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LABYRINTH SEAL PREPROCESSOR AND POST

1. Geometric Gas Parameter Properties v Sheet sheet Run Labyseal Button Generates a Data Generate Data file File Button its saves data in a txt Y file Geometric N Opens a Fortran based Diagram tooth exe file feeds the data position andleak file generated in the XC das 7 exe file Exe file generates an output file Excel imports data from the output file Aut and displays it in generates the Results A and six results plots Results B sheets Results Results B sheet Figure3 1 Process Flowchart 22 Macros consisting of preprocessor macros are as follows Import Data file The Import data file macro opens a GetOpenFileName application so that the user can search the file on his computer then select and import it The file has to be a LabyXL data file generated by either by Run Labyseal button or Generate Data File button shown in Figure 2 8 in chapter 2 A sample of the data file can be found in the Appendix A The macro imports all the values for the LabyXL data fields from the data file The macro is located under Microsoft Excel Objects Sheet1 Main Partial code for the macro is shown below Private Sub CommandButton2 Click Dim fileToOpen As Variant fileToOpen Application GetOpenFilename Text Files txt txt Dat F
2. a 1 2 EH eratife Sis cov oL ed pes Shs RR ERA ec A RE uio Chapter 2 PRE AND POST PROCESSOR CAPABILITIES AND LAYOUT 2 1 Program Capabilities us oor et hansen tvi ehe leta T e eX v OPE ri 2 2 Preprocessor Design Layout ppp 2 3 Post Processor Design Layout Chapter3 LABY XL MACROS ni cscssorssaivesetaccasdarcassasnaauleosoinsaasdarsereaesss 3 1 Preprocessor Macros 3 2 Post Processor Chapter 4 PARAMETRIC STUDY Rcx 4 1 API Seal Modeling and Comparison 207 4 2 Influence of Various Parameters of Labyrinth Eye Seal on Effective Cross coupline SOTIDess 4 3 Influence of Various Parameters of Balance Piston Labyrinth Seal on Effective Cross Co pling Stiffness Chapter 5 RESULTS AND CONCLUSION 5 1 LabyXL Pre and Post Processor Summary and Validation 5 2 Parametric Study Conclusions and Recommendations 5 3 Future Work and Conclusion RefereiEES Appendix A Example Input Data File for 8 speed Appendix B Labyrinth Types and Nomenc
3. ERE Figure 2 6 Gas Properties Table Speed Case Parameters button shown in Figure 2 5 redirects to gas property sheet to edit speed case parameters The gas property table speed cases 15 shown in Figure 2 6 The table consists 10 Speed Cases with the above variables associated with each speed case Speed Case Constants section consists of the following variables e System Natural Frequency and Non Synch Perturbation Whirl Rate in RPM Mass Flow rate in Ib sec Leave blank if using pressure solution e Absolute Velocity in Ft s e Flow correction Factor e Specific Heat at constant pressure e Gas Viscosity in Lbm Ft s Temperature and gas viscosity calculators shown in Figure 2 5 are provided to convert from Fahrenheit to Rankine and centipose to Lbm ft s respectively 12 4 Labyrinth Options This section shown in Figure 2 7 shows the computing options it has the following variables e Maximum number of Solution iterations default 50 Velocity Tolerance default 1e x RS x e Pressure Tolerance default 1e Mass Flow Tolerance default le Ratio Factor YNS Ratio Factor Cross Flow Factor 0 yes e YMS Cross Flow Factor 0 yes Surface Constant Options Maximum Number of defaut 50 5 00E 0 YNR Ratio Factor Solution Iterations Velocity Tolerance Ratio Factor default 1e 4 x R
4. uone no e 10 6 lt pue 10301 1 6 e Run Labyseal macro Run Labyseal button macro includes the entire Generate Data sheet macro besides it includes the following l The Run macro finishes all the tasks for Generate Data Sheet macro then it generates a text file named answers txt in a folder called Labyseal The macro prints the data sheet path on the first line of answers txt on the second line it prints the output file name with the same name as the Data file name but with out extension On the third and fourth line it prints current out and labxlin txt All the three output files have the same path as the data file Once the answers txt file has been created the Shell command first opens the command prompt then the FORTRAN based executable program file called laby2008 exe The Run macro feeds answers txt file to the executable program Open CALabyseallanswers txt For Output As 1 Print 1 filename Print 1 temp amp amp temp5 amp out Print 1 temp amp current out Print 1 temp amp Labxlin txt Print 1 Close cs Environ COMSPEC Shell cs amp C Labyseal laby2006 exe lt C Labyseal answers txt vbMaximizedFocus 2 The macro deletes all the contents of the results section The syntax 15 shown below Sheet4 Range A14 Q1 20 ClearContents Sheet5 Range A11 G450 ClearContents Sheet4 Range A15 Q120 Font Bold False Sheet5 Range
5. Rotor Stator Interlocking K amp C teeth Length in Inches Figure 2 10 Leak Path Geometric Diagram The output of LabyXL comprises of two sheets Results and Results Results sheet displays two tables shown in Table 2 1 and Table 2 2 15 Table 2 1 Results table Results A sheet Aa HYD DIA Swirl Case 1 Radius ASL a CER Rn AERE 03376 IND 1102 120 Chamber ar ae fey ee 0 5312 0 1149 0 3959 0 5818 0 2009 0 3738 1 102 0 5431 0 2744 Table 2 1 shows the following variables e Chamber number Radius Area of the chamber ASL Area wetted stator length Area wetter rotor length e HYD Diameter Hydraulic diameter e Swirl for various cases Table 2 2 shows a detail list of variables for various speed cases generated Maximum number of ten speed cases can be analyzed 16 Table 2 2 List of various speed case results Speed Case 1 Speed Case 2 Rotor Speed RPM Total Temp Deg R Static Temp Deg R Inlet Pres PSIA Discharge Pres PSIA Swirl Factor DIM No Teeth 4 Moleweight Gas Swirl at inlet Pressure at inlet PSl Pressure at exit PSl Gas Temperature Deg F Gas Compressibilty Gas Ratio of specific heats Start tooth for K C Calculation End tooth for Calculation Number of Iteration Leakage Ibrn sec Leakage SCFM
6. File name My Network Places Save as type Text Files txt Figure 2 9 Save Data File Application box The LabyXL program also has a macro to import a LabyXL data file Data files generated from previous version of Labyrinth Seal can also be imported Import a Data File button is situated above the comment lines on the top of the Main Sheet Reset Fields button situated next to the Import a Data File button erases all the data fields 2 3 Post Processor Design Layout The post processor is designed to import data from output file into tables to organize the results Several plots are generated to study gas properties in various chambers If multiple cases are run then parametric study can be performed as illustrated in Chapter 4 Furthermore the program provides the user with a diagram of the leak path geometry This 14 helps the user to understand the radial and axial tooth location and fluid flow Leak Path Geometric diagram in Figure 2 10 can be found on the Geometric Diagram sheet The macro automatically generates the diagram on entering the tooth geometry Capabilities of the diagram are summarized below It clearly identifies rotor and stator boundaries The radial and axial teeth K amp C teeth are explicitly displayed Leak path can be accurately modeled The diagram self adjusts itself to any changes made to the geometric parameter table Length in Inches
7. 57 57 58 59 59 67 69 69 70 vi Figure B 3 B 4 B 5 B 6 B 7 C 1 C 2 C 3 C 4 Caption Labyrinth Series All Axial Chambers Labyrinth Series Radial before and after the Laby Labyrinth Series Radial chamber after the Laby Labyrinth Seal Types Typical Stepped Shafting Assumption Survey Results for Impeller 1 compared with Synchronous LS 11 and Non synchronous LN 15 LabyXL results Survey Results for Impeller 5 compared with Synchronous LS 11 and Non synchronous LN 15 LabyXL results Survey Results for Balance Piston labyrinth seal compared with Synchronous LS 11 and Non synchronous LN 15 LabyXL results LabyXL results Synchronous LS and Non synchronous LN compared with API Survey Results for all three Labyrinths E e 70 71 72 73 74 76 76 77 77 Table 231 2 9 2 3 3 1 4 1 4 2 5 1 LIST OF TABLES Caption Results table Results sheet List of various speed case results Results table Results sheet Rotor and Stator Boundary Line Calculation API labyrinth seal parameters Results for the dynamic coefficients of the API survey Comparison of LabyXL and DYNLAB results for API Impeller 1 eye seal synchronous case E 17 17 37 45 46 61 viii ST NOMENCLATURE Description American Petroleum Institute Direct coupled damping Cross coupled damping Direct couple
8. 9 Synchronous 2000 0 5000 10000 15000 20000 25000 Rotor Speed Figure 4 6 Influence of Rotor Natural Frequency by setting Ner on Effective Cross Coupling Stiffness Influence of gas properties such as temperature and compressibility shown in Figure 4 7 and 4 8 affect Qe in an adverse manner compared to operating conditions rotor speed and swirl An increase in temperature and gas compressibility improves the stability of the system by reducing the aerodynamic excitation Whereas effect of specific heat ratio absolute velocity of gas and specific heat shown in Figure 4 9 4 10 and 4 11 respectively have negligible influence on Qe Figure 4 12 show influence of mole weight on Qe Mole weight is the only inimical gas property that on increase aggravates the excitation Thus using lighter gas in labyrinth eye seals is favorable 51 4000 3500 3000 E Non Sync Synchronous 2500 Qe Ibf in 2000 1500 1000 Q API reference case 200 400 600 Temperature Rankine 800 Figure 4 7 Influence of Temperature on Effective Cross Coupling Stiffness 3230 3730 reference case 2730 2230 M 1730 Qe Ibf in 1230 730 9 Synchronous 230 0 7 0 8 0 9 1 1 1 Compressibility 1 2 1 3 1 4 Figure 4 8 Influence of Gas Compressibili
9. Pressure Calculation Option Number of Iterations used on Swirl And Temp Calculation Figure 2 2 Control Parameters Number of total teeth Range of Teeth for Start AtTooth 8 C calculations End at Tooth Surface constants Defaults 0 079 Equal for all chambers 0 25 Equal for all chambers Radial Chambers Before Laby End t Radial Chambers After Laby Start At YNS 0 079 Equal YNS for all chambers 8 0 25 Equal YMS for all chambers Chamber 1 Tooth Height inch Equal tooth height for all chambe mz Tooth Spacing Inch Equal tooth spacing for all chambers Tooth Clearance Inch Equal tooth forall chambers Shaft Radius Inch Equal radius forall chambers Figure 2 3 Geometrical Parameters 2 Geometrical Parameters This section shown in Figure 2 3 consists of geometrical variables The section is further divided into two sections Chambers and Chamber 1 Chamber section consists of following variables The last tooth number at which the radial chambers end before the Laby The last tooth number at which the radial chambers end after the Laby Total number of teeth on the seal Range of teeth for the Stiffness and Damping calculation Surface constants YNR YNS YMR YMS A checkbox is provided next to all surface constants to give an option to make a
