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The conventional high-speed images of cavitation with a set of X-ray phase contrast images reveal the presence of three different types of mechanisms responsible for large cloud shedding: re-entrant jet mechanism, condensation shock wave mechanism, and collapse-induced pressure wave mechanism. At higher cavitation numbers, the sheet cavity is relatively short and the cavity detachment is a consequence of a re-entrant jet pinching off the cavity from its leading edge. At lower cavitation numbers, the re-entrant jet plays a smaller role in the cavitation instabilities and the primary reason for periodic cloud shedding is the condensation shock mechanism where a void fraction discontinuity propagates upstream until collapsing the entire cavity. If the amount of shed vapour cloud reaches a certain extent, the collapse will emit a pressure wave strong enough to disturb the growing cavity, and subsequently make it detached from the wall. This is the third mechanism observed in the experiments. We point out the inappropriate classification of combining condensation shock and collapse-induced pressure wave mechanisms in the literature, since we identify pronounced differences between them: (i) the pressure increase across the condensation front is very weak (a few kPa) while the amplitude of collapse-induced pressure wave can be hundreds of kPa, (ii) the travelling velocity of the collapse-induced pressure wave within the cavity is much faster than the condensation shock, and (iii) the collapse-induced pressure wave does not result in an obvious discontinuity in void fraction when it propagates through the cavity, in contrary to the condensation shock.

Abstract The present paper is focused on the optimization of the overlap length in various types of distributors in hydraulic systems. It has been shown that this length has a strong influence on cavitation in rotating distributors, so its optimization would be beneficial to reduce the detrimental effects of cavitation, such as noise, vibrations, and instabilities. The objective of the present study is to generalize the modelling of the overlap length to different types of distributors and to determine the critical length at cavitation inception. The results show that the pressure losses in rotating distributors and in other types of distributors are similar, including the slide-valves that are the vast majority of distributors in hydraulic systems. It is confirmed that the overlap length has a stronger influence on the cavitation development than the distributor rotation speed. A critical overlap length of 0.071 mm is obtained, below which no significant development of cavitation is obtained, at all rotation speeds. Article Highlights The pressure losses in a rotating distributor and in a slide-valve can be expressed similarly. The overlap length has a large influence on the cavitation development, much larger than the rotation speed. A critical overlap length of 0.071 mm was obtained, below which there is almost no cavitation, for any rotation speed.

International audience; As a new type of the propulsive devices, cycloidal rotor has been attracting more attention recently. The presentwork concentrates on the analysis of the performance and internal flow field of a two-bladed cycloidal rotoroperating at low Reynolds numbers, with special emphasis on understanding how the flow structure affects theperformance at different working conditions. The symmetrical/asymmetrical pitching motions are evaluatedinitially and the primary results show that the asymmetrical pitching with a mean pitching angle of 5◦ improvesthe efficiency of the rotating system. Then, the effect of the chord-to-radius ratio at three different conditions isdiscussed, which shows that the chord-to-radius ratio of 0.45 is the best value to maximise the performance. Theflow pattern, involving the blade-wake interaction, wake-wake interaction, three vortex structures on the bladesurface, roll-up vortices inside the laminar boundary layer, separation bubble, leading-edge vortex, trailing-edgevortex and flow separation vortex, are discussed in detail under various operating conditions. The study on theperformance of a single blade, the forces (lift and drag) distributions, the blade loadings and the near-wall flowson two blades, provide a new understanding of the global performance change of the propeller.

International audience; Flapping foil energy harvesting systems are considered as highly competitive devices for conventional turbines. Several research projects have already been carried out to improve performances of such new devices. This paper is devoted to study effects of non-sinusoidal heaving trajectory, non-sinusoidal pitching trajectory, and the effective angle of attack on the energy extraction performances of a flapping foil operating at low Reynolds number (Re=1100). An elliptic function with an adjustable parameter S (flattening parameter) is used to simulate various sinusoidal and non-sinusoidal flapping trajectories. The flow around the flapping foil is simulated by solving Navier–Stokes equations using the commercial software Star CCM+ based on the finite-volume method. Overset mesh technique is used to model the flapping motion. The study is applied to the NACA0015 foil with the following kinetic parameters: a dimensionless heaving amplitude h0 = 1c, a shift angle between heaving and pitching motions f = 90 , a reduced frequency f = 0:14, and an effective angle of attack amax varying between 15 and 50 , corresponding to a pitching amplitude in the range q0 = 55:51 to 90:51 . The results show that, the non-sinusoidal trajectory affects considerably the energy extraction performances. For the reference case (sinusoidal heaving and pitching motions, Sh = Sq = 1), best performances are obtained for the effective angle of attack, amax = 40 . At small effective angle of attack amax < 30 , the non-sinusoidal pitching motion combined with a sinusoidal heaving motion, greatly improve energy extraction performances. For amax = 15 , Sh = 1 and Sq = 2, energy extraction efficiency is improved by 52.22% and the power coefficient by 70.40% comparatively to sinusoidal pitching motion. At high effective angles of attack ( amax >40 ), non-sinusoidal pitching motion has a negative effect. Performance improvement is quite limited with the combined motions non-sinusoidal heaving/sinusoidal pitching.

