Laminar planar hydraulic jump in thin film flow of power-law liquids—Experimental, analytical and numerical study

Abstract

This study explores the physics of laminar planar hydraulic jump of power-law liquids in a horizontal channel through shallow water analysis. The theory is supplemented and validated by numerical simulation performed by the phase-field method in COMSOL Multiphysics. The analysis is applicable for shear thinning as well as thickening liquids and reduces to Newtonian equations when the flow behavior index (n) is unity. The analytical and numerical results are further validated with experimental data of the present study. The steady state free surface profile in conjunction with a modified Bélanger type equation predicts jump location and strength (the ratio of film height just after and before the jump). The analysis provides a modified scaled relationship between the jump location and the liquid flow rate compared to that proposed for inviscid and viscous Newtonian liquids. An order of magnitude analysis expresses the scaled jump location and strength as a function of inlet Reynolds number (Rein), inlet Froude number (Frin), scaled channel length, and n. We find that an increase in the flow consistency index and/or n favors jump formation and the jump shifts toward the channel exit with increasing n for the same channel geometry, Rein and Frin. The influence of scaled channel length is more pronounced for n < 1 as compared to n > 1 while shear thickening liquids are more significantly influenced by Frin at fixed Rein and scaled channel length. The coupled effect of flow parameters on jump characteristics is depicted in the Rein–Frin plane, which denote the range of the existence of different jump types as the function of n.