost surface The process of taking the interior temperature as a known value in the TPS computations is a technique known as nonlinear lagging or sometimes operator splitting and is discussed in the chapter entitled The Scope and Interaction of AFFTAC s Models details of the computations in 3 1 are discussed in the separate chapte
68. apor mixture is constant The integral form of the Bernoulli equation plus the constraint of isentropy provides the theoretical backbone of the algorithm to compute two phase flow through the relief device The integral in Equation 9 6 is approximated as this summation 9 8 V V 2 E ia P T iAT dT The summation is not carried out at once but instead in a step by step fashion Because of the temperature pressure relationship each addition of a term in the summation represents a small step along the streamline At each step the specific entropies recall AS AQ T of the liquid and vapor are computed as follows m 9 9 T Liquid State 5 T 8 c sig 2 1 Vapor State S T 5 Where is the liquid s specific heat Based on the assumption of isentropy the 9 10 Combined total entropy S T AS T 1 A S T must remain constant Therefore requiring 9 11 S T 45 15 1 4 at each step allows the ratio 2 to be computed at each step With the value obtained for V T and the ratio 2 which allows for the density to be computed the cross sectional area at step i can be computed Calculations proceed for i 2 at each step computing 4 and the cross sectional area When the cross sectional area reaches a minimum value the computations are 92 stopped That cross sectional area is used with the speed and density computed at that point t
69. arbitrary distance from the tank held at a fixed temperature during the simulation e g 1 500 deg F In a pool fire simulation this surface surrounds the tank entirely The lading inside the tank is assumed to be well mixed and at a uniform temperature The liquid and vapor phases are assumed to be in thermodynamic equilibrium with each other and thus are at the same temperature Second the tank car s innermost surface is considered to have two different temperature regions one for the segment of the tank adjacent to the liquid lading and one for the segment adjacent to the vapor This division is established because it is assumed the liquid has such a great thermal mass and is in intimate contact with the tank wall s innermost surface Thus the tank wall in contact with the liquid is assumed to be at the same temperature as the lading In contrast the tank wall adjacent to the vapor does not have intimate contact nor does the vapor have any appreciable thermal mass Therefore 19 the tank wall s innermost surface temperature can be very different from the vapor temperature In fact the temperature of the tank wall adjacent to the vapor is among the most important state variables for it is that temperature that will impact the strength and ultimate life of the tank wall Third a variety of models can be chosen for computing the heat transfer between the tank s innermost surface outermost surfe and the fire These are the therma
70. atabases is a well integrated and natural part of using AFFTAC However it is still helpful to know what the databases are and what they contain The details of the various models supported by these databases are described later For now a brief summary is provided below 1 Analysis db This file contains the inputs for the analyses you have performed and saved 2 Ladings db This file contains the thermodynamic properties of several ladings which are referred to by name in your analyses These ladings may be edited and also new ones may be added 3 Insulations db and TPS db These two files contain descriptions of various thermal protection system configurations one of these descriptions must be referred to by name in your analysis Insulations db file contains the descriptions for the legacy TPS models that were implemented by Dr Milt Johnson decades ago These models have undergone some revision since 2000 but remain largely unchanged They are simpler than the new general TPS model the inputs for which are contained in TPS db Because it is simpler and so well tested the legacy TPS model provides an important resource for comparison Also it contains some capabilities not yet in the generalized TPS model for example time dependent behavior of insulations 4 PRV db Although named as an acronym for pressure relief valve this database contains specifications for two kinds of pressure relief devices PRDs those being valve
71. ated as though it were a substance for the purpose of obtaining default values and the following guidelines should be used Vapor Pressure The test pressure of the tank car class authorized to transport a product is often an indication of the vapor pressure of the product Therefore two sets of values for default vapor pressure data are provided one for products that would be shipped in non pressure cars having a test pressure of 100 psi and the other for products that must be shipped in pressure tank cars having a test pressure of 300 psi or greater Some products that have low vapor pressures e g products classified as poison by inhalation must be shipped in pressure tank cars even though they may have low vapor pressures This is done to require the use of a stronger tank car providing added safety in the shipment of the product The suggested vapor pressures given below could be substantially over estimated for those ladings 119 Assuming that liquefied gases are shipped in pressure cars and liquids are shipped in non pressure cars the vapor pressure property values are estimated as follows Liquids non pressure cars Vapor Temperature CF Pressure psia 60 5 150 40 240 125 Liquefied gasses pressure cars Vapor Temperature CF Pressure psia 60 140 120 300 180 570 Some products such as bromine chlorine and hydrogen cyanide must be shipped in tank cars having a test pressure of 500 psi or greater This is done not be
72. ation 5 12 is the transient equation for the lading temperature AFFTAC uses a step wise transient approach known as the Forward Euler method with nonlinear lagging to solve this transient equation as well as the other transient heat and mass conservation equations In the Forward Euler method the derivative is estimated as follows for example dT Told 11 1 lading 4 lading lading dt At By substituting this approximate derivative an equation for is obtained That equation uses values of the other temperatures from the previous time step e g Ts The overall conceptual flow chart of the AFFTAC computations is shown in Figure 2 1 which illustrates the presence of the Forward Euler method Dampening The advantages and disadvantages of the Forward Euler method have been clearly discussed in the literature The advantages are that it eliminates the need to solve nonlinear equations Specifically at each time step the previous time step s solution is used to extrapolate forward in time also described in The Scope and Interaction of AFFTAC s Models The disadvantage is that if the time step is too large the extrapolation can cause the solution to overshoot acceptable bounds As a simple example of this phenomenon consider two stacked blocks of wood and where A is hotter than B Because is hotter heat flux will flow from it to The 105 amount of heat flux is proportional to their tempera
73. c Heat BTU b F 2 Tube Specific Volume ft 3 b i Table Heat of Vaporization BTU b Iz Edit Table Vapor Pressure psia 7 Edit Table Compressibility Factor 0 Edt Table T A Edit Lading Properties mes Name Hydrochloric Acid Type of Lading Molecular Weight Lading has a critical temperature Solution 36 5 Solute 18 Solvent 0 9090909 Emissivity 7 Substance Depends Value at Low Low Value at High High on Temp Concentration Concentration Concentration Concentration y Edit Table 5 032 Specific Heat BTU b F v Edit Table 5 0 32 Specific Volume ft 3 b 7 i Heat of Vaporization z 5 E v 7 Edit Table 032 0 38 Vapor Pressure Solute 7 Edit Table 032 Edit Table 038 Vapor Pressure Solvent psia i zi Edit Table Compressibility Factor Solute 7 Edit Table Compressibility Factor Solvent v Edit Table dosier i 7 Edit Table Solvent OK Figure 4 3 Example Edit Lading Properties window where thermodynamics properties of the lading are entered for a substance top or solution bottom 35 Editing Ladings When you double click a lading or highlight it and then click the Edit button the Edit Lading window like those shown in Figure 4 3 appears This multi faceted window allows for the input of the thermodynamic properties of the lading The Edit Lad
74. cause they have high vapor pressures but to insure they are shipped in stronger safer cars vapor pressures given above for pressure tank cars would be conservative for these products Specific Heat There is a wide range of values for the specific heat of the liquid for products shipped in tank cars Values can range from over 1 00 BTU Ib F for solutions containing a large percentage of water to as low as 0 10 BTU Ib for bromine at about 200 Also for most products the specific heat tends to rise with increasing temperature but for some products e g bromine it decreases This makes it difficult to suggest default properties for specific heat that are conservative but not overly conservative Since the specific heat of the liquid determines the rate of temperature increase of the product with a given heat input it is obvious that lower values for this parameter will lead to more conservative analyses The following default values are suggested although they may not always lead to conservative results Temperature Specific Heat F 60 0 40 300 0 70 Specific Volume It is assumed that the density of the product is known The specific volume is simply the inverse of this value expressed in ft Ib Since the density of materials tend to decrease 120 with increasing temperature the specific volume will increase with increasing temperature Again there is a considerable variation of this rate of i
75. ce 1 becomes liquid and 2 becomes wall to represent the tank wall The emissivity of the inside tank wall is assumed to be 0 8 when using the legacy TPS model but you may 42 change that in the Edit Tank Car Properties window When using the new generalized TPS model you are allowed to specify that value when editing the TPS setup The emissivity of the liquid surface is set in the Edit Lading Properties window accessible through the Ladings Database A reciprocal relationship is used to compute fwall tiquid To compute the view factor Fiiguia wa used in the above equation the geometry of the liquid surface relative to the tank wall must be computed Figure 5 4 shows a cross section of the tank The area of the bottom quadrant is z7 4 The area of the gold region above that is r 2 The area of the blue area is 0 2 Twice the sum of these three areas represents the entire area under the liquid surface Therefore liquid ay A 2 1 576 enn Or r sin 6 The ratio of this quantity to the total cross sectional area is the same as the fraction of the tank volume occupied by the liquid 1 5 7 EINE e 2 total This equation is solved through trial and error during the simulation to determine at each point in time From this value the surface area of the liquid and the tank wall over itis computed In addition this value is
76. ction still occurs to the left but radiative and convective heat transfer occurs to the right Again a heat balance on the interface states that the heat flowing into it must equal the heat flowing out of it That requirement is embodied in the following equation where heat conduction to the left is represented in the first terms and radiative plus convective heat flow is represented in the last terms F 10 n n alri r Aru fu 7 71 H 1 Ep 1 E jd In the above equation the radiative exchange is modeled as the exchange between two infinite parallel planes Behind this choice are the assumptions that the distance separating them is small compared to the communication area Along with that assumption the radiative and convective exchange between layers based on exposure of the walls surrounding the voids is neglected Left Side s Exposed Area Now consider the layer on the right of interface i Part of that layer will be exposed due to voids in Layer i Analogous to the above equation heat conduction will occur to the right while radiative and convective heat transfer will occur to the eft The heat balance is in the following analogous equation k A T n T pe T RON Ts E Wi Wi i olf T4 i l A a hi M T J T 2 LR vel L LR Ve 1 Ep 1 The same assumptions regarding radiative exchange for Equation F 10 apply here in an analogous way Boundary Conditions
77. ction to Generalized TPS Model and Database mean that an equation can be written that describes the area of exposure between any two adjacent areas To begin A is the total area represented Ac is the area of Layer i that is without voids while A 1 c is the area of Layer i that has voids When considering the right hand side of Layer i the area that is exposed to layers beyond Layer i is Ac 1 c Here the first c represents the non void part of Layer i where the 1 c represents the part of Layer i that is void Through this area Ac 1 c Layer i can exchange heat and radiation with Layer i 2 But if Layer 2 also has voids in it Layer 7 will exchange heat with Layer i 3 and so on For each layer to the right of Layer i the area of communication between i and j is reduced by the amount of coverage of the layers between them In general the communication area between the right side of Layer i and the left side of Layers i 2 1 3 etc are as follows 145 1 X3 Fl 1 1 2 where A is the communication area between the right side of i and the left side of j The communication area between i and the left side of i 3 is Agr Ac i Ys F2 Likewise for i and i 4 it is 1 T Xi Tf 4 In general the communication area between the right side of Layer i and the left side of Layer j gt 1 1 18 4
78. cur To be precise if one sets E which is the strain at which failure occurs and At which is the time at which failure occurs the above equation becomes AH A 8 6 E dni In In t The strain at which failure occurs is assumed to represent the damage state that accumulates during creep before failure It represents the final state at failure regardless of how that state was achieved and is therefore assumed to be independent of time temperature and stress For this reason the first term inside the brackets is considered to be a constant for the material Denoting that constant by C the above equation may be written as 78 tre ent 2 This equation is very similar to the Larson Miller relation the only difference being the use of the natural logarithm as opposed to the base 10 logarithm Larson Miller relation is LMP o T C log e 8 8 where LMP o is the Larson Miller parameter which is a function of stress and C is a constant It has been found that by experience C 20 for most metals In experiments that determine the Larson Miller parameter this assumption is often made at the outset i e is often not measured Solving for f LMP o 8 9 t o T 10 7 7 The Larson Miller parameter is found by loading a material at constant temperature and stress and measuring the time to failure In order to apply this value and the above relation in a transient situation an asserti
