Hi,
In papers regarding two-phase flow, the authors compare their results to exact solution for the shock-tube problem.
How should one derive the exact solution if each phase has its own equation of state (stiffened gas e.o.s) and volume fraction?
I am not aware of any "exact" analytical two phase flow shock tube problem. This might be a numerical solution of a 1-D model, as commonly used as test case for compressible flow solvers. By the way do you consider bubbly liquids or mist flow?
I'm almost sure that there is no exact (analytical) solution for multiphase flows.
and if each phase has its own equation of state (stiffened gas e.o.s) and volume fraction; what would you do for interaction?
There are exact solutions for 1D shock tubes, but with ideal gas at both sides.
Can you share the paper's information so as to understand which exact solution they use?
There are exact solutions for 1D shock tubes, but with ideal gas at both sides.
Can you share the paper's information so as to understand which exact solution they use?
There is not an exact solution but I recommend you to extract data of curves from articles using some software like CurveExport or same ones
There is not an exact solution but I recommend you to extract data of curves from articles using some software like CurveExport or same ones
The "exact" solution assumes initial conditions with on the high pressure side pure liquid water and at the low pressure side a perfect gas. The solution is an expansion fan in the water, which can be calculated using a linearised theory (because of the limited compressibility, we have an acoustical behaviour) and in the gas a shock wave (which you can calculate using the Rankine Hugoniot shock adiabatic). The final solution is found because at the contact between the two phases the pressure should be continuous. So this is not a "two phase solution), but two single phase solutions glued to each other at the contact surface.
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