i am working on solving the euler equations for water (water is given by tait equation of state with a simple cavitation model: if the pressure drops below a certain value pressure is set to this value). the equations are solved by a modified method of characteristics. Because of the cavitation model the speed of sound turns to zero in cavitated regions and the equations are no longer hyperbolic. i tried various formulations but all remained unsufficient. does anybody have an idea how to treat this sort of problem?

manfred

Hi,

can you give some more details of your work. Do you solve the energy equations also. Also, could you please tell which cavitation model you are using

Thanks Buvana

the equation of state for water is based on the tait model. the predicted pressure is not allowed to fall below the cavitation pressure pc, although the density can continue to decrease below its critical value rhoc:

p= B((rho/rho0))**gam - 1) + A if rho>rhoc

pc otherwise the numerical method is based on extrapolating values for half of the time step via characteristics to the cell edges and then solving linearized riemann problems. on my mind the speed of sound plays a major role in this region of cavitation and i do not know how to treat this problem or to calculate speed of sound, because with this model csound equals zero and the riemann problem can not be solved.

Hi!

We have done some extensive work on cavitation. Modeling cavitation by the method you are using will work only if some form of state equation relating the speed of soud to mixture pressure is provided. The experimental result suggests that this relationship is actually harmonic - the speed of sound in the liquid medium drops drastically even for small volume fractions of gas in the mixture. We have derived an equation of state that reproduces this relationship.

Once this relatioship is used, formulating the Reimann problem is a piece of cake. Although most formulations to date do not include the energy equation in them (ie. they assume that each phase is incompressible in itself, but account for the variation in speed of sound in the mixture) the compressible formulation is a direct extension of this. We have formulated this also. However, it is a lot messier than the incompressible formulation.

If you are interested in the incompressible formulation, you can look up our papers :

Simulations of Cavitating Flows using Hybrid Unstructured Meshes : To appear in Journal of Fluids Engineering, June 2001, Vol 123.

Earlier refs :

AIAA-99-3330

AIAA-97-2081

If you want electronic copies of any of these papers I can send them to you. Let me know.

Srinivasan Arunajatesan Research Scientist CRAFT Tech. Inc. Dublin, PA. www.craft-tech.com ajs@craft-tech.com