The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius‐time behavior is made with experimental observations in superheated water, and very good agreement is found.

The growth of vapor bubbles in superheated liquids. report no. 26-6

The subject of this monograph is the fluid dynamics of liquid turbomachines, particularly pumps. Rather than attempt a general treatise on turbomachines, we shall focus attention on those special problems and design issues associated with the flow of liquid through a rotating machine. There are two characteristics of a liquid that lead to these special problems, and cause a significantly different set of concerns than would occur in, say, a gas turbine. These are the potential for cavitation and the high density of liquids that enhances the possibility of damaging unsteady flows and forces.

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Hydrodynamics of Pumps

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics)

Large Eddy Simulation and theoretical investigations of the transient cavitating vortical flow structure around a NACA66 hydrofoil

The instability of a partial cavity induced by the development of a re-entrant jet is investigated on the basis of experiments conducted on a diverging step. Detailed visualizations of the cavity behaviour allowed us to identify the domain of the re-entrant jet instability which leads to classical cloud cavitation. The surrounding regimes are also investigated, in particular the special case of thin cavities which do not oscillate in length but surprisingly exhibit a re-entrant jet of periodical behaviour. The velocity of the re-entrant jet is measured from visualizations, in the case of both cloud cavitation and thin cavities. The limits of the domain of the re-entrant jet instability are corroborated by velocity fluctuation measurements. By varying the divergence and the confinement of the channel, it is shown that the extent of the auto-oscillation domain primarily depends upon the average adverse pressure gradient in the channel. This conclusion is corroborated by the determination of the pressure gradient on the basis of LDV measurements which shows a good correlation between the domain of the cloud cavitation instability and the region of high adverse pressure gradient. A simple phenomenological model of the development of the re-entrant jet in an adverse pressure gradient confirms the strong influence of the pressure gradient on the development of the re-entrant jet and particularly on its thickness. An ultrasonic technique is developed to measure the re-entrant jet thickness, which allowed us to compare it with the cavity thickness. By considering an estimate of the characteristic height of the perturbations developing on the interface of the cavity and of the re-entrant jet, it is shown that cloud cavitation requires negligible interaction between both interfaces, i.e. a thick enough cavity. In the case of thin cavities, this interaction becomes predominant; the cavity interface breaks at many points, giving birth to small-scale vapour structures unlike the large-scale clouds which are periodically shed in the case of cloud cavitation. The low-frequency content of the cloud cavitation instability is investigated using spectral analysis of wall pressure signals. It is shown that the characteristic frequency of cloud cavitation corresponds to a Strouhal number of about 0.2 whatever the operating conditions and the cavity length may be, provided the Strouhal number is computed on the basis of the maximum cavity length. For long enough cavities, another peak is observed in the spectra, at lower frequency, which is interpreted as a surge-type instability. The present investigations give insight into the instabilities that a partial cavity may undergo, and particularly the re-entrant jet instability. Two parameters are shown to be of most importance in the analysis of the re-entrant jet instability: the adverse pressure gradient and the cavity thickness compared to the re-entrant jet thickness. The present results allowed us to conduct a qualitative phenomenological analysis of the stability of partial cavities on cavitating hydrofoils. It is conjectured that cloud cavitation should occur for short enough cavities, of the order of half the chordlength, whereas the instability often observed at the limit between partial cavitation and super-cavitation is here interpreted as a cavitation surge-type instability.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2819429B69AFDF15C7C3ECFEAEB3A69D/S0022112001005420a.pdf/div-class-title-the-cavitation-instability-induced-by-the-development-of-a-re-entrant-jet-div.pdf

The cavitation instability induced by the development of a re-entrant jet

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.

A review of cavitation in hydraulic machinery

Oscillating cavitation of an inducer was observed through unsteady inlet pressure measurements and by use of high speed video picture, covering a wide range of flow coefficient and cavitation number. One of the purposes of the study is to identify a mode of rotating cavitation predicted by a linear analysis, and the other is to obtain a general view of oscillating cavitation. The number of rotating cavitation cells and their propagation velocity were carefully determined from the phase difference of pressure fluctuations at various circumferential locations. Various kinds of oscillating cavitation were observed: rotating cavitation rotating faster/slower than impeller rotation, cavitation in backflow vortices, and surge mode oscillations. Effects of inlet and outlet (effective) pipelength were also studied.

