Module CompAero.fanno_flow_relations
Provides a class around the Fanno Flow State
Expand source code
"""Provides a class around the Fanno Flow State"""
from enum import Enum
from math import log, nan, sqrt
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 FannoFlowChoice(Enum):
GAMMA_MACH = "gamma, mach"
GAMMA_T_T_ST = "gamma, T/T*"
GAMMA_P_P_ST = "gamma, P/P*"
GAMMA_RHO_RHO_ST = "gamma, rho/rho*"
GAMMA_PO_PO_ST = "gamma, P0/P0*"
GAMMA_4FLSTD_FLOW_TYPE = "gamma, 4FL*/D, flowtype"
GAMMA_U_U_ST = "gamma, U/U*"
FANNO_FLOW_VALID_OPTIONS = [x.value for x in FannoFlowChoice]
class FannoFlowRelations:
# pylint: disable=too-many-instance-attributes
"""This class is a collective name space for basic calculations regarding Fanno flows.
The constructor of this class can also determine the entire state of the flow given a
partial state of the flow
Args:
gamma (float): ratio of specific heats
mach (float, optional): mach number of the flow. Defaults to nan.
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): Ratio of Total pressure to sonic total pressre. Defaults to nan.
f4lst_d (float, optional): Effect of friction on pipe. 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 and the
rest are calculated.
Valid_Combinations_of_Parameters:
1: gamma, mach\n
2: gamma, T/T*\n
3: gamma, P/P*\n
4: gamma, rho/rho*\n
5: gamma, P0/P0*\n
6: gamma, 4FL*/D, 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,
f4lst_d: 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.f4lst_d = f4lst_d
""" Friction parameter 4fL*/D"""
self.u_u_st = u_u_st
""" Ratio of velocity to the sonic velcoity U/U*"""
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_length = nan
""" Pipe lenght required to choke the flow"""
self.pipe_length = nan
""" Current pipe lenght"""
self.pipe_diameter = nan
""" Diameter of the pipe"""
self.friction_coeff = nan
""" Friction coefficient"""
# 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
""" Ratio of stagnation pressure to sonic stagnation pressure P0/P0* at downstream point"""
self.dwn_strm_f4lst_d = nan
""" Friction parameter 4fL*/D of the downstream flow"""
self.dwn_strm_u_u_st = nan
""" Ratio of velocity to the sonic velcoity U/U* 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.f4ld2_f4ld1 = nan
""" Ratio of the downstream friction parameter to the upstream friction parameter"""
self.u2_u1 = nan
""" Ratio of downstream velocity to upstream velocity """
if not check_value(self.gamma):
raise GammaNotDefinedError()
if check_value(self.mach):
pass
elif check_value(self.t_t_st):
self.mach = FannoFlowRelations.calc_mach_from_t_t_star(self.t_t_st, self.gamma)
elif check_value(self.p_p_st):
self.mach = FannoFlowRelations.calc_mach_from_p_p_star(self.p_p_st, self.gamma)
elif check_value(self.rho_rho_st):
self.mach = FannoFlowRelations.calc_mach_from_rho_rho_star(self.rho_rho_st, self.gamma)
elif check_value(self.po_po_st):
self.mach = FannoFlowRelations.calc_mach_from_po_po_star(
self.po_po_st, self.gamma, flow_type=self.flow_type
)
elif check_value(self.f4lst_d, self.flow_type):
self.mach = FannoFlowRelations.calc_mach_from_4flst_d(
self.f4lst_d, self.gamma, flow_type=self.flow_type
)
elif check_value(self.u_u_st):
self.mach = FannoFlowRelations.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 flow has reached the choked condition (I.E. Sonic)"""
return self.pipe_length >= self.choked_length
def __str__(self) -> str:
color = (
Back.GREEN + Fore.BLACK
if self.pipe_length < self.choked_length
else Back.YELLOW + Fore.BLACK
)
return "".join(
[
named_header("Fanno 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("4FL*/D", self.f4lst_d, self.precision),
to_string("U/U*", self.u_u_st, self.precision, dot_line=True),
to_string("Flow Type", self.flow_type.name, self.precision),
seperator(),
named_subheader("Pipe Parameters"),
to_string("Length For Chocked Flow", self.choked_length, self.precision),
color,
to_string("Is Flow Choked? ", self.choked_flow, self.precision, dot_line=True),
to_string("Pipe Length", self.pipe_length, self.precision),
to_string("Pipe Diameter", self.pipe_diameter, self.precision, dot_line=True),
to_string("Friction Coefficient", self.friction_coeff, 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("4FL*/D", self.dwn_strm_f4lst_d, self.precision, dot_line=True),
to_string("U/U*", self.dwn_strm_u_u_st, self.precision),
seperator(),
named_subheader("Conditions Across Friction Area"),
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("4FL*/D2 / 4FL*/D 1", self.f4ld2_f4ld1, self.precision),
to_string("U2/U1", self.u2_u1, self.precision, dot_line=True),
footer(),
]
)
def apply_pipe_parameters(
self, diameter: float, length: float, friction_coeff: float = 0.005
) -> None:
"""This functions applies parameters of a known pipe to the determined state of the flow.
