Joule‐Thomson Cold Finger Design and Analysis
Contents
1. The load was modeled as a single diffusion node load 1 and it was tied to the downstream of the throttle using an HTU tie with UA 1 Some of the registers used to define the load and boundary conditions are shown below Name Integer Expression Comment a CpLoad O 300 Cp of load J kg K a Gload O 1 Conductance From load to reservoir WK 3 LoadMode 3 W 1 i 1 Qload set find Tmin 2 Tload set find Qmax a Mload O 0 03 mass of load kg E Psource O 5000 psi2Pa pressure of gas source compressor bottle in Pascals 6 Pyent O 101325 pressure of vent side Pa E Qload a i Heat dissipated by load Watts is Tload E 80 temperature required by load alternative to Qload 3 Tsource O 300 temperature of gas source K Modeling and Sizing the Throttle The throttle is initially modeled as a simple orifice since the adiabatic expansion in such a device will be similar to most mechanisms which cause a pressure drop An orifice essentially has only one degree of freedom the throat size or aperture This simplified treatment facilitates answering the central preliminary design question What minimum flow rate achieves 1W of cooling at 80K The orifice model will be replaced by a labyrinth seal model with more specific dimensions at a later stage but the primary goal of that more complex design will be to achieve the same mass flow rate as did the orifice albeit with a larger minimum flow area for reduced risk of clogging2. HP hot outlet LP cold outlet LP cold inlet The heat exchanger effectiveness register Eff was estimated using an estimate of the required NTU register NTU Because NTU is not entirely appropriate specifying NTU is really just a means of specifying effectiveness indirectly The calculation of the outlet QL is show below as extracted from FLOGIC 0 1 vtest vsv pli patmos tl2 abszro gas fi 2 htest vh pli patmos t1l2 abszro vtest gas fi 3 QmaxH fri h11000 htest 4 5 vtest vsv pl12000 patmos t11000 abszro gas fi 6 htest vh p12000 patmos t11000 abszro vtest gas fi Fi QmaxC fri htest hl2 8 9 Qmax min QmaxH QmaxC 10 qli Eff Qmax 11 ql3 Eff Qmax Note that in the above logic the possibility for the presence of liquid at junction 2 the LP or cold side inlet is taken into account by the direct use of the enthalpy of the lump itself HL2 No presumption of vapor state is made at the inlet unlike the outlets At the outlets the virtual states are assumed to be vapor per the use of the VH vapor enthalpy routine If liquid had been assumed the VHLIQ liquid enthalpy routine could have been used instead The VQUALH routine could have been used to determine the state if it were uncertain or if it were two phase Another reason for specifying NTU and then calculating effectiveness Eff is that the estimated actual NTU for the current heat exchanger NTUeff can be calculated with t
3. Unfortunately the flow rate cannot be determined separately from the heat exchanger design they must be sized simultaneously The strongest cross influence is the temperature of the precooled fluid at the outlet of the throttling device but a secondary influence is the pressure drop of the heat exchanger If a large heat exchanger is needed to accomplish the design then The diffusion node can be held as a temporary boundary node via a call to HTRNOD in OPERATIONS This call is optionally invoked via use of the LoadMode register Of course the node type could also be simply changed in Sinaps permanently a nonnegligible pressure drop in the heat exchanger will mean a lower pressure gradient available to the throttle both a decreased upstream pressure due to flow losses in the HP side of the heat exchanger and an increased downstream pressure due to flow losses in the LP side Some amount of iteration will therefore be needed In fact this would be a good problem for the SINDA FLUINT Solver design optimization module which could automatically achieve a honed preliminary design presuming that the user sufficiently explains the problem in terms of objectives and constraints However because this example problem is already lengthy and because the preliminary model is highly simplified a simpler but cruder method will be used a couple of parametric sweeps which are exercised a few times each in order to close the de
4. FASTIC A separate case Chilldown has been added to model the transient response starting from an initial temperature of 300K Since the prior models concerned themselves only with steady state operation the details of the housing mandrel labyrinth plug etc were not necessary They will be important for a transient chill down model However those details exceed the purpose of this sample problem To keep this demonstration simple the missing masses including those of the fins will be modeled as a simple augmentation factor for the HP line specific heat properties WoreMass 3 Because of the small diameter long lengths and high density in the HP line that line will be modeled with tubes instead of STUBEs This distinction was irrelevant for steady state analyses However because of the small volumes the mass within the HP line will be neglected junctions will be used instead of tanks If the transient were started with all the lumps at the low exhaust pressure then the considerable CPU would be wasted in the first few microseconds of the transient in order to pressurize the system at least the reservoir and establish initial flow rates Recognizing that this event is almost exclusively a thermal one and not a hydrodynamic one other than the filling and emptying of liquid in the reservoir enables considerable savings to be made This computational acceleration is achieved by starting the transient with the thermal bounda
