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Prandtl-Meyer Expansion


Figure 1. Mach contours of the Mach 2.5 15 Degree Prandtl-Meyer expansion.

Introduction

This is a steady, inviscid expansion case commonly used for validation. This documentation analyzes centerline pressure values at the expansion fan as well as Mach contours.

Download tar File

Table 1. Tar File
Wind-US 3.146
pm15.tar

Grid


Figure 2. Expansion grid with unstructured (tetrahedral) cells.


Figure 3. Zoom of the expansion fan.


Figure 4. 3D view of the grid.

This grid utilizes dense grid point packing near the expansion fan. The angled shape of the expansion fan makes it favorable to use an unstructured grid. This grid has 7,648 grid points, the majority of are packed near the expansion fan.

Unstructured grids must be extruded into 3D blocks in order to run with Wind-US algorithm. Figure 4 shows a 3D view of this grid.

After the cgd file was exported from Gridgen, CFPART was used to add lines to the grid in preparation to be solved with Wind-US 3.150 code. In Table 1, both the Common and Gridgen versions of the grid are attached as well as the CFPART script.

Table 2. Grids & Pre-processing
  Pre-processing Common Grid Gridgen
File cfpart.inp pm15.cgd pm15.gg

Freestream Conditions

Table 3. Total flow conditions
  Pressure (psia) Temperature (R) Mach Number
Freestream 12.0 550 2.5

Boundary Conditions


Figure 5. Boundary conditions.

Computation Strategy

Monitoring the residuals was the main way of determining the convergence of this case. Below are the algorithm settings established in the dat file.

Table 4. Algorithm Settings.
Field Parameter
Version Wind-US 3.150
Cycles 6000
Convergence Order 8
Method IMPLICIT UGAUSS EXACT_LHS VISCOUS_JACOBIAN FULL SUBITERATIONS 6
CFL AUTO CFLSTART 100 CFLMIN 0.1 CFLMAX 1e26
Limiters DQ LIMITER ON
Dissipation TVD BARTH 3.0
Boundaries IMPLICIT BOUNDARY ON
RHS HLLE SECOND
Gradients LEAST_SQUARES
Turbulence INVISCID

Input Parameters and Files

Table 5. Input files.
Wind-US 3.150
pm15.dat

Post-processing

One post-processing script was used for this case to calculate centerline pressure values at the expansion can. A "results" folder must be created in the scripts' directory in order to create the output files. The cgd and cfl files can be loaded into Tecplot using the Common File Format Loader. Variables can then be measured using the "Probe" tool. "Analyze>Calculate" can be used to calculate more variables and "Data>Alter" can be used to rescale data.

Table 6. Post-processing.
Script
post_process

Results

Table 7. Percent Error
Computation Exact WIND % Error Wind-US 3.150 % Error
M2 3.2368 3.0487 -5.8125 3.2325 0.1333
P2/P1 0.3274 0.3273 -0.0397 0.3275 -0.0232
Pt2/Pt1 1.0000 0.7568 -24.3210 0.9938 0.6254
rho2/rho1 0.4505 0.4213 -6.4883 0.4497 0.1730
T2/T1 0.7269 0.7769 6.8744 0.7282 -0.1751
Tt2/Tt1 1.0000 0.9871 -1.2910 1.0000 0.0040


Figure 6. Mach contours zoom of the expansion fan


Figure 7. Centerline pressures at the expansion fan


Figure 8. Residual plot for determining convergence

Contact Information

This validation test case was performed by Keven Lenahan. Contact: 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