Near-wall modification of Spalart-Allmaras Turbulence Model for Immersed Boundary Method

Abstract

An improved immersed boundary method for turbulent flow simulation on a Cartesian grid is proposed. To determine proper boundary conditions, the near-wall approximation of the mean-flow equation and the Spalart-Allmaras turbulence model are discussed. Then, a manufactured near-wall velocity profile is derived, which is linear with respect to the distance from the wall and which can be resolved by a numerical scheme with second-order spatial accuracy. Corresponding to the modification for the velocity, the eddy-viscosity profile is also altered to maintain the balance of the shear stress. To obtain the manufactured profile as a numerical solution, the immersed boundary method and the damping function in the Spalart-Allmaras turbulence model is modified. Verification cases based on the NASA turbulence modeling resource are conducted. The results with the modified immersed boundary method show close agreement with the reference results with body-fitted grids. Finally, a transonic flow around the NASA common-research model is simulated to show the capability of the modified immersed boundary method for three-dimensional problems.

An immersed boundary method with y+‐adaptive wall function for smooth wall shear

“…The total length of the plate is L = 2 m. As shown in Figure 6, grid cells were refined near the flat plate. The minimal grid size was 3.13 × 10 −3 L and 1.56 × 10 −3 L for aligned and inclined cases, respectively, which are comparable to the values used in Tamaki et al 18 …”

“…For typical engineering applications, the simulation domain is usually large and wall functions have to be used to reduce computational cost. However, the literature on turbulence wall functions for IB method is very limited 8,9,16‐19 . Our literature survey found that most of previous research efforts are not particularly aimed at better prediction of wall shear stress distribution, which is important if other processes depend on its value, gradient, divergence, or any other forms of differential operations.…”

A New Explicit Algebraic Wall Model for LES of Turbulent Flows Under Adverse Pressure Gradient

“…This is due to pressure oscillations observed close to the solid surface when using Cartesian grids as explained in Wilhelm et al (2018). This problem is linked to the use of non-body-fitted grids not only in LBM but also in the Navier-Stokes framework when immersed boundary methods (Capizzano 2011;Tamaki et al 2017) or cut-cell methods (Berger and Aftosmis 2012) are used. Farfield density and velocity are used for the non-dimensionalization in the C p calculation.…”

“…C p profiles obtained with both grids are very close and close to the Xfoil and elsA references independently of the wall model used. A modification of the wall model application has been proposed by Capizzano (2011) and taken up by Tamaki et al (2017) which smooth out pressure wiggles. However, as shown in Wilhelm et al (2018), this introduces artificial roughness to the NACA profile and deteriorates the drag coefficient prediction.…”