Academia.eduAcademia.edu

Rotordynamic Force Coefficients of Pocket Damper Seals

Profile image of Ahmed GamalAhmed Gamal

2006, Journal of Turbomachinery

visibility

…

description

297 pages

link

1 file

Abstract

This paper presents measured frequency dependent stiffness and damping coefficients for 12-bladed and 8-bladed pocket damper seals (PDS) subdivided into four different seal configurations. Rotating experimental tests are presented for inlet pressures at 69 bar (1000 psi), a frequency excitation range of 20–300 Hz, and rotor speeds up to 20,200 rpm. The testing method used to determine direct and cross-coupled force coefficients was the mechanical impedance method, which required the measurement of external shaker forces, system accelerations, and motion in two orthogonal directions. In addition to the impedance measurements, dynamic pressure responses were measured for individual seal cavities of the eight-bladed PDS. Results of the frequency dependent force coefficients for the four PDS designs are compared. The conclusions of the tests show that the eight-bladed PDS possessed significantly more positive direct damping and negative direct stiffness than the 12-bladed seal. The resu...

Figures (419)

Figure 1. Annular gas Seals in a Straight-Through Compressor dynamic behavior of machines can be predicted.
Figure 1. Annular gas Seals in a Straight-Through Compressor dynamic behavior of machines can be predicted.
1.2 Literature Review
1.2 Literature Review
the top in between the last blade of the PDS and the journal.
the top in between the last blade of the PDS and the journal.
Figure 4. Ransom’s Test rig (Ransom 1998) journal speeds, indicating the benefits of low destabilizing forces in the PDS. Further tests were conducted by Laos (1999), which involved both non-rotating and
Figure 4. Ransom’s Test rig (Ransom 1998) journal speeds, indicating the benefits of low destabilizing forces in the PDS. Further tests were conducted by Laos (1999), which involved both non-rotating and
Figure 5. Rotating Test Rig (Laos 1999) coefficients that possessed the same sign.
Figure 5. Rotating Test Rig (Laos 1999) coefficients that possessed the same sign.
Figure 6. Ball Bearing Test Rig (Ertas and Vance 2004) by one-third the response without the PDS.
Figure 6. Ball Bearing Test Rig (Ertas and Vance 2004) by one-third the response without the PDS.
Figure 7. Twelve Bladed PDS Configurations
Figure 7. Twelve Bladed PDS Configurations
Figure 8. Eight Bladed PDS Configurations
Figure 8. Eight Bladed PDS Configurations
Figure 9. Conventional Six Bladed PDS Configuration
Figure 9. Conventional Six Bladed PDS Configuration
Figure 10. New Fully Partitioned PDS Design
Figure 10. New Fully Partitioned PDS Design
Figure 12. Conventional Six Bladed PDS Blade Modification
Figure 12. Conventional Six Bladed PDS Blade Modification
Table 1. Summarized PDS Geometry and Parameters
Table 1. Summarized PDS Geometry and Parameters
Figure 13. High Pressure Annular Gas Seal Test Rig inlet air is supplied at the center plenum (between the test seals) of the stator assembly.
Figure 13. High Pressure Annular Gas Seal Test Rig inlet air is supplied at the center plenum (between the test seals) of the stator assembly.
Figure 14. High Pressure Test Rig Cross Section (Dawson, 2000)
Figure 14. High Pressure Test Rig Cross Section (Dawson, 2000)
Figure 15. Stator Assembly Isometric View
Figure 15. Stator Assembly Isometric View
Figure 16. Stator Assembly Standard Views
Figure 16. Stator Assembly Standard Views
Figure 17. Dynamic Measurements
Figure 17. Dynamic Measurements
Also note that each force equation has a contribution of direct coefficients and cross- part (determines stiffness) and an imaginary part (determines damping). direction equations of motion. The left hand side of Equations 3.1-3.4 is the effective force
Also note that each force equation has a contribution of direct coefficients and cross- part (determines stiffness) and an imaginary part (determines damping). direction equations of motion. The left hand side of Equations 3.1-3.4 is the effective force
Figure 18. Pseudorandom Force Excitation: 6 Bladed PDS Configurations tests are shown in the Appendix.
Figure 18. Pseudorandom Force Excitation: 6 Bladed PDS Configurations tests are shown in the Appendix.
and Y directions are calculated at each test frequency from the four independent equations. Before determining the test seal coefficients, one must realize that the impedance
and Y directions are calculated at each test frequency from the four independent equations. Before determining the test seal coefficients, one must realize that the impedance
coupling to be destabilizing. The effective damping is defined in Equation 3.19-3.20. Past research on PDS has shown that the cross-coupled stiffness coefficients in the hat for circular orbits the Ky, and Ky, term must be have opposite for stiffness cross- stiffness cross-coupling force component F’, is tangential to the whirl orbit. This implies
coupling to be destabilizing. The effective damping is defined in Equation 3.19-3.20. Past research on PDS has shown that the cross-coupled stiffness coefficients in the hat for circular orbits the Ky, and Ky, term must be have opposite for stiffness cross- stiffness cross-coupling force component F’, is tangential to the whirl orbit. This implies
fhe principle axis shift is illustrated in Figure 23 and Figure 24 shows the resultant conical
fhe principle axis shift is illustrated in Figure 23 and Figure 24 shows the resultant conical
radial component F, is a maximum at points 2, 4, 6, and 8 and zero at points 1, 3, 5, and 7.
radial component F, is a maximum at points 2, 4, 6, and 8 and zero at points 1, 3, 5, and 7.
Figure 26. Same Sign Stiffness Cross-Coupling Force Components
Figure 26. Same Sign Stiffness Cross-Coupling Force Components
Figure 27. Orbit Distortion from Same Sign Stiffness Cross-Coupling
Figure 27. Orbit Distortion from Same Sign Stiffness Cross-Coupling
generated cavity forces into the X and Y directions. Next, the matrix shown in Equatior 3.70-3.71), where F, is the pressure force. It is also important to decompose each pressure L
generated cavity forces into the X and Y directions. Next, the matrix shown in Equatior 3.70-3.71), where F, is the pressure force. It is also important to decompose each pressure L
pressure induced dynamic cavity forces and the vibratory motion (Equations 3.72-3.75). The positive X and Y direction motion is illustrated in Figure 28, and also shown is the 3.69 can be solved for the seal coefficients in the frequency domain as a function of the
pressure induced dynamic cavity forces and the vibratory motion (Equations 3.72-3.75). The positive X and Y direction motion is illustrated in Figure 28, and also shown is the 3.69 can be solved for the seal coefficients in the frequency domain as a function of the
Figure 28. Dynamic Pressure Response to Vibratory Motion
Figure 28. Dynamic Pressure Response to Vibratory Motion
Table 2. Data Acquisition Parameters direction. cavities at the 90 degree location. A shake test at 80 Hz was also performed in the >
Table 2. Data Acquisition Parameters direction. cavities at the 90 degree location. A shake test at 80 Hz was also performed in the >
Figure 29. Experimental Measurements: Pressure Response Method
Figure 29. Experimental Measurements: Pressure Response Method
Figure 30. Structural Baseline Test Set-up two configurations in Table 3.
Figure 30. Structural Baseline Test Set-up two configurations in Table 3.
Table 3. Baseline Test Matrix — Impact Hammer Tests curve fitting the real and imaginary components (Figure 32) of the dynamic stiffness. through the squirrel cages. The second method used to extract stiffness and damping wa:
Table 3. Baseline Test Matrix — Impact Hammer Tests curve fitting the real and imaginary components (Figure 32) of the dynamic stiffness. through the squirrel cages. The second method used to extract stiffness and damping wa:
Figure 31. Structural Compliance of Test Rig Stator Assembly did the damping for certain frequency ranges.
Figure 31. Structural Compliance of Test Rig Stator Assembly did the damping for certain frequency ranges.
Figure 33. Test Rig Vibration Decay summary of the results for the impact hammer tests are shown in Table 4. Table 4. Structural Baseline Coefficients-Impact Hammer Tests
Figure 33. Test Rig Vibration Decay summary of the results for the impact hammer tests are shown in Table 4. Table 4. Structural Baseline Coefficients-Impact Hammer Tests
Table 5. Baseline Impedance Test Matrix The coefficients for these pressurized impedance tests are not only generated from without the squirrel cage is not expected. structural components, but also the fluid pressure forces generated between stator and rotor
Table 5. Baseline Impedance Test Matrix The coefficients for these pressurized impedance tests are not only generated from without the squirrel cage is not expected. structural components, but also the fluid pressure forces generated between stator and rotor
Figure 34. Baseline Direct Coefficients Y Direction-Impedance Method as frequency is increased.
Figure 34. Baseline Direct Coefficients Y Direction-Impedance Method as frequency is increased.
Figure 35. Baseline Cross-coupled Coefficients-Impedance Method
Figure 35. Baseline Cross-coupled Coefficients-Impedance Method
Table 6. Test Matrix-12 Bladed PDS Impedance Method increase with excitation frequency.
Table 6. Test Matrix-12 Bladed PDS Impedance Method increase with excitation frequency.
Figure 36. Twelve Bladed PDS 10,200 rpm: Direct Coefficients Impedance Method Inlet Plenum Pressure 1,000 psi (68.9 bar)
Figure 36. Twelve Bladed PDS 10,200 rpm: Direct Coefficients Impedance Method Inlet Plenum Pressure 1,000 psi (68.9 bar)
Figure 37. Twelve Bladed PDS 15,200 rpm: Direct Coefficients Impedance Method rotor-bearing system.
