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NASA NTRS1993

A finite-element-based perturbation model for the rotordynamic analysis of shrouded pump impellers: Part 1: Model development and applications

This study concerns the rotor dynamic characteristics of fluid-encompassed rotors, with special emphasis on shrouded pump impellers. The core of the study is a versatile and categorically new finite-element-based perturbation model, which is based on a rigorous flow analysis and what we have generically termed the 'virtually' deformable finite-element approach. The model is first applied to the case of a smooth annular seal for verification purposes. The rotor excitation components, in this sample problem, give rise to a purely cylindrical, purely conical, and a simultaneous cylindrical/conical rotor whirl around the housing centerline. In all cases, the computed results are compared to existing experimental and analytical data involving the same seal geometry and operating conditions. Next, two labyrinth-seal configurations, which share the same tooth-to-tooth chamber geometry but differ in the total number of chambers, were investigated. The results, in this case, are compared to experimental measurements for both seal configurations. The focus is finally shifted to the shrouded-impeller problem, where the stability effects of the leakage flow in the shroud-to-housing secondary passage are investigated. To this end, the computational model is applied to a typical shrouded-impeller pump stage, fabricated and rotor dynamically tested by Sulzer Bros., and the results compared to those of a simplified 'bulk-flow' analysis and Sulzer Bros.' test data. In addition to assessing the computed rotor dynamic coefficients, the shrouded-impeller study also covers a controversial topic, namely that of the leakage-passage inlet swirl, which was previously cited as the origin of highly unconventional (resonance-like) trends of the fluid-exerted forces. In order to validate this claim, a 'microscopic' study of the fluid/shroud interaction mechanism is conducted, with the focus being on the structure of the perturbed flow field associated with the impeller whirl. The conclusions of this study were solidified by the outcome of a numerical-certainty exercise, where the grid dependency of the numerical results is objectively examined. The final phase of the shrouded-impeller investigation involves the validation of a built-in assumption, in all other perturbation models, whereby single-harmonic tangential distributions of all the flow thermophysical properties are imposed. The last phase of the investigation course is aimed at verifying the fine details of the perturbed flow field in light of recent set of detailed LDA measurements in a smooth annular seal. Grid dependency of the fluid-induced forces is also investigated, and specific recommendations are made.

Baskharone, Erian A.↗
NASA NTRS1987

Origins of hydrodynamic forces on centrifugal pump impellers

Hydrodynamic interactions that occur between a centrifugal pump impeller and volute are experimentally and theoretically investigated. The theoretical analysis considers the inability of the blades to perfectly guide the flow through the impeller, and also includes a quasi-one dimensional treatment of the flow in the volute. The disturbance at the impeller discharge and the resulting forces are determined by the theoretical model. The model is then extended to obtain the hydrodynamic force perturbations that are caused by the impeller whirling eccentrically in the volute. Under many operating conditions, these force perturbations were found to be destablizing. Comparisons are made between the theoretical model and the experimental measurements of pressure distributions and radial forces on the impeller. The theoretical model yields fairly accurate predictions of the radial forces caused by the flow through the impeller. However, it was found that the pressure acting on the front shroud of the impeller has a substantial effect on the destablizing hydrodynamic forces.

Adkins, Douglas R.↗
NASA NTRS1992

On the use of a three-dimensional Navier-Stokes solver for rocket engine pump impeller design

A 3D Reynolds-averaged Navier-Stokes Solver and a Fast Grid Generator (FGG), developed specially for centrifugal impeller design, were incorporated into the pump impeller design process. The impeller performance from the CFD analysis was compared to one-dimensional prediction. Both analyses showed good agreement of the impeller hydraulic efficiency, 94.5 percent, but with an 8 percent discrepancy of Euler head prediction. The impeller blade angle, discharge hub to shroud width, axial length and blade stacking were systematically changed to achieve an optimum impeller design. Impeller overall efficiency, loss distribution, hub-to-tip flow angle distortion and blade-to-blade flow angle change are among those criteria used to evaluate impeller performance. Two grid sizes, one with 10 K grid points and one with 80 K grid points were used to evaluate grid dependency issues. The effects of grid resolution on the accuracy and turnaround time are discussed. In conclusion, it is demonstrated that CFD can be effectively used for design and optimization of rocket engine pump components.

