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Turbulent Flat Plate: Study #2

Introduction

This case examines the boundary layer formation of a Mach 0.2 flow along a flat plate. Skin friction and y+ plots of the boundary layer were studied in this case. This case is analogous to that used for the structured grid flat plate validation.

Table 1. Freestream conditions. 
Mach Pressure (psia) Temperature (R) Angle-of-Attack (deg) Angle-of-Sideslip (deg)
0.2 14.7 530.0 0.0 0.0

Download tar File

Table 2. Tar File
Wind-US 3.150
fp0p2.tar

Grids

In Figure 1a, the same structured grid as that used for the structured grid validation is shown. The grid has 111 points in the axial direction and 81 points in the vertical direction. The grid was packed to the wall such that the first point corresponded to a y+ value of 1 or less. Note the y+ spacing study shown on the structured grid flat plate boundary layer test case page. For use with the unstructured solver, the individuals cells are hexahedrals. In the rest of the discussion on this webpage, "structured" grid refers to this hexahedral grid that indeed looks structured but is in fact saved in unstructured hexahedral cell format. In Figure 1b and 1c, a modified grid is used where the first 51 points away from the wall are retained as the original "structured" hexahedral cells, and then away from this region, the cells are triangular prisms. The entire grid is one cell wide in the z-direction.

The grids shown in Table 3 are all in unstructured format. The "structured" grid simply refers to the fact that the topology is exactly the same as that of the structured case. The "unstructured" grid combines hexahedral cells near the wall and triangular prisms away from the wall, as discussed above.


Figure 1a. Mach 0.2 Flat Plate ("structured") grid


Figure 1b. Mach 0.2 Flat Plate (unstructured) grid


Figure 1c. Mach 0.2 Flat Plate (unstructured) grid (zoom)

Table 3. Grid
  Common Grid ("Structured") Common Grid (Unstructured) Gridgen ("Structured") Gridgen (Unstructured)
File fp_uns_1.cgd fp_uns_2.cgd fp_uns_1.gg fp_uns_2.gg

Boundary Conditions

Boundary conditions for this flat plate case are as shown in Figure 2. Note that the first 14 points along the bottom are set to inviscid, such that the leading edge of the plate is at grid point 15 in the axial direction along the bottom of the grid. Although only the hexahedral or "structured" grid is shown in the figure, the boundary conditions are the same for the other grid, having triangular prisms away from the wall.


Figure 2. Boundary conditions.

Computation Strategy

Monitoring the residuals and key flow field quantities, for this case the wall skin friction coefficient, were the methods of determining convergence of this case. Below are the algorithm settings used in the dat file for these unstructured solver cases. Note that settings for the structured solver (i.e. choice of RHS method) were different, and may be found on the structured solver page for this flat plate case.

Table 4. Algorithm Settings.
Field Spalart-Allmaras Structured Grid with Unstructured Solver SST Structured Grid with Unstructured Solver Spalart-Allmaras Unstructured Grid with Unstructured Solver SST Unstructured Grid with Unstructured Solver
Version Wind-US 3.150 Wind-US 3.150 Wind-US 3.150 Wind-US 3.150
Cycles 5000 cycles 5000 cycles 5000 cycles 5000 cycles
Convergence Order 10 10 10 10
Method IMPLICIT UGAUSS LINE EXACT_LHS VISCOUS JACOBIAN FULL CONVERGE FREQUENCY 11 SUBITERATIONS 6 IMPLICIT UGAUSS LINE EXACT_LHS VISCOUS JACOBIAN FULL CONVERGE FREQUENCY 11 SUBITERATIONS 6 IMPLICIT UGAUSS LINE EXACT_LHS VISCOUS JACOBIAN FULL CONVERGE FREQUENCY 11 SUBITERATIONS 6 IMPLICIT UGAUSS LINE EXACT_LHS VISCOUS JACOBIAN FULL CONVERGE FREQUENCY 11 SUBITERATIONS 6
CFL AUTO DECREASE 2 CFLMAX 100000 AUTO DECREASE 2 CFLMAX 100000 AUTO DECREASE 2 CFLMAX 100000 AUTO DECREASE 2 CFLMAX 100000
Limiters DQ LIMITER ON RELAX 0.1 DQ LIMITER ON RELAX 0.1 DQ LIMITER ON RELAX 0.1 DQ LIMITER ON RELAX 0.1
Dissipation TVD BARTH 3.0 TVD BARTH 3.0 TVD BARTH 3.0 TVD BARTH 3.0
Boundaries IMPLICIT BOUNDARY ON IMPLICIT BOUNDARY ON IMPLICIT BOUNDARY ON IMPLICIT BOUNDARY ON
RHS HLLE SECOND HLLE SECOND HLLE SECOND HLLE SECOND
Gradients LEAST_SQUARES LEAST_SQUARES LEAST_SQUARES LEAST_SQUARES
Turbulence SPALART SST SPALART SST

Input Parameters and Files

Input files to prepare and run this case are as shown in Table 5. The first file, fp_cfpart.inp, is used with the cfpart utility to create solver lines, which enables most efficient use of the unstructured line solver. Next in the table, the two input files differ only in the selection of the Spalart-Allmaras or Menter SST turbulence model. Note that each input file maybe used with either the purely hexahedral grid or mixed hexahedral/triangular prism grid.
Table 5. Input files
cfpart - to create lines Spalart-Allmaras SST
fp_cfpart.inp sa.dat sst.dat

Computation

Post-processing

The post-processing files needed for this case are shown in Table 6.

Table 6. Post-processing.
Hexahedral "structured"
Post-processing FORTRAN code
Hexahedral / triangular
prism "unstructured"
Post-processing FORTRAN code
Velocity Skin Friction Coefficient Directions
POST.f POSTus.f vel.com cf.com README

Results

In the figures shown below, results obtained from the structured and unstructured solvers are presented. Note that only one unstructured solution is presented. This is because solutions obtained with the unstructured solver were identical whether the purely hexahedral "structured" grid or combined hexahedral/triangular prism "unstructured" grid was used.


Figure 3. Spalart-Allmaras skin friction coefficient


Figure 4. SST skin friction coefficient


Figure 6. Spalart-Allmaras velocity profile


Figure 7. SST velocity profile

Contact Information

This validation test case was performed by Nick Georgiadis, Keven Lenahan, and Manan Vyas. Contact: Nick Georgiadis, (216) 433-3958 or Manan Vyas, (216) 433-6053, MS 5-12, NASA Glenn Research Center, 21000 Brook Park Road, Cleveland, Ohio, 44135.


Last Updated: Thursday, 06-Jan-2011 12:45:21 EST