An analysis is developed for a compressible bulk-flow model of the leakage path between a centrifugal compressor's impeller shroud and housing along the front and back side of the impeller. This is an extension of analysis performed first by Childs (1989) for a shrouded pump impeller and its housing considering an incompressible fluid, and then later by Cao (1993) using a compressible bulk flow model for the shroud of a cryogenic fluid pump. The bulk-flow model is used to develop a reaction force and moment model for the shroud of a centrifugal compressor by solving the derived governing equations and integrating the pressure and shear stress distribution. Validation is done by comparing the results to published measured moment coefficients by Yoshida et al. (1996). The comparison shows that the shroud casing clearance flow and the fluid force moment can be simulated by the bulk flow model fairly well. An Iwatsubo-based labyrinth seal code developed by Childs and Scharrer (1986) is used to calculate the rotordynamic coefficients developed by the labyrinth seals in the compressor. Tangential force and transverse moment components acting on the rotor are found to have a destabilizing influence on the rotor for a range of precession frequencies. Rotordynamic coefficients are derived for a single stage of a multistage centrifugal compressor, and a comparison is made to stability predictions using Wachel's coefficient using the XLTRC (rotordynamic FEA code). For the model employed, Wachel's model predicts a slightly lower onset speed of instability. The results also show that leakage that flows radially inwards on the back shroud has a greater destabilizing influence than leakage flow that is radially outwards. Seal rub conditions are simulated by increasing the clearance and simultaneously decreasing the tooth height, which increased the leakage and the swirl tothe eye seal inlet; and therefore reduced stability. Calculated results are provided for different seal clearances and tooth height, for seal and shroud forces and moments.

Results are presented for measured and predicted rotordynamic coefficients and leakage for hole-pattern seals with a hole depth that varies axially along the seal. Testing was done to discover how pressure ratio, inlet preswirl, and rotor speed affect the seals’ rotordynamic characteristics and leakage. The results were compared to a constant hole depth hole-pattern seal. Experimental results show that the seals’ rotordynamic characteristics are not strongly influenced by pressure ratio. There were three preswirl conditions tested, each separated by a 6.9 bar (100 psi) difference in inlet pressure. Therefore, normalized preswirl results were compared. The normalized results indicate that introducing inlet fluid preswirl affects the crosscoupled stiffness and effective damping coefficients. Inlet preswirl increases the magnitude of cross-coupled stiffness. Effective damping decreases with inlet preswirl, as well as the effective damping cross-over frequency increasing. These results indicate that swirl brakes would be of great value. Rotor speed had a significant effect on the cross-coupled coefficients; both increased with speed. Experimental results were compared to results for a constant hole depth holepattern seal. The variable hole-depth seal has higher direct damping. The crosscoupled stiffness and cross-coupled damping coefficients were very similar. The direct stiffness was always lower at lower frequencies and higher at higher frequencies for the variable hole depth hole-pattern seal. This was also the case for effective stiffness. The effective damping of the variable hole-depth seal was not only larger than for the constant hole depth seal, it also had a drastically lower cross-over frequency. The difference in cross-over frequency was 40 percent on average. Experimental results for rotordynamic characteristics and leakage were compared to theoretical predictions by ISOTSEAL 2, a modified version of ISOTSEAL. Both cross-coupled stiffness and damping are reasonably predicted. Direct damping is always under-predicted. ISOTSEAL 2 does a poor job of predicting direct stiffness. Direct stiffness is over-predicted at lower frequencies and under-predicted at higher frequencies. This is also the case for effective stiffness. ISOTSEAL 2 under-predicts the direct damping, but does an excellent job of predicting the direct damping crossover frequency. Seal leakage is well predicted by ISOTSEAL 2.

A rotordynamic analysis of hole-pattern gas annular seals using a two-control-volume model, Ha and Childs and frequency dependent transfer-function model, Kleynhans and Childs is modified with four features. The energy equation is added, and real gas properties are used instead of the ideal gas equation of state. The depth of the hole-pattern is made variable with the axial distance along the seal. And last, the addition of deep grooves to hole-pattern seals is analyzed, and the code’s predictions for the influence of a groove are compared with test data.

