# A Study into the effect of underlining RANS model on a Delayed Detached-Eddy Simulation

Researcher: Neil Ashton

Supervisor(s): Dr A Revell, Dr R Prosser
Start Date: July 2008 End Date: July 2012
Keywords: DDES, Hybrid RANS-LES

## Overall Research Aim

The principle aim of this research is to undertake a comprehensive review of DDES formulations based on novel RANS models for industrial test cases.

## Introduction - Why Delayed Detached-Eddy Simulation (DDES)?

Hybrid RANS-LES models have become a viable alternative to RANS and LES methods for solving massively separated turbulent flows. The shortcomings of RANS models and the excessive computational expense of a fully resolved LES has provided a void for these hybrid approaches to fill. One such hybrid RANS-LES approach is Detached-Eddy Simulation (DES), or its successor, Delayed Detached-Eddy Simulation (DDES).

### DDES

This approach is based upon a seamless switch between a RANS and LES turbulent length scale depending on the local grid size, velocity gradient and eddy viscosity. Several DDES formulations have been implemented into Code_Saturne to establish the effect of the underlining RANS model on a DDES. The Decaying Isotropic Turbulence (DIT) test case has been used to partly validate and illustrate the importance of the correct numerical scheme and to calibrate each DDES formulation.
%BEGINLATEX{label="eq:fddes"}% \begin{equation*} L_{DDES} = \frac{L_{RANS}}{L_{RANS} - f_{d} \ max \left(0,L_{RANS} - L_{LES}\right)} \end{equation*}%ENDLATEX% %BEGINLATEX{label="eq:functions"}% \begin{align*} f_{d} \ &= 1 - tanh\left(\left[8r_{d}\right]^{3}\right) \r_{d} \ & = \ \frac{\nu_{t} + \nu}{\sqrt{U_{i,j}U_{i,j}}\kappa^{2}d_{w}^{2}} \\end{align*}%ENDLATEX% %BEGINLATEX{label="eq:length"}% \begin{align*} L_{RANS} \ &= \ \frac{k^{3/2}}{\varepsilon} & L_{LES} \ & = \ C_{DDES}\Delta \\end{align*}%ENDLATEX%

Calibration of the %$C_{DDES}$% constant

## Numerics - A Hybrid Numerical Scheme

Just as DDES seamlessly switches from a RANS branch to a LES-like branch depending on the local flow and grid conditions, the numerical scheme should also switch according to the requirement of each mode. A new hybrid numerical scheme has been developed consistent with the concept of DDES.

### Code_Saturne_ Implementation

In order for DDES to be optimum in the LES-like mode, a convective scheme exhibiting low numerical dissipation should be used. In the case of Code_Saturne, this is the 2nd order Central differencing scheme (CDS). It is known however that RANS models may suffer from excessive oscillations for high cell Péclet numbers and coarse grids when a central differencing scheme is employed. It is therefore optimum to utilize the 2nd order linear upwind scheme (SOLU) in these regions. In order to comply with both of these requirements, a new hybrid numerical scheme has also been developed to ensure that each branch of this approach is paired with the correct convective scheme. The hybrid numerical scheme uses localized flux blending for the convective fluxes, %$\phi_{f}$%,that is based on Equation 2. Its formulation is:
%BEGINLATEX{label="eq:numerics"}% \begin{align*} \phi_{f} \ &= \ \phi_{f,SOLU} & \ if \ L_{RANS} < L_{LES} \\phi_{f} \ & = \ (1-f_{d}) \phi_{f,SOLU} \ + \ f_{d} \ \phi_{f,CDS} & \ if \ L_{RANS} > L_{LES} \end{align*}%ENDLATEX%

Iso-Surfaces of the Q criteria for the 2-D wall-mounted hump

Last Modification: r29 - 2012-06-22 - 16:15:58 - DongHoSeo

Current Tags:
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Topic attachments
I Attachment Action Size Date Who Comment
jpg cddes_phif_etc.jpg manage 135.8 K 2011-06-21 - 21:47 NeilAshton
png humpiso.png manage 654.1 K 2010-12-18 - 20:39 NeilAshton iso surfaces over a 2D wall-mounted hump
png sstddesposter.png manage 312.9 K 2010-12-19 - 11:15 NeilAshton Calibration of the CDDES constant
Topic revision: r29 - 2012-06-22 - 16:15:58 - DongHoSeo
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06 Dec 2019

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