Xavier Escaler

Cavitation Influence on von Kármán Vortex Shedding and Induced Hydrofoil Vibrations

The present study deals with the shedding process of the von Karman vortices at the trailing edge of a 2D hydrofoil at high Reynolds number. This research focuses mainly on the effects of cavitation and fluid-structure interaction on the mechanism of the vortex generation. The vortex shedding frequency, derived from the flow-induced vibration measurement, is found to follow the Strouhal law provided that no hydrofoil resonance frequencies are excited, i.e., lock-off. For such a regime, the von Karman vortices exhibit strong spanwise 3D instabilities and the cavitation inception index is linearly dependent on the square root of the Reynolds number. In the case of resonance, the vortex shedding frequency is locked onto the hydrofoil eigenfrequency and the spatial coherence is enhanced with a quasi-2D shape. The measurements of the hydrofoil wall velocity amplitude and phase reveal the first torsion eigenmotion. In this case, the cavitation inception index is found to be significantly increased compared to lock-off conditions. It makes clear that the vortex roll-up is amplified by the phase locked vibrations of the trailing edge. For the cavitation inception index, a new correlation relationship that encompasses the entire range of Reynolds numbers, including both the lock-off and the lock-in cases, is proposed and validated. In contrast to the earlier models, the new correlation takes into account the trailing edge displacement velocity. In addition, it is found that the transverse velocity of the trailing edge increases the vortex strength linearly. This effect is important in the context of the fluid-structure interaction, since it implies that the velocity of the hydrofoil trailing edge increases the fluctuating forces on the body. It is also demonstrated that cavitation developing in the vortex street cannot be considered as a passive agent for the turbulent wake flow. In fact, for fully developed cavitation, the vortex shedding frequency increases up to 15%, which is accompanied by the increase of the vortex advection velocity and reduction of the streamwise vortex spacing. In addition, a significant increase of the vortex-induced vibration level is found at cavitation onset. These effects are addressed and thought to be a result of the increase of the vorticity by cavitation.

Computational Fluid Dynamics Modeling of Impinging Gas-Jet Systems: I. Assessment of Eddy Viscosity Models

Computational fluid dynamics plays an important role in engineering design. To gain insight into solving problems involving complex industrial flows, such as impinging gas-jet systems (IJS), an evaluation of several eddy viscosity models, applied to these IJS has been made. Good agreement with experimental mean values for the field velocities and Nusselt number was obtained, but velocity fluctuations and local values of Nusselt number along the wall disagree with the experiments in some cases. Experiments show a clear relation between the nozzle-to-plate distance and the Nusselt number at the stagnation point. Those trends were only reproduced by some of the numerical experiments. The conclusions of this study are useful in the field of heat transfer predictions in industrial IJS devices, and therefore for its design.

Dynamic analysis of Francis Runners-Experiment and numerical simulation

The present paper shows the results of numerical and experimental modal analyses of Francis runners, which were executed in air and in still water. In its first part this paper is focused on the numerical prediction of the model parameters by means of FEM and the validation of the FEM method. Influences of different geometries on modal parameters and frequency reduction ratio (FRR), which is the ratio of the natural frequencies in water and the corresponding natural frequencies in air, are investigated for two different runners, one prototype and one model runner. The results of the analyses indicate very good agreement between experiment and simulation. Particularly the frequency reduction ratios derived from simulation are found to agree very well with the values derived from experiment. In order to identify sensitivity of the structural properties several parameters such as material properties, different model scale and different hub geometries are numerically investigated. In its second part, a harmonic response analysis is shown for a Francis runner by applying the time dependent pressure distribution resulting from an unsteady CFD simulation to the mechanical structure. Thus, the data gained by modern CFD simulation are being fully utilized for the structural design based on life time analysis. With this new approach a more precise prediction of turbine loading and its effect on turbine life cycle is possible allowing better turbine designs to be developed.

Dynamics and Intensity of Erosive Partial Cavitation

An experimental work has been carried out to investigate the dynamic behavior and the intensity of erosive partial cavitation on a 2-D hydrofoil. Both sheet (stable) and cloud (unstable) cavitation have been tested in a cavitation tunnel for various free stream velocities. Special attention has been given to validate the use of acceleration transducers for studying the physical process. In particular, the modulation in amplitude of the cavitation induced vibrations in a high frequency band has allowed us to determine the shedding frequency and the relative intensity of the collapse process for each testing condition. Regarding the cavity dynamics, a typical Strouhal value based on its length of about 0.28 has been found for cloud cavitation; meanwhile, for sheet cavitation, it presents a value of about 0.16. Furthermore, the level of the vibration modulation in the band from 45 kHz to 50 kHz for cloud cavitation shows a power law dependency on the free stream velocity as well as a good correlation with the pitting rate measured on stainless steel samples mounted on the hydrofoil.