5. NTUEFF 88 5 4 95 88 4 945 87 5 4 94 4 935 87 4 93 Soe 4 925 86 4 92 85 5 4 915 2 491 3 3 85 Bs c s45 905 4 9 E 84 4 895 83 5 4 89 83 4 885 82 5 4 88 4 875 4 87 81 5 4 865 gt 4 86 80 5 4 855 80 4 85 79 5 4 845 4 7 4 75 4 8 4 85 4 9 4 95 5 5 05 5 1 5 15 5 2 NTU The above parametric sweep is made at the design throttle setting which was described above Note that the above throttle sizing sweep was made at the current heat exchanger size Both sweeps must be iterated since the Solver was not employed if there is substantial disagreement in the predicted NTUeff but small disagreements will be resolved by more detailed models that follow In the above diagram the required NTU is 5 to achieve 80K and the estimated performance of the heat exchange is in approximate agreement NTUeff 4 9 Detailed Analysis in Sinaps In the preliminary design rough sizing of the heat exchanger was performed using crudely estimated friction and heat transfer augmentation factors TurbMagF TurbMagh applied to the default plain tube correlations The throttle was modeled as a simple orifice whose aperture was sized to provide the minimum flow rate required to achieve a load temperature of 80K The original model will be expanded in stages to replace the top level heat exchanger model used in the prior model with a more detailed spatially resolved heat exchanger using typical data for such a heat exchanger detailed
6. MREF 1 option is used instead with GCF R g see the User s manual for details However the predictions are not completely out of line with other methods and this method has the benefit of letting the number of teeth be variable for sizing seals or throttles An alternative method is therefore also presented using a separate long ELLD gt O ORIFICE for each tooth and not just the last tooth Seven ORIFICE connectors in series with flow areas reduced in each tooth along the conical throttle This series of paths is also duped out such that it has no effect on the primary flow again allowing its clearance to be adjusted without disrupting the primary thermohydraulic solution based on the single orifice throttle 9 50e 4 9 00e 4 Taby Laby 1 Orifice Orifice Teeth 8 50e 4 8 00e 4 7 50e 4 7 00e 4 6 50e 4 6 00e 4 Mass Flow Rate kg s 5 50e 4 5 00e 4 4 50e 4 4 00e 4 3 50e 4 3 00e 4 5 6 7 8 9 10 11 12 13 14 15 GapLaby 10000 The end result noted abote is a prediction of a clearance of 0 11 thousands of an inch 2 8 microns Almost all of the pressure drop occurs in the last tooth which is choked Therefore a very small flow area is required to match the 91 reduction in area that was required in the HP line in the original single orifice approach noting that the HP line has an ID of only 0 013 0 33mm The above methods can only be described as being useful for preliminar
7. tube correlations can then be estimated as FK 4f fy TLEN DH where f cof Re and fg is calculated internally by FLUINT using the FRICT function see Section 7 in the User s Manual In order to be able to avoid the need to call a function within the FK expression FRICT will be 1 4 replaced by the approximation fy 0 316 Re The internal wall roughness fraction WRF will be left as zero to make this approximation more accurate In other words the FLUINT is allowed to calculate friction internally including for any two phase or laminar regimes encountered but then that circular tube correlation is corrected using an expression applied to all LP paths as follows FK 4 cof Max 1 REY this powf 0 316 max 1 REY this 0 25 TLEN this DH this Note that REY this means the current Reynolds number of this path and that extra effort must be undertaken to avoid raising an initial zero value to a power This is accomplished by only operating on the maximum of 1 and the current Reynolds number which considerably complicates the above expression Excluding also the this dereferencing yields the following invalid but easier to comprehend expression FK 4 cof REY powf 0 316 REY 0 25 TLEN DH An even more complex and complete expression may be required to avoid underestimating fa for laminar flow approximately REY this lt 2300 in which regime fa 64 REY this Eg Actually no method
8. UA is not to be confused with the FLUINT convection tie UA which is the local conductance of that tie Unless it is used as a segment tie the UA of a tie is actually the hA in heat exchanger terminology the local film coefficient times the local heat transfer area that is the basis of that coefficient In other words the overall UA of the heat exchanger can be calculated if all of the local tie UA s are known along with other factors such as fin efficiency constriction resistances fouling resistances etc The Sinaps model used for the preliminary design is available for inspection or for use as a starting point sizing smdl Therefore no attempt will be made to document the model in detail Rather this write up seeks to provide an explanation of the approach used and should be viewed as a companion to the data available in the model Basic familiarity with both Sinaps and SINDA FLUINT is assumed Modeling the Load Actually the specification of 1W at 80K would over specify any single steady state analysis either the load can be modeled as a boundary node at 80K and the design adjusted such that 1W is extracted from it or the load can be modeled as a diffusion or arithmetic node with a source of 1W and then the design is adjusted such that the node is maintained at 80K The latter mode given Q find T was used in this analysis but provisions for the opposite mode given T find Q are available as well
9. exists to correct them The incoming droplets would strike the fins and pipe wall and therefore the actual heat transfer will be higher than the default film boiling correlations will predict However this only causes the fluid on the LP side to transition to single phase vapor in an even shorter length total energy transfer would not be greatly affected by an improved estimate of the film boiling regime SINDA FLUINT is case insensitive Any capitalizations are made for clarity but are not required When the detailed model of the heat exchanger was created it out performed the estimates made in the preliminary model As a result the orifice aperture was reduced from Oratio 0 14 to 0 095 to yield 80K for a 1W load Design of an Equivalent Labyrinth Throttle General Pneumatics Corp uses a labyrinth seal a set of flat topped teeth arranged in series aS a throttling device Normally labyrinth seals are used to discourage leakage in rotating machinery such as in the gaps between impellors and pump housings In this case however both walls are stationary and the leakage is intentional The housing is a hollow conical approx 15 degree half angle nozzle Teeth are cut into a separate part the OD of a matching conic plug By moving the plug back and forth axially the gap between the top land of the teeth and the housing can be varied providing an adjustment of flow rate In the preliminary design an effective s
