Module CompAero.normal_shock_relations
This module contains the relationships for a normal shock flow
Expand source code
""" This module contains the relationships for a normal shock flow"""
from enum import Enum
from math import nan, sqrt
from scipy.optimize import brenth # type: ignore
from CompAero.greek_letters import LowerCaseGreek as lcg
from CompAero.internal import (
GammaNotDefinedError,
InvalidOptionCombinationError,
check_value,
footer,
named_header,
seperator,
to_string,
)
from CompAero.isentropic_relations import IsentropicRelations
NORMAL_SHOCK_VALID_OPTIONS = [
"gamma, mach",
"gamma, P2/P1",
"gamma, Rho2/Rho1",
"gamma, T2/T1",
"gamma, P02/P01",
"gamma, P02/P1",
"gamma, dwn_strm_mach",
]
class NORMAL_SHOCK_CHOICE(Enum):
MACH = "gamma, mach"
P2_P1 = "gamma, P2/P1"
RHO2_RHO1 = "gamma, Rho2/Rho1"
T2_T1 = "gamma, T2/T1"
PO2_PO1 = "gamma, P02/P01"
PO2_P1 = "gamma, P02/P1"
M2 = "gamma, dwn_strm_mach"
class NormalShockRelations:
"""
This class is a collective name space for basic calculations regarding Normal
Shock Properties.
The constructor of this class can also determine the entire state of the flow given a partial
state of the flow
Args:
gamma (float): Ratio of specific heats
mach (float, optional): mach number of the flow. Defaults to nan.
p2_p1 (float, optional): Ratio of pressure behind shock to ahead of shock. Defaults to nan.
rho2_rho1 (float, optional): Ratio of density behind shock to ahead of shock. Defaults to nan.
t2_t1 (float, optional): Ratio of temp behind shock to ahead of shock wave. Defaults to nan.
po2_po1 (float, optional): Ratio of total pressure to behind shock wave to ahead of shock wave.
Defaults to nan.
po2_p1 (float, optional): Ratio Total pressure behind shock wave to static pressure ahead of
shock wave. Defaults to nan.
m2 (float, optional): mach number behind shock wave. Defaults to nan.
Raises:
GammaNotDefinedError: Raised if Gamma is undefined
InvalidOptionCombinationError: Raised if an invalid combination of parameters is given and
flow state cannot be determined
Useage:
Usage: Pass gamma & one of the known parameters of the flow & the rest are calculated.
Valid_Combinations_of_Parameters:
1: gamma, mach\n
2: gamma, P2/P1\n
3: gamma, Rho2/Rho1\n
4: gamma, T2/T1\n
5: gamma, P02/P01\n
6: gamma, P02/P1\n
7: gamma, dwn_strm_mach\n"""
# pylint: disable=too-many-instance-attributes
def __init__(
self,
gamma: float,
mach: float = nan,
p2_p1: float = nan,
rho2_rho1: float = nan,
t2_t1: float = nan,
po2_po1: float = nan,
po2_p1: float = nan,
m2: float = nan,
) -> None:
# pylint: disable=too-many-arguments
# pylint: disable=too-many-statements
self.gamma = gamma
""" Ratio of specific heats """
self.mach = mach
""" Mach number of the flow """
self.p2_p1 = p2_p1
""" Ratio of pressure behind the shock wave to pressure before the shock wave P2/P1 """
self.rho2_rho1 = rho2_rho1
""" Ratio of density behind the shock wave to density before the shock wave rho2/rho1 """
self.t2_t1 = t2_t1
""" Ratio of temp behind the shock wave to temp before the shock wave T2/T1 """
self.po2_po1 = po2_po1
""" Ratio of pressure behind the shock wave to pressure before the shock wave P2/P1 """
self.po2_p1 = po2_p1
""" Ratio of total pressure behind the shock to pressure before the shock P02/P1 """
self.mach2 = m2
""" Mach number behind the shock wave """
self.precision = 4
""" Precision to use when printing output to the console defaults to four """
# Calculate parameters based on what was passed in
if not check_value(self.gamma):
raise GammaNotDefinedError()
if check_value(self.mach):
pass
elif check_value(self.p2_p1):
self.mach = NormalShockRelations.calc_mach_from_p2_p1(self.p2_p1, self.gamma)
elif check_value(self.rho2_rho1):
self.mach = NormalShockRelations.calc_mach_from_rho2_rho1(self.rho2_rho1, self.gamma)
elif check_value(self.t2_t1):
self.mach = NormalShockRelations.calc_mach_from_t2_t1(self.t2_t1, self.gamma)
