Module CompAero.oblique_shock_relations
This file contains the relationships for oblique shock waves
Expand source code
"""
This file contains the relationships for oblique shock waves
"""
from enum import Enum
from math import asin, atan, cos, degrees, nan, radians, sin, sqrt, tan
import matplotlib.pyplot as plt # type: ignore
import numpy as np
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,
named_subheader,
seperator,
to_string,
)
from CompAero.normal_shock_relations import NormalShockRelations
from CompAero.types import ShockType
class ObliqueShockChoice(Enum):
"""Valid Oblique Shock Initialization Choices"""
MACH_SHOCK_ANGLE = "gamma, mach, shock angle"
MACH_WEDGE_ANGLE = "gamma, mach, wedge angle"
MACH_N_1_SHOCK_ANGLE = "gamma, mach normal 1, shock angle "
M2_WEDGE_SHOCK_ANGLE = "gamma, mach behind shock (M2), wedge angle, shock angle"
P2_P1_SHOCK_ANGLE = "gamma, P2/P1, shock angle"
RHO2_RHO1_SHOCK_ANGLE = "gamma, Rho2/Rho1, shock angle"
T2_T1_SHOCK_ANGLE = "gamma, T2/T1, shock angle"
PO2_PO1_SHOCK_ANGLE = "gamma, P02/P01, shock angle"
PO2_P1_SHOCK_ANGLE = "gamma, P02/P1, shock angle"
MN2_SHOCK_ANGLE = "gamma, MN2, shock angle"
OBLIQUE_SHOCK_VALID_OPTIONS = [x.value for x in ObliqueShockChoice]
class ObliqueShockRelations(NormalShockRelations):
"""
This class is a collective name space for basic calculations regarding Oblique Shock Properties
The constructor of this class can determine the entire state of the flow given a partial state
Args:
gamma (float): Ratio of specific heats
use_degrees (bool, optional): If true then the angles provided to the class are in degrees.
Defaults to True.
shock_angle (float, optional): Angle of the oblique shock wave. Defaults to nan.
wedge_angle (float, optional): Angle of the wedge that is deflecting the flow. Defaults to
nan.
mn1 (float, optional): Normal component of mach number ahead of the shock. Defaults to nan.
mn2 (float, optional): Normal component of mach number behind the shock. Defaults to nan.
mach (float, optional): Mach number ahead of the shock. 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. Defaults to nan.
po2_po1 (float, optional): Ratio of total pressure to behind shock to ahead of shock.
Defaults to nan.
po2_p1 (float, optional): Ratio Total pressure behind shock to static pressure ahead of
shock. Defaults to nan.
m2 (float, optional): mach number behind shock wave. Defaults to nan.
shock_type (ShockType, optional): Describes whether the oblique shock is Weak or Strong.
Defaults to ShockType.WEAK.
Raises:
RuntimeError: If shock wave angle is found to be less than the mach wave angle at
RuntimeError: If the deflection angle is greater than the max deflection angle for the flow
GammaNotDefinedError: Raised if Gamma is undefined
InvalidOptionCombinationError: Raised if an invalid combination of parameters is given and
the flow state cannot be determined
Valid_Combinations_of_Parameters:
1: gamma, mach, shock angle\n
2. gamma, mach, wedge angle\n
2: gamma, mach normal 1, shock angle \n
3: gamma, mach behind shock, wedge angle, shock angle\n
4: gamma, shock angle, wedge angle\n
5: gamma, P2/P1, shock angle\n
6: gamma, Rho2/Rho1, shock angle\n
7: gamma, T2/T1, shock angle\n
8: gamma, P02/P01, shock angle\n
9: gamma, P02/P1, shock angle\n
10: gamma, dwn_strm_mach, shock angle\n
"""
# pylint: disable=too-many-instance-attributes
def __init__(
self,
gamma: float,
use_degrees: bool = True,
shock_angle: float = nan,
wedge_angle: float = nan,
mn1: float = nan,
mn2: float = nan,
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,
shock_type: ShockType = ShockType.WEAK,
) -> None:
# pylint: disable=too-many-arguments
# pylint: disable=too-many-statements
# pylint: disable=too-many-branches
# pylint: disable=too-many-locals
self.use_degrees = use_degrees
""" Angles passed to the constructor are in degrees"""
self.shock_angle = shock_angle
""" Angle Oblique shock"""
self.wedge_angle = wedge_angle
""" Angle of the flow deflection (wedge) angle"""
self.mach_normal_1 = mn1
""" The normal component of the mach number ahead the shock wave"""
self.mach_normal_2 = mn2
""" The normal component of the mach number behind the shock wave"""
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 to density before the shock rho2/rho1 """
self.t2_t1 = t2_t1
""" Ratio of temperature behind the shock to temperature 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.shock_type: ShockType = shock_type
""" The type of shock whether it is strong or weak """
self.precision = 4
""" Precision to use when printing output to the console defaults to four """
if self.use_degrees and check_value(self.shock_angle):
self.shock_angle = radians(self.shock_angle)
if self.use_degrees and check_value(self.wedge_angle):
self.wedge_angle = radians(self.wedge_angle)
if not check_value(self.gamma):
raise GammaNotDefinedError()
if check_value(self.mach, self.shock_angle):
mach_wave_angle = ObliqueShockRelations.calc_mach_wave_angle(self.mach)
if self.shock_angle < mach_wave_angle or self.shock_angle > radians(90):
sa = degrees(self.shock_angle)
mwa = degrees(mach_wave_angle)
m = self.mach
raise ValueError(
f"Shock Angle of [{sa}] must be between mach wave angle of [{mwa}] and 90"
f" degrees for mach [{m}]"
)
elif check_value(self.mach, self.wedge_angle):
max_shock_angle = ObliqueShockRelations.calc_max_shock_angle(self.mach, self.gamma)
max_wedge_angle = ObliqueShockRelations.calc_max_flow_deflection_angle(
max_shock_angle, self.mach, self.gamma
)
if self.wedge_angle > max_wedge_angle:
wa = degrees(self.wedge_angle)
mwa = degrees(max_wedge_angle)
m = self.mach
raise ValueError(
f"Wedge angle of [{wa}] is greater than a maximum wedge angle of [{mwa}] for"
f"mach [{m}]"
)
elif check_value(self.mach_normal_1, self.shock_angle):
if self.mach_normal_1 < 1:
raise ValueError(
"Normal Component of mach ahead of shock wave must be greater than 1"
)
self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock(
self.mach_normal_1, self.shock_angle
)
elif check_value(m2, self.wedge_angle, self.shock_angle):
self.mach_normal_2 = (
ObliqueShockRelations.calc_mach_normal_behind_shock_from_mach_behind_shock(
m2, self.shock_angle, self.wedge_angle
)
)
if self.mach_normal_2 > 1:
raise ValueError("Normal component of downstream mach number has to be less than 1")
self.mach_normal_1 = (
NormalShockRelations.calc_mach_before_normal_shock_from_mach_after_shock(
self.mach_normal_2, self.gamma
)
)
self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock(
self.mach_normal_1, self.shock_angle
)
elif check_value(self.shock_angle, self.wedge_angle):
self.mach = ObliqueShockRelations.calc_mach_from_theta_beta_mach(
self.shock_angle, self.wedge_angle, self.gamma
)
mach_angle = ObliqueShockRelations.calc_mach_wave_angle(self.mach)
max_shock_angle = ObliqueShockRelations.calc_max_shock_angle(self.mach, self.gamma)
max_deflection_angle = ObliqueShockRelations.calc_max_flow_deflection_angle(
max_shock_angle, self.mach, self.gamma
)
if mach_angle > self.shock_angle:
sa = round(self.shock_angle, 4)
ma = round(mach_angle, 4)
raise RuntimeError(
f"Shock Angle, {sa}, cannot be less than that of Mach Wave, {ma}"
)
if max_deflection_angle < self.wedge_angle:
wa = round(self.wedge_angle, 4)
mda = round(max_deflection_angle, 4)
raise RuntimeError(f"SHOCK DETACHED!! Deflection Angles: Given: {wa}\tMax: {mda}")
elif check_value(po2_p1, self.shock_angle):
self.mach_normal_1 = NormalShockRelations.calc_mach_from_po2_p1(po2_p1, self.gamma)
self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock(
self.mach_normal_1, self.shock_angle
)
elif check_value(p2_p1, self.shock_angle):
self.mach_normal_1 = NormalShockRelations.calc_mach_from_p2_p1(p2_p1, self.gamma)
self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock(
self.mach_normal_1, self.shock_angle
)
elif check_value(rho2_rho1, self.shock_angle):
self.mach_normal_1 = NormalShockRelations.calc_mach_from_rho2_rho1(
rho2_rho1, self.gamma
)
self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock(
self.mach_normal_1, self.shock_angle
)
elif check_value(t2_t1, self.shock_angle):
self.mach_normal_1 = NormalShockRelations.calc_mach_from_t2_t1(t2_t1, self.gamma)
self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock(
self.mach_normal_1, self.shock_angle
)
elif check_value(po2_po1, self.shock_angle):
self.mach_normal_1 = NormalShockRelations.calc_mach_from_po2_po1(po2_po1, self.gamma)
self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock(
self.mach_normal_1, self.shock_angle
)
elif check_value(self.mach_normal_2, self.shock_angle):
self.mach_normal_1 = (
NormalShockRelations.calc_mach_before_normal_shock_from_mach_after_shock(
self.mach_normal_2, self.gamma
)
)
self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock(
self.mach_normal_1, self.shock_angle
)
else:
raise InvalidOptionCombinationError()
if check_value(self.mach) and (
(check_value(self.shock_angle) or check_value(self.wedge_angle))
):
self._calc_state()
else:
raise RuntimeError(
"Values for mach and shock angle or wedge angle are needed to"
"determine flow state. For some reason those wasn't computed."