This allows the state at the downstream end of the pipe or pipe section to be found
Args:
diameter (float): Diameter of pipe
length (float): Length of pipe
friction_coeff (float, optional): Friction coefficient of the pipe. Defaults to 0.005
which holds for Reynolds > 10^5.
"""
self.pipe_diameter = diameter
self.pipe_length = length
self.friction_coeff = friction_coeff
self._calc_down_stream_state()
def _calc_state(self) -> None:
self.t_t_st = FannoFlowRelations.calc_t_t_star(self.mach, self.gamma)
self.p_p_st = FannoFlowRelations.calc_p_p_star(self.mach, self.gamma)
self.rho_rho_st = FannoFlowRelations.calc_rho_rho_star(self.mach, self.gamma)
self.po_po_st = FannoFlowRelations.calc_po_po_star(self.mach, self.gamma)
self.f4lst_d = FannoFlowRelations.calc_4flst_d(self.mach, self.gamma)
self.u_u_st = FannoFlowRelations.calc_u_u_starar(self.mach, self.gamma)
if self.mach < 1:
self.flow_type = FlowState.SUB_SONIC
else:
self.flow_type = FlowState.SUPER_SONIC
def _calc_down_stream_state(self) -> None:
if not check_value(self.pipe_diameter, self.pipe_length, self.friction_coeff):
return
self.choked_length = self.f4lst_d * self.pipe_diameter / 4 / self.friction_coeff
self.dwn_strm_f4lst_d = (
self.f4lst_d - 4 * self.friction_coeff * self.pipe_length / self.pipe_diameter
)
if self.pipe_length > self.choked_length:
self.dwn_strm_mach = 1
else:
self.dwn_strm_mach = FannoFlowRelations.calc_mach_from_4flst_d(
self.dwn_strm_f4lst_d, self.gamma, self.flow_type
)
self.dwn_strm_t_t_st = FannoFlowRelations.calc_t_t_star(self.dwn_strm_mach, self.gamma)
self.dwn_strm_p_p_st = FannoFlowRelations.calc_p_p_star(self.dwn_strm_mach, self.gamma)
self.dwn_strm_rho_rho_st = FannoFlowRelations.calc_rho_rho_star(
self.dwn_strm_mach, self.gamma
)
self.dwn_strm_po_po_st = FannoFlowRelations.calc_po_po_star(self.dwn_strm_mach, self.gamma)
self.dwn_strm_u_u_st = FannoFlowRelations.calc_u_u_starar(self.dwn_strm_mach, self.gamma)
self.dwn_strm_f4lst_d = FannoFlowRelations.calc_4flst_d(self.dwn_strm_mach, self.gamma)
# Calculate parameter ratios across the condition
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.f4ld2_f4ld1 = self.dwn_strm_f4lst_d / self.f4lst_d
self.u2_u1 = self.dwn_strm_u_u_st / self.u_u_st
@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 for a specific
value. Defaults to 0.0.