79. cut and pasted into other Microsoft Office applications r A Plotter arry Liquid Tank Wall intemal 4 Tank Burst 1000 Temperatures deg F Pressures psi Time min gt gt 3000 0 8 2000 Fraction e o 1000 2 o gt Rate of Release Ibs min Time Time min Plot Controls Temperature Pressure Click to hide intemal pressure Click to hide liquid temperature Click to hide tank wall temperature Click to hide burst pressure Click plot to copy ctri v to paste in MS Office Figure 12 5 Graphical results for Tutorial 1 111 112 Tutorial 2 Adding a Lading In this tutorial you will be guided through the process of adding a new lading to the Ladings Database Run the AFFTAC GUI and once in the Main Window select the menu option Edit Databases Ladings Upon doing so a window like that shown in Figure 13 1 will appear In that window are listed the various ladings that are already contained in the database file r A Ladings Database Manager i O New Name cw hb Paste Default Lig Low H20 Content LER jJ Default Lig Hi H20 Content Butane Water Propane Ethlyene Oxide Propylene Butadiene 1 3 Vinyl Chloride Monomethylamine v Propylene Oxide Done write to file Anhydrous Ammonia Done dont write yet
80. d Flow Capacity Valves This value describes the amount of air vapor that the PRV can discharge when tested at a specific pressure which is the Rating Pressure Rating Pressure Valves This is the pressure at which the PRV was tested to determine its rated flow capacity Vapor Discharge Coefficient Valves and Vents This is a coefficient used to make the flow model more accurate for modeling vapor flow Because of various obstructions and geometries unique to each PRD this coefficient is specific to a PRD type Liquid Discharge Coefficient Valves and Vents This coefficient has the same meaning as the Vapor Discharge coefficient but is for liquid discharge Start to Discharge Pressure Valves This is the value at which the valve will start to open and discharge lading Note that the valve opening and closing behavior involves other values and hysteresis Please refer to subsequent sections on PRV opening closing behavior for information Discharge Area Vents This is the area through which the lading flows when a vent is the PRD Note that for a valve the area is estimated from the rated flow capacity whereas for vents it is entered directly This aspect is different and is generalized in the PRD Database Closure Disk Burst Pressure Vents This is the analog of the start to discharge pressure for valves The difference is that a vent once ruptures never closes
81. d to never diffuse into or out of the liquid regardless of the pressure Once the relief device has opened the 99 padding gas pressure is calculated from the mass of the padding gas remaining in the tank and its temperature Aside The assumption described above is believed to have little or no impact on the simulation results The primary reason for it is the little likelihood that equilibrium conditions could ever be attained during the course of the fire There would not be sufficient time for the effect of the padding gas partial pressure to be communicated to all portions of the liquid within the tank for the gas to be absorbed or liberated quickly enough Additionally the assumption is believed to produce a conservative estimate for the padding gas pressure even though it has counteracting impacts Specifically during the initial stages of heating allowing mass exchange to maintain equilibrium would cause there to be an increase in the amount of gas in the liquid phase caused by the initial expansion of the liquid phase due to heating That dissolution into the liquid phase would lead to a decrease in the padding gas partial pressure However counteracting that effect is the fact that if mass exchange were allowed then after the initial opening of the safety relief device the decrease in pressure would lead to liberation of the padding gas from the liquid phase causing an increase in vapor pressure and an increased flow rate
82. dels all radiative exchange using a classical law 18 and represents every surface as being gray with a constant value of emissivity For radiative exchange between two surfaces the emissive powers of the two surfaces are E g oTt 5 1 _ 4 E 6 oT where ois the Stefan Boltzmann constant As shown in 18 a heat flux balance between two gray surfaces connected in the logical configuration indicated in Figure 5 3 results in the following relationship olt zm 5 2 1 2 1 lz AF A where Qi2 15 the net heat flux from surface 1 to surface 2 15 the geometric view factor which represents the line of sight exposure between surfaces 1 and 2 as defined in 18 and is the area of the surfaces i i 1 2 41 Surface 1 Aj E Surface 2 A5 lt Figure 5 3 Gray body configuration used AFFTAC Rearranging the above equation becomes s 53 A MES ZI Fiz A amp Through this equation the surface configuration factor f 5 is defined and used in AFFTAC to scale the radiative flux exchange That factor 1 5 4 fra 1 1 A 1 i A V is used in combination with the surface areas Stefan Boltzmann constant and temperatures of the exchanging surfaces to predict the radiant heat flux on a per area basis 1 gi BS In computing the radiative exchange between the inside tank wall and the liquid surfa
83. ductances of the wall and wall insulation respectively unknowns in the above equations are Touter ins and Touter noms solve the equations using the Newton Raphson method first the left hand side of the equations are given names fi f2 and fs 6 8 osfT 4 2 d zr 452 6 9 2 4 2 _ lt 4 2 E ies zd D E E E 6 10 452 o C JE n 55 Second an array containing the three unknown temperatures and an array containing the three functions are defined A 6 11 T I E E and f T T outer Ins The nonlinear system of three equations may now be expressed as follows f T 0 6 12 The Newton Raphson method of solving a nonlinear system such as that in Equation 6 11 is to start with an initial guess T and then update that guess as follows T T 6 13 Where 8 is the solution to the following linear system of equations of of of 6 14 OT of of of 5 S T OT OL outers of of of OD Rie The right hand side is an array of three entries which are the f functions evaluated at the previous guess The matrix is comprised of partial derivatives of the three functions with respect to the different temperatures also evaluated at the previous guess Working from Equations 6 8 6 10 the partial derivatives are as follows 6 15 LEE 4 i T OT
84. dynamics hereafter First Law reduces to dq dw du B 1 where u is the internal energy of the fluid q is the heat transferred into the fluid and w is the work done by the fluid 123 If this process is adiabatic reversible isentropic dq 0 Also fluid alone can only do work intrinsically through expansion so dw where is the infinitesimal change in volume Therefore the First Law for the fluid is du pdv The specific heat at constant volume c is defined as du Gum dT or du c dT so that c dT pdv Returning to Equation B 2 and adding pdv to both sides du pdv vdp vdp which means that d u pv or dh vdp where h is enthalpy The specific heat at constant pressure cp is defined as dh E dT or dh c dT so that c dT 124 B 2 B 2 B 4 B 5 B 6 B 7 B 8 B 9 B 10 B 11 Divide Equation B 11 by B 5 to get vdp B 12 C pdv Rearrange 13 p and define the ratio of specific heats as k c c so that dp B 14 v P Assume constant ratio k of specific heats and integrate dv B 15 ES constant B 16 The above equation means that the product of pressure and specific volume is everywhere constant in the quasi static process Introducing i to denote an inlet and to denote and outlet the above equation implies that D p
85. e min 60 240 o E 2 20 2 0 20 40 60 Time min 80 100 100 Release Rate intemal Tank Burst Figure 3 4 plotting window graphically displaying the results of an analysis 29 Administrative Information Administrative information is required in order to print the results of an analysis or to save it in the database To add the administrative information highlight the analysis and click the Edit Admin Data button in the Main Window The window used for entering that administrative information is shown in Figure 3 5 Your name and company may be more permanently set by selecting the menu option Options User Information in the Main Window rest of the user specific information you add in the window is shown in Figure 3 5 Administrative Information 8 Administrative information is reuqired to print results or add the analysis to the database Your Company Name Your company name Job Number Baseline Case 1 Your FirstName LastName Date 27 2013 Customer None Notes Old TPS Model Steel Jacketed 4 Figure 3 5 Administrative information window that must be completed for a simulation to be printed or added to the Analysis Database Table of Capability Setup Options AFFTAC is approximately forty years old and has been enhanced many times during its history A
86. e Computational Module scroll through the information in the top right pane of the Main Window r A Setup Lading Select Lading Default Liq Low H20 Content a Default Lig Hi H20 Content Bi Water Propane 4 Ethlyene Oxide 3 Propylene Butadiene 1 3 Vinyl Chloride Monomethylamine Propylene Oxide Anhydrous Ammonia Sulfuric Acid Hydrochloric Acid NS Manage Ladings Database 0 96 Fraction Filled e Initial Temperature deg F Padding Gas Present Figure 12 4 Lading setup for Tutorial 1 110 In the left pane of the Main Window look at the list of analyses Notice that this analysis is listed at the bottom However it has not yet been saved to the Analysis Database file Before it can be saved there the administrative information must be added Likewise to print the results of this analysis the administrative information must be added In the lower part of the Main Window click the Edit Admin Data button Enter the following information Job Number My First Tutorial Customer N A Click OK and then you can save the analysis and print the results Note that the default information for your name and your company name may be defined through the Main Window under the menu option Options User Information In the Main Window click the Plot Displayed Results button Doing so displays the plot window shown in Figure 12 5 These plots can be
87. e innermost layer via conduction d region ETE T us 6 3 which is simply the second term in Equation 6 2 Thus for the four combinations considered heat fluxes computed are as shown in the table below dreg ion Liquid Yes d mns liquid No FPnoms liquid Vapor Yes ins vapor No Fnols vapor Table 6 3 The heat fluxes computed by Equation 6 3 for the four regions in the legacy TPS model when a jacket is not present 53 To compute the total average flux through the tank wall for the liquid and vapor regions the fluxes for those regions in the parts that do and do not have insulation are combined using a weighted average liquid m A ms tiquid ins zm Fps 6 4 Arps vapor Tis 85 PNE n where F Ins is the fraction of insulation coverage Partial Insulation Coverage Inside Jacket In this case the model accommodates a variable amount of coverage from the insulation that is between the steel jacket and the tank wall The model assumes that the steel jacket 1s so thin that it does not support a temperature gradient 1 it is a uniform temperature The heat transfer equation is solved twice once for the part of the tank wall touching the liquid and once for where it is touching the vapor Analogous to the previous sub section the governing equation can be written once and applied to multiple regions by appropriately defining the variables
88. e material fails Creep is usually discussed using strain as a primary quantity of interest During a creep to failure test the material is loaded with a constant temperature and stress Many metals respond by straining at three different rates in distinct stages The first stage is characterized by a strain rate that is relatively large But this stage is short lived and quickly gives way to a prolonged second stage where the strain rate is relatively small The second stage ends by transitioning to a third stage that is relatively short lived and is nonlinear It is this third stage that ends relatively quickly and abruptly by failure of the material 72 300 400 Temperature deg C Larson Miller Parameter as a function of Stress Switch to table input method Y 221 75 X 0 x2 ERE NC NEN EE DUREE HE 150 200 Stress MPa X Range to w Figure 8 5 Property entry window The tabular of data entry is still available top But this window also accommodates polynomial data entry bottom The two modes are activated using the large button between the table and polynomial entry regions of the window 76 a Plotter lo Liquid Tank Wall intemal Tank Burst S S Pressures psi Temperatures deg F 0 1 1 1 0 20 40 60 80 100 0 20 40 60 80 100 Time min Time min Of
89. e the pressure increases beyond that burst pressure the disk is destroyed and the release area defined by the user is present for the remainder of the simulation fraction open 1 97 98 Models for Internal Pressure Stress and Strain Modeling Pressure Inside the Tank The pressure of the vapor is computed using the partial pressures of the vapor s constituents For ladings that are a pure substance the total vapor pressure is the sum of the vaporized lading s pressure plus that of the padding gas if present For a solution it is the sum of the partial pressures of the solution s vaporized constituents plus the pressure of the padding gas When the quantity of liquid in the tank is very small the remaining vapor is treated as an ideal gas The temperature from the previous time step is used thereby immediately allowing the computation of the vapor pressure p When the quantity of liquid in the tank is not small the vapor is assumed to be saturated The partial pressures of the lading s constituents are computed using pressure versus temperature data that you enter in tabular form in the Ladings Database That data is queried through quadratic interpolation during the simulation It is assumed that the padding gas first achieves an initial state of equilibrium before the fire but after that no further mass exchange occurs between the padding gas in the vapor and the liquid lading which is to say that the padding gas is assume
