Module CompAero.rayleigh_flow_relations
This module contains the relationships for rayleigh flows
Expand source code
"""
This module contains the relationships for rayleigh flows
"""
from enum import Enum
from math import nan
from colorama import Back, Fore
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.types import FlowState
class RayleighFlowChoice(Enum):
"""Valid choices for Rayleigh Flow initialization"""
GAMMA_MACH = "gamma, mach"
GAMMA_T_T_ST = "gamma, T/T*, flowtype"
GAMMA_P_P_ST = "gamma, P/P*"
GAMMA_RHO_RHO_ST = "gamma, rho/rho*"
GAMMA_PO_PO_ST = "gamma, P0/P0*, flowtype"
GAMMA_TO_TO_FLOW_TYPE = "gamma, T0/T0*, flowtype"
GAMMA_U_U_ST = "gamma, U/U*"
RAYLEIGH_FLOW_VALID_OPTIONS = [x.value for x in RayleighFlowChoice]
class RayleighFlowRelations:
# pylint: disable=too-many-instance-attributes
"""
This class is a collective name space for basic calculations regarding Fanno flows.
Args:
gamma (float): ratio of specific heats
mach (float, optional): mach number of the flow. Defaults to nan.
t_t_st (float, optional): Ratio of Temperature to sonic temperature. Defaults to nan.
p_p_st (float, optional): Ratio of Pressure to sonic pressure. Defaults to nan.
rho_rho_st (float, optional): Ratio of density to sonic density. Defaults to nan.
po_po_st (float, optional): Total pressure to sonic total pressure ratio. Defaults to nan.
to_to_star (float, optional): Ratio of Total Tempto sonic total temp. Defaults to nan.
u_u_st (float, optional): Velocity to sonic Velocity. Defaults to nan.
flow_type (FlowState, optional): States wether the flow is subsonic or supersonic. Used
for Area Ratio Calculations. Defaults to
FlowState.SUPER_SONIC.
Raises:
GammaNotDefinedError: Raised if Gamma is undefined
InvalidOptionCombinationError: Raised if an invalid combination of parameters is given
and flow state cannot be determined
Useage:
To use this class pass gamma and one of the known parameters of the flow
Valid_Combinations_of_Parameters:
1: gamma, mach\n
2: gamma, T/T*, flowtype (flow type defaults to super sonic)\n
3: gamma, P/P*\n
4: gamma, rho/rho*\n
5: gamma, P0/P0*, flowtype (flow type defaults to super sonic)\n
6: gamma, T0/T0*, flowtype (flow type defaults to super sonic)\n
7: gamma, U/U*\n
"""
def __init__(
self,
gamma: float,
mach: float = nan,
t_t_st: float = nan,
p_p_st: float = nan,
rho_rho_st: float = nan,
po_po_st: float = nan,
to_to_st: float = nan,
u_u_st: float = nan,
flow_type: FlowState = FlowState.SUPER_SONIC,
) -> 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.t_t_st = t_t_st
""" Ratio of temperature to the sonic temperature T/T*"""
self.p_p_st = p_p_st
""" Ratio of pressure to the sonic pressure P/P*"""
self.rho_rho_st = rho_rho_st
""" Ratio of the density to the sonic density rho/rho* """
self.po_po_st = po_po_st
""" Ratio of the stagnation pressure to the sonic stagnation pressure P0/P0*"""
self.u_u_st = u_u_st
""" Ratio of velocity to the sonic velcoity U/U*"""
self.to_to_st = to_to_st
""" Ratio of the total temperature to the sonic total temperature T0/T0*"""
self.flow_type = flow_type
""" Type of flow which is either subsonic or supersonic (Type: flowstate) """
self.precision = 4
""" Precision to use when printing output to the console defaults to four """
# Pipe parameters
self.choked_heat = nan
""" Amount of heat required to choke the flow"""
self.heat = nan
""" Amount of heat added to the flow """
self.gas_constant_r = nan
""" Gas constant used for flow calculations"""
self.cp = nan
""" Specific heat Coefficient at constant pressure for the gas used"""
# Down stream conditions if pipe parameters are given
self.dwn_strm_mach = nan
""" Mach number at the downstream point of the flow """
self.dwn_strm_t_t_st = nan
""" Ratio of temperature to the sonic temperature T/T* at the downstream point"""
self.dwn_strm_p_p_st = nan
""" Ratio of pressure to the sonic pressure P/P* at the downstream point"""
self.dwn_strm_rho_rho_st = nan
""" Ratio of the density to the sonic density rho/rho* at the downstream point"""
self.dwn_strm_po_po_st = nan
""" Stagnation to sonic stagnation pressure ratio P0/P0* at the down stream point"""
self.dwn_strm_u_u_st = nan
""" Ratio of velocity to the sonic velcoity U/U* at the downstream point"""
self.dwn_strm_to_to_st = nan
""" Ratio of the total temp to the sonic total temp T0/T0* at the downstream point"""
# Downstream / Initial Conditions
self.t2_t1 = nan
""" Ratio of downstream temperature to upstream temperature"""
self.p2_p1 = nan
""" Ratio of downstream pressure to upstream pressure"""
self.rho2_rho1 = nan
""" Ratio of downstream density to upstream density"""
self.po2_po1 = nan
""" Ratio of downstream total pressure to upstream total pressure"""
self.to2_to1 = nan
""" Ratio of downstream total temperature to upstream total temperature"""
self.u2_u1 = nan
""" Ratio of downstream velocity to upstream velocity """
self.to2 = nan
""" Downstream total temperature """
self.to1 = nan
""" Upstream total temperature"""
if not check_value(self.gamma):
raise GammaNotDefinedError()
if check_value(self.mach):
pass
elif check_value(self.t_t_st):
self.mach = RayleighFlowRelations.calc_mach_from_t_t_star(
self.t_t_st, self.gamma, flow_type=self.flow_type
)
elif check_value(self.p_p_st):
self.mach = RayleighFlowRelations.calc_mach_from_p_p_star(self.p_p_st, self.gamma)
elif check_value(self.rho_rho_st):
self.mach = RayleighFlowRelations.calc_mach_from_rho_rho_star(
self.rho_rho_st, self.gamma
)
elif check_value(self.po_po_st):
self.mach = RayleighFlowRelations.calc_mach_from_po_po_star(
self.po_po_st, self.gamma, flow_type=self.flow_type
)
elif check_value(self.to_to_st):
self.mach = RayleighFlowRelations.calc_mach_from_to_to_star(
self.to_to_st, self.gamma, flow_type=self.flow_type
)
elif check_value(self.u_u_st):
self.mach = RayleighFlowRelations.calc_mach_from_u_u_star(self.u_u_st, self.gamma)
else:
raise InvalidOptionCombinationError()
if check_value(self.mach):
self._calc_state()
@property
def choked_flow(self) -> bool:
"""True if the added heat is greater than the heat addition required to choke the flow"""
return self.heat > self.choked_heat
def _calc_state(self) -> None:
self.t_t_st = RayleighFlowRelations.calc_t_t_star(self.mach, self.gamma)
self.p_p_st = RayleighFlowRelations.calc_p_p_star(self.mach, self.gamma)
self.rho_rho_st = RayleighFlowRelations.calc_rho_rho_star(self.mach, self.gamma)
self.po_po_st = RayleighFlowRelations.calc_po_po_star(self.mach, self.gamma)
self.to_to_st = RayleighFlowRelations.calc_to_to_star(self.mach, self.gamma)
self.u_u_st = RayleighFlowRelations.calc_u_u_starar(self.mach, self.gamma)
self.flow_type = FlowState.SUPER_SONIC if self.mach > 1.0 else FlowState.SUB_SONIC
def simulate_heat_addition(self, heat: float, to1: float, gas_const_r: float) -> None:
"""
This functions calculates the downstream flow conditions caused due to applied heat.