Returns:
float: T/T*
"""
return (gamma + 1) / (2 + (gamma - 1) * pow(mach, 2)) - offset
@staticmethod
def calc_mach_from_t_t_star(t_t_st: float, gamma: float) -> float:
"""Calculates the mach number based of the ratio of static temp to 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
Returns:
float: mach number
"""
return brenth(
FannoFlowRelations.calc_t_t_star,
1e-9,
40,
args=(
gamma,
t_t_st,
),
) # type: ignore
@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 for a specific
value. Defaults to 0.0.
Returns:
float: P/P*
"""
return sqrt(FannoFlowRelations.calc_t_t_star(mach, gamma)) / mach - offset
@staticmethod
def calc_mach_from_p_p_star(p_p_st: float, gamma: float) -> float:
"""
Calculates the mach 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(
FannoFlowRelations.calc_p_p_star,
1e-9,
40,
args=(
gamma,
p_p_st,
),
) # type: ignore
@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 for a specific
value. Defaults to 0.0.
Returns:
float: Rho/Rho*
"""
return sqrt(1 / FannoFlowRelations.calc_t_t_star(mach, gamma)) / mach - 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(
FannoFlowRelations.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 for a specific
value. Defaults to 0.0.
Returns:
float: P0/P0*
"""
gp1 = gamma + 1
gm1 = gamma - 1
return (
pow(1 / FannoFlowRelations.calc_t_t_star(mach, gamma), gp1 / (2 * gm1)) / mach - 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 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(
FannoFlowRelations.calc_po_po_star,
1 + tolerance,
40,
args=(
gamma,
po_po_st,
),
) # type: ignore
if flow_type == FlowState.SUB_SONIC:
return brenth(
FannoFlowRelations.calc_po_po_star,
tolerance,
1 - tolerance,
args=(
gamma,
po_po_st,
),
) # type: ignore
err = f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow! {Fore.RESET}"
raise ValueError(err)
@staticmethod
def calc_4flst_d(mach: float, gamma: float, offset: float = 0.0) -> float:
"""Calculates friction parameter for flow
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 for a specific
value. Defaults to 0.0.
Returns:
float: 4FL*/D
"""
gp1 = gamma + 1
t_t_st = FannoFlowRelations.calc_t_t_star(mach, gamma)
m_sqr = pow(mach, 2)
return (1 - m_sqr) / (gamma * m_sqr) + (gp1 / (2 * gamma)) * log(t_t_st * m_sqr) - offset
@staticmethod
def calc_mach_from_4flst_d(
f4lst_d: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC
) -> float:
"""Calculates the mach number from the friction parameter
Args:
f4lSt_d (float): friction parameter 4FL*/D
gamma (float): ratio of specific heats
flow_type (FlowState, optional): Type of flow whether it is super sonic of subsonic.
Defaults to FlowState.SUPER_SONIC.
Raises:
ValueError: Raised if Flow State is not supersonic of subsonic
Returns:
float: mach number
"""
if f4lst_d == 0.0:
return 1
if flow_type == FlowState.SUPER_SONIC:
return brenth(
FannoFlowRelations.calc_4flst_d,
1.00001,
50,
args=(
gamma,
f4lst_d,
),
) # type: ignore
if flow_type == FlowState.SUB_SONIC:
return brenth(
FannoFlowRelations.calc_4flst_d,
1e-5,
0.9999,
args=(
gamma,
f4lst_d,
),
) # type: ignore
err = f"{Fore.RED}Flow Type [{flow_type}] not supported for FannoFlow!{Fore.RESET}"
raise ValueError(err)
@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 for a specific
value. Defaults to 0.0.
Returns:
float: U/U*
"""
t_t_st = FannoFlowRelations.calc_t_t_star(mach, gamma)
return mach * sqrt(t_t_st) - 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(
FannoFlowRelations.calc_u_u_starar, 1e-9, 40, args=(gamma, u_u_st)
) # type: ignoreClasses
class FannoFlowChoice (*args, **kwds)-
Create a collection of name/value pairs.