10. heat exchange to the theoretical maximum For single phase constant C flows the theoretical maximum heat transport is max Cmin Thot inlet a Tcold inlet which is based on the inflowing temperatures on the hot HP and cold LP sides of the heat exchanger For a counterflow heat exchanger e NTU 1 NTU NTU is a useful sizing parameter but it is difficult to generalize to two phase flows or even to single phase flows with strongly varying properties This design will definitely experience strong property variations because of the wide range of temperatures and pressures It may also experience two phase flow at the inlet to the LP side of the precooler Fortunately effectiveness can be easily generalized to complex single phase and even two phase flows using enthalpy as a function of pressure and temperature and quality h P T X Neglecting quality i e assuming single phase for clarity Qmax hot m h Phot outlet Thot inlet h Photoutlet T cold intet Qmax cold m h P cold outlet l cold outlet E A Pcold outlet Phot inet Q max MiN Qmax hot Qmax cola Heat exchanger sizing is more difficult in this model than in most because the cold inlet LP side conditions are not specified they must be simultaneously solved along with the rest of the thermal fluid network as part of any design iteration Using one node or lump to represent the inlet and another node lump to represent the exit there are
11. in the high pressure HP side and in the low pressure LP side Furthermore the metallic wall and fins will be 7 Not really Like much of this example data is guessed if unavailable These numbers are typical but are fictitious and should not be used for any real design work Corrections for viscosity which varies greatly within this heat exchanger should also be applied in a realistic case 8 SINDA FLUINT attempts to calculate a transitional Reynolds number as needed to achieve numerical continuity but does this number is constrained to the range between 1000 and 10 000 For this problem the transition occurs at the lower end about Re 1000 represented by SINDA thermal nodes including axial and radial conduction fin effectiveness etc Although the model will only be run in steady state mode tubes are used for the high density HP side and diffusion nodes are used for one side the HP side somewhat arbitrarily of the heat exchanger At a top level with the heat exchangers collapsed for clarity the network appears as follows HP hot inlet source q HP hot outlet gas 1000 gas 1 LP cold outlet LP cold inlet Heat load gas 2000 J Exhaust An extra mass metal volume factor ExtraVol is added to account for the mass of the heat exchanger inner and outer canister which is distributed evenly to all nodes Using diffusion nodes for both sides of the heat exchanger would unnecessarily sl
12. the LP side the fin effectiveness Feff can also be estimated Name Integer Expression Comment 1 emfin E sqrt Hhx 2 Kcopp Fthk m For Fin for fin eff calc 4 Hhx O 1750 heat transfer coeff off fin guessed early runs 3 inzm C Fintocm 100 4 Kcopp O 250 More likely all copper 5 Kcu i O i29 cond of CuNi 70 30 6 ml O emfin Lfins 0 5 Fthk mL For Fin id tanhyp O exp 2 ml 1 fexpl2 ml 1 tanh ml Expression pi Dmean Fpitch Fthk Lfins 2 ODhp Lhx 4 Acore DHhx Aheat Afront Ablock 2 0 25 pi FODhp 2 ODhp 2 pitFODhp Fthk 0 25 pi ODhx 2 IDhx 2 LenHP Fpitch Afin pi ODhp LenHP Fpitch Fthk 0 25 pi ODhp 2 IDhp 2 Comment 4rea blocked by fins pipe Check on heat transfer area Free flow area minimum flow area 4rea per Fin both sides Frontal area HX total heat transfer area fin and pipe OD X section area of HP line Aheat vtotal heat xfer area per volume 1 m FFif re1 powF f cof Re powF coefficient jhifre1 powyj _j coj Re pow coefficient 4 Lhx Acore Aheat Hydraulic diameter 4 RH of HX ODhx FODhp mean diam at HP line centerline LenHP Fpitch Afin 2 Fthk 1 5 extra metal volume for cooldown est Lfins Fthk Fin aspect ratio check 1 Fpitch Fthk Fthk Fin spacing ratio check tanhyp ml Fin effect
13. two ways to model a top level heat exchanger 1 calculate the current exit gt For a blow down system this liquid would be trapped in a reservoir such that ideally only saturated vapor entered the LP side of the precooler In this steady version there is no such transient accumulation of liquid Instead if liquid forms and is not vaporized by the load then it will enter the precooler where it will face supercritical wall temperatures and will vaporize quickly Nonetheless the effects of this high quality fluid can be significant and the model must be generalized to survive these conditions Even if the final answer is all vapor entering the LP side of the precooler during iterations some two phase flow may be experienced 1 Actually if C constant wall temperature perhaps because the opposite side is boiling or condensing then a third way is possible using either HTUS or HTNS segment ties Separate support notes on top level heat exchanger modeling are available at www crtech com temperatures of the nodes lumps representing the exit or 2 calculate the total heat exchange and set the current heat rates into and out of the exit nodes lumps accordingly For a SINDA thermal only network in which fluid flow is approximate using one way conductors if the temperature is specified method 1 above then the outlet should be a boundary or heater node whose temperature is adjusted in VARIABLES 1 If instead the heat rate at t
