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The present paper investigates the pressure oscillations with ultra-low frequency induced by the precessing vortex rope (PVR) whose frequency f PVR is one-fifth of runner frequency for a model Francis turbine operated at part-load condition. Numerical simulations based on the MSST PANS model are conducted to reveal the vortical flow and the DMD method is applied to analyze the modes for unstable flow inside the draft tubes. To make out the effect of draft tube structure on the PVR and pressure oscillation, both conventional elbow draft tube (EDT) and conical draft tube (CDT) are treated in the study. Two pressure oscillation components with ultra-low frequencies (near one third and two third of f PVR ) are captured in the EDT. The internal flow analysis depicts that the pressure oscillations with ultra-low frequency occur due to the strong interaction between the PVR and the backflow in the draft tube, and the elbow structure promotes the interaction and the swirling flow. It is noted that cavitation changes the dynamic characteristics of the vortex rope significantly. Cavitation alleviates the strong interaction between vortex rope and backflow, and suppresses the pressure oscillations with ultra-low frequency in the draft tube.

The effects of acoustic resonance and volute geometry on phase resonance are studied theoretically and experimentally using a centrifugal fan. One dimensional theoretical model is developed taking account of the reflection from the discharge pipe end. It was found that the phase resonance occurs, even with the effects of acoustic resonance, when the rotational speed of rotor-stator interaction pattern agrees with the sound velocity. This was confirmed by experiments with and without a silencer at the discharge pipe exit. The pressure wave measurements showed that there are certain effects of the cross-sectional area change of the volute which is neglected in the one dimensional model. To clarify the effects of area change, experiments were carried out by using a ring volute with a constant area. It was demonstrated that the phase resonance occurs for both interaction modes travelling towards/away from the volute. The amplitude of travelling wave grows towards the volute exit for the modes rotating towards the volute exit, in the same direction as the impeller. However, a standing wave is developed in the volute for the modes rotating away from the volute exit in the opposite direction as the impeller, as a result of the interaction of a growing wave while travelling towards the tongue and a reflected wave away from the tongue.

Rotordynamic forces on pump impellers and turbine runners are reviewed. First, it is shown that the rotordynamic instability occurs when the tangential component of the effective rotordynamic force is in the direction of rotor whirl. In many cases of centrifugal impellers, rotordynamic forces can cause forward whirl at supercritical speeds where the rotor is running more than twice the first critical speed. This occurs when the impeller is operating in a volute or a vaned diffuser, or when the clearance between the front shroud and the casing is small. However, when the change of the leakage flow due to displacement is important, the fluid force moment can cause rotor whirl even when the rotor speed is significantly lower than the first critical speed. The instability can be avoided by placing the seal at the exit of the leakage flow or changing the opening/closing convention of the seal associated with the deflection of the rotor.

A flow oscillation phenomenon of the dual-bell nozzle at low-altitude operationmode is investigated with cold-flow experiments and numerical simulations. Results indicate the existence of three kinds of periodic flow oscillation modes: a symmetric lowest-frequency oscillation mode, which is an acoustic resonance in the axial direction in an extensionpart of thenozzle, and twohigh-frequencymodes lateral to thenozzle axis originatingdue to vortex shedding andacoustic resonance in the extension nozzle cross section.These periodicflowoscillations are characteristic to dualbell nozzles, and the extension part is the cause of these fluctuations, which are not observed in single-bell nozzles.

Unsteady flow characteristics in a dual-bell altitude compensation nozzle at low altitude operation modes are examined. At the low altitude operation mode, a jet separation point is fixed at the nozzle wall inflection. However, experimental and numerical results show that three modes of periodic jet fluctuations take place at certain range of nozzle pressure ratios. The lowest frequency mode is a symmetric modes and is considered to be caused by the acoustic resonance in longitudinal direction in the extension part of the nozzle. Two kinds of asymmetric modes have higher frequency than the symmetric mode. According to the numerical results, one of them is a jet screech tone caused by the convection of large scale vortices beside the separated jet. The other mode has the same frequency with a resonance mode in the diametrical direction of the cross section of the extension part.

Phase resonance in a centrifugal compressor was experimentally observed and simulated with a commercial CFD code. It was found that pressure fluctuation at the volute outlet becomes the maximum when the rotational speed of the modes caused by the rotor-stator interaction agrees with the sound velocity. A simple one-dimensional theory is presented to explain the phase resonance in turbomachinery.

