Hi,
It is known that the speed of sound in the mixture region between two phases is lower than the speed of sound of each phase.
Therefore, is it still justified to use incompressible formulation for two-phase flow?
and why is it more common to see papers of multiphase turbulent flow mostly with imconpressible formulation?
Theodore Costopoulos,
This is exactly what I'm asking. I understand the pressure remains low but the speed of sound in the mixture region significantly decreases as well.
Hi,
Interesting question. In regions where acoustics is not significant, but instead larger velocities and transportation of matter, incompressibility could be valid, and describe the solution.
The wave equation can be derived from balance of mass and continuity of mass, if the first is linearised and the latter is assumed with time varying density, not incompressible. Then, the result will be as you say, a lower wave velocity for the mixture.
Turbulence may obey other acoustics, and nonlinear equations with additional assumptions are often used. I saw a reference recently, I can search later.
Based on the extensive review of the problem presented in the fundamentals of multiphase flow
http://authors.library.caltech.edu/25021/2/cabook.pdf
we can conclude (after analysis of eqs. (1.21)-(1.72) ) that assumption of incompressibility is not used. In most of cases the incompressible models are not applicable. One of the notable exceptions is the transport of particles suspended in the flow where the assumption div u = 0 is commonly applied (see chapter 2 in the fundamentals of the multiphase flow).
Dear Dr JP and others,
Is it possible to consider the entire time diff, as a time diff not including velocity dependency and what will that describe?
For a fast varying field, it is correct, and then one could integrate the density directly, and express in div u. For u being prop to sqrt r, this will give density solutions for a singularity.
Kind regards
Dear Lena and all,
The numerical simulation of a multi-phase flow with turbulence, acoustic waves, and cavitation effects is still not within the reach of the suite of numerical techniques available to us. In the same way the current computer hardware is also a limiting factor. The additional theoretical work is needed, particularly to develop the closure methods and parameterization a of the unresolved phenomena. The approach proposed in your answer belong to this category and it is certainly worth considering.
Kind regards
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