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Purpose The openings on aircraft structures can be modeled from an aerodynamical point of view as lid-driven cavities (LDC). This paper aims to show the primary verification and validation (V&V) process in computational fluid dynamics (CFD, and to investigate the influences of numerical settings on the efficiency and accuracy for solving the LDC problem. Design/methodology/approach To dig into the details of CFD approaches, this paper outlines the design, implementation, V&V and results of an efficient explicit algorithm. The parametric study is performed thoroughly focusing on various iteration methods, grid density discretization terms and Reynolds number effects. Findings This study parameterized the numerical implementation which provides empirical insights into how computational accuracy and efficiency are affected by changing numerical settings. At a low Reynolds number (not over 1,000), the time-derivative preconditioning is necessary, and k = 0.1 can be the optimal value to guarantee the efficiency, as well as the stability. A larger artificial viscosity (c = 1/16) would relieve the calculating oscillation issue but proportionally increase the discretization error. Furthermore, the iteration method and the mesh quality are two key factors that affect the convergence efficiency, thus need to be selected “wisely”. Practical implications The study shows how numerical implementation can enhance an accurate and efficient solution. This workflow can be used to determine the best parameter settings whenever CFD researchers applying this LDC problem as a complementary design tool for testing newly developed solvers. Originality/value The studied LDC problem is representative of CFD analysis in real aircraft structures. These numerical simulations provide a cost-effective and convenient tool to understand the parameter sensitivity, solution receptivity and physics of the CFD process.

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; The goal of the present work is to investigate the influence of several parameters on the performance and flow structures of reversed pitching airfoils. Firstly, the effect of the turbulence model is evaluated, and the results show that the SST transition model has a better prediction in the instantaneous lift coefficient of a reversed pitching airfoil and the transition locations of a stationary airfoil. Then, effects of the pitching angle, pitch-pivot-point, blade profile and morphed leading edge with various deflection angles and positions on the performance, unsteady vortical flow, near-wall transition and trajectory of main vortices, are analyzed. The main results show that both the mean pitching angle and pitching amplitude have the impact on the vortical flows, but depends on the reduced frequency. Then, the delayed flow structure by shifting the pitch-pivot-point from the leading edge (LE) to trailing edge (TE) can be explained by the distribution of the effective attack-of-angle. Moreover, the symmetrical, asymmetrical and inverse asymmetrical airfoils have great effect on the first (FMLC) and second maximal lift coefficients (SMLC). Finally, upward deflected LE decreases the negative lift coefficient while downward morphed LE improves it considerably due to the geometry curvature leading to the large flow separation. In addition, it is observed that the generation of vortices is earlier when the deflection position close to the middle surface. It is believed that this work can provide some guidelines to have a better design of energy devices with oscillating airfoils/hydrofoils.

The present paper is devoted to characterizing the three-dimensional effects in a cavitating flow generated in a venturi-type profile. Experimental measurements based on 2D3C (two-dimensional-three-component) stereoscopic particle image velocimetry are conducted to obtain the three components of the velocity field in multiple vertical planes aligned with the main flow direction, from the center of the channel to the side walls. Time-resolved acquisitions are conducted, so not only time-averaged quantities but also velocity fluctuations can be discussed. The attention was focused on configurations of cloud cavitation, where the attached cavity experiences large-scale periodical oscillations and shedding of clouds of vapor. Although the water channel is purely two-dimensional, some significant flow velocities in the third direction (depth of the test section) were measured. Some of those velocities were found to be related to small differences between the boundary conditions on the two sides, such as minor gaps between the sides and the bottom wall, while others reflect intrinsic three-dimensional mechanisms inside the cavitation area, such as side jets that contribute to the periodical instability process. These mechanisms are discussed, and a possible 3D (three-dimensional) structure of the cavitating flow is proposed.