elif check_value(self.po2_po1):
self.mach = NormalShockRelations.calc_mach_from_po2_po1(self.po2_po1, self.gamma)
elif check_value(self.po2_p1):
self.mach = NormalShockRelations.calc_mach_from_po2_p1(self.po2_p1, self.gamma)
elif check_value(self.mach2):
self.mach = NormalShockRelations.calc_mach_before_normal_shock_from_mach_after_shock(
self.mach2, self.gamma
)
else:
raise InvalidOptionCombinationError()
if check_value(self.mach):
if self.mach >= 1.0:
self._calc_state_from_mach()
else:
self.mach = nan
def _calc_state_from_mach(self) -> None:
self.p2_p1 = NormalShockRelations.calc_p2_p1(self.mach, self.gamma)
self.rho2_rho1 = NormalShockRelations.calc_rho2_rho1(self.mach, self.gamma)
self.t2_t1 = NormalShockRelations.calc_t2_t1(self.mach, self.gamma)
self.po2_po1 = NormalShockRelations.calc_po2_po1(self.mach, self.gamma)
self.po2_p1 = NormalShockRelations.calc_po2_p1(self.mach, self.gamma)
self.mach2 = NormalShockRelations.calc_mach_after_normal_shock(self.mach, self.gamma)
def __str__(self) -> str:
return "".join(
[
named_header("Normal Shock Relations at Mach", self.mach, self.precision),
seperator(),
to_string("P2/P1", self.p2_p1, self.precision),
to_string(f"{lcg.rho}2/{lcg.rho}1", self.rho2_rho1, self.precision, dot_line=True),
to_string("T2/T1", self.t2_t1, self.precision),
to_string("P02/P01", self.po2_po1, self.precision, dot_line=True),
to_string("P02/P1", self.po2_p1, self.precision),
to_string("Dowstream Mach", self.mach2, self.precision, dot_line=True),
footer(),
]
)
@staticmethod
def calc_p2_p1(mach: float, gamma: float, offset: float = 0.0) -> float:
"""Calculates Ratio of Pressure behind the shock wave to that of before the shock wave P2/P1
Args:
mach (float): mach number of the flow
gamma (float): ratio of specific heats
offset (float, optional): offset that can be used for root finding. Defaults to 0.0.
Raises:
ValueError: Raised if mach < 1.0
Returns:
float: P2/P1
"""
if mach < 1.0:
raise ValueError("Normal Shocks Require a mach greater than 1")
return 1 + 2 * gamma / (gamma + 1) * (pow(mach, 2) - 1) - offset
@staticmethod
def calc_mach_from_p2_p1(p2_p1: float, gamma: float) -> float:
"""
Calculates the mach number based on the ratio Pressure behind the shock to that of before
the shock P2/P1
Args:
p2_p1 (float): Ratio of Pressure behind the shock to that of before the shock P2/P1
gamma (float): ratio of specific heats
Returns:
float: mach number
"""
return brenth(NormalShockRelations.calc_p2_p1, 1.0, 30, args=(gamma, p2_p1)) # type: ignore
@staticmethod
def calc_rho2_rho1(mach: float, gamma: float, offset: float = 0.0) -> float:
"""
Calculates Ratio of density behind the shock to that of density before the shock Rho2/Rho1
Args:
mach (float): mach number of the flow
gamma (float): ratio of specific heats
offset (float, optional): offset that can be used for root finding. Defaults to 0.0.
Raises:
ValueError: Raised if mach < 1.0
Returns:
float: Rho2/Rho1
"""
if mach < 1.0:
raise ValueError("Normal Shocks Require a mach greater than 1")
return (gamma + 1) * pow(mach, 2) / (2 + (gamma - 1) * pow(mach, 2)) - offset
@staticmethod
def calc_mach_from_rho2_rho1(rho2_rho1: float, gamma: float) -> float:
"""
Calculates the mach number based on the ratio density behind the shock wave to that of
before the shock wave Rho2/Rho1
Args:
p2_p1 (float): Ratio of density behind the shock to that of before the shock Rho2/Rho1
gamma (float): ratio of specific heats
Returns:
float: mach number
"""
return brenth(
NormalShockRelations.calc_rho2_rho1, 1.0, 30, args=(gamma, rho2_rho1)
) # type: ignore
@staticmethod
def calc_t2_t1(mach: float, gamma: float, offset: float = 0.0) -> float:
"""
Calculates Ratio of temp behind the shock to that of temp before the shock T2/T1
Args:
mach (float): mach number of the flow
gamma (float): ratio of specific heats
offset (float, optional): offset that can be used for root finding. Defaults to 0.0.