Rotordynamic coefficients of a gas labyrinth seal are assumed to be frequency independent. However, this assumption loses its validity as rotor surface velocity approaches Mach 1. The solution procedure of 1CV model by Childs and Scharrer which assumes frequency independent force coefficients is modified to allow for calculating frequency dependent force coefficients. A comparative study of the impact of using frequency-dependent model and the original frequency-independent model on stability analysis is made. The results indicate that frequency dependency of force coefficients should be accounted for in stability analysis as rotor surface velocity approaches a significant fraction of Mach number. The bulk flow rotordynamic analysis model by Childs and Scharrer is modified to investigate the impact of leakage-flow models on predictions. A number of leakage models are incorporated in the one-control volume model, and a comparative study is made. Kinetic energy carryover factor of a leakage equation is one of the dominant factors in seal cross-force generation. A leakage equation based on a model proposed by Gamal which uses Hodkinson?s kinetic energy carryover factor is found to improve predictions of direct damping and cross-coupled stiffness. A test case is implemented to study the impact of variation of seal axial radial clearance on stability characteristics. The 1CV model by Childs and Scharrer and subsequent bulk flow models are based on the assumption of isothermal flow across the labyrinth seal. The 1CV model by Childs and Scharrer is modified to include energy equation, and the flow process is assumed to be adiabatic. However, predicted cross-coupled stiffness and direct damping coefficients using the new model do not compare well with the experimental results by Picardo as compared to the isothermal model. The impact of using real gas properties on static and rotordynamic characteristics of the seal is studied.

This dissertation discusses research on the leakage and rotordynamic characteristics of pocket damper seals (PDS) and see-through labyrinth seals, presents and evaluates models for labyrinth seal and PDS leakage and PDS force coefficients, and compares these seals to other annular gas seals. Low-pressure experimental results are used alongside previously-published high-pressure labyrinth and PDS data to evaluate the models. Effects of major seal design parameters; blade thickness, blade spacing, blade profile, and cavity depth; on seal leakage, as well as the effect of operating a seal in an off-center position, are examined through a series of non-rotating tests. Two reconfigurable seal designs were used, which enabled testing labyrinth seals and PDS with two to six blades. Leakage and pressure measurements were made with air as the working fluid on twenty-two seal configurations. Increasing seal blade thickness reduced leakage by the largest amount. Blade profile results were more equivocal, indicating that both profile and thickness affected leakage, but that the influence of one factor partially negated the influence of the other. Seal leakage increased with increased eccentricity at lower supply pressures, but that this effect was attenuated for higher pressure drops. While cavity depth effects were minor, reducing depths reduced leakage up to a point beyond which leakage increased, indicating that an optimum cavity depth existed. Changing blade spacing produced results almost as significant as those for blade thickness, showing that reducing spacing can detrimentally affect leakage to the point of negating the benefit of inserting additional blades. Tests to determine the effect of PDS partition walls showed that they reduce axial leakage. The pressure drop was found to be highest across the first blade of a seal for low pressure drops, but the pressure drop distribution became parabolic for high pressure drops with the largest drop across the last blade. Thirteen leakage equations made up of a base equations, a flow factor, and a kinetic energy carryover factor were examined. The importance of the carryover coefficient was made evident and a modified carryover coefficient is suggested. Existing fullypartitioned PDS models were expanded to accommodate seals of various geometries.

Rotordynamic coefficients of a gas labyrinth seal are assumed to be frequency independent. However, this assumption loses its validity as rotor surface velocity approaches Mach 1. The solution procedure of 1CV model by Childs and Scharrer which assumes frequency independent force coefficients is modified to allow for calculating frequency dependent force coefficients. A comparative study of the impact of using frequency-dependent model and the original frequency-independent model on stability analysis is made. The results indicate that frequency dependency of force coefficients should be accounted for in stability analysis as rotor surface velocity approaches a significant fraction of Mach number. The bulk flow rotordynamic analysis model by Childs and Scharrer is modified to investigate the impact of leakage-flow models on predictions. A number of leakage models are incorporated in the one-control volume model, and a comparative study is made. Kinetic energy carryover factor of a leakage equation is one of the dominant factors in seal cross-force generation. A leakage equation based on a model proposed by Gamal which uses Hodkinson?s kinetic energy carryover factor is found to improve predictions of direct damping and cross-coupled stiffness. A test case is implemented to study the impact of variation of seal axial radial clearance on stability characteristics. The 1CV model by Childs and Scharrer and subsequent bulk flow models are based on the assumption of isothermal flow across the labyrinth seal. The 1CV model by Childs and Scharrer is modified to include energy equation, and the flow process is assumed to be adiabatic. However, predicted cross-coupled stiffness and direct damping coefficients using the new model do not compare well with the experimental results by Picardo as compared to the isothermal model. The impact of using real gas properties on static and rotordynamic characteristics of the seal is studied.

