A numerical investigation of laminar planar hydraulic jump in Herschel-Bulkley fluid

Abstract

Laminar planar hydraulic jump during viscoplastic liquid flow in a horizontal channel is investigated through experiments and numerical simulation using Herschel-Bulkley (HB) model. The simulations are performed using the phase-field method with Papanastasiou regularization parameter and validated against experimental results. Both experiments and simulations show the free surface height to gradually increase upstream of jump and recede after the jump with a remarkable increase in free surface height and surface waviness at the jump. The model further reveals that an increase in any of the rheological parameters [yield stress (τo) flow behaviour index (n) and flow consistency index (k)] keeping the other properties constant increases film thickness. This increases jump strength and shifts jump towards the entry. However, each parameter influences free surface profile and jump characteristics in a different way. While a higher τo suppresses the development of the shear zone and results in a thicker plug zone, a higher n increases shear zone thickness and decreases the plug zone thickness. On the other hand, a higher k increases both shear and plug zone thickness. The steady state fully developed self-similar velocity profile is independent of k and depends on τo and n. Different jump types, obtained from simulations, are presented as phase diagrams in non-dimensional coordinates for a generalised approach.