Chen, Wei-Chung↗
NASA NTRS1991

Fluid-structure interaction forces at pump-impeller-shroud surfaces for axial vibration analysis

The axial forces developed on a pump impeller shroud surfaces are analyzed using a bulk-flow model of the leakage path between the impeller and the housing. Shear stresses at the impeller and the housing surfaces are modeled according to Hirs's turbulent lubrication model. The calculated results yield predictions of resonance peaks of the fluid within the annulus formed by the impeller shroud and housing. Numerical results are presented for a double-suction single-stage pump, showing that the direct stiffness of the perturbed impeller shroud forces is negligible; the forces become important only for pumps with very low axial natural frequencies in comparison to the running speed.

Childs, D. W.↗
NASA NTRS1985

Experimental measurements of hydrodynamic radial forces and stiffness matrices for a centrifugal pump-impeller

Measurements of the steady-state hydrodynamic forces on a centrifugal pump impeller are presented as a function of position within two geometrically different volutes. These correspond to the forces experienced by the impeller at zero whirl frequency. The hydrodynamic force matrices derived from these measurements exhibit both diagonal and off-diagonal terms of substantial magnitude. These terms are of the form which would tend to excite a whirl motion in a rotordynamic analysis of the pump; this may be the cause of 'rough running' reported in many pumps. Static pressure measurements in the impeller discharge flow show that the hydrodynamic force on the impeller contains a substantial component due to the nonisotropy of the net momentum flux leaving the impeller. A similar breakdown of the contributions to the stiffness matrices reveals that the major component of these matrices results from the nonisotropy of the momentum flux.

Chamieh, D. S.↗
NASA NTRS1987

Force and moment rotordynamic coefficients for pump-impeller shroud surfaces

Governing equations of motion are derived for a bulk-flow model of the leakage path between an impeller shroud and a pump housing. The governing equations consist of a path-momentum, a circumferential - momentum, and a continuity equation. The fluid annulus between the impeller shroud and pump housing is assumed to be circumferentially symmetric when the impeller is centered; i.e., the clearance can vary along the pump axis but does not vary in the circumferential direction. A perturbation expansion of the governing equations in the eccentricity ratio yields a set of zeroth and first-order governing equations. The zeroth-order equations define the leaking rate and the circumferential and path velocity distributions and pressure distributions for a centered impeller position. The first-order equations define the perturbations in the velocity and pressure distributions due to either a radial-displacement perturbation or a tilt perturbation of the impeller. Integration of the perturbed pressure and shear-stress distribution acting on the rotor yields the reaction forces and moments acting on the impeller face.

Childs, Dara W.↗
NASA NTRS1988

Analyses of hydrodynamic radial forces on centrifugal pump impellers

An experimental and theoretical study of the hydrodynamic interactions occurring between a centrifugal pump impeller and a volute is presented. The theoretical analysis provides a quasi-one-dimensional treatment of the flow in the volute, and it is extended to include the hydrodynamic force perturbations caused by the impeller whirling eccentrically in the volute. It is noted that these perturbations are often destabilizing. The theoretical models were found to accurately predict the radial forces caused by the flow through the impeller. The pressure acting on the front shroud of the impeller is shown to have a significant effect on the destabilizing hydrodyamic forces.

Adkins, D. R.↗
NASA NTRS1990

The rotordynamic forces on a centrifugal pump impeller in the presence of cavitation

Fluid-induced rotordynamic forces on a centrifugal pump impeller whirling along a trajectory eccentric to its undeflected position in the presence of cavitation were measured using the experimental facility described by Jery (1987). The force measured is a combination of a steady radial force due to the volute asymmetries and an unsteady force due to the eccentric motion of the rotor. It was found that, compared to the noncavitation condition, a cavitation corresponding to a head loss of 3 percent had little effect upon the unsteady force. However, a lesser degree of cavitation at the design point, was found to increase the destabilizing force for a particular set of whirl ratios.