The rotordynamic fluid forces acting on a closed type impeller in whirling motion were measured and the influence of the clearance geometry on the stability of the impeller was examined. At small positive whirling speed, the rotordynamic forces acted as destabilizing forces for all casings. A small clearance between the shroud of the impeller and the casing caused large fluid force, but did not change the destabilizing region. Radial grooves in the clearance were effective for reducing the fluid forces and destabilizing region due to the reduction of the circumferential velocity without the deterioration of the pump performance. A rotating phenomenon like a rotating stall of the impeller occurred at low flow rate and the resonance between it and the whirling motion led to a sudden increase in force at the whirling speed ratio of 0.7.

An attempt is made to clarify the flow instabilities downstream of inlet guide vanes by conducting experiments and performing a numerical simulation. The onset condition including the cell number and oscillating characteristics of the unsteady flow is discussed based on the measured pressure fluctuation. The propagating angular velocity ratio of the instability for various values of r3/r2 (ratio of the radius of the trailing edge of the vanes to the radius of the outlet of the device) is presented as a function of vane angle β2. The phenomenon taking place downstream of the inlet guide vanes is demonstrated to be of a different type from the rotating stall of the blades, where the amplitude of the flow oscillation depends on the number of cells and the chord length. In addition, applying the slope angle on the lower disc is found to be effective for controlling the flow instabilities.

Recent studies on the moment whirl due to leakage flow in the back shroud clearance of hydro-turbine runners or centrifugal pump impellers are summarized. First, destabilizing effect of leakage flow is discussed for lateral vibrations using simplified models. Then it is extended to the case of whirling motion of an overhung rotor and the criterion for the instability is obtained. The fluid moment caused by a leakage clearance flow between a rotating disk and a stationary casing was obtained by model tests under whirling and precession motion of the disk. It is shown that the whirl moment always destabilizes the whirl motion of the overhung rotor while the precession moment destabilizes the precession only when the precession speed is less than half the rotor speed. Then vibration analyses considering both whirl and precession are made by using the hydrodynamic moments determined by the model tests. For larger overhung rotors, the whirl moment is more important and cause whirl instability at all rotor speed. On the other hand, for smaller overhung rotors, the precession moment is more important and cancels the destabilizing effect of the whirl moment.

A Large Eddy Simulation (LES) of the flow in an inducer is carried out under flow rate oscillations. The present study focuses on the dynamic response of the backflow and the unsteady pressure performance to the flow rate fluctuations under non-cavitation conditions. The amplitude of angular momentum fluctuation evaluated by LES is larger than that evaluated by RANS. However, the phase delay of backflow is nearly the same as RANS calculation. The pressure performance curve exhibits a closed curve caused by the inertia effect associated with the flow rate fluctuations. Compared with simplified one dimensional evaluation of the inertia component, the component obtained by LES is smaller. The negative slope of averaged performance curve becomes larger under unsteady conditions. From the conservations of angular momentum and energy, an expression useful for the evaluation of unsteady pressure rise was obtained. The examination of each term of this expression show that the apparent decrease of inertia effects is caused by the response delay of Euler’s head and that the increase of negative slope is caused by the delay of inertial term associated with the delay of backflow response. These results are qualitatively confirmed by experiments.

Alternate blade cavitation, rotating cavitation and cavitation surge in rocket turbopump inducers were simulated by a three dimensional commercial CFD code. In order to clarify the cause of cavitation instabilities, the velocity disturbance caused by cavitation was obtained by subtracting the velocity vector under non-cavitating condition from that under cavitating condition. It was found that there exists a disturbance flow towards the trailing edge of the tip cavity. This flow has an axial flow component towards downstream which reduces the incidence angle to the next blade. It was found that all of the cavitation instabilities start to occur when this flow starts to interact with the leading edge of the next blade. The existence of the disturbance flow was validated by experiments.

Unlike usual turbopump inducers, the axial flow pump tested operates very stably at design flow rate without rotating cavitation nor cavitation surge. Flow visualization suggests that this is because the tip cavity smoothly extends into the flow passage without the interaction with the leading edge of the next blade. However, at low flow rate and low cavitation number, choked surge and rotating choke were observed. Their correlation with the performance curve under cavitation is discussed and their instantaneous flow fields are shown.