International audience; The present paper is devoted to the analysis of the impact of a raindrop on water. The studied configuration is focused on the effects of high energy splash regimes, caused by the impact of large droplets at high velocity. Such cases, which mimic raindrops falling on the surface of the ocean at their terminal speed, are characterized by short time scales and complex mechanisms, and they have received little attention until now. The GERRIS opensource solver is used to perform three-dimensional simulations of the impact. The capabilities of octree adaptative mesh refinement enable to capture the small-scale features of the flow, while the Volume Of Fluid (VOF) approach combined with a balanced force surface tension calculation is applied to advect the volume fraction of liquid and reconstruct the interfaces. A post-processing of the results has been developed to identify each object resulting from the splash and characterize their evolution in time. Specifically, the contour of the liquid/gas structure created at the impact is reconstructed as well as the size and position of the ligaments and droplets aerosolized in the atmosphere. The results are compared to experimental data obtained previously by Murphy et al. (J. Fluid Mech., vol. 780, pp. 536–577): both the crown formation above the cavity created by the impact, the ligaments emanating from the rim at the top of the crown, and the downward liquid jet that pierces through the bottom of the cavity, are correctly reproduced by the model. A very good quantitative agreement is also obtained regarding the time evolution of the crown dimensions, including its closure after the initial phase of expansion.

Inverse problems in computational mechanics consist of inferring physical fields that are latent in the model describing some observable fields. For instance, an inverse problem of interest is inferring the Reynolds stress field in the Navier–Stokes equations describing mean fluid velocity and pressure. The physical nature of the latent fields means they have their own set of physical constraints, including boundary conditions. The inherent ill-posedness of inverse problems, however, means that there exist many possible latent fields that do not satisfy their physical constraints while still resulting in satisfactory agreement in the observation space. These physical constraints must therefore be enforced through the problem formulation. So far there has been no general approach to enforce boundary conditions on latent fields in inverse problems in computational mechanics, with these constraints often simply ignored. In this work we demonstrate how to enforce boundary conditions in Bayesian inversion problems by choice of the statistical model for the latent fields. Specifically, this is done by modifying the covariance kernel to guarantee that all realizations satisfy known values or derivatives at the boundary. As a test case the problem of inferring the eddy viscosity in the Reynolds-averaged Navier–Stokes equations is considered. The results show that enforcing these constraints results in similar improvements in the output fields but with latent fields that behave as expected at the boundaries.

The cavitating flows created in a small Venturi tube with throat cross section 4 × 15.34 mm2 are investigated based on ultra-fast x-ray imaging. The instantaneous velocities of the liquid and vapor are measured simultaneously by tracking seeding particles and vapor structures respectively while the vapor volume fraction is derived from the different x-ray attenuation. Wavelet decomposition with appropriate thresholds is used to separate seeding particles from vapor structures, so that image cross-correlations could be applied on the two phases separately. This study presents data on mean velocity and void ratio field, statistical turbulent quantities in three different cavitation levels with the same reference velocity. A type of cavitation associated with a weak but persistent re-entrant jet is described. The comparison between the cavitation and the noncavitating flow shows that the averaged flow field is significantly altered by the presence of cavitation and the vapor formation near the throat area is observed to suppress velocity fluctuations.

International audience; This paper investigates the applicability of a hybrid data assimilation approach, namely ensemble-based variational method (EnVar), to optimise Reynolds Averaged Navier-Stokes (RANS) simulations in convergent-divergent channel from the perspective of Bayesian inference. Concretely, the ensemble-based variational method is applied to infer the inlet velocity and turbulence model corrections by assimilating Direct Numerical Simulation (DNS) results or limited experimental data. The approach is first adopted to infer the inlet velocity profile for the WallTurb Bump and Venturi geometry. The improvement can be achieved near the inlet region for the bump, but for Venturi in light of the view field limited in adverse pressure gradient region, the observation space is not sensitive to the perturbation of inlet condition. In a second step, the model corrections in k − ω SST model are investigated by assimilating the limited sparse experimental data. With the inferred model corrections, the predictions on both velocity and turbulent kinetic energy (TKE) get improved. The results indicate that the ensemble-based variational method is efficient in inferring unknown quantities of both low dimension (D=20) and high dimension (D=2400) with small ensemble size robustly and non-intrusively. This approach could prove very useful for Bayesian inference or optimisation in CFD problems.

