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Momentum balance

The most important assumption is that the correct momentum of, say, the liquid phase is approximated in the following way

$$\mbox{$<\!{(1-\alpha)A_c\rho_\ell u_\ell^2}\!>$} \approx \... ...\!{u_\ell}\!>$}_\ell ^2\rho_\ell(1-\mbox{$<\!{\alpha}\!>$})A_c$$ (6.28)

and this assumption is not very accurate according to Ishii and Mashima^6.3. In fact, it is necessary to introduce a correlation coefficient $C_{v \ell}$ defined by

$$C_{v \ell} \;\hbox{$=$\kern-0.68em\raise1.1ex \hbox{$\scri... ...\!>$})A_c}{\mbox{$<\!{(1-\alpha) A_c\rho_\ell u_\ell^2}\!>$}}$$ (6.29)

in order to account for the non-uniform profiles. The same comment applies to the vapor phase momentum equation.

Furthermore, the axial change of the cross-sectional average of the laminar and turbulent zz-stress ($\tau_{zz}$) is neglected--an acceptable assumption since we have a large $\mbox{\bf Re}$ in the reactor core.

 
 

 
 

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