A gas-kinetic scheme for the simulation of turbulent flows

Righi, Marcello

Publication type:	Conference paper
Type of review:	Not specified
Title:	A gas-kinetic scheme for the simulation of turbulent flows
Authors:	Righi, Marcello
Proceedings:	28th International Symposium on Rarefied Gas Dynamics 2012
Page(s):	481
Pages to:	488
Conference details:	28th International Symposium on Rarefied Gas Dynamics, Zaragoza, Spain, 9-13 July 2012
Issue Date:	2013
Publisher / Ed. Institution:	American Institute of Physics
ISBN:	978-0-7354-1116-6 978-0-7354-1117-3
ISSN:	0094-243X
Language:	English
Subjects:	Compressible flow; Rarefied gas; Gas-kinetic scheme; Turbulence modelling
Subject (DDC):	530: Physics
Abstract:	Numerical schemes derived from gas-kinetic theory can be applied to simulations in the hydrodynamics limit, in laminar and also turbulent regimes. In the latter case, the underlying Boltzmann equation describes a distribution of eddies, in line with the concept of eddy viscosity developed by Lord Kelvin and Osborne Reynolds at the end of the nineteenth century. These schemes are physically more consistent than schemes derived from the Navier-Stokes equations, which invariably assume infinite collisions between gas particles (or interactions between eddies) in the calculation of advective fluxes. In fact, in continuum regime too, the local Knudsen number can exceed the value 0.001 in shock layers, where gas-kinetic schemes outperform Navier-Stokes schemes, as is well known. Simulation of turbulent flows benefit from the application of gas-kinetic schemes, as the turbulent Knudsen number (the ratio between the eddies’ mean free path and the mean flow scale) can locally reach values well in excess of 0.001, not only in shock layers. A further advantage of gas-kinetic schemes is that the fluxes are accurate to ? 2, for instance in the scheme developed by Xu in 2001 for the finite-volume discretization. In laminar flow, this provides a better resolution of shocks and vortexes, whereas in turbulent flows, high-order fluxes allow for a better resolution of secondary flows in a manner comparable to higher-order turbulence models for the Navier-Stokes schemes. This study has investigated a few cases of shock – boundary layer interaction comparing a gas-kinetic scheme and a Navier-Stokes one, both with a standard k - ? turbulence model. Whereas the results obtained from the Navier-Stokes scheme are affected by the limitations of eddy viscosity two-equation models, the gas-kinetic scheme has performed much better without making any further assumption on the turbulent structures.
URI:	https://digitalcollection.zhaw.ch/handle/11475/13609
Fulltext version:	Published version
License (according to publishing contract):	Licence according to publishing contract
Departement:	School of Engineering
Organisational Unit:	Institute of Mechanical Systems (IMES)
Appears in collections:	Publikationen School of Engineering

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Righi, M. (2013). A gas-kinetic scheme for the simulation of turbulent flows [Conference paper]. 28th International Symposium on Rarefied Gas Dynamics 2012, 481–488.

Righi, M. (2013) ‘A gas-kinetic scheme for the simulation of turbulent flows’, in 28th International Symposium on Rarefied Gas Dynamics 2012. American Institute of Physics, pp. 481–488.

M. Righi, “A gas-kinetic scheme for the simulation of turbulent flows,” in 28th International Symposium on Rarefied Gas Dynamics 2012, 2013, pp. 481–488.

RIGHI, Marcello, 2013. A gas-kinetic scheme for the simulation of turbulent flows. In: 28th International Symposium on Rarefied Gas Dynamics 2012. Conference paper. American Institute of Physics. 2013. S. 481–488. ISBN 978-0-7354-1116-6

Righi, Marcello. 2013. “A Gas-Kinetic Scheme for the Simulation of Turbulent Flows.” Conference paper. In 28th International Symposium on Rarefied Gas Dynamics 2012, 481–88. American Institute of Physics.

Righi, Marcello. “A Gas-Kinetic Scheme for the Simulation of Turbulent Flows.” 28th International Symposium on Rarefied Gas Dynamics 2012, American Institute of Physics, 2013, pp. 481–88.