International audience; The present paper is devoted to the analysis of the various instabilities of cavitation attached to a two-dimensional (2D) profile. Time resolved stereo Particle Image Velocimetry (PIV) was conducted in a small-scale 2D venturi type section, in different vertical planes in the streamwise direction, located at varying positions in the depth of the channel. These experiments enabled to obtain the time evolution of the three components of the velocity field in the cavitation area, and to derive the time-averaged gradients in the spanwise direction. Test cases at various Reynolds number were conducted, maintaining either the pressure or the cavitation number constant, to discuss the impact of these parameters on the flow. Then, the attention was focused on three distinct flowdynamics, namely sheet cavitation, where no large-scale instability can be detected, single cloud cavitation, where a large cloud of vapor is shed periodically at the rear of the cavity, and multi-cloud cavitation, where the process is more complex, as more than one clouds are shed downstream. The data reveal that the structure and the structure of the re-entrant jet, which is one of the primary mechanisms of cloud cavitation, is more complex than reported in the previous studies. Although the jet can be detected as an intermittent low speed reverse flow in the streamwise direction, it is actually made of successive vortices about the channel depth, which are convected downstream while expanding in the vertical direction, causing the cavity lift and thus contributing to its final split and the cloud shedding

International audience; The pitching airfoils, applied to the vertical axis turbines and propellers, are critical to extract more energy from the environment. At retreating side, when the airfoil blunt leading edge becomes the trailing edge, the transition and vortex dynamics are quite different from that at advancing side. The goal of the present work is to investigate the transition and vortex evolution over the reversed pitching airfoil, with main focus on the parametrical effect, including the mean pitching angle and pitching amplitude, reduced frequency and Reynolds number. The main results show that the flow structure on the reversed airfoil is more complex compared with that over the forward airfoil due to the earlier flow separation near the sharp leading edge. Then, the transition on the reversed airfoil firstly occurs within the separated shear layer near the sharp leading edge, and then the flow reattaches, leading to the generation of the leading-edge vortex. Near the blunt trailing edge, the second transition appears on two sides, resulting in the asymmetrical boundary layer as the incidence increases continuously. This event is totally different from that on the forward airfoil, shown by the transition always moving from the trailing edge to the leading edge. The flow unsteadiness of the reversed airfoil is mainly induced by the separated shear layer and leading-edge vortex, which is greatly affected by different parameters. Besides, the trajectory of some specific vortices also depends on the working conditions significantly. It is believed that this work can deepen the understandings of underlying flow physics of the reversed airfoils.

In view of the long stagnation in traditional turbulence modeling, researchers have attempted using machine learning to augment turbulence models. This paper presents some of the recent progresses in our group on augmenting turbulence models with physics-informed machine learning. We also discuss our works on ensemble-based field inversion to provide training data for constructing machine learning models. Future and on-going research efforts are introduced.

Cavitation is a phenomenon of rupturing a liquid when the liquid is subjected to a decrease in pressure at roughly constant temperature. Cavitation is the fundamental reason for the material erosion when the bubbles are collapsing closer to the surface. These bubbles also produce a very high temperature (thousands of degrees Celsius) for a very short time (in the order of nano or microseconds). Cavitation is also being used in the non-invasive cancer tumor ablation treatment using high intensity focused ultrasound (HIFU) called histotripsy. So, our research in measuring the temperature of the bubble collapse will help the histotripsy treatment to understand its thermal behavior. We have designed a cold wire sensor of the thickness of ∼10 to 50 micrometers. And, the sensing region is 2 millimeter. These cold wires are made with kevlar or nylon fibers, titanium, nickel, silver, and silicon dioxide. The single bubble or histotripsy cloud, is allowed to collapse on the sensor, and we measure the temperature based on its change in resistance. These changes in resistance are corresponded to the temperature using the mathematical function which is calibrated prior to the experiment. We measure it in three different experimental settings like Tube Arrest Method (TAM), LASER induced bubbles, and HIFU induced bubbles. The preliminary results have shown that the temperature of the single spherical bubble collapse (TAM) can rise to thousands of degrees celsius as mentioned in the literature based on the theoretical analysis.

International audience; The unsteady vortical flows and separation-induced transition over a 2-bladed cycloidal rotor are investigated numerically at two advance coefficients, with special emphasis on the influence of two different turbulence models, namely the original SST k-ω model and SST γ-Reθt transition model. Firstly, the applicability of the transition model in predicting the transitional flows over a single airfoil at different incidences is evaluated, and the main results show a good agreement with the experiments, in terms of the mean pressure coefficients and transition locations. Then, the global performance and detailed internal flow structures of the cycloidal rotor are also used to compare with the existing numerical and experimental data. The primary results show that increasing the advanced coefficient can’t change the transition location of the performance of the single blade, but the magnitudes of these variables (vertical force, propulsive force and power coefficients). Then, combining the forces (lift and drag) acting on two blades, the blade loadings and the detailed near-wall flows, the difference of the vertical force and propulsive force of the rotating system and single blade are clarified clearly for two turbulence models. Finally, at advancing side, the transition and its evolution on a single blade is elaborated. It shows that the SST γ-Reθt transition model is superior in predicting the overall performance, but is highly subjected to the disturbances, characterized by the large-scale vortex structures and massive flow separation, compared with SST k-ω model. Simultaneously, it has the capability to capture the transition process, from growing waves of the laminar boundary layer induced by the roll-up vortices to the fully generation of the separation bubble. It believes that this work can deepen the understandings of underlying flow physics inside the cycloidal rotor at low Reynolds number.

