Numerical Methodology to Predict and Analyze Cavitating Flows in a Kaplan Turbine

International audienceA computational methodology to predict the cavitation phenomena appearance and evolution in a 5-blades Kaplan turbine scale model was developed. Two different inlet boundary conditions have been tested in both non-cavitating and cavitating regimes: the classical one, the mass flow rate and the new one, the total pressure. The best results were obtained applying a constant total pressure on the inlet. The torque and efficiency drop curves were well-predicted with the proposed calculation methodology and the numerical cavitation structures agreed with experimental observations. Indeed, this new inlet boundary condition allows to keep the machine head constant during the cavitation drop, as in experiments. Unsteady simulations are under investigation to improve the prediction and the analyses of more developed cavitating regimes

Élaboration d'un modèle d'usure par érosion de cavitation a partir de simulations d'écoulements cavitants

D’un point de vue industriel, la cavitation peut paraître au sein des circuits hydrauliques au niveau des diaphragmes,vannes ou venturi mais aussi des turbomachines, sur les pales des inducteurs, des pompes, au niveau de l’entrefer et sur les pales des navires. Elle donne lieu à des phénomènes de grossissement et d’implosions de structures de vapeur dont la taille et les vitesses caractéristiques varient très rapidement sur des intervalles de temps très réduits qui endommagent les surfaces considérées. Cette étude, financée à la fois par EDF et le CETIM, a pour objectif de proposer une nouvelle méthode de prédiction de l'érosion de cavitation à partir d'un post-traitement de calculs numériques d'écoulements cavitant. La méthode reposant sur le post-traitement de simulations URANS en régime cavitant, prend en compte la tension de surface et la quantité d'air dissous dans le fluide en considérant des bulles sphériques dans l'écoulement. Les équations de la dynamique des bulles de type Rayleigh-Plesset, sont ensuite utilisées pour quantifier les ondes de surpression générées par l'implosion des structures de vapeur. Les calculs sont réalisés avec le code « IZ » développé au sein du LEGI et également avec le code Fine-TurboTM développé par Numeca International. Les simulations reposent sur une approche modèle homogène avec utilisation de la loi barotrope et sans considération des effets thermodynamiques. Un modèle k-epsilon avec loi de paroi étendue est utilisée et la viscosité turbulente est modifiée à l'aide de la correction de Reboud. Les calculs sont réalisés sur des géométries de type hydrofoil et comparés à la fois d'un point de vue écoulement (taille de poche, pression en entrée, vitesse de l'écoulement,fréquence) mais aussi marquages (zone d'érosion, taille et formes des impacts) à des résultats expérimentaux

Simulation of unsteady cavitation with a two-equations turbulence model including compressibility effects

Unsteady effects associated with cavitation were investigated by numerical simulations in three configurations. The simplest one was a Venturi-type section in which the cavitation sheet oscillates periodically with vapour cloud shedding. The second one was a hydrofoil whose unsteady cavitating behaviour depends on the angle of attack, and the most complex one was a cascade of three hydrofoils. In this last configuration, in addition to the unsteadiness associated with each cavity, a coupling between the three channels was also observed. These cavitating flows were simulated by 2D computations. Resolution of Reynolds-averaged Navier-Stokes equations was based on a finite-volume discretization associated with a pressure correction algorithm. Cavitation was simulated by using a barotropic vapour/liquid state law that links the fluid density evolution to the pressure variations. As standard k–ϵ RNG or k–ω turbulence models were found to be weakly efficient to simulate unsteady cavitation, influence of the compressibility of the two-phase medium on turbulence was considered. Both k–ϵ RNG and k–ω turbulence models, including corrections of these compressibility effects, were applied and results obtained were consistent with experiments: in the three configurations, the oscillation frequencies, the cavity length, the void ratio and the velocity fields obtained by numerical simulation were in reliable agreement with the available experimental data

Evaluation of the turbulence model influence on the numerical simulation of unsteady cavitation

