• I have started practicing and learning GASP version 4. First I went over a tutorial case which was the calculation of 2-D, turbulent, transonic flow in a duct. In this case, the geometry is very similar to the one (Sajben transonic diffuser) that we consider for our study. I made two runs: One with a coarse grid and the other with a fine grid. These runs gave me a general understanding of how the code works, I/O, grid sequencing etc.

• Different runs for the STD geometry were performed by using a single zone grid with the dimensions of (81 x 51 x2). The grid file was downloaded from the NPARC alliance validation archive.

Figure 1. Single zone grid used in the transonic diffuser computation

The diffuser is 0.5583 m in length with a throat height of 0.0439979 meters. The bottom plate of the grid is aligned in the x-axis, with the origin located at the diffuser throat. The height of the duct at the inlet is 1.4 throat heights, and the exit is 1.5 heights:

Figure 2. Geometry of the STD.

The top wall of the diffuser is defined by:

Boundary Conditions:

• For the inflow boundary, a constant total pressure (P0) and temperature were specified:

• On the upper and lower walls, the adiabatic no-slip boundary cond. was used.
• The outflow boundary was set to a constant static pressure Pb (back pressure):

In each case, the inflow conditions were used in the computational domain  to initialize the solution.

Physical Models Used In the Computation:

• Inviscid fluxes were calculated by using the upwind biased 3rd order accurate Roe flux scheme.
• The Min-Mod limiter was used.
• In the viscous fluxes, the thin-layer approximation was made for the calculation of the viscous terms. The viscous gradients at the solid wall were computed by using a second order, one-sided algorithm.
• For the weak shock case, Spalart-Allmaras turbulence model and Wilcox k-w model (1998 version) were used. For the strong shock case, results presented here were obtained by using the Spalart-Allmaras turbulence model.
• As for the global iteration, Gauss-Seidel time integration scheme was used. In each cycle, 10 Gauss Seidel inner iterations were performed with an inner tolerance of 0.01.
• A constant CFL number based on the freestream values were used. The value of CFL number was set to 10. (The use of a constant CFL number avoids oscillations in the shock position)

• Mach Contours:

Figure 3. Mach Contours for the weak shock case. Turbulence model: Spalart-Allmaras

Figure 4. Mach Contours for the strong shock case. Turbulence model: Spalart-Allmaras

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• Mean Wall Pressure Distributions:

• Velocity Profiles:

Figure 9. u velocity profiles at x/h_t=2.882 for the weak shock case
 
 
 
 

Figure 10. u velocity profiles at x/h_t=7.493 for the weak shock case

Figure 11. u velocity profiles at x/h_t=2.882 for the strong shock case
 

Figure 12. u velocity profiles at x/h_t=7.493 for the strong shock case

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• Convergence:

Figure 13. Convergence history of weak shock solution with Roe flux and k-w turbulence model.

• In the figure above, the pressure watch point was located at i=40, j=27. This point corresponds to x/h_t=0.9375 and y/h_t=0.9678 just after the shock.