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Unsteady behaviors of free surface around a rotating vertical shaft in cylindrical stationary casing were investigated. Experiments were carried out with various rotating frequency of the shaft at two initial water levels. An axi-symmetrical free surface oscillation took place when the rotational speed of the shaft became larger than a certain value. The frequency of the free surface oscillation decreased as the rotating frequency increased. A theoretical model was developed, and the mechanisms of the free surface oscillation were clarified. The oscillation was found to be a sloshing mode excited by the change of fluid angular velocity, caused by the change of wetted areas on the inner rotating shaft and outer stationary casing, associated with the change in free surface height.

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 positive slope on the pump performance curve of pump-turbines suggests potential operational instabilities in pump mode. Previous research has indicated that the positive slope instability can be affected by cavitation conditions, however the detailed influences remain poorly understood. A low specific speed model pump-turbine was systematically examined by experiments for the first time in the present study. A new finding was made that the positive slope is alleviated at the large guide vane opening with decreasing cavitation coefficient, while there is little influence by cavitation at the medium opening. The positive slope occurs at larger discharge coefficient at the small opening when the cavitation coefficient decreases. FFT (Fast Fourier Transformation) results of pressure fluctuations revealed the occurrence of rotating stall close to the vaneless space between the runner and the guide vanes. The variation of cavitation coefficient influences greatly on the occurrence of rotating stall, but the pressure fluctuation frequency caused by rotating stall does not vary significantly. It is postulated that the influence of cavitation coefficient on the rotating stall may be responsible for the variation of the positive slope region.

Hydro turbines operating at partial flow conditions usually have vortex ropes in the draft tube that generate large pressure fluctuations. This unsteady flow phenomenon is harmful to the safe operation of hydropower stations. This paper presents numerical simulations of the internal flow in the draft tube of a Francis turbine with particular emphasis on understanding the unsteady characteristics of the vortex rope structure and the underlying mechanisms for the interactions between the air and the vortices. The pressure fluctuations induced by the vortex rope are alleviated by air admission from the main shaft center, with the water-air two phase flow in the entire flow passage of a model turbine simulated based on the homogeneous flow assumption. The results show that aeration with suitable air flow rate can alleviate the pressure fluctuations in the draft tube, and the mechanism improving the flow stability in the draft tube is due to the change of vortex rope structure and distribution by aeration, i.e. a helical vortex rope at a small aeration volume while a cylindrical vortex rope with a large amount of aeration. The preferable vortex rope distribution can suppress the swirl at the smaller flow rates, and is helpful to alleviate the pressure fluctuation in the draft tube. The analysis based on the vorticity transport equation indicates that the vortex has strong stretching and dilation in the vortex rope evolution. The baroclinic torque term does not play a major role in the vortex evolution most of the time, but will much increase for some specific aeration volumes. The present study also depicts that vortex rope is mainly associated with a pair of spiral vortex stretching and dilation sources, and its swirling flow is alleviated little by the baroclinic torque term, whose effect region is only near the draft tube inlet.

Cavitation instabilities such as rotating cavitation and cavitation surge often occur in high speed turbopumps. In the present study, numerical simulation of cavitation surge, which numerically solves the one-dimensional momentum and continuity equations with modelled dynamic cavitation characteristics, is conducted. The phase lag of cavity response against the inlet pressure and the suction flow rate variations is modeled in the form of the first-order lag system considering that the frequency of cavitation surge is small. Differently from linear stability analysis made in our previous study, the equations are solved in time domain with retaining some of non-linear terms. The method is validated through the comparison with the stability analysis. Then the effect of phase lags in dynamic cavitation characteristics is examined.