14. 1 smdi The orifice will then be resized using this refined heat exchanger and will then be replaced by a labyrinth throttle that provides the same flow rate under equivalent conditions detailed2 smd Higher Fidelity Heat Exchanger Modeling From heat exchangers of similar design the performance of the finned pipe Giauque Hampson sized at the system level is estimated at two Reynolds numbers based on the Fanning f factor and the Colburn jn factor This methodology is based on that described in Compact Heat Exchangers by Kays and London Reynolds Re Fanning f Colburn jn 2200 0 040 0 010 4400 0 033 0 008 From these values the following relationships can be fit f 0 476 Re in 0 177 Re These formulae are contained within the model via the use of registers as follows f cof Re powj jn coj Re For the laminar regime a Nusselt number XNUL of 12 0 is expected Detailed methods for incorporating the above parameters into a FLUINT model are documented at www crtech com and so they will only be briefly described below In the prior model the heat exchanger was modeled as two inlets and two outlets with heat transfer estimated in logic based on effectiveness and the resulting heat rates applied to the outlets with heat transfer performance estimated using fake FLUINT ties In this model the heat transfer passages will be subdivided into 20 segments axially both
15. Joule Thomson Cold Finger Design and Analysis A Joule Thomson JT device achieves cooling by throttling a real gas from a high pressure to a low pressure A perfect gas exhibits no JT effect the isenthalpic expansion of a perfect gas is also an isothermal process Therefore not all expansions result in a drop in temperature in some cases the temperature can rise Gases such as nitrogen argon krypton and helium exhibit a temperature drop with expansion and can therefore be used for cooling applications Furthermore each of these gases has a different starting pressure for achieving the maximum cooling effect For nitrogen for example the JT cooling effect peaks when starting near 5000 psia JT devices can be used in stages and in combination with other cryocooling techniques They are not very efficient thermodynamically so they tend to be used in applications where small compact and motionless cold fingers are required or in short lived applications in which a transient blow down source is sufficient such as cooling IR sensors in a missile or probe A closed loop cycle involving a JT throttle is called a Linde Hampson cooler which is basically a JT cold finger with continuous high pressure gas provided by a compressor instead of a bottle The hot gas at the outlet of the compressor is cooled using the environment as a sink A simple venture or orifice can be used as a throttling device but often a more complex option is employed
16. ad Temp Reserv Temp Qcold Bottle Press s 34 5M F 300 E 1T 340M 12E 280 C 1 aE E 260 33 5M 10 5 33 0M oF 240 g p s oO s D cS 220 325M 5 73 ao w E r i z ES SEF 200 B 32 0M ES S C E 180 31 5M4 47 t 3E 460 31 0M 2 H E 440 3 5M 1 F ag 0 500 1000 1500 2000 2500 3000 3500 Time Even with a generously sized pressurant bottle and an underestimated thermal mass the cold finger is still cooling down after 1 hour and is a long way from the target of 80K Removing the heat load entirely per the ChilldownNL case achieved by zeroing the conductance main g1 from the environment and the load makes little difference in the response This transient was performed for demonstration purposes only but it reveals a fundamental flaw in the preminary design procedure it was performed for steady conditions only with no margin or oversizing needed to achieve chilldown in a reasonable time
17. agnified to take into account the thermal mass of the fins and solder as will be described later The centerline has about 29 turns Nturns With a very fine resolution say 300 axial segments the lumps would appear to follow the centerline nicely But only coarse resolution about 20 30 is required For such low resolution the lumps appear to be following a looser helix and the paths appear to short circuit the fine coil jumping from lump to lump directly This is an artifice of the graphical methods and does not affect answers the Pipe knows about the finely coiled helix centerline a However helical Pipes can be slow to draw in CAD in the current version of Thermal Desktop V5 1 Under Preferences under Graphics Visibility leave the Pipe option unchecked as much as possible Under Graphics Size set the Curve Meshing Resolution to be as high as possible while working with the model setting it back to a smaller value for better accuracy before running the model The LP side is a different situation entirely In that case depicting each of the thousands of fins is impractical and explicitly modeling the gradients within those fins using tens or hundreds of nodes per fin is computationally intractable In other words for the LP side detailed geometry is a distraction rather than a feature Therefore the LP side is modeled as a single straight line visible at the top of the above diagram that connects thermally
18. d a more detailed model will be used once the basic design is known However the overall UA of the heat exchanger can only be estimated at this preliminary stage of design The overall UA will be a strong function not only of the geometry of the heat exchanger e g axial fin spacing and OD of the annular fins and of the throttle which largely determines the flow rate and which cannot be sized independently of the heat exchanger s performance But the overall UA will also be a function of the local temperatures and pressures which vary greatly on both sides of the heat exchanger Furthermore unlike many heat exchanger sizing exercises the temperature on the cold low pressure or LP side is not known ahead of time it is a function of the throttle and of the design of the heat exchanger itself In other words this is a strongly coupled problem Also the possibility of two phase fluid entering the LP side of the heat exchanger further complicates the design A detailed model could easily encompass all of these details but it would be slower to solve and clearly many iterations will be required to arrive at a satisfactory design Therefore a highly approximate model will first be used to narrow the range of possibilities and to arrive at a starting point for the more detailed design As will be seen this top level model is a cross between a spreadsheet analysis and a four point cycle thermodynamic state analysis The term overall
