RCAIDE.Library.Methods.Aerodynamics.Common.Drag.compressible_turbulent_flat_plate

compressible_turbulent_flat_plate#

compressible_turbulent_flat_plate(Re, Ma, Tc)[source]#

Computes the compressible skin friction coefficient for a fully turbulent flat plate.

Parameters:

  • Re (float) – Reynolds number based on chord length [unitless]

  • Ma (float) – Freestream Mach number [unitless]

  • Tc (float) – Freestream static temperature [K]

Returns:

  • cf_comp (float) – Compressible skin friction coefficient [unitless]

  • k_comp (float) – Compressibility correction factor [unitless]

  • k_reyn (float) – Reynolds number correction factor [unitless]

Notes

This function calculates the skin friction coefficient for a flat plate with fully turbulent boundary layer, accounting for compressibility effects through temperature corrections.

Major Assumptions

  • Reynolds number between 10^5 and 10^9

  • Fully turbulent boundary layer from leading edge

  • Smooth surface conditions

  • Adiabatic wall conditions

  • Perfect gas behavior

Theory

The incompressible turbulent skin friction coefficient follows Schlichting’s correlation:

\(C_{f,inc} = \frac{0.455}{(\log_{10}(Re))^{2.58}}\)

The compressibility correction accounts for temperature effects:

\(T_w = T_c(1 + 0.178 M^2)\)

\(T_d = T_c(1 + 0.035 M^2 + 0.45(\frac{T_w}{T_c} - 1))\)

\(k_{comp} = \frac{T_c}{T_d}\)

where: - \(T_w\) is the adiabatic wall temperature [K] - \(T_d\) is the reference temperature for viscosity [K] - \(T_c\) is the freestream static temperature [K] - \(M\) is the freestream Mach number

The Reynolds number correction accounts for temperature-dependent viscosity:

\(Re_d = Re(\frac{T_d}{T_c})^{1.5}(\frac{T_d + 216}{T_c + 216})\)

\(k_{reyn} = (\frac{Re}{Re_d})^{0.2}\)

The final compressible skin friction coefficient is:

\(C_{f,comp} = C_{f,inc} \cdot k_{comp} \cdot k_{reyn}\)

Definitions

‘Turbulent Boundary Layer’

Boundary layer characterized by chaotic, irregular fluid motion and high mixing rates.

‘Skin Friction Coefficient’

Dimensionless measure of the shear stress at the wall normalized by dynamic pressure.

‘Compressibility Correction’

Factor accounting for the effects of compressibility on boundary layer temperature and viscosity.

References

[1] Stanford AA241 Course Notes. adg.stanford.edu

See also

RCAIDE.Library.Methods.Aerodynamics.Common.Drag.compressible_mixed_flat_plate