# Rahman-Siikonen-Agarwal Model

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## Introduction

The Rahman-Agarwal-Siikonen (RAS) Turbulence model is a one-equation eddy viscosity model based on $k-\epsilon$ closure. The R-transport equation along with the Bradshaw and other empirical relations are used to solve for the turbulent viscosity. A damping function, $f_\mu$, is used to represent the kinematic blocking by the wall. To avoid defining a wall distance, a Helmholtz-type elliptic relaxation equation is used for $f_\mu$. The model has been validated against a few well-documented flow cases, yielding predictions in good agreement with DNS and experimental data.

## RAS Model

The turbulent eddy viscosity is given by

$\mu_t = C_\mu f_\mu \rho \tilde{R} = C_\mu f_\mu \rho k T_t$

The R-transport equation is

$\begin{matrix} \frac{\partial \rho R}{\partial t} + \frac{\partial \rho u_j R}{\partial x_j} & = & \frac{\partial}{\partial x_j} [ (\mu +\frac{\mu_t}{\sigma})\frac{\partial R}{\partial x_j} ] +C_1 \rho \sqrt{P \tilde{R}} - C_2 \rho (\frac{\partial \tilde{R}}{\partial x_k})^2 \end{matrix}$