Example enumeration:
>>> class Color(Enum): ... RED = 1 ... BLUE = 2 ... GREEN = 3Access them by:
- attribute access::
>>> Color.RED <Color.RED: 1>- value lookup:
>>> Color(1) <Color.RED: 1>- name lookup:
>>> Color['RED'] <Color.RED: 1>Enumerations can be iterated over, and know how many members they have:
>>> len(Color) 3>>> list(Color) [<Color.RED: 1>, <Color.BLUE: 2>, <Color.GREEN: 3>]Methods can be added to enumerations, and members can have their own attributes – see the documentation for details.
Expand source code
class FannoFlowChoice(Enum): GAMMA_MACH = "gamma, mach" GAMMA_T_T_ST = "gamma, T/T*" GAMMA_P_P_ST = "gamma, P/P*" GAMMA_RHO_RHO_ST = "gamma, rho/rho*" GAMMA_PO_PO_ST = "gamma, P0/P0*" GAMMA_4FLSTD_FLOW_TYPE = "gamma, 4FL*/D, flowtype" GAMMA_U_U_ST = "gamma, U/U*"Ancestors
- enum.Enum
Class variables
var GAMMA_4FLSTD_FLOW_TYPEvar GAMMA_MACHvar GAMMA_PO_PO_STvar GAMMA_P_P_STvar GAMMA_RHO_RHO_STvar GAMMA_T_T_STvar GAMMA_U_U_ST
class FannoFlowRelations (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, f4lst_d: 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. The constructor of this class can also determine the entire state of the flow given a partial state of the flow
Args
gamma:float- ratio of specific heats
mach:float, optional- mach number of the flow. Defaults to nan.
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- Ratio of Total pressure to sonic total pressre. Defaults to nan.
f4lst_d:float, optional- Effect of friction on pipe. 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 and the rest are calculated.
Valid_Combinations_Of_Parameters
1: gamma, mach
2: gamma, T/T*
3: gamma, P/P*
4: gamma, rho/rho*
5: gamma, P0/P0*
6: gamma, 4FL*/D, flowtype (flow type defaults to super sonic)
7: gamma, U/U*
Expand source code
class FannoFlowRelations: # pylint: disable=too-many-instance-attributes """This class is a collective name space for basic calculations regarding Fanno flows. The constructor of this class can also determine the entire state of the flow given a partial state of the flow Args: gamma (float): ratio of specific heats mach (float, optional): mach number of the flow. Defaults to nan. 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): Ratio of Total pressure to sonic total pressre. Defaults to nan. f4lst_d (float, optional): Effect of friction on pipe. 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 and the rest are calculated. Valid_Combinations_of_Parameters: 1: gamma, mach\n 2: gamma, T/T*\n 3: gamma, P/P*\n 4: gamma, rho/rho*\n 5: gamma, P0/P0*\n 6: gamma, 4FL*/D, 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, f4lst_d: 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.f4lst_d = f4lst_d """ Friction parameter 4fL*/D""" self.u_u_st = u_u_st """ Ratio of velocity to the sonic velcoity U/U*""" 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_length = nan """ Pipe lenght required to choke the flow""" self.pipe_length = nan """ Current pipe lenght""" self.pipe_diameter = nan """ Diameter of the pipe""" self.friction_coeff = nan """ Friction coefficient""" # 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 """ Ratio of stagnation pressure to sonic stagnation pressure P0/P0* at downstream point""" self.dwn_strm_f4lst_d = nan """ Friction parameter 4fL*/D of the downstream flow""" self.dwn_strm_u_u_st = nan """ Ratio of velocity to the sonic velcoity U/U* 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.f4ld2_f4ld1 = nan """ Ratio of the downstream friction parameter to the upstream friction parameter""" self.u2_u1 = nan """ Ratio of downstream velocity to upstream velocity """ if not check_value(self.gamma): raise GammaNotDefinedError() if check_value(self.mach): pass elif check_value(self.t_t_st): self.mach = FannoFlowRelations.calc_mach_from_t_t_star(self.t_t_st, self.gamma) elif check_value(self.p_p_st): self.mach = FannoFlowRelations.calc_mach_from_p_p_star(self.p_p_st, self.gamma) elif check_value(self.rho_rho_st): self.mach = FannoFlowRelations.calc_mach_from_rho_rho_star(self.rho_rho_st, self.gamma) elif check_value(self.po_po_st): self.mach = FannoFlowRelations.calc_mach_from_po_po_star( self.po_po_st, self.gamma, flow_type=self.flow_type ) elif check_value(self.f4lst_d, self.flow_type): self.mach = FannoFlowRelations.calc_mach_from_4flst_d( self.f4lst_d, self.gamma, flow_type=self.flow_type ) elif check_value(self.u_u_st): self.mach = FannoFlowRelations.