10. Guidry M J 1993 Three Dimensional Computations of Rotordynamic Force Distribution I a Labyrinth Seal STLE Tribology Transaction 36 3 pp461 469 10 Ishii E Kato C Kikuchi K and Ueyama Y 1997 Prediction of Rotordynamic Forces in a Labyrinth Seal Based on Three Dimensional Turbulent Flow Computation JSME International Journal Series C 40 4 pp 743 748 11 Kwanka K Sobotzik J and Nordman R 2000 Dynamic Coefficients of Labyrinth Gas Seals A Comparison of Experimental Results and Numerical Calculations ASME International Gas Turbine and Aeroengine Congress amp Exhibition 2000 GT 403 12 Moore J J 2001 Three dimensional CFD Rotordynamic Analysis of Gas Labyrinth Seals Proc DETC 01 VIB 21394 13 Hirano Toshio Guo Zenglin Kirk R G Application of CFD Analysis for Rotating Machinery Part 2 Labyrinth Seal Analysis accepted for ASME Transactions 63 14 Guo Zenglin Hirano Toshio Kirk R G Application of CFD Analysis for Rotating Machinery Part 2 Labyrinth Seal Analysis accepted for ASME Transactions 15 Sneck H J Labyrinth Seal Literature Review Journal of Lubrication Technology Transactions of the ASME October 1974 pp579 582 16 Benckert H Wachter J Flow Induced Spring Coefficients of Labyrinth Seals for application in Rotor Dynamics Rotordynamics Instability problems in High Performance Turbomachinery NASA CP No 2133 proceedi
11. Table1 Sheet4 Cells 14 ccc 6 Mid h 42 8 Sheet4 Cells 14 ccc 6 Borders LineStyle xlContinuous Sheet4 Cells 14 ccc 7 Mid h 52 8 Sheet4 Cells 14 ccc 7 Borders LineStyle xlContinuous ccc ccc 1 Line Input 1 Loop Table 2 Sheet4 Cells 17 ccc 1 Rotor Speed RPM Sheet4 Cells 18 ccc 1 Total Temp Deg R Sheet4 Cells 19 ccc 1 Static Temp Deg R Line Input 1 Sheet4 Cells 23 ccc 2 ww Mid h 27 10 Sheet4 Cells 23 ccc 2 ww Borders LineStyle xlContinuous Line Input 1 Sheet4 Cells 24 ccc 2 ww Mid h 27 10 Sheet4 Cells 24 ccc 2 ww Borders LineStyle xlContinuous do loop for the speed cases from sheet3 Do Until 6 Sheet4 Cells 25 ccc 2 ww Sheet3 Cells 5 ww 3 t Sheet4 Cells 25 ccc 2 ww Borders LineStyle xlContinuous ccc ccc 1 t tt1 Loop data import starting from start teeth for KC Line Input 1 h Sheet4 Cells 25 ccc 2 ww Mid h 27 10 Sheet4 Cells 25 ccc 2 ww Borders LineStyle xlContinuous 40 Table 3 Sheet5 Cells 11 ss 1 Speed Case amp dd Sheet5 Cells 11 ss 1 Font Bold True Dim na As Integer Do Until ss dd 2 Sheet1 Range F29 Value 1 ww If IsNumeric Mid h 2 8 Then Sheet5 Cells 11 ss 2 Mid h 2 8 Else Sheet5 Cells 11 ss 2 NA Sheet5 Cells 11 ss 2 Font Colorindex 2 End If Sheet5 Cells 11 ss 2 Borders
12. u 1 200 0 8 o 8 0 6 Effective Dampinz Ibf 4 s in 0 4 200 4 E 0 2 5 Effective 400 g Stifness Ibf in v B E gt 600 0 4 0 6 800 Figure 2 13 Plot of Effective Damping amp Stiffness Vs Speed Cases Labyrinth seal designer and rotordynamists are mostly interested in reducing the effective cross coupling stiffness Qe Forward whirling can be minimized and instability problem can be solved by reducing Qe Figure 2 13 shows a plot of Effective stiffness Qe and Effective damping for various speed cases Thus this plot is crucial for stability analysis Results sheet has the following plots Mach Number Vs Tooth Figure 2 14 e Temperature Vs Chamber Figure 2 15 e Pressure Vs Chamber Figure 2 16 19 Mach No Vs Tooth e Speed Case 1 m Speed Case 2 Mach No Speed Case 3 Tooth Figure 2 14 Plot of Mach No Vs Tooth Temperature Vs Chamber 665 660 655 650 645 640 635 e Speed Case 1 m Speed Case 2 Speed Case 3 Temperature R 630 625 620 Chamber Figure 2 15 Plot of Temperature Vs Chamber Pressure Vs Chamber Speed Case 1 E8 Speed Case 2 Speed Case 3 Figure 2 16 Plot of Pressure Vs Chamber 20 CHAPTER 3 LabyXL Macros A macro is a set of commands including functio
13. 0 Do Sheet3 Cells 5 2 Sheet1 Range F15 Sheet3 Cells 5 i 2 Interior ColorIndex 1 Loop Until i Sheet1 Range F16 Value Sheet2 Range B7 E7 Interior ColorIndex 24 Sheet2 Range B7 E7 Interior Pattern xIGray8 Sheet2 Range B7 E7 Interior PatternColorindex 2 Sheet3 Range B5 15 Interior ColorIndex 24 Sheet3 Range B5 15 Interior Pattern xIGray8 Sheet3 Range B5 15 Interior PatternColorlndex 2 Sheets Gas Properties Select d End Sub e Viscosity Calculator macro This macro converts gas viscosity from centipose units to Lbm ft sec It opens an Input Box for user to enter gas viscosity The equation for the conversion is Gas viscosity Lbm ft sec cp 12 386 1 45E 7 3 1 30 As soon as the macro receives the input in centipose it converts it to Lbm ft sec and pastes it in the gas viscosity input field The syntax is shown below Private Sub CommandButton8 Click Dim myvalue myvalue InputBox Enter a value for centipose cp amp Chr 10 amp Chr 10 amp Gas Visocity cp 12 0 386 0 1 45E 7 Gas Visocity Calculator If myvalue Then GoTo h Else Sheet1 Range F63 Value myvalue 12 386 0 000000145 End If h End Sub Generate Data File macro As the name implies the macro extracts data from the Excel spreadsheets into a fixed format text file The following are the steps in which the macro saves the data
14. 0 1 0 tip swirl influence 0 2472 085 0 3 AOZGIF1 tooth height 0 14 1 12 07 CROTOR SPEED RPM NSPD TYPE WHIRL 0 SYN I NON SPD 110 97E 02 08 0 CRAD OPT SERIES TYP 1 STA 2 ROT 3 LOCK STEP LIRS 08ST 11 IS 1 IB 3 CRADIAL OPT NUMBER OF TEETH PLUS RANGE FOR KXY IRE 16NT 21NS 10NE 14 CTOOTH HEIGHT IF KEY 1 INSERT LINE S 7G10 2 KEY 0000000001 10 00 04 100 00E 05100 00E 05100 00E 05100 00E 05100 00E 05100 00E 05100 00E 05 100 00E 05100 00E 05140 00E 03140 00E 03140 00E 03140 00E 03140 00E 03 100 00E 05100 00E 05100 00E 05100 00E 05100 00E 05100 00E 05100 00E 05 CTOOTH SPACING KEY 1 INSERT LINE S 7G10 2 KEY 0000000001L 17 00E 02 170 00E 03170 00E 03170 00E 03100 00E 03170 00E 03170 00E 03267 00E 03 170 00E 03900 00E 04150 00E 03150 00E 03150 00E 03150 00E 03150 00E 03 266 00E 03170 00E 03170 00E 03170 00E 03170 00E 03170 00E 03170 00E 03 CTOOTH CLEARANCE KEY 1 INSERT LINE S 7G10 2 KEY 0000000001 266 00 03 266 00 03266 00 03266 00 03266 00 03266 00 03266 00 03266 00 03 266 00 03160 00 03115 00 04115 00 04115 00 04115 00 04115 00 04 160 00 03266 00 03266 00 03266 00 03266 00 03266 00 03266 00 03 CSHAFT RADIUS KEY 1 INSERT LINE S 7G10 2 KEY 0000000001RS919 00E 02 919 00E 02840 60E 02759 40E 02681 00E 02652 60E 02600 00E 02567 00E 02 541 00E 02541 00E 02541 00E 02541 00E 02541 00E 02541 00E 02541 00E 02 541 00E 02557 00E 02600 00E 02650 00E 02700 00E 02750 00E 02850 00E 02 CS
15. 1 Loop Until i Sheet1 Range F29 Value Else sheet2 Cells 7 3 Sheet1 Range E38 End If i 0 If Sheet1 CheckBox7 Value False Then Do sheet2 Cells 7 i 8 0 079 sheet2 Cells 7 i 8 Interior Colorlndex xlNone i i 1 Loop Until i Sheet1 Range F29 Value Else sheet2 Cells 7 8 0 079 End If Furthermore the macro color codes the geometric parameter table The dummy cells are colored grey with color index equal to 15 radial chambers before the laby are colored light yellow with color index 36 The axial chambers for K amp C calculation are colored tan with color index of 40 Radial chambers after the laby are colored light green with color index of 35 A sample of color coding syntax is shown below Sheets Geometric Parameters Range B7 156 ClearContents Sheets Geometric Parameters Range B7 156 Interior Colorlndex 15 shading color index 40 for axial chambers c calculation Dim r As Integer Dim q As Integer Sheet1 Range I30 q Sheet1 Range l31 p q r 26 t 0 s 0 Do Until p t 1 sheet2 Cells 6 r tt s Interior Colorlndex 40 s st 1 If s 8 Then s 0 t tt1 End If Loop shading for radial before laby Sheet1 Range F28 t 0 5 0 Do Until t r 1 If r 0 Then GoToz End If sheet2 Cells 7 t 2 s Interior Colorindex 36 s st 1 If s 8 Then s 0 t tt1 End If Loop 7 b sheet2 Range BT ET Int
16. 2 JH 819 1845 8119 46 819 61 per yeus avue L19 pes yes 1118 11 81 1945 eouereo o JH 919 11845 9119 46 919 LI yeus avuro 919 yes SLLSuroedSs 91 per 1845 eoutieo o JH 19 11845 7118010845 pig SI 99UeTeeID pei yeys rid pes LYS el supeds Ig FI 99UeTeeID per yeys pes yeys 18 5 71d pe yeys pes yeys 1118 119 99UeTeeID pe yeys pes yeys 0118 018 II exy 99UeTeeID pei yeys 014 11945 6l9upeds 69 pe yeys 68 11945 8IL5uroedSs 89 6 IH per yeys 8H pes yes 18 8 1845 99Uereefo 11845 919 6 99 L 1845 eoutieo o 98 pes 11845 s Leuroeds eg 9 per 1845 99Uereefo SA pes yeys plsupeds pg S 1845 99Uereefo fH pes yeys 5 eg Y 0991 per 1845 99Uereefo H 1845 18 6 g per 1845 99Uereefo CH pes 11845 118 c yeus eouereo o 1H per yeus 0 I a O a s euIpiooo euIp1iooo X 9jeurpIooo A 9jeurpIooo X Arepunog 103235 Arepunog 10303
17. A11 G450 Font Bold False Sheet4 Range A15 Q120 Borders LineStyle Sheet4 Range A15 Q120 Font ColorIndex 1 Sheets Range A11 G450 Font ColorIndex 1 Sheet4 ChartObjects Delete sheet4 Activate Sheets ChartObjects Delete 38 The macro opens the data sheet saved by the user and acquires the directory information The output file labxlin txt is found in that directory and is renamed to labx txt Before renaming the file the macro checks for previously saved files and deletes them A Do loop is used to rename the file The syntax is shown below A Sheet1 Range E79 Open A For Input As 1 c CurDir d CurDir Mabxlin txt labx CurDir amp labx txt Close 1 If Len Dir labx gt 0 Then Kill labx Test for previous files and delete them msg MsgBox Successful To see results click OK vbOKOnly If msg vbOK Then Do Until Len Dir labx gt 0 Begin a loop to test for final output file labx txt Name d As labx Attempt to rename will fail until temp txt is closed On Error Resume Next Loop Else GoToq End If The macro opens labx txt to extract data It imports the data from the labx txt file to results section A and B The macro uses the syntax Line Input 1 h to go to the next line in the text file The data is imported in three tables 39 Open labx For Input As 1 Line Input 1 h Mid h 2 6 Line Input 1 Line Input 1
18. Ibf sec in Qe Component Kxx Kxy Kyx Kyy Cxx Oyx Ibf in Imp Syn 641 06 4193 50 4193 50 641 06 2 08 0 10 0 10 2 08 2734 6 1 eye Nass laby Syn 786 11 2623 20 2623 20 786 11 0 64 024 024 0 64 2174 9 Imp Syn 1288 10 5379 10 5379 10 1288 10 2 66 0 31 031 2 66 3510 Seye Non lab 1149 30 3413 00 3413 00 1149 00 0 84 0 35 0 35 0 84 2827 9 aby Syn Bal Syn 75232 23923 23923 75232 10 23 31 00 31 00 1023 16741 Piston Non 19564 65819 65819 19564 1 41 700 7 00 1 41 5592 46 El 1 5 m 21 SA O 2 d 4 3 10 0 D LabyXL synchronous results shown as RM syn LabyXL non synchronous results shown as RM non Respondents Figure 4 1 API survey results 22 for Normalized Destabilizing Force compared with LabyXL Synchronous and Non synchronous results stiffness results are normalized using the minimum stiffness supplied and same respondents damping results are used to normalize damping coefficients Effective cross coupling Qeff is then calculated using the normalized values Comparison plots with actual values not normalized can be found in Appendix C Kocur et al 22 studied the variability of the survey response and concluded date there remain significant differ