)
super().__init__(self.gamma, mach=self.mach_normal_1)
self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock(
self.mach_normal_1, self.shock_angle
)
self.mach_normal_2 = self.mach2
self.mach2 = ObliqueShockRelations.calc_mach_behind_shock(
self.mach_normal_2, self.wedge_angle, self.shock_angle
)
print(f"Here use degrees: {self.use_degrees} {self.wedge_angle} {self.shock_angle}")
if self.use_degrees:
self.wedge_angle = degrees(self.wedge_angle)
self.shock_angle = degrees(self.shock_angle)
print(f"Here use degrees: {self.use_degrees} {self.wedge_angle} {self.shock_angle}")
def _calc_state(self) -> None:
if check_value(self.wedge_angle):
if self.shock_type == ShockType.WEAK:
self.shock_angle = ObliqueShockRelations.calc_beta_from_theta_beta_mach_weak(
self.wedge_angle, self.mach, self.gamma
)
elif self.shock_type == ShockType.STRONG:
self.shock_angle = ObliqueShockRelations.calc_beta_from_theta_beta_mach_strong(
self.wedge_angle, self.mach, self.gamma
)
else:
raise ValueError(
f"Incorrect shock type specified -> [{self.shock_type}]. Choices: Strong, Weak"
)
elif check_value(self.shock_angle):
self.wedge_angle = ObliqueShockRelations.calc_theta_from_theta_beta_mach(
self.shock_angle, self.mach, self.gamma
)
self.mach_normal_1 = ObliqueShockRelations.calc_mach_normal_ahead_shock(
self.mach, self.shock_angle
)
def __str__(self) -> str:
return "".join(
[
named_header("Oblique Shock Relations at Mach", self.mach, self.precision),
seperator(),
named_subheader("Upstream Conditions"),
to_string(lcg.gamma, self.gamma, self.precision),
to_string("Mach", self.mach, self.precision, dot_line=True),
to_string("Mach Normal Component", self.mach_normal_1, self.precision),
to_string(
f"Flow Deflection Angle {lcg.theta}",
self.wedge_angle,
self.precision,
dot_line=True,
),
to_string(f"Shock Angle {lcg.beta}", self.shock_angle, self.precision),
to_string("Flow Turn Type", self.shock_type.name, self.precision),
seperator(),
named_subheader("Shock Jump Conditions"),
to_string("P2/P1", self.p2_p1, self.precision),
to_string(
"{}2/{}1".format(*[lcg.rho] * 2), 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),
seperator(),
named_subheader("Downstream Conditions"),
to_string("Mach", self.mach2, self.precision, dot_line=True),
to_string("Mach Normal Component", self.mach_normal_2, self.precision),
footer(),
]
)
@staticmethod
def calc_mach_normal_ahead_shock(mach: float, beta: float) -> float:
"""Calculates the normal component of the mach number ahead of the shock wave
Args:
mach (float): Mach number of flow ahead of shock wave
beta (float): Angle of oblique shock in radians
Raises:
ValueError: Raised if mach number is less than 1.0
Returns:
float: Normal component of upstream mach number
"""
if mach < 1.0:
raise ValueError("Normal Shocks Require a mach greater than 1")
mach_wave = ObliqueShockRelations.calc_mach_wave_angle(mach)
if abs(beta - mach_wave) < 1e-5:
return 1.0
if beta < mach_wave:
return nan
return mach * sin(beta)
@staticmethod
def calc_mach_ahead_shock_from_mach_normal_ahead_shock(
mach_normal_1: float, beta: float
) -> float:
"""Calculates the upstream mach number from the normal component of the upstream mach number
Args:
machNormal1 (float): Normal Component of mach number ahead of the shock wave
beta (float): Angle of oblique shock in radians
Returns:
float: Returns value of mach number of the flow ahead of the shock wave
"""
return mach_normal_1 / sin(beta)
@staticmethod
def calc_beta_from_mach_mach_normal_ahead_shock(mach: float, mach_normal_1: float) -> float:
"""
Calculates the Oblique shock angle from the normal component of the mach number that is
ahead of the shock wave
Args:
mach (float): Mach number of the flow ahead of the shock wave
mach_normal_1 (float): Normal Component of mach number of the flow that is ahead of an
oblique shock wave
Returns:
float: Oblique Shock Angle
"""
return asin(mach_normal_1 / mach)
@staticmethod
def calc_mach_behind_shock(mach_normal_2: float, theta: float, beta: float) -> float:
"""Calculates the Mach number behind the oblique shock wave
Args:
mach_normal_2 (float): Normal Component of the mach number behind the shock wave
theta (float): Flow Deflection Angle (radians) (Wedge angle)
beta (float): Oblique shock angle (radians)
Returns:
float: Mach number of flow behind the oblique shock
"""
return mach_normal_2 / sin(beta - theta)
@staticmethod
def calc_mach_normal_behind_shock_from_mach_behind_shock(
mach2: float, beta: float, theta: float
) -> float:
"""Calculates the normal component of the mach number behind the oblique shock
Args:
mach2 (float): Mach number of flow behind the oblique shock
beta (float): Oblique shock angle (radians)
theta (float): Flow deflections (Wedge) angle (radians)
Returns:
float: Normal component of mach numnber of the flow behind the shock wave
"""
return mach2 * sin(beta - theta)
@staticmethod
def calc_theta_from_theta_beta_mach(
beta: float, mach: float, gamma: float, offset: float = 0.0
) -> float:
"""Impliments the Theta-Beta-Mach (TBM) equation. Solves for Theta
Args:
beta (float): Oblique shock angle (radians)
mach (float): Mach number of flow ahead of the shock wave
gamma (float): Ratio of specific heats
offset (float, optional): [description]. Defaults to 0.0.