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 flow has reached the choked condition (I.E. Sonic)""" return self.pipe_length >= self.choked_length def __str__(self) -> str: color = ( Back.GREEN + Fore.BLACK if self.pipe_length < self.choked_length else Back.YELLOW + Fore.BLACK ) return "".join( [ named_header("Fanno 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("4FL*/D", self.f4lst_d, self.precision), to_string("U/U*", self.u_u_st, self.precision, dot_line=True), to_string("Flow Type", self.flow_type.name, self.precision), seperator(), named_subheader("Pipe Parameters"), to_string("Length For Chocked Flow", self.choked_length, self.precision), color, to_string("Is Flow Choked? ", self.choked_flow, self.precision, dot_line=True), to_string("Pipe Length", self.pipe_length, self.precision), to_string("Pipe Diameter", self.pipe_diameter, self.precision, dot_line=True), to_string("Friction Coefficient", self.friction_coeff, 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("4FL*/D", self.dwn_strm_f4lst_d, self.precision, dot_line=True), to_string("U/U*", self.dwn_strm_u_u_st, self.precision), seperator(), named_subheader("Conditions Across Friction Area"), 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("4FL*/D2 / 4FL*/D 1", self.f4ld2_f4ld1, self.precision), to_string("U2/U1", self.u2_u1, self.precision, dot_line=True), footer(), ] ) def apply_pipe_parameters( self, diameter: float, length: float, friction_coeff: float = 0.005 ) -> None: """This functions applies parameters of a known pipe to the determined state of the flow. This allows the state at the downstream end of the pipe or pipe section to be found Args: diameter (float): Diameter of pipe length (float): Length of pipe friction_coeff (float, optional): Friction coefficient of the pipe. Defaults to 0.005 which holds for Reynolds > 10^5. """ self.pipe_diameter = diameter self.pipe_length = length self.friction_coeff = friction_coeff self._calc_down_stream_state() def _calc_state(self) -> None: self.t_t_st = FannoFlowRelations.calc_t_t_star(self.mach, self.gamma) self.p_p_st = FannoFlowRelations.calc_p_p_star(self.mach, self.gamma) self.rho_rho_st = FannoFlowRelations.calc_rho_rho_star(self.mach, self.gamma) self.po_po_st = FannoFlowRelations.calc_po_po_star(self.mach, self.gamma) self.f4lst_d = FannoFlowRelations.calc_4flst_d(self.mach, self.gamma) self.u_u_st = FannoFlowRelations.calc_u_u_starar(self.mach, self.gamma) if self.mach < 1: self.flow_type = FlowState.SUB_SONIC else: self.flow_type = FlowState.SUPER_SONIC def _calc_down_stream_state(self) -> None: if not check_value(self.pipe_diameter, self.pipe_length, self.friction_coeff): return self.choked_length = self.f4lst_d * self.pipe_diameter / 4 / self.friction_coeff self.dwn_strm_f4lst_d = ( self.f4lst_d - 4 * self.friction_coeff * self.pipe_length / self.pipe_diameter ) if self.pipe_length > self.choked_length: self.dwn_strm_mach = 1 else: self.dwn_strm_mach = FannoFlowRelations.calc_mach_from_4flst_d( self.dwn_strm_f4lst_d, self.gamma, self.flow_type ) self.dwn_strm_t_t_st = FannoFlowRelations.calc_t_t_star(self.dwn_strm_mach, self.gamma) self.dwn_strm_p_p_st = FannoFlowRelations.calc_p_p_star(self.dwn_strm_mach, self.gamma) self.dwn_strm_rho_rho_st = FannoFlowRelations.calc_rho_rho_star( self.dwn_strm_mach, self.gamma ) self.dwn_strm_po_po_st = FannoFlowRelations.calc_po_po_star(self.dwn_strm_mach, self.gamma) self.dwn_strm_u_u_st = FannoFlowRelations.calc_u_u_starar(self.dwn_strm_mach, self.gamma) self.dwn_strm_f4lst_d = FannoFlowRelations.calc_4flst_d(self.dwn_strm_mach, self.gamma) # Calculate