Hydrodynamic cavitation is a complex two-phase flow phenomenon involving mass and heat transfer between liquid and vapor. It occurs in many widely-used hydraulic machines, such as pumps and marine propellers, and often leads to undesired effects like material erosion, noise, and vibration. To control these detrimental effects, the visualization of two-phase flow morphology inside the opaque cavity is a crucial point to improve the physical and numerical models of cavitation. The major challenge in experimental measurements of cavitating flow fields is the fact that multiple scattering and a direct reflection of visible light from phase boundaries make the flow optically opaque. In recent years, unlike traditional local measurements using various probes, the development of the third-generation synchrotron radiation sources promotes the application of Xray phase-contrast imaging, which enables clear visualization of boundaries between phases with different refractive indices. In this study, the partial cavity is formed in a convergent-divergent (Venturi) channel with a small contraction ratio where the relatively stable cavitation regime can be sustained in a wide range of cavitation numbers. The experiment performed at Advanced Photon Source (APS) of Argonne uses the short high-flux X-ray pulses emitted from synchrotron sources to capture fast dynamic events and minimize motion blur. The internal two-phase structures and bubble development dynamics inside the quasi-stable sheet cavitation can be identified. Aside from the detailed illustration of two-phase morphology, X-ray phase-contrast images were also used to perform velocimetry by tracking either seeded particles or phase interfaces inside the opaque regions. Through appropriate postprocessing to the recorded X-ray images of cavitation, the time resolved velocity and void fraction fields are obtained simultaneously. These unprecedented experimental data will be further explored in understanding fluid mechanics underneath the cavity, estimating slip velocity between fluid-vapor interactions, and reconstructing pressure fields for compressible flows.

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.

The fluid dynamics of a bubble collapsing near an elastic or viscoelastic material is coupled with the mechanical response of the material. We apply a multiphase fluid–solid coupled computational model to simulate the collapse of an air bubble in water induced by an ultrasound shock wave, near different types of materials including metals (e.g. aluminium), polymers (e.g. polyurea), minerals (e.g. gypsum), glass and foams. We characterize the two-way fluid–material interaction by examining the fluid pressure and velocity fields, the time history of bubble shape and volume and the maximum tensile and shear stresses produced in the material. We show that the ratio of the longitudinal acoustic impedance of the material compared to that of the ambient fluid, , the effect of acoustic impedance on the bubble's collapse time and minimum volume can be captured using phenomenological models constructed based on the solution of Rayleigh–Plesset equation.

International audience; The goal of the present work deals with the influence of the oscillating freestream on the global performance, transition and vortex dynamics of forward and reversed airfoils. Three important parameters, involving the phase lag, oscillating amplitude and mean reduced frequency, are analyzed systematically. The primary results show that both the phase lag and oscillating amplitude have great impact on the transition and flow structures, depending on the instantaneous freestream Reynolds number. The reversed airfoil is more prone to being affected by these parameters, characterized by the earlier flow separation near the sharp leading edge and the more complex vortex shedding, compared with that over the forward airfoil. It shows that increasing the oscillating amplitude can improve the mean performance, but it decreases with the increase of the mean reduced frequency. Additionally, it is observed that there is a second transition on both two sides near the trailing edge of the reversed airfoil, which becomes weak when the instantaneous freestream Reynolds number is relatively low. Afterwards, the time-averaged performance of the reversed airfoil is better than forward airfoil at low reduced frequency, but it deteriorates dramatically with the increase of the reduced frequency. Furthermore, the transition and vortex evolution are delayed as the reduced frequency increases, and the delayed flow structures can be inferred from the velocity profiles in the wake region. Moreover, it can be seen that the velocity profile has a transition from the drag-indicative to thrust-indicative type when the reduced frequency increases, and the velocity variation in the vertical direction is more evident for the reversed airfoil due to the massive flow separation.

