Rotordynamic Stability Effects of Shrouded Centrifugal Impellers With Combined Whirl and Precession

Whirling (translational) and precession (tilt) motion of the shrouded centrifugal impeller are possible vibration sources that can cause rotordynamic instability problems. Whirling motion of shrouded impellers and seals has been investigated by test and theory in the literature. However, there has been little study of the effects of coupled motion of whirling and precession of a centrifugal impeller on rotordynamic forces and moments using computational fluid dynamics (CFD). In the present study, the CFD approach for calculating the moment coefficients of the precessing impeller is developed and verified by comparison with the measured data for a precessing centrifugal compressor by Yoshida et al. (1996, “Measurement of the Flow in the Backshroud/Casing Clearance of a Precessing Centrifugal Impeller,” Sixth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, Hawaii, Vol. 2, pp. 151–160). A full set (4 × 4) of rotordynamic coefficient matrices is calculated, using two separate models of (a) a precessing impeller with a tilt angle and (b) a whirling impeller with dynamic eccentricity to investigate the stability of the impeller. Rotordynamic stability is evaluated by using the whirl frequency ratio of the coupled motion, obtained from the full rotordynamic coefficient matrices, to show that the precession motion has a significant impact on rotordynamic stability. A similar conclusion is reached based on the whirling plus precession response of a finite element (FE) structural rotordynamic model including the 4 × 4 rotordynamic coefficient matrices. A stability analysis using the rotordynamic coefficients indicates that the precession motion with the positive tilt angle increases the tendency toward destabilization of the rotor.

A direct numerical approach to compute the nonlinear rotordynamic coefficient of the noncircular gas journal bearing

Gas bearings are extensively used in several industrial applications to support the rotating load at high speed due to its favorable characteristics. The numerical computation of the gas film damping and stiffness coefficients is a difficult task due to nonlinearity in the Reynolds equation for compressible lubricant. In the present work, a numerical method based on the finite element method is developed for the direct computation of gas film damping and stiffness coefficients. In this method, a double partial differential equation approach has been used to compute the dynamic characteristics. Further, the numerical results presented shows that the bearing ellipticity ratio significantly affects the nonlinear trajectory of the journal.

Rotordynamic Characteristics of a Flexure Pivot Pad Bearing With an Active and Locked Integral Squeeze Film Damper

Measured rotordynamic coefficients are presented for a flexure-pivot-pad journal bearing (FPJB) in a load-between-pad configuration with: (1) an active, and (2) locked integral squeeze film damper (ISFD). Prior rotordynamic-coefficient test results have been presented for FPJBs (alone), and rotor-response results have been presented for rotors supported by FPJBS with ISFDs; however, these are the first rotordynamic-coefficient test results for FPJBs with ISFDs. A multi-frequency dynamic testing regime is employed. For both bearing configurations, quadratic curve fits provide good representation of the real portions of the dynamic-stiffness coefficients yielding a direct stiffness and a direct added-mass coefficient. The imaginary portions are well represented by linear curve fits, implying constant, frequency-independent direct-damping coefficients. Direct stiffness coefficients are ∼50% lower for the active-damper configuration, and direct damping coefficients are only modestly lower. The combination of ∼50% reduction in direct stiffness with a modest drop in direct damping indicates a very effective squeeze-film damper application. Added-mass coefficients are normally lower for the active-damper configuration, and all coefficient trends (for changes in loading and shaft speed) are “flatter” for the active flexure pivot-pad damper bearing. The measured rotordynamic coefficients are used to calculate the whirl frequency ratio and indicate high stability for both bearing configurations.

Rotordynamic-Coefficient and Leakage Characteristics for Hole-Pattern-Stator Annular Gas Seals—Measurements Versus Predictions

Selected test results are presented for an annular gas seal using a smooth rotor and a hole-pattern-roughness stator for a supply pressure of 70 bar, three pressure ratios, three speeds up to 20,000 rpm, two clearances, and three preswirl ratios. Dynamic data include frequency-dependent direct and cross-coupled stiffness and damping coefficients. Static data include leakage and upstream and downstream pressures and temperatures. Very good agreements are found between measurements and predictions from a two-control-volume bulk-flow model.

A Comparison of Rotordynamic-Coefficient Predictions for Annular Honeycomb Gas Seals Using Three Different Friction-Factor Models

A two-control-volume bulk-flow model is used to predict rotordynamic coefficients for an annular, honeycomb-stator/smooth-rotor gas seal. The bulk-flow model uses Hirs’ turbulent-lubrication model, which requires a friction factor model to define the shear stresses at the rotor and stator wall. Rotordynamic coefficients predictions are compared for the following three variations of the Blasius pipe-friction model: (i) a basic model where the Reynolds number is a linear function of the local clearance, fs=ns Rems (ii) a model where the coefficient is a function of the local clearance, and (iii) a model where both the coefficient and exponent are functions of the local clearance. The latter models are based on data that shows the friction factor increasing with increasing clearances. Rotordynamic-coefficient predictions shows that the friction-factor-model choice is important in predicting the effective-damping coefficients at a lower frequency range (60∼70 Hz) where industrial centrifugal compressors and steam turbines tend to become unstable. At a higher frequency range, irrespective of the friction-factor model, the rotordynamic-coefficient predictions tend to coincide. Blasius-based Models which directly account for the observed increase in stator friction factors with increasing clearance predict significantly lower values for the destabilizing cross-coupled stiffness coefficients.