19. LineStyle xIContinuous 5 The macro generates six plots Swirl Vs Chamber Area ASL amp Hyd Diameter Vs Chamber e Effective Damping and Stiffness Vs Speed Cases e Mach number Vs Tooth e Temperature Vs Chamber e Pressure Vs Chamber The Run Labyseal macro calls a function called pressplot to generate Pressure Vs chamber plot Syntax is shown below Function pressplot Sheet5 Activate Sheet5 Select Dim nosteth As Integer Dim num As Integer Dim num2 As Integer Dim casenum As Integer casenum 1 Dim startethrow As Integer startethrow 11 nosteth Sheet1 Range F29 num 2 nosteth 11 41 num2 11 Adds the chart to the active sheet Charts Add ActiveChart Chart Type xIXYScatterSmooth ActiveChart SeriesCollection NewSeries ActiveChart Location Where xlLocationAsObject Name Results B Selects the type of chart Do Until casenum Sheet1 Range F16 1 ActiveChart SeriesCollection casenum Results B R amp num2 amp ActiveChart SeriesCollection casenum Values Results B IR amp startethrow amp C6 R amp num amp C6 ActiveChart SeriesCollection casenum XValues Results BR amp startethrow amp C4 R amp num amp C4 casenum casenum 1 num2 num2 2 nosteth 1 startethrow startethrow 2 nosteth 1 num 2 nosteth 1 ActiveChart Location Where xlLocationAsObject Name Re
20. centrifugal compressor eye shaft and balance drum configurations The major advantage of the labyrinth code is the ability to estimate the seal entrance swirl given the impeller tip swirl which is a standard output of any aerodynamic design code The program has been tested and selected as the program of choice for toothed labyrinth designs by three major OEM compressor companies and two major oil companies in the US The program is being used for last 20 years at these companies and used as a consulting tool for the past 22 years The program can evaluate tooth on rotor on stator or interlocking teeth The seal can be straight through or stepped The program input can be adjusted to estimate the influence of honeycomb seal designs with typical cell size 2 2 Preprocessor Design Layout The LabyXL is an easy to use program incorporated in Microsoft Excel spreadsheet The spreadsheet consists of various macros in form of Buttons to automate series of tasks The section discusses the layout of these macros and input fields Macros are discussed in detail in the next chapter The data input for the spreadsheet is divided in four parts Control Parameters Figure 2 2 Geometrical Parameters Figure 2 3 Gas Properties Figure 2 5 and Labyrinth Options Figure 2 7 The input fields are color coded to help the user identify 1f input is required or not Figure 2 1 is a chart showing different color codes and its significance Three comment
21. divided in two sub sections Speed case 1 and Speed Case Constants Speed Case 1 section consists of the following variables Gas Swirl at inlet 0 700 Pressure at inlet i Temperature 806 0 P Temp Conversion i 1201 OO Psi Pressure at exit Ratio of specific heats 1 502 x Edit Speed Case Molecular Weight 28 013 mee Parameters Speed Case Constants System Natural Frequency and 8700 00 RPM Mass Flow rate in lh sec s Non Synch Perturbation Whirl Rate default 0 0 Compressibility Absolute Velocity 280 00 Ft s Flow Correction Factor default 1 0 Specific Heat at 0 2742 constant pressure Gas Viscosity L g 1 76E 05 Lbm Ft s Figure 2 5 Gas Properties 11 e Speed of shaft in RPM e Gas Swirl at inlet e Gas Pressure at inlet in psi e Gas Pressure at exit in psi e Gas Temperature in Rankin e Ratio of Specific Heat e Compressibility e Molecular Weight Make all the speed case equal to Speed Case 1 button makes all the speed case variables equal to variables of Speed Case 1 Swirlat Pressure at Pressure at Gas Gas Gas ratio of Gas Number speed RPM as inlet inlet Psi exit Psi temperature R compressibilty specific heats Moleweight 1 11500 0000 0 0000 948 0000 253 0000 660 0000 0 9800 HERE HEREDI 2 11500 0000 0 5000 948 0000 253 0000 660 0000 0 9800 1 38 28 97 3 11500 0000 0 8000 948 0000 253 0000 660 0000 0 9800 1 38 28 97 4 TEA
22. l The macro begins by calling a function checkfields to check for any missing data on the main sheet If any data is missing a message box displaying the missing parameter pops up and the macro ends The function uses a counter called trapy to check for missing fields If any data is missing then will be less than 25 and if trapy is less than 25 then the macro is forced to end The function is located in Module 7 and the Generate data file macro is located in Sheetl Main in project Sample syntax is shown below Function checkfields trapy 0 Dim mycheck IsNumeric Sheet1 Range F15 Value If IsNumeric Sheet1 Range F 15 Value And Sheet1 Range F15 Value lt gt Then trapy trapy 1 Else MsgBox Rotor Speed F15 field Missing End If If ISsNumeric Sheet1 Range F59 And Sheet1 Range F59 lt gt Then trapy trapy 1 Else MsgBox Absolute Velocity F59 field Missing 31 End If End Function Private Sub CommanaButton7_Click Call checkfields If trapy 25 Then GoTo endit End If The macro calls all the Checkbox subroutines to check their values Zero is assigned to the variable if the value is true and one if the value is false Syntax is shown below Call chkbox2 click Call chkbox3 click Call chkbox4 click Call chkbox5 click Call chkbox6 click Call chkbox7 click Call chkbox8 click Call chkbox9 click Sub chkbox7 click If Sheet1 CheckBox7 Valu
23. the divisor is seven Thus if the function returns a zero then the macro prints to the next line Printing of only seven values on a line is done to follows the DYNLAB data input file format The syntax is shown below Print 1 CTOOTH HEIGHT IF KEY 1 INSERT LINE S 7G10 2 KEY amp Format keyb 0000000000 amp B amp Format Sheet1 Range E37 00 00E 00 If keyb 1 Then n 0 For Each toothheight In Sheet2 Range B7 Sheet2 Range B7 End xlDown strnme toothheight Value If n Mod 7 0 And lt gt 0 Then Print 1 End If Print 1 Format toothheight 000 00 00 00 00 00 n n 1 Next toothheight Print 1 End If The macro uses a Do loop to print values from the gas property table to the data sheet It prints until variable caseno exceeds variable NSPD Variable NSPD stores the number of cases selected by the user If printing is successful then a message box displays the name and path of the filename Syntax is shown below Print 1 C SPEED SWIRL PS PE TABS Z GAMMA MW VABS MUXG Ncr Dim caseno As Integer caseno 1 Do Until caseno gt NSPD Print 1 Format Sheet3 Range B amp 4 caseno 000 00E 00 00 00E 00 amp Format Sheet3 Range C amp 4 caseno 000 00E 00 00 00E 00 34 Format Sheet3 Range D amp 4 000 00E 00 00 00E 00 amp Format Sheet3 Range E amp 4 caseno 000 00E 00 00 00E 00 amp Format Sheet3 Range F amp 4 ca
24. 800 704 800 712 Flow correction factor 257 35 259 63 Direct stiffness Ibf in Cross Stiffness Ibf in Direct Damping lbf s in Cross Damping Ibf s in Effective DampingfIbf s in Effective Stifness Ibf in 4232 4130 Results sheet displays Mach number Temperature Pressure and Pressure step for each chamber for various speed cases Table 2 3 shows the table of results on Results B sheet Table 2 3 Results table Results sheet Speed 1 0l 603 27 1548 1548 re j eae miw 503 27 143283 14328 2 89327 1378 33 1378 33 MERERI j 17 Results sheet has the following plots Swirl Vs Chamber Figure 2 11 Area ASL ARL and HYD DIA Vs Chamber Figure 2 12 Effective Damping amp Stiffness Vs Speed Cases Figure 2 13 Swirl Vs Chamber e Swirl Case 1 m Swirl Case 2 2 Swirl Case 3 Swirl Case 4 Swirl Swirl Case 5 e Swirl Case 6 Swirl Case 7 Swirl Case 8 Swirl Case 9 0 2 4 6 8 10 12 Swirl Case 10 Figure 2 11 Plot of Swirl Vs Chamber Area ASL ARL amp HydDia Vs Chamber z F m Aren in 2 ASL in ARL in amp o to Figure 2 12 Plot of Area ASL ARL and HYD DIA Vs Chamber 18 Effective Damping amp Stiffness Vs Speed Cases 1 4 400 1 2 3
25. LABYRINTH SEAL PREPROCESSOR AND POST PROCESSOR DESIGN AND PARAMETRIC STUDY by Rumeet Pradeep Mehta Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in MECHANICAL ENGINEERING Approved Dr R Gordon Kirk Chairman Dr Mary E Kasarda Dr Daniel J Inman 30 April 2008 Blacksburg Virginia Keywords Labyrinth Seal Excel Visual Basic Parametric Study API Survey LABYRINTH SEAL PREPROCESSOR AND POST PROCESSOR DESIGN AND PARAMETRIC STUDY by Rumeet Pradeep Mehta Dr R Gordon Kirk Chairman Mechanical Engineering Department Virginia Tech ABSTRACT Vibrations caused due to aerodynamic excitation may cause severe limitation to the performance of turbomachines The force resulting from the non uniform pressure distribution within the labyrinth cavity is identified as a major source of this excitation In order to perform rotor dynamic evaluation of rotor bearing seal system accurate prediction of this force is essential A visual basic based front end for a labyrinth seal analysis program has been designed herein In order to accurately predict the excitation force proper modeling of labyrinth leak path is important Thus the front end developed herein incorporates a leak path geometric diagram for visual analysis of labyrinth leak path and tooth location Furthermore to investigate in
26. Range F28 t 0 5 0 Do Until t 2 r 1 If r 0 Then GoToz End If Sheet2 Cells 7 t 2 s Interior Colorlndex 36 5 5 1 If s 8 Then 5 0 t t 1 End If Loop 7 Sheet2 Activate d End Sub e Make all Speed Cases equal to Speed Case 1 button macro The macro checks for Speed Case 1 parameters If any data field is empty then a message box flashes and asks the user to input that parameter and the macro ends Considering all the parameters for Speed Case 1 are entered the macro prompts the user 28 that if he is sure that he wants all Speed cases to be equal If the user clicks cancel then the macro ends but if the user clicks Ok then the macro copies Speed case 1 parameters to all the remaining speed cases For instance 1f a user chooses five speed cases then the Make all speed cases equal macro will make the first five speed cases equal and the remaining will be colored grey Private Sub CommandButton3 Click If Sheet1 Range E47 Then MsgBox Please enter a value for Pressure at Inlet GoTo d End If If Sheet1 Range E47 Then MsgBox Please enter a value for Pressure at inlet GoTo d End If response MsgBox All Speed Cases will equal to Speed Case 1 vbOKCancel If response vbOK Then GoTo A Else GoTo d End If A i 0 Do Sheet3 Cells 5 i 8 Sheet1 Range E50 Sheet3 Cells 5 i 8 Interior Colorlndex xINone i i 1 Loop Until i Sheet1 Rang