19. d ona rectangular fin and estimated film coefficient from prior runs but the result is so high as to be essentially unity for this rough sizing exercise In fact an adequate approximation would be to assume UA UAcoig since the cold LP side is the limiting bottleneck conductance Note also that the NTUeff calculation necessarily requires the assumption of single phase flow because of the need to calculate C using the VCPV vapor specific heat routine though the resulting model can tolerate departures into two phase flow during iterations In a nutshell the strategy of this approach is as follows 1 Choose an NTU value as required and calculate the corresponding effectiveness in registers 2 Impose the resulting effectiveness on the model assuming single phase but allowing for strong property variations using enthalpy functions VH VHLIQ Use the QL method versus the heater junction method with logic placed in FLOGIC 0 to set the outlet heat rates 3 Using fake ties to estimate the overall UA and use this value to calculate the actual NTU as NTUeff in OUTPUT CALLS 4 The design iteration can be considered converged if NTU required is approximately the same as the actual NTUeff for the current baseline orifice size If these values are too far apart then the current heat exchanger is either too small NTUeff lt NTU or too large NTUeff gt NTU 90 5 4 975 90 4 97 4 965 89 5 p 4 96 Load T1 4 955
20. e of these four ties 2 3 4 and 5 is to exploit FLUINT s built in heat transfer calculations to estimate the film coefficients on both sides leading up to the calculation of the overall UAo Direct calls to the underlying correlations could have been used instead These built in default pipe flow correlations are adequate on the HP side which is plain albeit small diameter tubing However the default correlations do not take into account the restarting of the turbulent boundary layer with each fin on the LP side and so they are known to underestimate the overall heat transfer for this regime An augmentation factor of TurbMaghH 3 is therefore applied to the ties XNTM turbulent Nusselt number multiplier This factor is chosen somewhat arbitrarily based roughly on experience with similar finned tube designs Application of more realistic Colburn Jp factor StPr is described in the detailed model Similarly the friction on the LP side will be higher than that predicted by the plain tube correlations so an augmentation factor of TurbMagF 4 is applied to the path s FCTM turbulent friction multiplier again based on experience with similar designs Application of a more realistic Fanning friction factor is also described in the detailed model Although slight the effects of fin efficiency wall and fin area corrections and temperature drop across the HP tube are all accounted for The fin efficiency Feff is estimated base
21. he expectation that when NTU is about the same as NTUeff a successful heat exchanger sizing has been achieved NTUeff is therefore estimated in logic specifically OUTPUT CALLS for the fluid submodel 8 a 9 c estimate NTU actual NTUeff first estimate UAeff 10 c 11 if UHP ULP aht3 aht2 ne 0 0 then 12 gtest 2 pi KcuNi LenHP alog ODhp IDhp 13 UAeff 1 0 1 0 Feff0 ULP aht2 2 1 0 gtest 1 0 UHP aht3 2 14 write nout UAeff UAeff 15 else 16 UAeff 0 0 17 endif 18 Chot fri vcpv pli 0 5 t11000 t11 gas fi 19 Ccold frit vcepv p12000 0 5 t12 t12000 gas fi 20 write nout C hot Chot 21 write nout C cold Ccold 22 Cmin min Chot Ccold 23 NTUeff UAeff Cmin 24 write nout NTUeff NTUeff 25 26 call tubtab all 27 call tb2tab all The above calculates UAeff use the UB and AHT heat transfer coefficient and heat transfer area respectively of four ties two for both inlets and two more for both outlets each with half of the heat transfer area for their respective sides This approach represents a crude attempt to average properties over the heat exchanger which has not been subdivided axially as will be done in subsequent models Similarly fake boundary nodes are used to represent the wall and the DUPL lump side DUP factor has been set to zero to keep the ties from actually transferring energy to from the endpoint junctions In other words the entire purpos
22. he outlet is specified method 2 a diffusion node or arithmetic node should be used to represent the outlet state In this model a single FLUINT fluid network is used to represent both sides of the heat exchanger For top level heat exchanger analysis the FLUINT equivalent of a boundary node at the exit method 1 above is not a plenum but rather a heater junction a junction for which HTRLMP has been called A heater junction will hold constant the lump enthalpy and therefore temperature approximately but not the pressure as well as would a plenum The alternative method 2 is to use tank or junction and apply the heat rate QL to the exits based on effectiveness calculations made in FLOGIC 0 This later method is chosen for this model because it is easier to calculate QL rather than HL or TL as would be needed for the heater junction method even though this approach can be a little less stable when converging The QL method is also more applicable to top level transients though those are not planned and would be of questionable value in this particular case unlike many liquid liquid heat exchangers oA simple running average method for damping is applicable if convergence problems occur such as QLnew QLnew 1 F QLold F where F 0 for no damping and F approaches unity for heavy damping Usually 0 1 lt F lt 0 5 is adequate No damping was required in this particular model Time 0 HP hot inlet source
