Laminar boundary layer

Problem definition

• Domain:
  
• Rectangular channel of length L = 1 m and height h = 0.06 m 
• Material:
  
• Polytropic Ideal Gas (PIG)
• Specific heat ratio gamma = 1.4
• Gas thermodynamic constant R = 287.05 J/kgK
• Sutherland's law to model dynamic viscosity - temperature law mu = mu(T)
  
• Constant Prandtl number Pr = 0.72
  
• Initial conditions: 
• Thermodynamic pressure Poo = 101325 Pa
  
• Temperature Too = 288.15 K
• Velocity Uoo = 100 m/s
  
• Boundary conditions:
• SupersonicInlet boundary conditions on the inlet section (front and top walls)
• ExtrapolatedOutlet boundary conditions on the outlet section
• AdiabaticViscousWall boundary conditions on the bottom wall

Figure: Problem definition.

Space and time discretization

• Space discretization:
• Boundary layer mesh created with blockMesh
• # of rectangular cells Nv = 2500
  
• # of nodes Nn = 2601
  
• Time discretization:
• Total simulation time endTime = 0.025 s
• Timestep deltaT = 5e-8 s
  
• Maximum Courant number maxCo =  1.5

Figure: Detail of the computational grid.

Numerical results

• Comparison with Blasius numerical solution of thin boundary layer equations
  
• Single iteration CPUtime = 0.03 s on AMD64 3500+ desktop PC with AMD Athlon 64 2.2 GHz CPU, 1 Gbyte RAM, 512 Kbyte L2 cache

Figure: Velocity profiles.

Download

• Blasius.tar.gz test problem folder. Uncompress this archive in the OpenFOAM work folder and execute AeroFoam . Blasius_3k_M030 from terminal to start the simulation. Download.