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Two-phase flows

For two-phase flows one may derive an expression for the pressure change, $\Delta p_{\mbox{\protect\scriptsize TP,exp}}$ [Pa], based on the two-phase separated flow mixture momentum equation. Such a derivation reveals that

$$\Delta p_{\mbox{\protect\scriptsize TP,exp}} = 2\sigma(1-\... ..._g}\frac{\mbox{$<\!{x}\!>$}^2}{\mbox{$<\!{\alpha}\!>$}}\right]$$ (5.29)

where $\mbox{$<\!{G}\!>$}_1$ is the mass flux in the smaller cross section [ ${\mbox{kg}}/({\mbox{m}}^2\cdot{\mbox{s}})$]. This way of evaluating the pressure change recommended by Lahey and Moody [18] is based on the so-called Romie multiplier which is the expression in the brackets. The derivation of (5.30) assumes that both $<\!{\alpha}\!>$ and $<\!{x}\!>$ are constant across the expansion.

Alternatively one could use a more general approach and choose not to assume constant void fraction across the expansion (see [11, p. 212] and [38, p. 247]). In this case the void fraction downstream the expansion, $\mbox{$<\!{\alpha}\!>$}_2$, is calculated by a void fraction constitutive relation at the lower mass flux $\mbox{$<\!{G}\!>$}_2$. In order to take full advantage of this approach the void fraction constitutive relation has to include a flow effect as the Zuber-Findlay, in fact, does.

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