MODELING LAMINAR FLOW IN CONVERGING-DIVERGING CHANNELS

Abstract

Converging-diverging channels have been known to have low net charge (flow parameters) due to associated high frictional flow resistance. Thus, there is a need to optimize frictional flow resistance in these channels. To this end, frictional flow resistance was optimized for a laminar, fully formed flow in a linearly varying cross-sectional converging-diverging channel in this study. To achieve this, an empirical frictional flow resistance model was developed using continuity and momentum equations, and this accurately represents a parabolic axial velocity profile in converging-diverging section. The developed model was solved and parametric investigations carried out on geometrical and fluid flow parameters using MATLAB 6.1. The results show that the frictional flow resistance decreases as radius ratios increases, but increases as Reynolds number and taper angle increase. Radius ratios and Reynolds numbers were found to be more significant than taper angles. Results in comparison to available literature showed that the developed frictional flow model is an accurate model as it predicts axial velocity and the flow resistance with a high degree of precision. The study concludes that, for frictional flow resistance to be kept at barest minimum in a converging diverging channel, radius ratio must be maintained at its highest value and Reynolds number at its lowest possible value.