27. S omega Pressure Tolerance YME Cross Flow Factor default 1e 2 0 yes Mass Flow Tolerance YMS Cross Flow Factor default 1e 4 0 yes Figure 2 7 Labyrinth Options Labyseal button shown in Figure 2 8 is provided to run the LabyXL program It opens a save data file application box shown in Figure 2 9 The application allows the user to select the directory and assign a filename to the data sheet Path and data sheet name CaDocuments and Settings Rumeet Mehtat Desktoptret tat Run Labyseal Generate Data File Figure 2 8 Run button 13 Once the user saves the data file command prompt window pops up user should wait for it to close and then click the Ok button to view the results To save a data file without running the analysis a Generate Data File button is provided Location of the data file generated 15 saved in the Path and data sheet name box Please select a folder and name to save the file Save in 8 Desktop e Tools Documents gft Ext P My Computer g hghg txt my Network Places hjy txt O Jimmy E jhjh txt new music t txt Wutever_data test februm txt My Documents 9cases txt testFeb8 txt 50791 15 testfebSrumeet txt AOZGIF1 txt venky txt E bbb txt E vvv txt Desktop bond password drexel txt B zz txt ctxt 222 prb2 txt E fds txt Favorites ff txt x
28. The static seal comparison was in excellent agreement for both tooth on stator and full labyrinth design 20 In addition the comparisons for full labyrinth at rotor speed of 9540 rpm showed good agreement if the perturbation is non synchronous In an effort to improve and validate predictions of Bulk Flow approaches theories of Iwatsubo Childs and Scharrer and Kirk Moore 12 utilized three dimensional computational fluid dynamics to model the Labyrinth seal flow path by solving the Reynolds Averaged Navier Stokes equations His study utilized a CFD code SCISEAL which uses a three dimensional whirling method developed by Athavale et al 21 Moore benchmarked the CFD code by modeling the experimental data presented by Pelletti in 1990 for his master s thesis He further compared the CFD results to Kirk s and Scharrer s Bulk Flow theories The comparison from Moore 12 is shown in Figure 2 Moore plotted Impedance N m which is cross coupling stiffness versus processional frequency ratio 15 the ratio of rotor whirl to rotor spin E Seal Only CFD Experimental Up Seal CFD Scharrer Bulk Flow 797 Kirk Bulk Flow E 2 9 c Figure 1 2 Comparison of seal models 16 krpm Pr 0 403 12 The comparison showed good agreement of CFD to Kirk s whereas Scharrer s had greatest deviation 12 CFD performs labyrinth coefficients and leakage analysis accurately but unfortu
29. Typical Compressor Labyrinth Seal Configuration Chamber i 1 81 Tooth i 1 Typical Chamber Nomenclature Figure B 2 Typical Chamber Nomenclature Gas Swirl for laby first tooth Series 00 Typical Isolated Labyrinth Figure B 3 Labyrinth Series All Axial Chambers 70 am 0 Tangential Velocity at Tip of Impeller Series 10 Typical System for Balance Drum Configuration Figure B 4 Labyrinth Series Radial before and after the Laby 71 Series 20 Typical System for Shaft Seal Labyrinth Figure B 5 Labyrinth Series Radial chamber after the Laby 72 TOOTH STATOR TYPE 1 2 TOOTH ON ROTOR INTERLOCKING TYPE 3 Figure B 6 Labyrinth Seal Types 73 m 4 t V Assumpt ion in ny Step down b Step up Chanber Configuration for Stepped Shaft Labyrinth Figure B 7 Typical Stepped Shafting Assumption 74 APPENDIX C Comparison of LabyXL results with API survey results 75 Qe Ibf s x 10 1 2 3 4 amp 6 7 8 8a 10 LS 12 13 14 LN 20 21 22 amp 23 24 25 11 15 Respondents Figure C 1 Survey Results for Impeller 1 compared with Synchronous LS 11 and Non synchronous LN 15 LabyXL results Qe 5 x 10 1 2 3 4 amp 5 6 7 8 8a 10 LS 12 13 14 LN 20 21 22 23 424 25 11 15 Respondents Figure C 2 Survey Results for Impeller 5 compared wi
30. U G LBM FT SEC PE 250 00E 00 MW 289 70E 01 TABS 660 00E 00 Z 980 00E 03 MUXG 122 40E 07 CMASS FLOW LB SEC IF P 1 gt 0 5 1 MDOT CCHAMBER PRESSURES 7G10 2 PER LINE IF KEY 1 KEY 0 CCHAMBER TEMP 7G10 2 IF KEY 1 2 VARA 0 TABS 2 CMAX SOLUTION ITERATIONS VC MDOT DEFAULT 50 ITER 50 CTOLERANCE DFAULT 1E 4 RS OMEGA CPRESSURE TOLERANCE DEFAULT 0 01 TOLERV 100 00E 05 TOLERP 100 00E 02 CMASS FLOW TOLERANCE DEFAULT 0 0001 TOLERP CPRINTMATRIX SETUP 1 PRINT ALL KEYDMP 0 C IF NSPD gt 1INPUT NSPD LINES AS FOLLOWS lt 6G10 2 2F5 1 gt 0 DEFAULTS INIT V C SPEED SWIRL PS PE TABS Z GAMMA MW 110 97E 02247 20E 03500 00E 00250 00E 00660 00E 00980 00E 0301 3828 97 110 97E 02500 00E 03500 00E 00250 00E 00660 00E 00980 00E 0301 3828 97 110 97E 02600 00E 03500 00E 00250 00E 00660 00E 00980 00E 0301 3828 97 110 97E 02700 00E 03500 00E 00250 00E 00660 00E 00980 00E 0301 3828 97 110 97E 02800 00E 03500 00E 00250 00E 00660 00E 00980 00E 0301 3828 97 110 97E 02100 00E 02500 00E 00250 00E 00660 00E 00980 00E 0301 3828 97 110 97E 02120 00E 02500 00E 00250 00E 00660 00E 00980 00E 0301 3828 97 110 97E 02140 00E 02500 00E 00250 00E 00660 00E 00980 00E 0301 3828 97 GAMMA 138 00E 02CP245 00E Figure A 1 Sample Data File 67 APPENDIX B Labyrinth Types and Nomenclature for LabyXL 68 22222 ET YA AO Figure B 1b
31. URFACE CONSTANT DEFAULT 0 079 F5 1 KEY YNR 790 00E 04001 0INR 1 790 00E 04850 00E 04850 00E 04850 00E 04850 00E 04850 00E 04850 00E 04 790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04 790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04 CSURFACE CONSTANT DEFAULT 0 25 XFLOWI KEY YMR 25 00E 02XFR IMR 1 25 00E 02 30 00E 02 30 00E 02 30 00E 02 30 00E 02 30 00E 02 30 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 66 CSURFACE CONSTANT DEFAULT 0 079 F5 1 KEY YNS 790 00 04001 0INS 1 790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04 790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04 790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04790 00E 04 CSURFACE CONSTANT DEFAULT 0 25 XFLOWII KEY YMS 25 00E 02XFS IMS 1 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 25 00E 02 CGAS SWIRL AT INLET PERCENT SPD NCR RPM SWIRL 247 20E 03NC600 00E 01 CGAS PRESSURE AT INLET GAS VELOCITY FT SEC PS 500 00E 00 V500 00E 01 CGAS PRESSURE AT EXIT CGAS MOLEWEIGHT CGAS TEMPERATURE CGAS COMPRESSIBILITY CGAS RATIO OF SPECIFIC HEATS AND CP 03 CGAS VISCOSITY M
32. act as a stabilizing force or could even produce backward rotor whirl instead of forward Pressure ratio on the other hand if increased reduces the magnitude of Qe as seen in Figure 4 4 Note increasing the pressure ratio for labyrinth seal would mean reducing the pressure drop across the seal conclusions made above apply to both synchronous and non synchronous type of whirl Figure 4 5 and 4 6 show results of variation of first natural frequency Ncr by setting rotor speed constant at 21662 rpm and by setting rotor speed equal to Ncr respectively By varying Ncr rotor whirl frequency at first natural frequency may also vary since LabyXL assumes both equal The cross coupling stiffness Kxy and direct damping Cxx remain constant for the synchronous case as expected but Qe significantly decreases refer to Figure 4 5 as Ncr increases because in order to calculate Qe Equation 4 2 Ncr is multiplied with Cxx and subtracted from Kxy For the non synchronous case Kxy and Cxx increase with increase in not shown in the figure However Qe gradually decreases due to substantial increase in direct damping Due to this gradual reduction Qe for the non synchronous case eventually becomes greater than Qe for the synchronous case when Ncr is about half the rotor speed When rotor speed is set equal to Ncr seen in Figure 4 6 in other words when synchronous and non synchronous conditions are same the system may experience re
33. alculation are highlighted in black whereas dummy teeth are white Refer to Figure 2 10 for the geometric diagram Part of the macro is shown below ActiveChart SeriesCollection 1 Select With Selection MarkerBackgroundColorlndex 1 MarkerForegroundColorlndex 1 MarkerStyle xINone 35 Smooth True Shadow False End With Sheet6 Range 03 Select End If ActiveSheet ChartObjects Chart 11 Activate If Sheet1 OptionButton6 Value True Then ActiveChart SeriesCollection 5 XValues Geometric Diagram IR35C22 R85C22 Active Chart SeriesCollection 5 Values Geometric Diagram IR35C23 R85C23 Active Chart SeriesCollection 5 Name K amp C teeth End If 36 11003 Jo snipez 3jeus IY sjuosoJdo1 3jeus U1001 9AHosdsaI y Jo 443194 OY sjuosoudoi1 U1001 oA12odsoi jo oouteo o IY sjuoso1do1 2 Jequinu 4100 Jo Suroeds oy sjuosoudoi loquinu 4100 pue O uuin oo 99 sjuosoudo 9 loquinu 4100 pue g J199 sjuesoudoi 9 1845 JH 079 pes 11845 5 0044 IZ quu qe 11845 eouereo JH 614 11845 6118 05 614 07 og 11945
34. and Gas Property sheet 2 4 Program Capabilities LabyXL 15 a labyrinth type gas seals analysis program that uses a bulk flow small perturbation solution to solve for the stiffness and damping characteristics of the labyrinth gas seal Gas leakage pressure and temperature are also determined The major features of LabyXL preprocessor and post processor can be summarized as follows 1 The program is capable of importing and generating a data file Refer to Figure A 1 in Appendix A for a sample data file 2 It provides a table for Geometric Parameters and Speed Case Parameters for easy understanding and data input 3 input boxes are color coded Figure 2 1 to identify if the variable is required or default could be used 4 On opening the Geometric Diagram sheet after entering labyrinth geometric data macro generates the leak path geometric diagram for better understanding of the labyrinth geometry 5 Gas property section provides a viscosity and temperature calculator for converting centipose units to Lbm Ft s and Fahrenheit to Rankine respectively 6 Labyrinth options section provides a field for input sheet name and path for easy location of data sheet generated 7 Post Processor macro imports results from output text files into tables for data analysis 8 In addition it generates several plots for better analysis This program as a whole is a design tool for analysis of gas labyrinth seals typical of
35. arameters 4 1 Operating conditions Impeller eye 1 Impeller eye 5 Balance Piston Gas Nitrogen Nitrogen Nitrogen Speed rpm 21662 21662 21662 Critical speed cpm 6700 6700 6700 Inlet Pressure psi 1548 3035 3035 Discharge Pressure psi 1201 2637 1201 Inlet temperature R 585 7 805 7 805 7 Geometric Parameters of Teeth 4 4 11 Diameter in 5 25 9 25 5 00 Tooth height in 0 089 0 089 0 100 Tooth spacing in 0 098 0 098 0 155 Tooth clearance in 0 005 0 005 0 005 Gas Properties Compressibility 1 02 1 104 1 104 Mole weight 28 0134 28 0134 28 0134 Specific Heat Ratio 1 535 1 502 1 502 Viscosity cP 0 021 0 026 0 026 45 Three cases are run using the above parameters Table 4 2 shows results for synchronous and non synchronous type of whirl Effective cross coupling stiffness is calculated using equation 4 2 developed by Kirk 5 Qe Kxy Cxx Wyner 4 2 where Qe effective cross coupling stiffness in Ibf in cross coupling stiffness in Ibf in direct damping in Ibf s in Wyner rotor natural frequency in rad sec Results are then compared to the results of the API survey respondents in Figure 4 1 Two respondents with major deviation have been removed from the comparison to get a better insight Table 4 2 Results for the dynamic coefficients of the API survey Stiffness Ibf in Damping
