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aero.Isentropic

The Isentropic module

Provides standart Stagnation to Static Ratios for Ideal gas

:Example:

import aerokit.aero.Isentropic as Is Is.TtTs_Mach(1.) 1.2 Is.TtTs_Mach(2., gamma=1.6) 2.2

Available functions

Provides Tt/Ts Pt/Ps ratios from Mach number and reversed functions. Specific heat ratio gamma is optional and can be specified in the functions itself or using aerokit.common.defaultgas module

Functions

Mach_PtPs(PtPs, gamma=defg._gamma)

Computes Mach number from Pt/Ps ratio

Parameters:

Name Type Description Default
PtPs

local Total over Static pressure ratio (either scalar or numpy array)

 required
gamma

(Default value = defg._gamma)

 _gamma

Returns:

Type Description

Mach number
Source code in aerokit/aero/Isentropic.py 
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def Mach_PtPs(PtPs, gamma=defg._gamma):
    """Computes Mach number from Pt/Ps ratio

    Args:
      PtPs: local Total over Static pressure ratio (either scalar or numpy array)
      gamma:  (Default value = defg._gamma)

    Returns:
        Mach number

    """
    return np.sqrt((PtPs ** ((gamma - 1.0) / gamma) - 1.0) * 2.0 / (gamma - 1.0))

Mach_TtTs(TtTs, gamma=defg._gamma)

Computes Mach number from Tt/Ts ratio

Parameters:

Name Type Description Default
TtTs

local Total over Static temperature ratio (either scalar or numpy array)

 required
gamma

(Default value = defg._gamma)

 _gamma

Returns:

Type Description

Mach number (same type as TtTs)
Source code in aerokit/aero/Isentropic.py 
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def Mach_TtTs(TtTs, gamma=defg._gamma):
    """Computes Mach number from Tt/Ts ratio

    Args:
      TtTs: local Total over Static temperature ratio (either scalar or numpy array)
      gamma:  (Default value = defg._gamma)

    Returns:
        Mach number (same type as TtTs)

    """
    return np.sqrt((TtTs - 1.0) * 2.0 / (gamma - 1.0))

PtPs_Mach(Mach, gamma=defg._gamma)

Computes Pt/Ps ratio from Mach number

        Long comment

Parameters:

Name Type Description Default
Mach

local Mach number (either scalar or numpy array)

 required
gamma

specific heat ratio, default from aerokit.common.defaultgas

 _gamma

Returns:

Type Description

result Pt/Ps ratio

Example:

>>> PtPs_Mach(1.) # with default gamma 1.4
1.892929158737854
>>> PtPs_Mach(2., gamma=1.6)
8.187044460255244
Source code in aerokit/aero/Isentropic.py 
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def PtPs_Mach(Mach, gamma=defg._gamma):
    """Computes Pt/Ps ratio from Mach number

                Long comment

    Args:
      Mach: local Mach number (either scalar or numpy array)
      gamma: specific heat ratio, default from aerokit.common.defaultgas

    Returns:
      result Pt/Ps ratio

    Example:

        >>> PtPs_Mach(1.) # with default gamma 1.4
        1.892929158737854
        >>> PtPs_Mach(2., gamma=1.6)
        8.187044460255244
    """
    return (1.0 + 0.5 * (gamma - 1.0) * Mach ** 2) ** (gamma / (gamma - 1.0))

TtTs_Mach(Mach, gamma=defg._gamma)

Computes Tt/Ts ratio from Mach number

Parameters:

Name Type Description Default
Mach

local Mach number (either scalar or numpy array)

 required
gamma

specific heat ratio, default from aerokit.common.defaultgas

 _gamma

Returns:

Type Description

result Tt/Ts ratio

Example:

>>> TtTs_Mach(1.) # with default gamma 1.4
1.2
Source code in aerokit/aero/Isentropic.py 
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def TtTs_Mach(Mach, gamma=defg._gamma):
    """Computes Tt/Ts ratio from Mach number

    Args:
      Mach: local Mach number (either scalar or numpy array)
      gamma: specific heat ratio, default from aerokit.common.defaultgas

    Returns:
      result Tt/Ts ratio

    Example:

        >>> TtTs_Mach(1.) # with default gamma 1.4
        1.2
    """
    return 1.0 + 0.5 * (gamma - 1) * Mach ** 2

Velocity_MachTt(Mach, Tt, r=defg._r, gamma=defg._gamma)

Computes velocity from

Parameters:

Name Type Description Default
Mach

Mach number

 required
Tt

Total temperature

 required
r

(Default value = defg._r)

 _r
gamma

(Default value = defg._gamma)

 _gamma

Returns:

Type Description

Velocity
Source code in aerokit/aero/Isentropic.py 
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def Velocity_MachTt(Mach, Tt, r=defg._r, gamma=defg._gamma):
    """Computes velocity from

    Args:
      Mach: Mach number
      Tt: Total temperature
      r:  (Default value = defg._r)
      gamma:  (Default value = defg._gamma)

    Returns:
        Velocity

    """
    return Mach * np.sqrt(gamma * r * Tt / TtTs_Mach(Mach, gamma))