The effects of foil geometry on partial and transitional cavity oscillations were examined by experiments. The transitional cavity oscillation can be observed in the upstream pressure fluctuation for all foils and the amplitude of oscillation becomes larger when the maximum cavity length becomes larger than about 75% of the chord length. The Stroulal number based on the chord length correlated with the value of a parameter σ∕2α and increased from 0.07 to 0.17 with the increase of σ∕2α from 2.0 to 6.0 for all foils. For thicker foils, the partial cavity oscillation could not be detected in the upstream pressure fluctuation. However, semi-periodical cavity shedding corresponding to the partial cavity oscillation could be visually observed for all foils and the Strouhal number based on the mean cavity length was about 0.15–0.35 for all foils. Thus, the effect of foil geometry appears only in the strength of partial cavity oscillation.

In the present paper, parametric numerical analyses of the separated transonic flows in overexpanded rocket nozzles are conducted. Several types of nozzles are examined numerically to clarify the detailed mechanisms of the occurrence of restricted shock separation (RSS) in compressed truncated perfect (CTP) nozzles. The effects of nozzle length and geometric compression factor are examined. In CTP nozzles with large length and small compression factor, a positive pressure gradient appears downstream of the Mach disk before the occurrence of RSS. Under the positive pressure gradient, the flow, which passed through the Mach disk, rolls up and forms a large vortex ring around the nozzle exit. The vortex ring pushes the separated jet towards the nozzle wall and results in RSS.

The present paper treats the backflow vortex structure observed at the turbomachinery inlet at reduced flow rate. It is caused by the roll-up of the shear layer between swirling backflow and axial main flow. In order to verify this, a simple model test was carried out in which the effect of impeller was represented by an axisymmetric swirling backflow. In the present paper, the flow field of a simplified model test is simulated by using LES calculations to investigate detailed flow structure. The computed results are compared with experimental results.

In centrifugal pumps for artificial hearts, a magnetic drive and lightly loaded journal bearing system are often used to avoid leakage and to minimize the damage on blood cells. In such system, the rigidity of the bearing is small and the impeller usually rotates over the critical speed. For such cases, the rotordynamic fluid forces play an important role for the stability of operation. In the present study, the characteristics of the rotordynamic fluid forces on the impeller were examined. The destabilizing fluid force which encourages the whirling motion of the impeller occurred in the range of 0

Flow instabilities in hydraulic machines often feature oscillating cavitation volumes, which locally introduce compliance and mass flow gain effects. These unsteady characteristics play a crucial role in one-dimensional stability models and can be determined through the definition of transfer functions for the state variables, where the cavitation volume is commonly estimated from the discharge difference between two points located upstream and downstream of the cavity. This approach is demonstrated on a test rig with a microturbine, featuring a self-oscillating vortex rope in its conical draft tube. The fluctuating discharges at the turbine inlet and the draft tube outlet are determined with the pressure–time method using differential pressure transducers. The cavitation volume is then calculated by integrating the corresponding discharge difference over time. In order to validate the results, an alternative volume approximation method is presented, based on the image processing of a high-speed flow visualization. In this procedure, the edges of the vortex rope are detected to calculate the local cross section areas of the cavity. It is shown that the cavitation volumes obtained by the two methods are in good agreement. Thus, the fluctuating part of the cavitation volume oscillation can be accurately estimated by integrating the difference between the volumetric upstream and downstream discharges. Finally, the volume and discharge fluctuations from the pressure–time method are averaged over one mean period of the pressure oscillation. This enables an analysis of the key physical flow parameters’ behavior over one characteristic period of the instability and a discussion of its sustaining mechanisms.

The response of backflow at the inlet of an inducer to the flow rate fluctuation is studied by using three-dimensional numerical calculations based on the k-ϵ turbulence model for the discussion of its effect on cavitation instabilities. It is first shown that the size of the backflow region can be correlated with the angular momentum in the upstream and the phase of the backflow significantly delays behind the quasi-steady response even at a very low frequency. It is then shown that the conservation relation of angular momentum is satisfied with minor effects of the shear stress on the boundary. The supply of the angular momentum by the negative flow is shown to be quasi-steady due to the fact that the pressure difference across the blade causing the backflow is quasi-steady at those frequencies examined. A response function of the angular momentum in the upstream to flow rate fluctuation is derived from the balance of the angular momentum and the results of the numerical calculations. This clearly shows that the backflow responds to the flow rate fluctuation as a first-order lag element. The effects of the backflow cavitation on cavitation instabilities are discussed assuming that the delay of cavity development is much smaller than the delay of the backflow. It was found that the backflow cavitation would destabilize low frequency disturbances due to the effects of the positive mass flow gain factor but stabilize high frequency disturbances due to the effect of the cavitation compliance.