36. ase of Imp 1 eye seal low pressure drop is favorable Gas properties such as temperature and mole weight could significantly affect the effective cross coupling stiffness for both cases Thus for reducing excitation higher temperature and lower mole weight is favorable 5 3 Future Work and Conclusion An Excel based pre and post processor has been successfully developed to analyze and model gas labyrinth seals An option to use either SI units or English units has also been made available However the following recommendations can be considered for further development LabyXL provides the user with an option to run multiple cases maximum 10 by varying operating conditions and gas properties The program can be modified to include an option to run multiple cases by varying geometric parameters A gas property lookup macro could be incorporated which would fill in all the gas properties once the gas name temperature and pressure are specified Presently LabyXL has a default surface friction factor used for all types of material An option to choose the labyrinth material can be provided in order to calculate accurate surface constants for improved LabyXL predictions 62 REFERENCES 1 Alford J S 1965 Protecting Turbomachinery from Self Excited Whirl ASME Journal of Engineering for Power Vol 38 pp 333 344 2 Iwatsubo T 1980 Evaluation of Instability Forces of Labyrinth Seals in Turbines or Com
37. ation is performed on API Rotor Stability Survey 2006 impeller 1 eye and balance piston labyrinth seal models using LabyXL program developed herein This study will help rotordynamic analysts to solve instability problems more efficiently This chapter covers modeling of all API survey labyrinth seals and comparison with actual respondents Furthermore a parametric study is performed on API s impeller 1 eye labyrinth and Balance Piston labyrinth seal 41 Seal Modeling and Comparison In order to improve American Petroleum Institute API specifications API conducted a survey of several turbomachinery analysts to determine dynamic coefficients of tilt pad bearing first and last impeller eye labyrinth and labyrinth balance piston This research focuses on modeling of first and last impeller eye labyrinth and balance piston labyrinth by utilizing LabyXL program 44 The three labyrinth seals mentioned above are modeled using the parameters provided by shown in Table 4 1 labyrinth seals are modeled as teeth on rotor for an operating speed of 21662 rpm Swirl ratio of 0 7 and the critical speed location at operating of 6700 cpm is assumed The absolute velocity for each labyrinth seal was calculated by using Vabs sr where Vabs absolute velocity in ft sec shaft radius in inches w shaft speed in radians sec sr swirl ratio of gas at inlet Table 4 1 API labyrinth seal p
38. b B 2 Caption Influence of Rotor Natural Frequency by setting Ncr N on Effective Cross Coupling Stiffness Influence of Temperature on Effective Cross Coupling Stiffness Influence of Gas Compressibility on Effective Cross Coupling Stiffness Influence of Specific Heat Ratio on Effective Cross Coupling Stiffness Influence of Absolute Velocity of Gas on Effective Cross Coupling Stiffness Influence of Specific Heat on Effective Cross Coupling Stiffness Influence of Mole Weight on Effective Cross Coupling Stiffness Influence of Rotor Speed on Effective Cross Coupling Stiffness Balance Piston Labyrinth Seal Influence of Inlet Gas Swirl Ratio on Effective Cross Coupling Stiffness Balance Piston Labyrinth Seal Influence of Pressure Ratio on Effective Cross Coupling Stiffness Balance Piston Labyrinth Seal Influence of Ncr on Effective Cross Coupling Stiffness by setting N constant Balance Piston Labyrinth Seal Influence of Ncr and N on Effective Cross Coupling Stiffness by setting N 7 Ner Balance Piston Labyrinth Seal Influence of Temperature on Effective Cross Coupling Stiffness Balance Piston Labyrinth Seal Influence of Mole Weight on Effective Cross Coupling Stiffness Balance Piston Labyrinth Seal Sample Data File Typical Compressor Labyrinth Seal Configuration Typical Compressor Labyrinth Seal Configuration Typical Chamber Nomenclature E e 51 52 52 53 53 54 54 55 56
39. d End Sub e Option Button Option button macros are utilized in Control Parameters in the Main Sheet for Type of Whirl Labyrinth Series and Labyrinth Type The options for each type are grouped together by assigning a different name to each one Grouping is important for proper functioning of option buttons The option button macro has been incorporated in the Run Labyrinth macro It is located in Module 7 of the VBA project A sample of the syntax is shown below Sub Datasheetgenerate If Sheet1 OptionButton4 Value True Then 1 End If If Sheet1 OptionButton5 Value True Then YY 2 End If If Sheet1 OptionButton6 Value True Then x 1 End If e Check box Check boxes are used for pressure calculation option surface constants and tooth geometry If the checkbox is clicked then its value becomes true or else it is false The syntax for the checkbox can be found in the Module 7 A sample is shown below 24 Sub chkbox7_click If Sheet1 CheckBoxT Value True Then YNS 0 If Sheet1 CheckBox7 Value False Then YNS 1 End Sub Sub chkbox8 click If Sheet1 CheckBox8 Value True Then YMR 0 If Sheet1 CheckBox8 Value False Then YMR 1 End Sub e Make all Chambers equal to Chamber 1 button macro The macro starts with prompting the user that if he is sure that he wants all chambers parameters to be equal to chamber 1 parameters If the user clicks cancel then the macro ends but if the us
40. d stiffness Direct coupled stiffness Labyrinth Seal Rotor Speed 1 critical speed Gas pressure at seal inlet Pressure ratio Effective cross coupling stiffness Effective cross coupling stiffness for balance piston Shaft radius Gas swirl ratio at seal inlet Gas absolute velocity Frequency Units F T L F T L F L F L Rev T Rev T F A Dim F L F L Dim L T Rad T 1 CHAPTER 1 Introduction and Literature Review 1 1 Introduction The Labyrinth seal is an innovation first introduced by A Parsons in the early 20 century His idea was to incorporate a torturous path between the high and low pressure regions by using non contacting teeth and separating chambers 15 Labyrinth seal since then have become an integral design element in high performance turbomachinery Main purpose of non contacting labyrinth seals is to reduce internal leakage While it does an excellent job in reducing the leakage but unfortunately due to uneven pressure distribution in labyrinth cavities it develops a destabilizing force capable enough to drive the rotor unstable In order to perform stability analysis of high performance turbomachinery it is essential to predict the magnitude of this destabilizing force Thus a labyrinth analysis program DYNLAB 20 was developed in early 1980 s to predict the leakage and the dynamic coefficients of labyrinth seals Even though to date several companies have been successfully using this pro
41. e True Then YNS 0 If Sheet1 CheckBox7 Value False Then YNS 1 End Sub Sub chkbox8 click If Sheet1 CheckBox8 Value True Then YMR 0 If Sheet1 CheckBox8 Value False Then YMR 1 End Sub The macro calls for a function GetSaveAsTxtFilename The function opens application called GetSaveAsFilename The application displays the standard open dialog box and gets a file name and path from the user to save it The file path and name is then saved on the Main sheet in cell E79 Call GetSaveAsTxtFilename If fun 1 Then GoTo Dumo Sub ends End If Function GetSaveAsTxtFilename Optional InitialFileName As Variant As String Dim vFilename As Variant fun 0 If ISsMissing InitialFileName Then InitialFileName 32 End If vFilename _ Application GetSaveAsFilename _ InitialFileName InitialFileName _ Title Please select a folder and name to save the file _ fileFilter T ext files txt txt If vFilename False Then GetSaveAsTxtFilename if cancel is pressed fun 1 Else GetSaveAsTxtFilename vFilename Sheet1 Range E79 vFilename End If End Function Set filename Sheet1 Range E79 The data file created by the user is opened to save the data Before printing any data in the macro truncates the path name from the string variable filename in order to get just the name of the data file This is done to save the results file in the same name but with out ext
42. e F16 Value i 0 Do Sheet3 Cells 5 i 9 Sheet1 Range E52 Sheet3 Cells 5 i 9 Interior ColorIndex i i 1 Loop Until i Sheet1 Range F16 Value Sheet2 Range B7 E7 Interior Colorlndex 24 Sheet2 Range B7 E7 Interior Pattern xIGray8 Sheet2 Range B7 E7 Interior PatternColorindex 2 Sheet3 Range B5 15 Interior ColorIndex 24 Sheet3 Range B5 I5 Interior Pattern xIGray8 Sheet3 Range B5 15 Interior PatternColorlndex 2 Sheets Gas Properties Select d End Sub 29 e Edit Speed Case button macro The Edit Speed Case macro similar to Make all speed case equal macro verifies that are all the Speed Case 1 parameters entered or not If any data field is empty then a message box flashes and asks the user to input that parameter and the macro ends If there is no missing data then it copies parameters of Speed Case 1 from the main sheet to the Gas Property table keeping the remaining speed cases undisturbed and it opens the Gas Properties sheet A sample of the code is shown below and the code can be found in VB applications Sheetl main Private Sub CommandButton6 Click Dim i As Integer If Sheet1 Range E47 Then MsgBox Please enter a value for Pressure at Inlet GoTo d End If If Sheet1 Range E47 Then MsgBox Please enter a value for Pressure at inlet GoTo d End If Sheets Gas Properties Range B5 I14 Interior Colorlndex 15 i
43. ences across the industry in the prediction of the dynamic coefficients for fluid film tilt pad bearings and labyrinth seals Well one of the major differences could be due to using synchronous or non synchronous assumption LabyXL results for synchronous and non synchronous are plotted in Figure 4 1 As far as LabyXL credibility is concerned Kirk et al 8 and Moore 12 have verified DYNLAB now called LabyXL results with CFD which has shown good agreement Moreover it is clearly seen in Figure 4 1 that LabyXL results lie in the ballpark of the median of survey results Thus assuming LabyXL results are near accurate a parametric study 15 performed using LabyXL on API seals 47 4 2 Influence of Various Parameters of Labyrinth Eye Seal on Effective Cross coupling Stiffness Effects of operating conditions and gas properties on effective cross coupling stiffness aerodynamic excitation are investigated by using Impeller 1 eye labyrinth seal API model parameters from Table 4 1 remain constant except for the parameter under investigation In the parametric study figures the reference case API LabyXL result is circled in black The results shown in Figure 4 2 and 4 3 make clear that increase in rotor speed and gas inlet swirl ratio aggravate the excitation The swirl ratio quite interestingly at least for this particular case if reduced to 0 4 would make the destabilizing force negative Meaning the destabilizing force would