90. el Jacketed Steel Jacketed 2 component 043 Initial conductance BTU hr4t 2 deg F Six 5 mil organic liner 1 Time interval for change min 3 16 inch thick rubber liner V Deteriorates overtime 1 Time interval min Temperature Independent A Legacy 5 Default Insulation 9 Type of Insulation Bare Temperatureindependent FRA Standard 7 Temperature Dependent Steel Jacketed Steel Jacketed 2 component Conductivitys change with time Linear Decay Constant 043 Final conductance BTU hr4 2 deg F liner 3 16 inch thick rubber liner V Deteriorates overtime 1 Temperature Dependent Legacy TPS Mc Default Insulation 9 Type of Insulation 7 Bare Temperatureindependent 7 FRA Standard Temperature Dependent Steel Jacketed Steel Jacketed 2 component 05 Insulation thickness inches K2 K3 0 017 0 019 0 042 Six 6 mil organic liner 3 16 inch thick rubber liner V Deteriorates over time 1 Steel Jacketed 2 component A Legacy TPS N Default Insulation 9 Type of Insulation Bare 7 Temperatureindependent FRA Standard 7 Temperature Dependent 7 Steel Jacketed Steel Jacketed 2 component with time 05 Insulation thickness inches K2 K3 0 017 0 019 0 042 043 intial conductance BTU hr amp 2 deg F 043 Final conductance BTU hr amp 2 deg F 1 Time interva
91. emissivity of the fire The value for c and the other variables take on the following meanings in the different regions to which the equation is applied 52 Liq uid Yes T ading Crankelns No T uter noms iquid T dins Crank Va po r Yes T Crankelis No Len ree Tiina Crank Table 6 2 The values that the variables in Equation 6 2 take on for the four regions of the tank wall present in the legacy TPS model when a steel jacket is not present As implied in the definitions above these nonlinear equations are solved four times twice for the tank wall adjacent to the liquid and twice for the tank wall adjacent to the vapor The reason AFFTAC makes the distinction between the liquid and vapor regions was explained Scope and Interaction of AFFTAC s Models chapter but is worth reviewing here When the liquid lading is touching the tank wall it provides a great deal of thermal mass in intimate contact with the tank wall Therefore the tank wall touching the liquid is assumed to be at the same temperature as the liquid However the tank wall adjacent to the vapor has no intimate contact with a large thermal mass Thus it can be at a different temperature from the lading Once the outermost surface temperature is determined for the four regions in Table 6 2 above it is used in combination with the appropriate innermost surface temperature to compute the heat flux into th
92. eratures equal to the radiating temperatures on the same surface Equations F 14 below and by setting the exposed area temperatures for the layer with zero coverage equal to their counterparts on the neighboring surfaces Equations F 15 below So when c 0 in place of the conduction equations we have 0 F 14 0 F 15 Angular Dependence There are two aspects in which the TPS model is in effect in the AFFTAC operator split metholodogy First the TPS model is used to compute the updated outer surface 150 temperature In this situation the interior boundary condition is applied as a known value and the outer surface temperature 77 is determined by solving the system of equations described above Second the TPS model is used in a heat balance equation for the innermost surface In this second application the inner surface temperature 7 is not known But in this situation the most recent value for T is used in with the thermal conductivity and thickness to compute the heat flux entering the innermost surface from the outside This heat flux is balanced with the heat flux from the innermost surface to the vapor and liquid to compute In this the generalized TPS model these two areas of application remain unchanged in principle However this model also admits the possibility that the coverage terms ci above may vary with angle Specifically the user is allowed to set up na segments of the tank car wherein the c array
93. f the tank wall that has been depleted Once all of the life has been depleted the tank is said to have burst The tank strength model interacts with AFFTAC s thermal model in fairly intricate ways If the legacy TPS model is used then the highest temperature experienced by the tank wall is that adjacent to the vapor and that temperature is used as input into relatively straightforward algebraic equations to compute an ultimate tensile strength In contrast to this AFFTAC s new Larson Miller model operates differently because it depends on the history of each point around the tank In the Larson Miller model 180 points are established around the tank at one degree intervals and those tracking points are used to track the temperature pressure life remaining metrics at their respective locations Thus when the legacy TPS model is used the Larson Miller tracking points are fed either the tank wall temperature adjacent to the liquid or the vapor depending on their location As the liquid level rises or falls the temperature fed into each Larson Miller tracking point may change If the general TPS model is invoked with significant angular dependence to the insulation the interactions are different still For the legacy strength model a search must be made through the TPS segments for the highest temperature and that temperature is fed to the algebraic equations mentioned above But for the Larson Miller model each of its 180 tracking p
94. go and then to enter the property values using the ENTER key to move down the rows Clicking Refresh will update the plot using the values you enter into the table By clicking on the plot itself the plot is copied to the Microsoft clipboard and can then be pasted into a variety of Microsoft Windows applications such as PowerPoint and Word It is important to remember that the AFFTAC Computational Module allows only 8 data points for each property except for vapor pressure which may have between 3 and 15 data points Also there must be an odd number of data points entered for vapor pressure A substance is matter that is comprised of only one type of molecule A solution is a mixture of two or more substances that is homogenous at the molecular level AFFTAC allows two component solutions 36 Specific Heat as a function of Temperature Refresh Temperature deg F 120 210 260 Cp BTU Ib 200 250 150 Temperature deg F Figure 4 4 Window for editing tabular input of thermodynamic properties 37 38 Details of the Overall Thermal Model Essential Constructs Below are the essential constructs of AFFTAC s thermal transport model You should be cognizant of these when seeking to understand the theory behind the Computational Module l The liquid and vapor phases of the lading are assumed to be at the same temperature Which ch
95. gure 6 1 The Legacy TPS Model Database manager When you double click a TPS or highlight it and then click the Edit button the Legacy TPS Model Setup window appears like one of those shown in Figure 6 2 This multi faceted window provides opportunities to create and customize six different TPS types Its appearance changes depending upon which type of TPS types is chosen When you are finished editing a particular TPS setup you will be returned to the Legacy TPS Model Database Manager window There are two ways to exit it One way saves the changes made to the database file The other way keeps the changes for use in the current AFFTAC session but does not yet save the changes to the database file This option is important because sometimes it is helpful to try a modification to an existing TPS without committing to it Be sure to save the file before exiting if you indeed want to keep those changes You may do so by clicking the Main Window menu option File Save Legacy TPS Model Database Setting up a TPS in the Legacy Model Described below are the various types of setups available in the legacy TPS model Refer again also to Figure 6 2 Bare The Bare option simply means that there is no thermal protection system No further input is required of you for this option 48 Steel Jacketed A Legacy TPS M Default Insulation 9 Type of Insulation Bare Temperatureindependent D FRA Standard Temperature Dependent Ste
96. h Other 81 ULTIMATE TENSILE STRENGTH 82 PRESSURE RELIEF DEVICES AND THE PRD 0 0 22 2 1 83 SPECIFYING A PRD DIRECTLY DURING THE EDITING SEQUENCE c 85 SPECIFYING PRD USING THE PRD 5 4 85 Specifics lel eee dace ouo BS es eas 88 Specifics for a Vent with Rupture Disk eee eese sesenta nennen 88 THEORY FOR MODELING FLOW THROUGH A 88 88 Choked Flow Model UG 89 Estimation of the PRD s Area using the Choked Flow Model 90 Low Speed bee Phe 91 Two Phase Flow nie t 9 Liquid Ejection in the Shell Full Condition 95 MODELING THE OPENING AND CLOSING 5 3468 95 Spring Loaded Pressure Relief Valve PRV essen 95 Frangible Disk iise e VA a Bes cu 97 MODELS FOR INTERNAL PRESSURE STRESS AND STRAIN 99 MODELING PRESSURE INSIDE THE TANK eee nnn nnn nna 99 MODELING TANK DEFORMATION eene e n e nennen enhn nnn nnne n n nnn n n n 101
97. hat part of the tank wall s temperature over time The ability to subdivide those two segments into smaller sub segments was added to allow you to specify variations in percent coverage of the insulation as a function of angle on the tank in the new generalized TPS model While all of the sub segments adjacent to the liquid are still set to the liquid s temperature with the angular dependence 81 capability the parts adjacent to the vapor may have temperatures that vary from sub section to sub section To implement a creep and failure model it is necessary to keep track of the history for each point on the tank Or put another way it is necessary to sum Equation 8 15 for each distinct angle Any given point on the tank wall may be adjacent to liquid and then later vapor This history must not be overlooked Rather it is tracked for each individual point on the tank To meet this requirement an array with 180 tracking points is established where each of the 180 points represent tank material over a span of one degree on the tank wall The life depleted value for the array is initialized to zero At each time step the life depleted value for each point is incremented using Equation 8 15 with the overall tank wall stress and the temperature at that point on the tank as inputs After the array is updated their values are compared to unity If any of them exceed unity a flag is set indicating that the tank has failed the simulation is
98. he results from its computations User interaction is eased through the use of databases that store different aspects of the analysis in convenient ways In the GUI you set up analyses which are grouped together and displayed in the Main Window as shown in Figure 1 2 Analyses have several inputs some of which are straightforward numerical inputs and choices Others however make reference to one of the databases that contain detailed information about specific aspects of an AFFTAC simulation For example in your analysis you must choose a lading by name That lading is specified in detail in the Ladings Database which is the database containing its thermodynamic properties Likewise you may choose a thermal protection system TPS model by name where that system is described in detail in one of the two TPS databases When you run AFFTAC it automatically reads its database files You do not have a choice regarding which files it reads it reads the ones in the installation directory 12 File Edit Databases Options Analysis Database Input Summary for Sample Job ID User Date DATA ENTERED INTO AFFTAC PROGRAM FOR ANALYSIS Computational Module Version 4 00 Sample FirstName LastName 05 15 2010 Baseline Case 1 Scott Runnels 2 7 2001 Baseline Case 2 failure Scott Runnels 06 15 2011 TANK PARAMETERS Baseline Case 3 rollover FirstName LastName 06 16 2011 Capacity gal 33000 0 Baseline Case 4 low fill Scott Runnels 06 16 2
99. ing Properties window changes its appearance depending upon the options chosen The most significant change is when you select the substance or solution option In the upper window of Figure 4 3 the Substance option is chosen In this mode you need only enter thermodynamic properties for the substance In the lower part of Figure 4 3 is the same window with the Solution option chosen where you are required to enter some of the thermodynamic properties for the solvent and solute at high and low concentrations To the extent possible those concentrations should bracket the solution concentration used in the analysis Inaccuracies can result from the bracketing being too wide You may enter any of the lading s thermodynamic properties as a constant or as a function of temperature If they are a constant the values are simply typed into the associated entry box AFFTAC converts that constant value into a table of two rows each with the same value you entered To enter properties that vary as a function of temperature you must enter the data by first clicking the appropriate Edit Table button that appears next to the property name Shown in Figure 4 4 is the Property Entry window for one of the lading s specific heat The table may be edited by entering the values as a function of temperature The recommended method is to clear the table first using the Clear Table button enter the temperature values using the ENTER key to create new rows as you
100. is 0 25 BTU hr ft deg F which implies a thermal conductance of 500 BTU hr ft deg F for a 6 mil thickness Its effectiveness would be expected to be retained for a fairly long period of time because its conductance is high which means the temperature of the inside of the tank wall would be close to the temperature of the product within the tank Thus it is less likely to be damaged by high temperature Again for all such liners C value is modified according to Equation 6 20 59 60 The Generalized TPS Model and Database This chapter discusses the scope and use of the generalized TPS model and database which is a separate modeling option that can be chosen instead of the legacy TPS model described in the previous chapter The legacy TPS model is very important because it has been part of AFFTAC a long time and through its many uses has undergone significant debugging and hardening Also it is a relatively simple model and so it inherently has less potential for errors For those reasons users are encouraged to always make test runs using the legacy TPS model as a check against runs made using the newer and more complex generalized TPS model described here The generalized TPS model offers several sophisticated advances over the legacy model Because of its complexity it has also undergone significant testing as described in the accompanying AFFTAC Verification and Validation Test document The capabilities of the generalized TP
