Boundary-Layer Thickness - Flat Plate
This module contains a lot of functions to estimate the boundary-layer thicknesses of a incompressible/compressible, laminar/turbulent flat plate.
The four most important functions are: deltas_lam_ic
, deltas_tur_ic
,
deltas_lam_c
, deltas_tur_c
as they are wrapper functions that allows
to estimates all thicknesses with a single call.
- pygasflow.atd.avf.thickness_fp.deltas_lam_ic(x, Re, to_dict=False)[source]
Compute different boundary-layer thicknesses for the incompressible laminar flat plate.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- 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
- deltafloat or array_like
Boundary-layer thickness computed with the
delta_lam_ic
.- delta_1float or array_like
Boundary-layer displacement thickness computed with
delta_1_lam_ic
.- delta_2float or array_like
Momentum thickness computed with the
delta_2_lam_ic
.- H12float or array_like
Shape factor computed with the
shape_factor_lam_ic
.
- pygasflow.atd.avf.thickness_fp.deltas_tur_ic(x, Re, to_dict=False)[source]
Compute different boundary-layer thicknesses for the incompressible turbulent flat plate.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- 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
- deltafloat or array_like
Boundary-layer thickness computed with
delta_tur_ic
.- delta_vsfloat or array_like, optional
Viscous sub-layer thickness computed with
delta_tur_ic_viscous
.- delta_scfloat or array_like, optional
Scaling thickness computed with
delta_tur_ic_scaling
.- delta_1float or array_like
Boundary-layer displacement thickness computed with
delta_1_tur_ic
.- delta_2float or array_like
Momentum thickness computed with
delta_2_tur_ic
.- H12float or array_like
Shape factor computed with
shape_factor_tur_ic
.
- pygasflow.atd.avf.thickness_fp.deltas_lam_c(x, Re, Tw_Tinf, Ts_Tinf, Minf, omega=0.65, gammainf=1.4, to_dict=False)[source]
Compute different boundary-layer thicknesses for the compressible laminar flat plate.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Tw_Tinffloat or array_like
Temperature Ratio Tw / Tinf between the wall temperature and the free stream temperature Tinf.
- Ts_Tinffloat or array_like
Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
- Minffloat or array_like
Free stream Mach number.
- omegafloat, optional
Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set
omega=1
otherwise.- gammainffloat, optional
Free stream specific heats ratio. Default to 1.4. Must be > 1.
- 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
- deltafloat or array_like
Boundary-layer thickness computed with
delta_lam_c
.- delta_1float or array_like
Boundary-layer displacement thickness computed with
delta_1_lam_c
.- delta_2float or array_like
Momentum thickness computed with
delta_2_lam_c
.- H12float or array_like
Shape factor computed with
shape_factor_lam_c
.
- pygasflow.atd.avf.thickness_fp.deltas_tur_c(x, Re, Tw_Tinf, Ts_Tinf, Minf, omega=0.65, gammainf=1.4, to_dict=False)[source]
Compute different boundary-layer thicknesses for the compressible turbulent flat plate.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Tw_Tinffloat or array_like
Temperature Ratio Tw / Tinf between the wall temperature and the free stream temperature Tinf.
- Ts_Tinffloat or array_like
Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
- Minffloat or array_like
Free stream Mach number.
- omegafloat, optional
Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set
omega=1
otherwise.- gammainffloat, optional
Free stream specific heats ratio. Default to 1.4. Must be > 1.
- 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
- deltafloat or array_like
Boundary-layer thickness computed with
delta_tur_c
.- delta_vsfloat or array_like, optional
Viscous sub-layer thickness computed with
delta_tur_c_viscous
.- delta_scfloat or array_like, optional
Scaling thickness computed with
delta_tur_c_scaling
.- delta_1float or array_like
Boundary-layer displacement thickness computed with
delta_1_tur_ic
.- delta_2float or array_like
Momentum thickness computed with
delta_2_tur_c
.- H12float or array_like
Shape factor computed with
shape_factor_tur_c
.