44. ension The string variable temp5 stores the truncated name of the data file Open filename For Output As 1 Dim Temp1 As String Dim Temp2 As String Dim temp4 As String Dim Temp3 As Integer Dim temp5 As String CurDir Temp1 Len filename Temp2 Len temp Temp3 15 Temp2 1 temp4 Right filename Temp3 temp5 Mid temp4 1 Temp3 4 The macro starts printing the data from the Mainsheet to the data file which includes variables of checkboxes option buttons and textboxes Each print command prints data on the new line If Sheet1 OptionButton1 Value True Then 0 End If Print 1 Sheet1 TextBox1 Value Print 1 Sheet1 TextBox2 Value 33 Print 1 Sheet1 TextBox3 Value Print 1 Print 1 CROTOR SPEED RPM NSPD TYPE WHIRL O SYN 1 NON SPD amp Format Range F 15 000 00E 00 00 00E 00 amp amp Format Range F16 Q0 amp amp Format y Print 1 CRAD OPT SERIES TYP 1 STAJ2 ROT 3 I LOCK STEP I IRS amp Format Range F28 00 amp ST amp Format YY 0 amp Format x ISz amp Format ISS amp amp Format Range F24 Geometrical Parameter table variable is printed in a way such that maximum of seven values can be printed on one line If it exceeds seven then it prints on the next line This is achieved my using the Mod function it returns the remainder after number is divided by divisor Here
45. er clicks Ok yes then the macro verifies that are all the Chamber 1 parameters entered or not If any data field is empty then a message box flashes and asks the user to input that parameter and the macro ends Private Sub CommandButton1 Click response MsgBox All current chambers will be equal to chamber 1 vbOKCancel If response vbOK Then GoTo A Else GoTo d End If A If Sheet1 Range E37 Then MsgBox Please enter a value for Tooth Height GoTo d End If If Sheet1 Range E38 Then MsgBox Please enter a value for Tooth Spacing GoTo d End If Considering if all chamber parameters are entered then the macro checks for check marks for tooth parameters and surface constants If the value is false meaning no check mark then it will copy the given value in all the fields for the user to edit any value However if the value is true then it will copy the given value only for the first tooth and the remaining will be blank Shown below is a part of the above macro Dim i As Integer 0 If Sheet1 CheckBox2 Value False Then 25 Do sheet2 Cells 7 i 2 Sheet1 Range E37 sheet2 Cells 7 i 2 Interior Colorindex xlNone 1 Loop Until i Sheet1 Range F29 Value Else sheet2 Cells 7 2 Sheet1 Range E37 End If i 0 If Sheet1 CheckBox3 Value False Then Do sheet2 Cells 7 i 3 Sheet1 Range E38 sheet2 Cells 7 i 3 Interior Colorlndex xINone i i
46. er under investigation similar to labyrinth eye seal study Operating conditions have a major influence on effective cross coupling stiffness for the balance piston labyrinth as shown in Figure 4 13 and 4 14 For synchronous assumption magnitude of excitation exponentially increases with rotor speed and directly increases with swirl ratio Qe for the impeller 1 labyrinth eye seal at a constant speed of 21662 rpm equals 2735 lbf in whereas for the balance piston seal at the same speed Qes is 6X greater reference case This eccentric behavior of the balance piston labyrinth could be due to high inlet pressure and an increase in number of axial teeth compared to eye seal However for non synchronous assumption with increase in rotor speed or swirl ratio increases only gradually 45100 40100 35100 30100 25100 20100 15100 10100 5100 100 9 Synchronous Qe Ibf in 0 5000 10000 15000 20000 25000 30000 Rotor Speed RPM Figure 4 13 Influence of Rotor Speed on Effective Cross Coupling Stiffness Balance Piston Labyrinth Seal 55 30000 O API reference case 20000 5 10000 5 0 10000 9 Synchronous Non syn 20000 0 0 2 0 4 0 6 0 8 1 Swirl Ratio Figure 4 14 Influence of Inlet Gas Swirl Ratio on Effective Cross Coupling Stiffness Balance Piston Labyrin
47. erior Colorlndex 24 sheet2 Range B7 E7 Interior Pattern xIGray8 sheet2 Range BT ET Interior PatternColorlndex 2 Sheet3 Range B5 15 Interior Colorlndex 24 Sheet3 Range B5 15 Interior Pattern xIGray8 Sheet3 Range B5 15 Interior PatternColorlndex 2 Sheets Geometric Parameters Select d End Sub e Edit Chambers button macro This macro is similar to Make all chamber equal to chamber 1 macro It checks for missing geometric parameters and prompts the user if any data is missing checks for check marks and if check mark is present then colors the column grey dummy in the Geometric Parameter table Unlike the Make all chambers equal macro it does not copy or delete any data from the table In a nut shell the edit chamber macro checks for any changes or missing data and opens the Geometric Parameter sheet Sample of the code is shown below 27 Private Sub CommandButton5 Click If Sheet1 Range E37 Then MsgBox Please enter a value for Tooth Height GoTod End If If Sheet1 Range E38 Then MsgBox Please enter a value for Tooth Spacing GoTo d End If Dim i As Integer i 0 If Sheet1 CheckBox2 Value False Then Do Sheet2 Cells 7 2 Sheet1 Range E37 Sheet2 Cells 7 i 2 Interior Colorindex i i 1 Loop Until i Sheet1 Range F29 Value Else Sheet2 Cells 7 2 Sheet1 Range E37 End If shading for radial before laby Sheet1
48. fluence of Mole Weight on Effective Cross Coupling Stiffness Balance Piston Labyrinth Seal 59 CHAPTER 5 Results and Conclusion 5 1 LabyXL Pre and Post Processor Summary and Validation A preprocessor and post processor for Labyrinth seal analysis program using Microsoft Excel s visual basic application is developed herein The LabyXL has two versions SI and English To demonstrate application of LabyXL API stability survey labyrinth seals are modeled and a parametric study is performed Capabilities of LabyXL are summarized below 1 The program is capable of importing and generating a data file It provides a table for Geometric Parameters and Speed Case Parameters for easy understanding and data input 2 The program generates a leak path geometric diagram to better model the labyrinth seal 3 Gas property section provides a viscosity and temperature calculator for converting centipose units to Lbm Ft s and Fahrenheit to Rankine respectively 4 Labyrinth options section provides a field for input sheet name and path for easy location of data sheet generated 5 Post Processor macro imports results from output text files into tables for data analysis 6 In addition it generates several plots for better analysis 60 To validate LabyXL pre and post processor ability to generate accurate data file and import results from output file LabyXL results are compared with DYNLAB results DYLAB is an older version
49. fluence of various operating conditions and gas properties on excitation force effective cross coupling stiffness a parametric study is performed on both the eye seal and the balance piston labyrinth seal ACKNOWLEDGMENTS I would like to express my deepest gratitude to my academic and research advisor Dr Kirk for giving me the opportunity for pursuing a master in science and moreover for his guidance and constant support through all the stages of this research This journey would not have to possible without him and hence I would also like to thank him for being the chairman of my graduate committee I would also like to thank Dr Mary E Kasarda and Dr Daniel J Inman for serving on my graduate committee I would like to take this opportunity to extend my sincere thanks to Dr Zenglin Guo and Ali Alsaeed for their continuous support through my research I would like to acknowledge the Members of the Rotor Dynamics Laboratory Affiliates Group for sponsoring this research Last but not the least I am greatly indebted to my parents and my brother for their unending help and encouragement throughout my career I would also like to thank my friend Neha Choudhary whose cheerful support made it possible iii TABLE OF CONTENTS Abstract EET AckiowledementS su dev dee oeste eo a star IS taka LTS OF T P Nomenclature Chapter 1 INTRODUCTION AND LITERATURE REVIEW
50. gram the DYNLAB s MS DOS based interface is gradually becoming obsolete with the recent advances in computer technology Thus a compatible user friendly and easy to use user interface was much needed This research has developed an easy to use Microsoft Excel visual basic based pre and post processor for the above mentioned program Furthermore the front end incorporates a leak path geometric diagram for visual analysis of labyrinth leak path and tooth location In addition a parametric study is performed on eye seal and balance piston labyrinth seal shown in Figure 1 1 Figure 1 1 Typical compressor labyrinth configuration 14 1 2 Literature Alford 1 identified labyrinth seal has a destabilizing effect on rotor whirl He considered two aerodynamic forces being the cause of the self excitation of the rotor whirl One is due to circumferential variation of static pressure within the labyrinth cavity and another exciting force being due to eccentricity of rotor causing circumferential variation of blade tip clearance Alford further explained that due to these forces whirl occurs in direction of rotation at systems natural frequency He concluded that by providing adequate stiffness to rotor and or to rotor support whirl is reduced considerably Alford also concluded that Labyrinth seals having minimum flow at inlet are more desirable and stable then having minimum flow clearance at discharge Since Alford several authors have wo
51. iles dat dat All Files If fileToOpen False Then Exit Sub End If Open file ToOpen For Input As 1 Line Input 1 d Line Input 1 e Sheet1 Range E79 fileToOpen Sheet1 TextBox1 Value Mid A 1 80 Sheet1 TextBox3 Value 1 80 Sheet1 Range F15 Mid e 51 10 If Mid e 70 1 1 Then Sheet1 OptionButton2 Value True Else Sheet1 OptionButton1 Value True End If If bbb Mod 7 0 And bbb lt gt 0 And bbb lt gt Mid f 59 2 Then Line Input 1 0 End If e Reset Data Fields The Reset Data Fields macro prompts the user by opening a message box displaying ALL FIELDS RESET Click OK to continue or Cancel to quit If the user clicks on Cancel then the macro ends but if the user clicks on OK then the macro erases all the data fields The full macro could be found under Main Sample of the code is shown below Private Sub CommandButton4 Click 23 response MsgBox All FIELDS RESET click OK to continue or cancel to QUIT vbOKCancel If response vbOK Then GoTo A Else GoTo d End If A Sheet1 TextBox1 Value ClearContents Sheet1 TextBox2 Value ClearContents Sheet1 TextBox3 Value ClearContents Range E50 E52 ClearContents Range E45 E52 ClearContents Range I45 149 ClearContents Sheet3 Range B5 15 Interior ColorIndex 24 Sheet3 Range B5 15 Interior Pattern xIGray8 Sheet3 Range B5 15 Interior PatternColorlndex 2