101. known The process for creating a new lading from a default lading is similar to creating one from any other existing lading Simply highlight the default lading of interest click Copy and then click Paste However when pasting from a default lading the dialog box shown in Figure 4 2 appears This window asks for the name of the new lading the molecular weight and the density at ambient 22 The creation of the new lading cannot proceed without these values The use of default ladings is not recommended If they are used you should understand how their thermodynamic properties were chosen as described in Appendix A Paste Default Lig Low H20 Content Defaut Lig Hi H20 Content Butane Ethlyene Oxide Butadiene 1 3 Vinyl Chloride Monomethylamine Propylene Oxide Done write to file Anhydrous Ammonia Figure 4 1 The window used for managing the Ladings Database You have chosen to create a new lading based on defaults The following information is required to complete that process Figure 4 2 Dialogue box asking for additional information when creating a new lading from a default lading 34 Name Butane of Lading Molecular Weight Lading has a critical temperature Solution 44 0 9090909 Emissi Substance MY Depends 2 Specifi
102. l for change min 5 mil organic liner inch thick rubber liner GroupBox3 V Deteriorates overtime Yes 1 No Use default of 40 BTU hrt 2 deg F Figure 6 2 The four types of legacy TPS types that require user input 49 FRA Standard This TPS sets an overall thermal conductance of 4 0 BTU hr ft deg F for the TPS which is the maximum conductance that will pass the FRA performance test specified in Appendix B to CFR 179 Insulation systems that pass the test would likely have conductances that are less than this value Temperature Independent Insulation This type of TPS uses an insulation that is constant with temperature but is allowed to change with time Two alternatives are offered one where the conductance of the system is constant and the other where the conductance changes linearly over a given time period from an initial value to a steady state value Temperature Dependent Insulation If this option is chosen you may enter three coefficients that are used in the following equation to describe how the thermal conductivity of the tank wall varies as a function of temperature KT 6 1 BTU hr ft deg F ft computed using the temperature dependent form temperature is in thousands of deg F and length is in feet So the units of conductivity are in the Computational Module BTU hr fi thousands of deg F ft parameters have units that accommodate the temperature functi
103. l protection system or 5 models When the TPS model is invoked at any time during the simulation it is given the current temperature of the interior surface of the tank wall and the temperature of the flame Using those two boundary conditions it computes the temperature of the tank s outermost surface and the heat flux through the TPS TPS model is invoked at least twice once for the segment of the tank wall adjacent to the liquid and again for that adjacent to the vapor In simulations where the TPS is specified to have angular dependence it is invoked multiple times one for each angular segment you specify Fourth the heat transferred into the lading is computed in two ways One way is the heat conducted through the tank wall adjacent to the liquid That heat flux is provided by the TPS model as mentioned above Another aspect is the heat radiated and convected from the inner surface of the tank wall into the lading The radiation occurs between the tank s innermost surface adjacent to the vapor and the top surface of the liquid while the convection is between the tank s innermost surface and the vapor Either way whether exchanged with the vapor or liquid phase the heat is considered to be exchanged with the lading as a whole which again is at one uniform temperature at each point in time Other heat related mechanisms include thermodynamic work associated with discharging lading through the pressure relief device and the as
104. le 6 1 The four outermost temperatures in the legacy TPS model when a steel jacket is not present 51 T jacket vapor wall vapor wall vapor lading lading outer noIns vapor outer Ins vapor outer nolns liquid outer Ins liquid Tank Wall Tank Wall Figure 6 3 Temperature definitions for the case of an unjacketed Left and jacketed Right TPS Bare Tank or Non Jacketed Tank with Partial Insulation Coverage Although a bare tank may perform and appear very different than a tank with insulation from the legacy TPS model s standpoint the two cases are identical in structure Specifically the heat transfer from the inside of the tank wall to the outermost surface is equal to the temperature difference on those two surfaces times a thermal conductivity divided by a thickness Granted the conductivity in the bare tank case will be much higher than in the insulated case but that does not change the fact that the equations are the same form And so in AFFTAC the bare tank and insulated tank are treated exactly the same way with different values for conductivity The treatment is a heat balance on the outermost surface that accommodates areas with and without insulation The equations are of the same form for all the regions os fT oT ap O 6 2 outer where T is the flame temperature c is thermal conductance and f is the
105. liquid were completely unconstrained The volume of the tank is subtracted from that volume and divided by the time step length to determine the flow rate Then the Bernoulli equation is used to provide an estimate of the pressure required to expel that amount during the time step For this situation which is depicted in Figure 9 5 the Bernoulli equation is 1 9 12 g 2 The velocity is related to the mass flow rate through the following relationship MassFlow Rate Ibs sec 9 13 V Liquid Discharge Coefficient x Device Opening Area x Density Ibs ft all of which are known Therefore the Bernoulli equation can be used to determine pe the upstream pressure in terms of ps To provide an estimate is assigned the value of the saturated vapor pressure or the atmospheric pressure whichever is higher Once p is See Appendix B for a discussion on the use of the liquid and vapor discharge coefficients 3 Consideration of two phase flow effects for high vapor pressure ladings might result in a slightly lower tank pressure but the difference would be small 93 computed it is used to determine what type of flow conditions exist The final form of the equation used to compute the pressure required to produce sufficient lading ejection is 2 k Ibf lbf 1 Ibf Pan Er Baal ar n 9 14 ft ft J 64 4v 720 Cpr A ft where Danan Taken to either atmospheric pressure or the lading
106. low rate lbs sec minimum cross sectional area of the valve f valve discharge coefficient P upstream gas pressure psia 89 upstream gas temperature absolute deg R gravitational constant ft sec gas compressibility factor gas constant equal to 1 545 molecular weight ft deg ratio of specific heats m NOS HM Most of the terms in the above equation are constants and are therefore separated into a single value Specifically the constant is defined as follows 9 2 4 Via ce Ry l so that the first equation for the mass flow rate may be written Cov ALP 9 3 The above equation is used for each constituent in the vapor where p becomes the constituent s partial pressure p The effect of the padding gas on the mass flow rate becomes negligible after a short period of time because its mass is small compared to that of the lading In this model and the ones that follow the above equation is multiplied by yet one other parameter the fraction open which varies between zero and unity The fraction open parameter is used to model the opening and closing of valves and has a model of its own which will be discussed in a subsequent section Estimation of the PRD s Area using the Choked Flow Model The choked flow model can be used in AFFTAC to compute the minimum cross sectional area of the PRD It does it by using experimental data entered by the
107. managed using windows launched from this window Setup Lading Window In this window you select the lading from a list of ladings stored in the Ladings Database You may edit this database to create new ladings by clicking the Manage Ladings Database button Also in this window you specify the fraction of tank filled by the lading its initial temperature and the padding gas if present 26 File Edit Databases Options Analysis Database Baseline Case 1 Help Input Summary for Sample Click here to run Sample and view it below FirstName LastName 0 Sample Baseline Case 2 failure Runnels 06152011 Baseline 3 FirstName LastName 6162011 above Baseline Case 4 qow fil Scott Runnels 06162011 Baseline Case 4 TPS version of Case 1 Scott Runnels 09262010 PRV Ful crcle test A 1400 PRV Fullcircle test A 37000 TPS Test Metal MetalwPartialCoverage Gap Metal FirstName LastName 10 02 2012 FirstName LastName 11 12 2012 FirstName LastName 11 12 2012 ITo run and then view the results for this case click the blue Model Results for Sample Dp Sample Create and Delete Edit Analyses Analyses Plotting button above zm mm aste Release 4 00 ITo run and then view the results for this case click the blue
108. n in AFFTAC is probably unneeded since the compact analytical form is readily available in Equation B 72 133 134 Appendix C Thermodynamic Identities for an Ideal Gas By definition dh _ i 1 dT ideal g pv RT CA And so u RT c R oe Theref c c R 4 135 Dividing both sides by c The ratio of specific heats appears often and is defined here as k Therefore using this definition so that 136 k C C 5 C 6 C 8 Appendix D Derivation of PRD Area Estimation Formula In the initialization part of AFFTAC s main routine the vapor discharge coefficient is used with the choked flow model to compute the area of the valve The line in the code is as follows avlv User ValveFlowCapacity User DischargeCoef Vap pasd 2644 0 discharge area of safety relief valve sq ft Derivation of that line of code starts with B 72 here labeled D 1 D 1 A Y exp k l k 2 k 1 C EA yz io With units 137 D 2 Gu n min ft Alft m 2 a ecl Co Pa e zd ft Ibf cal exp Ibm R In the line of code shown above pressure is in psi instead of the units given above and volumetric flow rate is used instead of mass flow rate Thus the following substitutions are made into Equation D 2 Ibm fe Ibm l min Q e 1bm D 3 Ga 0 55 gt 3 sec min ft 60 sec 60 sec Ibf Ibf in
109. n of total area covered by layer Figure 7 5 Illustration of a disassembled conceptual TPS which each layer laid out separately thereby exposing the voids in each layer Each layer has partial coverage Voids in adjacent layers permit Layer number 1 2 3 n radiative and convective exchange Three temperatures at each interface Conduction path and two radiation convection paths Nomenclature for exposed area temperatures Tre A Right or left Layer number Layer 2 Layer 3 Figure 7 6 Illustration of conceptual TPS with layer numbers showing how the voids and non void areas interact between layers and establising temperature nomenclature 65 Area in Contact Interface i is the interface between Layer i and Layer i Since this area is in contact with two layers conduction is the only mechanism for heat transfer A heat balance on the interface states that the heat flowing into it must equal the heat flowing out of it That requirement is embodied in the following equation 6 1 In the above equation you can see some of the complexities of the nomenclature In particular there are area terms variables that describe how much area is available for conduction That value depends on the amount of coverage specified for the layers Right Side s Exposed Area Consider again interface i but this time the part of that interface that is exposed due to a lack of
110. n predicting the discharge rate Another way to specify the PRD is to use the PRD Database As with the other databases in AFFTAC you can specify all the parameters describing a PRD by simply selecting an entry in the PRD database When the simulation is run these parameters are transmitted to the Computational Module Regardless of which data entry method is used the same models are used in the Computational Module The advantage of entering the values for the PRDs directly is that it can make performing trend studies and sensitivity studies easier With just a few clicks you can explore the sensitivity of the simulation to the PRD e g the flow capacity The advantage of using the database is that it contains PRDs referenced by model number where the parameters have been found through detailed calibration studies AFFTAC is shipped with 10 entries in the PRD database all calibrated using recently obtained data The calibration exercise is described in the accompanying AFFTAC Verification and Validation Testing document 83 In the following sections the two methods for entering PRD specifications are described After that a detailed description of the theory underpinning the flow models is provided A description of the input values required to specify a PRD is provided below A more thorough understanding of these values can be obtained by reading the theory section in this chapter Input Value Applies To Description Rate
111. ncrease among products shipped in tank cars making it difficult to suggest default properties Values range from an increase in specific volume of 13 percent for chlorosulfonic acid in the temperature range from 50 to 302 F to a 70 percent increase for hydrogen fluoride in the same temperature range The rate of increase in specific volume with temperature is an important parameter when the tank car becomes shell full and liquid is being expelled through the valve a larger valve capacity for liquid flow being required when the rate of increase is higher Tentative values are suggested as follows Liquids non pressure cars or Liquefied Gases Containing at least 50 water Temperature Percentage increase in Specific Volume from Ambient Value 60 Ambient Value 180 10 300 30 Liquefied gasses pressure cars Temperature 60 150 240 Percentage increase in Specific Volume from Ambient Value Ambient Value 20 50 Heat of Vaporization There is also considerable variation in the heat of vaporization among products shipped in tank cars ranging from about 1000 for solutions containing a high percentage of water to less than 100 BTU Ib for products such as bromine methyltrichlorosilane titanium tetrachloride and phosphorus trichloride Other factors being equal a lower heat of vaporization will result in the generation of greater volume of vaporized product requiring a larger capacity pressure relief valve