Figure 37. Twelve Bladed PDS 15,200 rpm: Direct Coefficients Impedance Method rotor-bearing system.
Figure 38. Twelve Bladed PDS: Cross-Coupled Stiffness Coefficients Impedance Method
Figure 38. Twelve Bladed PDS: Cross-Coupled Stiffness Coefficients Impedance Method
Figure 39. Twelve Bladed PDS— Cross-coupled Damping Coefficients Impedance Method inability of cross-coupled damping to directly influence rotordynamic stability. 4.3 Eight Bladed PDS Force Coefficients Experimental results presented in this section are for the eight bladed sea
Figure 39. Twelve Bladed PDS— Cross-coupled Damping Coefficients Impedance Method inability of cross-coupled damping to directly influence rotordynamic stability. 4.3 Eight Bladed PDS Force Coefficients Experimental results presented in this section are for the eight bladed sea
Table 7. Test Matrix-8 Bladed PDS Impedance Method Figures 40-42 display the direct damping and stiffness for all four seals at 10,200
Table 7. Test Matrix-8 Bladed PDS Impedance Method Figures 40-42 display the direct damping and stiffness for all four seals at 10,200
Figure 40. Eight Bladed PDS-Direct Coefficients 10,200 rpm Impedance Method
Figure 40. Eight Bladed PDS-Direct Coefficients 10,200 rpm Impedance Method
Figure 41. Eight Bladed PDS-Direct Coefficients 15,200 rpm Impedance Method
Figure 41. Eight Bladed PDS-Direct Coefficients 15,200 rpm Impedance Method
Figure 42. Eight Bladed PDS-Direct Coefficients 20,200 rpm Impedance Method
Figure 42. Eight Bladed PDS-Direct Coefficients 20,200 rpm Impedance Method
Figure 43. Eight Bladed PDS-Cross-Coupled Stiffness Coefficients Impedance Method
Figure 43. Eight Bladed PDS-Cross-Coupled Stiffness Coefficients Impedance Method
Table 8. Test Matrix-Conventional 6 Bladed PDS Impedance Method
Table 8. Test Matrix-Conventional 6 Bladed PDS Impedance Method
Figure 44. Conventional Six Bladed PDS-Direct Coefficients Impedance Method Inlet Plenum Pressure 1,000 psi (68.9 bar)
Figure 44. Conventional Six Bladed PDS-Direct Coefficients Impedance Method Inlet Plenum Pressure 1,000 psi (68.9 bar)
Figure 45. Conventional Six Bladed PDS-Cross-Coupled Coefficients Impedance Method
Figure 45. Conventional Six Bladed PDS-Cross-Coupled Coefficients Impedance Method
Inlet Plenum Pressure 1,000 psi (68.9 bar) Table 9. Test Matrix-Fully Partitioned 6 Bladed PDS Impedance Method
Inlet Plenum Pressure 1,000 psi (68.9 bar) Table 9. Test Matrix-Fully Partitioned 6 Bladed PDS Impedance Method
Figure 46. FP Six Bladed PDS-Direct Coefficients 10,200 rpm Impedance Method
Figure 46. FP Six Bladed PDS-Direct Coefficients 10,200 rpm Impedance Method
Figure 47. FP Six Bladed PDS-Direct Coefficients 15,200 rpm Impedance Method
Figure 47. FP Six Bladed PDS-Direct Coefficients 15,200 rpm Impedance Method
Figure 48. FP Six Bladed PDS-Cross-Coupled Coefficients 4.6 Comparison of Impedance Test Results
Figure 48. FP Six Bladed PDS-Cross-Coupled Coefficients 4.6 Comparison of Impedance Test Results
Table 10. Configurations Tested Using the Impedance Method
Table 10. Configurations Tested Using the Impedance Method
Figure 49. Direct Damping Coefficients: Impedance Method
Figure 49. Direct Damping Coefficients: Impedance Method
Figure 50. Direct Stiffness Coefficients: Impedance Method
Figure 50. Direct Stiffness Coefficients: Impedance Method
Figure 52. Pront Control Panel: NI 4472-16 Channel Simultaneous DAQ Board
Figure 52. Pront Control Panel: NI 4472-16 Channel Simultaneous DAQ Board
Figure 53. LABVIEW Front Panel-8 Bladed PDS
Figure 53. LABVIEW Front Panel-8 Bladed PDS
Figure 54. Phasor Plot for Diverging and Straight-Through Cavities
Figure 54. Phasor Plot for Diverging and Straight-Through Cavities
Figure 55. Static Seal Cavity Pressure Measurements the following results were linear unidirectional vibration tests based on a single degree of
Figure 55. Static Seal Cavity Pressure Measurements the following results were linear unidirectional vibration tests based on a single degree of
Figure 56. Peak Pressures and Vibration Amplitudes 8 Bladed PDS 1:1 Clr Ratio
Figure 56. Peak Pressures and Vibration Amplitudes 8 Bladed PDS 1:1 Clr Ratio
Figure 57. Stiffness and Damping 8 Bladed 1:1 Clr Ratio
Figure 57. Stiffness and Damping 8 Bladed 1:1 Clr Ratio
Figure 58. Pressure Phase and Force Density: 8 Bladed PDS 1:1 Clr Ratio
Figure 58. Pressure Phase and Force Density: 8 Bladed PDS 1:1 Clr Ratio
Table 12. Cavity Flow Parameters: 8 Bladed 1:1
Table 12. Cavity Flow Parameters: 8 Bladed 1:1
Figure 59. Asynchronous Pressure Frequencies 8 Bladed PDS 1:1 Clr Ratio One major difference between the two cavities is the static pressure, which alsc
Figure 59. Asynchronous Pressure Frequencies 8 Bladed PDS 1:1 Clr Ratio One major difference between the two cavities is the static pressure, which alsc
Figure 60. Stiffness and Damping 8 Bladed 1:1.5 Clr Ratio ~1.2 mils pk-pk amplitudes (1.2 mils and 1.8 mils) are almost identical in magnitude and trend. Vibration and pressure amplitudes for each of the diverging seal test are shown in Figure 62.
Figure 60. Stiffness and Damping 8 Bladed 1:1.5 Clr Ratio ~1.2 mils pk-pk amplitudes (1.2 mils and 1.8 mils) are almost identical in magnitude and trend. Vibration and pressure amplitudes for each of the diverging seal test are shown in Figure 62.
Figure 61. Stiffness and Damping 8 Bladed PDS 1:1.5 Clr Ratio ~1.8 mils pk-pk The stiffness results also show significant change due to the notch. whereas the phase in Figures 63-64 exhibits a weaker dependence on increasing frequency.
Figure 61. Stiffness and Damping 8 Bladed PDS 1:1.5 Clr Ratio ~1.8 mils pk-pk The stiffness results also show significant change due to the notch. whereas the phase in Figures 63-64 exhibits a weaker dependence on increasing frequency.
Figure 62. Peak Pressures and Vibration 8 Bladed 1:1.5 Clr Ratio ~1.2 mils pk-pk
Figure 62. Peak Pressures and Vibration 8 Bladed 1:1.5 Clr Ratio ~1.2 mils pk-pk
Figure 63. Phase and Force Density 8 Bladed PDS 1:1.5 Clr Ratio ~1.2 mils pk-pk
Figure 63. Phase and Force Density 8 Bladed PDS 1:1.5 Clr Ratio ~1.2 mils pk-pk
Figure 64. Phase and Force Density 8 Bladed PDS 1:1.5 Clr Ratio ~1.8 mils pk-pk
Figure 64. Phase and Force Density 8 Bladed PDS 1:1.5 Clr Ratio ~1.8 mils pk-pk
Figure 65. Pressure Spectrum for Diverging 8 Bladed PDS (200 Hz
Figure 65. Pressure Spectrum for Diverging 8 Bladed PDS (200 Hz
Figure 66. Conventional Six Bladed PDS Single Row of Cavities: Transducer Installation static pressure measurements aided in determining discharge coefficients. For determining seal coefficients only the dynamic measurements were used; whereas, the
Figure 66. Conventional Six Bladed PDS Single Row of Cavities: Transducer Installation static pressure measurements aided in determining discharge coefficients. For determining seal coefficients only the dynamic measurements were used; whereas, the
Figure 67. Front Panel Dynamic Measurements Display: 0 Degree Angle X Direction Excitation 40 Hz
Figure 67. Front Panel Dynamic Measurements Display: 0 Degree Angle X Direction Excitation 40 Hz
Figure 69. Dynamic Pressure Phase: 45 Degree Location
Figure 69. Dynamic Pressure Phase: 45 Degree Location
Figure 70. Direct Stiffness and Damping: Cavity Coefficients Conventional Six Bladed PDS
Figure 70. Direct Stiffness and Damping: Cavity Coefficients Conventional Six Bladed PDS
Figure 71. Cavity Coefficients: 0 Degree Position Cross-Coupled Stiffness and Damping
Figure 71. Cavity Coefficients: 0 Degree Position Cross-Coupled Stiffness and Damping
Figure 72. Row Coefficients: 45 Degree Position Cross-Coupled and Direct Stiffness
Figure 72. Row Coefficients: 45 Degree Position Cross-Coupled and Direct Stiffness
Figure 73. Row Coefficients: 45 Degree Position Cross-Coupled and Direct Damping
Figure 73. Row Coefficients: 45 Degree Position Cross-Coupled and Direct Damping
Figure 74. Conventional 6 Bladed PDS Y Dir. Direct Coefficients- Pressure Method
Figure 74. Conventional 6 Bladed PDS Y Dir. Direct Coefficients- Pressure Method
Figure 75. Conventional 6 Bladed PDS X Dir. Direct Coefficients- Pressute Method
Figure 75. Conventional 6 Bladed PDS X Dir. Direct Coefficients- Pressute Method
Figure 76. Conventional 6 Bladed PDS Y Dir. Cross-Coupled Coefficients-Pressure Method
Figure 76. Conventional 6 Bladed PDS Y Dir. Cross-Coupled Coefficients-Pressure Method
Figure 77. Conventional 6 Bladed PDS X Dir. Cross-Coupled Coefficients-Pressure Method
Figure 77. Conventional 6 Bladed PDS X Dir. Cross-Coupled Coefficients-Pressure Method
Figure 78. Local Pressure Modulation-Inactive Plenums 2 and 4, 90 and 0 Degrees
Figure 78. Local Pressure Modulation-Inactive Plenums 2 and 4, 90 and 0 Degrees
Figure 79. Local Pressure Modulation-Inactive Plenums 2 and 4, 270 Degrees
Figure 79. Local Pressure Modulation-Inactive Plenums 2 and 4, 270 Degrees
Figure 80. X Direction Excitation- 0 Degree Position 100 Hz
Figure 80. X Direction Excitation- 0 Degree Position 100 Hz
Figure 81. X Direction Excitation- 0 Degree Position 200 Hz
Figure 81. X Direction Excitation- 0 Degree Position 200 Hz
Figure 82. X Direction Excitation- 45 Degree Position 100 Hz
Figure 82. X Direction Excitation- 45 Degree Position 100 Hz
Table 13. Inactive Plenum Pressure Magnitudes
Table 13. Inactive Plenum Pressure Magnitudes
Figure 86. Single Row of Pockets FP 6 Bladed PDS: Pressure Transducer Installation from Figure 80 to Figure 87. higher pressure modulations that are approximately 10 times larger, when comparing results
Figure 86. Single Row of Pockets FP 6 Bladed PDS: Pressure Transducer Installation from Figure 80 to Figure 87. higher pressure modulations that are approximately 10 times larger, when comparing results
Figure 87. Pully Partitioned Seal: Y Direction Excitation 100 Hz -90 Degree Angle Position
Figure 87. Pully Partitioned Seal: Y Direction Excitation 100 Hz -90 Degree Angle Position
Rotordynamic Coefficients Row Values Y Direction Rotordynamic Coefficients Row Values X Direction Figure 88. Front Panel: Data Reduction Fully Partitioned Six Bladed PD
