Rayleigh Flow

gas_dynamics.rayleigh.rayleigh.rayleigh_pressure_ratio(mach_initial: float, mach_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the pressure ratio pressure_final / pressure_initial given the two Mach numbers

Notes

Given two Mach numbers, determine the resulting pressure ratio pressure two over pressure one in the non-adiabatic constant area frictionless flow. Default fluid is air.

Parameters

  • mach_initial (flaot) – The Mach number at region 1

  • mach_final (float) – The Mach number at region 2

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The rayleigh pressure ratio pressure_final / pressure_initial

Return type

float

Examples

>>> import gas_dynamics as gd
>>> mach_initial, mach_final = 3, 2
>>> p2_p1 = gd.rayleigh_pressure_ratio(mach_initial, mach_final)
>>> p2_p1
2.0606060606060606
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_temperature_ratio(mach_initial: float, mach_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the temperature ratio T2/T1 given the two Mach numbers

Notes

Given two Mach numbers, determine the resulting Temperature ratio temperature two over temperature one in the non-adiabatic constant area frictionless flow. Default fluid is air.

Parameters

  • mach_initial (flaot) – The Mach number at region 1

  • mach_final (float) – The Mach number at region 2

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The rayleigh temperature ratio T2 / T1

Return type

float

Examples

>>> import gas_dynamics as gd
>>> mach_initial, mach_final = .8, .3
>>> T2_T1 = gd.rayleigh_temperature_ratio(mach_initial, mach_final)
>>> T2_T1
0.39871485855083627
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_density_ratio(mach_initial: float, mach_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the density ratio rho2/rho1 given the two Mach numbers

Notes

Given two Mach numbers, determine the resulting density ratio density two over density one in the non-adiabatic constant area frictionless flow. Default fluid is air.

Parameters

  • mach_initial (flaot) – The Mach number at region 1

  • mach_final (float) – The Mach number at region 2

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The rayleigh density ratio rho2 / rho1

Return type

float

Examples

gas_dynamics.rayleigh.rayleigh.rayleigh_stagnation_temperature_ratio(mach_initial: float, mach_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the stagnation temperature ratio Tt2/Tt1 given the two Mach numbers

Notes

Given two Mach numbers, determine the resulting stagnation temperature ratio stagnation temperature two over stagnation temperature one in the non-adiabatic constant area frictionless flow. Default fluid is air.

Parameters

  • mach_initial (flaot) – The Mach number at region 1

  • mach_final (float) – The Mach number at region 2

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The rayleigh stagnation temperature ratio pt2 / pt1

Return type

float

Examples

>>> import gas_dynamics as gd
>>> mach_initial, mach_final = .8, .3
>>> Tt2_Tt1 = gd.rayleigh_stagnation_temperature_ratio(mach_initial, mach_final)
>>> Tt2_Tt1
0.35983309042974404
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_stagnation_pressure_ratio(mach_initial: float, mach_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the stagnation pressure ratio pt2/pt1 given the two Mach numbers

Notes

Given two Mach numbers, determine the resulting stagnation pressure ratio stagnation pressure two over stagnation pressure one in the non-adiabatic constant area frictionless flow. Default fluid is air.

Parameters

  • mach_initial (flaot) – The Mach number at region 1

  • mach_final (float) – The Mach number at region 2

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The rayleigh stagnation pressure ratio pt2 / pt1

Return type

float

Examples

>>> import gas_dynamics as gd
>>> mach_initial, mach_final = .8, .3
>>> pt2_pt1 = gd.rayleigh_stagnation_pressure_ratio(mach_initial, mach_final)
>>> pt2_pt1
1.1758050380938454
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_mach_from_pressure_ratio(mach_initial: float, pressure_initial: float, pressure_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the mach number given the Mach number and two pressures

Notes

Given the initial Mach number, initial pressure, and final pressure, determine the resulting Mach number in the non-adiabatic constant area frictionless flow with heat transfer. Default fluid is air.

Parameters

  • M (float) – The Mach number

  • pressure_initial (flaot) – pressure 1

  • pressure_final (float) – pressure 2

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The resulting Mach number

Return type

float

Examples

>>> import gas_dynamics as gd
>>> mach_final = gd.rayleigh_mach_from_pressure_ratio(mach_initial=.8, pressure_initial=1.5, pressure_final=2.5)
>>> mach_final
0.31350552512789054
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_mach_from_temperature_ratio(mach_initial: float, temperature_initial: float, temperature_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the Mach number given the Mach number and two temperatures

Notes

Given the initial Mach number, initial temperature, and final temperature, determine the resulting Mach number in the non-adiabatic constant area frictionless flow with heat transfer. Default fluid is air.

Parameters

  • mach (float) – The Mach number

  • temperature_initial (float) – Temperature 1

  • temperature_final (float) – Temperature 2

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The resulting Mach number

Return type

float

Examples

>>> import gas_dynamics as gd
>>> mach_initial, T1, T2 = .8, 250, 100
>>> mach_final = gd.rayleigh_mach_from_temperature_ratio(mach_initial, T1, T2)
>>> mach_final
0.3006228581671002
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_mach_from_stagnation_temperature_ratio(mach_initial: float, stagnation_temperature_initial: float, stagnation_temperature_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the Mach number given the Mach number and two stagnation temperatures

Notes

Given the initial Mach number, initial stagnation temperature, and final stagnation temperature, determine the resulting Mach number in the non-adiabatic constant area frictionless flow with heat transfer. Default fluid is air.

