Wall Shear Stress - Stagnation Point

This module contains functions to estimate the wall shear stress along the attachment line of a swept cylinder for a compressible, laminar/turbulent flow.

pygasflow.atd.avf.wall_shear_stress_sp.velocity_gradient(R, pinf, ps, rhos, k=1.33, phi=0)[source]

Compute the gradient of the inviscid velocity along the stagnation point or a stagnation line.

Parameters:

Rfloat or array_like: Radius of the infinite-long swept cylinder.
pinffloat or array_like: Free stream pressure.
psfloat or array_like: Pressure at the stagnation point.
rhosfloat or array_like: Density at the stagnation point.
kfloat, optional: Proportionality factor. Default to k=1.33 for a cylinder. Set k=1 for a sphere.
phifloat or array_like, optional: Sweep angle in case of cylinder [radians]. phi=0 corresponds to a cylinder normal to the free stream.

Returns:

outfloat or array_like

References

Basic of Aerothermodynamics, Ernst H. Hirschel
“Hypersonic Aerothermodynamics”, John J. Bertin

Examples

Compute the velocity gradient at the stagnation point of a sphere of radius 1 feet, flying at 24000 ft/s at an altitude of 240000 ft. Assume the wall temperature is 2500°R.

>>> import pygasflow
>>> import pint
>>> from pygasflow import *
>>> from pygasflow.atd.avf.wall_shear_stress_sp import velocity_gradient
>>> ureg = pint.UnitRegistry()
>>> ureg.formatter.default_format = "~"
>>> ureg.define("pound_mass = 0.45359237 kg = lbm")
>>> pygasflow.defaults.pint_ureg = ureg
>>> R = ureg.Quantity(0.06856070504972671, "Btu / lbm / degR")
>>> r = 1 * ureg.ft
>>> u1 = 24e03 * ureg.ft / ureg.s
>>> Tw = 2500 * ureg.degR
>>> gamma = 1.4

From the atmospheric model at an altitude of 240000 ft:

>>> T1 = 381.61885288502907 * ureg.degR
>>> rho1 = 3.2852596810182865 * ureg.lbm / ureg.ft**3
>>> p1 = 0.0668887801071935 * ureg.lbf / ureg.ft**2

Then:

>>> a1 = sound_speed(gamma, R, T1).to("feet / s")
>>> M1 = u1 / a1
>>> res1 = isentropic_solver("m", M1, gamma=gamma, to_dict=True)
>>> Tt1 = (1 / res1["tr"]) * T1
>>> pt1 = (1 / res1["pr"]) * p1
>>> shock = normal_shockwave_solver("mu", M1, gamma=gamma, to_dict=True)
>>> pt2 = shock["tpr"] * pt1
>>> Tt2 = Tt1
>>> rhot2 = (pt2 / (R * Tt2)).to("lbf * s**2 / feet**4")
>>> u_grad = velocity_gradient(r, p1, pt2, rhot2, k=1)
>>> u_grad
<Quantity(12871.5403, '1 / second')>

pygasflow.atd.avf.wall_shear_stress_sp.wss_cyl_c(R, phi, u_grad, mu_inf, u_inf, rho_inf, pe_pinf, Ts_Tinf, omega=0.65, laminar=True)[source]

Compute the wall shear stress along the stagnation line of a infinite long swept cylinder for a compressible laminar/turbulent flow.

Parameters:

Rfloat or array_like: Radius of the infinite-long swept cylinder.
phifloat or array_like: Sweep angle [radians]
u_gradfloat or array_like: Velocity gradient at the stagnation line.
mu_inffloat or array_like: Free stream viscosity.
u_inffloat or array_like: Free stream velocity.
rho_inffloat or array_like: Free stream density.
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.
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.

Returns:

tau_w_scyfloat or array_like: Wall shear stress for a swept cylinder.