It is well known that strong pressure fluctuation will occur in the draft tube of a Francis turbine operated under part-load operation. The pressure fluctuation is usually due to the vortex rope as well as cavitation. However, the vortical flow and pressure field are dependent on the geometry of draft tube of Francis turbine. In this study, hydraulic performance and pressure fluctuation have been tested for a model Francis turbine. The internal flow for the turbine is investigated numerically. It is confirmed that the numerical results predict reasonably the hydraulic performance and the pressure fluctuation due to vortex rope at part-load operation. For a better understanding of the vortical flow in the model turbine, a conical draft tube is used instead of the conventional elbow draft tube. The vorticity transport equation is applied to analyze the vortex evolution inside Francis turbine based on the unsteady flow simulation. The flow mechanism of the vortex rope and pressure fluctuation with different draft tubes is discussed. It is shown that both cavitation and the bending structure influence the vortex rope, which will cause a significant difference in the distribution of pressure fluctuation.

The strong swirling flow at the exit of the runner of a Francis turbine at part load causes flow instabilities and cavitation surges in the draft tube, deteriorating the performance of the hydraulic power system. The unsteady cavitating turbulent flow in the draft tube is simplified and modeled by a diffuser with swirling flow using the Scale-adaptive simulation method. Unsteady characteristics of the vortex rope structure and the underlying mechanisms for the interactions between the cavitation and the vortices are both revealed. The generation and evolution of the vortex rope structures are demonstrated with the help of the iso-surfaces of the vapor volume fraction and the Qcriterion. Analysis based on the vorticity transport equation suggests that the vortex dilatation term is much larger along the cavity interface in the diffuser inlet and modifies the vorticity field in regions with high density and pressure gradients. The present work is validated by comparing two types of cavitation surges observed experimentally in the literature with further interpretations based on simulations.

This paper mainly summarizes the recent progresses for the cavitation study in the hydraulic machinery including turbo-pumps, hydro turbines, etc.. Especially, the newly developed numerical methods for simulating cavitating turbulent flows and the achievements with regard to the complicated flow features revealed by using advanced optical techniques as well as cavitation simulation are introduced so as to make a better understanding of the cavitating flow mechanism for hydraulic machinery. Since cavitation instabilities are also vital issue and rather harmful for the operation safety of hydro machines, we present the 1-D analysis method, which is identified to be very useful for engineering applications regarding the cavitating flows in inducers, turbine draft tubes, etc. Though both cavitation and hydraulic machinery are extensively discussed in literatures, one should be aware that a few problems still remains and are open for solution, such as the comprehensive understanding of cavitating turbulent flows especially inside hydro turbines, the unneglectable discrepancies between the numerical and experimental data, etc.. To further promote the study of cavitation in hydraulic machinery, some advanced topics such as a Density-Based solver suitable for highly compressible cavitating turbulent flows, a virtual cavitation tunnel, etc. are addressed for the future works.

Researches on the mechanism of surging and the surge behaviors in the systems of pumps, or fans or compressors, and the effects of flow-paths had been initiated and had made a great progress in Japan in the decades from the nineteen-forties to the nineteen-sixties. In 1947, the essential cause of the surges, i.e., self-excited oscillation nature of the flow-system, was discovered analytically by Professor Sumiji Fujii of Tokyo University, and most of the characteristic behaviors of the phenomena had been explained clearly. Successive studies by many other Japanese researchers continued to prove experimentally the mechanism, to extend the analytical studies, and to attempt preventing surge occurrence, etc. in the following two decades. The historical information on the early surge studies could be helpful to some concerned people. At the same time, the basic and plain ways of discussions and reasoning about the phenomena in the pioneering researches could give us much to be learned even in the present time of high-power computing systems. Regrettably, many of the original research works have been published only in Japanese. The present review introduces very briefly the situations in memories of the pioneering researchers and engineers.

In cardiopulmonary support systems with a membrane oxygenation such as a percutaneous cardiopulmonary support (PCPS) or an extracorporeal membrane oxygenation (ECMO), blood pumps need to generate the pressure rise of approximately 200mmHg or higher, due to the high hydraulic resistances of the membrane oxygenation and of the cannula tubing. In order to realize the blood pump with higher pressure rise, higher anti-hemolysis and thrombosis performances, the development of novel centrifugal blood pump composed of two-stage has been conducted by the authors. In the present paper, effective attempts to decrease the wall shear stress and to suppress the stagnation are introduced for the prevention of hemolysis and thrombosis in blood pumps. The hemolysis test was also carried out and it was clarified that the decrease of wall shear stress is effective as a guideline of design of blood pumps for improving the anti-hemolysis performance. Keywords: Centrifugal Pump, Artificial Heart, Blood, Hemolysis, Thrombosis

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.

