Abstract
A closed mathematical model of the liquid friction factor for flow occurring in triangular grooves is presented. The model considers the interfacial shear stresses due to liquid-vapor frictional interactions for countercurrent flow. Using a coordinate transformation and the Nachtsheim-Swigert iteration scheme, a method is developed by which the asymptotic, two-point boundary value problem with one point-value varying can be solved. The coordinate transformation provides a means by which the irregular cross section of the liquid flow can be changed into a regular shape, which can then be solved numerically. The solution yields the velocity distribution for countercurrent liquid-vapor flow and allows the governing liquid flow equations to be solved for cases where the liquid surface is strongly influenced by the vapor flow direction and velocity. To verify the analytical results, an experimental test facility was constructed. The numerical solutions for channel angles of 20°, 40°, and 60° are compared with the corresponding experimental data and found to be in good agreement.
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