Quandt 



Axial Momentum Conservation: 



Gas — ^ dV„ = A„ dP - dF - T 77D„ dx 



Liquid — dVp = -Ap dP + dF 



The frictional drag force dF from the gas to the liquid droplets may be ana- 

 lyzed using Fig. 3. At this point, and in further 

 analysis, the axial pressure gradient force on the 

 droplets will be neglected, since it is small in 



Fd "* ^^ZI^;; ►p^ comparison to the frictional drag. It will further 



be assumed in this analysis that the gas phase has 

 a higher velocity than the liquid droplets. Hence, 

 for a single droplet, 



'"=^" — '^--11^ 

 The number of droplets in a differential length is 



6Ap dx 6Ap dx 

 dN : 



k-D^ 



Fig. 3 - Droplet 

 drag force model 



77D3 7tD3 



hence the differential drag force between the phases is 



Pg(Vg- Vp)2 Ap 

 dF = F^ dN = 3Cn ■ dx 



D "^'^ " -"-D 



4g. D 



*R dVp 



Total: -^ dV„ + Wr; -— = -A dP - T.tt D dx 



Energy Conservation: 



Gas W (Cp„ dT + — ^|=-dO, 



dVp2\ 



Liquid W^ |Cpp dip + dP/pp + = dQ . 



The heat transfer between the phases may be analyzed similarly to the drag 

 force to yield 



6Ap 

 dQ= hg_p(Tg-Tp)-^ dx . 



Again a tacit assumption here is that evaporation of the liquid phase is negligi- 

 ble. Consideration of the temperature distribution between phases shows that 

 the gas will be hotter than the liquid at the point of mixing due to the work of 



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