Results are presented for experimental and theoretical rotordynamic coefficients and leakage of straight smooth annular gas seals. Experimental rotordynamic coefficients were measured and trends in changes of rotordynamic coefficients with operating variables such as rotor speed, back-pressure, fluid preswirl, and seal clearance are analyzed. Experimental results show that cross-coupled stiffness coefficients are highly influenced by fluid preswirl and only moderately influenced by other operating parameters, whereas direct damping is nearly unaffected by changes in operating parameters. Effective damping, a good indicator of stability, is highly affected by fluid preswirl. Although rotordynamic coefficients of straight smooth annular gas seals are assumed to be frequency independent, experimental results suggest a frequency dependent nature at high back-pressures and high excitation frequencies. Experimental results for rotordynamic coefficients and leakage are compared with theoretical predictions of ISOTSEAL, an isothermal-flow, two-control-volume, bulk-flow rotordynamic analysis program. All rotordynamic coefficients are underpredicted. Direct stiffness is poorly predicted while cross-coupled stiffness and direct damping are predicted reasonably well. Leakage is also consistently under-predicted. Theory predicts a slight frequency dependent nature for a limited number of test configurations.

The present work describes experiments conducted on several pocket damper seal (PDS) designs using a high pressure annular gas seal test rig. Both rotating and non-rotating tests were conducted for a 12, 8, and 6 bladed PDS. The objective of the tests was to determine the rotordynamic force coefficients and leakage for the different PDS while varying parameters such as: (1) clearance ratio, (2) rotor surface speed, (3) PDS pressure differential, and (4) excitation frequency. Two different methods were used to determine frequency dependent force coefficients: (1) the impedance method, which involved using a baseline subtraction and (2) the dynamic pressure response method, which comprised of measuring seal cavity dynamic pressure and phase relationship to vibration. Both methods were used to determine coefficients, but the dynamic pressure response method revealed insights to the dynamics of the PDS that were the first of its kind and allowed the comparison to the damper seal theory at the most fundamental of levels. The results indicated that the conventional PDS possessed high positive damping, negative and positive stiffness, and same sign cross-coupled coefficients. Another objective of the work is to investigate a new fully partitioned PDS design and accompany experimental results with the development of a modified damper seal theory. The new fully partitioned PDS design was shown to give twice as much damping as the conventional design and revealed the ability to modify direct stiffness without degradation in direct damping. Finally, both the conventional theory and the newly proposed theory predictions are compared to experimentally determined force coefficients. The last objective was to evaluate the leakage characteristics of the different designs and to investigate the effect of blade profile on seal leakage. Results showed that beveled tooth blade profiles yield higher mass flow leakage compared to rectangular blade profiles.

A rotordynamic analysis of hole-pattern gas annular seals using a two-control-volume model, Ha and Childs and frequency dependent transfer-function model, Kleynhans and Childs is modified with four features. The energy equation is added, and real gas properties are used instead of the ideal gas equation of state. The depth of the hole-pattern is made variable with the axial distance along the seal. And last, the addition of deep grooves to hole-pattern seals is analyzed, and the code’s predictions for the influence of a groove are compared with test data.

This dissertation discusses research on the leakage and rotordynamic characteristics of pocket damper seals (PDS) and see-through labyrinth seals, presents and evaluates models for labyrinth seal and PDS leakage and PDS force coefficients, and compares these seals to other annular gas seals. Low-pressure experimental results are used alongside previously-published high-pressure labyrinth and PDS data to evaluate the models. Effects of major seal design parameters; blade thickness, blade spacing, blade profile, and cavity depth; on seal leakage, as well as the effect of operating a seal in an off-center position, are examined through a series of non-rotating tests. Two reconfigurable seal designs were used, which enabled testing labyrinth seals and PDS with two to six blades. Leakage and pressure measurements were made with air as the working fluid on twenty-two seal configurations. Increasing seal blade thickness reduced leakage by the largest amount. Blade profile results were more equivocal, indicating that both profile and thickness affected leakage, but that the influence of one factor partially negated the influence of the other. Seal leakage increased with increased eccentricity at lower supply pressures, but that this effect was attenuated for higher pressure drops. While cavity depth effects were minor, reducing depths reduced leakage up to a point beyond which leakage increased, indicating that an optimum cavity depth existed. Changing blade spacing produced results almost as significant as those for blade thickness, showing that reducing spacing can detrimentally affect leakage to the point of negating the benefit of inserting additional blades. Tests to determine the effect of PDS partition walls showed that they reduce axial leakage. The pressure drop was found to be highest across the first blade of a seal for low pressure drops, but the pressure drop distribution became parabolic for high pressure drops with the largest drop across the last blade. Thirteen leakage equations made up of a base equations, a flow factor, and a kinetic energy carryover factor were examined. The importance of the carryover coefficient was made evident and a modified carryover coefficient is suggested. Existing fullypartitioned PDS models were expanded to accommodate seals of various geometries.