In real three-dimensional inducers, most of the cavitation instabilities appear when the steady cavity length at the tip becomes about 65% of the blade spacing. This agrees with the results of two-dimensional stability analysis assuming blade surface cavitation. However, in real flows, tip cavitation is most significant. So, this chapter discusses about cavitation instabilities mainly based on three-dimensional CFD.

【In the cardiopulmonary support system with an ECMO (extracorporeal membrane oxygenation), a higher pump head is demanded for a blood pump. In order to realize a blood pump with higher pump head, higher anti-hemolysis and thrombosis performances, a study on the development of unprecedented multistage blood pump was conducted. In consideration of the application of the blood pump for pediatric patients, a miniature two-stage centrifugal blood pump with the impeller's diameter of 40mm was designed and the performance was examined in experiments and computations. Some useful knowledge for a design of the blood pump with higher anti-hemolysis and thrombosis performances was obtained.】

Phase resonance in Francis type hydraulic turbine is studied. The phase resonance is a phenomenon that the pressure fluctuation in the penstock of hydraulic turbine installation can become very large when the pressure waves from each guide vane caused by the interaction with the runner vane reach the penstock with the same phase. Experimental and numerical studies have been carried out using a centrifugal fan. In the present study, comparisons between the pump mode and the turbine mode operations are made. The experimental and numerical results show that the rotational direction of the rotor does not affect characteristics of the pressure fluctuation but the propagation direction of the rotorstator interaction mode plays an important role. Flow rate fluctuations through the stator are examined numerically. It has been found that the blade passing flow rate fluctuation component can be evaluated by the difference of the fluctuating pressure at the inlet and the outlet of the stator. The amplitude of the blade passage component of the pressure fluctuation is greater at the stator inlet than the one at the stator outlet. The rotor-stator interaction mode component is almost identical at the inlet and the outlet of the stator. It was demonstrated that the pressure fluctuation in the volute and connecting pipe normalized by the flow rate fluctuation becomes the same for pump and turbine mode operations, and depends on the rotational direction on the interaction mode.

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.

Model tests and CFD were carried out to find out the cause of cavitation surge in hydraulic power plants. In experiments the cavitation surge was observed at flow rate, both with and without a surge tank placed just upstream of the inlet volute. The surge frequency at smaller flow rate was much smaller than the swirl mode frequency caused by the whirl of vortex rope. An unsteady CFD was carried out with two boundary conditions: (1) the flow rate is fixed to be constant at the volute inlet, (2) the total pressure is kept constant at the volute inlet, corresponding to the experiments without/with the surge tank. The surge was observed with both boundary conditions at both higher and lower flow rates. Discussions as to the cause of the surge are made based on additional tests with an orifice at the diffuser exit, and with the diffuser replaced with a straight pipe.

Main steam control valves in power plants are required to operate underwide ranges of valve openings and pressure ratios. In the present paper, experimental and numerical investigations are conducted using rigid and flexible valve head supports to clarify the mechanisms of valve head vibrations that are caused by unsteady flows around the valve. The results obtained using the rigid support without valve head vibration show that the unsteady flow around the valve head causes pressure fluctuations on the valve head surface with random and impulsive wave forms. When using the flexible support, the valve head vibrates near the natural frequency of the valve head support system, and vibrations are excited around the operating conditions where the pressure fluctuation becomes greater when using the rigidly supported valve head. When the valve head vibration increases, the pressure fluctuation becomes periodic with the same frequency as the valve head vibration. The numerical results show that the response of the separated jet lags behind the valve head motion. As a result, the lateral fluid force adds negative damping on the vibration on the valve head.

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.