112. nity if j 2i and zero otherwise The entries of the Jacobian will now be derived below First to assist in the taking of partial derivatives the functions are re written with each term split apart and made separate To assist with the algebra the following terms are defined 153 F 23 F A fe Ven 116 1 Fi A eS Ve lle 1 Gri Agi h k Apr Exposed Left Side Balance F 24 jd y bs y 1 lt lt k 8 s fa PON D R di Jr Tp T 4T Tg 0 0 22 Tolo i l Exposed Right Side Balance F 25 T 1 5 Xe f Ri 1 k i 1 W i 1 1 lt lt n k gt Fru y ED y 1 i Te T AT 7T 0 c 20 k k Asin A as Jr doe ire AOE H USN i i Contact Balance F 26 154 Jr 4 A r Ji k A 2 y 1 lt lt W Wizi W W PCED a pr 1 7 D i Wi Wis T Tuc T C 0 i n Using the functions expressed as above the Jacobian can now be written as follows First row of blocks k i i F 27 Aa r y 4 1 lt lt of 1 k l c 0 Lj 1 28 k a I u M 1 lt lt ib Of i ja c 0 OT x 0 i l 29 246 1 l
113. ns for Tank Cars Association of American Railroads Mechanical Division 5 McAdams W H Heat Transmission 25d Edition McGraw Hill Book Company 1942 pp 133 141 and 294 337 6 Townsend W Anderson C Zook J and Cowgill G Comparison of Thermally Coated and Uninsulated Rail Tank cars filled with LPG Subjected to a Fire Environment Federal Railroad Administration Report No FRA OR amp D 75 32 December 1974 7 Braker W and Mossman A L The Matheson Unabridged Gas Data Book 1974 117 8 Gallant R W Physical Properties of Hydrocarbons Volume 1 Gulf Publishing Co Houston Texas 1968 9 Macriss A Liquid and Vapor Phase Enthalpy of Monomethlamine Journal of Chemical and Engineering Data Volume 12 No 1 January 1967 pp 28 33 10 Gallant R W Physical Properties of Hydrocarbons Part 12 C2 C4 Oxides Hydrocarbon Processing Vol 46 No 3 March 1967 pp 143 150 11 International Critical Tables of Numerical Data Physics Chemistry and Technology Volume III 12 Kirk and Othermer Encyclopedia of Chemical Technology Interscience Publishers 3 Edition John Wiley amp Sons 13 Slack A V editor Phosphoric Acid Marcel Depper Inc New York 1968 14 Properties and Selection Non Ferous Alloys and Pure Metals Metals Handbook Ninth Edition Volume 2 1979 15 Report a Study of Metal Specimens Removed from Tank Car Tanks Involved in a Derailment and Expl
114. nsidered to have failed This quantity is referred to in AFFTAC as the Fraction of Life Depleted When it equals zero none of the life of the material has been depleted When it equals unity it has all been depleted and the tank fails Burst Pressure for the Larson Miller Failure Model In the legacy failure model a straightforward algebraic equation relates the material s temperature to its ultimate tensile strength From that using simple geometric considerations described in the Models for Internal Pressure Stress and Strain chapter the pressure inside the tank that will lead to bursting can be computed Thus when using the legacy models one of the outputs in AFFTAC is the burst pressure as a function of time That pressure is plotted on the same plot as the tank internal pressure When those two lines cross the tank fails In the Larson Miller model the relationship between temperature and failure is more complex It involves time and also the stress history However the idea of a burst pressure is still extremely valuable and so AFFTAC defines one for the Larson Miller model to be as follows Larson Miller burst pressure is the pressure that would cause the tank given its temperature stress history and accumulated damage to fail in one minute To derive the equation for that pressure we start with the summation in Equation 8 15 above evaluated at time step 1 nAf 80 E At 8 16 2e o t T
115. nt during 2000 2002 Thanks also to those who tested the earlier versions including Bill Bitting Al Henzi Thomas Petrunich and Andy Rohrich The late Dr Milton Johnson s contributions to the earlier versions of this manual are gratefully acknowledged Much of his contributions remain in this revision in particular the Aside comments and Appendix A Likewise Mr Joe Cardinal at Southwest Research Institute also provided helpful input on earlier versions of this manual 15 16 The Scope and Interaction of AFFTAC s Models AFFTAC is a simulator combining the effects of several physical phenomena that together comprise a complex nonlinear system In this chapter the scope and interaction of those multiple physics models are described AFFTAC is best thought of as a transient quasi two dimensional model The heat transfer through the tank wall is one dimensional However some models in AFFTAC support variation in the insulation properties as a function of angle around the tank Conversely the liquid and vapor are at a uniform temperature at any point in time and in that sense AFFTAC is a zero dimensional model Yet the tank may be modeled as rolled over meaning the location of the liquid surface and its interaction with the location of the pressure relief device is accommodated In short separate assumptions regarding dimensionality are made The individual models are then combined in a consistent way Physics Aspects of a
116. ntal data obtained using vapor flow and the experimental data obtained using liquid two phase flow In the PRD database the specifications relating vapor flow and liquid flow may be kept separate if you wish For example you may enter a rated flow capacity and rating pressure which together allow AFFTAC to estimate an area for the PRD But then you may still choose to enter a value for area times the coefficient of liquid discharge When vapor is flowing through the PRD the rated flow capacity and pressure are used When liquid is flowing through the PRD the area times coefficient of liquid discharge is used These two sets of data may be different from each other and in practice do not even have to be consistent However you may also choose to link the liquid and vapor discharge inputs For example you may request that AFFTAC estimate the PRD area which uses the flow capacity and pressure you input and then enter only a coefficient of discharge for the liquid flow Doing so will require AFFTAC to use the area it estimates from the vapor flow data AFFTAC s method of estimation is described in the theory section of this chapter and more fully in Appendix D 86 Rated Flow Capacity SCFM of air Rating Pressure psig Vapor Discharge Coefficient decimal fraction Options for Liquid Discharge Coefficient Liquid Discharge Coefficient 9 Liquid Discharge Coefficient X Area 0 0034 Discharge Coef X Area sq ft Options for Area
117. o provide the estimate for the mass flow rate for the two phase flow However as with the other flow models e g the choked vapor flow model if the PRD is a valve the resulting cross sectional area is multiplied by the fraction open parameter to represent the opening and closing of the valve The model for the fraction open parameter is provided in a later section For alternative wording describing this model you might also find it helpful to consult the chapter on PRV flow model validation in the AFFTAC Verification and Validation Testing document Liquid Ejection in the Shell Full Condition The shell full condition occurs when the tank is completely full of liquid In that scenario the flow model is used for a different purpose which is to compute the tank s internal pressure The flow rate is already known by computing the difference between the volume of the liquid as it expands due to heating and the volume of the tank That required flow rate is used as an input into the flow model to compute the amount of pressure that would be required to drive that much flow That required pressure is then reported as the pressure inside the tank which is in turn used to help compute the amount of expansion in the tank wall and more importantly to determine if the tank has failed under that pressure The specific volume which is specified as a function of temperature by the user is used to compute the expansion that would occur if the
118. oalescing units leaves lbf _ Ibf y Ibf Pon gi Pu ar 5 g ft However in the code pressure is in psi thus 142 E 2 E 3 E 4 E 5 E 6 E 7 Df ay en lbf E 8 144 _ 144 mE bes in 3 Pcom is substituted to produce 9 5 14 F i sp ft ft 2g ft Dividing through by 144 and expressing 144 as 12 squared p 102 I 12ufY bf E 10 ft Prin ft 2 g 12 ft Or using specific volume instead while substituting g 32 2 mt mt 1 Pong JT 12 ft The units of velocity V is ft min It is the required volumetric flor rate divided by the area and the liquid discharge coefficient with factors to provide the appropriate conversion of units Q R E 12 _ Q ft areq ft 5 sec 60 jm Cp ft min Substituting that equation into Equation E 11 yields 2 lbf 1 Ibf ES gt 60 12 Vf or 2 Wf 1 Qj Ibf FE com amp 2 P min 2 2 ft ft 64 4v 720 C5 J ft 143 which corresponds to the line of code originally cited pcom pmint pow reql 720 0 DischargeCoef Liq areq 2 64 4 splq 144 Appendix F Governing Equations for the Generalized TPS Model Convection and Radiation Communication Areas The assumptions in the introdu
119. of data Other examples include the TPS setup the tank material and can also include the pressure relief device The process of setting up a simulation is divided into four steps which are conducted using four sequential windows Edit Analysis Conditions Edit Tank Car Properties Select TPS Model and Setup Lading These four windows are shown in Figure 3 2 Edit Analysis Conditions Window In this window you may set basic analysis conditions including the flame type and the length of the simulation From this window you can launch a sub window that allows you to set the time step and the frequency of printouts Edit Tank Car Properties Window In this window you set up the properties of the tank car including the material from which the tank is made and the safety relief device properties Both the material setup and the PRD setup may be handled in two ways You may choose to use the legacy models and setup methods by making choices directly in this window Or you may choose to use the PRD Database with the click of the appropriate button These new databases will be discussed at length in subsequent chapters Select TPS Window In this window you choose the type of thermal protection system on the tank car by selecting one of the systems that is displayed AFFTAC has two completely separate TPS models the legacy model and a new more general model The specification for these two models are in separate databases each of which may be
120. of stress the Larson Miller model will be described in more detail in a later section Data is entered for these two models by clicking the appropriate buttons in Figure 8 4 which opens a property data entry window An example of that window is shown in Figure 8 5 and allows for tabular entry of data top of Figure 8 5 or conversely algebraic data entry bottom of Figure 8 5 The Larson Miller strength model output is in two forms which occupy two columns in the output viewed in the Main Window The primary output of the Larson Miller model is a metric referred to here as Life Depleted This value which starts at zero represents the amount of accumulated damage in the tank material due to temperature and stress It is a non dimensional value once it reaches the value of one the life is completely depleted from the tank wall and it fails thereby ending the simulation The Life Depleted output might change very slowly at first and then grow rapidly as failure is neared Therefore the log of its value is displayed Another useful metric output by the Larson Miller model is the internal tank pressure that would cause the tank wall to fail in one minute given the damage that has accumulated in the tank wall up that that point in time That internal burst pressure output takes the place 73 of the burst pressure column of data which is displayed using the legacy strength model Shown in Figure 8 6 is a set of plots fr
121. oints uses the temperatures in their respective TPS segments Thus one can imagine a variety of complex scenarios arising depending on the type of simulation carried out For example consider a setup using the general TPS model with angular dependence such that significant defects in the insulation exist around the liquid level As the liquid expands or lading is discharged there may be significant changes into the input of the strength model for those points This type of complexity testifies to 22 the need for a computer model to understand it and also to the need for careful use and understanding of the model Material Expansion Modeling Both the liquid lading and the tank itself can expand during a simulation The liquid lading may expand due to heating The tank may expand due to heating and also due to stress The interaction of these expansions is very important when the tank is completely full of liquid 1 the shell full condition In that case further expansion of the liquid can lead to tremendous stresses in the tank wall that can result in failure Thus there is an important interaction between the models computing the expansion of the liquid its possible release through the PRD the expansion of the tank wall due to heat and stress and the tank failure model 23 24 Creating and Running AFFTAC Simulations Setting up an Analysis Each analysis in AFFTAC is stored in AFFTAC s Analysis Database The Analysis Dat
122. om a simulation that uses the Larson Miller strength model In the bottom left plot the life depleted is shown In the upper right plot the burst pressure is plotted again this is the pressure at which the tank would fail in one minute given its accumulated damage r A Edit Tank Car Properties 4 Tank Geometry Tank Material 20000 Nominal Capacity gal TC 128B Non Nomalized E ASTM A516 Non Normalized 108 Inside Diameter TC 128B Non Normalized No UTS gl TC 128B Non Normalized UTS Only 05 Wall Thickness in ASTM A516 Non Nomalized TC 128B yrs 1968 2002 ac I 08 Emissivity of Tank s Inner Surface Used old TPS model only supersceded if new TPS model is used v v ns Safety Relief Device Device Type 25800 Rated Flow Capacity SCFM of air D None 285 5 Rating Pressure psig 9 Valve 255 StarttoDischarge Pressure psig Vent with Rupture Disc 24 100 08 Vapor Discharge Coefficient decimal fraction 0 6 Liquid Discharge Coefficient decimal fraction Switch to PRD Database Previous Net Ces Run Now Figure 8 2 The Edit Tank Car Properties window in which the Strength Model Database has been selected r 3 _ Strength Model Database Manager C LEM 128B Non Normalized ASTM A516 Non Normalized TC 128B Non Normalized No UTS TC 128B Non Nommalized UTS Only ASTM A516