Rotordynamic Coefficients Row Values Y Direction Rotordynamic Coefficients Row Values X Direction Figure 88. Front Panel: Data Reduction Fully Partitioned Six Bladed PD
Figure 89. Stand Alone Cavities- Diverging and Converging Configurations of the five cavities in the 0 degree location.
Figure 89. Stand Alone Cavities- Diverging and Converging Configurations of the five cavities in the 0 degree location.
Figure 90. Phasor Diagram- Stand Alone Cavities
Figure 90. Phasor Diagram- Stand Alone Cavities
direction force coefficients for both the FP design and the conventional design.
direction force coefficients for both the FP design and the conventional design.
Figure 92. Direct Damping-Cavity Coefficients Fully Partitioned Seal 0 Degree Position
Figure 92. Direct Damping-Cavity Coefficients Fully Partitioned Seal 0 Degree Position
Figure 93. Direct Stiffness-Cavity Coefficients Fully Partitioned Seal 0 Degree Position
Figure 93. Direct Stiffness-Cavity Coefficients Fully Partitioned Seal 0 Degree Position
Figure 94. Direct Force Coefficients Y Dir: FP PDS vs. Conventional PDS
Figure 94. Direct Force Coefficients Y Dir: FP PDS vs. Conventional PDS
Figure 95. Direct Force Coefficients X Dir: FP PDS vs. Conventional PDS
Figure 95. Direct Force Coefficients X Dir: FP PDS vs. Conventional PDS
Figure 96. Cross-Coupled Force Coefficients Y Dir: FP PDS vs. Conventional PDS
Figure 96. Cross-Coupled Force Coefficients Y Dir: FP PDS vs. Conventional PDS
Figure 97. Cross-Coupled Force Coefficients X Dir: FP PDS vs. Conventional PDS become positive. Cross-coupled damping coefficients are positive and also possess the sami In the previous sections showing the pressure signals in the time domain, there exists
Figure 97. Cross-Coupled Force Coefficients X Dir: FP PDS vs. Conventional PDS become positive. Cross-coupled damping coefficients are positive and also possess the sami In the previous sections showing the pressure signals in the time domain, there exists
Table 14. Gamal’s Results for Static Direct and Cross-coupled Stiffness (2003) directions. Table 14 summarizes his results.
Table 14. Gamal’s Results for Static Direct and Cross-coupled Stiffness (2003) directions. Table 14 summarizes his results.
Figure 99. Benckert and Wachter’s Test Rig and Experimental Results (1980
Figure 99. Benckert and Wachter’s Test Rig and Experimental Results (1980
Figure 100. Static Pressure Measurements Displacement Pattern: 15,200 rpm
Figure 100. Static Pressure Measurements Displacement Pattern: 15,200 rpm
Table 15. Cavity Pressure Measurements: Rotating Displacement Test Results
Table 15. Cavity Pressure Measurements: Rotating Displacement Test Results
Figure 101. Static Pressure Measurements: Rotor Offset Displacement Tests bottom pocket, Ph is the high inlet pressure and Pb is the lower back pressure.
Figure 101. Static Pressure Measurements: Rotor Offset Displacement Tests bottom pocket, Ph is the high inlet pressure and Pb is the lower back pressure.
Figure 103. Stand-Alone Cavities vs. Sequential Cavities must utilize a coupled analysis between the conservation of mass equations.
Figure 103. Stand-Alone Cavities vs. Sequential Cavities must utilize a coupled analysis between the conservation of mass equations.
Figure 104. Single Row of Three Pressurized Pockets rotor the flow through the seal is in a steady state condition and can be described using
Figure 104. Single Row of Three Pressurized Pockets rotor the flow through the seal is in a steady state condition and can be described using
ras, the enthalpy (Equation 6.9) can be manipulated using the ideal gas law, definitions for
ras, the enthalpy (Equation 6.9) can be manipulated using the ideal gas law, definitions for
A useful parameter to note from Equation 6.19 is the non-dimensional flow coefficient (y) the ideal gas law (6.18) can be written as Equation 6.19. defined in Equation 6.20. The flow coefficient is helpful when determining the choked flow condition across a constriction. Choking through a nozzle or an area constriction occurs
A useful parameter to note from Equation 6.19 is the non-dimensional flow coefficient (y) the ideal gas law (6.18) can be written as Equation 6.19. defined in Equation 6.20. The flow coefficient is helpful when determining the choked flow condition across a constriction. Choking through a nozzle or an area constriction occurs
6.2 Control Volume Analysis for Compressible Flow cavity are calculated using (6.24-6.27) in an iterative method, where C, is the discharge
6.2 Control Volume Analysis for Compressible Flow cavity are calculated using (6.24-6.27) in an iterative method, where C, is the discharge
function of arbitrary rotor displacement.
function of arbitrary rotor displacement.
Figure 107. PDS Cavity Clearance Area for Arbitrary Rotor Displacement
Figure 107. PDS Cavity Clearance Area for Arbitrary Rotor Displacement
Figure 108. Area of a Sector Using Polar Coordinates which is a function of 8, one can calculate the area within the sector using Equation 6.53
Figure 108. Area of a Sector Using Polar Coordinates which is a function of 8, one can calculate the area within the sector using Equation 6.53
Figure 109. PDS Clearance Area for Cavity-Centered Rotor Displacement and the cavity centered displacement amplitude X. Now consider a rotor displacement where the displacement 6 is centered (Equation 6.61)
Figure 109. PDS Clearance Area for Cavity-Centered Rotor Displacement and the cavity centered displacement amplitude X. Now consider a rotor displacement where the displacement 6 is centered (Equation 6.61)
The total flow rate (steady state and dynamic) can be found by expanding Equations 6.64-
The total flow rate (steady state and dynamic) can be found by expanding Equations 6.64-
The resultant dynamic cavity pressures are composed of a sine and a cosine component, as rewrite Equations 6.75-6.77 in the form shown in (6.90-6.92). Substituting the results from Equations 6.84-6.89 into Equations 6.90-6.92 results in Equations 6.93-6.95. Note that
The resultant dynamic cavity pressures are composed of a sine and a cosine component, as rewrite Equations 6.75-6.77 in the form shown in (6.90-6.92). Substituting the results from Equations 6.84-6.89 into Equations 6.90-6.92 results in Equations 6.93-6.95. Note that
The remaining terms from 6.75-6.77 are defined in 6.80-6.83.
The remaining terms from 6.75-6.77 are defined in 6.80-6.83.
Figure 110. Dynamic Cavity Pressures-Theoretical Predications Fully Partitioned PDS
Figure 110. Dynamic Cavity Pressures-Theoretical Predications Fully Partitioned PDS
Table 16. Cases for Fully Partitioned PDS-Variable Pitch Ratio
Table 16. Cases for Fully Partitioned PDS-Variable Pitch Ratio
Figure 111. Direct Damping Coefficients for Varying Pitch Ratios * Axial Pitch Ratio=(Diverging Cavity Axial Pitch) /(Converging Cavity Axial Pitch)
Figure 111. Direct Damping Coefficients for Varying Pitch Ratios * Axial Pitch Ratio=(Diverging Cavity Axial Pitch) /(Converging Cavity Axial Pitch)
Figure 112. Direct Stiffness Coefficients for Varying Pitch Ratios positive direct stiffness at higher frequencies.
Figure 112. Direct Stiffness Coefficients for Varying Pitch Ratios positive direct stiffness at higher frequencies.
Figure 113. Theory vs. Impedance Method: 12 Bladed PDS Direct Damping however do not agree well with the theory.
Figure 113. Theory vs. Impedance Method: 12 Bladed PDS Direct Damping however do not agree well with the theory.
Figure 114. Theory vs. Impedance Method: 12 Bladed PDS Direct Stiffness
Figure 114. Theory vs. Impedance Method: 12 Bladed PDS Direct Stiffness
Figure 115. Theory vs. Impedance Method: 8 Bladed PDS Stiffness and Damping where the experiment starts to deviate away from the theory.
Figure 115. Theory vs. Impedance Method: 8 Bladed PDS Stiffness and Damping where the experiment starts to deviate away from the theory.
Figure 116. Theory vs. Experiments: Conventional 6 Bladed PDS Stiffness and Damping coefficients. the impedance method has higher damping coefficients and lower valued stiffnes:
Figure 116. Theory vs. Experiments: Conventional 6 Bladed PDS Stiffness and Damping coefficients. the impedance method has higher damping coefficients and lower valued stiffnes:
Figure 117. Theory vs. Experiments: FP 6 Bladed PDS Stiffness and Damping
Figure 117. Theory vs. Experiments: FP 6 Bladed PDS Stiffness and Damping
Figure 118. Six Bladed PDS Experimental Results
Figure 118. Six Bladed PDS Experimental Results
Figure 119. Static Cavity Pressure Measurements vs Theory: FP PDS
Figure 119. Static Cavity Pressure Measurements vs Theory: FP PDS
Table 17. Leakage Results for 6 Bladed PDS Configurations
Table 17. Leakage Results for 6 Bladed PDS Configurations
Table 18. Inlet Blade and Exit Blade Discharge Coefficients
Table 18. Inlet Blade and Exit Blade Discharge Coefficients
Curve Fitting Program for Modal Vibration Tests
Curve Fitting Program for Modal Vibration Tests
DOOD ooo
DOOD ooo
Phase Conversion and Complex Number Generation
Phase Conversion and Complex Number Generation
Direct and Cross-Coupled Impedance Calculations (90, 270 Degree position)
Direct and Cross-Coupled Impedance Calculations (90, 270 Degree position)
Direct and Cross-Coupled Impedance Calculations (45, 135, 225, 315 Degree position)
Direct and Cross-Coupled Impedance Calculations (45, 135, 225, 315 Degree position)
Direct and Cross-Coupled Impedance Calculations (0, 180 Degree position)
Direct and Cross-Coupled Impedance Calculations (0, 180 Degree position)
Conversion of Time Data to FFT Magnitudes and Phases (0, 45, 90 degree)
Conversion of Time Data to FFT Magnitudes and Phases (0, 45, 90 degree)
Conversion of Time Data to FFT Magnitudes and Phases (135 degree)
Conversion of Time Data to FFT Magnitudes and Phases (135 degree)
Conversion of Time Data to FFT Magnitudes and Phases (180, 225, 270 degree)
Conversion of Time Data to FFT Magnitudes and Phases (180, 225, 270 degree)