Returns:
float: Flow deflection (Wedge) angle (radians)
"""
m_sqr = pow(mach, 2)
num = m_sqr * pow(sin(beta), 2) - 1
denom = m_sqr * (gamma + cos(2 * beta)) + 2
theta = atan(2 * 1 / tan(beta) * num / denom) - offset
return theta
@staticmethod
def calc_beta_from_theta_beta_mach_weak(theta: float, mach: float, gamma: float) -> float:
"""
Impliments the Theta-Beta-Mach (TBM) equation. Solves for Beta (shock angle) assuming the
shock is weak
Args:
theta (float): Flow deflection (Wedge) angle (radians)
mach (float): Mach number of the flow ahead of the oblique shock
gamma (float): ratio of specific heats
Returns:
float: Oblique shock angle (radians)
"""
max_shock_angle = ObliqueShockRelations.calc_max_shock_angle(mach, gamma)
min_shock_angle = ObliqueShockRelations.calc_mach_wave_angle(mach)
return brenth(
ObliqueShockRelations.calc_theta_from_theta_beta_mach,
min_shock_angle,
max_shock_angle,
args=(mach, gamma, theta),
) # type: ignore
@staticmethod
def calc_beta_from_theta_beta_mach_strong(theta: float, mach: float, gamma: float) -> float:
"""
Impliments the Theta-Beta-Mach (TBM) equation. Solves for Beta (shock angle) assuming a
strong shock wave
Args:
theta (float): Flow deflection (Wedge) angle (radians)
mach (float): Mach number of the flow ahead of the oblique shock
gamma (float): ratio of specific heats
Returns:
float: Oblique shock angle (radians)
"""
maxshock_angle = ObliqueShockRelations.calc_max_shock_angle(mach, gamma)
return brenth(
ObliqueShockRelations.calc_theta_from_theta_beta_mach,
maxshock_angle,
radians(90),
args=(mach, gamma, theta),
) # type: ignore
@staticmethod
def calc_mach_from_theta_beta_mach(beta: float, theta: float, gamma: float) -> float:
"""Impliments the Theta-Beta-Mach (TBM) Equation. Solves for the mach number
Args:
beta (float): Oblique shock angle (radians)
theta (float): Flow deflection (wedge) angle (radians)
gamma (float): Ratio of specific heats
Returns:
float: Mach number of the flow ahead of the shock wave
"""
numerator = -2 * (1 + tan(theta) * tan(beta))
denominator = tan(theta) * tan(beta) * (gamma + cos(2 * beta)) - 2 * (sin(beta)) ** 2
return sqrt(numerator / denominator)
@staticmethod
def calc_max_flow_deflection_angle(maxshock_angle: float, mach: float, gamma: float) -> float:
"""Calculates the max flow deflection angle for a flow
Args:
maxshock_angle (float): Maximum oblique shock angle (radians)
mach (float): Mach number of flow ahead of the oblique shock
gamma (float): Ratio of specific heats
Returns:
float: Mac flow deflection angle (radians)
"""
msa = maxshock_angle
numerator = (pow(mach, 2) * (sin(msa)) ** 2 - 1) / tan(msa)
denominator = pow(mach, 2) * (gamma + 1) / 2 - pow(mach, 2) * (pow(sin(msa), 2)) + 1
return atan(numerator / denominator)
@staticmethod
def calc_max_shock_angle(mach: float, gamma: float) -> float:
"""Calculates the maximum oblique shock angle
Args:
mach (float): Mach number of flow ahead of the shock wave
gamma (float): Ratio of specific heats
Returns:
float: Maximum value of the oblique shock angle (radians)
"""
gp1 = gamma + 1
gm1 = gamma - 1
# splitting up of beta_max equation
isissq = gp1 * (1 + gm1 * pow(mach, 2) / 2 + gp1 / 16 * pow(mach, 4))
issq = 1 / (gamma * pow(mach, 2)) * (gp1 * pow(mach, 2) / 4 + sqrt(isissq) - 1)
return asin(sqrt(issq))
@staticmethod
def calc_mach_wave_angle(mach: float) -> float:
"""
Calculates the mach wave angle given the mach number
Args:
mach float: Mach number
Returns (float): Returns the mach wave angle in radians
"""
return asin(1 / mach)
@staticmethod
def calc_mach_from_mach_wave_angle(mach_angle: float) -> float:
"""Calculates the Mach number fromt he mach wave angle
Args:
mach_angle (float): Mach wave angle (mu) (radians)
Returns:
float: mach number
"""
return 1 / sin(mach_angle)
def plot_theta_beta_mach_chart(self) -> None:
"""Plots the Theta-Beta-Mach plot from the data already in the class"""
mach = self.mach
mach_wave_angle = degrees(ObliqueShockRelations.calc_mach_wave_angle(mach))
max_shock_angle = degrees(ObliqueShockRelations.calc_max_shock_angle(mach, self.gamma))
max_deflection_angle = degrees(
ObliqueShockRelations.calc_max_flow_deflection_angle(
radians(max_shock_angle), mach, self.gamma
)
)
weak_deflection_angles = np.linspace(0, max_deflection_angle - 0.1, 100)
weak_shock_angles = np.zeros(weak_deflection_angles.shape)
strong_shock_angles = np.zeros(weak_deflection_angles.shape)
for ii in range(weak_deflection_angles.shape[0]):
if weak_deflection_angles[ii] == 0:
weak_shock_angles[ii] = mach_wave_angle
strong_shock_angles[ii] = 90
continue
weak_shock_angles[ii] = degrees(
ObliqueShockRelations.calc_beta_from_theta_beta_mach_weak(
radians(weak_deflection_angles[ii]), mach, self.gamma
)
)
strong_shock_angles[ii] = degrees(
ObliqueShockRelations.calc_beta_from_theta_beta_mach_strong(
radians(weak_deflection_angles[ii]), mach, self.gamma
)
)
weak_deflection_angles = np.append(weak_deflection_angles, [max_deflection_angle])
strong_shock_angles = np.append(strong_shock_angles, [max_shock_angle])
weak_shock_angles = np.append(weak_shock_angles, [max_shock_angle])
# vertPointLine = np.linspace(0, self.shock_angle, 20)
# horzPointLine = np.linspace(0, self.wedge_angle, 20)
_, ax = plt.subplots(1, 1)
ax.plot(weak_deflection_angles, weak_shock_angles, label=" Oblique Weak Shock")
ax.plot(weak_deflection_angles, strong_shock_angles, label="Oblique Strong Shock")
shock_angle = degrees(self.shock_angle)
wedge_angle = degrees(self.wedge_angle)
ax.scatter(wedge_angle, shock_angle, label="This Flow", color="r")
# ax.plot(np.ones(vertPointLine.shape) * self.wedge_angle, vertPointLine, 'g')
# ax.plot(horzPointLine, np.ones(horzPointLine.shape) * self.shock_angle, 'g')
ax.annotate(
f"Shock {round(max_shock_angle, 2)}\nWedge {round(max_deflection_angle, 2)}",
xy=(max_deflection_angle, max_shock_angle),
xytext=(
max_deflection_angle + 0.02 * max_deflection_angle,
max_shock_angle + 0.1 * max_shock_angle,
),
arrowprops={"facecolor": "black", "shrink": 0.05},
)
ax.annotate(
f"Shock {round(shock_angle, 2)}\nWedge {round(wedge_angle, 2)}",
xy=(wedge_angle, shock_angle),
xytext=(wedge_angle - 0.2 * wedge_angle, shock_angle - 0.4 * shock_angle),
arrowprops={"facecolor": "black", "shrink": 0.05},
)
# ax.set_xlim(0, maxDeflectionAngle + 5)
# ax.set_ylim(0, 90)
ax.set_xticks(list(range(0, int(max_deflection_angle) + 5, 2)))
ax.set_yticks(list(range(0, 92, 2)))
ax.set_xlabel("Flow Deflection Angle, \u03B8 (\u00b0)")
ax.set_ylabel("Shock Anlge, \u03B2 (\u00b0)")
ax.set_title(f"Mach {round(self.mach, self.precision)} Flow")
ax.legend()
ax.grid()
plt.show()Classes
class ObliqueShockChoice (*args, **kwds)-
Valid Oblique Shock Initialization Choices
Expand source code
class ObliqueShockChoice(Enum): """Valid Oblique Shock Initialization Choices""" MACH_SHOCK_ANGLE = "gamma, mach, shock angle" MACH_WEDGE_ANGLE = "gamma, mach, wedge angle" MACH_N_1_SHOCK_ANGLE = "gamma, mach normal 1, shock angle " M2_WEDGE_SHOCK_ANGLE = "gamma, mach behind shock (M2), wedge angle, shock angle" P2_P1_SHOCK_ANGLE = "gamma, P2/P1, shock angle" RHO2_RHO1_SHOCK_ANGLE = "gamma, Rho2/Rho1, shock angle" T2_T1_SHOCK_ANGLE = "gamma, T2/T1, shock angle" PO2_PO1_SHOCK_ANGLE = "gamma, P02/P01, shock angle" PO2_P1_SHOCK_ANGLE = "gamma, P02/P1, shock angle" MN2_SHOCK_ANGLE = "gamma, MN2, shock angle"Ancestors
- enum.Enum
Class variables
var M2_WEDGE_SHOCK_ANGLEvar MACH_N_1_SHOCK_ANGLEvar MACH_SHOCK_ANGLEvar MACH_WEDGE_ANGLEvar MN2_SHOCK_ANGLEvar P2_P1_SHOCK_ANGLEvar PO2_P1_SHOCK_ANGLEvar PO2_PO1_SHOCK_ANGLEvar RHO2_RHO1_SHOCK_ANGLEvar T2_T1_SHOCK_ANGLE
class ObliqueShockRelations (gamma: float, use_degrees: bool = True, shock_angle: float = nan, wedge_angle: float = nan, mn1: float = nan, mn2: float = nan, 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, shock_type: ShockType = ShockType.WEAK)-
This class is a collective name space for basic calculations regarding Oblique Shock Properties The constructor of this class can determine the entire state of the flow given a partial state
Args
gamma:float- Ratio of specific heats
use_degrees:bool, optional- If true then the angles provided to the class are in degrees. Defaults to True.