It is well known that a backflow occurs in the upstream of an impeller at low flow rate. Such backflow often accompanies a vortex structure. It is considered that the vortex structure is caused by the roll-up of the shear layer between the swirling backflow and an axial main flow. In order to verify this, a simple model test was carried out in which the effect of impeller was represented by an axisymmetric swirling backflow. In the present paper, the flow field of the simplified model test is simulated by using the LES to investigate detailed flow pattern. The computed results are compared with experimental results.

Studies on cavitation instabilities of hydrofoils and cascades are reviewed to obtain fundamental understandings of the instabilities observed in turbopump inducers. Most of them are based on the stability analysis of two-dimensional inviscid cavitating flow. The most important finding of the analysis is that the cavitation instabilities depend only on the mean cavity length. For a hydrofoil, the characteristic length is the chord length and partial/transitional cavity oscillation occurs with shorter/longer cavity than 75% of the chord length. For cascades, the characteristic length is the blade spacing and various modes of instabilities are predicted when the mean cavity is longer than 65% of the spacing. In the last part, rotating choke is shown to occur when the cavity becomes longer than the spacing.

Turbopump inducers often have swirling backflow under a wide range of flow rates because they are designed with a certain angle of attack even at the design point in order to attain high cavitation performance. When the flow rate is decreased, the backflow region extends upstream and may cause various problems by interacting with upstream elements. It is also known that the backflow vortex structure occurs in the shear layer between the main flow and the swirling backflow. Experimental studies on the backflow from an inducer have given us insight into the characteristics of backflow vortex structure, but the limited information has not lead to the complete understanding of the phenomena. Numerical studies based on Reynolds-averaged Navier-Stokes (RANS) computations usually deteriorate when the flow field of interest involves large-scale separations, as shown by a previous study by Tsujimoto et al. (2005). On the other hand, the numerical approach using the Large Eddy Simulation (LES) technique has the potential to predict unsteady flows and/or flow fields that include regions of large-scale separation much more accurately than RANS computations does in general. The present paper describes the application of the LES code developed by one of the authors (Kato) to further understand the backflow vortex structure at the inlet of an inducer. First, the internal flow of the inducer was simulated, as a way to evaluate the validity of the proposed method, under a wide range of inlet flow coefficients. The static pressure peformance and the length of the backflow region was compared with measured values, and good agreement was obtained. Second, using the validated LES code, the fundamental characteristics of the backflow vortex was investigated in detail. It was found that the backflow vortices are formed in a circumferentially twisted manner at the boundary between the swirling backflow and the straight inlet flow. Also, the backflow vortices rotate in the same direction as the inducer, but with half of the circumferential flow velocity in the backflow region. Another finding was that the backflow region expands toward the center of the flow field and the number of vortices decrease, as the flow coefficient decreases. To the best of our knowledge, this is the first computation of the backflow at the inducer inlet to achieve quantitative agreement with measured results, and give new findings to the complicated three-dimensional structure of the backflow, which was very limited under experimental studies.

The present paper describes the vortex structure and the flow field of model experiments simulating the inlet flow of turbomachines at low flow coefficients. A new experimental apparatus was devised to freely set the axial velocity of the main flow and the axial and tangential components of the swirling backflow. The vortex structure was visualized by small air bubbles. It occurs in the shear layer between the main flow and the backflow. The number and the radial location of vortices are determined mainly by the axial and tangential velocities of the backflow normalized by the axial velocity of the main flow. These characteristics agree with those of the backflow vortex structure of real turbomachines. This shows that the vortex structures are caused by the roll-up of the shear layer between the axial main flow and swirling backflow, not associated with the flow interaction with individual blade of the impeller. It was shown that a two-dimensional linear stability analysis can reasonably predict the relation between the number of vortices and their radial location.

During the development stage of the liquid hydrogen turbopump for the main engine LE-7A of the H-IIA rocket, a new type of cavitation instability was observed. This instability occurs at lower cavitation numbers where the head of the inducer starts to decrease due to choke. The disturbance rotates around the rotor at about 50% of the inducer rotational speed. So, it is called “rotating choke.” In order to predict the instability, a cavity model with a cavity wake is developed. The region of instability and the frequency predicted by the model are in agreement with experiment. Discussions are made as to the relationship between rotating choke and rotating cavitation.