23. id cool down as well as sustained operation In such a blow down system a reservoir is usually available downstream of the throttle to store any liquid that is generated and some means is provided for preferentially exhausting only vapor from that reservoir or at least discouraging loss of low enthalpy liquid For a steady system a small amount of liquid e g high quality two phase fluid may enter the low pressure side of the precooler Many details are obviated by assuming that this device operates at steady state since the purpose of this model is to demonstrate other modeling techniques e g laby seals and heat exchangers However since many JT applications are indeed blow down systems in which cool down characteristics and liquid production and consumption are important the FloCAD based model includes a demonstration of such transient capabilities The high pressure line is 0 013 0 33mm ID and is made of 70 30 copper nickel alloy Soldered copper fins are available but with the smallest fin thickness available being 0 0025 0 064mm Preliminary Design For preliminary design purposes the throttle will be treated as an effective orifice and a toothed labyrinthine passage or laby seal will be sized later to provide the same throttling action once the JT flow rate and throttle inlet conditions are known Similarly the heat exchanger will largely be sized based on NTU system level inlet outlet methods an
24. ingle orifice was used to size the flow rate At the design point any device which achieves the same pressure drop and flow rate under the same conditions will suffice This single orifice will be replaced by a series of labyrinth teeth that achieve the same throttling effect The cone upon which the teeth are cut has a diameter of Dhx 0 25 or 6 35mm at the entrance and 0 032 0 81 mm at the exit as can be seen in the above diagram Seven Nteeth teeth of spacing 0 06 1 52mm 1 PitchLab fit on this cone using a depth of cut of 0 008 DeepLaby The clearance between the land area of the teeth and the housing GapLaby will be adjusted until it achieves the same throttling effect as the simple orifice at the design point www gpcvalves com downloads jt pdf Differences will appear at other operating points and during transients WideLaby LandLaby 1 PitchLab LandLaby DeepLaby OutDLaby InDLaby _ IDhx Y GapLaby For modeling high temperature near perfect gas labyrinth seals a method outlined in the SINDA FLUINT User s Manual using the Martin Vermes option for TABULAR connectors may be used One drawback of this method is that if choking occurs at an unknown point such that it cannot be built into the tabular input array then it is better to model the first upstream N 1 teeth using the TABULAR connector and then use a separate ORIFICE connector to model the final tooth This treatment
25. is especially important in a JT model in case the fluid changes phase before flowing past the final tooth The example Sinaps model detailed2 smdl shows such a TABULAR ORIFICE model of labyrinth seals The inlet i end of the TABULAR has been duped out DUPI 0 as has the outlet j end of the ORIFICE DUPJ 0 leaving the original single orifice still in control of the flow rate Using this method the clearance GapLaby can be adjusted until the flow through the TABULAR ORIFICE path is the same as that through the original orifice After the clearance has been sized the original ORIFICE could be deleted or duped out using DUPI DUPJ 0 and the TABULAR ORIFICE path opened setting its DUP factors back to unity Using an ORIFICE to represent losses through an annular gap is clearly an approximation The long orifice option is invoked using the hydraulic diameter of Dp 2 GapLaby resulting in ELLD LandLaby 2 GapLaby where LandLaby is the length of the tooth land area Using the Martin Vermes method for representing the labyrinth flow is clearly a strained approach for this supercritical dense cold and even flashing situation It is really only provided for demonstration purposes and is not a recommended approach for cryostats In fact the normal use of the MREF 4 option for TABULAR connectors is impossible since the inlet can contain liquid during solution iterations and that situation is illegal for MREF 4 Therefore the
26. iveness guessed rectangular 1 LenHp Fpitch Afin Aheat 1 FefF Overall fin effectiveness with land area 0 040 Fanning f at point 1 data From plot 0 033 Fanning f at point 2 data from plot ODhp 2 _OD of pipe with Fins 72 in2m Fin pitch per meter LI 0 0025 in2m Fin thickness 0 013 in2m ID of HP line 0 25 in2m ID of HX 0 010 Colburn j at point 1 data from plot 0008 Colburn j at point 1 data From plot Nturns pi Dmean length of HP line FODhp ODhp 2 In FF 1 FF2 In ret rez Ingjh1 jh2 In ret rez Lenath of fins 1 1 in2m Overall length Lhx FODhp Number of turns coils of HP line IDhp 2 ThkHP OD of HP line IDhx 2 FODhp Overall Diameter OD of Hx f cof Re powF exponent j coj Re powj exponent 2200 Re at point 1 data from plot 4000 Re at point 2 data from plot 20 axial resolution Acore Afront sigma ratio of free to Frontal area 0 003 in2m thickness of HP line NTU is the number of heat transfer units defined as the overall UA of the heat exchanger UA which corresponds to the register UAeff divided by the minimum m C product C for the HP or LP sides NTU UA Cmin where Crin min Chot Ccold NTU is the nondimensional size of any heat exchanger and it may be related to the effectiveness of the heat exchanger s where is defined as the ratio of actual