shock_angle:float, optional- Angle of the oblique shock wave. Defaults to nan.
wedge_angle:float, optional- Angle of the wedge that is deflecting the flow. Defaults to nan.
mn1:float, optional- Normal component of mach number ahead of the shock. Defaults to nan.
mn2:float, optional- Normal component of mach number behind the shock. Defaults to nan.
mach:float, optional- Mach number ahead of the shock. 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. Defaults to nan.
po2_po1:float, optional- Ratio of total pressure to behind shock to ahead of shock. Defaults to nan.
po2_p1:float, optional- Ratio Total pressure behind shock to static pressure ahead of shock. Defaults to nan.
m2:float, optional- mach number behind shock wave. Defaults to nan.
shock_type:ShockType, optional- Describes whether the oblique shock is Weak or Strong. Defaults to ShockType.WEAK.
Raises
RuntimeError- If shock wave angle is found to be less than the mach wave angle at
RuntimeError- If the deflection angle is greater than the max deflection angle for the flow
GammaNotDefinedError- Raised if Gamma is undefined
InvalidOptionCombinationError- Raised if an invalid combination of parameters is given and the flow state cannot be determined
Valid_Combinations_Of_Parameters
1: gamma, mach, shock angle
- gamma, mach, wedge angle
2: gamma, mach normal 1, shock angle
3: gamma, mach behind shock, wedge angle, shock angle
4: gamma, shock angle, wedge angle
5: gamma, P2/P1, shock angle
6: gamma, Rho2/Rho1, shock angle
7: gamma, T2/T1, shock angle
8: gamma, P02/P01, shock angle
9: gamma, P02/P1, shock angle
10: gamma, dwn_strm_mach, shock angle
Expand source code
class ObliqueShockRelations(NormalShockRelations): """ This class is a collective name space for basic calculations regarding Oblique Shock Properties The constructor of this class can determine the entire state of the flow given a partial state Args: gamma (float): Ratio of specific heats use_degrees (bool, optional): If true then the angles provided to the class are in degrees. Defaults to True. shock_angle (float, optional): Angle of the oblique shock wave. Defaults to nan. wedge_angle (float, optional): Angle of the wedge that is deflecting the flow. Defaults to nan. mn1 (float, optional): Normal component of mach number ahead of the shock. Defaults to nan. mn2 (float, optional): Normal component of mach number behind the shock. Defaults to nan. mach (float, optional): Mach number ahead of the shock. 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. Defaults to nan. po2_po1 (float, optional): Ratio of total pressure to behind shock to ahead of shock. Defaults to nan. po2_p1 (float, optional): Ratio Total pressure behind shock to static pressure ahead of shock. Defaults to nan. m2 (float, optional): mach number behind shock wave. Defaults to nan. shock_type (ShockType, optional): Describes whether the oblique shock is Weak or Strong. Defaults to ShockType.WEAK. Raises: RuntimeError: If shock wave angle is found to be less than the mach wave angle at RuntimeError: If the deflection angle is greater than the max deflection angle for the flow GammaNotDefinedError: Raised if Gamma is undefined InvalidOptionCombinationError: Raised if an invalid combination of parameters is given and the flow state cannot be determined Valid_Combinations_of_Parameters: 1: gamma, mach, shock angle\n 2. gamma, mach, wedge angle\n 2: gamma, mach normal 1, shock angle \n 3: gamma, mach behind shock, wedge angle, shock angle\n 4: gamma, shock angle, wedge angle\n 5: gamma, P2/P1, shock angle\n 6: gamma, Rho2/Rho1, shock angle\n 7: gamma, T2/T1, shock angle\n 8: gamma, P02/P01, shock angle\n 9: gamma, P02/P1, shock angle\n 10: gamma, dwn_strm_mach, shock angle\n """ # pylint: disable=too-many-instance-attributes def __init__( self, gamma: float, use_degrees: bool = True, shock_angle: float = nan, wedge_angle: float = nan, mn1: float = nan, mn2: float = nan, 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, shock_type: ShockType = ShockType.WEAK, ) -> None: # pylint: disable=too-many-arguments # pylint: disable=too-many-statements # pylint: disable=too-many-branches # pylint: disable=too-many-locals self.use_degrees = use_degrees """ Angles passed to the constructor are in degrees""" self.shock_angle = shock_angle """ Angle Oblique shock""" self.wedge_angle = wedge_angle """ Angle of the flow deflection (wedge) angle""" self.mach_normal_1 = mn1 """ The normal component of the mach number ahead the shock wave""" self.mach_normal_2 = mn2 """ The normal component of the mach number behind the shock wave""" 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 to density before the shock rho2/rho1 """ self.t2_t1 = t2_t1 """ Ratio of temperature behind the shock to temperature 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.shock_type: ShockType = shock_type """ The type of shock whether it is strong or weak """ self.precision = 4 """ Precision to use when printing output to the console defaults to four """ if self.use_degrees and check_value(self.shock_angle): self.shock_angle = radians(self.shock_angle) if self.use_degrees and check_value(self.wedge_angle): self.wedge_angle = radians(self.wedge_angle) if not check_value(self.gamma): raise GammaNotDefinedError() if check_value(self.mach, self.shock_angle): mach_wave_angle = ObliqueShockRelations.calc_mach_wave_angle(self.mach) if self.shock_angle < mach_wave_angle or self.shock_angle > radians(90): sa = degrees(self.shock_angle) mwa = degrees(mach_wave_angle) m = self.mach raise ValueError( f"Shock Angle of [{sa}] must be between mach wave angle of [{mwa}] and 90" f" degrees for mach [{m}]" ) elif check_value(self.mach, self.wedge_angle): max_shock_angle = ObliqueShockRelations.calc_max_shock_angle(self.mach, self.gamma) max_wedge_angle = ObliqueShockRelations.calc_max_flow_deflection_angle( max_shock_angle, self.mach, self.gamma ) if self.wedge_angle > max_wedge_angle: wa = degrees(self.wedge_angle) mwa = degrees(max_wedge_angle) m = self.mach raise ValueError( f"Wedge angle of [{wa}] is greater than a maximum wedge angle of [{mwa}] for" f"mach [{m}]" ) elif check_value(self.mach_normal_1, self.shock_angle): if self.mach_normal_1 < 1: raise ValueError( "Normal Component of mach ahead of shock wave must be greater than 1" ) self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock( self.mach_normal_1, self.shock_angle ) elif check_value(m2, self.wedge_angle, self.shock_angle): self.mach_normal_2 = ( ObliqueShockRelations.calc_mach_normal_behind_shock_from_mach_behind_shock( m2, self.shock_angle, self.wedge_angle ) ) if self.mach_normal_2 > 1: raise ValueError("Normal component of downstream mach number has to be less than 1") self.mach_normal_1 = ( NormalShockRelations.calc_mach_before_normal_shock_from_mach_after_shock( self.mach_normal_2, self.gamma ) ) self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock( self.mach_normal_1, self.shock_angle ) elif check_value(self.shock_angle, self.wedge_angle): self.mach = ObliqueShockRelations.calc_mach_from_theta_beta_mach( self.shock_angle, self.wedge_angle, self.gamma ) mach_angle = ObliqueShockRelations.calc_mach_wave_angle(self.mach) max_shock_angle = ObliqueShockRelations.calc_max_shock_angle(self.mach, self.gamma) max_deflection_angle = ObliqueShockRelations.calc_max_flow_deflection_angle( max_shock_angle, self.mach, self.gamma ) if mach_angle > self.shock_angle: sa = round(self.shock_angle, 4) ma = round(mach_angle, 4) raise RuntimeError( f"Shock Angle, {sa}, cannot be less than that of Mach Wave, {ma}" ) if max_deflection_angle < self.wedge_angle: wa = round(self.wedge_angle, 4) mda = round(max_deflection_angle, 4) raise RuntimeError(f"SHOCK DETACHED!! Deflection Angles: Given: {wa}\tMax: {mda}") elif check_value(po2_p1, self.shock_angle): self.mach_normal_1 = NormalShockRelations.calc_mach_from_po2_p1(po2_p1, self.gamma) self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock( self.mach_normal_1, self.shock_angle ) elif check_value(p2_p1, self.shock_angle): self.mach_normal_1 = NormalShockRelations.calc_mach_from_p2_p1(p2_p1, self.gamma) self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock( self.mach_normal_1, self.shock_angle ) elif check_value(rho2_rho1, self.shock_angle): self.mach_normal_1 = NormalShockRelations.calc_mach_from_rho2_rho1( rho2_rho1, self.gamma ) self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock( self.mach_normal_1, self.shock_angle ) elif check_value(t2_t1, self.shock_angle): self.mach_normal_1 = NormalShockRelations.calc_mach_from_t2_t1(t2_t1, self.gamma) self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock( self.mach_normal_1, self.shock_angle ) elif check_value(po2_po1, self.shock_angle): self.mach_normal_1 = NormalShockRelations.calc_mach_from_po2_po1(po2_po1, self.gamma) self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock( self.mach_normal_1, self.shock_angle ) elif check_value(self.mach_normal_2, self.shock_angle): self.mach_normal_1 = ( NormalShockRelations.calc_mach_before_normal_shock_from_mach_after_shock( self.mach_normal_2, self.gamma ) ) self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock( self.mach_normal_1, self.shock_angle ) else: raise InvalidOptionCombinationError() if check_value(self.mach) and ( (check_value(self.shock_angle) or check_value(self.wedge_angle)) ): self._calc_state() else: raise RuntimeError( "Values for mach and shock angle or wedge angle are needed to" "determine flow state. For some reason those wasn't computed." ) super().__init__(self.gamma, mach=self.mach_normal_1) self.mach = ObliqueShockRelations.calc_mach_ahead_shock_from_mach_normal_ahead_shock( self.mach_normal_1, self.shock_angle ) self.mach_normal_2 = self.mach2 self.mach2 = ObliqueShockRelations.calc_mach_behind_shock( self.mach_normal_2, self.wedge_angle, self.shock_angle ) print(f"Here use degrees: {self.use_degrees} {self.wedge_angle} {self.shock_angle}") if self.use_degrees: self.wedge_angle = degrees(self.wedge_angle) self.shock_angle = degrees(self.shock_angle) print(f"Here use degrees: {self.use_degrees} {self.wedge_angle} {self.shock_angle}") def _calc_state(self) -> None: if check_value(self.wedge_angle): if self.shock_type == ShockType.WEAK: self.shock_angle = ObliqueShockRelations.calc_beta_from_theta_beta_mach_weak( self.wedge_angle, self.mach, self.gamma ) elif self.shock_type == ShockType.STRONG: self.shock_angle = ObliqueShockRelations.calc_beta_from_theta_beta_mach_strong( self.wedge_angle, self.mach, self.gamma ) else: raise ValueError( f"Incorrect shock type specified -> [{self.shock_type}]. Choices: Strong, Weak" ) elif check_value(self.shock_angle): self.wedge_angle = ObliqueShockRelations.calc_theta_from_theta_beta_mach( self.shock_angle, self.mach, self.gamma ) self.mach_normal_1 = ObliqueShockRelations.calc_mach_normal_ahead_shock( self.mach, self.shock_angle ) def __str__(self) -> str: return "".join( [ named_header("Oblique Shock Relations at Mach", self.mach, self.precision), seperator(), named_subheader("Upstream Conditions"), to_string(lcg.gamma, self.gamma, self.precision), to_string("Mach", self.mach, self.precision, dot_line=True), to_string("Mach Normal Component", self.mach_normal_1, self.precision), to_string( f"Flow Deflection Angle {lcg.theta}", self.wedge_angle, self.precision, dot_line=True, ), to_string(f"Shock Angle {lcg.beta}", self.shock_angle, self.precision), to_string("Flow Turn Type", self.shock_type.name, self.precision), seperator(), named_subheader("Shock Jump Conditions"), to_string("P2/P1", self.p2_p1, self.precision), to_string( "{}2/{}1".format(*[lcg.rho] * 2), 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), seperator(), named_subheader("Downstream Conditions"), to_string("Mach", self.mach2, self.precision, dot_line=True), to_string("Mach Normal Component", self.mach_normal_2, self.precision), footer(), ] ) @staticmethod def calc_mach_normal_ahead_shock(mach: float, beta: float) -> float: """Calculates the normal component of the mach number ahead of the shock wave Args: mach (float): Mach number of flow ahead of shock wave beta (float): Angle of oblique shock in radians Raises: ValueError: Raised if mach number is less than 1.0 Returns: float: Normal component of upstream mach number """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") mach_wave = ObliqueShockRelations.calc_mach_wave_angle(mach) if abs(beta - mach_wave) < 1e-5: return 1.0 if beta < mach_wave: return nan return mach * sin(beta) @staticmethod def calc_mach_ahead_shock_from_mach_normal_ahead_shock( mach_normal_1: float, beta: float ) -> float: """Calculates the upstream mach number from the normal component of the upstream mach number Args: machNormal1 (float): Normal Component of mach number ahead of the shock wave beta (float): Angle of oblique shock in radians Returns: float: Returns value of mach number of the flow ahead of the shock wave """ return mach_normal_1 / sin(beta) @staticmethod def calc_beta_from_mach_mach_normal_ahead_shock(mach: float, mach_normal_1: float) -> float: """ Calculates the Oblique shock angle from the normal component of the mach number that is ahead of the shock wave Args: mach (float): Mach number of the flow ahead of the shock wave mach_normal_1 (float): Normal Component of mach number of the flow that is ahead of an oblique shock wave Returns: float: Oblique Shock Angle """ return asin(mach_normal_1 / mach) @staticmethod def calc_mach_behind_shock(mach_normal_2: float, theta: float, beta: float) -> float: """Calculates the Mach number behind the oblique shock wave Args: mach_normal_2 (float): Normal Component of the mach number behind the shock wave theta (float): Flow Deflection Angle (radians) (Wedge angle) beta (float): Oblique shock angle (radians) Returns: float: Mach number of flow behind the oblique shock """ return mach_normal_2 / sin(beta - theta) @staticmethod def calc_mach_normal_behind_shock_from_mach_behind_shock( mach2: float, beta: float, theta: float ) -> float: """Calculates the normal component of the mach number behind the oblique shock Args: mach2 (float): Mach number of flow behind the oblique shock beta (float): Oblique shock angle (radians) theta (float): Flow deflections (Wedge) angle (radians) Returns: float: Normal component of mach numnber of the flow behind the shock wave """ return mach2 * sin(beta - theta) @staticmethod def calc_theta_from_theta_beta_mach( beta: float, mach: float, gamma: float, offset: float = 0.0 ) -> float: """Impliments the Theta-Beta-Mach (TBM) equation. Solves for Theta Args: beta (float): Oblique shock angle (radians) mach (float): Mach number of flow ahead of the shock wave gamma (float): Ratio of specific heats offset (float, optional): [description]. Defaults to 0.0. Returns: float: Flow deflection (Wedge) angle (radians) """ m_sqr = pow(mach, 2) num = m_sqr * pow(sin(beta), 2) - 1 denom = m_sqr * (gamma + cos(2 * beta)) + 2 theta = atan(2 * 1 / tan(beta) * num / denom) - offset return theta @staticmethod def calc_beta_from_theta_beta_mach_weak(theta: float, mach: float, gamma: float) -> float: """ Impliments the Theta-Beta-Mach (TBM) equation. Solves for Beta (shock angle) assuming the shock is weak Args: theta (float): Flow deflection (Wedge) angle (radians) mach (float): Mach number of the flow ahead of the oblique shock gamma (float): ratio of specific heats Returns: float: Oblique shock angle (radians) """ max_shock_angle = ObliqueShockRelations.calc_max_shock_angle(mach, gamma) min_shock_angle = ObliqueShockRelations.calc_mach_wave_angle(mach) return brenth( ObliqueShockRelations.calc_theta_from_theta_beta_mach, min_shock_angle, max_shock_angle, args=(mach, gamma, theta), ) # type: ignore @staticmethod def calc_beta_from_theta_beta_mach_strong(theta: float, mach: float, gamma: float) -> float: """ Impliments the Theta-Beta-Mach (TBM) equation. Solves for Beta (shock angle) assuming a strong shock wave Args: theta (float): Flow deflection (Wedge) angle (radians) mach (float): Mach number of the flow ahead of the oblique shock gamma (float): ratio of specific heats Returns: float: Oblique shock angle (radians) """ maxshock_angle = ObliqueShockRelations.calc_max_shock_angle(mach, gamma) return brenth( ObliqueShockRelations.calc_theta_from_theta_beta_mach, maxshock_angle, radians(90), args=(mach, gamma, theta), ) # type: ignore @staticmethod def calc_mach_from_theta_beta_mach(beta: float, theta: float, gamma: float) -> float: """Impliments the Theta-Beta-Mach (TBM) Equation. Solves for the mach number Args: beta (float): Oblique shock angle (radians) theta (float): Flow deflection (wedge) angle (radians) gamma (float): Ratio of specific heats Returns: float: Mach number of the flow ahead of the shock wave """ numerator = -2 * (1 + tan(theta) * tan(beta)) denominator = tan(theta) * tan(beta) * (gamma + cos(2 * beta)) - 2 * (sin(beta)) ** 2 return sqrt(numerator / denominator) @staticmethod def calc_max_flow_deflection_angle(maxshock_angle: float, mach: float, gamma: float) -> float: """Calculates the max flow deflection angle for a flow Args: maxshock_angle (float): Maximum oblique shock angle (radians) mach (float): Mach number of flow ahead of the oblique shock gamma (float): Ratio of specific heats Returns: float: Mac flow deflection angle (radians) """ msa = maxshock_angle numerator = (pow(mach, 2) * (sin(msa)) ** 2 - 1) / tan(msa) denominator = pow(mach, 2) * (gamma + 1) / 2 - pow(mach, 2) * (pow(sin(msa), 2)) + 1 return atan(numerator / denominator) @staticmethod def calc_max_shock_angle(mach: float, gamma: float) -> float: """Calculates the maximum oblique shock angle Args: mach (float): Mach number of flow ahead of the shock wave gamma (float): Ratio of specific heats Returns: float: Maximum value of the oblique shock angle (radians) """ gp1 = gamma + 1 gm1 = gamma - 1 # splitting up of beta_max equation isissq = gp1 * (1 + gm1 * pow(mach, 2) / 2 + gp1 / 16 * pow(mach, 4)) issq = 1 / (gamma * pow(mach, 2)) * (gp1 * pow(mach, 2) / 4 + sqrt(isissq) - 1) return asin(sqrt(issq)) @staticmethod def calc_mach_wave_angle(mach: float) -> float: """ Calculates the mach wave angle given the mach number Args: mach float: Mach number Returns (float): Returns the mach wave angle in radians """ return asin(1 / mach) @staticmethod def calc_mach_from_mach_wave_angle(mach_angle: float) -> float: """Calculates the Mach number fromt he mach wave angle Args: mach_angle (float): Mach wave angle (mu) (radians) Returns: float: mach number """ return 1 / sin(mach_angle) def plot_theta_beta_mach_chart(self) -> None: """Plots the Theta-Beta-Mach plot from the data already in the class""" mach = self.mach mach_wave_angle = degrees(ObliqueShockRelations.calc_mach_wave_angle(mach)) max_shock_angle = degrees(ObliqueShockRelations.calc_max_shock_angle(mach, self.gamma)) max_deflection_angle = degrees( ObliqueShockRelations.calc_max_flow_deflection_angle( radians(max_shock_angle), mach, self.gamma ) ) weak_deflection_angles = np.linspace(0, max_deflection_angle - 0.1, 100) weak_shock_angles = np.zeros(weak_deflection_angles.shape) strong_shock_angles = np.zeros(weak_deflection_angles.shape) for ii in range(weak_deflection_angles.shape[0]): if weak_deflection_angles[ii] == 0: weak_shock_angles[ii] = mach_wave_angle strong_shock_angles[ii] = 90 continue weak_shock_angles[ii] = degrees( ObliqueShockRelations.calc_beta_from_theta_beta_mach_weak( radians(weak_deflection_angles[ii]), mach, self.gamma ) ) strong_shock_angles[ii] = degrees( ObliqueShockRelations.calc_beta_from_theta_beta_mach_strong( radians(weak_deflection_angles[ii]), mach, self.gamma ) ) weak_deflection_angles = np.append(weak_deflection_angles, [max_deflection_angle]) strong_shock_angles = np.append(strong_shock_angles, [max_shock_angle]) weak_shock_angles = np.append(weak_shock_angles, [max_shock_angle]) # vertPointLine = np.linspace(0, self.shock_angle, 20) # horzPointLine = np.linspace(0, self.wedge_angle, 20) _, ax = plt.subplots(1, 1) ax.plot(weak_deflection_angles, weak_shock_angles, label=" Oblique Weak Shock") ax.plot(weak_deflection_angles, strong_shock_angles, label="Oblique Strong Shock") shock_angle = degrees(self.shock_angle) wedge_angle = degrees(self.wedge_angle) ax.scatter(wedge_angle, shock_angle, label="This Flow", color="r") # ax.plot(np.ones(vertPointLine.shape) * self.wedge_angle, vertPointLine, 'g') # ax.plot(horzPointLine, np.ones(horzPointLine.shape) * self.shock_angle, 'g') ax.annotate( f"Shock {round(max_shock_angle, 2)}\nWedge {round(max_deflection_angle, 2)}", xy=(max_deflection_angle, max_shock_angle), xytext=( max_deflection_angle + 0.02 * max_deflection_angle, max_shock_angle + 0.1 * max_shock_angle, ), arrowprops={"facecolor": "black", "shrink": 0.05}, ) ax.annotate( f"Shock {round(shock_angle, 2)}\nWedge {round(wedge_angle, 2)}", xy=(wedge_angle, shock_angle), xytext=(wedge_angle - 0.2 * wedge_angle, shock_angle - 0.4 * shock_angle), arrowprops={"facecolor": "black", "shrink": 0.05}, ) # ax.set_xlim(0, maxDeflectionAngle + 5) # ax.set_ylim(0, 90) ax.set_xticks(list(range(0, int(max_deflection_angle) + 5, 2))) ax.set_yticks(list(range(0, 92, 2))) ax.set_xlabel("Flow Deflection Angle, \u03B8 (\u00b0)") ax.set_ylabel("Shock Anlge, \u03B2 (\u00b0)") ax.set_title(f"Mach {round(self.mach, self.precision)} Flow") ax.legend() ax.grid() plt.show()Ancestors
Static methods
def calc_beta_from_mach_mach_normal_ahead_shock(mach: float, mach_normal_1: float) ‑> float-
Calculates the Oblique shock angle from the normal component of the mach number that is ahead of the shock wave
Args
mach:float- Mach number of the flow ahead of the shock wave
mach_normal_1 (float): Normal Component of mach number of the flow that is ahead of an oblique shock wave
Returns
float- Oblique Shock Angle
Expand source code
@staticmethod def calc_beta_from_mach_mach_normal_ahead_shock(mach: float, mach_normal_1: float) -> float: """ Calculates the Oblique shock angle from the normal component of the mach number that is ahead of the shock wave Args: mach (float): Mach number of the flow ahead of the shock wave mach_normal_1 (float): Normal Component of mach number of the flow that is ahead of an oblique shock wave Returns: float: Oblique Shock Angle """ return asin(mach_normal_1 / mach) def calc_beta_from_theta_beta_mach_strong(theta: float, mach: float, gamma: float) ‑> float-