Args:
heat (float): The amount of heat being applied
to1 (float): The initial temperature of the flow
gas_const_r (float): The gas constant of the flow
"""
self.gas_constant_r = gas_const_r
self.to1 = to1
self.heat = heat
self.cp = self.gamma * gas_const_r / (self.gamma - 1)
self.to2 = self.to1 + self.heat / self.cp
temp_star = self.to1 / self.to_to_st
self.choked_heat = self.cp * (temp_star - self.to1)
self.to2_to1 = self.to2 / self.to1
self.dwn_strm_to_to_st = self.to2_to1 * self.to_to_st
if self.heat > self.choked_heat:
self.dwn_strm_to_to_st = 1
self.dwn_strm_mach = RayleighFlowRelations.calc_mach_from_to_to_star(
self.dwn_strm_to_to_st, self.gamma, self.flow_type
)
self.dwn_strm_t_t_st = RayleighFlowRelations.calc_t_t_star(self.dwn_strm_mach, self.gamma)
self.dwn_strm_p_p_st = RayleighFlowRelations.calc_p_p_star(self.dwn_strm_mach, self.gamma)
self.dwn_strm_rho_rho_st = RayleighFlowRelations.calc_rho_rho_star(
self.dwn_strm_mach, self.gamma
)
self.dwn_strm_po_po_st = RayleighFlowRelations.calc_po_po_star(
self.dwn_strm_mach, self.gamma
)
self.dwn_strm_to_to_st = RayleighFlowRelations.calc_to_to_star(
self.dwn_strm_mach, self.gamma
)
self.dwn_strm_u_u_st = RayleighFlowRelations.calc_u_u_starar(self.dwn_strm_mach, self.gamma)
self.to2_to1 = self.dwn_strm_to_to_st / self.to_to_st
self.t2_t1 = self.dwn_strm_t_t_st / self.t_t_st
self.p2_p1 = self.dwn_strm_p_p_st / self.p_p_st
self.rho2_rho1 = self.dwn_strm_rho_rho_st / self.rho_rho_st
self.po2_po1 = self.dwn_strm_po_po_st / self.po_po_st
self.u2_u1 = self.dwn_strm_u_u_st / self.u_u_st
def __str__(self) -> str:
color = (
Back.GREEN + Fore.BLACK if self.heat < self.choked_heat else Back.YELLOW + Fore.BLACK
)
return "".join(
[
named_header("Rayleigh Relations at Mach", self.mach, precision=self.precision),
seperator(),
to_string(lcg.gamma, self.gamma, self.precision),
to_string("T/T*", self.t_t_st, self.precision, dot_line=True),
to_string("P/P*", self.p_p_st, self.precision),
to_string(f"{lcg.rho}/{lcg.rho}", self.rho_rho_st, self.precision, dot_line=True),
to_string("P0/P0*", self.po_po_st, self.precision),
to_string("U/U*", self.u_u_st, self.precision, dot_line=True),
to_string("T0/T0*", self.to_to_st, self.precision),
to_string("Flow Type", self.flow_type.name, self.precision, dot_line=True),
seperator(),
named_subheader("Pipe Parameters"),
to_string("Heat Req. For Chocked Flow", self.choked_heat, self.precision),
color,
to_string("Is Flow Choked? ", self.choked_flow, self.precision, dot_line=True),
to_string("Added Heat", self.heat, self.precision),
to_string("Gas Constant R", self.gas_constant_r, self.precision, dot_line=True),
to_string("Cp", self.cp, self.precision),
to_string("T01", self.to1, self.precision, dot_line=True),
to_string("T02", self.to2, self.precision),
seperator(),
named_subheader("Down Stream Conditions"),
to_string("Mach", self.dwn_strm_mach, self.precision),
to_string("T/T*", self.t_t_st, self.precision, dot_line=True),
to_string("P/P*", self.dwn_strm_p_p_st, self.precision),
to_string("P0/P0*", self.dwn_strm_po_po_st, self.precision, dot_line=True),
to_string(f"{lcg.rho}/{lcg.rho}*", self.dwn_strm_rho_rho_st, self.precision),
to_string("T0/T0*", self.to_to_st, self.precision, dot_line=True),
to_string("U/U*", self.dwn_strm_u_u_st, self.precision),
seperator(),
named_subheader("Conditions Across Heat Addition"),
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("T02/T01", self.to2_to1, self.precision),
to_string("U2/U1", self.u2_u1, self.precision, dot_line=True),
footer(),
]
)
@staticmethod
def calc_p_p_star(mach: float, gamma: float, offset: float = 0.0) -> float:
"""Calculates Ratio of static pressure to sonic pressure P/P*
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.
Returns:
float: P/P*
"""
return (1 + gamma) / (1 + gamma * pow(mach, 2)) - offset
@staticmethod
def calc_mach_from_p_p_star(p_p_st: float, gamma: float) -> float:
"""
Calculates the mach number based of the ratio of static pressure to sonic static
pressure P/P*
Args:
p_p_st (float): Ratio of static pressure to sonic static pressure P/P*
gamma (float): ratio of specific heats
Returns:
float: mach number
"""
return brenth(
RayleighFlowRelations.calc_p_p_star,
1e-9,
40,
args=(
gamma,
p_p_st,
),
) # type: ignore
@staticmethod
def calc_t_t_star(mach: float, gamma: float, offset: float = 0.0) -> float:
"""Calculates Ratio of static temperature to sonic temperature T/T*
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.