27. ow any transient solution because of the small resistance between each side of the heat exchanger In other words the temperature drop within the metal itself is almost negligible a thin walled heat exchanger could have been modeled using a single row of nodes The depiction of the expanded heat exchanger postprocessed to show temperatures at the design point is show below IP hot riet source a e eee Gan a s22 eee cee om The conductance between the ID and OD of the HP tube is used to calculate the conductance between the two rows of nodes Then the fin efficiency nt and the corrected efficiency no No 1 Afin Aneat 1 ne is set to be the register FeffO which is applied to the tie scaling factor UAM on the LP side No corrections are necessary on the HP side since it is a circular tube By having subdivided it however the SINDA FLUINT code will calculate heat transfer and pressure drop along its length including slight pressure recovery as the fluid cools to a large density along the length For the LP side the compact heat exchanger CHX f and jn factors need to be applied to the STUBE connectors and HTNC ties representing the LP flow passages The heat transfer is represented using the registers coj and powj as described above These registers are applied to the ties as CDB coj and UER 1 powj with UEC UEH 1 3 The CDB is the Dittus Boelter coefficient UER is the Reynolds numbe
28. r exponent and UEC and UEH are the heating and cooling exponents on the Prandtl number respectively Setting these HTN HTNC tie constants overrides the internal turbulent correlations to correspond to the equation presented above jn coj Re For laminar flow the Nusselt number XNUL is set to 12 The above corrections do not overwrite the two phase calculations within SINDA FLUINT When the throttle generates two phase fluid at steady state then some liquid enters the LP side of the heat exchanger because there is no accumulation of liquid in the cold reservoir downstream of the throttle However this liquid encounters a hot wall the pipe and fins will be above the critical point of nitrogen approx 126K Therefore film boiling will occur based on internal correlations as can be seen by the F in the 2P column of the TIETAB text output The resulting predictions are not far from that of the subsequent single phase zone in the LP so no effort was made to correct them Note also that the Reynolds number in the LP side were always greater than 1000 so the XNUL laminar Nusselt number input was irrelevant though useful during solution iterations The friction relationship is applied by estimating a K factor correction Recall that FK fy TLEN DH where fy is the Darcy friction factor or 4f TLEN DH where fris the Fanning friction factor The extra losses above and beyond those calculated by SINDA FLUINT using its default
29. ry conditions held at the initial 300K but allowing the fluid submodel to start from a flowing state coming to equilibrium with the hot walls around it gt Liquid is trapped during a transient since a tank has actual volume in that case However during a steady state when the reservoir is treated as a junction there is no place to store liquid so it continues to flow out of the junction but leaves the junction in a very wet full of liquid state that is the only effect of STAT VS during a steady state Inside of OPERATIONS the thermal submodels MAIN and HPSIDE are held making all diffusion nodes act as temporary boundary nodes using the BDYMOD utility A steady state is called to initialize the fluid submodel with again the inlet bottle temporarily held then the holds are released before the transient is initiated Finally to make the problem more realistic the 1W load is converted into an equivalent conductor from a boundary the environment at 300K In other words the source is modeled as a parasitic heat leak not as a dissipative source A new node main 2 and conductor are added to represent this situation Transient Results and Discussion The plot below depicts the temperature profiles for the first hour of the transient cooldown After an hour the load has been cooled to 140K and 12 of the original nitrogen pressure has been expended 0 m m C a Lo
30. sign iteration Assuming that an approximate heat exchanger design has been established as explained in the next section a simple parametric sweep of orifice hole sizes is made plotting both the temperature of the load at 1W dissipation and the estimated NTU of the heat exchanger register NTUeff The required design will be that which achieves the 80K requirement and which doesn t require more than the estimated heat exchanger performance As seen in the plot below the minimum orifice size is 0 14 times the flow area of the HP line corresponding to a mass flow rate of about 0 86 gm s or 6 8 b hr since that is the size that yields an 80K load This throttle flow area fraction is expressed as the register Oratio noting that the ID of the HP line is contained in the register Dhp Name Integer Expression Comment Oratio O 0 14 OrifEff O Oratio pi 4 IDhp 2 effective orifice opening for sizing analyses The plot below was made using an input assumed NTU of 5 effectiveness of 0 8333 for counterflow and at the design point Oratio 0 14 the estimated performance of the heat exchanger is about NTUeff 4 9 This agreement verifies that the predicted performance of the heat exchanger NTUeff is about the same as that required NTU the orifice sizing can therefore be trusted If the heat exchanger design was enlarged or reduced then the above sizing would need to be repeated using the new baseline heat exchanger design Fortuna
31. tely few such iterations are required to close on a design 5 4 85 5 5 3 85 5 2 Load T1 NTUEFF 5 1 84 5 5 84 4 9 4 8 83 5 4 7 v s 2 83 4 6 5 4 3 45 amp 82 5 o 4 4 s 82 4 3 81 5 nz 4 1 81 4 80 5 3 9 3 8 80 3 7 3 6 0 08 0 09 0 1 0 11 0 12 0 13 0 14 0 15 0 16 0 17 0 18 0 19 0 2 Oratio The sudden jump in the NTUeff at an Oratio of about 0 08 corresponds to the transition from laminar to turbulent on the LP side In other words the design chosen corresponds to a turbulent flow solution on the LP side but not by much Also the design is very close to producing liquid in the outlet of the orifice slight variations can cause two phase fluid to enter the LP side of the heat exchanger This can be seen past an Oratio of 0 15 or past an assumed NTU of 5 05 as shown below Modeling and Sizing the Heat Exchanger precooler SINDA FLUINT registers play an important role in defining the heat exchanger The key variables are defined below in terms of a not to scale sketch Tim Fthk 1 Fpitch Y ODhx From a few key variables the HP line ID Dhp the OD of each fin disk FODhp the fin density Fpitch and thickness Fthk the configuration can be defined The blockage ratio sigratio heat transfer area Aheat and area per volume AtoVrat core minimum flow area Acore and hydraulic diameter DHhx can all be calculated With a guess at a heat transfer coefficient on
