Jean-Pierre Franc

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

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

Partial Cavities: Global Behavior and Mean Pressure Distribution

The results of an experimental work concerning the behavior of flows with partial cavities are presented. The tests were carried out using a plano-convex foil placed in the free surface channel of the I.M.G. Hydrodynamic Tunnel. The experimental conditions concerning ambient pressure, water velocity, and body size were such that various and realistic kinds of flows could be realized. The main flow regimes are described and correlated to the values of foil incidence and cavitation parameter

An Experimental Investigation of Thermal Effects in a Cavitating Inducer

The thermal effects which affect the development of leading edge cavitation in an inducer were investigated experimentally using refrigerant R114. For different operating conditions, the evolution of the cavity length with the cavitation parameter was determined from visualizations. The tests were conducted up to two-phase breeding. The comparison of tests in R114 and in cold water allowed us to estimate the amplitude of the thermodynamic effect. The results show that the B-factor depends primarily upon the degree of development of cavitation but not significantly upon other parameters such as the inducer rotation speed or the fluid temperature, at least in the present domain of investigation. These trends are qualitatively in agreement with the classical entrainment theory. In addition, pressure fluctuations spectra were determined in order to detect the onset of cavitation instabilities and particularly of alternate blade cavitation and rotating cavitation. If the onset of alternate blade cavitation appeared to be connected to a critical cavity length, the results are not so clear concerning the onset of rotating cavitation. NOMENCLATURE a thermal diffusivity or eddy diffusivity B B-factor of Stepanoff (eq.2) p C pressure coefficient l p c liquid heat capacity D characteristic diameter of the inducer e cavity thickness l cavity length h convection heat transfer coefficient L latent heat of vaporization l

Attached cavitation and the boundary layer: experimental investigation and numerical treatment

Attached cavitation on a wall with continuous curvature is investigated on the basis of experiments carried out on various bodies (circular and elliptic cylinders, NACA 16 012 foil). Visualization of the boundary layer by dye injection at the leading edge shows that a strong interaction exists between attached cavitation and the boundary layer. In particular, it is shown that the cavity does not detach from the body at the minimum pressure point, but behind a laminar separation, even in largely developed cavitating flow. A detachment criterion which takes into account this link between attached cavitation and boundary layer is proposed. It consists of connecting a cavitating potential-flow calculation and a boundary-layer calculation. Among all the theoretically possible detachment points, the actual detachment point is chosen to be the one for which the complete calculation predicts a laminar separation just upstream. This criterion, applied to the NACA foil, leads to a prediction which is in good agreement with experimental results.

Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction

This book provides a comprehensive treatment of the cavitation erosion phenomenon and state-of-the-art research in the field. It is divided into two parts. Part 1 consists of seven chapters, offering a wide range of computational and experimental approaches to cavitation erosion. It includes a general introduction to cavitation and cavitation erosion, a detailed description of facilities and measurement techniques commonly used in cavitation erosion studies, an extensive presentation of various stages of cavitation damage (including incubation and mass loss), and insights into the contribution of computational methods to the analysis of both fluid and material behavior. The proposed approach is based on a detailed description of impact loads generated by collapsing cavitation bubbles and a physical analysis of the material response to these loads. Part 2 is devoted to a selection of nine papers presented at the International Workshop on Advanced Experimental and Numerical Techniques for Cavitation Erosion (Grenoble, France, 1-2 March 2011), representing the forefront of research on cavitation erosion. Innovative numerical and experimental investigations illustrate the most advanced breakthroughs in cavitation erosion research.