International audience; In order to obtain higher propulsion efficiency for marine transportation, the authors have numerically tested a novel trochoidal propeller using a sinusoidal blade pitch function. The main results presented here are the evaluation of thrust and torque, as well as the calculated hydrodynamic efficiency, for various absolute advance coefficients. The performance of the present sinusoidal-pitch trochoidal propeller is compared with previous analytical calculations of transverse propeller performances. Calculations for the trochoidal propeller are performed using a two-dimensional model. The numerical calculation is used to optimize the foil pitch function in order to achieve the highest efficiency for a given geometry and operational parameters. Foil-to-foil interactions are also studied for multiple-foil propellers to determine the effects of the blade number on the hydrodynamic efficiency.

International audience; In this paper, a new model based on bubble-bubble interactions is proposed for cavitation. Unlike the well-known existing models (Rayleigh-Plesset, Gilmore), which are derived from the local balance equations in the vicinity of a single cavitation bubble, the present approach is based on the mutual interaction between two spherical bubbles of different sizes. The mass and momentum conservation equations, coupled with the local flowdivergence, lead to two equations for the evolution of the bubble radii and one equation for the local pressure. The bubble size variations predicted by the model are found in close agreement with the previous experimental data reported by Ohl [“Cavitation inception following shock wave passage,” Phys. Fluids 14(10), 3512–3521 (2002)]. The distinct radii of bubbles located close to each other, as well as the premature collapse of small bubbles during the initial stage of cavitation inception, are correctly reproduced by the model. The results generally show that bubble/bubble interactions play a primary role in the physics of cavitation inception, which is a preponderant phenomenon in cavitation-induced noise and erosion. The influence of the size of the nuclei on these interactions is discussed. During the expansion phases, the variations in the local flow divergence only slightly affect the growth of the big nuclei, which is mainly governed by their interaction with the neighboring bubbles, while it triggers the expansion of the small nuclei. Conversely, in the compression phase, the behavior of the bubbles is not influenced anymore by the initial size of the nuclei. It is also shown that large amplitude pressure variations resulting from the multiple collapses of small bubbles should be taken into account, in addition to the ambient pressure evolution, to calculate the instantaneous local pressure in the liquid and eventually evaluate the flow aggressiveness and the resulting erosion.

International audience; The present work focuses on the analysis of the extreme conditions encountered during the process of collapse of cavitation bubbles. The objective is to characterize the temperature variations inside the vapor/gas bubble, and also in the surrounding liquid. This information is especially relevant to address the issues of cavitation erosion and develop appropriate models that take into account the thermal effects in cavitation. The work is based on an experimental approach where temperature measurements are performed with cold wires technique. This technique is characterized by a very small time response, and can be applied to both phases during the growth and collapse of the bubbles.

International audience; This paper is focused on the dynamics of cloud cavitation at Sub-millimeter scales, between 0.1 and 10 mm. A simple flow configuration consisting in a small diameter jet impacting a wall at 90° and then flowing radially between two plates is used. Cavitation is obtained in the gap between the two plates, due to the local flow acceleration. The scale of the setup was changed by varying separately the gap between the two plates, and the nozzle diameter. Observations were performed from the transparent bottom plate, using a high-speed camera and intense illumination, for various Reynolds and cavitation numbers. The analysis is focused on the variations of the cavity length and the Strouhal number based on the characteristic frequency of the flow instability.

Cavitation is a limiting phenomenon in many domains of fluid mechanics. Instabilities of a partial cavity developed on an hydrofoil, a converging-diverging step or in an inter-blade channel in turbomachinery, have already been investigated and described in many previous works. The aim of this study is to evaluate a passive control method of the sheet cavity. According to operating conditions, cavitation can be described by two different regimes: an unstable regime with a cloud cavitation shedding and a stable regime with only a pulsating sheet cavity. Avoiding cloud cavitation can limit structure damages since a pulsating sheet cavity is less agressive. The surface condition of a converging-diverging step, like a Venturi-type obstacle, is here studied as a solution for a passive control of the cavitation. This study discusses the effect of an organized roughness, in the shape of longitudinal grooves, on the developed sheet cavity. Analyzes conducted with Laser Doppler Velocimetry, visualisations and pressure measurements show that the grooves geometry, and especially the groove depth, acts on the sheet cavity dynamics. Results show that modifying the surface condition, by varying the grooves geometry, can reduce cavity sheet length and even suppress the cloud cavitation shedding., Comment: Submitted to Journal of Fluids Engineering

