Literature review RANS derivation and analysis
LITERATURE REVIEW ON TURBULENCE MODELLING AND THE RANS APPROACH
- N.Abhinandhan
Abstract: The objective of this project is to review available literature on turbulence models and to apply the Reynolds decomposition to Navier Stokes equation and derive the expression for Reynolds Stress. The turbulent viscosity term has been explained and the difference between turbulence viscosity and molecular viscosity is elucidated.
What is Turbulence?
Fluid flow can be split into three types:
- Laminar Flow
- Transitional Flow
- Turbulent Flow
The type of flow can be determined using the Reynolds Number. A low Reynolds number corresponds to Laminar flow where the flow is in an orderly manner and parameters like pressure and velocity remain steady. A high Reynolds number corresponds to turbulent flow where the flow is chaotic and the parameters are fluctuating.
Turbulence is not really chaos, at least in the sense of the word that the dynamical systems people use, since turbulent flows are not only time-dependent but space dependent as well. Turbulence is mainly characterised by three- dimensional vorticity.
Turbulence Modelling:
The primary aim of turbulence modelling is to calculate the Reynold’s stress term and the turbulent viscosity. The effect of turbulence can be modelled by a method called Direct Numerical Simulation which involves solving the Navier-Stokes equation over the turbulent time step. But the turbulent time step is so small thus the computational cell size that will be required to solve the equation is in the order of 1e-6 m. Thus, a turbulence model is required to capture the effects of turbulence using a coarser grid.
Types of Turbulence Models:
There are three types of turbulence models:
- Reynolds Averaged Navier Stokes Equation (RANS)
- Large Eddy Simulation (LES)
- Direct Numerical Simulation (DNS)
In this project we will mainly focus upon the RANS method.
The variation of velocity in a turbulent flow field is shown above. The velocity at any instant can be divided into a mean component and instantaneous component.