Temperatures

pygasflow.atd.temperatures.recovery_factor(Pr, laminar=True)[source]

Compute the recovery factor.

Parameters

Prfloat or array_like: Prandtl number
laminarbool, optional: If True, compute the recovery factor for a laminar flow. Otherwise, compute it for a turbulent flow.

Returns

outfloat or array_like

See also

recovery_factor

Notes

Quotes from Section 3.1:

Consider a wall with finite thickness and finite heat capacity, which is completely insulated from the surroundings, except at the surface, where it is exposed to the (viscous) flow. Without radiation cooling, the wall material will be heated up by the flow, depending on the heat amount penetrating the surface and the heat capacity of the material. The surface temperature will always be that of the gas at the wall: Tw = Tgw, apart from a possible temperature jump, which can be present in the slip-flow regime. If enough heat has entered the wall material (function of time), the temperature in the entire wall and at the surface will reach an upper limit, the recovery temperature Tw = Tr (the heat flux goes to zero). The surface is then called an adiabatic surface: no exchange of heat takes place between gas and wall material. With steady flow conditions the recovery (adiabatic) temperature Tr is somewhat smaller than the total temperature Tt, but always of the same order of magnitude.

The total enthalpy at hypersonic flight is proportional to the flight velocity squared. This holds also for the total temperature, if perfect gas behaviour can be assumed, which is permitted for v_inf < 1.0 km/s. The total temperature Tt then is only a function of the total enthalpy ht, which can be expressed as function of the flight Mach number Minf.

At flight velocities larger than approximately 1.0 km/s they lose their validity, since high-temperature real-gas effects appear. The temperature in thermal and chemical equilibrium becomes a function of two variables, for instance the enthalpy and the density. At velocities larger than approximately 5.0 km/s, non-equilibrium effects can play a role, complicating even more these relations.

References

Basic of Aerothermodynamics, Ernst H. Hirschel

pygasflow.atd.temperatures.reference_temperature(Te, Tw, Me=None, rs=None, Tr=None, gamma_e=1.4, mod=False)[source]

Compute the reference temperature for compressible boundary layers.

There are three modes of operations:

reference_temperature(Te, Tw, rs=rs, Me=Me, gamma_e=gamma_e)
reference_temperature(Te, Tw, Prs=Prs, Me=Me, gamma_e=gamma_e)
reference_temperature(Te, Tw, Tr=Tr)

Parameters

Tefloat or array_like: Temperature at the edge of the boundary layer.
Twfloat or array_like: Temperature of the gas at the wall.
MeNone or float or array_like, optional: Mach number at the edge of the boundary layer. If Me=None, then Tr must be provided.
rsNone or float or array_like, optional: Reference recovery factor. If rs=None, then Tr must be provided.
TrNone or float or array_like, optional: Recovery temperature. If Tr=None, then Me and rs/Prs must be provided.
gamma_efloat, optional: Specific heats ratio at the edge of the boundary layer. Default to 1.4. Must be > 1.
modbool, optional: Use a modified formula that gives more weight to the recovery temperature and less on the wall temperature. Useful for computations at stagnation points/lines. Default to False.

Returns

outfloat or array_like