Right Side Element Matrix:
Right Side Element Matrix:
Solution Matrix-Dynamic Pressure Components P:
Solution Matrix-Dynamic Pressure Components P:
Converging Cavities: Dynamic Cavity Pressure and Rotor Vibration
Converging Cavities: Dynamic Cavity Pressure and Rotor Vibration
Cavity Cross-coupled Coefficients
Cavity Cross-coupled Coefficients
Cavity Pressure Phase Respect to X Direction
Cavity Pressure Phase Respect to X Direction
Total Row Cross-coupled Coefficients
Total Row Cross-coupled Coefficients
Cavity Cross-coupled Coefficients
Cavity Cross-coupled Coefficients
Cavity Pressure Phase Respect to Y Direction
Cavity Pressure Phase Respect to Y Direction
Total Row Cross-coupled Coefficients
Total Row Cross-coupled Coefficients
Cavity Cross-coupled Coefficients
Cavity Cross-coupled Coefficients
Cavity Pressure Phase Respect to X Direction
Cavity Pressure Phase Respect to X Direction
Total Row Cross-coupled Coefficients
Total Row Cross-coupled Coefficients
Cavity Cross-coupled Coefficients
Cavity Cross-coupled Coefficients
Cavity Pressure Phase Respect to Y Direction
Cavity Pressure Phase Respect to Y Direction
Total Row Cross-coupled Coefficients
Total Row Cross-coupled Coefficients
Y Direction Cavity Direct Coefficients & X Direction Cavity Cross-coupled Coefficients
Y Direction Cavity Direct Coefficients & X Direction Cavity Cross-coupled Coefficients
X Direction Cavity Direct Coefficients & Y Direction Cavity Cross-coupled Coefficients
X Direction Cavity Direct Coefficients & Y Direction Cavity Cross-coupled Coefficients
Dynamic Cavity Pressure Phase
Dynamic Cavity Pressure Phase
Total Row Coefficients- Y Direction Direct and X Direction Cross-coupled
Total Row Coefficients- Y Direction Direct and X Direction Cross-coupled
Total Row Coefficients- X Direction Direct and Y Direction Cross-coupled
Total Row Coefficients- X Direction Direct and Y Direction Cross-coupled
Y Direction Cavity Direct Coefficients & X Direction Cavity Cross-coupled Coefficients
Y Direction Cavity Direct Coefficients & X Direction Cavity Cross-coupled Coefficients
X Direction Cavity Direct Coefficients & Y Direction Cavity Cross-coupled Coefficients
X Direction Cavity Direct Coefficients & Y Direction Cavity Cross-coupled Coefficients
Total Row Coefficients- Y Direction Direct and X Direction Cross-coupled
Total Row Coefficients- Y Direction Direct and X Direction Cross-coupled
Total Row Coefficients- X Direction Direct and Y Direction Cross-coupled
Total Row Coefficients- X Direction Direct and Y Direction Cross-coupled
Y Direction Cavity Direct Coefficients & X Direction Cavity Cross-coupled Coefficients
Y Direction Cavity Direct Coefficients & X Direction Cavity Cross-coupled Coefficients
X Direction Cavity Direct Coefficients & Y Direction Cavity Cross-coupled Coefficients
X Direction Cavity Direct Coefficients & Y Direction Cavity Cross-coupled Coefficients
Total Row Coefficients- Y Direction Direct and X Direction Cross-coupled
Total Row Coefficients- Y Direction Direct and X Direction Cross-coupled
Total Row Coefficients- X Direction Direct and Y Direction Cross-coupled
Total Row Coefficients- X Direction Direct and Y Direction Cross-coupled
Y Direction Cavity Direct Coefficients & X Direction Cavity Cross-coupled Coefficients
Y Direction Cavity Direct Coefficients & X Direction Cavity Cross-coupled Coefficients
X Direction Cavity Direct Coefficients & Y Direction Cavity Cross-coupled Coefficients
X Direction Cavity Direct Coefficients & Y Direction Cavity Cross-coupled Coefficients
Total Row Coefficients- Y Direction Direct and X Direction Cross-coupled
Total Row Coefficients- Y Direction Direct and X Direction Cross-coupled
Total Row Coefficients- X Direction Direct and Y Direction Cross-coupled
Total Row Coefficients- X Direction Direct and Y Direction Cross-coupled
Cavity Cross-coupled Damping
Cavity Cross-coupled Damping
Cavity Cross-coupled Stiffness
Cavity Cross-coupled Stiffness
Cavity Phase Respect to X direction Excitation
Cavity Phase Respect to X direction Excitation
Total Row Cross-coupled Coefficients
Total Row Cross-coupled Coefficients
Total Row Direct Coefficients
Total Row Direct Coefficients
Cavity Direct Stiffness
Cavity Direct Stiffness
Cavity Cross-coupled Damping
Cavity Cross-coupled Damping
Cavity Cross-coupled Stiffness
Cavity Cross-coupled Stiffness
Cavity Phase Respect to Y direction Excitation
Cavity Phase Respect to Y direction Excitation
Total Row Cross-coupled Coefficients
Total Row Cross-coupled Coefficients
Total Row Direct Coefficients
Total Row Direct Coefficients
Cavity Direct Stiffness
Cavity Direct Stiffness
Cavity Cross-coupled Damping
Cavity Cross-coupled Damping
Cavity Cross-coupled Stiffness
Cavity Cross-coupled Stiffness
Cavity Phase Respect to X direction Excitation
Cavity Phase Respect to X direction Excitation
Total Row Cross-coupled Coefficients
Total Row Cross-coupled Coefficients
Total Row Direct Coefficients
Total Row Direct Coefficients
Cavity Direct Stiffness
Cavity Direct Stiffness
Cavity Cross-coupled Damping
Cavity Cross-coupled Damping
Cavity Cross-coupled Stiffness
Cavity Cross-coupled Stiffness
Cavity Phase Respect to Y direction Excitation
Cavity Phase Respect to Y direction Excitation
Total Row Cross-coupled Coefficients
Total Row Cross-coupled Coefficients
Total Row Direct Coefficients
Total Row Direct Coefficients
Y Direction Direct Damping & X-Direction Cross-coupled Damping
Y Direction Direct Damping & X-Direction Cross-coupled Damping
Y Direction Direct Stiffness & X-Direction Cross-coupled Stiffness
Y Direction Direct Stiffness & X-Direction Cross-coupled Stiffness
X Direction Direct Damping & Y-Direction Cross-coupled Damping
X Direction Direct Damping & Y-Direction Cross-coupled Damping
X Direction Direct Stiffness & Y-Direction Cross-coupled Stiffness
X Direction Direct Stiffness & Y-Direction Cross-coupled Stiffness
Y Direction Direct Coefficients & X-Direction Cross-coupled Coefficients
Y Direction Direct Coefficients & X-Direction Cross-coupled Coefficients
X Direction Direct Coefficients & Y-Direction Cross-coupled Coefficients
X Direction Direct Coefficients & Y-Direction Cross-coupled Coefficients
Y Direction Direct Damping & X-Direction Cross-coupled Damping 6 Bladed Fully Partitioned Seal Cavity Coefficients: 135 Degree Position
Y Direction Direct Damping & X-Direction Cross-coupled Damping 6 Bladed Fully Partitioned Seal Cavity Coefficients: 135 Degree Position
Y Direction Direct Stiffness & X-Direction Cross-coupled Stiffness
Y Direction Direct Stiffness & X-Direction Cross-coupled Stiffness
X Direction Direct Damping & Y-Direction Cross-coupled Damping
X Direction Direct Damping & Y-Direction Cross-coupled Damping
X Direction Direct Stiffness & Y-Direction Cross-coupled Stiffness
X Direction Direct Stiffness & Y-Direction Cross-coupled Stiffness
Y Direction Direct Coefficients & X-Direction Cross-coupled Coefficients
Y Direction Direct Coefficients & X-Direction Cross-coupled Coefficients
X Direction Direct Coefficients & Y-Direction Cross-coupled Coefficients
X Direction Direct Coefficients & Y-Direction Cross-coupled Coefficients
Y Direction Direct Damping & X-Direction Cross-coupled Damping
Y Direction Direct Damping & X-Direction Cross-coupled Damping
Y Direction Direct Stiffness & X-Direction Cross-coupled Stiffness
Y Direction Direct Stiffness & X-Direction Cross-coupled Stiffness
X Direction Direct Damping & Y-Direction Cross-coupled Damping
X Direction Direct Damping & Y-Direction Cross-coupled Damping
X Direction Direct Stiffness & Y-Direction Cross-coupled Stiffness
X Direction Direct Stiffness & Y-Direction Cross-coupled Stiffness
Y Direction Direct Coefficients & X-Direction Cross-coupled Coefficients
Y Direction Direct Coefficients & X-Direction Cross-coupled Coefficients
X Direction Direct Coefficients & Y-Direction Cross-coupled Coefficients
X Direction Direct Coefficients & Y-Direction Cross-coupled Coefficients
Y Direction Direct Damping & X-Direction Cross-coupled Damping
Y Direction Direct Damping & X-Direction Cross-coupled Damping
Y Direction Direct Stiffness & X-Direction Cross-coupled Stiffness
Y Direction Direct Stiffness & X-Direction Cross-coupled Stiffness
X Direction Direct Damping & Y-Direction Cross-coupled Damping
X Direction Direct Damping & Y-Direction Cross-coupled Damping
X Direction Direct Stiffness & Y-Direction Cross-coupled Stiffness
X Direction Direct Stiffness & Y-Direction Cross-coupled Stiffness
Y Direction Direct Coefficients & X-Direction Cross-coupled Coefficients
Y Direction Direct Coefficients & X-Direction Cross-coupled Coefficients
X Direction Direct Coefficients & Y-Direction Cross-coupled Coefficients
X Direction Direct Coefficients & Y-Direction Cross-coupled Coefficients
40 Hz 8 Bladed No Divergence
40 Hz 8 Bladed No Divergence
80 Hz 8 Bladed No Divergence 60 Hz 8 Bladed No Divergence
80 Hz 8 Bladed No Divergence 60 Hz 8 Bladed No Divergence
120 Hz 8 Bladed No Divergence
120 Hz 8 Bladed No Divergence
160 Hz 8 Bladed No Divergence
160 Hz 8 Bladed No Divergence
200 Hz 8 Bladed No Divergence
200 Hz 8 Bladed No Divergence
40 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk)
40 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk)
80 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk) 60 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk)
80 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk) 60 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk)
120 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk) 100 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk)
120 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk) 100 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk)
160 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk) 140 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk)
160 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk) 140 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk -pk)