Unsteady cavitation in a Venturi-type section was simulated by two-dimensional computations of viscous, compressible, and turbulent cavitating flows. The numerical model used an implicit finite volume scheme (based on the SIMPLE algorithm) to solve Reynolds-averaged Navier-Stokes equations, associated with a barotropic vapor/liquid state law that strongly links the density variations to the pressure evolution. To simulate turbulence effects on cavitating flows, four different models were implemented (standard $k-\varepsilon$ RNG; modified $k-\varepsilon$ RNG; $k-\omega$ with and without compressibility effects), and numerical results obtained were compared to experimental ones. The standard models $k-\varepsilon$ RNG and $k-\omega$ without compressibility effects lead to a poor description of the self-oscillation behavior of the cavitating flow. To improve numerical simulations by taking into account the influence of the compressibility of the two-phase medium on turbulence, two other models were implemented in the numerical code: a modified $k-\varepsilon$ model and the $k-\omega$ model including compressibility effects. Results obtained concerning void ratio, velocity fields, and cavitation unsteady behavior were found in good agreement with experimental ones. The role of the compressibility effects on turbulent two-phase flow modeling was analyzed, and it seemed to be of primary importance in numerical simulations

A numerical model to predict unsteady cavitating flow behaviour in inducer blade cascades

The cavitation behaviour of a four-blade rocket engine turbopump inducer is simulated. A 2D numerical model of unsteady cavitation was applied to a blade cascade drawn fromthe inducer geometry. The physical model is based on a homogeneous approach of cavitation, coupled with a barotropic state law for the liquid/vapour mixture. The numericalresolution uses a pressure-correction method derived from the SIMPLE algorithm and a finite volume discretization. Unsteadybehaviour of sheet cavities attached to the blade suction side depends on the flow rate and cavitation number. Two differentunstable configurations of rotating cavitation, respectively sub-synchronous and super-synchronous, are identified. The mechanisms that are responsible for these unstable behaviours are discussed, and the stress fluctuations induced on the blade by the rotating cavitation are estimated

3D numerical simulation of pump cavitating behavior

The quasi-steady cavitating behavior of three pumps was investigated by 3D unsteady viscous computations. The numerical model is based on the commercial code FINE/TURBO™, which was adapted to take into account the cavitation phenomenon. The resolution resorts to a time-marching algorithm initially devoted to compressible flows. A low-speed preconditioner is applied to treat low Mach number flows. The vaporization and condensation processes are controlled by a barotropic state law that links the void ratio evolution to the pressure variations. A radial pump, a centrifugal pump, and a turbopump inducer were calculated and the cavitating behaviors obtained by the computations were compared to experimental measurements and visualizations. A reliable agreement is obtained for the two pumps concerning both the head drop charts and the extension of the vapor structures. A qualitative good agreement with experiments is also observed in the case of the turbopump inducer. The accuracy of the numerical model is discussed for the three geometries. These simulations are a first attempt to simulate the complete 3D cavitating flows in turbomachinery. Results are promising, since the quasi-steady behaviors of the pumps in cavitating condition are found quantitatively close to the experimental ones. A continuing effort is pursued to improve the prediction accuracy, and to simulate unsteady effects observed in experiments, as, for example, rotating cavitation

Numerical and experimental investigations on the cavitating flow in a cascade of hydrofoils

The cavitating flow in a cascade of three hydrofoils was investigated by experimental means and numerical simulation. Experiments on the 2D-hydrofoils cascade were carried out at Darmstadt University of Technology in a rectangular test section of a cavitation tunnel. A numerical model developed at LEGI (Grenoble) to describe the unsteady behaviour of cavitation including the shedding of vapour structures was applied to the hydrofoils cascade geometry. Results of both experimental and numerical studies show a strong interaction between the cavities of each flow channel besides the typical self-oscillation of cloud cavitation. A detailed comparison of the results allows proposing an interpretation of the interaction mechanisms

Experimental and numerical studies on a centrifugal pump with 2D-curved blades in cavitation condition

In the presented study a special test-pump with 2D curvature blade geometry in cavitating and non-cavitating conditions was investigated using different experimental techniques and a 3D numerical model of cavitating flows. Experimental and numerical results concerning pump characteristics and performance breakdown were compared at different flow conditions. Appearing types of cavitation and the spatial distribution of vapour structures within the runner were also analysed

Numerical and experimental investigation on the cavitating flow in a cascade of hydrofoils

The cavitating flow in a cascade of three hydrofoils was investigated by experimental means and numerical simulation. Experiments on the 2D-hydrofoils cascade were carried out at Darmstadt University of Technology in a rectangular test section of a cavitation tunnel. A numerical model developed at LEGI (Grenoble) to describe the unsteady behaviour of cavitation, including the shedding of vapour structures, was applied to the hydrofoils cascade geometry. Results of both experimental and numerical studies show a strong interaction between the cavities of each flow channel besides the typical self-oscillation of cloud cavitation. A detailed comparison of the results allows an interpretation of the interaction mechanisms to be proposed