Contrary to natural cavitation, ventilated cavitation is controllable and is not harmful. It is particularly used to reduce the drag of the hydraulic vehicles. The ventilated cavitation is characterized by various gas regimes. The mechanisms of ventilated cavitation are investigated in the present work with CFD based on a 2D solver. The attention is especially focused on the transition between the reentrant jet and twin vortex regimes. The results confirm that the product of ventilated cavitation number and Froude number is lower than 1 (σcFr 1) in the reentrant jet regime, as reported in the literature. Further analysis shows that ventilated cavitation is significantly influenced by the natural cavitation number.

If a liquid pressure drops below the critical pressure of the cavitation nuclei—typically tiny bubble of non-condensable gas—these ones expand rapidly because of intense vaporization and become vapour bubbles. The concentration of cavitation nuclei significantly influences the critical pressure where cavitation is initiated, which is corroborated by previous studies showing that the interaction phenomena between bubbles are important at the early stage of cavitation inception. However, prediction of the critical pressure of cavitation nuclei, considering the interaction of other germs, is still beyond the current state of the art. In this work, a simplified analysis of the theoretical formulation of critical pressure for multiple bubbles, taking into account the interactions between bubbles, is conducted. The critical pressure derived explicitly from the Rayleigh–Plesset equation—using either a quasi-static or a linear dynamic approach—is compared with the inception pressure obtained from the numerical model proposed previously in Adama Maiga (Int J Eng Res 8(4):183–213, 2015). The comparison shows a significant disagreement in case the quasi-static is applied, whereas a fair agreement is obtained if the linear dynamic is used. The results also show that increasing the polytropic exponent $$\gamma$$ , i.e. the effect of temperature, delays the bubble nucleation. Conversely, the Reynolds and Weber numbers based on the average bubble radius are not influenced by $$\gamma$$ . The study also confirms that the inter-bubble distance $$D_{ij}$$ significantly influences the critical pressure, i.e. the process of bubble nucleation. The critical Reynolds and Weber number, which trigger the activation of the small bubbles, depend significantly on the number of interacting bubbles.

The oscillating hydrofoils used in underwater propulsion devices often experience large variations of the flow incidence, which favors cavitation at large angle of attack, and therefore a severe degradation of the performance, additional flow instability, and even cavitation erosion. These various phenomena make numerical simulations of the flow around oscillating hydrofoils quite challenging, especially in cases where the laminar-turbulent transition usually occurs when the blade has a high angle of attack. In the present study, the unsteady flow around a stationary Clark-Y hydrofoil is simulated at five fix incidence angles using the Star CCM+ software. The results show that the lift coefficient increases continuously with the incidence angle up to 15°, even after a separation vortex is generated near the trailing edge. Then, as a slight stall occurs at 20°, the lift coefficients obtained with the k-ω SST and SST \(\gamma - \overline{{Re_{\theta t} }}\) transition models become significantly different, mostly because of the different prediction of laminar to turbulence transition at the hydrofoil leading edge. Under deep stall condition at 25°, the flow is much more complex and the hydrofoil performance decreases dramatically. The lift force predicted by the SST transition model is more periodic than with the SST k-ω model. Although the general vortex evolution predicted by the two turbulence models is similar, the local pressure experiences larger amplitude variations with the k-ω SST model, as can be also observed from the evolution of the lift coefficient.

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.

The effects of temperature on hydraulic cavitation dynamics are investigated under various operating conditions, in a close loop cavitation tunnel with a small-scale venturi type section. A systematic study is performed with temperatures varying between 24°C and 85°C, using a high-speed visualization system to observe the cavitating flow. The image processing methods provided in the paper present a quantitative comparison of the cavitation dynamics and structure development. The results show that the increase of the fluid temperature induces the growth of the cavitation volume up to about 55°C, thereafter an additional increase in temperature has the opposite effect. This evolution is interpreted as a competition between a Reynolds effect and the well-known thermal effect. Cavitation is more closely investigated within the temperature range 50°C - 65°C, to analyze the changes in the structure and the cavitation dynamics. For the prediction of thermal suppression head, the thermal effect parameter Σ which can be used empirically, is derived at the maximum cavitation length. This fluid thermodynamic parameter Σ(Ttrans) at the transition peak can be referred to to avoid the maximum cavitation aggressiveness induced vibration or erosion for thermos-fluids around the thermal transition temperature. Finally, the factors influencing cavitation length and shedding frequency are presented and analyzed.