A cavity wake model based on the flow interaction between the viscous wake behind the cavity and external inviscid cavity flow is proposed. The conditions of interaction between viscous and inviscid flows make it possible to obtain a unique solution of the problem. The viscous wake model is formulated within the theory of boundary layers. The problem for the external inviscid flow is considered in both nonlinear and linear formulation. The developed cavity wake model provides reasonable agreement with experimental data for cavitation performance and cavitation compliance over a wide range of cavitation numbers from cavitation inception to the super cavity flow. The cavity model is applied to predict nonsymmetric flows in inducers with two and more blades. The regions of nonsymmetric cavity flow are compared with those in experiments. It is found that the local head decrease of an inducer might be caused by the nonsymmetric cavity patterns. The predicted regions of a steady nonsymmetric cavity flow correlate with the region of cavitation instability observed in experiments.

This paper reports an experimental investigation of the rotordynamic fluid force and moment on a centrifugal impeller with three types of wear-ring seals; i.e., a face seal and two types of toothed seals. The impeller is equipped with a vaneless diffuser. Rotordynamic fluid forces and moments on the impeller in whirling motion were measured directly by using four-axis force sensor. Unsteady pressures were measured at several locations in the diffuser. It was found that, (1) at low flow rate, the fluid force and fluid force moment become maximum at a certain whirling speed caused by a coupling between the whirl motion and vaneless diffuser rotating stall and (2) the seal geometry with axial seal affects the direction of the coupled fluid force relative to the direction of eccentricity through the change in the unsteady leakage flow due to the whirl.

This paper treats the flow instabilities in a vaned diffuser by using CFD. A commercial code with the standard κ-ε turbulence model was used for the present work. It was found that the flow instabilities in the vaned diffuser: i.e., rotating stall, alternate blade stall, and asymmetric stall, could be simulated by the present calculations. These instabilities were observed in a range with negative slope of the pressure performance curve of the diffuser. The rotating stall onset flow rate is larger for the case with larger clearance between the impeller and diffuser vanes.

Flow instability in a vaned diffuser with an even number of blades was examined experimentally and analytically. In the experiments, an alternate blade stall, an asymmetric stall, and two types of rotating stalls (backward/forward rotating stall) were observed depending on the impeller/diffuser clearance. For narrow clearance with strong impeller/diffuser interaction, the alternate blade stall and backward rotating stall mainly occurred. With increasing the clearance, the forward rotating stall also occurred, and the onset of rotating stall shifted toward the higher flow rate corresponding to the pressure performance in the vaned diffuser. Simple 2D stability analysis showed that the impeller/diffuser clearance affects the speed and direction of the stall propagation, and the slope of the diffuser pressure performance vs. flow rate curve affects fundamentally the onset of the flow instability within the diffuser.

This paper describes a new time marching calculation of blade surface cavitation based on a linearized free streamline theory using a singularity method. In this calculation, closed cavity models for partial and super cavities are combined to simulate the transitional cavity oscillation between partial and super cavities. The results for an isolated hydrofoil located in a 2-D channel are presented. Although the re-entrant jet is not taken into account, the transitional cavity oscillation with large amplitude, which is known to occur when the cavity length exceeds 75 percent of the chord length, was simulated fairly well. The partial cavity oscillation with relatively high frequency was simulated as damping oscillations. The frequency of the damping oscillation agrees with that of a stability analysis and of experiments. The present calculation can be easily extended to simulate other cavity instabilities in pumps or cascades.

In recent years, increasing interest has been given to the rotordynamic fluid forces on impellers, from the view point of the shaft vibration analysis. Previous experimental and analytical results have shown that the fluid-induced forces and moments on closed type pump impellers contribute substantially to the potential destabilization of subsynchronous shaft vibrations. However, to date few papers are known of the rotordynamic fluid forces on open-type centrifugal impellers. This paper reports about experimental investigations of the rotordynamic fluid force moments on an open-type centrifugal compressor impeller in precessing motion. For open-type impellers, the variations of the tip clearance and the clearance between the back shroud and casing due to the precessing motion contribute to the rotordynamic fluid force moments. Experiments were conducted to measure the rotordynamic fluid force moments directly using the 4-axis sensor, and the unsteady pressure on the front and back casing wall. In this paper, following results are obtained: (1) The fluid force moment becomes destabilizing in the region of negative precessing speed ratio(-0.3<Ω/ω<0), at the design flow rate; (2) At reduced flow rate, the destabilizing fluid force moments occurred at small positive precessing speed ratio(0.2<Ω/ω<0.4); (3) From the comparison of direct measured fluid force moments with those estimated from the unsteady pressure measured on the front and back casing walls, it was found that the destabilizing moments in the backward precession are mainly caused by the fluid forces on the front surface of the present impeller, where there is large clearance between the back shroud and casing.