Returns:
float: T/T*
"""
return pow(mach, 2) * pow(RayleighFlowRelations.calc_p_p_star(mach, gamma), 2) - offset
@staticmethod
def calc_mach_from_t_t_star(
t_t_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC
) -> float:
"""
Calculates the mach number based of the ratio of static tempto sonic static temp T/T*
Args:
t_t_st (float): Ratio of static temperature to sonic static temperature T/T*
gamma (float): ratio of specific heats
flow_type (FlowState, optional): States whether the flow is currently supersonic or
subsonic. Defaults to FlowState.SUPER_SONIC.
Returns:
float: mach number
"""
tolerance = 1e-5
if t_t_st == 1.0:
return 1
if flow_type == FlowState.SUPER_SONIC:
return brenth(
RayleighFlowRelations.calc_t_t_star,
1 + tolerance,
40,
args=(
gamma,
t_t_st,
),
) # type: ignore
if flow_type == FlowState.SUB_SONIC:
return brenth(
RayleighFlowRelations.calc_t_t_star,
tolerance,
1 - tolerance,
args=(
gamma,
t_t_st,
),
) # type: ignore
raise ValueError(
f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow!{Fore.RESET}"
)
@staticmethod
def calc_rho_rho_star(mach: float, gamma: float, offset: float = 0.0) -> float:
"""Calculates Ratio of static density to sonic density Rho/Rho*
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.
Returns:
float: Rho/Rho*
"""
return 1 / RayleighFlowRelations.calc_p_p_star(mach, gamma) / pow(mach, 2) - offset
@staticmethod
def calc_mach_from_rho_rho_star(rho_rho_st: float, gamma: float) -> float:
"""Calculates the mach number based of the ratio of density to sonic density Rho/Rho*
Args:
rho_rho_st (float): Ratio of density to sonic density Rho/Rho*
gamma (float): ratio of specific heats
Returns:
float: mach number
"""
return brenth(
RayleighFlowRelations.calc_rho_rho_star,
1e-9,
40,
args=(
gamma,
rho_rho_st,
),
) # type: ignore
@staticmethod
def calc_po_po_star(mach: float, gamma: float, offset: float = 0.0) -> float:
"""Calculates Ratio of static density to sonic density P0/P0*
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.
Returns:
float: P0/P0*
"""
gp1 = gamma + 1
gm1 = gamma - 1
p_p_st = RayleighFlowRelations.calc_p_p_star(mach, gamma)
ratio = (2 + gm1 * pow(mach, 2)) / gp1
return p_p_st * pow(ratio, gamma / gm1) - offset
@staticmethod
def calc_mach_from_po_po_star(
po_po_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC
) -> float:
"""
Calculates the mach number based of the ratio of total pressure to sonic total pressure
P0/P0*
Args:
po_po_st (float): Ratio of total pressure to sonic total pressure P0/P0*
gamma (float): ratio of specific heats
flow_type (FlowState, optional): States whether the flow is currently supersonic or
subsonic. Defaults to FlowState.SUPER_SONIC.
Returns:
float: mach number
"""
tolerance = 1e-5
if po_po_st == 1.0:
return 1
if flow_type == FlowState.SUPER_SONIC:
return brenth(
RayleighFlowRelations.calc_po_po_star,
1 + tolerance,
40,
args=(
gamma,
po_po_st,
),
) # type: ignore
if flow_type == FlowState.SUB_SONIC:
return brenth(
RayleighFlowRelations.calc_po_po_star,
tolerance,
1 - tolerance,
args=(
gamma,
po_po_st,
),
) # type: ignore
raise ValueError(
f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow!{Fore.RESET}"
)
@staticmethod
def calc_to_to_star(mach: float, gamma: float, offset: float = 0.0) -> float:
"""Calculates To_To* given gamma and Mach, offset can be applied for root finding"""
gp1 = gamma + 1
gm1 = gamma - 1
m_sqr = pow(mach, 2)
return gp1 * m_sqr / pow((1 + gamma * m_sqr), 2) * (2 + gm1 * m_sqr) - offset
@staticmethod
def calc_mach_from_to_to_star(
t_t_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC
) -> float:
"""
Calculates the mach number based of the ratio of total tempto sonic total temp T0/T0*
Args:
po_po_st (float): Ratio of total temperature to sonic total temperature T0/T0*
gamma (float): ratio of specific heats
flow_type (FlowState, optional): States whether the flow is currently supersonic or
subsonic. Defaults to FlowState.SUPER_SONIC.
Returns:
float: mach number
"""
tolerance = 1e-5
if t_t_st == 1.0:
return 1
if flow_type == FlowState.SUPER_SONIC:
return brenth(
RayleighFlowRelations.calc_to_to_star,
1 + tolerance,
40,
args=(
gamma,
t_t_st,
),
) # type: ignore
if flow_type == FlowState.SUB_SONIC:
return brenth(
RayleighFlowRelations.calc_to_to_star,
tolerance,
1 - tolerance,
args=(
gamma,
t_t_st,
),
) # type: ignore
raise ValueError(
f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow!{Fore.RESET}"
)
@staticmethod
def calc_u_u_starar(mach: float, gamma: float, offset: float = 0.0) -> float:
"""Calculates Ratio of static velocity to sonic velocity U/U*
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.
Returns:
float: U/U*
"""
gp1 = gamma + 1
m_sqr = pow(mach, 2)
return gp1 * m_sqr / (1 + gamma * m_sqr) - offset
@staticmethod
def calc_mach_from_u_u_star(u_u_st: float, gamma: float) -> float:
"""Calculates the mach number based of the ratio of velocity to sonic velocity U/U*
Args:
u_u_st (float): Ratio of velocity to sonic velocity U/U*
gamma (float): ratio of specific heats
Returns:
float: mach number
"""
return brenth(
RayleighFlowRelations.calc_u_u_starar, 1e-9, 40, args=(gamma, u_u_st)
) # type: ignoreClasses
class RayleighFlowChoice (*args, **kwds)-
Valid choices for Rayleigh Flow initialization
Expand source code
class RayleighFlowChoice(Enum): """Valid choices for Rayleigh Flow initialization""" GAMMA_MACH = "gamma, mach" GAMMA_T_T_ST = "gamma, T/T*, flowtype" GAMMA_P_P_ST = "gamma, P/P*" GAMMA_RHO_RHO_ST = "gamma, rho/rho*" GAMMA_PO_PO_ST = "gamma, P0/P0*, flowtype" GAMMA_TO_TO_FLOW_TYPE = "gamma, T0/T0*, flowtype" GAMMA_U_U_ST = "gamma, U/U*"Ancestors
- enum.Enum
Class variables
var GAMMA_MACHvar GAMMA_PO_PO_STvar GAMMA_P_P_STvar GAMMA_RHO_RHO_STvar GAMMA_TO_TO_FLOW_TYPEvar GAMMA_T_T_STvar GAMMA_U_U_ST
class RayleighFlowRelations (gamma: float, mach: float = nan, t_t_st: float = nan, p_p_st: float = nan, rho_rho_st: float = nan, po_po_st: float = nan, to_to_st: float = nan, u_u_st: float = nan, flow_type: FlowState = FlowState.SUPER_SONIC)-
This class is a collective name space for basic calculations regarding Fanno flows.