Incubation Time and Cavitation Erosion Rate of Work-Hardening Materials

A phenomenological analysis of the cavitation erosion process of ductile materials is proposed. On the material side, the main parameters are the thickness of the hardened layer together with the conventional yield strength and ultimate strength. On the fluid side, the erosive potential of the cavitating flow is described in a simplified way using three integral parameters: rate, mean amplitude, and mean size of hydrodynamic impact loads. Explicit equations are derived for the computation of the incubation time and the steady-state erosion rate. They point out two characteristic scales. The time scale, which is relevant to the erosion phenomenon, is the covering time-the time necessary for the impacts to cover the material surface-whereas the pertinent length scale for ductile materials is the thickness of the hardened layer. The incubation time is proportional to the covering time with a multiplicative factor, which strongly depends on flow aggressiveness in terms of the mean amplitude of impact loads. As for the erosion rate under steady-state conditions, it is scaled by the ratio of the thickness of hardened layers to the covering time with an additional dependence on flow aggressiveness, too. The approach is supported by erosion tests conducted in a cavitation tunnel at a velocity of 65 m/s on stainless steel 316 L. Flow aggressiveness is inferred from pitting tests. The same model of material response that was used for mass loss prediction is applied to derive the original hydrodynamic impact loads due to bubble collapses from the geometric features of the pits. Long duration tests are performed in order to determine experimentally the incubation time and the mean depth of penetration rate and to validate the theoretical approach.

A Cavitation Erosion Model for Ductile Materials

An analytical model is proposed for the prediction of cavitation erosion of ductile materials. It is based upon a physical analysis of the work-hardening process due to the successive bubble collapses. The material is characterized by its classical stress-strain relationship and its metallurgical behaviour is analysed from microhardness measurements on cross sections of eroded samples. The flow aggressiveness is determined from pitting tests, using the material properties to go back to the impact loads. The histogram of impact loads is applied numerically a large number of times on the material surface and the evolution of the mass loss with the exposure time is computed. The approach is supported by experimental tests.

UNSTEADY ATTACHED CAVITATION ON AN OSCILLATING HYDROFOIL

A series of visualisations of non-cavitating and cavitating unsteady flows around an oscillating hydrofoil has been carried out in order to investigate the effect of unsteadiness on attached cavitation. The major conclusion of the present experimental analysis is that the strong interaction that was previously pointed out in the case of steady cavitation between an attached cavity and the boundary layer which develops upstream cavity detachment, still plays a prominent role in unsteady cavitation. We propose to generalise for the case of unsteady attached cavitation the two following points which were initially established under steady conditions and which constitute a cavitation detachment criterion; i) a cavity detaches behind laminar separation of the boundary layer; and ii) transition to turbulence sweeps away an attached cavity.

A Statistical Analysis of Cavitation Erosion Pits

An optical interferometric technique has been used to determine the 3-D shape of cavitation erosion pits. The method which is particularly suitable to the determination of pit diameter and pit depth is used for a statistical analysis of cavitation erosion pits. We analyzed numerous samples which were eroded at various velocities with two different fluids (mercury and water) on two geometrically similar venturi test sections of different length scales. General properties of histograms of pit size are pointed out.

Cavitation in the rotational structures of a turbulent wake

Experiments show that cavitation, if moderately developed, makes three kinds of vortical coherent structures visible inside the turbulent wake of a two-dimensional obstacle: Benard–Karman vortices, streamwise three-dimensional vortices and finally the vortices which appear on the borders of the very near wake. The latter, which are called here near-wake vortices , result by successive pairing in the first ones and there is some indication that they are also the origin of streamwise vortices. Cavitation is not a passive agent of visualization, as can be established on the basis of fundamental arguments, and it reacts with the flow as soon as it appears; when it is developed, it breaks the connection between the elongation rate and the vorticity rate of the vortex filaments. Then the subsequent evolution of a cavitating vortex and its final implosion are rather complicated. Despite its active character, cavitation in rotational structures, if properly interpreted, can give information of interest on the basic non-cavitating turbulent flow. By adapting a simple model due to Kermeen & Parkin (1957) and Arndt (1976), and counting near-wake vortices, it is possible to accurately predict the conditions of cavitation inception: consideration of coherent rotational structures is probably the best approach to explain, in an almost deterministic way, the large difference between the absolute value of the mean pressure coefficient at the obstacle base and the incipient cavitation number.