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.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 convective 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=0.63 for the frozen case.

Returns:

q_dotfloat 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

Examples

Compute the convective heat flux using these parameters (coming from Exercise 5.2, “Hypersonic Aerothermodynamics”, John J. Bertin):

>>> import pint
>>> import pygasflow
>>> from pygasflow.atd.avf.heat_flux_sp import heat_flux_fay_riddell
>>> from pygasflow.utils.common import canonicalize_pint_dimensions
>>> ureg = pint.UnitRegistry()
>>> ureg.formatter.default_format = "~"
>>> ureg.define("pound_mass = 0.45359237 kg = lbm")
>>> pygasflow.defaults.pint_ureg = ureg
>>> lbf, lbm, Btu, ft, s = ureg.lbf, ureg.lbm, ureg.Btu, ureg.ft, ureg.s
>>> Pr = 0.7368421052631579
>>> u_grad = 12871.540335275073 * 1 / s
>>> rho_w = 1.2611943627968788e-05 * lbf * s ** 2 / ft ** 4
>>> rho_e = 6.525428485981234e-07 * lbf * s ** 2 / ft ** 4
>>> mu_w = 1.0512765233552152e-06 * lbf * s / ft ** 2
>>> mu_e = 4.9686546490717815e-06 * lbf * s / ft ** 2
>>> h_t2 = 11586.824574050748 * Btu / lbm
>>> h_w = 599.5031167908519 * Btu / lbm
>>> q = heat_flux_fay_riddell(u_grad, Pr, rho_w, mu_w, rho_e, mu_e, h_t2, h_w, sphere=True)
>>> q = canonicalize_pint_dimensions(q)
>>> q
<Quantity(2.36807802, 'force_pound * second * british_thermal_unit / foot ** 3 / pound_mass')>

pygasflow.atd.avf.heat_flux_sp.heat_flux_scott(R, u_inf, rho_inf)[source]

Compute the convective 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:

q_dotfloat 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.

Examples

>>> import pint
>>> import pygasflow
>>> from pygasflow.atd.avf.heat_flux_sp import heat_flux_scott
>>> ureg = pint.UnitRegistry()
>>> ureg.formatter.default_format = "~"
>>> pygasflow.defaults.pint_ureg = ureg
>>> m, s, kg = ureg.m, ureg.s, ureg.kg
>>> R = 0.3 * m
>>> u_inf = 4000 * m / s
>>> rho_inf = 0.0019662686791414754 * kg / m**3
>>> q_dot = heat_flux_scott(R, u_inf, rho_inf)
>>> q_dot
<Quantity(90.5721895, 'watt / centimeter ** 2')>

pygasflow.atd.avf.heat_flux_sp.heat_flux_detra(R, u_inf, rho_inf, u_co, rho_sl, metric=True)[source]

Compute the convective 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 [Btu / ft^2 / s] depending on the value of metric.

Parameters:

Rfloat or array_like: Radius of the sphere, in meters if metric=True, otherwise in foot.
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: R [m] and the heat flux will be [W / cm^2]. If False, use imperial system: R [ft] and the heat flux will be in [Btu / ft^2 / s].

Returns:

q_dotfloat 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

Examples

>>> import pint
>>> import pygasflow
>>> from pygasflow.atd.avf.heat_flux_sp import heat_flux_detra
>>> ureg = pint.UnitRegistry()
>>> ureg.formatter.default_format = "~"
>>> pygasflow.defaults.pint_ureg = ureg
>>> m, s, kg = ureg.m, ureg.s, ureg.kg
>>> R = 0.3 * m
>>> u_inf = 4000 * m / s
>>> u_co = 7950 * m / s
>>> rho_inf = 0.0019662686791414754 * kg / m**3
>>> rho_sl = 1.225000018124288 * kg / m**3
>>> q_dot = heat_flux_detra(R, u_inf, rho_inf, u_co, rho_sl)
>>> q_dot
<Quantity(92.7451074, 'watt / centimeter ** 2')>

pygasflow.atd.avf.heat_flux_sp.wall_temperature(eps, R, u_inf, u_grad, Reinf_R, pe_pinf, Ts_Tinf, Tr, Pr, k_inf, omega=0.65, laminar=True, phi=0, sphere=True)[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.

Parameters:

epsfloat: Emissivity (0 <= eps <= 1).
Rfloat or array_like: Radius of the sphere or cylinder.
u_inffloar 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.
k_inffloat: Free stream thermal conductivity of the gas.
phifloat or array_like, optional.: Cylinder’s sweep angle [radians]. Default to 0 deg: cylinder surface is normal to the free stream.
omegafloat, optional: Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set omega=1 otherwise.
laminarbool, optional: Default to True, which computes the results for the laminar case. Set laminar=False to compute turbulent results.
spherebool, optional: If True, compute the results for a sphere. Otherwise, compute the result for a sweep cylinder.