Args
gamma:float- ratio of specific heats
mach:float, optional- mach number of the flow. Defaults to nan.
t_t_st:float, optional- Ratio of Temperature to sonic temperature. Defaults to nan.
p_p_st:float, optional- Ratio of Pressure to sonic pressure. Defaults to nan.
rho_rho_st:float, optional- Ratio of density to sonic density. Defaults to nan.
po_po_st:float, optional- Total pressure to sonic total pressure ratio. Defaults to nan.
to_to_star:float, optional- Ratio of Total Tempto sonic total temp. Defaults to nan.
u_u_st:float, optional- Velocity to sonic Velocity. Defaults to nan.
flow_type:FlowState, optional- States wether the flow is subsonic or supersonic. Used for Area Ratio Calculations. Defaults to FlowState.SUPER_SONIC.
Raises
GammaNotDefinedError- Raised if Gamma is undefined
InvalidOptionCombinationError- Raised if an invalid combination of parameters is given and flow state cannot be determined
Useage
To use this class pass gamma and one of the known parameters of the flow
Valid_Combinations_Of_Parameters
1: gamma, mach
2: gamma, T/T*, flowtype (flow type defaults to super sonic)
3: gamma, P/P*
4: gamma, rho/rho*
5: gamma, P0/P0*, flowtype (flow type defaults to super sonic)
6: gamma, T0/T0*, flowtype (flow type defaults to super sonic)
7: gamma, U/U*
Expand source code
class RayleighFlowRelations: # pylint: disable=too-many-instance-attributes """ This class is a collective name space for basic calculations regarding Fanno flows. Args: gamma (float): ratio of specific heats mach (float, optional): mach number of the flow. Defaults to nan. t_t_st (float, optional): Ratio of Temperature to sonic temperature. Defaults to nan. p_p_st (float, optional): Ratio of Pressure to sonic pressure. Defaults to nan. rho_rho_st (float, optional): Ratio of density to sonic density. Defaults to nan. po_po_st (float, optional): Total pressure to sonic total pressure ratio. Defaults to nan. to_to_star (float, optional): Ratio of Total Tempto sonic total temp. Defaults to nan. u_u_st (float, optional): Velocity to sonic Velocity. Defaults to nan. flow_type (FlowState, optional): States wether the flow is subsonic or supersonic. Used for Area Ratio Calculations. Defaults to FlowState.SUPER_SONIC. Raises: GammaNotDefinedError: Raised if Gamma is undefined InvalidOptionCombinationError: Raised if an invalid combination of parameters is given and flow state cannot be determined Useage: To use this class pass gamma and one of the known parameters of the flow Valid_Combinations_of_Parameters: 1: gamma, mach\n 2: gamma, T/T*, flowtype (flow type defaults to super sonic)\n 3: gamma, P/P*\n 4: gamma, rho/rho*\n 5: gamma, P0/P0*, flowtype (flow type defaults to super sonic)\n 6: gamma, T0/T0*, flowtype (flow type defaults to super sonic)\n 7: gamma, U/U*\n """ def __init__( self, gamma: float, mach: float = nan, t_t_st: float = nan, p_p_st: float = nan, rho_rho_st: float = nan, po_po_st: float = nan, to_to_st: float = nan, u_u_st: float = nan, flow_type: FlowState = FlowState.SUPER_SONIC, ) -> 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.t_t_st = t_t_st """ Ratio of temperature to the sonic temperature T/T*""" self.p_p_st = p_p_st """ Ratio of pressure to the sonic pressure P/P*""" self.rho_rho_st = rho_rho_st """ Ratio of the density to the sonic density rho/rho* """ self.po_po_st = po_po_st """ Ratio of the stagnation pressure to the sonic stagnation pressure P0/P0*""" self.u_u_st = u_u_st """ Ratio of velocity to the sonic velcoity U/U*""" self.to_to_st = to_to_st """ Ratio of the total temperature to the sonic total temperature T0/T0*""" self.flow_type = flow_type """ Type of flow which is either subsonic or supersonic (Type: flowstate) """ self.precision = 4 """ Precision to use when printing output to the console defaults to four """ # Pipe parameters self.choked_heat = nan """ Amount of heat required to choke the flow""" self.heat = nan """ Amount of heat added to the flow """ self.gas_constant_r = nan """ Gas constant used for flow calculations""" self.cp = nan """ Specific heat Coefficient at constant pressure for the gas used""" # Down stream conditions if pipe parameters are given self.dwn_strm_mach = nan """ Mach number at the downstream point of the flow """ self.dwn_strm_t_t_st = nan """ Ratio of temperature to the sonic temperature T/T* at the downstream point""" self.dwn_strm_p_p_st = nan """ Ratio of pressure to the sonic pressure P/P* at the downstream point""" self.dwn_strm_rho_rho_st = nan """ Ratio of the density to the sonic density rho/rho* at the downstream point""" self.dwn_strm_po_po_st = nan """ Stagnation to sonic stagnation pressure ratio P0/P0* at the down stream point""" self.dwn_strm_u_u_st = nan """ Ratio of velocity to the sonic velcoity U/U* at the downstream point""" self.dwn_strm_to_to_st = nan """ Ratio of the total temp to the sonic total temp T0/T0* at the downstream point""" # Downstream / Initial Conditions self.t2_t1 = nan """ Ratio of downstream temperature to upstream temperature""" self.p2_p1 = nan """ Ratio of downstream pressure to upstream pressure""" self.rho2_rho1 = nan """ Ratio of downstream density to upstream density""" self.po2_po1 = nan """ Ratio of downstream total pressure to upstream total pressure""" self.to2_to1 = nan """ Ratio of downstream total temperature to upstream total temperature""" self.u2_u1 = nan """ Ratio of downstream velocity to upstream velocity """ self.to2 = nan """ Downstream total temperature """ self.to1 = nan """ Upstream total temperature""" if not check_value(self.gamma): raise GammaNotDefinedError() if check_value(self.mach): pass elif check_value(self.t_t_st): self.mach = RayleighFlowRelations.calc_mach_from_t_t_star( self.t_t_st, self.gamma, flow_type=self.flow_type ) elif check_value(self.p_p_st): self.mach = RayleighFlowRelations.calc_mach_from_p_p_star(self.p_p_st, self.gamma) elif check_value(self.rho_rho_st): self.mach = RayleighFlowRelations.calc_mach_from_rho_rho_star( self.rho_rho_st, self.gamma ) elif check_value(self.po_po_st): self.mach = RayleighFlowRelations.calc_mach_from_po_po_star( self.po_po_st, self.gamma, flow_type=self.flow_type ) elif check_value(self.to_to_st): self.mach = RayleighFlowRelations.calc_mach_from_to_to_star( self.to_to_st, self.gamma, flow_type=self.flow_type ) elif check_value(self.u_u_st): self.mach = RayleighFlowRelations.calc_mach_from_u_u_star(self.u_u_st, self.gamma) else: raise InvalidOptionCombinationError() if check_value(self.mach): self._calc_state() @property def choked_flow(self) -> bool: """True if the added heat is greater than the heat addition required to choke the flow""" return self.heat > self.choked_heat def _calc_state(self) -> None: self.t_t_st = RayleighFlowRelations.calc_t_t_star(self.mach, self.gamma) self.p_p_st = RayleighFlowRelations.calc_p_p_star(self.mach, self.gamma) self.rho_rho_st = RayleighFlowRelations.calc_rho_rho_star(self.mach, self.gamma) self.po_po_st = RayleighFlowRelations.calc_po_po_star(self.mach, self.gamma) self.to_to_st = RayleighFlowRelations.calc_to_to_star(self.mach, self.gamma) self.u_u_st = RayleighFlowRelations.calc_u_u_starar(self.mach, self.gamma) self.flow_type = FlowState.SUPER_SONIC if self.mach > 1.0 else FlowState.SUB_SONIC def simulate_heat_addition(self, heat: float, to1: float, gas_const_r: float) -> None: """ This functions calculates the downstream flow conditions caused due to applied heat. Args: heat (float): The amount of heat being applied to1 (float): The initial temperature of the flow gas_const_r (float): The gas constant of the flow """ self.gas_constant_r = gas_const_r self.to1 = to1 self.heat = heat self.cp = self.gamma * gas_const_r / (self.gamma - 1) self.to2 = self.to1 + self.heat / self.cp temp_star = self.to1 / self.to_to_st self.choked_heat = self.cp * (temp_star - self.to1) self.to2_to1 = self.to2 / self.to1 self.dwn_strm_to_to_st = self.to2_to1 * self.to_to_st if self.heat > self.choked_heat: self.dwn_strm_to_to_st = 1 self.dwn_strm_mach = RayleighFlowRelations.calc_mach_from_to_to_star( self.dwn_strm_to_to_st, self.gamma, self.flow_type ) self.dwn_strm_t_t_st = RayleighFlowRelations.calc_t_t_star(self.dwn_strm_mach, self.gamma) self.dwn_strm_p_p_st = RayleighFlowRelations.calc_p_p_star(self.dwn_strm_mach, self.gamma) self.dwn_strm_rho_rho_st = RayleighFlowRelations.calc_rho_rho_star( self.dwn_strm_mach, self.gamma ) self.dwn_strm_po_po_st = RayleighFlowRelations.calc_po_po_star( self.dwn_strm_mach, self.gamma ) self.dwn_strm_to_to_st = RayleighFlowRelations.calc_to_to_star( self.dwn_strm_mach, self.gamma ) self.dwn_strm_u_u_st = RayleighFlowRelations.calc_u_u_starar(self.dwn_strm_mach, self.gamma) self.to2_to1 = self.dwn_strm_to_to_st / self.to_to_st self.t2_t1 = self.dwn_strm_t_t_st / self.t_t_st self.p2_p1 = self.dwn_strm_p_p_st / self.p_p_st self.rho2_rho1 = self.dwn_strm_rho_rho_st / self.rho_rho_st self.po2_po1 = self.dwn_strm_po_po_st / self.po_po_st self.u2_u1 = self.dwn_strm_u_u_st / self.u_u_st def __str__(self) -> str: color = ( Back.GREEN + Fore.BLACK if self.heat < self.choked_heat else Back.YELLOW + Fore.BLACK ) return "".join( [ named_header("Rayleigh Relations at Mach", self.mach, precision=self.precision), seperator(), to_string(lcg.gamma, self.gamma, self.precision), to_string("T/T*", self.t_t_st, self.precision, dot_line=True), to_string("P/P*", self.p_p_st, self.precision), to_string(f"{lcg.rho}/{lcg.rho}", self.rho_rho_st, self.precision, dot_line=True), to_string("P0/P0*", self.po_po_st, self.precision), to_string("U/U*", self.u_u_st, self.precision, dot_line=True), to_string("T0/T0*", self.to_to_st, self.precision), to_string("Flow Type", self.flow_type.name, self.precision, dot_line=True), seperator(), named_subheader("Pipe Parameters"), to_string("Heat Req. For Chocked Flow", self.choked_heat, self.precision), color, to_string("Is Flow Choked? ", self.choked_flow, self.precision, dot_line=True), to_string("Added Heat", self.heat, self.precision), to_string("Gas Constant R", self.gas_constant_r, self.precision, dot_line=True), to_string("Cp", self.cp, self.precision), to_string("T01", self.to1, self.precision, dot_line=True), to_string("T02", self.to2, self.precision), seperator(), named_subheader("Down Stream Conditions"), to_string("Mach", self.dwn_strm_mach, self.precision), to_string("T/T*", self.t_t_st, self.precision, dot_line=True), to_string("P/P*", self.dwn_strm_p_p_st, self.precision), to_string("P0/P0*", self.dwn_strm_po_po_st, self.precision, dot_line=True), to_string(f"{lcg.rho}/{lcg.rho}*", self.dwn_strm_rho_rho_st, self.precision), to_string("T0/T0*", self.to_to_st, self.precision, dot_line=True), to_string("U/U*", self.dwn_strm_u_u_st, self.precision), seperator(), named_subheader("Conditions Across Heat Addition"), 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("T02/T01", self.to2_to1, self.precision), to_string("U2/U1", self.u2_u1, self.precision, dot_line=True), footer(), ] ) @staticmethod def calc_p_p_star(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of static pressure to sonic pressure P/P* 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. Returns: float: P/P* """ return (1 + gamma) / (1 + gamma * pow(mach, 2)) - offset @staticmethod def calc_mach_from_p_p_star(p_p_st: float, gamma: float) -> float: """ Calculates the mach number based of the ratio of static pressure to sonic static pressure P/P* Args: p_p_st (float): Ratio of static pressure to sonic static pressure P/P* gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( RayleighFlowRelations.calc_p_p_star, 1e-9, 40, args=( gamma, p_p_st, ), ) # type: ignore @staticmethod def calc_t_t_star(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of static temperature to sonic temperature T/T* 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. Returns: float: T/T* """ return pow(mach, 2) * pow(RayleighFlowRelations.calc_p_p_star(mach, gamma), 2) - offset @staticmethod def calc_mach_from_t_t_star( t_t_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC ) -> float: """ Calculates the mach number based of the ratio of static tempto sonic static temp T/T* Args: t_t_st (float): Ratio of static temperature to sonic static temperature T/T* gamma (float): ratio of specific heats flow_type (FlowState, optional): States whether the flow is currently supersonic or subsonic. Defaults to FlowState.SUPER_SONIC. Returns: float: mach number """ tolerance = 1e-5 if t_t_st == 1.0: return 1 if flow_type == FlowState.SUPER_SONIC: return brenth( RayleighFlowRelations.calc_t_t_star, 1 + tolerance, 40, args=( gamma, t_t_st, ), ) # type: ignore if flow_type == FlowState.SUB_SONIC: return brenth( RayleighFlowRelations.calc_t_t_star, tolerance, 1 - tolerance, args=( gamma, t_t_st, ), ) # type: ignore raise ValueError( f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow!