compile and run

• The code computes the self-similar solution of a flat-plate, compressible boundary layer with variable shear viscosity $\mu(T)$ and thermal conductivity $k(T)$, constant Prandtl number Pr, constant Mach number Ma, and constant heat capacity ratio $\gamma$ (Stewartson, 1964). $$\left(\frac{\mu}{T}F^{\prime\prime}\right)^\prime + FF^{\prime\prime} = 0$$ $$FT^\prime +\left(\gamma-1\right)\mathrm{Ma}^2 \frac{\mu}{T}\left(F^{\prime\prime}\right)^2 + \mathrm{Pr}^{-1}\left(\frac{k}{T}T^\prime\right)^\prime = 0$$
• The code uses a standard block-elimination algorithm (Cebeci, 2002).
• To run the code, open BL_main.jl and press CTRL+F5.
• You can choose your physical parameters in BL_input.jl

  ## INPUT FILE
  
  # discretization
  eta_max     = 10.0          # maximum value of eta
  N_max       = 1000          # discretization
  tol         = 1e-12         # tolerance
  
  # physical parameters
  gamma       = 1.4           # heat capacity ratio
  Prandtl     = 0.72          # free-stream Prandtl number
  Mach        = 3.0           # free-stream Mach number
  TwTad_ratio = 1.1           # wall-to-adiabatic temperature ratio
  chi_mu      = 0.43          # non-dimensional sutherland constant (viscosity)
  chi_k       = 0.66          # non-dimensional sutherland constant (conductivity)
  

• All the variables are non-dimensional and normalized to the free-stream values. The parameter TwTad_ratio is the ratio of the non-dimensional wall temperature $T_w$ to the adiabatic recovery temperature $$T_{ad,w} = 1+\frac{\gamma-1}{2}\mathrm{Pr}^{1/2}\mathrm{Ma}^2$$
• chi_mu and chi_k denote the non-dimensional Sutherland constants $\chi_\mu$ and $\chi_k$ $$\mu = T^{3/2}\frac{1+\chi_\mu}{T+\chi_\mu} \mbox{ and } k = T^{3/2}\frac{1+\chi_k}{T+\chi_k}$$

Comparison of the output of this code (solid curves) with the experimental results of Graziosi and Brown, JFM 2002.

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Reads

Cebeci, T. (2002). Convective Heat Transfer. Heidelberg: Horizons Pub. ISBN: 9780966846140, LCCN: 2002068512.

Graziosi, P., & Brown, G. L. (2002). Experiments on stability and transition at Mach 3. J. Fluid Mech., 472, 83–124. DOI: 10.1017/S0022112002002094

Ricco, P., & Fossà, L. (2023). Receptivity of compressible boundary layers over porous surfaces. Phys. Rev. Fluids, 8(7), 073903. DOI: 10.1103/PhysRevFluids.8.073903

Stewartson, K. (1964). The Theory of Laminar Boundary Layers in Compressible Fluids. Oxford: Clarendon Press.