52. l 57 1000 500 P 0 g s 500 1000 1500 9 Synchronous 2000 0 5000 10000 15000 20000 25000 Rotor Speed N Ncr Figure 4 17 Influence of Ncr and N on Effective Cross Coupling Stiffness by setting Balance Piston Labyrinth Seal Figure 4 18 show influence of temperature on effective cross coupling stiffness for the balance piston labyrinth seal refer to Table 4 1 for seal parameters For synchronous assumption with temperature has an inverse exponential relationship However for the non synchronous assumption decreases gradually as temperatures increases Figure 4 19 show influence of mole weight on for the balance piston labyrinth seal For synchronous and non synchronous assumption increases with mole weight However for synchronous assumption Qesr increases predominantly 58 80000 70000 60000 50000 40000 8 30000 20000 10000 API reference case 9 Synchronous Non Sync Ibf in 250 450 650 850 1050 Temperature Rankine Figure 4 18 Influence of Temperature on Effective Cross Coupling Stiffness Balance Piston Labyrinth Seal 30000 25000 _ 79 Synchronous non syn 20000 15000 Qe Ibf in 10000 COAPI reference case 0 20 22 24 26 28 30 32 34 Mole Weight Figure 4 19 In
53. lature for LabyXL Appendix C Comparison of LabyXL results with API survey results iv Figure 1 9 25 229 2 3 2 4 2 5 2 6 25 2 8 2 9 2 10 2 12 2 13 2 14 2 15 2 16 3 4 1 4 2 4 3 4 4 4 5 LIST OF FIGURES Caption Typical compressor labyrinth configuration 14 Comparison of seal models 16 krpm Pr 0 403 12 Input field color chart Control Parameters Geometrical Parameters Geometric Parameter Table Gas Properties Gas Properties Table Labyrinth Options Run button Save Data File Application box Leak Path Geometric Diagram Plot of Swirl Vs Chamber Plot of Area ASL ARL and HYD DIA Vs Chamber Plot of Effective Damping amp Stiffness Vs Speed Cases Plot of Mach No Vs Tooth Plot of Temperature Vs Chamber Plot of Pressure Vs Chamber Process Flowchart API survey results for Normalized Destabilizing Force compared with LabyXL Synchronous RM syn and Non synchronous RM non results Influence of Rotor Speed on Effective Cross Coupling Stiffness Influence of Inlet Gas Swirl Ratio on Effective Cross Coupling Stiffness Influence of Pressure Ratio on Effective Cross Coupling Stiffness Influence of Rotor Natural Frequency by setting Rotor Speed Constant on Effective Cross Coupling Stiffness E NO o oco N 49 49 50 50 Figure 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 1 1 B 1
54. lines are provided for remarks necessary for the proper labeling of the data set The four input sections are discussed in the following section calor cade data must be entered default usually used value as entered at bop of this page values from main sheet input Figure 2 1 Input field color chart 1 Control Parameters Control Parameters are the parameters required to run the Labyrinth seal analysis it includes the following variables e The Speed of the Rotor in RPM Number of cases to run Range 1 to 10 cases e Type of Whirl o Synchronous Non Synchronous e Labyrinth Series o All axial chambers Refer to Figure B 3 in Appendix B o Radial chambers before and or after the Laby Refer to Figure B 4 in Appendix B o Radial chambers after the Laby Refer to Figure B 5 in Appendix B e Labyrinth Type Tooth Orientation Refer to Figure B 6 in Appendix B o Tooth on Stator o Tooth on Rotor o Interlocking e Step Shafting Data o The Step shafting Pressure Option Refer to Figure B 7 in Appendix B o The number of iterations on swirl for Stepped Shafting and for Temperature Calculation Control Parameters Rotor Speed in RPM Type of Whirl Number of cases to run Labyrinth Series Non Synchronous Ca Tp Ld Labyrinth Radial Chambers Before And r After The Laby Toothon Stator Radial Chambers After The Laby C Tooth on Rotor Interlocki Stepped Shafting erlocking
55. ll surface constants equal for all chambers Thus if a check mark is placed in the checkbox then the program will use a default value as indicated A different value for surface constants could also be used by not placing a checkmark in the checkbox provided and entering the desired value in the Geometric Parameter table shown in Figure 2 4 The Chamber 1 section of the Geometrical Parameter section consists of tooth geometry of chamber 1 refer to Figure B 2 in Appendix B It consists of the following variables Tooth Height Tooth Spacing Tooth Clearance Shaft Radius By placing a checkmark in the checkbox next to any geometric variable and clicking the Make all chamber equal to chamber 1 button makes that variable value equal for all chambers in the geometric parameter table shown in Figure 2 4 10 Surface Constants YNR YMR YNS Default 0 079 Default 0 25 Default 0 079 0 25 0 0010 0 1000 0 3300 5 4100 0 079 D 0 079 4 250 0 0010 0 1000 0 1000 5 4100 0 079 i 0 079 2 250 Figure 2 4 Geometric Parameter Table By clicking on the Edit Chamber button shown in Figure 2 3 chamber parameters can be edited Edit chamber button will open the Geometric Parameter table shown in Figure 2 4 The table consists of 50 chamber parameters with the above variables associated with each chamber 3 Gas Properties Figure 2 5 shows gas property parameters This section is further
56. nately has a drawback of computational time Bulk flow programs on the other hand can perform analysis in few seconds but with reasonable accuracy Bulk flow continues to be used for day to day lateral rotordynamic stability analysis in the industry 12 Guo and Kirk 13 in 2005 utilized a commercial CFD program CFX TASCFlow to calculate leakage and rotordynamic force components of a labyrinth seal The leakage results on comparison with DYNLAB results showed good agreement whereas prediction of the destabilizing force by DYNLAB was pessimistic as compared to TASCFlow CHAPTER 2 Pre and Post Processor Capabilities and Layout A preprocessor and post processor for a Labyrinth seal analysis code written by Dr Kirk is developed to meet industry needs The processor design utilizes Excel s Visual Basic for Application functions and macros The preprocessor is designed in a simple Excel spreadsheet to facilitate easy data entry of labyrinth geometry and gas properties It exports the data entered in to a fixed format text file and feeds the file to the FORTRAN based program DYNLAB The post processor imports the output file generated by DYNLAB into tables and generates plots to analyze the results This chapter covers the capabilities and describes the pre and post processor layout The programming involved in designing the processors is discussed in chapter 3 The preprocessor is comprised of three worksheets Main Geometric Parameters
57. ngs of a workshop held at Texas A amp M University pp 189 212 17 Wyssmann H Pham T and Jenny R 1984 Prediction of Stiffness and Damping Coefficients for Centrifugal Compressor Labyrinth Seals Journal of Engineering for Gas Turbines and Power 106 920 926 18 Childs D W 1993 Turbomachinery Rotordynamics John Wiley amp Sons New York p 290 354 19 Childs D W Scharrer J K 1984 An Iwatsubo Based Solution for Seals Comparison to Experimental Results Journal of Engineering for Gas Turbines and Power 325 331 20 Kirk R G 1985 Evaluation of Aerodynamic Instability Mechanism for Centrifugal Compressor ASME paper 85 DET 147 Presented at Design Engineering Vibration Conference Cincinnati Ohio 21 Athavale M M and Przekwas A J SCISEAL Manual 1995 SCISEAL A Computer Program for Study of Fluid Dynamic Forces in Seals Developed under contract by NASA Lewis Research Center NAS3 25644 22 Kocur A J Nicholas C J Lee C C Surveying Tilting Pad Journal Bearing And Gas Labyrinth Seal Coefficients and their Effect on Rotor Stability Proceedings of the thirty sixth Turbomachinery Symposium 2007 64 APPENDIX A Example Input Data File for 8 speed cases 65 Sample Input File The sample input file is a text file generated by the Labyrinth Seal Analysis program sample of this data file is shown in Figure 1 Virginia Tech Rotor Lab CFD Evaluation 1
58. ns that are stored in a Microsoft Visual Basic module and can be run whenever user needs to perform a task LabyXL program spreadsheet comprises of preprocessor and post processor macros in form of check box text box option buttons and command buttons This chapter illustrates preprocessor and post processor macros and serves as a technical user s manual 3 1 Preprocessor Macros The preprocessor macros are formulated to provide a user friendly interface for easy data entry Input data is processed into an output fixed format data file which serves as an input data file for DYNLAB A schematic representation of the process is shown in Figure 3 1 The post processor starts after the Run Labyseal button and includes the geometric leak path diagram as seen in the flowchart Likewise the preprocessor is comprised of everything above the Run Labyseal button Input fields process macros and results are represented by parallelograms rectangle and display symbol respectively 2 e Start Main Sheet Import Data File Control Geometric Gas Parameters Parameter Properties section section section Input i Surface i Chambers Chamber 1 2 constant type Start tooth description soptions whirl etc end constants I Y Equal Chamber Edit Chamber All Equal Viscosity button button Case button Calculator from centipose
59. of LabyXL which uses an obsolete FORTRAN based preprocessor with limited functions Impeller 1 eye labyrinth seal modeled in chapter 4 is used to perform the validation Table 5 1 show results of LabyXL for dynamic coefficients compared with results of DYNLAB output file The comparison is in excellent agreement Table 5 1 Comparison of LabyXL and DYNLAB results for API Impeller 1 eye seal synchronous case Stiffness Ibf in Damping Ibf sec in Cxx Processor Kyx Kyy Cyx Cyy 641 06 2 0793 LabyXL Ibf in 2 0793 2734 6 Qe 641 06 2 0793 2 0793 27 DYNLAB 34 59 5 2 Parametric Study Conclusions and Recommendations The following conclusions and recommendations can be made from the parametric study performed on API impeller 1 eye seal and balance piston labyrinth seal e Rotor speed and swirl ratio have a major influence on Qe in both cases Moreover for balance piston labyrinth the effects are magnified e A small decrease in swirl ratio can significantly reduce the excitation for both cases Thus placing radial chambers or swirl brakes 16 before the axial chambers is recommended 61 It is apparent from comparing both cases that longer the labyrinth seals greater the excitation At high inlet pressure as in case of balance piston high pressure drop is desirable Whereas for low pressure at inlet as in c