{Fore.RESET}" ) @staticmethod def calc_rho_rho_star(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of static density to sonic density Rho/Rho* 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. Returns: float: Rho/Rho* """ return 1 / RayleighFlowRelations.calc_p_p_star(mach, gamma) / pow(mach, 2) - offset @staticmethod def calc_mach_from_rho_rho_star(rho_rho_st: float, gamma: float) -> float: """Calculates the mach number based of the ratio of density to sonic density Rho/Rho* Args: rho_rho_st (float): Ratio of density to sonic density Rho/Rho* gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( RayleighFlowRelations.calc_rho_rho_star, 1e-9, 40, args=( gamma, rho_rho_st, ), ) # type: ignore @staticmethod def calc_po_po_star(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of static density to sonic density P0/P0* 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. Returns: float: P0/P0* """ gp1 = gamma + 1 gm1 = gamma - 1 p_p_st = RayleighFlowRelations.calc_p_p_star(mach, gamma) ratio = (2 + gm1 * pow(mach, 2)) / gp1 return p_p_st * pow(ratio, gamma / gm1) - offset @staticmethod def calc_mach_from_po_po_star( po_po_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC ) -> float: """ Calculates the mach number based of the ratio of total pressure to sonic total pressure P0/P0* Args: po_po_st (float): Ratio of total pressure to sonic total pressure P0/P0* gamma (float): ratio of specific heats flow_type (FlowState, optional): States whether the flow is currently supersonic or subsonic. Defaults to FlowState.SUPER_SONIC. Returns: float: mach number """ tolerance = 1e-5 if po_po_st == 1.0: return 1 if flow_type == FlowState.SUPER_SONIC: return brenth( RayleighFlowRelations.calc_po_po_star, 1 + tolerance, 40, args=( gamma, po_po_st, ), ) # type: ignore if flow_type == FlowState.SUB_SONIC: return brenth( RayleighFlowRelations.calc_po_po_star, tolerance, 1 - tolerance, args=( gamma, po_po_st, ), ) # type: ignore raise ValueError( f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow!{Fore.RESET}" ) @staticmethod def calc_to_to_star(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates To_To* given gamma and Mach, offset can be applied for root finding""" gp1 = gamma + 1 gm1 = gamma - 1 m_sqr = pow(mach, 2) return gp1 * m_sqr / pow((1 + gamma * m_sqr), 2) * (2 + gm1 * m_sqr) - offset @staticmethod def calc_mach_from_to_to_star( t_t_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC ) -> float: """ Calculates the mach number based of the ratio of total tempto sonic total temp T0/T0* Args: po_po_st (float): Ratio of total temperature to sonic total temperature T0/T0* gamma (float): ratio of specific heats flow_type (FlowState, optional): States whether the flow is currently supersonic or subsonic. Defaults to FlowState.SUPER_SONIC. Returns: float: mach number """ tolerance = 1e-5 if t_t_st == 1.0: return 1 if flow_type == FlowState.SUPER_SONIC: return brenth( RayleighFlowRelations.calc_to_to_star, 1 + tolerance, 40, args=( gamma, t_t_st, ), ) # type: ignore if flow_type == FlowState.SUB_SONIC: return brenth( RayleighFlowRelations.calc_to_to_star, tolerance, 1 - tolerance, args=( gamma, t_t_st, ), ) # type: ignore raise ValueError( f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow!{Fore.RESET}" ) @staticmethod def calc_u_u_starar(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of static velocity to sonic velocity U/U* 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. Returns: float: U/U* """ gp1 = gamma + 1 m_sqr = pow(mach, 2) return gp1 * m_sqr / (1 + gamma * m_sqr) - offset @staticmethod def calc_mach_from_u_u_star(u_u_st: float, gamma: float) -> float: """Calculates the mach number based of the ratio of velocity to sonic velocity U/U* Args: u_u_st (float): Ratio of velocity to sonic velocity U/U* gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( RayleighFlowRelations.calc_u_u_starar, 1e-9, 40, args=(gamma, u_u_st) ) # type: ignoreStatic methods
def calc_mach_from_p_p_star(p_p_st: float, gamma: float) ‑> float-
Calculates the mach number based of the ratio of static pressure to sonic static pressure P/P*
Args
p_p_st:float- Ratio of static pressure to sonic static pressure P/P*
gamma:float- ratio of specific heats
Returns
float- mach number
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@staticmethod def calc_mach_from_p_p_star(p_p_st: float, gamma: float) -> float: """ Calculates the mach number based of the ratio of static pressure to sonic static pressure P/P* Args: p_p_st (float): Ratio of static pressure to sonic static pressure P/P* gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( RayleighFlowRelations.calc_p_p_star, 1e-9, 40, args=( gamma, p_p_st, ), ) # type: ignore def calc_mach_from_po_po_star(po_po_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC) ‑> float-
Calculates the mach number based of the ratio of total pressure to sonic total pressure P0/P0*
Args
po_po_st:float- Ratio of total pressure to sonic total pressure P0/P0*
gamma:float- ratio of specific heats
flow_type:FlowState, optional- States whether the flow is currently supersonic or subsonic. Defaults to FlowState.SUPER_SONIC.
