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Direct- and Large Eddy Simulations of Turbulent Flow in CS0 Diffuser on Resolved and Under-resolved Meshes

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Abstract

A Direct Numerical and Large Eddy Simulation study is conducted to establish the NASA CS0 diffuser as a test case for scale-resolving simulation methods and to evaluate the ability of such simulations to accurately predict flows with adverse pressure gradients and shallow separation from a smooth surface. The results of fine grid studies are in a good agreement with experimental data and substantially supplement them. These data are used as a basis for testing of LES on reduced grids, using different combinations of wall treatments and turbulence model formulations.

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Acknowledgements

All the computations were conducted with the use of the cluster Tornado of the Computer Center “Polytechnichesky”.

Funding

Russian authors’ research was funded by the Ministry of Science and Higher Education of the Russian Federation as part of World-class Research Center program: Advanced Digital Technologies (contract No. 075-15-2022-311 of Apr. 20, 2022).

Author information

Authors and Affiliations

  1. ANSYS Germany GmbH, Otterfing, Germany

    Florian R. Menter

  2. St. Petersburg Polytechnic University, 29, Polytechnicheskaya Str., 195251, St. Petersburg, Russia

    Dmitry K. Kolmogorov, Andrey V. Garbaruk & Andrey S. Stabnikov

Authors
  1. Florian R. Menter
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  2. Dmitry K. Kolmogorov
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  3. Andrey V. Garbaruk
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  4. Andrey S. Stabnikov
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Correspondence to Florian R. Menter.

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Appendices

Appendix

Algebraic Wall-Modeled LES Formulation

The model is similar to the algebraic WMLES formulation given in Shur et al. (2008), but differs in some details, by not using the strain rate S of the Smagorinsky model in the LES part, but a formulation using the difference between the strain rate and the vorticity rate \(\Omega\). This change avoids the known deficiency of the Smagorinsky model to produce non-zero eddy-viscosity in constant shear regions. The model formulation is:

$$ \nu_{t} = f_{sw} \nu_{t,RANS} + \left( {1 - f_{sw} } \right)\nu_{t,LES} $$
(7)
$$ f_{sw} = e^{{ - \left( {\frac{{C_{w1} d_{w} }}{{h_{max} }}} \right)^{{C_{w2} }} }} $$
(8)
$$ \nu_{t,LES} = l_{LES}^{2} \left| {S - \Omega } \right|, \nu_{t,RANS} = l_{RANS}^{2} S $$
(9)

With coefficients \(C_{w1} = 2,{ }C_{w2} = 3\). In this formulation, \(d_{w}\) is the wall distance, \(h_{max}\) is the maximum edge length of the cell, \(S\) is the strain rate and \(\Omega\) is the vorticity rate.

The length scales are defined as:

$$ l_{RANS} = 0.41d_{w} \sqrt {f_{wd} } $$
$$ f_{wd} = 1 - e^{{ - \left( {\frac{{l^{ + } }}{25}} \right)^{3} }} $$
$$ l^{ + } = \frac{{\sqrt {\left( {\nu + \nu_{t} } \right)S} d_{w} }}{\nu } $$
(10)
$$ l_{LES} = C_{smag} \Delta $$
$$ \Delta = min\left( {C_{w} max\left( {d_{w} ,h_{max} } \right),h_{max} } \right) $$
(11)

with coefficients \(C_{smag} = 0.2, C_{w} = 0.15\).

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Menter, F.R., Kolmogorov, D.K., Garbaruk, A.V. et al. Direct- and Large Eddy Simulations of Turbulent Flow in CS0 Diffuser on Resolved and Under-resolved Meshes. Flow Turbulence Combust 110, 515–546 (2023). https://doi.org/10.1007/s10494-023-00399-1

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