In addition to aspiration drag, the advantages gained by dual-bell nozzle utilization in practice are circumvented with a dip of thrust during operation mode transitions that occur outside of the optimal conditions. Practical transition from lowto high-altitude operationmode occurs at lower nozzle pressure ratios (NPRs) than the optimum transition point. The influence of the film-cooling flow on nozzle operationmode transition is investigated. It is found that the operationmode transitionNPR is increased, and the thrust dip during the transition is decreased through the injection of the film-cooling flow with an appropriate inlet pressure and flow rate.

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.

Dual-bell nozzle is one of the altitude compensation nozzle concepts, which consists of two bell-type nozzle with different geometric area ratios. The dual bell nozzle has two operation modes—a low altitude operation mode and a high altitude operation mode. However, the practical transition between these operation modes occurs at lower nozzle pressure ratio (NPR) than the optimum one. In the present study, the effect of introduction of film-cooling flow into the nozzle is examined in order to control the operation mode transition NPR. The experimental and numerical results show that the operation mode transition can be control by injecting the film cooling flow at appropriate inlet pressure and flow rate. By injecting the film cooling flow, the axial momentum near the wall in the extension part becomes small and the separation point movement becomes slower. As a result, the dip of the thrust coefficient during the operation mode transition becomes smaller.

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.

The purpose of the present research is to suppress cavitation instabilities by using a circumferential groove. The circumferential groove was designed based on CFD so that the tip leakage vortex is trapped by the groove and does not interact with the next blade. Experimental results show that the groove can suppress rotating cavitation, asymmetric cavitation and cavitation surge. However, weak instabilities with higher frequency could not be suppressed by the groove. From the analysis of pressure pattern similar to that for rotor-stator interaction, it was found that the higher frequency components are caused by the interaction of backflow vortices with the inducer blades.

Severe flexural vibration of the rotor shaft of a Francis turbine runner was experienced in the past. It was shown that the vibration was caused by the fluid forces and moments on the backshroud of the runner associated with the leakage flow through the back chamber. The aim of the present paper is to study the self-excited rotor vibration caused by the fluid force moments on the backshroud of a Francis turbine runner. The rotor vibration includes two fundamental motions, one is a whirling motion which only has a linear displacement and the other is a precession motion which only has an angular displacement. Accordingly, two types of fluid force moment are exerted on the rotor, the moment due to whirl and the moment due to precession. The main focus of the present paper is to clarify the contribution of each moment to the self-excited vibration of an overhung rotor. The runner was modeled by a disk and the whirl and the precession moments on the backshroud of the runner caused by the leakage flow were evaluated from the results of model tests conducted before. A lumped parameter model of a cantilevered rotor was used for the vibration analysis. By examining the frequency, the damping rate, the amplitude ratio of lateral and angular displacements for the cases with longer and shorter overhung rotor, it was found that the precession moment is more important for smaller overhung rotors and the whirl moment is more important for larger overhung rotors, although both types of moment due to the leakage flow can cause self-excited vibration of an overhung rotor.

Based on the one-dimensional stability analysis, the self-excited oscillation in hydraulic power generating systems was studied by a simple experiment and numerical simulation. It was shown that a cavity in a conical diffuser can cause surge. With the diffuser, a high amplitude and low frequency oscillation occurs at low cavitation number. This oscillation was not observed with the straight pipe. It was confirmed that the diffuser effect of the draft tube can be the cause of the full load surge in hydraulic power system. Numerical results were also analyzed to check the validity of the one-dimensional stability analysis.

A steam control valve is used to control the flow from the steam generator to the steam turbine in thermal and nuclear power plants. During startup and shutdown of the plant, the steam control valve is operated under a partial flow conditions. In such conditions, the valve opening is small and the pressure deference across the valve is large. As a result, the flow downstream of the valve is composed of separated unsteady transonic jets. Such flow patterns often cause undesirable large unsteady fluid force on the valve head and downstream pipe system. In the present study, various flow patterns are investigated in order to understand the characteristics of the unsteady flow around the valve. Experiments are carried out with simplified two-dimensional valve models. Two-dimensional unsteady flow simulations are conducted in order to understand the experimental results in detail. Scale effects on the flow characteristics are also examined. Results show three types of oscillating flow pattern and three types of static flow patterns.