Oblique shock

Problem definition

• Domain:
  
• Rectangular channel of length L = 4.17 m and height h = 1 m 
• Material:
  
• Polytropic Ideal Gas (PIG)
• Specific heat ratio gamma = 1.4
• Gas thermodynamic constant R = 287.05 J/kgK
• Initial conditions: 
• Thermodynamic pressure Poo = 101325 Pa
  
• Temperature Too = 288.15 K
• Mach number Moo = 2.9
• Boundary conditions:
• SupersonicInlet boundary conditions on the inlet section (front and top walls)
• ExtrapolatedOutlet boundary conditions on the outlet section
• Slip boundary conditions on the bottom wall
  

Space and time discretization

• Space discretization:
• Progressively refined meshes created with blockMesh
• # of rectangular cells Nv = 400 - 1600 - 6400 - 25600
  
• # of nodes Nn = 451 - 1701 - 6601 - 26001
  
• Time discretization:
• Total simulation time endTime = 0.01 s
• Timestep deltaT = 4e-5 - 2e-5 - 1e-5 - 5e-6 s
  
• Maximum Courant number maxCo =  1.95

Figure: Computational grid.

Numerical results

• Comparison with exact solution and with OpenFOAM built-in inviscid compressible solvers rhoSonicFoam, rhopSonicFoam and sonicFoam
  
• Single iteration CPUtime = 8.16e-3 - 2.07 e-2 - 6.11e-2 - 2.22e-2 s on AMD64 3500+ desktop PC with AMD Athlon 64 2.2 GHz CPU, 1 Gbyte RAM, 512 Kbyte L2 cache

Figure: Thermodynamic pressure P contours at t = 0.02.



Table: Comparison of the accuracy and efficiency performances of the evaluated solvers.



Figure: Thermodynamic pressure P contours as a function of time t = 0 - 0.02.

Download

• ObliqueShock.tar.gz test problem folder. Uncompress this archive in the OpenFOAM work folder and execute AeroFoam . ObliqueShock_AeroFoam from terminal to start the simulation. Download.