Impliments the Theta-Beta-Mach (TBM) equation. Solves for Beta (shock angle) assuming a strong shock wave
Args
theta:float- Flow deflection (Wedge) angle (radians)
mach:float- Mach number of the flow ahead of the oblique shock
gamma:float- ratio of specific heats
Returns
float- Oblique shock angle (radians)
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@staticmethod def calc_beta_from_theta_beta_mach_strong(theta: float, mach: float, gamma: float) -> float: """ Impliments the Theta-Beta-Mach (TBM) equation. Solves for Beta (shock angle) assuming a strong shock wave Args: theta (float): Flow deflection (Wedge) angle (radians) mach (float): Mach number of the flow ahead of the oblique shock gamma (float): ratio of specific heats Returns: float: Oblique shock angle (radians) """ maxshock_angle = ObliqueShockRelations.calc_max_shock_angle(mach, gamma) return brenth( ObliqueShockRelations.calc_theta_from_theta_beta_mach, maxshock_angle, radians(90), args=(mach, gamma, theta), ) # type: ignore def calc_beta_from_theta_beta_mach_weak(theta: float, mach: float, gamma: float) ‑> float-
Impliments the Theta-Beta-Mach (TBM) equation. Solves for Beta (shock angle) assuming the shock is weak
Args
theta:float- Flow deflection (Wedge) angle (radians)
mach:float- Mach number of the flow ahead of the oblique shock
gamma:float- ratio of specific heats
Returns
float- Oblique shock angle (radians)
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@staticmethod def calc_beta_from_theta_beta_mach_weak(theta: float, mach: float, gamma: float) -> float: """ Impliments the Theta-Beta-Mach (TBM) equation. Solves for Beta (shock angle) assuming the shock is weak Args: theta (float): Flow deflection (Wedge) angle (radians) mach (float): Mach number of the flow ahead of the oblique shock gamma (float): ratio of specific heats Returns: float: Oblique shock angle (radians) """ max_shock_angle = ObliqueShockRelations.calc_max_shock_angle(mach, gamma) min_shock_angle = ObliqueShockRelations.calc_mach_wave_angle(mach) return brenth( ObliqueShockRelations.calc_theta_from_theta_beta_mach, min_shock_angle, max_shock_angle, args=(mach, gamma, theta), ) # type: ignore def calc_mach_ahead_shock_from_mach_normal_ahead_shock(mach_normal_1: float, beta: float) ‑> float-
Calculates the upstream mach number from the normal component of the upstream mach number
Args
machNormal1:float- Normal Component of mach number ahead of the shock wave
beta:float- Angle of oblique shock in radians
Returns
float- Returns value of mach number of the flow ahead of the shock wave
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@staticmethod def calc_mach_ahead_shock_from_mach_normal_ahead_shock( mach_normal_1: float, beta: float ) -> float: """Calculates the upstream mach number from the normal component of the upstream mach number Args: machNormal1 (float): Normal Component of mach number ahead of the shock wave beta (float): Angle of oblique shock in radians Returns: float: Returns value of mach number of the flow ahead of the shock wave """ return mach_normal_1 / sin(beta) def calc_mach_behind_shock(mach_normal_2: float, theta: float, beta: float) ‑> float-
Calculates the Mach number behind the oblique shock wave
Args
mach_normal_2:float- Normal Component of the mach number behind the shock wave
theta:float- Flow Deflection Angle (radians) (Wedge angle)
beta:float- Oblique shock angle (radians)
Returns
float- Mach number of flow behind the oblique shock
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@staticmethod def calc_mach_behind_shock(mach_normal_2: float, theta: float, beta: float) -> float: """Calculates the Mach number behind the oblique shock wave Args: mach_normal_2 (float): Normal Component of the mach number behind the shock wave theta (float): Flow Deflection Angle (radians) (Wedge angle) beta (float): Oblique shock angle (radians) Returns: float: Mach number of flow behind the oblique shock """ return mach_normal_2 / sin(beta - theta) def calc_mach_from_mach_wave_angle(mach_angle: float) ‑> float-
Calculates the Mach number fromt he mach wave angle
Args
mach_angle:float- Mach wave angle (mu) (radians)
Returns
float- mach number
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@staticmethod def calc_mach_from_mach_wave_angle(mach_angle: float) -> float: """Calculates the Mach number fromt he mach wave angle Args: mach_angle (float): Mach wave angle (mu) (radians) Returns: float: mach number """ return 1 / sin(mach_angle) def calc_mach_from_theta_beta_mach(beta: float, theta: float, gamma: float) ‑> float-
Impliments the Theta-Beta-Mach (TBM) Equation. Solves for the mach number
Args
beta:float- Oblique shock angle (radians)
theta:float- Flow deflection (wedge) angle (radians)
gamma:float- Ratio of specific heats
Returns
float- Mach number of the flow ahead of the shock wave
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@staticmethod def calc_mach_from_theta_beta_mach(beta: float, theta: float, gamma: float) -> float: """Impliments the Theta-Beta-Mach (TBM) Equation. Solves for the mach number Args: beta (float): Oblique shock angle (radians) theta (float): Flow deflection (wedge) angle (radians) gamma (float): Ratio of specific heats Returns: float: Mach number of the flow ahead of the shock wave """ numerator = -2 * (1 + tan(theta) * tan(beta)) denominator = tan(theta) * tan(beta) * (gamma + cos(2 * beta)) - 2 * (sin(beta)) ** 2 return sqrt(numerator / denominator) def calc_mach_normal_ahead_shock(mach: float, beta: float) ‑> float-
Calculates the normal component of the mach number ahead of the shock wave
Args
mach:float- Mach number of flow ahead of shock wave
beta:float- Angle of oblique shock in radians
Raises
ValueError- Raised if mach number is less than 1.0
Returns
float- Normal component of upstream mach number
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@staticmethod def calc_mach_normal_ahead_shock(mach: float, beta: float) -> float: """Calculates the normal component of the mach number ahead of the shock wave Args: mach (float): Mach number of flow ahead of shock wave beta (float): Angle of oblique shock in radians Raises: ValueError: Raised if mach number is less than 1.0 Returns: float: Normal component of upstream mach number """ if mach < 1.0: raise ValueError("Normal Shocks Require a mach greater than 1") mach_wave = ObliqueShockRelations.calc_mach_wave_angle(mach) if abs(beta - mach_wave) < 1e-5: return 1.0 if beta < mach_wave: return nan return mach * sin(beta) def calc_mach_normal_behind_shock_from_mach_behind_shock(mach2: float, beta: float, theta: float) ‑> float-
Calculates the normal component of the mach number behind the oblique shock
Args
mach2:float- Mach number of flow behind the oblique shock
beta:float- Oblique shock angle (radians)
theta:float- Flow deflections (Wedge) angle (radians)
Returns
float- Normal component of mach numnber of the flow behind the shock wave
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@staticmethod def calc_mach_normal_behind_shock_from_mach_behind_shock( mach2: float, beta: float, theta: float ) -> float: """Calculates the normal component of the mach number behind the oblique shock Args: mach2 (float): Mach number of flow behind the oblique shock beta (float): Oblique shock angle (radians) theta (float): Flow deflections (Wedge) angle (radians) Returns: float: Normal component of mach numnber of the flow behind the shock wave """ return mach2 * sin(beta - theta) def calc_mach_wave_angle(mach: float) ‑> float-