Returns
float- mach number
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@staticmethod def calc_mach_from_po_po_star( po_po_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC ) -> float: """ Calculates the mach number based of the ratio of total pressure to sonic total pressure P0/P0* Args: po_po_st (float): Ratio of total pressure to sonic total pressure P0/P0* gamma (float): ratio of specific heats flow_type (FlowState, optional): States whether the flow is currently supersonic or subsonic. Defaults to FlowState.SUPER_SONIC. Returns: float: mach number """ tolerance = 1e-5 if po_po_st == 1.0: return 1 if flow_type == FlowState.SUPER_SONIC: return brenth( RayleighFlowRelations.calc_po_po_star, 1 + tolerance, 40, args=( gamma, po_po_st, ), ) # type: ignore if flow_type == FlowState.SUB_SONIC: return brenth( RayleighFlowRelations.calc_po_po_star, tolerance, 1 - tolerance, args=( gamma, po_po_st, ), ) # type: ignore raise ValueError( f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow!{Fore.RESET}" ) def calc_mach_from_rho_rho_star(rho_rho_st: float, gamma: float) ‑> float-
Calculates the mach number based of the ratio of density to sonic density Rho/Rho*
Args
rho_rho_st:float- Ratio of density to sonic density Rho/Rho*
gamma:float- ratio of specific heats
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_from_rho_rho_star(rho_rho_st: float, gamma: float) -> float: """Calculates the mach number based of the ratio of density to sonic density Rho/Rho* Args: rho_rho_st (float): Ratio of density to sonic density Rho/Rho* gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( RayleighFlowRelations.calc_rho_rho_star, 1e-9, 40, args=( gamma, rho_rho_st, ), ) # type: ignore def calc_mach_from_t_t_star(t_t_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC) ‑> float-
Calculates the mach number based of the ratio of static tempto sonic static temp T/T*
Args
t_t_st:float- Ratio of static temperature to sonic static temperature T/T*
gamma:float- ratio of specific heats
flow_type:FlowState, optional- States whether the flow is currently supersonic or subsonic. Defaults to FlowState.SUPER_SONIC.
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_from_t_t_star( t_t_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC ) -> float: """ Calculates the mach number based of the ratio of static tempto sonic static temp T/T* Args: t_t_st (float): Ratio of static temperature to sonic static temperature T/T* gamma (float): ratio of specific heats flow_type (FlowState, optional): States whether the flow is currently supersonic or subsonic. Defaults to FlowState.SUPER_SONIC. Returns: float: mach number """ tolerance = 1e-5 if t_t_st == 1.0: return 1 if flow_type == FlowState.SUPER_SONIC: return brenth( RayleighFlowRelations.calc_t_t_star, 1 + tolerance, 40, args=( gamma, t_t_st, ), ) # type: ignore if flow_type == FlowState.SUB_SONIC: return brenth( RayleighFlowRelations.calc_t_t_star, tolerance, 1 - tolerance, args=( gamma, t_t_st, ), ) # type: ignore raise ValueError( f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow!{Fore.RESET}" ) def calc_mach_from_to_to_star(t_t_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC) ‑> float-
Calculates the mach number based of the ratio of total tempto sonic total temp T0/T0*
Args
po_po_st:float- Ratio of total temperature to sonic total temperature T0/T0*
gamma:float- ratio of specific heats
flow_type:FlowState, optional- States whether the flow is currently supersonic or subsonic. Defaults to FlowState.SUPER_SONIC.
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_from_to_to_star( t_t_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC ) -> float: """ Calculates the mach number based of the ratio of total tempto sonic total temp T0/T0* Args: po_po_st (float): Ratio of total temperature to sonic total temperature T0/T0* gamma (float): ratio of specific heats flow_type (FlowState, optional): States whether the flow is currently supersonic or subsonic. Defaults to FlowState.SUPER_SONIC. Returns: float: mach number """ tolerance = 1e-5 if t_t_st == 1.0: return 1 if flow_type == FlowState.SUPER_SONIC: return brenth( RayleighFlowRelations.calc_to_to_star, 1 + tolerance, 40, args=( gamma, t_t_st, ), ) # type: ignore if flow_type == FlowState.SUB_SONIC: return brenth( RayleighFlowRelations.calc_to_to_star, tolerance, 1 - tolerance, args=( gamma, t_t_st, ), ) # type: ignore raise ValueError( f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow!{Fore.RESET}" ) def calc_mach_from_u_u_star(u_u_st: float, gamma: float) ‑> float-
Calculates the mach number based of the ratio of velocity to sonic velocity U/U*
Args
u_u_st:float- Ratio of velocity to sonic velocity U/U*
gamma:float- ratio of specific heats
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_from_u_u_star(u_u_st: float, gamma: float) -> float: """Calculates the mach number based of the ratio of velocity to sonic velocity U/U* Args: u_u_st (float): Ratio of velocity to sonic velocity U/U* gamma (float): ratio of specific heats Returns: float: mach number """ return brenth( RayleighFlowRelations.calc_u_u_starar, 1e-9, 40, args=(gamma, u_u_st) ) # type: ignore def calc_p_p_star(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates Ratio of static pressure to sonic pressure P/P*
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.
Returns
float- P/P*
Expand source code
@staticmethod def calc_p_p_star(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of static pressure to sonic pressure P/P* 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. Returns: float: P/P* """ return (1 + gamma) / (1 + gamma * pow(mach, 2)) - offset def calc_po_po_star(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates Ratio of static density to sonic density P0/P0*
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.
Returns
float- P0/P0*
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@staticmethod def calc_po_po_star(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of static density to sonic density P0/P0* 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. Returns: float: P0/P0* """ gp1 = gamma + 1 gm1 = gamma - 1 p_p_st = RayleighFlowRelations.calc_p_p_star(mach, gamma) ratio = (2 + gm1 * pow(mach, 2)) / gp1 return p_p_st * pow(ratio, gamma / gm1) - offset def calc_rho_rho_star(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates Ratio of static density to sonic density Rho/Rho*
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.
