VVF21 - Incompressible turbulent flow over a flat plate with zero pressure gradient

Description

This validation case investigates the incompressible turbulent flow over a flat plate with a zero pressure gradient for two types of turbulence models: Shear Stress Transport (SST) and Spalart-Allmaras. The drag and surface skin friction coefficients results that ther solver computes are compared with the NASA CFD results [45].

Geometry

The geometry consists of a rectangle of 2333 mm in length, 1000 mm in height, and 1000 mm in width. The same geometry is used for both the SST and Spalart-Allmaras turbulence models.

The following figure shows a simple plate layout [46]. The plate extends from x=0 to x=2.

Simulation Model

This model uses the Advanced Flow solution type.

The mesh used in this validation case is a series of five 3D grids, of the same family, ranging from the finest to coarsest grid. This grid is created in the PLOT3D format defined by the NASA Langley Research Center [46]. After the grid is imported, the model includes only a single layer of 3D hexahedral elements. To obtain results that are similar to 2D results, the imported mesh is split into two element layers along Y direction, as shown in the following figure.

The element length along the Y direction for each layer is 500 mm.

The following table represents the mesh characteristics. The X, Y, and Z columns list the number of elements in each direction.

The fluid is modeled using incompressible air with the following properties:

• Mass density: ρ = 1.33 kg/m³
• Gas constant: R = 286.90 J/kg · K
• Dynamic viscosity: µ = 1.85 × 10⁻⁵ kg/m · s, based on Sutherland's law at T_ref = 300 K
• Speed of sound: a_ref = (γ·R·Tref)^0.5 = 347.19 m/s
• Specific heat ratio of air: γ = 1.4
• Kinematic viscosity: ν = L (a_ref M)/ Re = 1.39 × 10⁻⁵ m²/s
• Mach number: M = 0.2
• Reynolds number: Re = 5 × 10⁶

The gas constant is kept blank to simulate a truly incompressible flow.

The following boundary conditions are applied:

• Flow Boundary Condition: Inlet Flow on the front of the prism with a velocity of U_ref = 69.44 m/s (129.6 ft/s) with specified external conditions.

• Flow Boundary Condition: Static Pressure on the top of the prism with specified external conditions.

• Flow Boundary Condition: Static Pressure on the opposite side to the inlet with external conditions set to ambient.
• Flow Surface: Boundary Flow Surface on the bottom from x= – 0.35 to x=0 using a Slip Wall condition.
• Flow Surface: Boundary Flow Surface on the bottom from x=0 to x=2 using No Slip Wall condition.
• Symmetry Plane on the +Y-dir and -Y -dir walls.
• Modeling Objects: Turbulence Characteristics with K-Omega, a turbulent kinetic energy (1.125·U_ref)²/Re = 1084.86 mm²/s², a specific dissipation rate (125·U_ref)²/Re = 8679.71773734607 sec⁻¹

For every boundary condition with the external conditions, use the Turbulence Characteristics modeling object.

Theory

The NASA CFD results are provided from two compressible codes: cell-centered structured-grid (CFL3D) and node-centered unstructured-grid (FUN3D) codes, that compute the zero-pressure-gradient flat plate flow with the Menter shear stress transport model. Both codes use Roe's Flux Difference Splitting and a UMUSCL upwind approach. In the CFL3D code, the standard UMUSCL (kappa=0.33333) scheme is used, and in the FUN3D code the option UMUSCL= 0.5 is used. Both codes are run with full Navier-Stokes and both codes use first-order upwinding for the advective terms of the turbulence model. Multiple grids are used to identify trends with grid refinement [45], [46], [47].

Results

The following figures compare the flow solver results with the NASA CFD results for the wall skin friction at x = 0.97008 and the drag coefficient with a grid size for both SST and Spalart- Allmaras turbulence models.

The following figures compare the flow solver results with the NASA CFD results for the surface skin friction coefficient on the finest 545x385 grid, over the entire plate for SST and Spalart-Allmaras turbulence models.