parameter ratios across the condition 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.f4ld2_f4ld1 = self.dwn_strm_f4lst_d / self.f4lst_d self.u2_u1 = self.dwn_strm_u_u_st / self.u_u_st @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 for a specific value. Defaults to 0.0. Returns: float: T/T* """ return (gamma + 1) / (2 + (gamma - 1) * pow(mach, 2)) - offset @staticmethod def calc_mach_from_t_t_star(t_t_st: float, gamma: float) -> float: """Calculates the mach number based of the ratio of static temp to 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 Returns: float: mach number """ return brenth( FannoFlowRelations.calc_t_t_star, 1e-9, 40, args=( gamma, t_t_st, ), ) # type: ignore @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 for a specific value. Defaults to 0.0. Returns: float: P/P* """ return sqrt(FannoFlowRelations.calc_t_t_star(mach, gamma)) / mach - offset @staticmethod def calc_mach_from_p_p_star(p_p_st: float, gamma: float) -> float: """ Calculates the mach 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( FannoFlowRelations.calc_p_p_star, 1e-9, 40, args=( gamma, p_p_st, ), ) # type: ignore @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 for a specific value. Defaults to 0.0. Returns: float: Rho/Rho* """ return sqrt(1 / FannoFlowRelations.calc_t_t_star(mach, gamma)) / mach - 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( FannoFlowRelations.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 for a specific value. Defaults to 0.0. Returns: float: P0/P0* """ gp1 = gamma + 1 gm1 = gamma - 1 return ( pow(1 / FannoFlowRelations.calc_t_t_star(mach, gamma), gp1 / (2 * gm1)) / mach - 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 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( FannoFlowRelations.calc_po_po_star, 1 + tolerance, 40, args=( gamma, po_po_st, ), ) # type: ignore if flow_type == FlowState.SUB_SONIC: return brenth( FannoFlowRelations.calc_po_po_star, tolerance, 1 - tolerance, args=( gamma, po_po_st, ), ) # type: ignore err = f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow! {Fore.RESET}" raise ValueError(err) @staticmethod def calc_4flst_d(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates friction parameter for flow 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 for a specific value. Defaults to 0.0. Returns: float: 4FL*/D """ gp1 = gamma + 1 t_t_st = FannoFlowRelations.calc_t_t_star(mach, gamma) m_sqr = pow(mach, 2) return (1 - m_sqr) / (gamma * m_sqr) + (gp1 / (2 * gamma)) * log(t_t_st * m_sqr) - offset @staticmethod def calc_mach_from_4flst_d( f4lst_d: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC ) -> float: """Calculates the mach number from the friction parameter Args: f4lSt_d (float): friction parameter 4FL*/D gamma (float): ratio of specific heats flow_type (FlowState, optional): Type of flow whether it is super sonic of subsonic. Defaults to FlowState.SUPER_SONIC. Raises: ValueError: Raised if Flow State is not supersonic of subsonic Returns: float: mach number """ if f4lst_d == 0.0: return 1 if flow_type == FlowState.SUPER_SONIC: return brenth( FannoFlowRelations.calc_4flst_d, 1.00001, 50, args=( gamma, f4lst_d, ), ) # type: ignore if flow_type == FlowState.SUB_SONIC: return brenth( FannoFlowRelations.calc_4flst_d, 1e-5, 0.9999, args=( gamma, f4lst_d, ), ) # type: ignore err = f"{Fore.RED}Flow Type [{flow_type}] not supported for FannoFlow!{Fore.RESET}" raise ValueError(err) @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 for a specific value. Defaults to 0.0. Returns: float: U/U* """ t_t_st = FannoFlowRelations.calc_t_t_star(mach, gamma) return mach * sqrt(t_t_st) - 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( FannoFlowRelations.calc_u_u_starar, 1e-9, 40, args=(gamma, u_u_st) ) # type: ignoreStatic methods
def calc_4flst_d(mach: float, gamma: float, offset: float = 0.0) ‑> float-
Calculates friction parameter for flow
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 for a specific value. Defaults to 0.0.
