Wall Shear Stress - Flat Plate

This module contains functions to estimate the wall shear stress and related coefficients for a incompressible/compressible, laminar/turbulent flat plate.

The two most important functions are: wss_ic, wss_c, as they are wrapper functions that allows to estimates all parameters with a single call.

pygasflow.atd.avf.wall_shear_stress_fp.wss_ic(rho, u, Re, laminar=True, to_dict=None)[source]

Compute the wall shear stress and friction coefficients for an incompressible flat plate.

Parameters:

rhofloat or array_like: Free stream density.
ufloat or array_like: Free stream velocity.
Refloat or array_like: Free stream Reynolds number computed at some location.
laminarbool, optional: Default to True, which computes the results for the laminar case. Set laminar=False to compute turbulent results.
to_dictbool, optional: If False, the function returns a list of results. If True, it returns a dictionary in which the keys are listed in the Returns section. Default to False (return a list of results).

Returns:

tau_wfloat or array_like: Wall shear stress.
cffloat or array_like: Skin friction coefficient.
CDffloat or array_like: Friction drag coefficient.

See also

wss_c

Examples

Compute the wall shear stree, the skin friction coefficient and the friction drag coefficient for the following incompressible laminar flow:

>>> from pygasflow.atd.avf.wall_shear_stress_fp import wss_ic
>>> import pint
>>> ureg = pint.UnitRegistry()
>>> rho_inf = 0.0184101009 * ureg.kg / ureg.m**3
>>> u_inf = 1810.2429106370967 * ureg.m / ureg.s
>>> Re_inf = 169116173.74147075
>>> res = wss_ic(rho_inf, u_inf, Re_inf, laminar=True, to_dict=True)
>>> res.show()
key     quantity              
------------------------------
tau_w   τw [kg / m / s ** 2]       1.54019387
cf      cf                         0.00005106
CDf     CDf                        0.00010212

pygasflow.atd.avf.wall_shear_stress_fp.wss_c(rhoinf, uinf, Reinf, Ts_Tinf, laminar=True, omega=0.65, to_dict=None)[source]

Compute the wall shear stress and friction coefficients for a compressible flat plate.

Parameters:

rhoinffloat or array_like: Free stream density.
uinffloat or array_like: Free stream velocity.
Reinffloat or array_like: Free stream Reynolds number computed at some location.
Ts_Tinffloat or array_like: Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
laminarbool, optional: Default to True, which computes the results for the laminar case. Set laminar=False to compute turbulent results.
omegafloat, optional: Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set omega=1 otherwise.
to_dictbool, optional: If False, the function returns a list of results. If True, it returns a dictionary in which the keys are listed in the Returns section. Default to False (return a list of results).

Returns:

tau_wfloat or array_like: Wall shear stress.
cffloat or array_like: Skin friction coefficient.
CDffloat or array_like: Friction drag coefficient.

See also

wss_ic

Examples

Compute the wall shear stree, the skin friction coefficient and the friction drag coefficient for the following compressible laminar flow:

>>> from pygasflow.atd.avf.wall_shear_stress_fp import wss_c
>>> import pint
>>> ureg = pint.UnitRegistry()
>>> T_inf = 226.509084 * ureg.K
>>> rho_inf = 0.0184101009 * ureg.kg / ureg.m**3
>>> u_inf = 1810.2429106370967 * ureg.m / ureg.s
>>> Re_inf = 169116173.74147075
>>> T_star = 921.8977042109084 * ureg.K
>>> res = wss_c(rho_inf, u_inf, Re_inf, T_star / T_inf, 
...     laminar=True, to_dict=True)
>>> res.show()
key     quantity              
------------------------------
tau_w   τw [kg / m / s ** 2]       1.20474712
cf      cf                         0.00003994
CDf     CDf                        0.00007988

pygasflow.atd.avf.wall_shear_stress_fp.skin_friction(tau_w, q)[source]

Compute the skin friction coefficient, cf.

Parameters:

tau_wfloat or array_like: Wall Shear Stress.
qfloat or array_like: Dynamic pressure.

Returns:

outfloat or array_like

Laminar Incompressible

pygasflow.atd.avf.wall_shear_stress_fp.wss_lam_ic(rho, u, Re)[source]

Compute the wall shear stress for a laminar incompressible flat plate.

Parameters:

rhofloat or array_like: Free stream density.
ufloat or array_like: Free stream velocity.
Refloat or array_like: Free stream Reynolds number computed at some location.

Returns:

outfloat or array_like

See also

skin_friction

pygasflow.atd.avf.wall_shear_stress_fp.friction_drag_lam_ic(Re)[source]

Compute the friction drag coefficient, C_Df, for a laminar incompressible flat plate.

Parameters:

Refloat or array_like: Free stream Reynolds number computed with a reference length.

Returns:

outfloat or array_like

Laminar Compressible

pygasflow.atd.avf.wall_shear_stress_fp.wss_lam_c(rhoinf, uinf, Reinf, Ts_Tinf, omega=0.65)[source]

Compute the wall shear stress for a laminar compressible flat plate.

Parameters:

rhoinffloat or array_like: Free stream density.
uinffloat or array_like: Free stream velocity.
Reinffloat or array_like: Free stream Reynolds number computed at some location.
Ts_Tinffloat or array_like: Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
omegafloat, optional: Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set omega=1 otherwise.

Returns:

outfloat or array_like

See also

skin_friction

pygasflow.atd.avf.wall_shear_stress_fp.friction_drag_lam_c(Re, Ts_Tinf, omega=0.65)[source]

Compute the friction drag coefficient, C_Df, for a laminar compressible flat plate.

Parameters:

Refloat or array_like: Free stream Reynolds number computed with a reference length.
Ts_Tinffloat or array_like: Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
omegafloat, optional: Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set omega=1 otherwise.

Returns:

outfloat or array_like

Turbulent Incompressible

pygasflow.atd.avf.wall_shear_stress_fp.wss_tur_ic(rho, u, Re)[source]

Compute the wall shear stress for a turbulent incompressible flat plate.

Parameters:

rhofloat or array_like: Free stream density.
ufloat or array_like: Free stream velocity.
Refloat or array_like: Free stream Reynolds number computed at some location.

Returns:

outfloat or array_like

See also

skin_friction

pygasflow.atd.avf.wall_shear_stress_fp.friction_drag_tur_ic(Re)[source]

Compute the friction drag coefficient, C_Df, for a turbulent incompressible flat plate.

Parameters:

Refloat or array_like: Free stream Reynolds number computed with a reference length.

Returns:

outfloat or array_like

Turbulent Compressible

pygasflow.atd.avf.wall_shear_stress_fp.wss_tur_c(rhoinf, uinf, Reinf, Ts_Tinf, omega=0.65)[source]

Compute the wall shear stress for a turbulent compressible flat plate.

Parameters:

rhoinffloat or array_like: Free stream density.
uinffloat or array_like: Free stream velocity.
Reinffloat or array_like: Free stream Reynolds number computed at some location.
Ts_Tinffloat or array_like: Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
omegafloat, optional: Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set omega=1 otherwise.

Returns:

outfloat or array_like

See also

skin_friction

pygasflow.atd.avf.wall_shear_stress_fp.friction_drag_tur_c(Re, Ts_Tinf, omega=0.65)[source]

Compute the friction drag coefficient, C_Df, for a turbulent compressible flat plate.

Parameters:

Refloat or array_like: Free stream Reynolds number computed with a reference length.
Ts_Tinffloat or array_like: Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
omegafloat, optional: Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set omega=1 otherwise.

Returns:

outfloat or array_like