Laminar Incompressible
- pygasflow.atd.avf.thickness_fp.delta_lam_ic(x, Re, c=5)[source]
Boundary-layer thickness of the incompressible laminar flat plate.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- cfloat, optional
Proportionality constant from Blasius theory. Default to 5.
- Returns
- outfloat or array_like
Notes
delta_lam_ic is the distance at which locally the tangential velocity component u(y) has approached the inviscid external velocity u_e by eps * u_e:
u_e - u(y) <= eps * u_e
Usually, the boundary-layer thickness is defined with eps=0.01, which gives c=5. If eps=0.001 is taken, then c=6.
References
“Basic of aerothermodynamics” by Ernst Heinrich
- pygasflow.atd.avf.thickness_fp.delta_1_lam_ic(x, Re)[source]
Compute the integral parameter delta_1, also known as the boundary-layer displacement thickness, for the laminar incompressible case.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Returns
- outfloat or array_like
See also
References
“Basic of aerothermodynamics” by Ernst Heinrich
- pygasflow.atd.avf.thickness_fp.delta_2_lam_ic(x, Re)[source]
Compute the integral parameter delta_2, also known as the momentum thickness, for the laminar incompressible case.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Returns
- outfloat or array_like
See also
References
“Basic of aerothermodynamics” by Ernst Heinrich
Laminar Compressible
- pygasflow.atd.avf.thickness_fp.delta_lam_c(x, Re, Ts_Tinf, omega=0.65, c=5)[source]
Boundary-layer thickness of the compressible laminar flat plate.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Ts_Tinffloat or array_like
Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
- omegafloat
Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set
omega=1
otherwise.- cfloat, optional
Proportionality constant from Blasius theory. Default to 5.
- Returns
- outfloat or array_like
See also
References
“Basic of aerothermodynamics” by Ernst Heinrich
- pygasflow.atd.avf.thickness_fp.delta_1_lam_c(x, Re, Tw_Tinf, Ts_Tinf, Minf, omega=0.65, gammainf=1.4)[source]
Compute the integral parameter delta_1, also known as the boundary-layer displacement thickness, for the laminar compressible case.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Tw_Tinffloat or array_like
Temperature Ratio Tw / Tinf between the wall temperature and the free stream temperature Tinf.
- Ts_Tinffloat or array_like
Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
- Minffloat or array_like
Free stream Mach number.
- omegafloat, optional
Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set
omega=1
otherwise.- gammainffloat, optional
Free stream specific heats ratio. Default to 1.4. Must be > 1.
- Returns
- outfloat or array_like
- pygasflow.atd.avf.thickness_fp.delta_2_lam_c(x, Re, Ts_Tinf, omega=0.65)[source]
Compute the integral parameter delta_2, also known as the momentum thickness, for the laminar compressible case.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- 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.thickness_fp.delta_tur_ic(x, Re)[source]
Boundary-layer thickness of the incompressible turbulent flat plate. This is valid for a low Reynolds number. It comes from the (1/7) power velocity distribution law.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Returns
- outfloat or array_like
References
“Basic of aerothermodynamics” by Ernst Heinrich
- pygasflow.atd.avf.thickness_fp.delta_tur_ic_viscous(x, Re)[source]
Viscous sub-layer thickness of the incompressible turbulent flat plate.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Returns
- outfloat or array_like
References
“Basic of aerothermodynamics” by Ernst Heinrich
- pygasflow.atd.avf.thickness_fp.viscous_edge_velocity(ue, Re)[source]
Viscous sub-layer edge velocity. It is the velocity corresponding to
delta_tur_ic_viscous
.- Parameters
- uefloat or array_like
Edge velocity at the boundary layer.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Returns
- outfloat or array_like
References
“Basic of aerothermodynamics” by Ernst Heinrich
- pygasflow.atd.avf.thickness_fp.delta_tur_ic_scaling(x, Re)[source]
