Heat Flux - Stagnation Point
This module contains functions to estimate the heat flux of the gas at the stagnation point or at a stagnation line.
- pygasflow.atd.avf.heat_flux_sp.wall_temperature(eps, R, uinf, u_grad, Reinf_R, pe_pinf, Ts_Tinf, Tr, Pr, kinf, laminar=True, omega=0.65, sphere=True, phi=0)[source]
Compute the wall temperature at a stagnation point or stagnation line for a sphere, a cylinder or a swept-cylinder. The wall temperature (radiation adiabatic temperature) is computed with the assumption that the vehicle surface is radiation cooled and the heat flux into the wall, q_w, is small.
Notes
The general heat balance is: q_w = q_rad - q_gw where q_w is the heat flux into the wall, q_gw is the heat flux in the gas at the wall, q_rad is the heat flux radiated away.
Quoting from the book:
In the assumption that q_w is small, then q_gw = q_rad: the heat flux coming to the surface is radiated away from it. Hence, the “radiation-adiabatic temperature” Tra will result: no heat is exchanged between gas and material, but the surface radiates heat away.
With steady flow conditions and a steady heat flux q_w into the wall, Tra also is a conservative estimate of the surface temperature. Depending on the employed structure and materials concept (either a cold primary structure with a thermal protection system (TPS), or a hot primary structure), and on the flight trajectory segment, the actual wall temperature during flight may be somewhat lower, but will be in any case near to the radiation-adiabatic temperature.
Tw < Tra < Tr < Tt
References
Basic of Aerothermodynamics, Ernst H. Hirschel
- pygasflow.atd.avf.heat_flux_sp.heat_flux(R, uinf, u_grad, Reinf_R, pe_pinf, Ts_Tinf, Tw, Tr, Pr, kinf, sphere=True, phi=0, laminar=True, omega=0.65)[source]
Compute the heat flux of the gas at the wall at a stagnation point or at a stagnation line for a sphere/sweep cylinder in a laminar/turbulent flow.
- Parameters
- Rfloat or array_like
Radius of the sphere or cylinder.
- uinffloar or array_like
Free stream velocity.
- u_gradfloat or array_like
Velocity gradient at the stagnation line.
- Reinf_Rfloat or array_like
Free stream Reynolds number computed at R.
- pe_pinffloat or array_like
Pressure ratio between the pressure at the edge of the boundary layer and the free stream pressure.
- Ts_Tinffloat or array_like
Temperature ratio between the reference temperature and the the free stream temperature.
- Twfloat or array_like
Wall temperature.
- Trfloat or array_like
Recovery temperature.
- Prfloat or array_like
Prandtl number.
- kinffloat
Free stream thermal conductivity of the gas.
- spherebool, optional
If True, compute the results for a sphere. Otherwise, compute the result for a sweep cylinder.
- phifloat or array_like, optional.
Cylinder’s sweep angle [radians]. Default to 0 deg: cylinder surface is normal to the free stream.
- laminarbool, optional
Default to True, which computes the results for the laminar case. Set
laminar=Falseto compute turbulent results.- omegafloat, optional
Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set
omega=1otherwise.
- Returns
- outfloat or array_like
- pygasflow.atd.avf.heat_flux_sp.heat_flux_fay_riddell(u_grad, Pr_w, rho_w, mu_w, rho_e, mu_e, he, hw, Le=None, hD=None, sphere=True, m=0.52)[source]
Compute the heat flux of the gas at the wall at a stagnation point or at a stagnation line for a sphere/cylinder in a laminar flow, according to Fay and Riddell.
- Parameters
- u_gradfloat or array_like
Velocity gradient at the stagnation line.
- Pr_wfloat or array_like
Prandtl number.
- rho_wfloat or array_like
Density at the wall.
- mu_wfloat or array_like
Viscosity at the wall.
- rho_efloat or array_like
Density at the edge of the boundary layer.
- mu_efloat or array_like
Viscosity at the edge of the boundary layer.
- Lefloat or array_like
Lewis number. Default to None, indicating perfect gas (which is equivalent to set
Le=1).- hDfloat or array_like
Average atomic dissociation energy multiplied by the atom mass fraction at the edge of the boundary layer.
- hefloat or array_like
Boundary-layer edge enthalpy.
- hwfloat or array_like
Wall enthalpy.
- spherebool, optional
If True, compute the results for a sphere. Otherwise, compute the result for a 2D cylinder.
- mfloat, optional
Default to 0.52 (for equilibrium case). Set
m=0.63for the frozen case.
- Returns
- outfloat or array_like
References
Basic of Aerothermodynamics, Ernst H. Hirschel
Theory of Stagnation Point Heat Transfer in Dissociated Gas, J. A. Fay and F. R. Riddell
- pygasflow.atd.avf.heat_flux_sp.heat_flux_scott(R, u_inf, rho_inf)[source]
Compute the heat flux of the gas at the wall at a stagnation point of a sphere, according to Scott. The heat flux is in [W / cm^2]
- Parameters
- Rfloat or array_like
Radius of the sphere [m].
- u_inffloat or array_like
Free stream velocity [m / s].
- rho_inffloat or array_like
Free stream density [kg / m^3].
- Returns
- outfloat or array_like
References
Hypersonic Aerothermodynamics, John J. Bertin
An AOTV Aeroheating and Thermal Protection Study, Scott, C. D., Ried, R. C., Maraia, R. J., Li, C. P., and Derry, S. M.
- pygasflow.atd.avf.heat_flux_sp.heat_flux_detra(R, u_inf, rho_inf, u_co, rho_sl, metric=True)[source]
Compute the heat flux of the gas at the wall at a stagnation point of a sphere, according to Detra et al. The heat flux is in [W / cm^2] or [Bt / ft^2] depending on the value of
metric.- Parameters
- Rfloat or array_like
Radius of the sphere [m].
- u_inffloat or array_like
Free stream velocity [m / s].
- rho_inffloat or array_like
Free stream density [kg / m^3].
- u_cofloat or array_like
Circular orbit velocity [m / s].
- rho_slfloat or array_like
Density at sea level [kg / m^3].
- metricbool, optional
If True (default value) use metric system: Rn [m] and the heat flux will be [W / cm^2]. If False, use imperial system: Rn [ft] and the heat flux will be in [Btu / ft^2].
- Returns
- outfloat or array_like
References
Hypersonic Aerothermodynamics, John J. Bertin
Addendum to Heat Transfer to Satellite Vehicles Reentering the Atmosphere, Detra, R. W., Kemp, N. H., and Riddell, F. R