Raises:
ValueError: Raised if mach < 1.0
Returns:
float: T2/T1
"""
if mach < 1.0:
raise ValueError("Normal Shocks Require a mach greater than 1")
return (
NormalShockRelations.calc_p2_p1(mach, gamma)
/ NormalShockRelations.calc_rho2_rho1(mach, gamma)
- offset
)
@staticmethod
def calc_mach_from_t2_t1(t2_t1: float, gamma: float) -> float:
"""
Calculates the mach number based on the ratio of temperature behind the shock wave to
that of before the shock wave T2/T1
Args:
t2_t1 (float): Ratio of temp behind the shock to that of before the shock T2/T1
gamma (float): ratio of specific heats
Returns:
float: mach number
"""
return brenth(NormalShockRelations.calc_t2_t1, 1, 30, args=(gamma, t2_t1)) # type: ignore
@staticmethod
def calc_mach_after_normal_shock(mach: float, gamma: float, offset: float = 0.0) -> float:
"""Calculates the mach number behind the shock wave
Args:
mach (float): mach number of the flow
gamma (float): ratio of specific heats
offset (float, optional): offset that can be used for root finding. Defaults to 0.0.
Raises:
ValueError: Raised if mach < 1.0
Returns:
float: mach number behind shock wave
"""
if mach < 1.0:
raise ValueError("Normal Shocks Require a mach greater than 1")
gm1 = gamma - 1
m_sqr = pow(mach, 2)
num = 1 + gm1 / 2 * m_sqr
denom = gamma * m_sqr - gm1 / 2
return sqrt(num / denom) - offset
@staticmethod
def calc_mach_before_normal_shock_from_mach_after_shock(mach2: float, gamma: float) -> float:
"""
Calculates the mach number before a shock wave based on the mach number after a shock wave
Args:
mach2 (float): mach number after the shock wave
gamma (float): ratio of specific heats
Returns:
float: mach number
"""
return brenth(
NormalShockRelations.calc_mach_after_normal_shock, 1, 30, args=(gamma, mach2)
) # type: ignore
@staticmethod
def calc_po2_po1(mach: float, gamma: float, offset: float = 0.0) -> float:
"""
Calculates Ratio of Total Pressure behind the shock wave to that of Total Pressure before
the shock wave P02/P01
Args:
mach (float): mach number of the flow
gamma (float): ratio of specific heats
offset (float, optional): offset that can be used for root finding. Defaults to 0.0.
Raises:
ValueError: Raised if mach < 1.0
Returns:
float: P02/P01
"""
if mach < 1.0:
raise ValueError("Normal Shocks Require a mach greater than 1")
m2 = NormalShockRelations.calc_mach_after_normal_shock(mach, gamma)
upstream = IsentropicRelations(gamma, mach=mach)
downstream = IsentropicRelations(gamma, mach=m2)
p2_p1 = NormalShockRelations.calc_p2_p1(mach, gamma)
return downstream.p0_p * p2_p1 / upstream.p0_p - offset
@staticmethod
def calc_mach_from_po2_po1(po2_po1: float, gamma: float) -> float:
"""
Calculates the mach number based on the ratio of Total Pressure behind the shock wave to
that of before the shock wave P02/P01
Args:
po2_po1 (float): Ratio of Total Pressure behind the shock to before the shock P02/P01
gamma (float): ratio of specific heats
Returns:
float: mach number
"""
return brenth(
NormalShockRelations.calc_po2_po1, 1, 30, args=(gamma, po2_po1)
) # type: ignore
@staticmethod
def calc_po2_p1(mach: float, gamma: float, offset: float = 0.0) -> float:
"""
Calculates Ratio of Total Pressure behind the shock wave to that of static Pressure before
the shock wave P02/P1
Args:
mach (float): mach number of the flow
gamma (float): ratio of specific heats
offset (float, optional): offset that can be used for root finding. Defaults to 0.0.
Raises:
ValueError: Raised if mach < 1.0
Returns:
float: P02/P1
"""
gm1 = gamma - 1
gp1 = gamma + 1
m_sqr = pow(mach, 2)
first_ratio = pow(gp1, 2) * m_sqr / (4 * gamma * m_sqr - 2 * gm1)
second_ratio = (1 - gamma + 2 * gamma * m_sqr) / gp1
return pow(first_ratio, gamma / gm1) * second_ratio - offset
@staticmethod
def calc_mach_from_po2_p1(po2_p1: float, gamma: float) -> float:
"""
Calculates the mach number based on the ratio of Total Pressure behind the shock wave to
that of before the shock wave P02/P1
Also known as the "Rayleigh Pitot Tube Formula"
Args:
po2_p1 (float): Ratio of temp behind the shock to that of before the shock P02/P1
gamma (float): ratio of specific heats
Returns:
float: mach number
"""
return brenth(NormalShockRelations.calc_po2_p1, 1, 30, args=(gamma, po2_p1)) # type: ignoreClasses
class NORMAL_SHOCK_CHOICE (*args, **kwds)-
Create a collection of name/value pairs.