Scaling thickness for the incompressible turbulent flat plate, where the non-dimensional velocity u+ and the wall distance y+ are equal. It is somewhat similar to the viscous sub-layer thickness.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Returns
- outfloat or array_like
References
“Basic of aerothermodynamics” by Ernst Heinrich
- pygasflow.atd.avf.thickness_fp.delta_1_tur_ic(x, Re)[source]
Compute the integral parameter delta_1, also known as the boundary-layer displacement thickness, for the turbulent incompressible case.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Returns
- outfloat or array_like
See also
References
“Basic of aerothermodynamics” by Ernst Heinrich
- pygasflow.atd.avf.thickness_fp.delta_2_tur_ic(x, Re)[source]
Compute the integral parameter delta_1, also known as the momentum thickness, for the turbulent incompressible case.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Returns
- outfloat or array_like
See also
References
“Basic of aerothermodynamics” by Ernst Heinrich
Turbulent Compressible
- pygasflow.atd.avf.thickness_fp.delta_tur_c(x, Re, Ts_Tinf, omega=0.65)[source]
Boundary-layer thickness of the compressible turbulent flat plate. This is valid for a low Reynolds number. It comes from the (1/7) power velocity distribution law.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Ts_Tinffloat or array_like
Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
- omegafloat
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
References
“Basic of aerothermodynamics” by Ernst Heinrich
- pygasflow.atd.avf.thickness_fp.delta_tur_c_viscous(x, Re, Ts_Tinf, omega=0.65)[source]
Viscous sub-layer thickness of the compressible turbulent flat plate.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Ts_Tinffloat or array_like
Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
- omegafloat
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
References
“Basic of aerothermodynamics” by Ernst Heinrich
- pygasflow.atd.avf.thickness_fp.delta_tur_c_scaling(x, Re, Ts_Tinf, omega=0.65)[source]
Scaling thickness for the compressible turbulent flat plate, where the non-dimensional velocity u+ and the wall distance y+ are equal. It is somewhat similar to the viscous sub-layer thickness .
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Ts_Tinffloat or array_like
Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
- omegafloat
Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set
omega=1
otherwise.
- Returns
- outfloat or array_like
References
“Basic of aerothermodynamics” by Ernst Heinrich
- pygasflow.atd.avf.thickness_fp.delta_1_tur_c(x, Re, Tw_Tinf, Ts_Tinf, Minf, omega=0.65, gammainf=1.4)[source]
Compute the integral parameter delta_1, also known as the boundary-layer displacement thickness, for the turbulent compressible case.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Tw_Tinffloat or array_like
Temperature Ratio Tw / Tinf between the wall temperature and the free stream temperature Tinf.
- Ts_Tinffloat or array_like
Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
- Minffloat or array_like
Free stream Mach number.
- omegafloat, optional
Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set
omega=1
otherwise.- gammainffloat, optional
Free stream specific heats ratio. Default to 1.4. Must be > 1.
- Returns
- outfloat or array_like
- pygasflow.atd.avf.thickness_fp.delta_2_tur_c(x, Re, Ts_Tinf, omega=0.65)[source]
Compute the integral parameter delta_2, also known as the momentum thickness, for the turbulent compressible case.
- Parameters
- xfloat or array_like
Location where to compute the thickness.
- Refloat or array_like
Free-stream Reynolds number computed at x.
- Tw_Tinffloat or array_like
Temperature Ratio Tw / Tinf between the wall temperature and the free stream temperature Tinf.
- Ts_Tinffloat or array_like
Temperature ratio T* / Tinf between the reference temperature T* and the free stream temperature Tinf.
- Minffloat or array_like
Free stream Mach number.
- omegafloat, optional
Exponent of the viscosity power law. Default to 0.65, corresponding to T > 400K. Set
omega=1
otherwise.- gammainffloat, optional
Free stream specific heats ratio. Default to 1.4. Must be > 1.
- Returns
- outfloat or array_like