60. pressors Proc Rotordynamic Instability Problems in High Performance Turbomachinery NASA CP 2133 Texas A amp M University pp139 167 3 Scharrer J K 1987 Theory versus Experiment for the Rotordynamic Coefficients of Labyrinth Gas Seals Part I A Two control Volume Model Proc ASME 11th Biennial Conference on Mechanical Vibration and Noise Rotating Machinery Dynamics Volume Two pp411 426 4 Childs D W Scharrer J K 1987 Theory versus Experiment for the Rotordynamic Coefficients of Labyrinth Gas Seals Part II A Comparison to Experiment Proc ASME 11th Biennial Conference on Mechanical Vibration and Noise Rotating Machinery Dynamics Volume Two pp427 434 5 Kirk G 1988 Evaluation of Aerodynamic Instability Mechanisms for Centrifugal Compressors Part II Advanced Analysis Journal of Vibration Acoustics Stress and Reliability in Design 110 2 pp 207 212 6 Kirk R G 1990 A Method for Calculating Labyrinth Seal Inlet Swirl Velocity ASME J Vibration and Acoustics 112 3 pp 380 383 7 Kirk R G K V S Raju and K Ramesh 1999 PC Based Analysis of Turbomachinery Vibration The Shock and Vibration Digest 31 6 pp 449 454 8 Kirk R G Guo Z Calibration of Labyrinth Seal Bulk Flow Design Analysis Prediction to CFD Simulation Results Proc IMechE Eighth International Conference on Vibrations in Rotating Machinery Swansea UK 2004 9 Rhode D L Hensel S J
61. rked on theories for calculation of labyrinth seal coefficients Benckert and Wachter 16 presented formulas for lateral forces due to shaft rotation and inlet swirl which they developed through experiments Their discussion included the effects of operational conditions such as differential pressure speed inlet flow conditions and geometry of labyrinth seal on the spring characteristics of labyrinth seals They asserted the fact that lateral forces resulting out of labyrinth cavities have to be accounted for in rotor dynamics and they permit a more accurate stability analysis Benckert further concluded that by placing swirl web brakes upstream of the labyrinth effectively reduces the inlet swirl and in turn reduces the lateral force sensitivity Iwatsubo 2 performed theoretical analysis to evaluate the instability forces of labyrinth seals in turbomachinery He extended the fundamental equation proposed by Kostyuk 1972 to consider the variation of chamber cross section but he neglected the area derivative in circumferential direction Iwatsubo wrote continuity and momentum equation to define the average circumferential velocity within a labyrinth chamber His experimental studies showed that the fluid in the labyrinth cavity forms a continuous vortex and flows in circumferential direction In addition Wyssmann et al 17 also presented a theory for calculation of stiffness and damping coefficients for centrifugal compressor labyrin
62. seno 000 00E 00 00 00E 00 amp Format Sheet3 Range G 8 4 000 00E 00 00 00E 00 Format Sheet3 Range H amp 4 caseno 000 00E 00 00 00E 00 amp Format Sheet3 Range amp 4 caseno 000 00 00 00 00 00 amp Format Sheet3 Range J amp 4 000 00E 00 00 00E 00 amp Format Sheet3 Range K 8 4 000 00E 00 00 00E 00 amp Format Sheet3 Range L amp 4 caseno 000 00E 00 00 00E 00 amp Format Sheet3 Range M amp 4 caseno 000 00E 00 00 00E 00 caseno caseno 1 Loop Close 1 MsgBox Successfull Data File saved amp filename 3 2 Post Processor Macros LabyXL s post processor is developed to model the labyrinth seal accurately and to study influence of change in various parameters The post processor generates a gas leak path graph with tooth location for the user to visualize the labyrinth geometry Furthermore it imports and tabulates the results and generates six different graphs to better analyze the results The post processor comprises of two major macros Geometric Diagram macro and Run Labyseal macro Geometric Diagram macro The macro automatically generates the leak path and tooth location of the labyrinth seal Stator and rotor boundaries formulate the leak path Table 3 1 gives the detail calculations for X and Y axis coordinates for both stator and rotor boundary points Labyrinth teeth for K amp C c
63. sonance or critical 48 condition and Qe results in a negative value and further decreases as rotor speed and increase 3730 3230 2730 2230 1730 Cc Synchronous 730 m Non Syn O API reference case Qe Ibf in 230 0 5000 10000 15000 20000 25000 30000 Rotor Speed RPM Figure 4 2 Influence of Rotor Speed on Effective Cross Coupling Stiffness 4500 Q API reference case 2500 T 500 9 Synchronous 1500 Non syn 3500 5500 0 0 2 0 4 0 6 0 8 1 Swirl Ratio Figure 4 3 Influence of Inlet Gas Swirl Ratio on Effective Cross Coupling Stiffness 49 3730 3230 2730 2230 1730 1230 730 230 Qe Ibf in Q API reference case Synchronous m Non Sync 0 4 0 5 0 6 0 7 0 8 0 9 1 Pressure Ratio Pinet 1548 psi Figure 4 4 Influence of Pressure Ratio on Effective Cross Coupling Stiffness 3730 3230 2 2730 2230 1730 1230 730 230 m Qe N 21662 rpm e Synchronous 0 2000 4000 6000 8000 Qar reference case m Non Syn 10000 12000 14000 Ncr RPM Figure 4 5 Influence of Rotor Natural Frequency by setting Rotor Speed Constant on Effective Cross Coupling Stiffness 50 1000 Qe Ibf in 1500
64. sults B Adds a new series to the active chart ActiveChart SeriesCollection NewSeries Loop ActiveChart SeriesCollection casenum Delete Labels the X Y axis and the title With ActiveChart HasTitle True ChartTitle Characters Text Pressure Vs Chamber Axes xlCategory xlPrimary HasTitle True Axes xlCategory xlPrimary AxisTitle Characters Text Chamber Axes xlValue True Axes xlValue xlPrimary AxisTitle Characters Text Pressure End With With Active Chart HasAxis xlCategory xlPrimary True HasAxis xlValue xlPrimary True End With ActiveChart Axes xlCategory xlAutomatic Set rngi Sheet5 Range I50 P66 With Sheet5 ChartObjects 3 42 Places the chart at the right position with the right size Top rngi Top Left rngi Left Width rngi Width Height rngi Height End With End Function The Run Labyseal macro ends after calling the TempPlot and PressPlot functions 43 CHAPTER 4 Parametric Study Parametric study plays a vital role in understanding influence of various factors governing the dynamics of a system The objective of this parametric study 1s to examine influence of different operating conditions and gas properties on effective cross coupling stiffness Effect of synchronous and non synchronous rotor whirl on parameters of major influence is also examined Investig
65. th Seal Effect of pressure ratio Pr variation in Figure 4 15 for non synchronous type of case on has minimal influence However for synchronous type of case instead of Qe decreasing with increase in Pr as in the case of Impeller 1 labyrinth eye seal radically increases Figure 4 16 show results of variation of by setting rotor speed N constant at 21662 rpm A similar trend to eye seal Figure 4 5 is observed here except Qesr for non synchronous case remains constant and both curves cross each other at a higher Ncr Likewise Figure 4 17 show results of variation of Ncr and N by setting both equal On comparing the results with eye seal Figure 4 6 adverse influence on is observed 56 35000 30000 Synchronous _ 25000 Non Sync amp 20000 2 15000 10000 5000 reference case 0 0 2 0 4 0 6 0 8 Pressure Ratio Pintet 3035 psi Figure 4 15 Influence of Pressure Ratio on Effective Cross Coupling Stiffness Balance Piston Labyrinth Seal 25000 9 Synchronous 20000 Non Syn 15000 N 21662 rpm 9 10000 5000 0 reference case 0 2000 4000 6000 8000 10000 12000 14000 RPM Figure 4 16 Influence of Ncr on Effective Cross Coupling Stiffness by setting N constant Balance Piston Labyrinth Sea
66. th Synchronous LS 11 and Non synchronous LN 15 LabyXL results 76 300 0 250 0 200 0 150 0 100 0 11 flo 4 amp 5 6 8 Bao 10 ls 12 13 14 LN 20 21 22 amp 23 04 25 11 15 Respondents Qe Ibf s x 10 o Qe Ibf in x 10 Figure C 3 Survey Results for Balance Piston labyrinth seal compared with Synchronous LS 11 and Non synchronous LN 15 LabyXL results Gimp 1 B Imp 5 15 amp 23 24 Respondents Figure 4 LabyXL results Synchronous LS and Non synchronous LN compared with API Survey Results for all three Labyrinths T
67. th seals based on turbulent flow calculations Unlike Iwatsubo s one control volume model Wyssmann et al 17 proposed two control volume model for circumferential flow in a labyrinth chamber One control volume is for throughflow regime the other is for the vortex region between labyrinth teeth 18 p 344 Wyssmann et al 17 studied the influence of labyrinth geometry operating conditions and mole weight on labyrinth cross coupling stiffness He concluded that labyrinth coefficients are strongly dependent on tooth height and inlet swirl velocity Childs and Scharrer 19 extended Iwatsubo s theories and compared it to experimental results of Benckert and Wachter 16 The model developed gave results that were within 25 of the experimental results This discrepancy could have been due to known uncertainty in Wachter and Benckert experimental results Their results included only the influence of entry swirl and not the rotating shaft on cross coupling stiffness However the model was only valid for see through type of labyrinth seal since the model fared very poorly in comparison with interlocking and grooved seal data Kirk 20 developed a labyrinth analysis program DYNLAB based on theories of Iwatsubo and Scharrer with several important extensions and modifications in the derivation of the perturbation equations Furthermore he compared the results of DYNLAB to full load shop test data and Childs 19 computer program results
68. ty on Effective Cross Coupling Stiffness 52 Qe Ibf in Synchronous 12 1 3 1 4 1 5 Specific Heat Ratio 1 6 1 7 Figure 4 9 Influence of Specific Heat Ratio on Effective Cross Coupling Stiffness 3730 3230 2730 2230 1730 1230 730 230 API reference case Qe Ibf in 9 Synchronous 100 200 300 400 500 Absolute Velocity Ft sec 600 Figure 4 10 Influence of Absolute Velocity of Gas on Effective Cross Coupling Stiffness 23 3730 3230 2730 2230 1730 1230 730 230 0 15 0 2 0 25 0 3 Specific Heat BTU Ibm R Qe Ibf in Synchronous Figure 4 11 Influence of Specific Heat on Effective Cross Coupling Stiffness 3500 Q API reference case 3000 2 2500 9 2058 pas T ROTE T 9 Synchronous 1977 non syn 1000 20 22 24 26 28 30 32 34 Mole Weight Figure 4 12 Influence of Mole Weight on Effective Cross Coupling Stiffness 54 4 3 Influence of Various Parameters of Balance Piston Labyrinth Seal on Effective Cross Coupling Stiffness Effects of operating conditions and gas properties on effective cross coupling stiffness are investigated here by using API s Balance Piston labyrinth seal model parameters in Table 4 1 are held constant except for the paramet

LABYRINTH SEAL PREPROCESSOR AND POST

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