Numerical Investigation of Steady Density Currents Flowing Down an Incline Using v2¯−f Turbulence Model

Abstract

The governing equations of two-dimensional steady density currents are solved numerically using a finite volume method. The v2¯−f turbulence model, based on standard k−ε model, is used for the turbulence closure. In this method, all Reynolds stress equations are replaced with both a transport equation for v2¯ and an elliptic relaxation equation for f, a parameter closely related to the pressure strain redistribution term. The Simple-C procedure is used for pressure-velocity coupling. In addition, Boussinesq’s approximation is used to obtain the momentum equation. The computed height of the progressive density current is compared to the measured data in the literature, resulting in good agreement. The present results show that the flow rate is the most dominant parameter among those affecting the density currents hydrodynamics. The results also show that the v2¯−f turbulence model is able to predict and simulate the characteristics of the low Reynolds turbulent density currents successfully, although it is based on a high Reynolds number turbulence model, i.e., the standard k−ε model. The use of boundary layer convention, saying that the density current’s height is a height at which the concentration is ∼1% of the inlet concentration, seems to yield reasonable results.