20 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk) 200 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk-pk)
20 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk) 200 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.2 mils pk-pk)
40 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
40 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
60 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
60 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
80 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
80 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
100 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
100 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
140 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk) 120 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
140 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk) 120 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
180 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk) 160 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
180 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk) 160 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
200 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
200 Hz 8 Bladed Diverging Seal 1:1.5 Clr Ratio (Vibration amp. 1.8 mils pk-pk)
20 Hz 0 Degree Position X Direction Excitation
20 Hz 0 Degree Position X Direction Excitation
40 Hz 0 Degree Position X Direction Excitation
40 Hz 0 Degree Position X Direction Excitation
80 Hz 0 Degree Position X Direction Excitation
80 Hz 0 Degree Position X Direction Excitation
100 Hz 0 Degree Position X Direction Excitation
100 Hz 0 Degree Position X Direction Excitation
140 Hz 0 Degree Position X Direction Excitation
140 Hz 0 Degree Position X Direction Excitation
160 Hz 0 Degree Position X Direction Excitation
160 Hz 0 Degree Position X Direction Excitation
200 Hz 0 Degree Position X Direction Excitation
200 Hz 0 Degree Position X Direction Excitation
40 Hz 0 Degree Position Y Direction Excitation
40 Hz 0 Degree Position Y Direction Excitation
80 Hz 0 Degree Position Y Direction Excitation
80 Hz 0 Degree Position Y Direction Excitation
100 Hz 0 Degree Position Y Direction Excitation
100 Hz 0 Degree Position Y Direction Excitation
140 Hz 0 Degree Position Y Direction Excitation
140 Hz 0 Degree Position Y Direction Excitation
160 Hz 0 Degree Position Y Direction Excitation
160 Hz 0 Degree Position Y Direction Excitation
200 Hz 0 Degree Position Y Direction Excitation
200 Hz 0 Degree Position Y Direction Excitation
20 Hz 45 Degree Position X Direction Excitation
20 Hz 45 Degree Position X Direction Excitation
40 Hz 45 Degree Position X Direction Excitation
40 Hz 45 Degree Position X Direction Excitation
80 Hz 45 Degree Position X Direction Excitation
80 Hz 45 Degree Position X Direction Excitation
100 Hz 45 Degree Position X Direction Excitation
100 Hz 45 Degree Position X Direction Excitation
140 Hz 45 Degree Position X Direction Excitation
140 Hz 45 Degree Position X Direction Excitation
160 Hz 45 Degree Position X Direction Excitation
160 Hz 45 Degree Position X Direction Excitation
200 Hz 45 Degree Position X Direction Excitation
200 Hz 45 Degree Position X Direction Excitation
20 Hz 45 Degree Position Y Direction Excitation
20 Hz 45 Degree Position Y Direction Excitation
40 Hz 45 Degree Position Y Direction Excitation
40 Hz 45 Degree Position Y Direction Excitation
80 Hz 45 Degree Position Y Direction Excitation
80 Hz 45 Degree Position Y Direction Excitation
100 Hz 45 Degree Position Y Direction Excitation
100 Hz 45 Degree Position Y Direction Excitation
140 Hz 45 Degree Position Y Direction Excitation
140 Hz 45 Degree Position Y Direction Excitation
160 Hz 45 Degree Position Y Direction Excitation
160 Hz 45 Degree Position Y Direction Excitation
200 Hz 45 Degree Position Y Direction Excitation
200 Hz 45 Degree Position Y Direction Excitation
20 Hz 90 Degree Position X Direction Excitation
20 Hz 90 Degree Position X Direction Excitation
40 Hz 90 Degree Position X Direction Excitation
40 Hz 90 Degree Position X Direction Excitation
80 Hz 90 Degree Position X Direction Excitation
80 Hz 90 Degree Position X Direction Excitation
100 Hz 90 Degree Position X Direction Excitation
100 Hz 90 Degree Position X Direction Excitation
140 Hz 90 Degree Position X Direction Excitation
140 Hz 90 Degree Position X Direction Excitation
160 Hz 90 Degree Position X Direction Excitation
160 Hz 90 Degree Position X Direction Excitation
200 Hz 90 Degree Position X Direction Excitation
200 Hz 90 Degree Position X Direction Excitation
20 Hz 90 Degree Position Y Direction Excitation
20 Hz 90 Degree Position Y Direction Excitation
40 Hz 90 Degree Position Y Direction Excitation
40 Hz 90 Degree Position Y Direction Excitation
80 Hz 90 Degree Position Y Direction Excitation
80 Hz 90 Degree Position Y Direction Excitation
100 Hz 90 Degree Position Y Direction Excitation
100 Hz 90 Degree Position Y Direction Excitation
140 Hz 90 Degree Position Y Direction Excitation
140 Hz 90 Degree Position Y Direction Excitation
160 Hz 90 Degree Position Y Direction Excitation
160 Hz 90 Degree Position Y Direction Excitation
200 Hz 90 Degree Position Y Direction Excitation
200 Hz 90 Degree Position Y Direction Excitation
20 Hz 0 Degree Position X Direction Excitation
20 Hz 0 Degree Position X Direction Excitation
40 Hz 0 Degree Position X Direction Excitation
40 Hz 0 Degree Position X Direction Excitation
80 Hz 0 Degree Position X Direction Excitation
80 Hz 0 Degree Position X Direction Excitation
100 Hz 0 Degree Position X Direction Excitation
100 Hz 0 Degree Position X Direction Excitation
140 Hz 0 Degree Position X Direction Excitation
140 Hz 0 Degree Position X Direction Excitation
160 Hz 0 Degree Position X Direction Excitation
160 Hz 0 Degree Position X Direction Excitation
200 Hz 0 Degree Position X Direction Excitation
200 Hz 0 Degree Position X Direction Excitation
20 Hz 0 Degree Position Y Direction Excitation
20 Hz 0 Degree Position Y Direction Excitation
40 Hz 0 Degree Position Y Direction Excitation
40 Hz 0 Degree Position Y Direction Excitation
80 Hz 0 Degree Position Y Direction Excitation
80 Hz 0 Degree Position Y Direction Excitation
100 Hz 0 Degree Position Y Direction Excitation
100 Hz 0 Degree Position Y Direction Excitation
140 Hz 0 Degree Position Y Direction Excitation
140 Hz 0 Degree Position Y Direction Excitation
160 Hz 0 Degree Position Y Direction Excitation
160 Hz 0 Degree Position Y Direction Excitation
200 Hz 0 Degree Position Y Direction Excitation
200 Hz 0 Degree Position Y Direction Excitation
20 Hz 45 Degree Position X Direction Excitation
20 Hz 45 Degree Position X Direction Excitation
40 Hz 45 Degree Position X Direction Excitation
40 Hz 45 Degree Position X Direction Excitation
80 Hz 45 Degree Position X Direction Excitation
80 Hz 45 Degree Position X Direction Excitation
100 Hz 45 Degree Position X Direction Excitation
100 Hz 45 Degree Position X Direction Excitation
140 Hz 45 Degree Position X Direction Excitation
140 Hz 45 Degree Position X Direction Excitation
160 Hz 45 Degree Position X Direction Excitation
160 Hz 45 Degree Position X Direction Excitation
20 Hz 45 Degree Position Y Direction Excitation 200 Hz 45 Degree Position X Direction Excitation
20 Hz 45 Degree Position Y Direction Excitation 200 Hz 45 Degree Position X Direction Excitation
40 Hz 45 Degree Position Y Direction Excitation
40 Hz 45 Degree Position Y Direction Excitation
80 Hz 45 Degree Position Y Direction Excitation
80 Hz 45 Degree Position Y Direction Excitation
100 Hz 45 Degree Position Y Direction Excitation
100 Hz 45 Degree Position Y Direction Excitation
140 Hz 45 Degree Position Y Direction Excitation
140 Hz 45 Degree Position Y Direction Excitation
160 Hz 45 Degree Position Y Direction Excitation
160 Hz 45 Degree Position Y Direction Excitation
200 Hz 45 Degree Position Y Direction Excitation
200 Hz 45 Degree Position Y Direction Excitation
20 Hz 90 Degree Position X Direction Excitation
20 Hz 90 Degree Position X Direction Excitation
40 Hz 90 Degree Position X Direction Excitation
40 Hz 90 Degree Position X Direction Excitation
80 Hz 90 Degree Position X Direction Excitation
80 Hz 90 Degree Position X Direction Excitation
100 Hz 90 Degree Position X Direction Excitation
100 Hz 90 Degree Position X Direction Excitation
140 Hz 90 Degree Position X Direction Excitation
140 Hz 90 Degree Position X Direction Excitation
160 Hz 90 Degree Position X Direction Excitation
160 Hz 90 Degree Position X Direction Excitation
200 Hz 90 Degree Position X Direction Excitation
200 Hz 90 Degree Position X Direction Excitation
20 Hz 90 Degree Position Y Direction Excitation
20 Hz 90 Degree Position Y Direction Excitation
40 Hz 90 Degree Position Y Direction Excitation
40 Hz 90 Degree Position Y Direction Excitation
80 Hz 90 Degree Position Y Direction Excitation
80 Hz 90 Degree Position Y Direction Excitation
100 Hz 90 Degree Position Y Direction Excitation
100 Hz 90 Degree Position Y Direction Excitation
140 Hz 90 Degree Position Y Direction Excitation
140 Hz 90 Degree Position Y Direction Excitation
160 Hz 90 Degree Position Y Direction Excitation
160 Hz 90 Degree Position Y Direction Excitation
200 Hz 90 Degree Position Y Direction Excitation
200 Hz 90 Degree Position Y Direction Excitation
TEST RIG CLOSE-UP 12 BLADED PDS
TEST RIG CLOSE-UP 12 BLADED PDS
12 BLADED PDS WITH ASSEMBLY MANDREL
12 BLADED PDS WITH ASSEMBLY MANDREL
BASELINE INSERT
BASELINE INSERT
ROTOR REMOVED: TES RIG SIDE VIEW ROTOR REMOVED: 12 BLADED ASSEMBLY
ROTOR REMOVED: TES RIG SIDE VIEW ROTOR REMOVED: 12 BLADED ASSEMBLY
HYDRAULIC ZONIC SHAKERS
HYDRAULIC ZONIC SHAKERS
SQUIRREL CAGE AND PITCH STABILZERS
SQUIRREL CAGE AND PITCH STABILZERS
PRESSURE TRANSDUCERS: INSTALLED AT 90 DEGREE POSITION
PRESSURE TRANSDUCERS: INSTALLED AT 90 DEGREE POSITION
PRESSURE TRANSDUCERS: INSTALLED AT 270 DEGREE POSITION
PRESSURE TRANSDUCERS: INSTALLED AT 270 DEGREE POSITION