Returns
float- Rho/Rho*
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@staticmethod def calc_rho_rho_star(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of static density to sonic density Rho/Rho* 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. Returns: float: Rho/Rho* """ return 1 / RayleighFlowRelations.calc_p_p_star(mach, gamma) / pow(mach, 2) - offset def calc_t_t_star(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates Ratio of static temperature to sonic temperature T/T*
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.
Returns
float- T/T*
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@staticmethod def calc_t_t_star(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of static temperature to sonic temperature T/T* 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. Returns: float: T/T* """ return pow(mach, 2) * pow(RayleighFlowRelations.calc_p_p_star(mach, gamma), 2) - offset def calc_to_to_star(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates To_To* given gamma and Mach, offset can be applied for root finding
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@staticmethod def calc_to_to_star(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates To_To* given gamma and Mach, offset can be applied for root finding""" gp1 = gamma + 1 gm1 = gamma - 1 m_sqr = pow(mach, 2) return gp1 * m_sqr / pow((1 + gamma * m_sqr), 2) * (2 + gm1 * m_sqr) - offset def calc_u_u_starar(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates Ratio of static velocity to sonic velocity U/U*
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.
Returns
float- U/U*
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@staticmethod def calc_u_u_starar(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates Ratio of static velocity to sonic velocity U/U* 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. Returns: float: U/U* """ gp1 = gamma + 1 m_sqr = pow(mach, 2) return gp1 * m_sqr / (1 + gamma * m_sqr) - offset
Instance variables
var choked_flow : bool-
True if the added heat is greater than the heat addition required to choke the flow
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@property def choked_flow(self) -> bool: """True if the added heat is greater than the heat addition required to choke the flow""" return self.heat > self.choked_heat var choked_heat-
Amount of heat required to choke the flow
var cp-
Specific heat Coefficient at constant pressure for the gas used
var dwn_strm_mach-
Mach number at the downstream point of the flow
var dwn_strm_p_p_st-
Ratio of pressure to the sonic pressure P/P* at the downstream point
var dwn_strm_po_po_st-
Stagnation to sonic stagnation pressure ratio P0/P0* at the down stream point
var dwn_strm_rho_rho_st-
Ratio of the density to the sonic density rho/rho* at the downstream point
var dwn_strm_t_t_st-
Ratio of temperature to the sonic temperature T/T* at the downstream point
var dwn_strm_to_to_st-
Ratio of the total temp to the sonic total temp T0/T0* at the downstream point
var dwn_strm_u_u_st-
Ratio of velocity to the sonic velcoity U/U* at the downstream point
var flow_type-
Type of flow which is either subsonic or supersonic (Type: flowstate)
var gamma-
Ratio of specific heats
var gas_constant_r-
Gas constant used for flow calculations
var heat-
Amount of heat added to the flow
var mach-
Mach number of the flow
var p2_p1-
Ratio of downstream pressure to upstream pressure
var p_p_st-
Ratio of pressure to the sonic pressure P/P*
var po2_po1-
Ratio of downstream total pressure to upstream total pressure
var po_po_st-
Ratio of the stagnation pressure to the sonic stagnation pressure P0/P0*
var precision-
Precision to use when printing output to the console defaults to four
var rho2_rho1-
Ratio of downstream density to upstream density
var rho_rho_st-
Ratio of the density to the sonic density rho/rho*
var t2_t1-
Ratio of downstream temperature to upstream temperature
var t_t_st-
Ratio of temperature to the sonic temperature T/T*
var to1-
Upstream total temperature
var to2-
Downstream total temperature
var to2_to1-
Ratio of downstream total temperature to upstream total temperature
var to_to_st-
Ratio of the total temperature to the sonic total temperature T0/T0*
var u2_u1-
Ratio of downstream velocity to upstream velocity
var u_u_st-
Ratio of velocity to the sonic velcoity U/U*
Methods
def simulate_heat_addition(self, heat: float, to1: float, gas_const_r: float) ‑> None-
This functions calculates the downstream flow conditions caused due to applied heat.
Args
heat:float- The amount of heat being applied
to1:float- The initial temperature of the flow
gas_const_r:float- The gas constant of the flow
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def simulate_heat_addition(self, heat: float, to1: float, gas_const_r: float) -> None: """ This functions calculates the downstream flow conditions caused due to applied heat. Args: heat (float): The amount of heat being applied to1 (float): The initial temperature of the flow gas_const_r (float): The gas constant of the flow """ self.gas_constant_r = gas_const_r self.to1 = to1 self.heat = heat self.cp = self.gamma * gas_const_r / (self.gamma - 1) self.to2 = self.to1 + self.heat / self.cp temp_star = self.to1 / self.to_to_st self.choked_heat = self.cp * (temp_star - self.to1) self.to2_to1 = self.to2 / self.to1 self.dwn_strm_to_to_st = self.to2_to1 * self.to_to_st if self.heat > self.choked_heat: self.dwn_strm_to_to_st = 1 self.dwn_strm_mach = RayleighFlowRelations.calc_mach_from_to_to_star( self.dwn_strm_to_to_st, self.gamma, self.flow_type ) self.dwn_strm_t_t_st = RayleighFlowRelations.calc_t_t_star(self.dwn_strm_mach, self.gamma) self.dwn_strm_p_p_st = RayleighFlowRelations.calc_p_p_star(self.dwn_strm_mach, self.gamma) self.dwn_strm_rho_rho_st = RayleighFlowRelations.calc_rho_rho_star( self.dwn_strm_mach, self.gamma ) self.dwn_strm_po_po_st = RayleighFlowRelations.calc_po_po_star( self.dwn_strm_mach, self.gamma ) self.dwn_strm_to_to_st = RayleighFlowRelations.calc_to_to_star( self.dwn_strm_mach, self.gamma ) self.dwn_strm_u_u_st = RayleighFlowRelations.calc_u_u_starar(self.dwn_strm_mach, self.gamma) self.to2_to1 = self.dwn_strm_to_to_st / self.to_to_st self.t2_t1 = self.dwn_strm_t_t_st / self.t_t_st self.p2_p1 = self.dwn_strm_p_p_st / self.p_p_st self.rho2_rho1 = self.dwn_strm_rho_rho_st / self.rho_rho_st self.po2_po1 = self.dwn_strm_po_po_st / self.po_po_st self.u2_u1 = self.dwn_strm_u_u_st / self.u_u_st