In this paper, by using the system potential of two bubbles and with a special interest in the interaction by exchange of volume and without exchange of mass, a system of equations governing the evolution of two bubbles is proposed. This two-bubble model shows terms that do not appear in the models of interaction between bubbles. The two-bubble model is compared with the modified Rayleigh–Plesset equation and a validation with the experimental study of Ohl [2002] is presented. The numerical results show that, on one hand, the development of small nearby bubbles can slow down the evolution of the biggest local one, while their disappearance can favor its growing. Furthermore, in the case of two bubbles in particular, the small bubble exchanges volume with the big one during their evolutions. On the other hand, contrary to the modified Rayleigh–Plesset model, the two-bubble model predicts appearance and disappearance of small bubbles in the neighborhood of the big bubble as it is observed in the experimental study of Ohl [2002]. The present findings show in particular that the interaction by exchange of volume can be very important in the cavitation born phase and it is necessary to take into account the interaction between bubbles as well as the disappearance of small ones on the evolution of the biggest local bubble. Also, this two-bubble model predicts an exchange of volume between both bubbles equal to zero when they are perfectly identical.

International audience; The unsteady character of the sheet cavity dynamics on the suction side of hydrofoils, on convergent-divergent nozzles or on blades in turbines and propellers is responsible for many issues like erosion, noise and vibrations. This two-phase flow dynamics is investigated using a robust method based on Proper Orthogonal Decomposition (POD). This method is applied to sequences of sheet cavity images, in order to identify the cavitation regimes (sheet cavity or cloud cavitation regimes). Once this method is validated on a reference case, POD calculation is used to evaluate the efficiency of a passive control method. Different longitudinal grooved surfaces are machined on the diverging wall of a Venturi. The grooves geometry allows to change the cavitation regime for a fixed cavitation number, and even to avoid the cloud cavitation shedding, which may damage structures.

International audience; The start-up of rocket engine turbopumps is generally performed in a few seconds or even less. It implies that these pumps reach their nominal operating conditions after a few rotations only. During the start-up, the flow evolution within the pump is governed by transient phenomena, based mainly on the flow rate and rotation speed increase. Significant pressure fluctuations, which may result in the development of cavitation, are observed. A centrifugal impeller whose transient behavior during start-ups has been detailed in a previous publication is considered. Three different cases of fast start-ups have been identified according the final operating point (Duplaa et al., 2010, "Experimental Study of a Cavitating Centrifugal Pump During Fast Start-Ups," ASME J. Fluids Eng., 132(2), p. 021301). The aim of this paper is to analyze the evolution during the start-ups of the local amount of vapor in the blade to blade channels of the pump by fast X-ray imaging. This technique has enabled to calculate the time-evolution of the fluid density within the pump, which appears to be correlated with pressure time-evolutions. For each investigated start-up, X-ray measurements have been performed at three different sections of the impeller height. For each investigated start-up and section tested, measurements have been performed for several initial positions of the impeller, to estimate the measurement uncertainty, and to obtain records from different beam angles, like in tomography.

International audience; Previous investigations showed that a single cavitation bubble collapse can cause more than one erosion pit (Philipp & Lauterborn [1]). But our preliminary study showed just the opposite - that in some cases a single cavitation pit can result from more than one cavitation event. The present study shows deeper investigation of this phenomenon. An investigation of the erosion effects of ultrasonic cavitation on a thin aluminum foil was made. In the study we observed the formation of individual pits by means of high speed cameras (>1000 fps) and quantitatively evaluated the series of images by stereoscopy and the shape from shading method. This enabled the reconstruction of the time evolution of the pit shape. Results show how the foil is deformed several times before a hole is finally punctured. It was determined that larger single pits result from several impacts of shock waves on the same area, which means that they are merely special cases of pit clusters (pit clusters where pits overlap perfectly). Finally it was shown that a thin foil, which is subjected to cavitation, behaves as a membrane. It was concluded that the physics behind erosion depends significantly on the means of generating cavitation (acoustic, hydrodynamic, laser light) and the specimen characteristics (thin foil, massive specimen), which makes comparison of results of materials resistance to cavitation from different experimental set-ups questionable. Further development of the shape from shading method in the scope of cavitation erosion testing will enable better evaluation of cavitation erosion models.

