NASA NTRS1993
A modified approach to Childs' previous work on fluid-structure interaction forces in the leakage path between an impeller shroud and its housing is presented in this paper. Three governing equations consisting of continuity, path-momentum, and circumferential-momentum equations were developed to describe the leakage path inside a pump impeller. Radial displacement perturbations were used to solve for radial and circumferential force coefficients. In addition, impeller-discharge pressure disturbances were used to obtain pressure oscillation responses due to precessing impeller pressure wave pattern. Childs' model was modified from an incompressible model to a compressible barotropic-fluid model (the density of the working fluid is a function of the pressure and a constant temperature only). Results obtained from this model yielded interaction forces for radial and circumferential force coefficients. Radial and circumferential forces define reaction forces within the impeller leakage path. An acoustic model for the same leakage path was also developed. The convective, Coriolis, and centrifugal acceleration terms are removed from the compressible model to obtain the acoustics model. A solution due to impeller discharge pressure disturbances model was also developed for the compressible and acoustics models. The results from these modifications are used to determine what effects additional perturbation terms in the compressible model have on the acoustic model. The results show that the additional fluid mechanics terms in the compressible model cause resonances (peaks) in the force coefficient response curves. However, these peaks only occurred at high values of inlet circumferential velocity ratios greater than 0.7. The peak pressure oscillation was shown to occur at the wearing ring seal. Introduction of impeller discharge disturbances with n = 11 diametral nodes showed that maximum peak pressure oscillations occurred at nondimensional precession frequencies of f = 6.4 and f = 7.8 for this particular pump. Bolleter's results suggest that for peak pressure oscillations to occur at the wearing ring seal, the nondimensional excitation frequency should be on the order of f = 2.182 for n = 11. The resonances found in this research do not match the excitation frequencies predicted by Bolleter. At the predicted peak excitation frequencies given by Bolleter, the compressible model shows an attenuation of the pressure oscillations at the seal exit. The compressibility of the fluid does not have a significant influence on the model at low values of nondimensional excitation frequency. At high values of nondimensional frequency, the effects of compressibility become more significant. For the acoustic analysis, the convective, Coriolis, and centrifugal acceleration terms do affect the results to a limited extent for precession excitation and to a large extent for a pressure excitation when the fluid operates at relatively high Mach numbers.