Related papers

General approach to the construction of non-contact seals dynamic characteristics
Тарас Гуменюк

Higher parameters of centrifugal machines are constantly required, such as the pressure of the medium to be sealed and the speed of rotation of the shaft. However, as the parameters increase, it becomes more and more difficult to ensure the effectiveness of sealing. In addition, sealing systems affect the overall safety of equipment operation, especially vibration. Non-contact seals are considered as hydrostatic-dynamic bearings that can effectively dampen rotor oscillations. Models of "rotor-gap seals" system and impulse seals have been studied to assess the effect of these seal systems on the oscillatory characteristics of the rotor. Analytical dependencies are obtained for calculating the dynamic characteristics and stability limits of seals as hydromechanical systems. The proposed general technique makes it possible to purposefully select the design parameters of seals to adjust sealing systems to work in vibration-safe modes due to a targeted increase in the rigidity of non-contact seals are determined. It leads to an increase in the vibration resistance of the centrifugal machine's rotor. Comparison of the results of calculations of frequency characteristics according to the obtained expressions with the data of experimental studies showed that the calculation errors do not exceed 5%, which allows using for practice the obtained dependencies in the calculation and design of centrifugal machines sealing systems with sufficient accuracy.

View PDFchevron_right
Analytical and experimental evaluation of the leakage and stiffness characteristics of high pressure pocket damper seals
Ahmed Mansour

2003

Analytical and Experimental Evaluation of the Leakage and Stiffness Characteristics of High Pressure Pocket Damper Seals.

View PDFchevron_right
Measurements of Rotordynamic Force Coefficients of Metallic Type Brush Seals
pascal jolly

Mechanisms and Machine Science, 2018

The present paper presents experimental measurements of rotordynamic force coefficients for a multistage arrangement of four identical brush seals. The bristles are metallic, with a lay angle of 50 • from radial centerline and have an initial radial interference with the shaft of 0.12 mm. According to a radial feeding groove, two pairs of two seals are tested face to face. The supply pressures are 0.54, 0.82, 1.1, 1.75 and 2.4 MPa, with a discharge pressure of 0.4 MPa. The working fluid is water. The rotor is centered and the operating spinning speeds are 50, 3000 and 6000 rpm. For given working conditions (supply pressure and rotor speed), a set of dynamic excitations (two directions and 8 frequencies), imposed to the rotor, provide complex impedances that are used for identifying rotordynamic force coefficients. Results are discussed in order to highlight the respective impact of rotor speed and supply pressure on brush seals performances.