123. on regarding the secondary strain rate is made Specifically it is asserted that while the secondary strain rate 2 is a constant in time for a fixed temperature and stress it will change instantaneously to a new fixed value if the temperature and or stress change thus 2 o r T 1 Using this assertion the time at which failure occurs during a transient simulation can be determined by integrating o 1 T r over time When its time integral equals failure will occur In other words t is the solution to this equation 1 8 10 2100 70 0 8 11 120 70 4 0 Er Here it is important to note that i o T t lo T e 8 12 which is a way of restating the notion that the secondary strain rate is considered to be temporally invariant for a given stress and temperature but that it will change in time if 79 stress and temperature change in time This notion then results in a failure time that can also change in that same way From Equation 8 12 the strain ratio is a oo Using that in Equation 8 11 produces i 8 14 dt 1 t o t T where f is known from experimental data i e Equation 8 9 In an AFFTAC simulation the above integral is computed using the rectangle rule At each time step i 1 2 3 n with i and the summation At 8 15 n ot TE is compared to unity When it equals or surpasses unity the material is co
124. on that multiplies them In summary Note that conductivity typically has units of When conductivity is The k parameter has those units while the other two Parameter Units k BTU hr ft thousands of deg F ft k2 BTU hr ft thousands of deg FY ft k3 BTU hr ft thousands of deg FY ft Steel Jacketed 2 component Insulation As the name implies this TPS option has two layers For the inner layer you may enter an initial and final thermal conductivity value and a time interval over which AFFTAC 50 will interpolate between those values just as in the temperature independent option described above For the outer layer you may specify its thickness and also make its conductivity a function of temperature Legacy TPS Model Theory Before attempting to understand the theory for the legacy TPS model it is highly recommended that you read the chapter entitled Details of the Overall Thermal Model The material there will help you understand how the calculations of the TPS model fit in to the overall solution process and also some of the parameters used in the model description As discussed in that chapter the primary role of the TPS model is to compute the heat flux through the TPS The legacy TPS model operates in two modes one in which the tank is bare or perhaps partially covered by an insulating layer and another mode in which an air gap exists bet
125. or greater than for a valve it is assumed that two phase flow occurs In this situation the two phase flow model discussed previously is invoked to determine the mass flow rate If in the case of an upright car enough lading can be expelled in the vapor phase so that the tank will not be shell full at the end of the time step the tank is no longer considered to be shell full and a logical flag in the program is set to record that fact Otherwise the tank remains shell full Modeling the Opening and Closing of PRDs AFFTAC accommodates two different types of pressure relief devices The opening and closing models for these two types both have the same purpose to provide a multiplier the fraction open value for the flow area available which is used in the flow models previously described The models for these two types of devices are described below Spring Loaded Pressure Relief Valve PRV A pressure relief valve PRV is spring loaded so that it remains closed unless a sufficient amount of pressure builds up inside the tank If a certain pressure is exceeded the valve opens an amount that is approximately proportional to the excess pressure As lading is released and the pressure differential decreases the valve s spring begins to close it again There are some subtleties to how the valve performs most notably hysteresis This subtlety and others are captured in Figure 9 6 The path followed during opening is indicated by
126. osions at Laurel Mississippi Association of American Railroads Report No MR 453 July 1969 16 Properties and Selection Irons and Steels Metals handbook Ninth Edition Volume 1 1979 17 Design Guidelines for the Selection and Use of Stainless Steel AISI Committee of Stainless Steel Producers 1977 18 Chapman Alan J Heat Transfer Fourth Edition Macmillan Publishing Company New York 1984 ISBN 0 02 321470 8 19 Shames Irving H Mechanics of Fluids Second Edition McGraw Hill Inc New York 1982 20 ASME Handbook on Certification of Capacity of Pressure Relief Devices Section VIII Division I 21 Trostel Bryan Pressure Relief Valve Testing for US Dept of Transportation IORN CE10015 Rev 1 Nov 29 2010 118 Appendix A Default Ladings By Milton Johnson Ph D The use of default values for the thermal properties is not recommended If at all possible a search for the thermal properties of a lading should be conducted and the values that are obtained entered into the AFFTAC database If this is not feasible then the default lading templates may be used keeping in mind the following guidelines that have been followed to estimate their thermal properties These guidelines do not apply to tank cars transporting cryogenic liquids compressed gases such as helium or slurries products such as liquid sulfur which solidify upon heating If the product being considered is a solution it should be tre
127. ow model is used in some of those cases The flow models for choked flow and two phase flow are discussed in the following sub sections summary of the mass transport scenarios is tabulated below Tank Contents Flowing Out Supporting Model Liquid and Vapor Vapor Choked Flow or Low Speed Flow Liquid and Vapor Liquid Two Phase Flow Liquid Liquid Liquid or Two Phase Flow Vapor Vapor Choked Flow or Low Speed Flow 88 As mentioned above AFFTAC has the ability to estimate the discharge area of the PRD which is the minimum area The choked flow model which is used for vapor discharge is also used for that purpose Therefore the choked flow model is described first Then the liquid and two phase discharge models which require information about area are described Liquid and Vapor Liquid and Vapor Venting Vapor Venting Liquid Liquid Only Shell Full Vapor Only Venting Liquid Venting Vapor Figure 9 4 Illustration of the four different scenarios for lading release Choked Flow Model If the total pressure within the tank is greater than 27 0 psia 12 3 psig the flow of vapor through the relief device can be modeled as choked flow The value of 12 3 psig is the pressure required to sustain choked flow classical equation for choked flow of a compressible gas flow through a nozzle is therefore used That model is derived in detail in Appendix B and is 9 1 w 1AC A P EL V ZRT y 4 1 where w mass f
128. r Properties window changes to display the PRD database as shown in the right part of Figure 9 1 From the list in the lower part of the window you can select a PRD for your analysis You can also edit the database by clicking the Edit Database button When you do the window in Figure 9 2 appears in which you can create new edit or delete PRDs 85 r PRD Database Manager Sex New Midland A 1075 Midland A 1225 Midland A 1280 Midland A 1475 Midland A 14225 Paste Midland 14375 Sey Midland A 2165 er Midland 37225 Midland A 37280 Default PRV Model NEW AxCDL Verification Midland A 1400 NoRelease Midland A 37225 No Release Done write to file LS Figure 9 2 PRD database manager To edit a PRD either double click on the name or highlight it and click the Edit button When you do a window that resembles the one in Figure 9 3 will appear The version of the window shown in the upper part of Figure 9 3 is for a PRV while the one in the lower part of the figure is for a vent with rupture disk The inputs common to both valves and vents will be discussed below after which specifics to PRVs and vents will be discussed Similar to the old style of PRD inputs the window for PRD Database entries has the flow rating and flow rating pressure However the PRD Database allows for more flexibility regarding the relationship between the experime
129. rs on the TPS models The details of computing the fluxes in 3 ii and 3 iii are discussed in this chapter Computing these fluxes also requires knowledge of the temperature of the innermost surface of the tank wall adjacent to the vapor That key variable is determined vall vapor using an equation that balances the net flux into the wall from the outside with the net flux leaving the wall on the inside through convection and radiation to the lading That heat balance is shown graphically in Figure 5 2 with 3 1 this method of computation which splits governing equations into parts and solves them piecewise is known as nonlinear lagging or operator splitting and is discussed in the chapter entitled Scope and Interaction of AFFTAC s Models Tank Wall Liquid Heat convected through vapor into lading Net heat radiated to liquid from wall Heat transmitted through tank wall Figure 5 1 Heat flowing into the vapor and liquid phases of the lading 40 Arps vapor Flux into wall A T ui vapor Conv wall vapor Q Rad wall vapor Convection to vapor Radiation to liquid Figure 5 2 Heat balance on the tank wall adjacent to the vapor Constructs of Radiative Heat Exchange As discussed in the previous section radiative heat exchange occurs between the tank car s outermost surface and the flame as well as the tank s innermost surface and the lading s liquid surface AFFTAC mo
130. s and vents with frangible disks Use of this database gives you access 13 to pre established PRV setups calibrated in an extensive validation exercise which is discussed in the AFFTAC Verification and Validation Testing document It also gives you more freedom in how you specify PRD performance However in setting up an analysis you do not have to use this database the GUI also still allows you to input values directly into the analysis to describe the pressure relief device That method is more restrictive but is in some ways faster especially if you want to vary a PRD parameter in a study 5 Strength db This database contains specifications for tank material failure models particularly the Larson Miller creep and failure model as well as ultimate tensile strength data expressed in tabular and formulaic form as a function of temperature You may reference these inputs by name when choosing to use the Strength Database However you do not have to use this database The GUI also still allows you to specify tank material names directly as part of the analysis Doing so calls upon legacy failure models that are hard coded inside the Computational Module All of this will be explained in greater detail in later chapters 6 Regression db This database contains the specifications for the regression tests which are used to help maintain AFFTAC s quality You need not worry about the regression tests However some of the regression tests may
131. s any derivative works of AFFTAC the Licensee hereby agrees that such property shall be the sole property of Licensor The Licensee hereby waives all moral rights and any other ownership rights therein b Rights Reserved Licensor reserves all rights not expressly granted to the Licensee AFFTAC is protected by copyright laws and international copyright treaties as well as other intellectual property laws and treaties 3 NO WARRANTIES LICENSOR AND ITS LICENSORS HEREBY DISCLAIM ALL EXPRESS OR IMPLIED CONDITIONS REPRESENTATIONS AND WARRANTIES INCLUDING ANY IMPLIED WARRANTY OF MERCHANTABILITY FITNESS FOR A PARTICULAR PURPOSE DATA ACCURACY QUIET ENJOYMENT NON INFRINGEMENT EXCEPT TO THE EXTENT THAT SUCH DISCLAIMERS ARE HELD TO BE LEGALLY INVALID THE LICENSEE AGREES TO HOLD LICENSOR AND ITS LICENSORS HARMLESS FOR ANY CLAIMS OR LIABILITY ARISING FROM The Licensee S USE OF OR RELIANCE UPON AFFTAC FOR ANY PURPOSE 4 TERM AND TERMINATION This Agreement shall commence on execution of the installation software 5 ASSIGNMENT AND SUBLICENSE Licensee may not assign sublicense or transfer any of its rights or obligations under this Agreement 6 GOVERNING LAW Disputes which cannot be settled amicably will be governed by the laws of the District of Columbia USA Choice of law rules of any jurisdiction and the United Nations Convention on Contracts for the International Sale of Goods will not apply The venue for litigation
132. s chapter s Table 3 1 lading properties are described by entering values into the Ladings Database Then when setting up an analysis the lading is referred to by its name When the simulation is run AFFTAC extracts the appropriate thermodynamic data from the database and writes it to a file for the Computational Module to read The Ladings Database may be edited by choosing the Edit Databases Ladings menu option in the Main Window or by clicking the Manage Ladings Database button in the Setup Lading window which is displayed during the editing of an analysis When you choose to manage the Ladings Database a window like that shown in Figure 4 is displayed In this window ladings can be edited by highlighting them and clicking the Edit button New ladings can be created by either highlighting an existing one and clicking Copy then Paste which creates a copy of the highlighted lading or by clicking New which creates a new lading from scratch You can exit the window with or without saving your changes to the database file If you choose not to save them to the file they will still be available for the current AFFTAC session and AFFTAC will ask you if you want to save them when you try to exit the session Using Default Ladings The first three entries in the database are default ladings These cannot be used for an analysis but instead serve as a template from which new ladings can be created when not all of the thermodynamic properties are