International audience; The cavitating behavior of a four-blade inducer tested in the LML laboratory large test facility is considered in the present paper. Experimental investigations based on unsteady pressure measurements and records from a six-component balance mounted on the inducer shaft are performed. Spectral analysis of the signals enables to detect several characteristic frequencies related to unbalanced two-phase flow patterns. The objective of the present paper is the understanding of the physical phenomena associated to these frequencies. Therefore, wavelet decomposition, flow visualizations, and direct analysis of the high-frequency force, moment, and pressure signals are applied. Results at nominal flow rate only are considered. Not only classical unbalanced cavitation patterns, but also unexpected flow organizations are discussed.

International audience; No experiment was conducted, yet, to investigate the scale effects on the dynamics of developed cavitating flow with periodical cloud shedding. The present study was motivated by the unclear results obtained from the experiments in a Venturi-type section that was scaled down 10 times for the purpose of measurements by ultra-fast X-ray imaging (Coutier-Delgosha et al. 2009). Cavitation in the original size scale section (Stutz and Reboud in Exp Fluids 23:191-198, 1997, Exp Fluids 29:545-552 2000) always displays unsteady cloud separation. However, when the geometry was scaled down, the cavitation became quasi steady although some oscillations still existed. To investigate this phenomenon more in detail, experiments were conducted in six geometrically similar Venturi test sections where either width or height or both were scaled. Various types of instabilities are obtained, from simple oscillations of the sheet cavity length to large vapor cloud shedding when the size of the test section is increased. It confirms that small scale has a significant influence on cavitation. Especially the height of the test section plays a major role in the dynamics of the re-entrant jet that drives the periodical shedding observed at large scale. Results suggest that the sheet cavity becomes stabile when the section is scaled down to a certain point because re-entrant jet cannot fully develop.

International audience; The startup of rocket engine turbopumps is generally performed only in a few seconds. It implies that these pumps reach their nominal operating conditions after only a few rotations. During these first rotations of the blades, the flow evolution in the pump is governed by transient phenomena, based mainly on the flow rate and rotation speed evolution. These phenomena progressively become negligible when the steady behavior is reached. The pump transient behavior induces significant pressure fluctuations, which may result in partial flow vaporization, i.e., cavitation. An existing experimental test rig has been updated in the LML Laboratory (Lille, France) for the startups of a centrifugal pump. The study focuses on the cavitation induced during the pump startup. Instantaneous measurement of torque, flow rate, inlet and outlet unsteady pressures, and pump rotation velocity enable to characterize the pump behavior during rapid starting periods. Three different types of fast startup behaviors have been identified. According to the final operating point, the startup is characterized either by a single drop of the delivery static pressure, by several low-frequency drops, or by a water hammer phenomenon that can be observed in both the inlet and outlet of the pump. A physical analysis is proposed to explain these three different types of transient flow behavior.

The goal of the work is to develop an expert system for monitoring and control of cavitation in hydraulic machines and to research the possibility of cavitation erosion prediction using CFD tools only. The geometry in question is a simple single hydrofoil, which is exposed to the developed cavitating flow at different flow conditions. The work was divided in more parts: numerical simulation of cavitating flow, experimental evaluation of the simulation, measurements of cavitation erosion, development of cavitation erosion model and finally the prediction of cavitation erosion using solely CFD. A study of erosion effects of cavitation on simple single hydrofoil configurations in a cavitation tunnel was made. A thin copper foil, applied to the surface of the hydrofoils, was used as an erosion sensor. A pit-count method was used to evaluate the damage. The cavitation phenomenon on hydrofoils at different flow conditions (system pressure, flow velocity) was observed. The erosion model is based on the physical description of different phenomena (cavitation cloud implosion, pressure wave emission and its attenuation, micro-jet formation and finally pit formation), which are involved in the process of pit formation. The cavitating flow was simulated using an “in house” CFD code which uses barotropic state law. The code was previously tested on numerous experiments. For the present case the predictions of velocity profiles and pressure evolutions in the vicinity of the hydrofoil were compared to experimentally measured data. In all cases a very good correlation was obtained. The erosion model was implemented into the code. It used values of local pressure, local void fraction and flow velocity to determine the magnitude of damage at a certain point. The results of prediction were compared to the experimentally measured damage on the hydrofoil and it was shown that it is possible, for this simple case, to use solely CFD tools to predict cavitation erosion evolution in time, final extent and final magnitude with a very good accuracy.Copyright © 2008 by ASME

