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Supersonic Wedge Flow at Mach=2.5

 

 

Figure 1. Computational domain

The grid size is 155x101x1. Mach number is Ma=1.5 and the flow is inviscid. For the spatial scheme, the MUSCL (Roe(MUSCL)) scheme and 2nd-order central difference scheme for the metrics are used. The Beam-Warming scheme (BW2) is used for time integration. The time step size 忖t is 5.0 ´ 10-3. Five sub-iterations are used for each time step. The problem runs for 30,000 time steps. The boundary conditions and initial conditions are listed in Table 1.

 

Boundary Conditions

I=1

1.      老=1

2.      u=1

3.      v=0

4.      w=0

5.      P=1/ 污M2

I=157

6.      Neumann for 老

7.      Neumann for u

8.      Neumann for v

9.      Neumann for w

10.  Neumann for P

J=1

11.  slip wall

J=71

12.  老=1

13.  u=1

14.  v=0

15.  w=0

16.  P=1/ 污M2

Initial Conditions

1.      老=1

2.      u=1.0

3.      v=0

4.      w=0

5.      P=1/ 污M2

 

Table 1. Boundary conditions and initial conditions for supersonic wedge flow.

 

 

Obtain the Files

 

Both of the mesh files and project input files can be accessed below. Remember to place the grid files in subfolder with respect to the set up file /wedge with respect to the set up file in order to conform to the FOLDER directive in the set up file.

Setup file (wedge.afl)

Grid file (wedge.plot3d).

 

Start the Simulation

 

Change the directory to the subfolder with the set up file. Start the simulation by

 

mpirun 每np 1 mpiaeroflo.exe < wedge.afl

 

Simulation Results

 

 

The Mach number contours are shown in Fig. 2. The surface Mach number distribution is compared with theoretical distribution curve in Fig. 3. Table 2 summarizes both of the theoretical and simulation results.

 

Figure 2. Mach number contours

 

Figure 3. Surface Mach number profile (compared with theoretical results)

 

 

 

 

 

Property

Theory

AEROFLO

Error (%)

Mach number behind the oblique shock

1.873526

1.882939

0.502

Pressure ratio (P2/P1)

2.467500

2.468054

0.022

Density ratio (老2/老1)

1.866549

1.868800

0.225

Temperature ratio (T2/T1)

1.321958

1.320662

-0.098

 

Table 2. Comparison between the AEROFLO results and theory results for supersonic wedge flow at Mach=2.5