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TECHNICAL PAPERS

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

[+] Author and Article Information

School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., P.O.Box 11365-9567, Tehran, Irannimakhakzad@yahoo.com

School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., P.O.Box 11365-9567, Tehran, Iranfiroozabadi@sharif.ir

Bijan Farhanieh

School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., P.O.Box 11365-9567, Tehran, Iranbifa@sharif.ir

1

Corresponding author.

J. Fluids Eng 129(9), 1172-1178 (Mar 30, 2007) (7 pages) doi:10.1115/1.2754318 History: Received May 31, 2006; Revised March 30, 2007

## 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.

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## Figures

Figure 1

Concentration contour of saline density current developing on a slope of Run 1

Figure 4

Distance evolution of the bulk properties of a typical density current: (a) depth-averaged bulk Richardson number and concentration, (b) depth-averaged velocity and flow height, Run 1

Figure 2

Comparison of the current height for (a) Run 1 and (b) Run 2 with experimental data

Figure 8

Flow height of saline density current using three different inlet heights and identical Reynolds number (i.e., Re=3000, cin=1.2%, slope=14%)

Figure 7

Flow height obtained using three different values of inlet Reynolds number (cin=1.2%,hin=4cm, slope=14%)

Figure 6

Flow height of saline density current: (a) different inlet concentration and (b) different bed slope

Figure 5

Vertical profiles of concentration at some distances from the inlet, Run 1 (cin=1.2%, hin=4cm, and bed slope=14%)

Figure 3

Comparison of the dense layer height of Run 1 obtained from v2¯−f model with standard k−ε model and measurement

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