For numerical simulations of cavitating flows, many physical models are currently used. One approach is the void fraction transport equation-based model including source terms for vaporization and condensation processes. Various source terms have been proposed by different researchers. However, they have been tested only in different flow configurations, which make direct comparisons between the results difficult. A comparative study, based on the expression of the source terms as a function of the pressure, is presented in the present paper. This analytical approach demonstrates a large resemblance between the models, and it also clarifies the influence of the model parameters on the vaporization and condensation terms and, therefore, on the cavity shape and behavior. Some of the models were also tested using a 2D CFD code in configurations of cavitation on two-dimensional foil sections. Void fraction distributions and frequency of the cavity oscillations were compared to existing experimental measurements. These numerical results confirm the analytical study.; International audience; For numerical simulations of cavitating flows, many physical models are currently used. One approach is the void fraction transport equation-based model including source terms for vaporization and condensation processes. Various source terms have been proposed by different researchers. However, they have been tested only in different flow configurations, which make direct comparisons between the results difficult. A comparative study, based on the expression of the source terms as a function of the pressure, is presented in the present paper. This analytical approach demonstrates a large resemblance between the models, and it also clarifies the influence of the model parameters on the vaporization and condensation terms and, therefore, on the cavity shape and behavior. Some of the models were also tested using a 2D CFD code in configurations of cavitation on two-dimensional foil sections. Void fraction distributions and frequency of the cavity oscillations were compared to existing experimental measurements. These numerical results confirm the analytical study.

International audience; The paper refers to the behavior of a vaneless diffuser of a radial flow pump in partial flow operating conditions. Some experimental data have been obtained using 2D/2C PIV and unsteady pressure measurements within the diffuser, in various operating conditions. The experimental results at the lower flow rate are compared with two-dimensional numerical calculations.

The unsteady structure of cavitating flows is investigated by coupled experimental and numerical means. Experiments focus on the structure and dynamics of sheet cavitation on the upper side of a two-dimensional foil section in the ENSTA cavitation tunnel. Various flow conditions are investigated by varying the pressure, the flow velocity, and the incidence of the foil section. High-frequency local measurements of volume fractions of the vapour phase are performed inside the liquid/vapour mixture by a X-ray absorption method. The numerical approach is based on a macroscopic formulation of the balance equations for a two-phase flow. The assumptions required by this formulation are detailed and they are shown to be common to almost all the models used to simulate cavitating flows. In the present case we apply a single-fluid model associated with a barotropic state law that governs the mixture density evolution. Numerical simulations are performed at the experimental conditions and the results are compared to the experimental data. A reliable agreement is obtained for the internal structure of the cavity for incidence varying between 3° and 6°. Special attention is paid to the mechanisms of partial and transitional instabilities, and to the effects of the interaction between the two sides of the foil section.

The present work was carried out in the scope of a numerical-experimental collaborative research program, whose main objective is to understand the mechanisms of instabilities in partial cavitating flow. Experiments were conducted in the configuration of a rectangular foil located in a cavitation tunnel. Partial cavitation was investigated by multipoint wall-pressure measurements together with lift and drag measurements and numerical videos. The computations were conducted on two-dimensional hydrofoil section and are based on a single fluid model of cavitation: the liquid/vapor mixture is considered as a homogeneous fluid whose composition is regulated by a barotropic state law. The algorithm of resolution is derived from the SIMPLE approach, modified to take into account the high compressibility of the medium. Several physical features were pointed out by this joint approach. Particularly two distinct cavity self-oscillation dynamics characterized by two different frequencies (dynamics 1 and dynamics 2) were obtained experimentally and numerically at the angles of incidence of 6° and 8°. In both cases, the reentrant jet was found to be mainly responsible for the cavity breakdown. Dynamics 2 corresponds to the ``classical`` cavity breakdown and resulting cloud cavitation. A more complex flow pattern was evidenced for dynamics 1. In this case the growth/breakdown cycle of the cavity was observed at a lower Strouhal number (~0.07/0.09) than dynamics 2 (~0.3). Moreover, the mechanism is composed of two successive steps: (i) an interaction between the reentrant jet and the cavity interface in the closure region leading to the periodic shedding of secondary cavitation clouds before the main cloud detachment occurs, and (ii) a shock wave induced by the collapse of the main cloud, which influences the growth of the residual cavity.