Example enumeration:
>>> class Color(Enum): ... RED = 1 ... BLUE = 2 ... GREEN = 3Access them by:
- attribute access::
>>> Color.RED <Color.RED: 1>- value lookup:
>>> Color(1) <Color.RED: 1>- name lookup:
>>> Color['RED'] <Color.RED: 1>Enumerations can be iterated over, and know how many members they have:
>>> len(Color) 3>>> list(Color) [<Color.RED: 1>, <Color.BLUE: 2>, <Color.GREEN: 3>]Methods can be added to enumerations, and members can have their own attributes – see the documentation for details.
Expand source code
class NORMAL_SHOCK_CHOICE(Enum): MACH = "gamma, mach" P2_P1 = "gamma, P2/P1" RHO2_RHO1 = "gamma, Rho2/Rho1" T2_T1 = "gamma, T2/T1" PO2_PO1 = "gamma, P02/P01" PO2_P1 = "gamma, P02/P1" M2 = "gamma, dwn_strm_mach"Ancestors
- enum.Enum
Class variables
var M2var MACHvar P2_P1var PO2_P1var PO2_PO1var RHO2_RHO1var T2_T1
class NormalShockRelations (gamma: float, mach: float = nan, p2_p1: float = nan, rho2_rho1: float = nan, t2_t1: float = nan, po2_po1: float = nan, po2_p1: float = nan, m2: float = nan)-
This class is a collective name space for basic calculations regarding Normal Shock Properties.
The constructor of this class can also determine the entire state of the flow given a partial state of the flow
Args: gamma (float): Ratio of specific heats mach (float, optional): mach number of the flow. Defaults to nan. p2_p1 (float, optional): Ratio of pressure behind shock to ahead of shock. Defaults to nan. rho2_rho1 (float, optional): Ratio of density behind shock to ahead of shock. Defaults to nan. t2_t1 (float, optional): Ratio of temp behind shock to ahead of shock wave. Defaults to nan. po2_po1 (float, optional): Ratio of total pressure to behind shock wave to ahead of shock wave. Defaults to nan. po2_p1 (float, optional): Ratio Total pressure behind shock wave to static pressure ahead of shock wave. Defaults to nan. m2 (float, optional): mach number behind shock wave. Defaults to nan.
Raises: GammaNotDefinedError: Raised if Gamma is undefined InvalidOptionCombinationError: Raised if an invalid combination of parameters is given and flow state cannot be determined
Useage: Usage: Pass gamma & one of the known parameters of the flow & the rest are calculated.
Valid_Combinations_of_Parameters: 1: gamma, mach
2: gamma, P2/P1
3: gamma, Rho2/Rho1
4: gamma, T2/T1
5: gamma, P02/P01
6: gamma, P02/P1
7: gamma, dwn_strm_mach
Expand source code
class NormalShockRelations: """ This class is a collective name space for basic calculations regarding Normal Shock Properties. The constructor of this class can also determine the entire state of the flow given a partial state of the flow Args: gamma (float): Ratio of specific heats mach (float, optional): mach number of the flow. Defaults to nan. p2_p1 (float, optional): Ratio of pressure behind shock to ahead of shock. Defaults to nan. rho2_rho1 (float, optional): Ratio of density behind shock to ahead of shock. Defaults to nan. t2_t1 (float, optional): Ratio of temp behind shock to ahead of shock wave. Defaults to nan. po2_po1 (float, optional): Ratio of total pressure to behind shock wave to ahead of shock wave. Defaults to nan. po2_p1 (float, optional): Ratio Total pressure behind shock wave to static pressure ahead of shock wave. Defaults to nan. m2 (float, optional): mach number behind shock wave. Defaults to nan. Raises: GammaNotDefinedError: Raised if Gamma is undefined InvalidOptionCombinationError: Raised if an invalid combination of parameters is given and flow state cannot be determined Useage: Usage: Pass gamma & one of the known parameters of the flow & the rest are calculated. Valid_Combinations_of_Parameters: 1: gamma, mach\n 2: gamma, P2/P1\n 3: gamma, Rho2/Rho1\n 4: gamma, T2/T1\n 5: gamma, P02/P01\n 6: gamma, P02/P1\n 7: gamma, dwn_strm_mach\n""" # pylint: disable=too-many-instance-attributes def __init__( self, gamma: float, mach: float = nan, p2_p1: float = nan, rho2_rho1: float = nan, t2_t1: float = nan, po2_po1: float = nan, po2_p1: float = nan, m2: float = nan, ) -> None: # pylint: disable=too-many-arguments # pylint: disable=too-many-statements self.gamma = gamma """ Ratio of specific heats """ self.mach = mach """ Mach number of the