32. to avoid the need for very small openings which can clog due to the freezing of contaminant gases One option is a nozzle tube or orifice tube Another is a labyrinth seal effectively a series of larger aperture orifices in series The performance of a JT device can be significantly enhanced by precooling the high pressure HP fluid using the colder exhaust fluid from the low pressure LP side of the throttle A Giauque Hampson counter flow finned pipe heat exchanger also known as a precooler or recuperator is a common option The purpose of this document and the associated thermal fluid models is to illustrate the application of SINDA FLUINT Sinaps and Thermal Desktop FIoCAD to e JT cryostat analysis e Modeling of gas labyrinth seals even though they purposely leak in this application e Modeling of heat exchangers in general at both the system and detailed levels 1 www gpcvalves com downloads jt pdf Labyrinth flow spoilers is the term used by GPC but since many applications of stepped labyrinths are to reduce flow in rotating turbomachinery the term seal or throttle will be used here A preliminary design will be developed first At this top level the throttle will be considered as a simple single orifice and the heat exchanger will be treated at a system level using effectiveness NTU methods This preliminary model will be prepared using Sinaps Subsequently a more detailed model will be de
33. to the OD of the HP tube using overall corrections No or Feff0 as explained in the detailed model and applying the heat transfer corrections for the j relationship again as documented earlier In other words the effect of the fins on heat transfer will be modeled using coefficients and correction factors to avoid their explicit depiction and meshing The LP pipe Pipe 2 is tied to the surface represented by the HP helix Pipe 1 with the UAM CDB UER etc factors specified to represent the no and jp calculations As with the detailed Sinaps model the f calculation has been performed using an estimated K factor correction based on FK 4f fy TLEN DH Transient Chilldown Example The supply is no longer infinite it has been assigned a volume Vbottle equal to 100 liters Heat transfer from the wall of the bottle is neglected Similarly the reservoir s volume Vreser is specified as 10cc If liquid is formed in this reservoir it is trapped The mechanism for trapping liquid is not specified so it is modeled as vapor only egress STAT VS in the exhaust path A steady run case Steady verifies substantially the same answers as the detailed Sinaps model Because the source is now a tank representing the finite volume bottle instead of a plenum in order to run a steady state this supply must be held made to act like a temporary plenum using the utility HLDLMP in OPERATIONS before the call to STEADY a k a
34. veloped in which the labyrinth seal will be designed and modeled in more detail Also the heat exchanger will be modeled in more detail in this second round demonstrating application of compact heat exchanger techniques This detailed model will also be prepared using Sinaps although a Thermal Desktop FloCAD representation of the final design will also be presented Design Requirements and Constraints The unit will be required to cool a 1W load at 80K The load has a thermal mass of 30 gm 0 066 lbm and a specific heat Cp of 300 J kg K and is connected to the cold finger via a linear conductance of 1 W K Nitrogen at 300K and 5000 psia 35 MPa is available and may be exhausted to ambient pressure Minimal nitrogen consumption is desired A compact single stage cryostat is desired with an overall length of no more than about 4cm approx 1 5 and diameter no greater than about 1 5cm approx The details of the source of nitrogen have been purposely omitted it might be a very large bottle and it might be the compressor and gas cooler in a Linde Hampson cycle Either way the implication of assuming an infinite source is that only a steady state analysis need be used This has tremendous impact on the resulting design and analysis Therefore it should be mentioned that blow down JT systems can and have been analyzed using SINDA FLUINT including cool down transients and even automated optimization of components to achieve both rap
35. y design when test data is lacking If test data for similar units were available models could be calibrated as required to match including estimating an appropriate K value in the Martin Vermes model register KayLaby or the Cy of the orifices in series Equivalent Geometric FloCAD Model A FloCAD based model JTtransient dwg was constructed that was based on the detailed1 smdl Sinaps model using a simple single orifice as a throttle The primary purpose of this model is to make the model available to FloCAD users but a secondary purpose is the simulation of a blow down chill down transient There is no reason why such a transient model could not have been done using the Sinaps based model as well FIoCAD enables but does not require the use of geometry for model construction In some cases the use of geometry assists both the generation of the model and the presentation of the results In other cases detailed geometry can be a distraction The plain tube HP side of the precooler for example could be represented as a single straight line FloCAD Pipe with the depicted length equal to 1 1 LenHX while the actual length was much longer due to coiling However it is not difficult to depict a helical centerline for the FIOCAD Pipe representing the HP line The HP pipe Pipe 1 is a simple plain circular tube Diffusion nodes are used for the ID and OD of the HP line The capacitance of the wall material will be m
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