133. s that use the generalized TPS model discussed in the next chapter The inputs that specify the legacy TPS model are grouped together and stored by name in the Legacy TPS Database filename Insulations db Thus each named entry in the Legacy TPS Database represents multiple pieces of data When setting up an analysis the third editing window requires you to select which TPS model you want to use the legacy model or the new general TPS model If you select the legacy TPS model you will see the list of named entries in the Legacy TPS Model Database In that same window you may launch a window from which you may edit the Legacy TPS Model Database You may also edit the Legacy TPS Model Database from the Main Window by choosing the option Edit Databases Legacy TPS Model Managing the Legacy TPS Model Database When you choose to manage the Legacy TPS database the window shown in Figure 6 1 is displayed In this window TPS setups can be edited by double clicking them or by highlighting them and clicking the Edit button New TPSs can be created by either highlighting an existing one and clicking Copy then Paste which creates a copy of the highlighted TPS or by clicking New which creates a new insulation using default values 47 New Example 1 Example 2 Delete Copy Example 3 Paste Sensitivity Test Bare Tank Perfect Insulation Deteriorating Steel Jacketed Done write to file Done dont write yet Fi
134. s with increasing temperature More explicitly in AFFTAC the tensile strength of the tank wall material is S T S f T 8 1 where S is the hard coded value of the material s ultimate tensile strength at room temperature and f T is the multiplier that decreases with increasing temperature Values of S are provided inside AFFTAC for twenty seven different materials And for each material there is a hard coded model for f T 69 r Tank Geometry Tank Material 20000 Nominal Capacity gal ASTM A 537 80 Class 1 Min Tensile Strength 70 Kpsi 108 Inside Diameter in 500 Minimum Bursting Pressure psig 05 Wall Thickness in 81000 Tenslie Strength of Tank Material psi Switch to Strength Model Database 08 Emissivity of Tank s Inner Surface Used by old TPS model only supersceded if new TPS model is used Safety Relief Device Device Type 25800 Rated Flow Capacity SCFM of air METS 285 5 Rating Pressure psig Valve 255 Start amp oDischarge Pressure psig Vent with Rupture Disc 08 Vapor Discharge Coefficient decimal fraction 06 Liquid Discharge Coefficient decimal fraction Switch to PRD Database ae ae Figure 8 1 Edit Tank Car Properties window which the legacy model is selected Tables 8 1 8 3 on the subsequent pages show these models for each of the materials The units in the tables are T R 1000 8 2 S Kpsi Note that the
135. s with any code of that age and type efforts are made to maintain legacy capabilities while adding enhancements As a result of that AFFTAC has a variety of input options and style of input methods In many places in this manual you will find that you have the option of using a legacy model or a new model And you will find that you have the option of inputting values in different ways To help avoid confusion the table on the next page is provided to clarify these aspects 30 As the table indicates some aspects of the simulation may only be entered directly into the analysis by specifying values Others have multiple options For example if the legacy PRD setup method is used the values are entered directly in the analysis If you choose to use the new PRD setup method you will instead access the PRD Database and enter the values there Table of Capability Setup Options Yes No Yes No Yes for legacy Yes for Larson Miller Yes for legacy Yes for general TPS Yes for legacy Yes for PRD database No Yes two different databases one for legacy one for general model Yes No No Yes Yes No Yes No Table 3 1 This table provides an overview of what methods may be used for inputting values for different models in AFFTAC Because there is a mix of legacy and new modeling capability input options vary 3l 32 The Ladings Database As shown in the previou
136. sociated heat of vaporization Fifth a heat balance on the innermost tank wall is used to determine the temperature of the tank wall for the portion of the tank over the vapor region Pressure Relief Device Modeling AFFTAC accommodates pressure relief devices PRDs that under appropriate conditions allow lading to be discharged Depending on the amount of liquid lading present and the angle of tank rollover the discharge may be purely liquid purely vapor ora mix The details of how the pressure relief device s opening and closing action are modeled as well as the fluid flow through it are described in a separate chapter One important note to make here however is that you have two ways of entering specifications for the PRD One is to specify them directly as numerical entries as part of an analysis Another way is to choose from a list of PRDs that are contained in a separate database which you can also edit 20 The vapor and liquid are at the same uniform temperature Properties are taken from the Ladings Database Models the conduction radiation convection inside the wall insulation jacket Multiple temperatures for different parts of the wall are computed There is a legacy and a new general TPS model strength models determine how much it expands due to pressure and heating There are also multiple models that can be used to determine strength and failure Lading in various states may be discharged through
137. stituting this expression for the work term on the left hand side of the First Law produces the following form of the First Law B 32 40 PV dA dt eo 127 In the release of vapor through the safety relief device the flow is sufficiently fast to completely neglect any heat exchanged between the fluid and the valve Hence the flow is adiabatic isentropic and the dQ dt term is zero and the First Law becomes pV dA dA B 33 eo The term on the left hand side can be combined with the term on the right hand side by inserting ov which is unity Doing so produces dA B 34 eo Then combining the two integrals f ole pv V idA 0 B 35 The energy of the material is comprised of kinetic gravitational potential and internal energy In other words y B 36 dedecus where g is the acceleration due to gravity z is the height above a datum and u is the internal energy Inserting this expression for energy into the preceding equation produces the following form of the First Law 2 V B 37 gz u V fidA 0 eO 2 In flow through the pressure relief device there is no appreciable altitude change Therefore the total surface integral of gz can be neglected And so the First Law becomes y B 38 tet pv V ndA 0 00 Using enthalpy which is defined as h pv the First Law can be expressed as y B 39 Sth
138. t We seek a stress olt such that S 1 in 1 minute Or 8 17 S t o t T Solving for t min 8 18 t o t T t Ls This value can be used to solve for stress in a two step process starting first with Equation 8 8 in which the above expression for is t inserted producing 8 19 LMP o T r5 C This is the first step in computing the burst strength it gives a value for the Larson Miller parameter The second step to finding the burst stress is to perform an inverse lookup o LMP of the experimental data or the curve fit to that experimental data In other words given the value of LMP from the above equation the experimental data or curve fit is used to find the corresponding value of c Lastly that value of tensile stress is converted to an internal pressure through geometric considerations described in the chapter entitled Models for Internal Pressure Stress and Strain Interactions with Other Models In AFFTAC s thermal model the tank wall is divided into different segments In the simplest applications of AFFTAC the tank wall is divided into two with one segment being adjacent to the liquid and the other adjacent to the vapor In the liquid segment the tank wall s temperature is set equal to the lading temperature because of the liquid s relatively large thermal mass But in the vapor segment a thermal model specifically for the wall is used to evolve t
139. t lt 7 z 0 i l 155 Second row of blocks c M ar Eia Ras l lt i lt n ij of i S f C 20 oT k i n Wi k n n E Air T y gt Fay 1 lt lt of k i 1 k i 1 2 20 Ul eT i j l i 5 k 3 Aca 4A pr T 6 i n k Mee Pics l lt i lt n 2 23 _ of _ p j k A W Third row of blocks ESE l lt i lt n 3 v 40 1 n Lj zs 0 Duy e 1 lt lt E of Wi E i norif c 20 156 F 30 31 32 33 34 35 Ab A lt lt of W Wray 7 Wi and 6 c 0 j i n ij The above expressions for the Jacobian are cumbersome from a programming standpoint A more helpful representation is as follows First row of blocks k i il F 36 Diagonal entry 4 k 4 F x y lt lt W Eds n ER 4 Diagonal entry 1 0 Diagonal entry 1 i l F 37 Diagonal entry 1 Beforethediagonal G 4F 1 lt lt W ij prj j 12 3 Jj 4 Before the diagonal 1 c 0 0 i l F 38 Diagonal oaie 5 A 1 lt lt Ww 1 0 i 1 Second row of blocks 157 W i Diagonal entry After thediagonal zo i AF iti l lt i lt n 4 After thediagonal 1 Diagonal entry E
140. that the condition in AFFTAC s Computational 23 ASTM B 209 70 30 000 Module that says TankMatID 25 should say TankMatID 25 Alloy 5154 Min 24 ASTM B 209 70 30 000 Alloy 5254 Min 25 ASTM B 209 70 31 000 Alloy 5454 Min 26 ASTM B 209 70 possible 1 0 48 0 610 0 25 6 1 lt T 8 6 Alloy 5652 Min Bug N Bug No f 10 52 0 52 T 0 86 0 40 8 6 lt T 1 26 pone 0 T gt 1 26 Here it is noted that T gt 86 might should be T gt 1 260 in the Computational Module 27 ASTM B 209 70 34 000 1 0 83 T 0 610 0 35 6 1 T 9 6 f 0 17 0 17 0 96 0 30 9 6 T 1 26 0 T 1 26 Here it is noted that T gt 86 might should be T gt 1 260 in the Computational Module Table 8 3 For different types of aluminum hard coded room temperature tensile strength column 3 and multiplicative adjustment factor that reduces that strength due to higher temperatures column 4 Here temperature T is in thousandths of Rankines There were possible corrections needed to the legacy strength model found as part of this background research See 12 Before moving into a discussion of these models it is worth noting that although the legacy hard coded algebraic models mentioned at the beginning of this chapter are less general and are not available for editing by the user they have been part of AFFTAC for decades Therefore they have been used more and have been part of more tests Most importantly however they are
141. the temperature where Layer 2 and Layer 3 are in contact is the temperature of Layer 2 s right side that is exposed to convection and radiation with layers to its right is the temperature of Layer 3 s left side that is exposed to convection and radiation with layers to its left A governing equation is required for each one of these areas The new TPS model makes the following assumptions 1 The voids have a random size distribution meaning that on average there is no pattern that would cause voids to line up thereby unduly exposing one layer to another layer several layers away Instead the exposure of each layer to other layers is gradually reduced by the coverage of the intermediate layers 2 The voids are large enough such that lateral conduction i e in the plane of Figure 7 5 need not be considered 64 Because the generalized TPS model is designed to handle an arbitrary number of layers each with an arbitrary amount of coverage there is a non trivial amount of nomenclature that must be established before the actual governing equations can be written Appendix F describes that nomenclature and proceeds to give an exhaustive account of the governing equations and solution algorithm Here the equations are summarized so you can get a reasonably good understanding of the model s basic theory Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 Do E o o Co Cs 9 Fractio
142. the expression for the mass flow rate as follows v B 61 C 62 RT Introducing the subscript for outlet the above equation may be used to express the mass flow rate at the outlet of a control volume n B 63 G p AM Iw Into this equation pressures and temperatures at the inlet subscript i will be introduced in ratios that equal unity Then the terms are rearranged B 64 RT 7 B 65 or P G Pe AM ES y Into this equation the relationships derived earlier for p p and T T Equations B 51 and B 53 are substituted MA Eos B 66 ey eet 2 Ge For M 1 B 67 k l 1 Or combining terms 132 ku B 68 k 2 k l G p A POV RT 5 1 AFFTAC s Sub Sonic Vapor Flow Model If the pressure is not sufficiently high then it is assumed choked flow has not occurred and so lt 1 Therefore the applicable equation is not Equation B 68 but rather its predecessor Equation B 66 which modified to include the vapor discharge coefficient results in M AC k p B 73 1 1 j VR JT 1 G 2 sub sonic However it is noted here that AFFTAC instead uses a simplified linear model for sub sonic flow Specifically AFFTAC computes the flow rate as if the flow is choked and then linearly scales it according to pressure This simplificatio
143. the relief device Multiple flow models are used for different discharge scenarios Heat is exchanged between the lading surface and the interior tank wall over the vapor space It is also conducted through the tank wall to the liquid C While also modeled in the TPS separate Figure 2 2 Overview of AFFTAC s primary models 21 Tank Failure Modeling The strength of the tank is a very important model in AFFTAC It provides a determination regarding whether the tank will burst during the simulation There is more than one strength model from which to choose in AFFTAC legacy model only requires the current highest temperature of the tank wall From that temperature and knowledge of the material from which the tank wall is constructed the legacy model computes a current value for the tank s ultimate tensile strength That value is compared to the stress required to contain the pressure inside the tank If it is insufficient the tank bursts In addition to the legacy model AFFTAC now also offers a Larson Miller creep and failure model that has been validated very successfully against recently acquired data Instead of only using the current temperature to determine the tank material s strength the Larson Miller model computes the damage accumulated at the microscopic level as the tank material is heated and stretched As this accumulated damage is computed it is used to compute the amount of life so to speak o