A 3D numerical model is proposed to simulate complex unsteady cavitating flows. The final objective is to predict instabilities due to cavitation in turbopump inducers. It was previously applied to simpler two-dimensional simulations such as a Venturi type section [Int. J. Numer. Meth. Fluids, in press] and foil sections [Int. J. JSME B 45(3) (2002)]. The model is based on the code FineTurbo significantly modified to take into account the cavitation process. The numerical scheme consists in a time-marching algorithm initially devoted to compressible flows. A low-speed preconditioner is applied to treat low Mach number flows. This numerical resolution is coupled to a single-fluid model of cavitation. The evolution of the density is governed by a barotropic state law proposed and validated previously by Delannoy and Kueny [Proc 1990 ASME Cavitation Multiphase Flow Forum 98 (1990) p. 153] and Coutier-Delgosha et al. [Int. J. Numer. Meth. Fluids 42 (2003) 527]. The present work focuses on the numerical stability of the Navier–Stokes equations associated to the barotropic state law. Fourier footprint representations are applied to several two-dimensional non-cavitating and cavitating flow field configurations, and the influence of the numerical and physical parameters on the stability is investigated. The influence of the preconditioner is also discussed: a modification is proposed in the two-phase areas, and its effect is tested in a two-dimensional Venturi type section flow configuration. A significant improvement is obtained concerning both the convergence level and speed.

A computational method is proposed to simulate 3D unsteady cavitating flows in spatial turbopump inducers. It is based on the code FineTurbo, adapted to take into account two-phase flow phenomena. The initial model is a time-marching algorithm devoted to compressible flow, associated with a low-speed preconditioner to treat low Mach number flows. The presented work covers the 3D implementation of a physical model developed in LEGI for several years to simulate 2D unsteady cavitating flows. It is based on a barotropic state law that relates the fluid density to the pressure variations. A modification of the preconditioner is proposed to treat efficiently as well highly compressible two-phase flow areas as weakly compressible single-phase flow conditions. The numerical model is applied to time-accurate simulations of cavitating flow in spatial turbopump inducers. The first geometry is a 2D Venturi type section designed to simulate an inducer blade suction side. Results obtained with this simple test case, including the study of its general cavitating behaviour, numerical tests, and precise comparisons with previous experimental measurements inside the cavity, lead to a satisfactory validation of the model. A complete three-dimensional rotating inducer geometry is then considered, and its quasi-static behaviour in cavitating conditions is investigated. Numerical results are compared to experimental measurements and visualizations, and a promising agreement is obtained. Copyright © 2004 John Wiley & Sons, Ltd.

The present paper is devoted to the experimental study of unsteady cavitation on the suction side of a two-dimensional foil section positioned in a cavitation tunnel with a small incidence angle. When the pressure is decreased in the tunnel, a sheet of cavitation characterized by large amplitude fluctuations is obtained on the foil. The present study focuses on the effects of the foil wall roughness on the cavity unsteady behavior. Four different sizes d of irregularities have been tested, from the smooth surface to a 400μm grain size. The characteristic frequency of the flow unsteadiness is investigated by analyzing the data measured by a pressure transducer mounted flush on one vertical wall of the test section, whereas the mean cavity length is obtained by visual measurements on the foil side. Several types of cloud cavitation are identified in the case of the smooth surface. The effect of roughness is a significant decrease of the cavity length and a large increase of the oscillation frequency. It results in Strouhal numbers higher than the classical values obtained for partial cavity fluctuations. Moreover, the cavitation cycle is disorganized by the increase of the roughness, as it can be detected by the fast fourier transform analysis of the pressure signal. The general effect is a reduction of the pressure fluctuation intensity.

In the present study a numerical model of 3D cavitating flows is proposed. It is applied to investigate the behavior of a spatial turbopump inducer in noncavitating and cavitating conditions. Experimental and numerical results concerning inducer characteristics and performance breakdown are compared at different flow conditions. The cavitation development and the spatial distribution of vapor structures within the inducer are also analyzed. The results show the ability of the code to simulate the quasi-steady cavitating behavior of such a complex geometry. Discrepancies concerning the breakdown prediction are also discussed.

The present study deals with the edge-tone phenomenon. Gas injection is performed through a nozzle with a 0.6×20 mm2 cross-section and two possible lengths of 20 and 50 mm. The effect of the nature of the injected gas on both the flow arrangement and sound frequency is investigated by a coupled experimental and numerical approach. In the experiments, special attention is paid to the definition and experimental measurement of the velocity at the nozzle outlet for the three injected gases. If the head losses in the injection duct are correctly taken into account, no influence of its length is obtained, which contradicts the results published recently by Segoufin et al. [2004. Experimental investigation of the flue channel geometry influence on edge-tone oscillations. Acta Acustica 90, 966–975]. Injections of air, Neon, and CO2 into air are then successively considered. The numerical simulations are based on the two-dimensional resolution of the unsteady Navier–Stokes equations, in association with a two-fluid physical model. A homogeneous approach is used to treat the behaviour of the mixture composed of the two gases. The density of the injected gas is found to have a significant influence on the flow pattern and the sound frequency, which suggests that the fluid density should be included in the relations that give the frequency of the edge tone instability. Moreover, it is shown that the jet oscillation frequencies obtained both numerically and experimentally can be derived from a theoretical analysis of the Kelvin–Helmholtz instability, on condition that the parabolic shape of the gas velocity at the nozzle outlet is taken into account.

