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2D Shock Wave/Laminar Boundary-Layer Interaction

 

 

Problem Description

 

The problem simulates the complex separated flow field generated by the impingement of an oblique shock on a laminar boundary layer developed along a flat plate. The flow conditions are freestream Mach number of 2.0, shock flow deflection angle 6º, and Reynolds number ReL (based on the distance from the plate leading edge to the inviscid shock impingement location) equal to 3.0 ´ 105.

 

Mesh

 

The size of the 2D computational domain is 286 ´ 131. The mesh grid is shown in Figure 1.

 

Figure 1. Computational Mesh

Simulation Parameters

 

The simulation parameters are summarized in Table 1.

 

Overall Flow Conditions

Mach No.

2.0

Reynolds No.

300000.0

Viscosity

laminar

Spatial Scheme

MUSCL

WENO 33

WENO 34

Time Scheme

BW2 

2 subiteration per time step. 

 from a restart file   

Final

Boundary Conditions

I=1: Inlet

Specified with the grid

I=286: Outlet

Outflow boundary condition:

(Neumann for ¦Ñ, u, v, w, P)

J=1: Wall

Wall boundary condition

 (Specified wall temperature)

J=131

Freestream boundary condition:

(Neumann for ¦Ñ, u, v, w, P)

 

Table 1. Simulation Parameters

 

Obtain the Files

 

Both mesh files and project input files can be accessed below. Remember to place the grid files in a subfolder with the set up file /shockbl.

Setup file (miguelplate.afl)

Grid file (myres.cgns).

 

Start the Simulation

 

Change the directory to the subfolder with the selected grid and spatial scheme. Start the simulation by

 

mpirun ¨Cnp 1 mpiaeroflo.exe < shockbl.afl

Simulation Results

 

Figures 2, 3 and 4 show the pressure contours of flow field for MUSCL, WENO 33 and WENO 34 procedures, respectively.

 

Figure 2. Pressure contours in shock/boundary layer interaction region (MUSCL)

 

Figure 3. Pressure contours in shock/boundary layer interaction region (WENO 33)

 

Figure 4. Pressure contours in shock/boundary layer interaction region (WENO 34)

 

Comparison of Different Spatial Schemes 

 

Figure 5 shows the surface pressure profiles for MUSCL and WENO procedures. The simulation results are also compared with Visbal and Gaitonde¡¯s 3rd-order Roe scheme simulation using the same size mesh grid and a fine (476 ´ 265) mesh grid, respectively. WENO 34 scheme provide better results compared with MUSCL results.

 

 

CFL Test

 

The CFL performances for different spatial schemes are also tested for this problem. The test results are summarized in Table 2.

Figure 5. Surface pressure for Mach 2 shock/laminar boundary-layer interaction

 

 

 

Spatial Scheme

Time Scheme

Turbulence Model

Grid Size

¦¤s=min(¦¤xi)

Test Value  CFL= ¦¤t/ ¦¤s, CFLa=(1+1/M)CFL

Converge (¡Ì) or Diverge(x)

 

 

 

 

¡Ì

¡Ì

x

Shockwave/Laminar Boundary Layer Interaction

 

Ma=2.0

MUSCL

BW2

laminar

7.5E-5

1.0E-3

CFL=13.33

CFLa=20

2.0E-2

CFL=266.67

CFLa=400

3.0E-2

CFL=400

CFLa=600

N=5841

WENO 33

BW2

laminar

1.0E-3

CFL=

CFLa=

8.0E-2

CFL=1066.7

CFLa=1600

9.0E-2

CFL=1200

CFLa=1800

N=95

WENO 34

BW2

laminar

1.0E-3

CFL=

CFLa=

1.0E-2

CFL=133.33

CFLa=200

1.1E-2

CFL=146.67

CFLa=220

N=2081

* The test is from the initial calculation.

**  The CFL condition is computed by CFL= ¦¤t/ ¦¤s, which assume the reference flow velocity u=1.0.

***  ¦¤s=min(¦¤xi) is the minimum computational grid spacing

**** CFLa=(u+a) ¦¤t/ ¦¤s=u(1+1/M)CFL is a measure of how far a sound wave can travel through the flow.

 

Table 2. CFL Number Test for Different Schemes

 

 

 

 

Reference:

 

  1. Visbal, M. R. and Gaitonde, D. V., ¡°Shock Capturing Using Compact-Differencing-Based Methods,¡± AIAA Paper 2005-1265.
  2. M. Visbal ¨C private communication.