Franz, R.↗
NASA NTRS1986

Experimental study of unsteady hydrodynamic force matrices on whirling centrifugal pump impellers

An experimental facility was constructed and instrumented. A set of centrifugal flow pumps whose impellers were made to follow a controlled circular whirl motion were studied. The aim was to characterize the steady and unsteady fluid forces measured on the impeller under various pump operating conditions. The postulation was that the unsteady lateral forces result from interactions between the impeller and the surrounding diffuser and/or volute (via the working fluid), and that under certain flow regimes these forces can drive unstable lateral motions of the pump rotor. The lateral hydrodynamic forces were decomposed into their steady and unsteady parts, the latter being further expressed in terms of a generalized fluid stiffness matrix. Conclusions regarding the effect of impeller geometry could not be reached given the similarity of the tested designs. However, other results on phenomena such as skin friction and leakage flow are presented. Some of the findings are compared to experimental and theoretical data from other sources. Finally, the rotordynamic consequences of the results are discussed as the present data were applied to the case of the Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump (HPOTP).

Belgacem, Jery↗
NASA NTRS1993

A finite-element-based perturbation model for the rotordynamic analysis of shrouded pump impellers: Part 2: User's guide

This report describes the computational steps involved in executing a finite-element-based perturbation model for computing the rotor dynamic coefficients of a shrouded pump impeller or a simple seal. These arise from the fluid/rotor interaction in the clearance gap. In addition to the sample cases, the computational procedure also applies to a separate category of problems referred to as the 'seal-like' category. The problem, in this case, concerns a shrouded impeller, with the exception that the secondary, or leakage, passage is totally isolated from the primary-flow passage. The difference between this and the pump problem is that the former is analytically of the simple 'seal-like' configuration, with two (inlet and exit) flow-permeable stations, while the latter constitutes a double-entry / double-discharge flow problem. In all cases, the problem is that of a rotor clearance gap. The problem here is that of a rotor excitation in the form of a cylindrical whirl around the housing centerline for a smooth annular seal. In its centered operation mode, the rotor is assumed to give rise to an axisymmetric flow field in the clearance gap. As a result, problems involving longitudinal or helical grooves, in the rotor or housing surfaces, go beyond the code capabilities. Discarding, for the moment, the pre- and post-processing phases, the bulk of the computational procedure consists of two main steps. The first is aimed at producing the axisymmetric 'zeroth-order' flow solution in the given flow domain. Detailed description of this problem, including the flow-governing equations, turbulence closure, boundary conditions, and the finite-element formulation, was covered by Baskharone and Hensel. The second main step is where the perturbation model is implemented, with the input being the centered-rotor 'zeroth-order' flow solution and a prescribed whirl frequency ratio (whirl frequency divided by the impeller speed). The computational domain, in the latter case, is treated as three dimensional, with the number of computational planes in the circumferential direction being specified a priori. The reader is reminded that the deformations in the finite elements are all infinitesimally small because the rotor eccentricity itself is a virtual displacement. This explains why we have generically termed the perturbation model the 'virtually' deformable finite-element category. The primary outcome of implementing the perturbation model is the tangential and radial components, F(sub theta)(sup *) and F(sub r)(sup *) of the fluid-exerted force on the rotor surface due to the whirling motion. Repetitive execution of the perturbation model subprogram over a sufficient range of whirl frequency ratios, and subsequent interpolation of these fluid forces, using the least-square method, finally enable the user to compute the impeller rotor dynamic coefficients of the fluid/rotor interaction. These are the direct and cross-coupled stiffness, damping, and inertia effects of the fluid/rotor interaction.

Baskharone, Erian A.↗
NASA NTRS1991

Centrifugal acceleration modes for incompressible fluid in the leakage annulus between a shrouded pump impeller and its housing

An algorithm is developed for calculating complex eigenvalues and eigenvectors associated with the fluid resonances and is used to analyze the perturbed flow in the leakage path between a shrouded-pump impeller and its housing. The eigenvalues obtained are consistent with the forced-response curves. First- and second-natural-frequency eigensolutions are presented for mode shapes corresponding to lateral excitations, and first-natural-frequency eigensolutions are presented for mode shapes corresponding to axial excitation.

Childs, D. W.↗
NASA NTRS1993

Compressibility effects on rotor forces in the leakage path between a shrouded pump impeller and its housing

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.

Cao, Nhai The↗