For turbomachines operating at supercritical shaft speed, it is important to understand the characteristics of unsteady fluid forces on the impeller that occur due to shaft vibration. The present paper treats the forces on an open-type centrifugal impeller in whirling motion using unsteady potential flow theory. The whirling forces obtained agree reasonably with experimental results and show a destabilizing region at small positive whirl. It was found that the destabilizing force is due to the forces on the hub caused by temporal change in the thickness of the flow channel, with minor contribution of tip leakage on the destabilization.

A three-dimensional linear analysis of rotating cavitation is carried out using an annular cascade model. The purpose is to investigate three-dimensional effects of cavitation, including the radial change of peripheral velocity and the hub/tip ratio of the impeller, on rotating cavitation in inducers. A semi-actuator disk method is employed. It is assumed that the mean stream surface does not radially shift across the impeller. It is shown that there are many modes of instabilities corresponding to rotating cavitation with various radial modes travelling forward and backward. The 0th radial modes are found to correspond to the forward and backward travelling modes predicted by a previous two-dimensional analysis (Tsujimoto et al, 1993). The three-dimensionality of the geometry has the effects of diminishing the amplifying region of these fundamental modes. It is also shown that the amplifying regions of higher radial modes may be larger than those of 0th radial modes. However, it is shown that the three-dimensionality of cavitation does not significantly affect rotating cavitation.

We describe a vortex structure at the inlet of an inducer which appears on the boundary of backflow region. The vortex structure was visualized by the cavitation voids found by operating at cavitation number of σ-0.050 and recorded by a high speed video. It was measured quantitatively by two laser displacement sensors. The passing frequency and the shape of vortex filaments were determined from the outputs of the laser displacement sensors which respond to the passage of the vortex cavitation. The results show that the number of vortex filaments, their propagation angular velocity and radial location depend on the steady velocity profile at the inlet

This paper reports about experimental investigations of rotordynamic fluid force moments on an open type centrifugal impeller in precessing motion. The results show, at design flow rate, that the fluid force moment becomes destabilizing in the region of negative precession frequency ratio: -0.3

A three-dimensional linear analysis of rotating stall is carried out to clarify the effects of spanwise distribution of cascade characteristics. A semi-actuator disk model of annular cascade is employed. Linear spanwise distributions of the local performance slope are considered to examine the effects of the three-dimensionality in the cascade characteristics. Many eigenvalues were found corresponding to various kinds of radial mode. It was found that the 0th order radial mode is more unstable than higher order modes. It was also found that uneven spanwise distribution of cascade characteristics makes the 0th mode more unstable, and makes the amplitude of the disturbance larger at radial locations where the positive slope of the performance is larger.

Measurements of the internal flow velocity distributions in a cross-flow fan were made by particle-tracking velocimetry (PTV). The flow paths (pathlines) were photographed using a digital camera and analyzed using a computer program developed by Tsurusaki and Urata (1989) in order to obtain the velocity distributions. From the velocity distributions, the vorticity distributions were calculated and the vorticity supply and diffusion in the eccentric vortex region was discussed based on an axisymmetric vortex model. A numerical simulation was carried out using a random walk model. The work done by the impeller was also discussed based on the measured velocity distributions.

Experimental results of fluid moment on a centrifugal impeller shroud in precessing motion are discussed based on the bulk flow model to elucidate the fundamental flow mechanism. It is shown that the backshroud/casing clearance flow and the destabilizing fluid force moment can be simulated by the bulk flow model fairly well if the measured behavior of the resistance is correctly incorporated in the model. From the calculations with and without steady and unsteady wall shear stresses, the unsteady component of the clearance flow is shown to be basically a two-dimensional inviscid flow induced by the change in the flow thickness. The effects of the leakage flow rate and the resistance at the leakage flow entry are discussed, paying attention to the steady tangential velocity of the leakage flow.

This paper presents the experimental results of rotordynamic forces on an open-type centrifugal impeller in whirling motion. For the whirling open-type impeller, the variation of the tip clearance produces the rotordynamic force. It was found that, [1] destabilizing force occures at small whirling/rotation ratio throughout all of the flow range, and [2] At smaller flow rate the magnitude of the force changes dramatically at a whirling/rotation ratio. The forces estimated from unsteady pressure distribution on the casing and that estimated from the pressure difference across the blades are compared with the measured rotordynamic forces.