View PDFchevron_right
Rotordynamic forces in labyrinth seals: Theory and experiment
Manuel Martinez-sanchez

A theoretical and experimental investigation of the aerodynamic forces generated by a single gland labyrinth seal executing a simultaneous spinning/whirling motion has been conducted. A lumped parameter model for a single gland seal with coupling to an upstream cavity with leakage is developed along with an appropriate solution technique. From this theory, it is shown that the presence of the upstream cavity can, in some cases, augment the cross-stiffness and direct damping by a factor of four. The parameters that govern the coupling are presented along with predictions on their influence. A simple uncoupled model is used to identify the mechanisms responsible for cross force generation. This reduced system is nondimensionalized and the physical significance of the reduced parameters is discussed.

View PDFchevron_right
Dynamic Seals Behaviour under Effect of Radial Vibration
Alessandro Tasora

2004

SUMMARY This paper presents the results of experimental and numerical tests on the behaviour of radial lip seals in order to characterize a model of the effects of vibrations and working temperature. Starting validation of the numerical analysis, performed with the Finite Element Method, is obtained measuring the frequency response function (FRF) by using different excitation signals. Seal's lip displacement near the dynamic clearance is measured with a strain gauge transducer in actual operating conditions.

View PDFchevron_right
Modeling and analysis of rotating seal and friction damper; calculation of damper stiffness
Innovative Research Publications

In this paper modeling of rotating seal and friction damper is explained using NX7.5 and ANSYS130x64 software.

View PDFchevron_right
Honeycomb seal effect on rotor response to unbalance
Nicola Mitaritonna

2014

High pressure centrifugal compressors are often equipped with honeycomb seal on balance drum in order to optimize rotordynamic stability. In very high pressures applications (>200 bar) the direct stiffness and damping of the honeycomb seal may reach the same order of magnitude of the journal bearings, thus altering the peak frequency and amplification factor of rotor critical speeds as well as their mode shapes. This phenomenon is ultimately due to the density and viscosity of the gas leakage flowing through the seal, and it has a substantial effect on the rotordynamic behavior of the compressor. According to current standards, aerodynamic seal effects are not necessarily included in the calculation of rotor response to unbalance. For high pressure compressors equipped with a honeycomb seal, the associated aerodynamic effects may have major impacts on rotor critical speeds in terms of frequency, amplitude and amplification factor. A procedure for the calculation of rotor response...

View PDFchevron_right
Numerical Modeling of Fluid-Induced Rotordynamic Forces in Seals With Large Aspect Ratios
Costin Untaroiu

2013

Traditional annular seal models are based on bulk flow theory. While these methods are computationally efficient and can predict dynamic properties fairly well for short seals, they lack accuracy in cases of seals with complex geometry or with large aspect ratios (above 1.0). In this paper, the linearized rotordynamic coefficients for a seal with a large aspect ratio are calculated by means of a three-dimensional CFD analysis performed to predict the fluid-induced forces acting on the rotor.

View PDFchevron_right
Development and Validation of Test Rig for Measurements of Leakage and Rotordynamic Performance of Interlocking Gas Labyrinth Seals
Mauricio Alan

2017

Understanding the rotordynamic and leakage characteristics of gas annular seals is important for the design of efficient and reliable turbomachinery. This work sets the foundation to advance the understanding of gas interlocking labyrinth seals. Data for such seals are vague and scarce in literature. A test rig for interlocking seals is developed and validated via tests for a see-through tooth-on-stator labyrinth seal. Test procedures by Millsaps in 1994 and Wagner et al. in 2009 are adapted. Dynamic forces are integrated from the perturbed pressure fields created inside the seal cavities while precessing the rotor using magnetic bearings. Measurements are made by adapting a test rig at the Turbomachinery Lab at Texas A&M University, previously used in 2006 for a different purpose. The see-through seal has eight stator teeth and a smooth rotor. The rotor has a 75 mm radius, 3 mm tooth height, and 0.2 mm radial clearance. Tests at a rotor speed of 10 kRPM are performed for a range of inlet pressures, pressure ratios, and precession frequencies between 15 and 50 Hz. Forward and backward precessions are imposed. Measured leakage values and rotordynamic coefficients validate the performance of the test rig. Experience showed that differential pressure transducers, a well-machined stator, and precise centering and alignment are required for correct measurements. Two sensors 180° apart from each other in a representative cavity demonstrate the development of a theoretically correct pressure wave inside the seal. All results are repeatable. Static pressure measurements in the seal cavities show pressure dropping linearly across the seal's cavities. Results show frequency-independent rotordynamic coefficients. As noted above, only one of the seal's cavities was provided with dynamic pressure measurements, and the following rotordynamic coefficients apply for that cavity, not the entire seal. Measured negative values of direct stiffness K and crosscoupled damping c confirm the lagging pressure wave is behind the rotor, pushing it radially towards the stator. Positive values of cross-coupled stiffness k and direct damping C counteract each other in the circumferential direction, the former being iii destabilizing. Effective damping Ceff combines the impact of direct damping C and cross-coupled stiffness k. For the cavity chosen, Ceff values are negative, and thus destabilizing in the circumferential direction. Future work involves testing interlocking labyrinth seals and using the test results to benchmark CFD codes. iv DEDICATION To my parents for their love and sacrifice. v ACKNOWLEDGEMENTS I am extremely grateful for the opportunity to work under the supervision of Dr. Dara Childs. The support and confidence he bestowed on me became essential in the completion of this project and in my development as an engineer. His amiability and kindness turned a very challenging project into an enjoyable graduate school experience. I would like to thank Professors Luis San Andrés, and Ray James for kindly serving as committee members and helping in the preparation of this thesis. I would like to express appreciation to Doosan Škoda Power for sponsoring the master's research project on this test rig. Its realization was at all times graciously supported by Zdeněk Kubin, and Dan Hasnedl. Special thanks to Mr. Stephen Phillips for his guidance throughout the project. His insights became key in the design, troubleshooting, and implementation of the test rig. And to Mr. Ray Mathews for assisting with the tools and workspace required on a daily basis. Many thanks to my friend and colleague Andrew Crandall for his selfless help throughout the project, especially in the implementation of a data acquisition system.

View PDFchevron_right
The application of automatic differentiation techniques for the prediction of rotor-dynamic coefficients of labyrinth seals
Jiří Fürst

EPJ Web of Conferences, 2016

The article describes the development of bulk-flow code for the prediction of rotor-dynamic coefficients of labyrinth seals. The code is based on the so-called single control volume approach by Childs and Scharrer [1] and the the forces are evaluated using the automatic differentiation technique. The resulting code is very simple and provides reasonable predictions of stiffness and damping coefficients at short computational time.

View PDFchevron_right

References (33)