Parameters

  • mach_initial (float) – The Mach number

  • stagnation_temperature_initial (float) – Stagnation temperature 1

  • stagnation_temperature_final (float) – Stagnation temperature 2

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The resulting Mach number

Return type

float

Examples

>>> import gas_dynamics as gd
>>> mach_initial, Tt1, Tt2 = .8, 250, 105
>>> mach_final = gd.rayleigh_mach_from_stagnation_temperature_ratio(mach_initial, Tt1, Tt2)
>>> mach_final
0.33147520792270446
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_mach_from_stagnation_pressure_ratio(mach_initial: float, stagnation_pressure_initial: float, stagnation_pressure_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the Mach number given the Mach number and two stagnation pressures

Notes

Given the initial Mach number, initial stagnation pressure, and final stagnation pressure, determine the resulting Mach number in the non-adiabatic constant area frictionless flow with heat transfer. Default fluid is air.

Parameters

  • M (float) – The Mach number

  • stagnation_pressure_initial (float) – Stagnation pressure 1

  • stagnation_pressure_final (float) – Stagnation pressure 2

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The resulting Mach number

Return type

float

Examples

>>> import gas_dynamics as gd
>>> mach_initial, pt1, pt2 = .8, 2.3, 2.6
>>> mach_final = gd.rayleigh_mach_from_stagnation_pressure_ratio(mach_initial, pt1, pt2)
>>> mach_final
0.40992385119887326
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_pressure_star_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the ratio of pressure over pressure where Mach is equal to one

Notes

Given a mach number, return the ratio of the pressure of the mach number over the pressure over where the mach number is equal to one for a non-adiabatic fricionless constant area system. Default fluid is air.

Parameters

  • M (flaot) – The Mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The ratio of p / p*

Return type

float

Examples

>>> gas_dynamics as gd
>>> M = 2
>>> p_pstar = gd.rayleigh_pressure_star_ratio(M)
>>> p_pstar
0.36363636363636365
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_temperature_star_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the ratio of temperature over temperature where Mach is equal to one

Notes

Given a mach number, return the ratio of the temperature of the mach number over the temperature over where mach number is equal to one for a non-adiabatic frictionless constant area system. Default fluid is air.

Parameters

  • mach (flaot) – The Mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The ratio of T / T*

Return type

float

Examples

>>> import gas_dynamics as gd
>>> M = 2
>>> T_Tstar = gd.rayleigh_temperature_star_ratio(M)
>>> T_Tstar
0.5289256198347108
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_density_star_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the ratio of density over density where Mach is equal to one

Notes

Given a mach number, return the ratio of the density of the mach number over the density over where mach number is equal to one for a non-adiabatic constant area frictionless system. Default fluid is air.

Parameters

  • mach (flaot) – The Mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The ratio of rho / rho*

Return type

float

Examples

gas_dynamics.rayleigh.rayleigh.rayleigh_stagnation_pressure_star_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the ratio of stagnation pressure over stagnation pressure where Mach is equal to one

Notes

Given a mach number, return the ratio of the stagnation pressure of the mach number over the stagnation pressure where mach number is equal to one for a non-adiabatic frictionless system. Default fluid is air.

Parameters

  • mach (flaot) – The Mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The ratio of pt / pt*

Return type

float

Examples

>>> import gas_dynamics as gd
>>> M = 2
>>> pt_ptstar = gd.rayleigh_stagnation_pressure_star_ratio(M)
>>> pt_ptstar
1.5030959785260414
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_stagnation_temperature_star_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the ratio of stagnation temperature over stagnation temperature where Mach is equal to one

Notes

Given a mach number, return the ratio of the stagnation temperature of the mach number over the stagnation temperature where mach number is equal to one for a non-adiabatic frictionless constant area system. Default fluid is air.

Parameters

  • mach (flaot) – The Mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The ratio of Tt / Tt*

Return type

float

Examples

>>> import gas_dynamics as gd
>>> M = 2
>>> Tt_Ttstar = gd.rayleigh_stagnation_temperature_star_ratio(M)
>>> Tt_Ttstar
0.793388429752066
>>>
gas_dynamics.rayleigh.rayleigh.rayleigh_heat_flux(stagnation_temperature_initial: float, stagnation_temperature_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the heat per unit mass in our out given the two stagnation temperatures and the fluid

Notes

Given the initial and final stagnation temperatures, determine the specific heat flux to satisfy the constant area frictionless flow system. Default fluid is air.

Parameters

  • Tt1 (float) – The stagnation temperature at region 1

  • Tt2 (float) – The stagnation temperature at region 2

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The change in specific heat.

Return type

float

Examples

>>> from gas_dynamics.fluids import air
>>> air.cp = 1000
>>> Tt1, Tt2 = 280, 107.9
>>> gd.rayleigh_heat_flux(Tt1=Tt1, Tt2=Tt2, ,air)
-172100.0
>>>