International audience; The increasing development of storage systems connected to electrical networks is stimulated by network management issues related to recent energetic landscape evolutions such as the increasing integration of renewable production sources. Hydro-pneumatic systems seem to offer a clean and cheap energy storage solution among the set of existing storage techniques. The present study analyses an air–water direct contact accumulation system, in closed cycle, using a rotodynamic reversible pump/turbine. The use of a unique energy conversion machine and easy-to-recycle materials could lead to cost-effective, environmentally friendly storage technique with long service life. The paper is focused on the experimental implementation and analysis of the system in a Lab environment, and the modeling of its multi-physic dynamic behavior. To deal with the variable operating conditions of the system, two different real time control strategies of the hydraulic machine were successfully tested. Finally, the global system efficiency is discussed. The efficiency control strategy was achieved with a 31% round trip efficiency and the power control strategy lead to 5% and 23% precision on exchanged power in charge and discharge modes respectively. The multi-physic dynamic model led to a 4% error of turbine mode acceleration prediction showing the interest of such a modeling method for such transient systems.

The Reynolds-averaged Naviers-Stokes (RANS) method coupling with cavitation model is still a practical tool to predict cavitating flows, particularly in industrial applications, due to its computational efficiency. However, the compressibility effects induced by cavitation are not well considered in conventional RANS methods, which often causes the blockage of the reentrant jet and the total steadiness of the simulated cavity. To this end, modeling of compressibility effects becomes critical to predict the characteristics of unsteady cavitating flows. An empirical eddy viscosity correction [Reboudet al., “Two phase flow structure of cavitation: experiment and modeling of unsteady effects,” in 3rd International Symposium on Cavitation CAV1998, Grenoble, France (1998), Vol. 26.] was proposed to consider the compressibility effects induced by cavitation. Although this modification is able to capture unsteady behaviors of cavitating flows in various configurations, it is still not fully analyzed in terms of the turbulent quantities, e.g., Reynolds shear stress. In this work, we investigate the effects of this compressibility correction on the Reynolds shear stress, by comparing with x-ray experimental data in a small Venturi channel. It is shown that the Reboud correction reduces the eddy viscosity in the entire cavity region, which improves the prediction of Reynolds shear stress near the wall significantly. However, the correction depends only on the simulated mixture density, leading to poor predictions near the phase interface where the simulated mixture density has large discrepancies. Based on the results, we propose an empirical eddy viscosity limiter to confine the original correction beneath the cavitating layer and demonstrate the merits of the proposed correction by comparing with experimental measurements.

The purpose of this paper is to investigate experimentally the influence of the cavitation extent on the pressure and velocity fluctuations in a small convergent–divergent channel. The mean cavity length is determined from high-speed photography images. The mean pressure and the intensity of the pressure fluctuations are obtained from the transient pressure signals recorded by two pressure transducers at the inlet and outlet of the test section. The statistical turbulence quantities are derived from the instantaneous velocity fields measured by the laser-induced fluorescent particle image velocimetry (PIV-LIF) technique. The experimental results show that the decrease of the cavitation number (the increase in the extent of cavitation) leads to a rise in the turbulent fluctuations in the wake region due to the impact of vapour clouds collapsing, while the presence of a vapour phase is found to reduce the streamwise and cross-stream velocity fluctuations in the attached cavity. It might be attributed to two mechanisms: the presence of a vapour phase modifies the vortex-stretching process, and the cavitation compressibility damps out the turbulent fluctuations. Similar effects of cavitation are also observed in the pressure fluctuations.