144. the system The derivation of the Reynold s Transport Theorem can be made from geometrical considerations and can be applied to any material state variable For energy it is stated as follows DE B 26 A 0 mold June 126 where OQ is the boundary of e is the material intensive energy V is the velocity vector at the boundary and fi is the outward normal at the boundary For steady state flow the second term on the right hand side is zero Using the resulting expression for DE Dt in the First Law dQ dW 27 aa di d 7 It is helpful to separate the work term on the left hand side into two parts B 28 214 VdA Shaft work rate Flow work rate dt dt x where T is the stress tensor The product of T and V represent stress through a distance per time When integrated over an area it represents the rate of work done by the fluid The first term is the rate of work done on the fluid by moving parts inside the control volume e g a fan For flow through the pressure relief device there are no moving parts that do any appreciable work on the fluid so the shaft work rate is zero which leaves only the flow work rate so that dW B 29 m DRY In flow through the pressure relief device it is assumed the flow is frictionless so the only stress at the surface is normal stress In other words T B 30 So the flow work rate is dW B 31 T VdA pV fidA dt 00 Sub
145. though this expansion is relatively small in a shell full condition it has an impact because as the liquid heats it also expands and needs more room linear thermal expansion law is used as the basis for the tank expansion computation It is that Lylli a 7 10 2 where L T is length as a function temperature T L e is the length at a reference temperature and is the coefficient of thermal expansion The ratio of lengths at two different temperatures is therefore Lr 1 041 10 3 LT adr T can be taken to be zero with no loss of generality Therefore the relationship reduces to L ten 10 4 L oT If T is taken to be the initial temperature of the tank then the above ratio represents the thermal strain l aT 10 5 l al init E T The tank can also expand due to internal stresses imposed through the pressure build up inside As shown in Figure 10 1 the pressure differential represented as p in the figure is balanced by the circumferential stress inside the tank wall Through geometrical considerations the following stress balance in the radial direction can be written A0 A0 10 6 pr Canceling terms and using half the diameter d 2 instead of radius r produces 101 10 7 pu 2t In a similar way the axial strain can be related to the internal pressure by writing a stress balance in the axial direction Referring to Figure 10 2 the balance of stresses requires
146. tial summary of your inputs for the problem The panel below it is some of the key numerical output values Typical results are shown in Figure 3 3 These results may be visualized by clicking the Plot Displayed Results button in the Main Window which displays a window like that shown in Figure 3 4 The plot window has several controls that allow some modification to the displayed plots Clicking on a plot copies it to the Microsoft clipboard from which it can be pasted into a number of other applications To print the results and input summary in the Main Window select the menu option File Print Currently Shown Results Also you may copy the contents of the displayed textual output to the Microsoft clipboard by painting the text displayed in the Main Window and typing Ctrl C These contents may then be pasted into a variety of Microsoft Windows applications such as Word or PowerPoint 28 File Edit Databases Options Analysis Database Input Summary for Baseline Case 1 Job ID User Date DATA ENTERED INTO AFFTAC PROGRAM FOR ANALYSIS FirstName LastName 05 15 2010 Computational Module Version 4 00 p nels 01 L3 Baseline Case 2 failure Scott Runnels 06 15 2011 TANK PARAMETERS Baseline Case 3 rollover FirstName LastName 06 16 2011 Capacity gal 20000 0 Baseline Case 4 ow fill Scott Runnels 06 16 2011 Inside Diameter ins
147. to accommodate the expulsion of lading quickly enough In that case the pressure inside the tank car builds up to be high enough to rupture the tank In addition to the models for the pressure relief device and the flow through it AFFTAC has other supporting models that play key roles in the simulation There are models for how the insulating layers of the tank wall change with time and temperature There are also auxiliary models including a stress model that computes the strain in the tank wall and subsequent change in the tank volume Finally there is a temperature dependent and temperature and pressure dependent failure model for the tank walls structural layer An overview of the AFFTAC simulation is shown in Figure 2 1 and a summary of the models is shown in Figure 2 2 As shown in Figure 2 1 each of the models are linked and executed in a time marching loop that proceeds through the simulation in small time increments The equations describing these models are all linked and in principle must be solved simultaneously at each point in time In practice however they are separated and solved in an alternating fashion where some values from the previous time step are used to update other values Then those newly updated values are used to update the first set of values In reality there are more than just two groups like this At multiple steps in the calculations a mixture of old values and newly updated values are used to propagate the
148. ture difference So in reality as B warms up and A cools off the heat flux falls off to zero In a Forward Euler scheme the initial temperature difference would be used to compute an initial flux between them That flux would be multiplied by a time step and used to extrapolate to determine the temperatures at the end of the time step If the time step is not too big the result will be that B is a little warmer and A is a little cooler In that case the method works fine But if the time step 15 too big the initial flux will be extrapolated out in time too long causing B to actually become warmer than A and A cooler than B This scenario is unstable and causes the simulation to fail catastrophically One approach to solving this problem is to continue to use a larger time step but arbitrarily reduce the result obtained The effect is to dampen the transient behavior Although there are errors associated with this approach often an appropriate dampening factor can be used that causes the solution to be stable Although the transient solution will be in error the steady state solution will still be correct unless nonlinear effects play a dominant role AFFTAC makes heavy use of this approach It is manifested in the source code as a weighted average between the previous time step s solution for say temperature and the prediction for the temperature at the new time step e g quen ar sar 11 2 where T is the value predicted without d
149. uctance If it does not the effective conductance is adjusted and the process is repeated until convergence is achieved The other insulation behaviors in AFFTAC s legacy TPS model accommodate different insulations used in tank cars For example rubber liners are used on some acid cars They would initially offer a high value of insulation A typical value for the conductivity of rubber is 0 1 BTU hr ft deg F This value would imply a conductance of 6 4 BTU hr ft deg F for a 3 16 in thick rubber liner which would provide a high degree of resistance to heat flow into the tank It is likely however that the effectiveness of the rubber as a thermal insulator would soon be destroyed on cars that do not have any exterior insulation because the adjacent steel tank wall would soon be heated to over 1000 deg F which would melt the surface of the rubber in contact with it Therefore in an analysis of this condition it is recommended that the rubber liner be considered to have an initial conductance of 6 4 BTU hr ft deg F but that this would be degraded linearly over a 15 minute period The rubber liner on an insulated car is likely to remain effective for a much longer time because the exterior insulation would keep the tank wall at a moderate temperature 58 Some cars have an organic coating on the inside of the tank It would offer less resistance to heat flow than a rubber liner because of its small thickness An estimate of its conductivity
150. vapor pressure whichever is less Oi The amount of lading that must be ejected A The area of the pressure relief device areq liquid discharge coefficient The hard coded numbers in the above equation are to handle units and mass to volume conversion A thorough derivation of that equation is given in Appendix E Point s Velocity V Pressure p Tank oe c Point Velocity 0 Pressure p Figure 9 5 Configuration representing the expulsion of liquid due to thermal expansion while in the shell full condition In addition to determining the pressure required to expunge the lading the model attempts to determine if any additional lading is expelled during the current time step In one case if p is not sufficiently high the flow through the relief device is assumed to be in the liquid phase It is assumed that the device will accommodate the amount of mass flow but no more than that will leave Therefore the tank will remain shell full having expelled exactly the amount that is due to thermal expansion This situation occurs for a 94 vent if p lt atmospheric pressure and as a result the total pressure inside the tank is set to Pam Likewise this situation occurs for a valve if p lt Pelose valve closing pressure and a result the total pressure in the tank is set to Preise If ps is sufficiently high greater than Pam for a vent
151. ween the insulated tank and a steel jacket Although all of the underlying assumptions and approaches are the same for the two modes it is convenient to describe them separately The overall thermal model discussed in the chapter entitled Details of the Overall Thermal Model has certain constructs such as the fact that the lading is a uniform temperature and that same temperature is shared by the part of the tank wall adjacent to the liquid Likewise the legacy TPS model has certain constructs The most important one is that the legacy TPS model assumes the tank s outermost surface can have up to four distinct temperatures Since partial insulation coverage is modeled different outermost temperatures exist for the regions with insulation compared to those regions without insulation Also both of those regions may exist in the part of the tank adjacent to the vapor or the liquid Thus four combinations result as listed in the table below And to solidify these definitions the temperatures are shown in Figure 6 3 for the two different cases jacketed and non jacketed Notice in both cases that there is one temperature for the lading both vapor and liquid and that same temperature is the temperature of the interior tank wall adjacent to the liquid Outermost Temperature in Adjacent to Insulation Present that Region Liquid Yes outer noIns liquid Vapor Yes y e No outer noIns vapor Tab
152. will be the appropriate courts located in the District of Columbia 7 IMPORT AND EXPORT LAWS AFFTAC may be subject to U S and local export laws and may be subject to export or import regulations of other countries The Licensee agrees to comply strictly with all such laws and regulations and acknowledges that it has the responsibility to obtain such licenses to export re export or import as may be required after delivery to the Licensee 8 ENTIRE AGREEMENT SEVERABILITY WAIVER This Agreement constitutes the entire agreement between the parties with regard to the subject matter of this Agreement and supersedes all previous communications whether oral or written between the parties with respect to such subject matter No waiver or modification of any of the provisions hereof shall be binding unless in writing and signed by duly authorized representatives of Licensee and Licensor Any provision of this Agreement that is held to be invalid by a court of competent jurisdiction shall be severed from this Agreement and the remaining provisions shall remain in full force and effect Neither the course of conduct between the parties nor trade usage shall modify or alter this Agreement Failure or delay by either party to enforce compliance with any term or conditions of this Agreement shall not constitute a waiver of such term or condition Contents INTRODUCTION one 11 HISTOR Y ennac T 11 SOFTWARE COMPONENTS GUI COMPUT
153. words Exposed Left Side Balance T fus 41 Ls W Exposed Right Side Balance Tp 52 53 1 ise Tp Vs T W F T Tr T AT 7T 0 k Te T Tp T T TEER fT Contact Balance k 7 A n e 1 i ST Tr 1 Ly b T F 16 i l if c 0 ou f ar x 2 i n U Vey l ey 1 F 17 Tips A tr i l lt i lt n Bree EET if c 0 i n F 18 7 7 4 Aai T l 0 Isi n In so doing the simultaneous nonlinear equations may be written as 152 ED PAO 44123 F 19 iG T 0 i 12 3 n ff Dsl Dye 112 350 and the Newton Raphson algorithm for this system may be written as follows Let denote the iteration number then T 51 i 1 2 3 n 1 F 20 Ti eT bor m1 T T 6 i 1 2 3 n 1 The deltas are the solution to the following linear system J J Jj g f F 21 J J J f Ri J J J f I 1 where the Jacobian entries are given by of pe of Bl oj E22 AE EM pli pl pma OP npo K j J 9ff J d i J af oT 31 These entries may be evaluated analytically using Equations F 9 F 11 assist with notation it is helpful to review and define the following to functions The Kronecker delta is unity if i j and zero otherwise Second the integer unit step function is u
154. y emissivity and 1 2 3 percent coverage asa function of temperature User User assigns User saves selects thickness and System in Material a materials initial coverage Thermal s in order Protection pe System i D Material G atabase Material ze Material E 1 Material D Material C Material Mmm m Material A Figure 7 3 Process for specifying a TPS in the generalized TPS model Using the Generalized TPS Model While editing an analysis the third window of the four window editing sequence requires you to choose either the legacy TPS model or the generalized TPS model If you choose the generalized TPS model you will see the list of previously established TPS setups for that model You may select one of the setups in the list for your analysis Also you may edit that list of setups by clicking the Manage Generalized TPS Database button You may also manage the Generalized TPS Database by choosing the Main Window menu option Edit Databases Generalized TPS Model Shown in Figure 7 4 is the window for managing the Generalized TPS Model Database Toward the far left of the window bulk materials are defined and for each one at least one table describing their thermal conductivity is specified Multiple thermal conductivity tables can be specified for each material each table becoming active at a specific temperature These bulk materials can be used to describe a TPS component

AFFTAC 3 - Scott Runnels Consulting

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