Observations of Oscillating Cavitation of an Inducer

A liquid oxygen turbopump has been developed for the main engine (LE-7) of the H-II rocket. The LE-7 LOX pump requires an inducer with quite high suction performance and high head, because a low-speed and low-pressure pump is not used ahead of the main pump in the LE-7 engine. The inducer was designed using the customary method, and its hydraulic and mechanical performances were investigated in tests of LE-7 LOX turbopumps. The original combination of an inducer and an inducer housing satisfied the required hydraulic performance criteria. However, this combination was found to result in supersynchronous shaft vibrations due to rotating cavitation which occurred in the inducer. This problem was almost completely solved by a simple modification of the inducer upstream housing. Furthermore, the rotating cavitation of the present inducer was investigated using a new theory of such cavitation. I. Introduction A LIQUID oxygen turbopump has been developed for the main engine (LE-7) of the H-II rocket, the next generation of Japanese launch vehicle. This turbopump requires a high-flow, high-pressure liquid oxygen pump. Because a low-speed, low-pressure pump is not used ahead of the main pump in the LE-7 engine, it is very important to operate the main pump at higher speed to obtain a smaller-size, lighterweight turbopump. The operational speed of the present turbopump was restricted by the suction performance of the main pump inducer. In this article, we report both the design and test results of the inducer. The main pump of the LE-7 LOX turbopump has a singlestage centrifugal impeller with an inducer. 1 The inducer is characterized by a low flow coefficient, a small inlet angle, a sharp leading edge, etc., to achieve higher suction performance. The inducer was designed using the customary method.2-3

Hydraulic and Mechanical Performance of LE-7 LOX Pump Inducer

Rotating cavitation (R.C.) is one of the most important problems in the development of modern rocket turbopump inducers (Kamijo et al., 1993, Goirand et al., 1993, Ryan et al., 1994). By 2-D linear analysis (Tsujimoto et al., 1993), rotating cavitation was found to be caused by the positive mass flow gain factor, namely, the increase of cavity volume due to the decrease of flow rate, and to be completely different from rotating stall (R.S.) which is caused by the positive slope of the head characteristic. Moreover, 2-D analysis predicted that there can be two modes of rotating cavitation: the forward rotating mode which propagates faster than the impeller, and the backward rotating mode which propagates in the direction opposite to that of the impeller. Nonlinear (Tsujimoto et al., 1996) and 3-D (Watanabe et al., 1997) analyses resulted in basically the same results as those obtained for the previous 2-D cases and predicted forward and backward propagating modes. These were reported at the last meeting of the conference (Tsujimoto et al., 1995). However, most R.C. found in experiments propagates forward, although the backward mode was also found recently (Hashimoto et al., 1996).

A Theoretical Analysis of Rotating Cavitation in Inducers

Research on rotating cavitation progressed during the development of a liquid oxygen (LOX) turbopump for the LE-7 engine of the H-II rocket In some ranges of cavitation numbers, supersynchronous shaft vibrations were observed in the LE-7 LOX main pump inducer From a comparison with the results of our previous studies it was concluded that such shaft vibrations were caused by rotating cavitation in the inducer A simple modie cation of the inducer upstream housing almost completely extinguished such shaft vibrations Some characteristics of rotating cavitation have been fairly well elucidated However, we were not able to fully explain the mechanism of the ine uence of the simple modie cation of the inducer upstream housing on the rotating cavitation We thus commenced further experimental studies to investigate rotating cavitation in more detail In the present study, some visual observations of rotating cavitation were conducted using the same inducer test facility as that used in our previous work

Yoshinobu Tsujimoto

Papers

A review of cavitation in hydraulic machinery

Observations of Oscillating Cavitation of an Inducer

Hydraulic and Mechanical Performance of LE-7 LOX Pump Inducer

A Theoretical Analysis of Rotating Cavitation in Inducers

Experimental Study on Rotating Cavitation of Rocket Propellant Pump Inducers