The cavitating flows in a small convergent–divergent channel are studied experimentally using a fast synchrotron x-ray imaging method that enables simultaneous acquisition of the velocity and void fraction fields as well as the two-phase morphology inside the opaque cavitation areas. According to the x-ray measurement results, the quasi-stable sheet cavitation is classified into three representative stages based on the status of the re-entrant flow: (i) at the early stage, the incipient cavity is short and no reverse flow is observed, (ii) at the intermediate stage, an intermittent re-entrant flow is identified underneath the sheet cavity, and (iii) at the developed stage, the re-entrant flow becomes continuous and it can penetrate the entire sheet cavity. The comparison of the three typical sheet cavities illustrates that the occurrence of the re-entrant flow does not result in the transition of sheet-to-cloud cavitation, but it influences the distribution of the mean void fraction and the spectrum of the void fraction variation. The development of cavitation also influences the turbulent velocity fluctuations. On one hand, cavitation alters mean velocity field, which affects velocity fluctuations due to the positive correlation between the velocity gradient and turbulence intensity. One the other hand, the presence of vapor/liquid mixture is observed to greatly suppress velocity fluctuations. The collapse of small vapor structures does not cause an evident augmentation of streamwise velocity fluctuations but increases the shear stress significantly.

International audience; The quasi-stable sheet cavitation produced in a small Venturi channel is investigated using a fast synchrotron X-ray imaging technique aided with conventional high speed photography. The use of X-rays instead of visible light solves cavitation opacity related issues, and X-ray phase contrast-based edge enhancement enables high-definition visualization of the internal two-phase morphology. The simultaneous acquisition of time-resolved velocity and void fraction fields through post-processing the recorded X-ray images reveals, for the first time, the complex diphasic flow structures inside the sheet cavity, which is essentially divided into 6 characteristic parts. Distinct from the current mainstream view, the globallysteady sheet cavitation is found to be characterized by a weak but constantly-existing re-entrant flow that can penetrate the entire cavity. The turbulent velocity fluctuations inside the sheet cavity are also investigated. The turbulence level in the reverse flow region is observed to be as low as in the outer main flow demonstrating the relatively steady status of the reentrant flow. Unlike the streamwise and cross-stream fluctuations, the shear stress appears to be weakly correlated with the velocity gradient. The collapse of vapor phase and the vaporization at the upstream cavity interface are found to be the primary causes of shear stress intensification.

Bayesian uncertainty quantification (UQ) is of interest to industry and academia as it provides a framework for quantifying and reducing the uncertainty in computational models by incorporating available data. For systems with very high computational costs, for instance, the computational fluid dynamics (CFD) problem, the conventional, exact Bayesian approach such as Markov chain Monte Carlo is intractable. To this end, the ensemble-based Bayesian methods have been used for CFD applications. However, their applicability for UQ has not been fully analyzed and understood thus far. Here, we evaluate the performance of three widely used iterative ensemble-based data assimilation methods, namely ensemble Kalman filter, ensemble randomized maximum likelihood method, and ensemble Kalman filter with multiple data assimilation for UQ problems. We present the derivations of the three ensemble methods from an optimization viewpoint. Further, a scalar case is used to demonstrate the performance of the three different approaches with emphasis on the effects of small ensemble sizes. Finally, we assess the three ensemble methods for quantifying uncertainties in steady-state CFD problems involving turbulent mean flows. Specifically, the Reynolds averaged Navier–Stokes (RANS) equation is considered the forward model, and the uncertainties in the propagated velocity are quantified and reduced by incorporating observation data. The results show that the ensemble methods cannot accurately capture the true posterior distribution, but they can provide a good estimation of the uncertainties even when very limited ensemble sizes are used. Based on the overall performance and efficiency from the comparison, the ensemble randomized maximum likelihood method is identified as the best choice of approximate Bayesian UQ approach among the three ensemble methods evaluated here.

International audience; The effect of nonsinusoidal trajectory on the propulsive performances and the vortex shedding process behind a flapping airfoil is investigated in this study. A movement of a rigid NACA0012 airfoil undergoing a combined heaving and pitching motions at low Reynolds number (Re¼11,000) is considered. An elliptic function with an adjustable parameter S (flattening parameter) is used to realize various nonsinusoidal trajectories of both motions. The two-dimensional (2D) unsteady and incompressible Navier–Stokes equation governing the flow over the flapping airfoil are resolved using the commercial software STAR CCMþ. It is shown that the nonsinusoidal flapping motion has a major effect on the propulsive performances of the flapping airfoil. Although the maximum propulsive efficiency is always achievable with sinusoidal trajectories, nonsinusoidal trajectories are found to considerably improve performance: a 110% increase of the thrust force was obtained in the best studied case. This improvement is mainly related to the modification of the heaving motion, more specifically the increase of the heaving speed at maximum pitching angle of the foil. The analysis of the flow vorticity and wake structure also enables to explain the drop of the propulsive efficiency for nonsinusoidal trajectories.

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.