Hello, dear RG community.
Very often, gas fraction (also known as void fraction or gas holdup) is thought of as a ratio of the gas volume to the total volume:
αG = VG/V (eqn.1)
That been said, Dr. Mamoru Ishii in his "Thermo-fluid dynamics of two-phase flow", 2011, 2nd ed., Springer, defines local gas fraction as a time average gas mass density function (see. pages 71, 72 and 73 in the cited book):
αG(x0,t0) = lim(1/Δt) integral(Mk(x0,t0)dt) (eqn.2)
I have been able neither to find the derivation of the volume based gas fraction formula (eqn.1) in Dr. Ishii's book, nor derive it myself starting from the definition of the local gas fraction (eqn.2).
I am wondering if anybody can show me a rigorous step-by-step derivation of eqn.1 starting from eqn.2, please.
Thank you in advance.
Ivan
P.S. Please, pay attention that I am asking a very specific question. For the sake of maintaining order in the discussion under this post, I will be deleting unrelated musings or spam posts.
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