I have little experience with multi-phase flows and would like some advice on the best approach to model the following problem:

A compressed gas sits above a liquid in a tank that has a release valve which can be likened to a convergent-divergent nozzle. The flow starst when the valve releases; i.e. the expanding gas forces the liquid and then itself out of the valve. High-speed photographic imagery and other measurements in the case of air over water reveals some characteristics of the flow relevant to the modelling

a) The water forms a swirl in the tank whilst being blown out.

b) As the air expands and the temperature drops, homogeneous condensation occurs in the gas due to vapor presence.

c) As the end of the expulsion phase, a mixture of water, air and vapor exits the valve.

d) Maximum water flow speed is approx. 30 m/s.

e) Maximum gas pressure is 10 bar, maximum gas exhaust speed approx. twice local speed of sound.

f) The flow is turbulent.

To simplify matters I initially disregard condensation as the gas is not always moist air and hence will not necessarily exhibit condensation.

I have considered the following options:

Use an interface capturing method like VOF. This entails solving one set of equations for the entire flow. This implies the liquid must be described as a compressible fluid. My problem then, I believe, is that I need an EOS common to both fluids to close the system. Choices known to me are the stiffened gas EOS (Tamman) and Tait's EOS. However, neither is applicable in this very low pressure situation; they apply only to kbar or Mbar regions it seems. If one could use different EOS's for each fluid then a much better EOS for the liquid phase could be found in the JANAF tables, but would different EOS's for the VOF method not be contradictory to its main idea of only solving one set of flow equations ?

Use the two-fluid method. I have derived the equations, and the averaging procedure inherent in the method produces some terms that account for inter-phase momentum transfer and turbulence. These terms need modelling for closing the system. The model depends crucially on correct modelling of these terms, and probably requires a level of insight into the physics that eludes me. I have not been able to find any references for modelling these terms in similar flow scenarios. Lots of references for modelling these terms in case of bubbly flow exist, but seem inappropriate in this case. So, how to proceed from here ?

Any advice on how to model this flow and as well as feedback on my own thoughts are most welcome.

Thanks, Martin

You probably have cavitation in your release (or releave) valve when it's blowing liquid.

I wouldn't try to solve all this in one go. Some parts can be done analytically.

Success,

Bart

Thanks for your response.

Which parts are you thinking of? Whilst the initial gas expansion might be modelled as a 1D adiabatic expansion, I don't see how the initial water flow could be solved analytically.

If cavitation determines your liquid mass flow in the valve it is hard to do it analytically. If not, then it should be do-able given friction factor and a decreasing gas pressure over time. If the releave valve is a simple venturi and you do not have cavitation then it depends on how accurate you need your solution (given the uncertainties in your CFD modelling).