An Analysis of Two-Dimensional Stratified Gravity Current Flow using Open FOAM

W.K Lam,H Hasini,L Chan,A Ooi

doi:10.14419/ijet.v7i4.35.22919

Abstract

Direct numerical simulations (DNSs) of two-dimensional stratified gravity-current are simulated using OpenFOAM. Three different aspect ratio, h0/l0 (where h0 is the height of the dense fluid and l0 is the length of the dense fluid) are simulated with stratification ranging from 0 (homogenous ambient) to 0.2 with a constant Reynolds number (Re) of 4000. The stratificationof the ambient air is determined by the density difference between the bottom and the top walls of the channel (ρb- ρ0, where ρb is the density at the bottom of the domain and ρ0 is the density at the top). The magnitude of the stratification (S=ԑb/ԑ) can be determined by calculating the reduced density differences of the bottom fluid with the ambient fluid (ԑb = (ρb- ρ0)/ ρ0) and the dense fluid with the ambient fluid (ԑ = (ρc-ρ0)/ ρ0, where ρc represents the density of the dense fluid). The configuration of the simulation is validated with a test case from Birman, Meiburg & Ungraish and the contour and front velocity (propagation speed) were in good agreement. The gravity current flow in the stratified ambient is analyzed qualitatively and compared with the gravity current in the homogenous ambient. Gravity current in homogenous ambient (S=0) and weak stratification (S=0.2) are supercritical flow where the flow is turbulent and Kelvin-Helmholtz (K-H) billow formed behind the gravity current head. The front location of the gravity is reduced as the stratification increase and denotes that the front velocity of the gravity current is reduced by the stratification.

Highlights

Gravity current or density current is a type of fluid flow that occurs mainly in the horizontal domain due to density difference of two fluids
The configuration of the simulation is validated with a test case from Birman et al [12] who investigated the prediction of the front velocity by theoretical analysis by Ungarish [10]
The propagation velocity in the current simulation is slightly slower by approximately 1.7% compared to Birman et al [12]

Summary

Introduction

Gravity current or density current is a type of fluid flow that occurs mainly in the horizontal domain due to density difference of two fluids. Simpson [1] has reviewed a wide range of experimental studies on gravity current flow. Gravity current flow has been widely studied with a variety of lock configurations such as lock shape [2] (elliptical release [3], [4] and circular release [5]), lock depth and initial aspect ratio [6]. When the Froude number is less than 1/π (Fr < 1/π), the gravity current resides in the subcritical flow regime. The flow is slow, and the formation of the gravitational waves which propagates faster than the front of the gravity current occurs.

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