Returns
float- 4FL*/D
Expand source code
@staticmethod def calc_4flst_d(mach: float, gamma: float, offset: float = 0.0) -> float: """Calculates friction parameter for flow 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 for a specific value. Defaults to 0.0. Returns: float: 4FL*/D """ gp1 = gamma + 1 t_t_st = FannoFlowRelations.calc_t_t_star(mach, gamma) m_sqr = pow(mach, 2) return (1 - m_sqr) / (gamma * m_sqr) + (gp1 / (2 * gamma)) * log(t_t_st * m_sqr) - offset def calc_mach_from_4flst_d(f4lst_d: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC) ‑> float-
Calculates the mach number from the friction parameter
Args
f4lSt_d:float- friction parameter 4FL*/D
gamma:float- ratio of specific heats
flow_type:FlowState, optional- Type of flow whether it is super sonic of subsonic. Defaults to FlowState.SUPER_SONIC.
Raises
ValueError- Raised if Flow State is not supersonic of subsonic
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_from_4flst_d( f4lst_d: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC ) -> float: """Calculates the mach number from the friction parameter Args: f4lSt_d (float): friction parameter 4FL*/D gamma (float): ratio of specific heats flow_type (FlowState, optional): Type of flow whether it is super sonic of subsonic. Defaults to FlowState.SUPER_SONIC. Raises: ValueError: Raised if Flow State is not supersonic of subsonic Returns: float: mach number """ if f4lst_d == 0.0: return 1 if flow_type == FlowState.SUPER_SONIC: return brenth( FannoFlowRelations.calc_4flst_d, 1.00001, 50, args=( gamma, f4lst_d, ), ) # type: ignore if flow_type == FlowState.SUB_SONIC: return brenth( FannoFlowRelations.calc_4flst_d, 1e-5, 0.9999, args=( gamma, f4lst_d, ), ) # type: ignore err = f"{Fore.RED}Flow Type [{flow_type}] not supported for FannoFlow!{Fore.RESET}" raise ValueError(err) def calc_mach_from_p_p_star(p_p_st: float, gamma: float) ‑> float-
Calculates the mach 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
Expand source code
@staticmethod def calc_mach_from_p_p_star(p_p_st: float, gamma: float) -> float: """ Calculates the mach 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( FannoFlowRelations.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 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
Expand source code
@staticmethod def calc_mach_from_po_po_star( po_po_st: float, gamma: float, flow_type: FlowState = FlowState.SUPER_SONIC ) -> float: """Calculates the mach 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( FannoFlowRelations.calc_po_po_star, 1 + tolerance, 40, args=( gamma, po_po_st, ), ) # type: ignore if flow_type == FlowState.SUB_SONIC: return brenth( FannoFlowRelations.calc_po_po_star, tolerance, 1 - tolerance, args=( gamma, po_po_st, ), ) # type: ignore err = f"{Fore.RED} Flow Type [{flow_type}] not supported for Fanno Flow! {Fore.RESET}" raise ValueError(err) 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( FannoFlowRelations.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) ‑> float-
Calculates the mach number based of the ratio of static temp to 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
Returns
float- mach number
Expand source code
@staticmethod def calc_mach_from_t_t_star(t_t_st: float, gamma: float) -> float: """Calculates the mach number based of the ratio of static temp to 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 Returns: float: mach number """ return brenth( FannoFlowRelations.calc_t_t_star, 1e-9, 40, args=( gamma, t_t_st, ), ) # type: ignore 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( FannoFlowRelations.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 for a specific value. 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 for a specific value. Defaults to 0.0. Returns: float: P/P* """ return sqrt(FannoFlowRelations.calc_t_t_star(mach, gamma)) / mach - 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 for a specific value. 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 for a specific value. Defaults to 0.0. Returns: float: P0/P0* """ gp1 = gamma + 1 gm1 = gamma - 1 return ( pow(1 / FannoFlowRelations.calc_t_t_star(mach, gamma), gp1 / (2 * gm1)) / mach - 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 for a specific value. Defaults to 0.0.
