Modification of the LS-STAG Immersed Boundary Method for Simulating Turbulent Flows

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ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2017. № 5 19
DOI: 10.18698/1812-3368-2017-5-19-34
MODIFICATION OF THE LS-STAG IMMERSED BOUNDARY METHOD
FOR SIMULATING TURBULENT FLOWS
I.K. Marchevsky
V.V. Puzikova
Bauman Moscow State Technical University, Moscow, Russian Federation
Abstract Keywords
We constructed the LS-STAG discretisation for 2D Reynolds-
averaged Navier — Stokes equations, filtered Navier — Stokes
equations (as used for large eddy simulation and detached eddy
simulation) and equations employed in the Smagorinsky,
Spalart — Allmaras,  , k   k and   k Menter’s Shear
Stress Transport turbulence models. We added a fourth grid to
the LS-STAG mesh consisting of three staggered grids.
We computed the following parameters at the centres of the
additional mesh cells: turbulent shear stress and, depending on
the turbulence model used, turbulence kinetic energy, turbu-
lent viscosity, and turbulent kinetic energy dissipation rate. We
verified the developed numerical method by solving the prob-
lem of flow around a circular airfoil when the flow has a high
Reynolds number (  2 7 10 10 ). The obtained results are in
good agreement with published experimental data and nume-
rical results of other researchers. Our modification of the
LS-STAG immersed boundary method made it possible to
model the so-called "drag crisis" phenomenon for a circular
airfoil when  5 6 Re =10 10
Immersed boundary method,
LS-STAG method, turbulence
models, Reynolds-averaged
Navier — Stokes equations,
large eddy simulation, deta-
ched eddy simulation, airfoil
Received 23.01.2017
© BMSTU, 2017
The research is supported by Russian Ministry of Education and Science (proj. 9.2422.2017/PP),
Russian Federation President grant for young Russian PhD scientists (proj. MK-7431.2016.8),
Russian Foundation for Basic Research (proj. 17-08-01468a)
Introduction. In number of engineering applications, for example in flow simulation
around wind turbine rotors, heat exchanger pipes, overhead and underwater cables
and pipes, building structures, marine infrastructure elements, etc., it is necessary to
solve coupled hydroelastic problems. Such problems are enough difficult for the
numerical solution and require high-precision numerical methods usage. There is a
special class of numerical methods — the immersed boundary methods — in which
the mesh is not connected to the body boundary and is not modified during the entire
computation, despite the immersed body movement [1]. These methods involve the
rectangular meshes usage. Cells of irregular shape, called the ''cut-cells'', are formed at
the intersection of a rectangular mesh with the immersed boundary. One of the most
effective methods in this class is the LS-STAG method [2]. This method has not been
implemented in both commercial and free software packages.