The challenge consists in simulating the unsteady behavior of cavitation pockets formed at the throat of a converging-diverging channel. Comparisons with existing numerical predictions and experimental data are suggested.

One source of unsteadiness in turbopump inducers consists in a rotating cavitation behavior, characterized by different cavity shapes on the different blades, which leads to super- or subsynchronous disturbances. This phenomenon is simulated for the case of a simple two-dimensional blade cascade corresponding to a typical four-blade inducer. A numerical model of unsteady cavitating flows was adapted to take into account nonmatching connections and periodicity conditions. Single-channel and four-channel computations were performed, and in the latter case, nonsymetrical unstable flow patterns were obtained. Limits of stability according to the mass flow rate and the cavitation number are presented. Qualitative comparisons with experiments, instability criterion, and the mechanisms of instabilities are also investigated

A numerical study of the cavitation behaviour of two-dimensional hydrofoils simulating a section of an inducer blade is presented. Two leading edge shapes were chosen to approach rocket engine inducer designs. They was tested with respect to the development of sheet cavitation. The numerical model of cavitating flows is based on the 3D code FINE/TURBOTM, developed by NUMECA International. The cavitation process is taken into account by using a single fluid model, which considers the liquid vapour mixture as a homogeneous fluid whose density varies with respect to the static pressure. Numerical results are compared with experimental ones, obtained in the CREMHyG large cavitation tunnel [Reboud et al. 1996]. Pressure distributions along the foil suction side and the tunnel walls were measured for different cavity lengths. Total pressure measurements along the foil suction side allow characterizing the effects of cavitation on the liquid flow. Influence of the leading edge shape on the cavitation behaviour and comparison between experiments and numerical predictions are discussed.

Cavitation is a complex phenomenon involving mass transfer between liquid and vapour phase at nearly constanttemperature. Advances in the understanding of the physical processes of cavitating flows are challenging, mainlydue to the lack of quantitative experimental data on the two-phase structures and dynamics inside the opaquecavitation areas. In this thesis, partial cavitation developed in small convergent-divergent (Venturi) channels wasstudied experimentally in detail for a better knowledge of the physical mechanisms governing the cavitationinstabilities. This was achieved by using an ultra-fast synchrotron X-ray imaging technique aided withconventional high speed photography and Particle Image Velocimetry. The main contributions of the presentstudy can be summarized as follows: (1) detailed description of the two-phase flow structures in quasi-stablesheet cavitation, which is characterized by a low-speed re-entrant flow existing continuously underneath thecavity; (2) analysis of the complex effect of cavitation on turbulent velocity fluctuations; (3) identification ofthree distinct mechanisms responsible for the transition of sheet-to-cloud cavitation, with a discussion of thedifferences between them; (4) analysis of the scale effect on cavitation in the studied Venturi flows.; La cavitation est un phénomène complexe impliquant un transfert de masse entre la phase liquide et vapeur à des températures presque constantes.Les processus physiques qui contrôlent les instabilités dans les écoulements cavitants ne sont pas encore compris, principalement en raison du manque de données expérimentales quantitatives sur les structures diphasiques et la dynamique à l'intérieur des zones de cavitation opaques. Dans cette thèse, la cavitation partielle développée dans de petits canaux convergents-divergents (Venturi) a été étudiée expérimentalement en détail pour élucider ces mécanismes. Ceci a été réalisé en combinant une technique d'imagerie par rayons X ultra-rapide, la visualisation conventionnelle à haute fréquence et la vélocimétrie par images de particules. Les principales contributions de la présente étude portent sur les quatre aspects suivants:(1) une description détaillée des structures d'écoulement diphasique au sein des poches de cavitation quasi stables,qui se caractérisent par un écoulement rentrant à faible vitesse existant en continu sous la cavité; (2) analyse de l'effet complexe de la cavitation sur les fluctuations de vitesses turbulentes; (3) identification et discussion de trois mécanismes distincts responsables de la transition vers un comportement instable périodique ; (4) analyse de l'effet d'échelle sur les comportements cavitants, dans le cas des profils Venturi étudiés.