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Research Papers: Techniques and Procedures

An Automatic Wall Treatment for Spalart–Allmaras Turbulence Model

[+] Author and Article Information
Ashwani Assam

Department of Mechanical and Aerospace
Engineering,
Indian Institute of Technology,
Hyderabad 502285, Telangana State, India
e-mail: me12m14p000004@iith.ac.in

Nikhil Narayan Kalkote

Department of Mechanical and Aerospace
Engineering,
Indian Institute of Technology,
Hyderabad 502285, Telangana State, India
e-mail: me14resch11002@iith.ac.in

Vatsalya Sharma

Department of Mechanical and Aerospace
Engineering,
Indian Institute of Technology,
Hyderabad 502285, Telangana State, India
e-mail: me12m14p000005@iith.ac.in

Vinayak Eswaran

Professor
Department of Mechanical and
Aerospace Engineering,
Indian Institute of Technology,
Hyderabad 502285, Telangana State, India
e-mail: eswar@iith.ac.in

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 19, 2017; final manuscript received December 13, 2017; published online February 23, 2018. Assoc. Editor: Daniel Livescu.

J. Fluids Eng 140(6), 061403 (Feb 23, 2018) (10 pages) Paper No: FE-17-1514; doi: 10.1115/1.4039087 History: Received August 19, 2017; Revised December 13, 2017

The Spalart–Allmaras (SA) is one of the most popular turbulence models in the aerospace computational fluid dynamics (CFD) community. In its original (low-Reynolds number) formulation, it requires a very tight grid spacing near the wall to resolve the high flow gradients. However, the use of wall functions with an automatic feature of switching from the wall function to the low-Reynolds number approach is an effective solution to this problem. In this work, we extend Menter's automatic wall treatment (AWT), devised for the k–ω-shear stress transport (SST), to the SA model in our in-house developed three-dimensional unstructured grid density-based CFD solver. It is shown, for both momentum and energy equations, that the formulation gives excellent predictions with low sensitivity to the grid spacing near the wall and allows the first grid point to be placed at y+ as high as 150 without loss of accuracy, even for the curved walls. In practical terms, this means a near-wall grid 10–30 times as coarse as that required in the original model would be sufficient for the computations.

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Figures

Grahic Jump Location
Fig. 1

Turbulence boundary layer u-velocity profile. The velocity profile modified from [28] is also shown.

Grahic Jump Location
Fig. 2

Case 1: flow domain and conditions for turbulent flow over a flat plate

Grahic Jump Location
Fig. 8

Case 3: flow domain for turbulent flow over a bump in a channel

Grahic Jump Location
Fig. 11

Case 3: contours of eddy viscosity (normalized by free-stream laminar viscosity =1.846×10−5) for the three different mesh configuration compared with the fine grid results obtained using CFL3D

Grahic Jump Location
Fig. 9

Case 3: the y+ variation of the first grid point for the three different meshes considered

Grahic Jump Location
Fig. 10

Case 3: surface pressure coefficient for three mesh configurations and Ref. [37]

Grahic Jump Location
Fig. 3

Case 1: the y+ variation of the first grid point for the four different meshes considered

Grahic Jump Location
Fig. 4

Case 1: turbulent flat plate with an inlet Ma=0.2 with the four mesh configurations: (a) The u-velocity profile at x = 0.97008 and 1.90334 versus y and (b) surface skin friction coefficient

Grahic Jump Location
Fig. 5

Case 2: flow conditions for forced convection over a flat plate

Grahic Jump Location
Fig. 6

Case 2: y+ variation of the first grid point for the four different meshes considered

Grahic Jump Location
Fig. 7

Case 2: forced convection over a flat plate with four different mesh configurations: (a) The u-velocity profile at the outlet and (b) plot of Reynolds number versus Nusselt number along the wall

Grahic Jump Location
Fig. 12

Case 3: flow over bump in a channel with inlet Ma=0.2, with the three mesh configurations and Ref. [37]: (a) the u-velocity profile at x =0.75 and 1.20148 and (b) surface skin friction coefficient

Grahic Jump Location
Fig. 13

Case 4: flow domain for turbulent flow over the NACA 0012 airfoil with a zoomed view of the nose of the airfoil

Grahic Jump Location
Fig. 15

Case 4: flow over the NACA 0012 airfoil with Ma=0.15 with the three mesh configurations and reference: (a) surface pressure coefficient and (b) surface skin friction coefficient for the upper surface

Grahic Jump Location
Fig. 14

Case 4: the y+ variation of the first grid point for the three different meshes considered: (a) the y+ plot along the lower surface of the airfoil with a zoom view to show its variation in the first half of the airfoil and (b) the y+ plot along the upper surface of the airfoil

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