flow """ self.p2_p1 = p2_p1 """ Ratio of pressure behind the shock wave to pressure before the shock wave P2/P1 """ self.rho2_rho1 = rho2_rho1 """ Ratio of density behind the shock wave to density before the shock wave rho2/rho1 """ self.t2_t1 = t2_t1 """ Ratio of temp behind the shock wave to temp before the shock wave T2/T1 """ self.po2_po1 = po2_po1 """ Ratio of pressure behind the shock wave to pressure before the shock wave P2/P1 """ self.po2_p1 = po2_p1 """ Ratio of total pressure behind the shock to pressure before the shock P02/P1 """ self.mach2 = m2 """ Mach number behind the shock wave """ self.precision = 4 """ Precision to use when printing output to the console defaults to four """ # Calculate parameters based on what was passed in if not check_value(self.gamma): raise GammaNotDefinedError() if check_value(self.mach): pass elif check_value(self.p2_p1): self.mach = NormalShockRelations.calc_mach_from_p2_p1(self.p2_p1, self.gamma) elif check_value(self.rho2_rho1): self.mach = NormalShockRelations.calc_mach_from_rho2_rho1(self.rho2_rho1, self.gamma) elif check_value(self.t2_t1): self.mach = NormalShockRelations.calc_mach_from_t2_t1(self.t2_t1, self.gamma) elif check_value(self.po2_po1): self.mach = NormalShockRelations.calc_mach_from_po2_po1(self.po2_po1, self.gamma) elif check_value(self.po2_p1): self.mach = NormalShockRelations.calc_mach_from_po2_p1(self.po2_p1, self.gamma) elif check_value(self.mach2): self.mach = NormalShockRelations.calc_mach_before_normal_shock_from_mach_after_shock( self.mach2, self.gamma ) else: raise InvalidOptionCombinationError() if check_value(self.mach): if self.mach >= 1.0: self._calc_state_from_mach() else: self.mach = nan def _calc_state_from_mach(self) -> None: self.p2_p1 = NormalShockRelations.calc_p2_p1(self.mach, self.gamma) self.rho2_rho1 = NormalShockRelations.calc_rho2_rho1(self.mach, self.gamma) self.t2_t1 = NormalShockRelations.calc_t2_t1(self.mach, self.gamma) self.po2_po1 = NormalShockRelations.calc_po2_po1(self.mach, self.gamma) self.po2_p1 = NormalShockRelations.calc_po2_p1(self.mach, self.gamma) self.mach2 = NormalShockRelations.calc_mach_after_normal_shock(self.mach, self.gamma) def __str__(self) -> str: return "".join( [ named_header("Normal Shock Relations at Mach", self.mach, self.precision), seperator(), to_string("P2/P1", self.p2_p1, self.precision), to_string(f"{lcg.rho}2/{lcg.rho}1", self.rho2_rho1, self.precision, dot_line=True), to_string("T2/T1", self.t2_t1, self.precision), to_string("P02/P01", self.po2_po1, self.precision, dot_line=True), to_string("P02/P1", self.po2_p1, self.precision), to_string("Dowstream Mach", self.mach2, self.precision, dot_line=True), footer(), ] ) @staticmethod def calc_p2_p1(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of Pressure behind the shock wave to that of before the shock wave P2/P1 Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: P2/P1 """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") return 1 + 2 * gamma / (gamma + 1) * (pow(mach, 2) - 1) - offset @staticmethod def calc_mach_from_p2_p1(p2_p1: float, gamma: float) -> float: """ Calculates the mach number based on the ratio Pressure behind the shock to that of before the shock P2/P1 Args: p2_p1 (float): Ratio of Pressure behind the shock to that of before the shock P2/P1 gamma (float): ratio of specific heats Returns: float: mach number """ return brenth(NormalShockRelations.calc_p2_p1, 1.0, 30, args=(gamma, p2_p1)) # type: ignore @staticmethod def calc_rho2_rho1(mach: float, gamma: float, offset: float = 0.0) -> float: """ Calculates Ratio of density behind the shock to that of density before the shock Rho2/Rho1 Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: Rho2/Rho1 """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") return (gamma + 1) * pow(mach, 2) / (2 + (gamma - 1) * pow(mach, 2)) - offset @staticmethod def calc_mach_from_rho2_rho1(rho2_rho1: float, gamma: float) -> float: """ Calculates the mach number based on the ratio density behind the shock wave to that of before the shock wave Rho2/Rho1 Args: p2_p1 (float): Ratio of density behind the shock to that of before the shock Rho2/Rho1 gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( NormalShockRelations.calc_rho2_rho1, 1.0, 30, args=(gamma, rho2_rho1) ) # type: ignore @staticmethod def calc_t2_t1(mach: float, gamma: float, offset: float = 0.0) -> float: """ Calculates Ratio of temp behind the shock to that of temp before the shock T2/T1 Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: T2/T1 """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") return ( NormalShockRelations.calc_p2_p1(mach, gamma) / NormalShockRelations.calc_rho2_rho1(mach, gamma) - offset ) @staticmethod def calc_mach_from_t2_t1(t2_t1: float, gamma: float) -> float: """ Calculates the mach number based on the ratio of temperature behind the shock wave to that of before the shock wave T2/T1 Args: t2_t1 (float): Ratio of temp behind the shock to that of before the shock T2/T1 gamma (float): ratio of specific heats Returns: float: mach number """ return brenth(NormalShockRelations.calc_t2_t1, 1, 30, args=(gamma, t2_t1)) # type: ignore @staticmethod def calc_mach_after_normal_shock(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates the mach number behind the shock wave Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: mach number behind shock wave """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") gm1 = gamma - 1 m_sqr = pow(mach, 2) num = 1 + gm1 / 2 * m_sqr denom = gamma * m_sqr - gm1 / 2 return sqrt(num / denom) - offset @staticmethod def calc_mach_before_normal_shock_from_mach_after_shock(mach2: float, gamma: float) -> float: """ Calculates the mach number before a shock wave based on the mach number after a shock wave Args: mach2 (float): mach number after the shock wave gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( NormalShockRelations.calc_mach_after_normal_shock, 1, 30, args=(gamma, mach2) ) # type: ignore @staticmethod def calc_po2_po1(mach: float, gamma: float, offset: float = 0.0) -> float: """ Calculates Ratio of Total Pressure behind the shock wave to that of Total Pressure before the shock wave P02/P01 Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: P02/P01 """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") m2 = NormalShockRelations.calc_mach_after_normal_shock(mach, gamma) upstream = IsentropicRelations(gamma, mach=mach) downstream = IsentropicRelations(gamma, mach=m2) p2_p1 = NormalShockRelations.calc_p2_p1(mach, gamma) return downstream.p0_p * p2_p1 / upstream.p0_p - offset @staticmethod def calc_mach_from_po2_po1(po2_po1: float, gamma: float) -> float: """ Calculates the mach number based on the ratio of Total Pressure behind the shock wave to that of before the shock wave P02/P01 Args: po2_po1 (float): Ratio of Total Pressure behind the shock to before the shock P02/P01 gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( NormalShockRelations.calc_po2_po1, 1, 30, args=(gamma, po2_po1) ) # type: ignore @staticmethod def calc_po2_p1(mach: float, gamma: float, offset: float = 0.0) -> float: """ Calculates Ratio of Total Pressure behind the shock wave to that of static Pressure before the shock wave P02/P1 Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: P02/P1 """ gm1 = gamma - 1 gp1 = gamma + 1 m_sqr = pow(mach, 2) first_ratio = pow(gp1, 2) * m_sqr / (4 * gamma * m_sqr - 2 * gm1) second_ratio = (1 - gamma + 2 * gamma * m_sqr) / gp1 return pow(first_ratio, gamma / gm1) * second_ratio - offset @staticmethod def calc_mach_from_po2_p1(po2_p1: float, gamma: float) -> float: """ Calculates the mach number based on the ratio of Total Pressure behind the shock wave to that of before the shock wave P02/P1 Also known as the "Rayleigh Pitot Tube Formula" Args: po2_p1 (float): Ratio of temp behind the shock to that of before the shock P02/P1 gamma (float): ratio of specific heats Returns: float: mach number """ return brenth(NormalShockRelations.calc_po2_p1, 1, 30, args=(gamma, po2_p1)) # type: ignoreSubclasses
Static methods
def calc_mach_after_normal_shock(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates the mach number behind the shock wave
Args
mach:float- mach number of the flow
gamma:float- ratio of specific heats
offset:float, optional- offset that can be used for root finding. Defaults to 0.0.