Calculates the mach wave angle given the mach number
Args
mach float: Mach number Returns (float): Returns the mach wave angle in radians
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@staticmethod def calc_mach_wave_angle(mach: float) -> float: """ Calculates the mach wave angle given the mach number Args: mach float: Mach number Returns (float): Returns the mach wave angle in radians """ return asin(1 / mach) def calc_max_flow_deflection_angle(maxshock_angle: float, mach: float, gamma: float) ‑> float-
Calculates the max flow deflection angle for a flow
Args
maxshock_angle:float- Maximum oblique shock angle (radians)
mach:float- Mach number of flow ahead of the oblique shock
gamma:float- Ratio of specific heats
Returns
float- Mac flow deflection angle (radians)
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@staticmethod def calc_max_flow_deflection_angle(maxshock_angle: float, mach: float, gamma: float) -> float: """Calculates the max flow deflection angle for a flow Args: maxshock_angle (float): Maximum oblique shock angle (radians) mach (float): Mach number of flow ahead of the oblique shock gamma (float): Ratio of specific heats Returns: float: Mac flow deflection angle (radians) """ msa = maxshock_angle numerator = (pow(mach, 2) * (sin(msa)) ** 2 - 1) / tan(msa) denominator = pow(mach, 2) * (gamma + 1) / 2 - pow(mach, 2) * (pow(sin(msa), 2)) + 1 return atan(numerator / denominator) def calc_max_shock_angle(mach: float, gamma: float) ‑> float-
Calculates the maximum oblique shock angle
Args
mach:float- Mach number of flow ahead of the shock wave
gamma:float- Ratio of specific heats
Returns
float- Maximum value of the oblique shock angle (radians)
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@staticmethod def calc_max_shock_angle(mach: float, gamma: float) -> float: """Calculates the maximum oblique shock angle Args: mach (float): Mach number of flow ahead of the shock wave gamma (float): Ratio of specific heats Returns: float: Maximum value of the oblique shock angle (radians) """ gp1 = gamma + 1 gm1 = gamma - 1 # splitting up of beta_max equation isissq = gp1 * (1 + gm1 * pow(mach, 2) / 2 + gp1 / 16 * pow(mach, 4)) issq = 1 / (gamma * pow(mach, 2)) * (gp1 * pow(mach, 2) / 4 + sqrt(isissq) - 1) return asin(sqrt(issq)) def calc_theta_from_theta_beta_mach(beta: float, mach: float, gamma: float, offset: float = 0.0) ‑> float-
Impliments the Theta-Beta-Mach (TBM) equation. Solves for Theta
Args
beta:float- Oblique shock angle (radians)
mach:float- Mach number of flow ahead of the shock wave
gamma:float- Ratio of specific heats
offset:float, optional- [description]. Defaults to 0.0.
Returns
float- Flow deflection (Wedge) angle (radians)
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@staticmethod def calc_theta_from_theta_beta_mach( beta: float, mach: float, gamma: float, offset: float = 0.0 ) -> float: """Impliments the Theta-Beta-Mach (TBM) equation. Solves for Theta Args: beta (float): Oblique shock angle (radians) mach (float): Mach number of flow ahead of the shock wave gamma (float): Ratio of specific heats offset (float, optional): [description]. Defaults to 0.0. Returns: float: Flow deflection (Wedge) angle (radians) """ m_sqr = pow(mach, 2) num = m_sqr * pow(sin(beta), 2) - 1 denom = m_sqr * (gamma + cos(2 * beta)) + 2 theta = atan(2 * 1 / tan(beta) * num / denom) - offset return theta
Instance variables
var mach_normal_1-
The normal component of the mach number ahead the shock wave
var mach_normal_2-
The normal component of the mach number behind the shock wave
var shock_angle-
Angle Oblique shock
var shock_type-
The type of shock whether it is strong or weak
var use_degrees-
Angles passed to the constructor are in degrees
var wedge_angle-
Angle of the flow deflection (wedge) angle
Methods
def plot_theta_beta_mach_chart(self) ‑> None-
Plots the Theta-Beta-Mach plot from the data already in the class
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def plot_theta_beta_mach_chart(self) -> None: """Plots the Theta-Beta-Mach plot from the data already in the class""" mach = self.mach mach_wave_angle = degrees(ObliqueShockRelations.calc_mach_wave_angle(mach)) max_shock_angle = degrees(ObliqueShockRelations.calc_max_shock_angle(mach, self.gamma)) max_deflection_angle = degrees( ObliqueShockRelations.calc_max_flow_deflection_angle( radians(max_shock_angle), mach, self.gamma ) ) weak_deflection_angles = np.linspace(0, max_deflection_angle - 0.1, 100) weak_shock_angles = np.zeros(weak_deflection_angles.shape) strong_shock_angles = np.zeros(weak_deflection_angles.shape) for ii in range(weak_deflection_angles.shape[0]): if weak_deflection_angles[ii] == 0: weak_shock_angles[ii] = mach_wave_angle strong_shock_angles[ii] = 90 continue weak_shock_angles[ii] = degrees( ObliqueShockRelations.calc_beta_from_theta_beta_mach_weak( radians(weak_deflection_angles[ii]), mach, self.gamma ) ) strong_shock_angles[ii] = degrees( ObliqueShockRelations.calc_beta_from_theta_beta_mach_strong( radians(weak_deflection_angles[ii]), mach, self.gamma ) ) weak_deflection_angles = np.append(weak_deflection_angles, [max_deflection_angle]) strong_shock_angles = np.append(strong_shock_angles, [max_shock_angle]) weak_shock_angles = np.append(weak_shock_angles, [max_shock_angle]) # vertPointLine = np.linspace(0, self.shock_angle, 20) # horzPointLine = np.linspace(0, self.wedge_angle, 20) _, ax = plt.subplots(1, 1) ax.plot(weak_deflection_angles, weak_shock_angles, label=" Oblique Weak Shock") ax.plot(weak_deflection_angles, strong_shock_angles, label="Oblique Strong Shock") shock_angle = degrees(self.shock_angle) wedge_angle = degrees(self.wedge_angle) ax.scatter(wedge_angle, shock_angle, label="This Flow", color="r") # ax.plot(np.ones(vertPointLine.shape) * self.wedge_angle, vertPointLine, 'g') # ax.plot(horzPointLine, np.ones(horzPointLine.shape) * self.shock_angle, 'g') ax.annotate( f"Shock {round(max_shock_angle, 2)}\nWedge {round(max_deflection_angle, 2)}", xy=(max_deflection_angle, max_shock_angle), xytext=( max_deflection_angle + 0.02 * max_deflection_angle, max_shock_angle + 0.1 * max_shock_angle, ), arrowprops={"facecolor": "black", "shrink": 0.05}, ) ax.annotate( f"Shock {round(shock_angle, 2)}\nWedge {round(wedge_angle, 2)}", xy=(wedge_angle, shock_angle), xytext=(wedge_angle - 0.2 * wedge_angle, shock_angle - 0.4 * shock_angle), arrowprops={"facecolor": "black", "shrink": 0.05}, ) # ax.set_xlim(0, maxDeflectionAngle + 5) # ax.set_ylim(0, 90) ax.set_xticks(list(range(0, int(max_deflection_angle) + 5, 2))) ax.set_yticks(list(range(0, 92, 2))) ax.set_xlabel("Flow Deflection Angle, \u03B8 (\u00b0)") ax.set_ylabel("Shock Anlge, \u03B2 (\u00b0)") ax.set_title(f"Mach {round(self.mach, self.precision)} Flow") ax.legend() ax.grid() plt.show()
Inherited members
NormalShockRelations:calc_mach_after_normal_shockcalc_mach_before_normal_shock_from_mach_after_shockcalc_mach_from_p2_p1calc_mach_from_po2_p1calc_mach_from_po2_po1calc_mach_from_rho2_rho1calc_mach_from_t2_t1calc_p2_p1calc_po2_p1calc_po2_po1calc_rho2_rho1calc_t2_t1gammamachmach2p2_p1po2_p1po2_po1precisionrho2_rho1t2_t1