Modal behavior of a reduced scale pump-turbine impeller. Part 1: Experiments

An experimental investigation has been carried out to quantify the effects of surrounding fluid on the modal behavior of a reduced scale pump-turbine impeller. The modal properties of the fluid-structure system have been obtained by Experimental Modal Analysis (EMA) with the impeller suspended in air and inside a water reservoir. The impeller has been excited with an instrumented hammer and the response has been measured by means of miniature accelerometers. The Frequency Response Functions (FRFs) have been obtained from a large number of impacting positions in order to ensure the identification of the main mode shapes. As a result, the main modes of vibration have been well characterized both in air and in water in terms of natural frequency, damping ratio and mode shape. The first mode is the 2 Nodal Diameter (ND), the second one is the 0ND and the following ones are the 3ND coupled with the 1ND. The visual observation of the animated mode shapes and the level of the Modal Assurance Criterion (MAC) have permitted to correlate the homologous modes of vibration of the fluid-structure system in air and in water. From this comparison the added mass effect on the natural frequencies and the fluid effect on the damping ratios have been quantified for the most significant modes. With the surrounding water, the natural frequencies decrease in average by 10%. On the other hand, the damping ratios increase in average by 0.5%. In any case, the damping ratio appears to decrease with the frequency value of the mode.

Implicit large eddy simulation of unsteady cloud cavitation around a plane-convex hydrofoil

The present paper focuses on the erosive cavitation behavior around a plane convex hydrofoil. The Zwart-Gerber-Belamri cavitation model is implemented in a library form to be used with the OpenFOAM. The implicit large eddy simulation (ILES) is app-lied to analyze the three dimensional unsteady cavitating flow around a plane convex hydrofoil. The numerical results in the cases under the hydrodynamic-conditions, which were experimentally tested at the high speed cavitation tunnel of the École Polytechnique Fédérale de Lausanne (EPFL), clearly show the sheet cavitation development, the shedding and the collapse of vapor clouds. It is noted that the cavitation evolutions including the maximum vapor length, the detachment and the oscillation frequency, are captured fairly well. Furthermore, the pressure pulses due to the cavitation development as well as the complex vortex structures are reasonably well predicted. Consequently, it may be concluded that the present numerical method can be used to investigate the unsteady cavitation around hydrofoils with a satisfactory accuracy.

Experimental investigation on forces due to vortex cavitation collapse for different materials

Tests are conducted in a Vortex Cavitation Generator (VCG) to evaluate the erosion characteristics of different materials under similar conditions. Accelerations due to vortex cavitation collapses are measured and the corresponding forces are inferred for each material by means of transmissibility functions obtained using an instrumented hammer. Pits due to cavitation are determined using a new image processing method from pictures of the samples surface taken before and after the tests. A short-term (about 2 h) test allows to establish a direct correlation between the impact forces and the pit counting on a reference material (REF), and to estimate a damaging threshold, force value above which the material suffers the first damage. Long-term (60 h) tests permit to investigate the consequences of intense erosion on the hydrodynamic response of the cavitation collapses, and to estimate the aptitude of different materials and coatings to sustain prolonged cavitation erosion. Analysis of the results shows that the maximum amplitude of the accelerations increases with time, and therefore with material removal, and that the value of the cumulated forces correlate linearly with the initial roughness of the tested samples.

Numerical investigation of unsteady cavitation around a NACA 66 hydrofoil using OpenFOAM

The prediction and control of cavitation damage in pumps, propellers, hydro turbines and fluid machinery in general is necessary during the design stage. The present paper deals with a numerical investigation of unsteady cloud cavitation around a NACA 66 hydrofoil. The current study is focused on understanding the dynamic pressures generated during the cavity collapses as a fundamental characteristic in cavitation erosion. A 2D and 3D unsteady flow simulation has been carried out using OpenFOAM. Then, Paraview and Python programming language have been used to characterize dynamic pressure field. Adapted Large Eddy Simulation (LES) and Zwart cavitation model have been implemented to improve the analysis of cloud motion and to visualize the bubble expansions. Additional results also confirm the correlation between cavity formation and generated pressures.

Numerical simulation of added mass effects on a hydrofoil in cavitating flow using acoustic FSI

A fluid-structure interaction system has been solved using the coupled acoustic structural finite element method to simplify the cavitating flow conditions around a hydrofoil. The modes of vibration and the added mass effects have been numerically simulated for various flow conditions including leading edge attached partial cavitation on a 2D NACA0009 hydrofoil. The hydrofoil has been first simulated surrounded by only air and by only water. Then, partial cavities with different lengths have been modeled as pure vapor fluid domains surrounded by the corresponding water and solid domains. The obtained numerical added mass coefficients and mode shapes are in good agreement with the experimental data available for the same conditions. The study confirms that the fluid added mass effect decreases with the cavitation surface ratio and with the thickness of the cavitation sheet. Moreover, the simulations also predict slight mode shape variations due to cavitation that have also been detected in the experiments. Finally, the effects of changes in cavity location have been evaluated with the previously validated model.

Experimental mode shape determination of a cantilevered hydrofoil under different flow conditions

The first three mode shapes of a cantilevered NACA0009 hydrofoil were experimentally investigated in air and under different flow conditions in a cavitation tunnel. First and second bending modes and first torsion mode were determined in resonance conditions with the hydrofoil vibrating in air, in still water, in flowing water, or with leading edge sheet cavitation. The hydrofoil was excited with embedded piezoelectric ceramic patches, and the response was measured along the surface at selected positions by means of a laser Doppler vibrometer. The modes of vibration obtained from a cross correlation analysis of the signals were compared for the different conditions, and the most significant differences were identified. In particular, it was found that the mode shape deformation and the location of the nodal lines are dependent on the fluid conditions.