Raises
ValueError- Raised if mach < 1.0
Returns
float- mach number behind shock wave
Expand source code
@staticmethod def calc_mach_after_normal_shock(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates the mach number behind the shock wave Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: mach number behind shock wave """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") gm1 = gamma - 1 m_sqr = pow(mach, 2) num = 1 + gm1 / 2 * m_sqr denom = gamma * m_sqr - gm1 / 2 return sqrt(num / denom) - offset def calc_mach_before_normal_shock_from_mach_after_shock(mach2: float, gamma: float) ‑> float-
Calculates the mach number before a shock wave based on the mach number after a shock wave
Args
mach2:float- mach number after the shock wave
gamma:float- ratio of specific heats
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_before_normal_shock_from_mach_after_shock(mach2: float, gamma: float) -> float: """ Calculates the mach number before a shock wave based on the mach number after a shock wave Args: mach2 (float): mach number after the shock wave gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( NormalShockRelations.calc_mach_after_normal_shock, 1, 30, args=(gamma, mach2) ) # type: ignore def calc_mach_from_p2_p1(p2_p1: float, gamma: float) ‑> float-
Calculates the mach number based on the ratio Pressure behind the shock to that of before the shock P2/P1
Args
p2_p1:float- Ratio of Pressure behind the shock to that of before the shock P2/P1
gamma:float- ratio of specific heats
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_from_p2_p1(p2_p1: float, gamma: float) -> float: """ Calculates the mach number based on the ratio Pressure behind the shock to that of before the shock P2/P1 Args: p2_p1 (float): Ratio of Pressure behind the shock to that of before the shock P2/P1 gamma (float): ratio of specific heats Returns: float: mach number """ return brenth(NormalShockRelations.calc_p2_p1, 1.0, 30, args=(gamma, p2_p1)) # type: ignore def calc_mach_from_po2_p1(po2_p1: float, gamma: float) ‑> float-
Calculates the mach number based on the ratio of Total Pressure behind the shock wave to that of before the shock wave P02/P1 Also known as the "Rayleigh Pitot Tube Formula"
Args
po2_p1:float- Ratio of temp behind the shock to that of before the shock P02/P1
gamma:float- ratio of specific heats
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_from_po2_p1(po2_p1: float, gamma: float) -> float: """ Calculates the mach number based on the ratio of Total Pressure behind the shock wave to that of before the shock wave P02/P1 Also known as the "Rayleigh Pitot Tube Formula" Args: po2_p1 (float): Ratio of temp behind the shock to that of before the shock P02/P1 gamma (float): ratio of specific heats Returns: float: mach number """ return brenth(NormalShockRelations.calc_po2_p1, 1, 30, args=(gamma, po2_p1)) # type: ignore def calc_mach_from_po2_po1(po2_po1: float, gamma: float) ‑> float-
Calculates the mach number based on the ratio of Total Pressure behind the shock wave to that of before the shock wave P02/P01
Args
po2_po1:float- Ratio of Total Pressure behind the shock to before the shock P02/P01
gamma:float- ratio of specific heats
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_from_po2_po1(po2_po1: float, gamma: float) -> float: """ Calculates the mach number based on the ratio of Total Pressure behind the shock wave to that of before the shock wave P02/P01 Args: po2_po1 (float): Ratio of Total Pressure behind the shock to before the shock P02/P01 gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( NormalShockRelations.calc_po2_po1, 1, 30, args=(gamma, po2_po1) ) # type: ignore def calc_mach_from_rho2_rho1(rho2_rho1: float, gamma: float) ‑> float-
Calculates the mach number based on the ratio density behind the shock wave to that of before the shock wave Rho2/Rho1
Args
p2_p1:float- Ratio of density behind the shock to that of before the shock Rho2/Rho1
gamma:float- ratio of specific heats
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_from_rho2_rho1(rho2_rho1: float, gamma: float) -> float: """ Calculates the mach number based on the ratio density behind the shock wave to that of before the shock wave Rho2/Rho1 Args: p2_p1 (float): Ratio of density behind the shock to that of before the shock Rho2/Rho1 gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( NormalShockRelations.calc_rho2_rho1, 1.0, 30, args=(gamma, rho2_rho1) ) # type: ignore def calc_mach_from_t2_t1(t2_t1: float, gamma: float) ‑> float-
Calculates the mach number based on the ratio of temperature behind the shock wave to that of before the shock wave T2/T1
Args
t2_t1:float- Ratio of temp behind the shock to that of before the shock T2/T1
gamma:float- ratio of specific heats
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_from_t2_t1(t2_t1: float, gamma: float) -> float: """ Calculates the mach number based on the ratio of temperature behind the shock wave to that of before the shock wave T2/T1 Args: t2_t1 (float): Ratio of temp behind the shock to that of before the shock T2/T1 gamma (float): ratio of specific heats Returns: float: mach number """ return brenth(NormalShockRelations.calc_t2_t1, 1, 30, args=(gamma, t2_t1)) # type: ignore def calc_p2_p1(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates Ratio of Pressure behind the shock wave to that of before the shock wave P2/P1
Args
mach:float- mach number of the flow
gamma:float- ratio of specific heats
offset:float, optional- offset that can be used for root finding. Defaults to 0.0.
