Numerical study of thin-film flows and open-channel flows

Abstract

A numerical procedure is developed capable of simulating gravity-driven film flows in two-dimensions. The moving boundary problem is handled through the ALE formulation. In the case of turbulent fluid flows, the two-equations $k-\epsilon$ closure model is used to model the turbulence. A Chorin-type projection scheme is utilized to decouple the velocity and pressure fields, and the spatial discretization is done using the Finite Element Method. Thin liquid films draining down vertical or inclined planes are susceptible to long wavelength disturbances. An extensive numerical study of the surface wave instability in isothermal thin film flows is done by solving the full-scale nonlinear system. Temporal stability analysis of a spatially periodic disturbance reveals interesting wave dynamics. The transition from nearly sinusoidal supercritical waves to broad-banded solitary waves is found to go through a quasi-periodic regime. In this quasi-periodic state, the fundamental mode and several of its harmonics are in an oscillatory state, with continuous exchange of energy. An extensive parametric search has been done to obtain the phase boundary delineating the quasi-periodic regime. Complex wave interactions such as wave-splitting and wave-merging are discussed. Spatial stability analysis akin to the usual experimental studies is done and comparisons are made with the experiments. For the development of successful theories capable of predicting the formation of bedforms, it is essential to understand the turbulent fluid flow on top of the bed. To this end, mean flow and turbulence characteristics for flow over artificial stream-wise periodic bedforms are obtained. Due to the local accelerations associated with stream-line bending, very large velocities and stresses are found to exist at the tip of the dune The separation wake turbulence is found to completely dominate the wall-generated turbulence, and the maximum turbulence intensity levels occur at a distance, approximately equal to the dune height, away from the bed. The accuracy of the rigid-lid approximation is determined by computing the flow field with and without the rigid-lid approximation. The rigid-lid approximation is found to over-predict the shear at the dune crest. Lastly, the mean flow and turbulence characteristics in hydraulic jump are obtained. In the case of flow with inlet supercritical Froude number 2.0, a small recirculation zone is found to exist at the foot of the jump. The mixing layer turbulence associated with the surface roller and the recirculation zone are found to dominate the wall-generated turbulence