Influence of the Perturbation Amplitude and the Froude Number on the Establishment Length of Roll Waves

Abstract

This paper presents a theoretical and numerical analysis of the length required for roll waves to become stationary in a free-surface laminar flow of a Newtonian fluid. Two types of stability analysis are brought to verify flow stability and obtain parameters for wave growth rate in a Saint-Venant like system. Then, numerical simulations are performed of the free-surface laminar transient flow of glycerin. The Navier-Stokes equations were solved using the finite volumes method, Euler schemes and PIMPLE, and the VoF technique to solve the interface. Boundary conditions were specified to obtain a steady and uniform regime given a Froude number. Then, a sinusoidal perturbation with controllable properties was applied to the inlet velocity. From the numerical results, the spatial development of the roll waves was evaluated, focusing on the establishment length as a function of the Froude number and the perturbation amplitude. The analyses performed allowed the verification of the influence of flow hydraulic regime over the establishment length, and it was possible to obtain a new equation as a function of the perturbation amplitude.