Rayleigh Flow

pygasflow.rayleigh.get_ratios_from_mach(M, gamma)

Compute all Rayleigh ratios given the Mach number.

Parameters

Marray_like

Mach number

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

prsarray_like

Critical Pressure Ratio \(\frac{P}{P^{*}}\)

drsarray_like

Critical Density Ratio \(\frac{\rho}{\rho^{*}}\)

trsarray_like

Critical Temperature Ratio \(\frac{T}{T^{*}}\)

tprsarray_like

Critical Total Pressure Ratio \(\frac{P_{0}}{P_{0}^{*}}\)

tprsarray_like

Critical Total Temperature Ratio \(\frac{T_{0}}{T_{0}^{*}}\)

ursarray_like

Critical Velocity Ratio \(\frac{U}{U^{*}}\)

epsarray_like

Critical Entropy Ratio \(\frac{s^{*} - s}{R}\)

pygasflow.rayleigh.critical_total_temperature_ratio(M, gamma=1.4)

Compute the Rayleigh’s Critical Total Temperature Ratio \(\frac{T_{0}}{T_{0}^{*}}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Total Temperature Ratio \(\frac{T_{0}}{T_{0}^{*}}\).

pygasflow.rayleigh.critical_temperature_ratio(M, gamma=1.4)

Compute the Rayleigh’s Critical Temperature Ratio \(\frac{T}{T^{*}}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Total Temperature Ratio \(\frac{T}{T^{*}}\).

pygasflow.rayleigh.critical_pressure_ratio(M, gamma=1.4)

Compute the Rayleigh’s Critical Pressure Ratio \(\frac{P}{P^{*}}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Pressure Ratio \(\frac{P}{P^{*}}\).

pygasflow.rayleigh.critical_density_ratio(M, gamma=1.4)

Compute the Rayleigh’s Critical Density Ratio \(\frac{\rho}{\rho^{*}}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Density Ratio \(\frac{\rho}{\rho^{*}}\).

pygasflow.rayleigh.critical_total_pressure_ratio(M, gamma=1.4)

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Total Pressure Ratio \(\frac{P_{0}}{P_{0}^{*}}\).

pygasflow.rayleigh.critical_velocity_ratio(M, gamma=1.4)

Compute the Rayleigh’s Critical Velocity Ratio \(\frac{U}{U^{*}}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Velocity Ratio \(\frac{U}{U^{*}}\).

pygasflow.rayleigh.critical_entropy_parameter(M, gamma=1.4)

Compute the Rayleigh’s Critical Entropy parameter \(\frac{s^{*} - s}{R}\).

Parameters

Marray_like

Mach number. If float, list, tuple is given as input, a conversion will be attempted. Must be \(M > 0\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Critical Entropy parameter \(\frac{s^{*} - s}{R}\).

pygasflow.rayleigh.m_from_critical_total_temperature_ratio(ratio, flag='sub', gamma=1.4)

Compute the Mach number given Rayleigh’s Critical Total Temperature Ratio \(\frac{T_{0}}{T_{0}^{*}}\).

Parameters

ratioarray_like

Rayleigh’s Critical Total Temperature Ratio \(\frac{T_{0}}{T_{0}^{*}}\). If float, list, tuple is given as input, a conversion will be attempted. Must be \(0 \le \frac{T_{0}}{T_{0}^{*}} < 1\).

flagstring, optional

Can be either 'sub' (subsonic) or 'super' (supersonic). Default to 'sub'.

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.rayleigh.m_from_critical_temperature_ratio(ratio, flag='sub', gamma=1.4)

Compute the Mach number given Rayleigh’s Critical Temperature Ratio \(\frac{T}{T^{*}}\).

Parameters

ratioarray_like

Rayleigh’s Critical Temperature Ratio \(\frac{T}{T^{*}}\). If float, list, tuple is given as input, a conversion will be attempted. Must be \(0 < \frac{T}{T^{*}} < \frac{T}{T^{*}}\left(\left.M\right|_{\frac{d \left(T / T^{*}\right)}{d M} = 0}, \gamma\right)\)

flagstring, optional

Can be either:

• 'sub' for subsonic case.

• 'super' for supersonic case.

Default to 'sub'.

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.rayleigh.m_from_critical_pressure_ratio(ratio, gamma=1.4)

Compute the Mach number given Rayleigh’s Critical Pressure Ratio \(\frac{P}{P^{*}}\).

Parameters

ratioarray_like

Rayleigh’s Critical Pressure Ratio \(\frac{P}{P^{*}}\). If float, list, tuple is given as input, a conversion will be attempted. Must be \(0 < \frac{P}{P^{*}} < \left.\frac{P}{P^{*}}\right|_{M=0, \gamma}\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.rayleigh.m_from_critical_total_pressure_ratio(ratio, flag='sub', gamma=1.4)

Compute the Mach number given Rayleigh’s Critical Total Pressure Ratio \(\frac{P_{0}}{P_{0}^{*}}\).

Parameters

ratioarray_like

Rayleigh’s Critical Total Pressure Ratio \(\frac{P_{0}}{P_{0}^{*}}\). If float, list, tuple is given as input, a conversion will be attempted. If flag='sub', it must be \(1 \le \frac{P_{0}}{P_{0}^{*}} < \left.\frac{P_{0}}{P_{0}^{*}}\right|_{M=0, \gamma}\). Else, \(\frac{P_{0}}{P_{0}^{*}} \ge 1\).

flagstring, optional

Can be either 'sub' (subsonic) or 'super' (supersonic). Default to 'sub'.

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.rayleigh.m_from_critical_density_ratio(ratio, gamma=1.4)

Compute the Mach number given Rayleigh’s Critical Density Ratio \(\frac{\rho}{\rho^{*}}\).

Parameters

ratioarray_like

Rayleigh’s Critical Density Ratio \(\frac{\rho}{\rho^{*}}\). If float, list, tuple is given as input, a conversion will be attempted. Must be \(\frac{\rho}{\rho^{*}} > \frac{\gamma}{\gamma + 1}\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.rayleigh.m_from_critical_velocity_ratio(ratio, gamma=1.4)

Compute the Mach number given Rayleigh’s Critical Velocity Ratio \(\frac{U}{U^{*}}\).

Parameters

ratioarray_like

Rayleigh’s Critical Velocity Ratio \(\frac{U}{U^{*}}\). If float, list, tuple is given as input, a conversion will be attempted. Must be \(0 < \frac{U}{U^{*}} < \frac{\gamma + 1}{\gamma}\).

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.

pygasflow.rayleigh.m_from_critical_entropy(ratio, flag='sub', gamma=1.4)

Compute the Mach number given Rayleigh’s Critical Entropy \(\frac{s^{*} - s}{R}\).

Parameters

ratioarray_like

Rayleigh’s Critical Critical Entropy \(\frac{s^{*} - s}{R}\). If float, list, tuple is given as input, a conversion will be attempted. Must be \(\frac{s^{*} - s}{R} \ge 0\).

flagstring, optional

Can be either 'sub' (subsonic) or 'super' (supersonic). Default to 'sub'.

gammafloat, optional

Specific heats ratio. Default to 1.4. Must be \(\gamma > 1\).

Returns

outndarray

Mach Number.