Raises
ValueError- Raised if mach < 1.0
Returns
float- P2/P1
Expand source code
@staticmethod def calc_p2_p1(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of Pressure behind the shock wave to that of before the shock wave P2/P1 Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: P2/P1 """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") return 1 + 2 * gamma / (gamma + 1) * (pow(mach, 2) - 1) - offset def calc_po2_p1(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates Ratio of Total Pressure behind the shock wave to that of static Pressure before the shock wave P02/P1
Args
mach:float- mach number of the flow
gamma:float- ratio of specific heats
offset:float, optional- offset that can be used for root finding. Defaults to 0.0.
Raises
ValueError- Raised if mach < 1.0
Returns
float- P02/P1
Expand source code
@staticmethod def calc_po2_p1(mach: float, gamma: float, offset: float = 0.0) -> float: """ Calculates Ratio of Total Pressure behind the shock wave to that of static Pressure before the shock wave P02/P1 Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: P02/P1 """ gm1 = gamma - 1 gp1 = gamma + 1 m_sqr = pow(mach, 2) first_ratio = pow(gp1, 2) * m_sqr / (4 * gamma * m_sqr - 2 * gm1) second_ratio = (1 - gamma + 2 * gamma * m_sqr) / gp1 return pow(first_ratio, gamma / gm1) * second_ratio - offset def calc_po2_po1(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates Ratio of Total Pressure behind the shock wave to that of Total Pressure before the shock wave P02/P01
Args
mach:float- mach number of the flow
gamma:float- ratio of specific heats
offset:float, optional- offset that can be used for root finding. Defaults to 0.0.
Raises
ValueError- Raised if mach < 1.0
Returns
float- P02/P01
Expand source code
@staticmethod def calc_po2_po1(mach: float, gamma: float, offset: float = 0.0) -> float: """ Calculates Ratio of Total Pressure behind the shock wave to that of Total Pressure before the shock wave P02/P01 Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: P02/P01 """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") m2 = NormalShockRelations.calc_mach_after_normal_shock(mach, gamma) upstream = IsentropicRelations(gamma, mach=mach) downstream = IsentropicRelations(gamma, mach=m2) p2_p1 = NormalShockRelations.calc_p2_p1(mach, gamma) return downstream.p0_p * p2_p1 / upstream.p0_p - offset def calc_rho2_rho1(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates Ratio of density behind the shock to that of density before the shock Rho2/Rho1
Args
mach:float- mach number of the flow
gamma:float- ratio of specific heats
offset:float, optional- offset that can be used for root finding. Defaults to 0.0.
Raises
ValueError- Raised if mach < 1.0
Returns
float- Rho2/Rho1
Expand source code
@staticmethod def calc_rho2_rho1(mach: float, gamma: float, offset: float = 0.0) -> float: """ Calculates Ratio of density behind the shock to that of density before the shock Rho2/Rho1 Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: Rho2/Rho1 """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") return (gamma + 1) * pow(mach, 2) / (2 + (gamma - 1) * pow(mach, 2)) - offset def calc_t2_t1(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates Ratio of temp behind the shock to that of temp before the shock T2/T1
Args
mach:float- mach number of the flow
gamma:float- ratio of specific heats
offset:float, optional- offset that can be used for root finding. Defaults to 0.0.
Raises
ValueError- Raised if mach < 1.0
Returns
float- T2/T1
Expand source code
@staticmethod def calc_t2_t1(mach: float, gamma: float, offset: float = 0.0) -> float: """ Calculates Ratio of temp behind the shock to that of temp before the shock T2/T1 Args: mach (float): mach number of the flow gamma (float): ratio of specific heats offset (float, optional): offset that can be used for root finding. Defaults to 0.0. Raises: ValueError: Raised if mach < 1.0 Returns: float: T2/T1 """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") return ( NormalShockRelations.calc_p2_p1(mach, gamma) / NormalShockRelations.calc_rho2_rho1(mach, gamma) - offset )
Instance variables
var gamma-
Ratio of specific heats
var mach-
Mach number of the flow
var mach2-
Mach number behind the shock wave
var p2_p1-
Ratio of pressure behind the shock wave to pressure before the shock wave P2/P1
var po2_p1-
Ratio of total pressure behind the shock to pressure before the shock P02/P1
var po2_po1-
Ratio of pressure behind the shock wave to pressure before the shock wave P2/P1
var precision-
Precision to use when printing output to the console defaults to four
var rho2_rho1-
Ratio of density behind the shock wave to density before the shock wave rho2/rho1
var t2_t1-
Ratio of temp behind the shock wave to temp before the shock wave T2/T1