Experimental Rotordynamic Coefficient Results for (a) a Labyrinth Seal With and Without Shunt Injection and (b) a Honeycomb Seal

Centrifugal compressors are increasingly required to operate at higher pressures, speeds, and fluid density. In these conditions, compressors are susceptible to rotordynamic instabilities. To remedy this situation, labyrinth seals have sometimes been modified by using shunt injection. In shunt injection, the gas is taken from the diffuser or discharge volute and injected into an upstream chamber of the balance-piston labyrinth seal. The injection direction can be radial or against rotation. This study contains the first measured rotordynamic data for labyrinth seals with shunt injection. A comparison has been made between conventional labyrinth seals, labyrinth seals with shunt injection (radial and against rotation), and a honeycomb seal. Labyrinth seals with injection against rotation are better able to control rotordynamic instabilities than labyrinth seals with radial injection; however, the leakage is slightly higher. The leakage comparison for all seals demonstrates that the honeycomb seal has the best flow control. Test data are presented for a top rotor surface velocity of 110 m/sec, a supply pressure of 13.7 bars, and IPr = 0.95 (injection pressure is 1.05 = 1/0.95 times the seal inlet pressure). For these conditions, and considering effective damping, the labyrinth seal with injection against rotation is better than the honeycomb seal when the pressure ratio across the seal PR < 0.45. On the other hand, the honeycomb seal is better when PR > 0.45. The effectiveness of the shunt-injection against rotation in developing effective damping is reduced with increasing rotor surface velocity.

Experimental Rotordynamic Coefficient Results for: (a) A Labyrinth Seal With and Without Shunt Injection and (b) A Honeycomb Seal

Centrifugal compressors are increasingly required to operate at higher pressures, speeds, and fluid density. In these conditions, compressors are susceptible to rotordynamic instabilities. To remedy this situation, labyrinth seals have sometimes been modified by using shunt injection. In shunt injection, the gas is taken from the diffuser or discharge volute and injected into an upstream chamber of the balance-piston labyrinth seal. The injection direction can be radial or against rotation. This study contains the first measured rotordynamic data for labyrinth seals with shunt injection. A comparison has been made between conventional labyrinth seals, labyrinth seal with shunt injection (radial and against rotation), and a honeycomb seal. Labyrinth seals with injection against rotation are better able to control rotordynamic instabilities than labyrinth seals with radial injection; however, the leakage is slightly higher. The leakage comparison for all seals demonstrates that the honeycomb seal has the best flow control. Test data are presented for a top rotor surface velocity of 110 m/sec, a supply pressure of 13.7 bars, and IPr = 0.95 (injection pressure is 1.05 = 1/0.95 times the seal inlet pressure). For these conditions, and considering effective damping, the labyrinth seal with injection against rotation is better than the honeycomb seal when the pressure ratio across the seal PR<0.45. On the other hand, the honeycomb seal is better when PR>0.45. The effectiveness of the shunt-injection against rotation in developing effective damping is reduced with increasing rotor surface velocity.

Experimental Leakage and Rotordynamic Results for Helically Grooved Annular Gas Seals

Rotordynamic-coefficient and leakage test results are presented for three grooved seals with helix angles of 0, 15, and 30 deg against rotation. The seals are 50.8 mm long and 152.4 mm in diameter. Tests were done for two supply pressures (up to 17 bars), three speeds (5000, 12,000, and 16,000 rpm), four pressure ratios, and three inlet fluid prerotation conditions. The results showed that increasing the helix angle yields a progressive reduction in the cross-coupled stiffness coefficient k and a progressive increase in leakage. The helically grooved seals consistently yield negative cross-coupled stiffness coefficients for nonprerotated inlet flow; hence, k in these seals would oppose forward whirl of a rotor. Helically grooved seals become less effective at reducing k with increasing preswirl; hence, for optimum effectiveness they should be used with a swirl brake. Comparison between helically grooved and honeycomb-stator seals showed that helically grooved stators had reduced (negative) whirl-frequency ratios for nonprerotated flows but were no better than honeycomb-stator seals for elevated fluid prerotation. The 15 and 30 deg helix grooves leaked about 1.6 and 2.2 times, respectively, as much as the honeycomb-stator seals.

Experimental Leakage and Rotordynamic Results for Helically Grooved Annular Gas Seals

Rotordynamic-coefficient and leakage test results are presented for three grooved seals with helix angles of 0°, 15°, and 30° against rotation. The seals are 50.8 mm long and 152.4 mm in diameter. Tests were done for two supply pressures (up to 17 bars), three speeds (5000, 12000, and 16000 rpm), four pressure ratios, and three inlet fluid prerotation conditions. The results showed that increasing the helix angle yields a progressive reduction in the cross-coupled stiffness coefficient k and a progressive increase in leakage. The helically-grooved seals consistently yield negative cross-coupled stiffness coefficients for nonprerotated inlet flow; hence, k in these seals would oppose forward whirl of a rotor. Helically grooved seals become less effective at reducing k with increasing preswirl; hence, for optimum effectiveness they should be used with a swirl brake. Comparison between helically-grooved and honeycomb-stator seals showed that helically-grooved stators had reduced (negative) whirl-frequency ratios for nonprerotated flows but were no better than honeycomb-stator seals for elevated fluid prerotation. The 15° and 30° helix grooves leaked about 1.6 and 2.2 times, respectively, as much as the honeycomb-stator seals.