The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

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.

/pdf/evaluation-of-the-turbulence-model-influence-on-the-zcydbuowhd.pdf

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

Large Eddy Simulation and theoretical investigations of the transient cavitating vortical flow structure around a NACA66 hydrofoil

Detection of cavitation in hydraulic turbines

Experimental study of characteristic curves of centrifugal pumps working as turbines in different specific speeds

http://www2.arnes.si/~mdula/Relationship%20between%20cavitation%20structures%20and%20cavitation%20damage.pdf

Relationship between cavitation structures and cavitation damage

http://www2.arnes.si/%7Emdula/Development%20of%20a%20cavitation%20erosion%20model.pdf

Development of a cavitation erosion model

Cavitation in hydraulic machines causes different problems that can be related to its unsteady nature. An experimental and numerical study of developed cavitating flow was performed. Until now simulations of cavitating flow were limited to the self developed “in house” CFD codes. The goal of the work was to experimentally evaluate the capabilities of a commercial CFD code (Fluent) for simulation of a developed cavitating flow. Two simple hydrofoils that feature some 3D effects of cavitation were used for the experiments. A relatively new technique where PIV method combined with LIF technique was used to experimentally determine the instantaneous and average velocity and void ratio fields (cavity shapes) around the hydrofoils. Distribution of static pressure on the hydrofoil surface was determined. For the numerical simulation of cavitating flow a bubble dynamics cavitation model was used to describe the generation and evaporation of vapour phase. An unsteady RANS 3D simulation was performed. Comparison between numerical and experimental results shows good correlation. The distribution and size of vapour structures and the velocity fields agree well. The distribution of pressure on the hydrofoil surface is correctly predicted. The numerically predicted shedding frequencies are in fair agreement with the experimental data.

Experimental evaluation of numerical simulation of cavitating flow around hydrofoil

In the presented study a special test pump with two-dimensional curvature blade geometry was investigated in cavitating and noncavitating conditions using different experimental techniques and a three-dimensional numerical model implemented to study 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 vapor structures within the impeller were also analyzed. These results show the ability of the model to simulate the complex three-dimensional development of cavitation in a rotating machinery, and the associated effects on the performance.

https://hal.archives-ouvertes.fr/hal-00211209/document

Experimental and Numerical Studies in a Centrifugal Pump With Two-Dimensional Curved Blades in Cavitating Condition

Cavitation on two-dimensional hydrofoils with swept leading edges always displays some 3-dimensional effects. It is well known that the cavity closure on such hydrofoil is not perpendicular to the channel walls, but is curved in a distinctive pattern. The cavitation pocket is longer in the region where the hydrofoil is the shortest. Also the dynamics of cavitation is very distinctive. In the region where the hydrofoil is the longest attached and steady cavitation with no cloud separation exists. On the other side, where the hydrofoil is the shortest, cavitation cloud separations occur. Different explanations for this pattern were proposed in the past but they have not jet been clearly confirmed neither experimentally nor by numerical simulation. In the present paper a clear explanation supported by the numerical simulation and also by experimental measurements, is given.

/pdf/investigation-of-a-re-entrant-jet-reflection-at-an-inclined-2wvk7xnfny.pdf

Bernd Stoffel

Papers

Relationship between cavitation structures and cavitation damage

Development of a cavitation erosion model

Experimental evaluation of numerical simulation of cavitating flow around hydrofoil

Experimental and Numerical Studies in a Centrifugal Pump With Two-Dimensional Curved Blades in Cavitating Condition

Investigation of a re-entrant jet reflection at an inclined cavity closure line