Returns
float- Rho/Rho*
Expand source code
@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 for a specific value. Defaults to 0.0. Returns: float: Rho/Rho* """ return sqrt(1 / FannoFlowRelations.calc_t_t_star(mach, gamma)) / mach - 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 for a specific value. Defaults to 0.0.
Returns
float- T/T*
Expand source code
@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 for a specific value. Defaults to 0.0. Returns: float: T/T* """ return (gamma + 1) / (2 + (gamma - 1) * pow(mach, 2)) - 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 for a specific value. Defaults to 0.0.
Returns
float- U/U*
Expand source code
@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 for a specific value. Defaults to 0.0. Returns: float: U/U* """ t_t_st = FannoFlowRelations.calc_t_t_star(mach, gamma) return mach * sqrt(t_t_st) - offset
Instance variables
var choked_flow : bool-
True if the flow has reached the choked condition (I.E. Sonic)
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@property def choked_flow(self) -> bool: """True if the flow has reached the choked condition (I.E. Sonic)""" return self.pipe_length >= self.choked_length var choked_length-
Pipe lenght required to choke the flow
var dwn_strm_f4lst_d-
Friction parameter 4fL*/D of the downstream flow
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-
Ratio of stagnation pressure to sonic stagnation pressure P0/P0* at downstream 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_u_u_st-
Ratio of velocity to the sonic velcoity U/U* at the downstream point
var f4ld2_f4ld1-
Ratio of the downstream friction parameter to the upstream friction parameter
var f4lst_d-
Friction parameter 4fL*/D
var flow_type-
Type of flow which is either subsonic or supersonic (Type: flowstate)
var friction_coeff-
Friction coefficient
var gamma-
Ratio of specific heats
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 pipe_diameter-
Diameter of the pipe
var pipe_length-
Current pipe lenght
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 u2_u1-
Ratio of downstream velocity to upstream velocity
var u_u_st-
Ratio of velocity to the sonic velcoity U/U*
Methods
def apply_pipe_parameters(self, diameter: float, length: float, friction_coeff: float = 0.005) ‑> None-
This functions applies parameters of a known pipe to the determined state of the flow. This allows the state at the downstream end of the pipe or pipe section to be found
Args
diameter:float- Diameter of pipe
length:float- Length of pipe
friction_coeff:float, optional- Friction coefficient of the pipe. Defaults to 0.005 which holds for Reynolds > 10^5.
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def apply_pipe_parameters( self, diameter: float, length: float, friction_coeff: float = 0.005 ) -> None: """This functions applies parameters of a known pipe to the determined state of the flow. This allows the state at the downstream end of the pipe or pipe section to be found Args: diameter (float): Diameter of pipe length (float): Length of pipe friction_coeff (float, optional): Friction coefficient of the pipe. Defaults to 0.005 which holds for Reynolds > 10^5. """ self.pipe_diameter = diameter self.pipe_length = length self.friction_coeff = friction_coeff self._calc_down_stream_state()