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A compressible, flat-plate, laminar boundary layer solver in Julia! This routine computes the velocity and temperature profiles with variable viscosity and thermal conductivity. The numerical results are validated against wind-tunnel measurements.

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milo-thatch/compressible-laminar-boundary-layer

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

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


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.

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A compressible, flat-plate, laminar boundary layer solver in Julia! This routine computes the velocity and temperature profiles with variable viscosity and thermal conductivity. The numerical results are validated against wind-tunnel measurements.

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