  1. Aguilar, R., 2002, "Rotordynamic Analysis of a Pocket Damper Seal Using Circular Orbits of Large Amplitudes," Ph.D. Dissertation, Texas A&M University, College Station.
  2. Alford, J.S., 1965, "Protecting Turbomachinery from Self Excited Rotor Whirl," ASME Journal of Engineering for Power, Vol. 87, No. 4, pp. 333-344.
  3. Benckert , H. and Wachter, J., 1980, "Flow Induced Spring Coefficients of Labyrinth Seals for Application in Rotordynamics," NASA CP-21333, Proceedings of a Workshop on Rotordynamic Instability Problems in High Performance Turbomachinery, Texas A&M University, College Station, pp. 189-212.
  4. Childs, D.W., 1993, Turbomachinery Rotordynamics, John Wiley and Sons, New York.
  5. Childs, D.W. and Hale, K., 1994, "A Test Apparatus and Facitlity to Identify the Rotordynamic Coefficients of High Speed Hydrostatic Bearings," ASME Journal of Tribology, Vol. 116, pp.337-334.
  6. Dawson, M., 2000, "A Comparison of the Static and Dynamic Characteristics of Straight- Bore and Convergent Tapered-Bore Honeycomb Annular Gas Seals," M.S. Thesis, Texas A&M University, College Station.
  7. Droste, M.R., 1995, "Evaluation of Instability Forces of Labyrinth Seals in Turbines or Compressors,"NASA CP No. 2133, Proceedings of a Workshop on Rotordynamic Instability Problems in High Performance Turbomachinery, Texas A&M University, College Station, pp. 139-167.
  8. Ertas, B.H.. and Vance, J.M.., 2004, "Effect of Static and Dynamic Misalignment on Ball Bearing Radial Stiffness," AIAA Journal of Propulsion and Power, Vol. 20, No. 4, July-August, pp. 634-647.
  9. Gamal, A., 2003, "Analytical and Experimental Evaluation of the Leakage and Stiffness Characteristics of High Pressure Pocket Damper Seals," M.S. Thesis, Texas A&M University, College Station.
  10. Hibner, D. and Bansal, P., 1979, "Effects of Fluid Compressibility on Viscous Damper Characteristics," Proceedings of the Conference on the Stability and Dynamic Response of Rotors with Squeeze Film Bearings, University of Virginia, pp. 348-355
  11. Kaneko, S., Takashi, I., Takuro, S., and Shin, I., 2003, "Dynamic Characteristics of Liquid Annular Convergent-Tapered Damper Seals with Honeycomb Roughness Pattern," ASME Transactions of the ASME, Vol. 125, July, pp. 592-599.
  12. Kwanka , K., Ortinger, W., and Steckel, J., 1993, "Calculation and Measurement of the Influence of Flow Parameters on Rotordynamic Coefficients in Labyrinth Seals," Proceedings of a Workshop on Rotordynamic Instability Problems in High Performance Turbomachinery, Texas A&M University, College Station, pp. 121-129.
  13. Laos, H. E., 1999, "Rotordynamic Effect of Pocket Damper Seals," Ph.D. Dissertation, Texas A&M University, College Station.
  14. Li, J., and Vance, J.M., 1995, "Effects of Clearance and Clearance Ratio on Two and Three Bladed TAMSEALS, TRC-Seal-4-95", Turbomachinery Laboratory Research Progress Report, Texas A&M University, College Station.
  15. Li, J., Aguilar, R., San Andrés, L., and Vance, J. M., 2000, "Dynamic Force Coefficients of a Multiple Blade, Multiple-Pocket Gas Damper Seal: Test Results and Predictions," ASME Journal of Tribology, Vol. 122, pp. 317-322.
  16. Li, J., Kushner, F., and DeChoudhury, P., 2002," Experimental Evaluation of Slotted Pocket Damper Seals on a Rotating Test Rig," The 47 th ASME Turbo Expo Land Sea &Air, pp 230- 240.
  17. Li, J., San Andrés, L., and Vance, J. M., 1998, "A Bulk Flow model Analysis of Multiple- Pocket Gas Damper seals," ASME Paper 98-GT-13.
  18. Lucas, M.J., Noreen, R.A., Sutherland, L.C., Cole, J.E., and Junger, M.C., 1997, Handbook of the Characteristics of Turbomachinery Cavities, The American Society of Mechanical Engineers, New York.
  19. Millsaps , K. and Sanchez, M., 1993, "Rotordynamic Forces in Labyrinth Seals: Theory and Experiment," Proceedings of a Workshop on Rotordynamic Instability Problems in High Performance Turbomachinery, Texas A&M University, College Station.
  20. Murphy, B. T., 1984, "Eigenvalues of Rotating Machinery," Ph.D. Dissertation, Texas A&M University, College Station.
  21. Picardo, A., 2003, "High Pressure Testing of See-Through Labyrinth Seals," M.S. Thesis, Texas A&M University, College Station.
  22. Ransom, D., Li, J., San Andrés, L., and Vance, J. M., 1998, "Experimental Force Coefficients for a Two-Bladed Labyrinth Seal and a Four Pocket Damper Seal," ASME Journal of Tribology, Vol. 28, pp. 98-109.
  23. San Andres, L. A., 1985, "Effect of Fluid Inertia on Squeeze Film Damper Force Response," Ph.D. Dissertation, Texas A&M University, College Station.
  24. Sundararajan, P., and Vance, J. M., 1993a, "A Theoretical and Experimental Investigation of a Gas Operated Bearing Damper for Turbomachinery -Part I: Theoretical Model and Predictions," Proceedings of the 14 th Vibration and Noise Conference, Albuquerque, NM, ASME DE-Vol. 60, pp. 67-83.
  25. Sundararajan, P., and Vance, J. M., 1993b, "A Theoretical and Experimental Investigation of a Gas Operated Bearing Damper for Turbomachinery -Part II: Experimental Results and Comparison with Theory," Proceedings of the 14 th Vibration and Noise Conference, Albuquerque, NM, ASME DE-Vol. 60, pp. 85-119.
  26. Vance, J. M., Cardon, B. P., San Andrés, L., and Storace, A. F., 1993, "A Gas Operated Bearing Damper for Turbomachinery," ASME Journal of Engineering for Gas Turbines and Power, Vol. 115, pp. 383-389.
  27. Vance, J. M. and Kirton, A. J., 1975, "Experimental Measurement of the Dynamic Force Response of A Squeeze-Film Damper," Journal of Engineering for Industry, November, pp. 1282-1290.
  28. Vance, J.M., Sharma , A, and Jayakar, N., 2002, "Effect of Frequency and Design Parameters on Pocket Damper Seal Performance," Proceedings of Fluid Structure Interactions, New Orleans, LA, No. 23, pp. 208-217.
  29. Vance, J. M., and Shultz, R. R., 1993, "A New Damper Seal for Turbomachinery," Proceedings of the 14 th Vibration and Noise Conference, Albuquerque, NM, ASME DE-Vol. 60, pp. 139-148.
  30. Zeidan, F., 1989, "Cavitation Effects on the Rotordynamic Performance of SFD Bearings," Ph.D. Dissertation, Texas A&M University, College Station. Radial Blade Clearances : Blade1 Radial Clearance (in) R1 0.005 := Blade4 Radial Clearance (in) R4 0.01
  31. = Blade2 Radial Clearance (in) R2 0.01 := Blade5 Radial Clearance (in) R5 0.005
  32. = Blade3 Radial Clearance (in) R3 0.005 := Blade6 Radial Clearance (in) R6 0.01
  33. =

Related papers

Dynamic simulation and monitoring of a non-contacting flexibly mounted rotor mechanical face seal
Joshua Dayan

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2000

View PDFchevron_right
Theoretical Rotordynamic Coefficients of Labyrinth Gas Seals: a Parametric Study on a Bulk Model
Paola Forte, Fabio Latini

International Journal of Rotating Machinery, 1999

View PDFchevron_right
Effect of shaft eccentricity on dynamic characteristics for different geometries of stationary labyrinth seals
Rola Afify
View PDFchevron_right
Time Transient Analysis of Horizontal Rigid Rotor Supported With O-Ring Sealed Squeeze Film Damper
Saeid Dousti

Volume 4A: Dynamics, Vibration and Control, 2013

View PDFchevron_right
Measurements of Apex Seal Behavior in a Rotary Engine using Four Displacement Sensors
frank herfert

1997

View PDFchevron_right
Experimental Rotordynamic Coefficient Results for (a) a Labyrinth Seal With and Without Shunt Injection and (b) a Honeycomb Seal
Elias Requena Soto

Journal of Engineering for Gas Turbines and Power, 1999

View PDFchevron_right
Rotordynamic Analysis of Textured Annular Seals With Multiphase (Bubbly) Flow
Gérard PINEAU

INCAS BULLETIN, 2011

View PDFchevron_right
Nonlinear dynamic analysis of a rotor-bearing-seal system under two loading conditions
辉 马
View PDFchevron_right
Evaluation of Pressure-Stiffness Coupling in Brush Seals
Serdar Aksoy

46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2010

View PDFchevron_right
An Approach to Calculate Leakage Flow, Stiffness and Damping of Annular Seals in Turbulent Flow Using Lubrication Theory, Part I: Analysis
Shivam Kumar

Tribology Online, 2007

View PDFchevron_right
The relative Behavior of a Rotary Engine Apex Seal to the Walls of a Slot
frank herfert

1976

View PDFchevron_right
An Approach to Calculate Leakage Flow, Stiffness and Damping of Annular Seals in Turbulent Flow Using Lubrication Theory, Part II: Results
Shivam Kumar

Tribology Online, 2007

View PDFchevron_right
Research Into Flows in Turbine Blade Seals Part I: Research Methods
Marian Piwowarski

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk, 2003

View PDFchevron_right
Prediction of Carry-Over Coefficient for Fluid Flow Through Teeth on Rotor Labyrinth Seals Using Computational Fluid Dynamics
basim ajeel

2014

View PDFchevron_right
RADIAL LIP SEALS EFFICIENCY UNDER DYNAMIC OPERATING CONDITIONS
Alessandro Tasora
View PDFchevron_right
A dynamic Analysis of Rotary Combustion Engine Seals
frank herfert

1984

View PDFchevron_right
INTERNATIONAL JOURNAL OF ENERGY AND ENVIRONMENT SPECIAL ISSUE ON APPLIED MECHANICS RESEARCH Effect of fluid damping on vibration response of immersed rotors
Mahmud Ismail
View PDFchevron_right
Demonstration of a Dynamic Clearance Seal in a Rotating Test Facility
Simon Hogg

Volume 8: Microturbines, Turbochargers and Small Turbomachines; Steam Turbines, 2017

View PDFchevron_right
An experimental study on leakage flow in different geometrical disk seals
Torbjörn Nielsen

Journal of Hydrodynamics, Ser. B, 2010

View PDFchevron_right
Gas Damper Seal Test Results, Theoretical Correlation, and Applications in Design of High-Pressure Compressors
frank kushner

Proceedings of the 29th Turbomachinery …, 2000

View PDFchevron_right
Effects of the Back Plate Inner Diameter on the Frictional Heat Input and General Performance of Brush Seals
Jens Friedrichs

Aerospace, 2018

View PDFchevron_right
Investigation of Hydrostatic Fluid Forces in Varying Clearance Turbomachinery Seals
Simon Hogg

Journal of Engineering for Gas Turbines and Power

View PDFchevron_right

Related topics

Mechanical EngineeringAerospace Engineering
580 California St., Suite 400
San Francisco, CA, 94104