a = isent.sound_speed(T)
M = isent.mach_number(v, T)
print('M=', M, 'a=', a)
print('Tt_T=', isent.stagnation_static_rel(M))
print('Tt=', isent.stag_temp_from_mach(M, T))
print('Tt=', isent.stag_temp_from_vel(v, T))
print('pt=', isent.stag_pressure_from_mach(M, p))
print('qi=', isent.impact_pressure_from_mach(M, p))
print('qi=', isent.dynamic_pressure(v, rho))
print('v=', isent.vel_from_stag_temp(isent.stag_temp_from_mach(M, T), T))
print('v=', isent.vel_from_mach(M, T))
print('rho=', rho, 'rhot=', isent.stag_density_from_mach(M, rho))
print('T=', isent.stat_temp_from_mach(M, isent.stag_temp_from_mach(M, T)))
print('p=',
isent.stat_pressure_from_mach(M, isent.stag_pressure_from_mach(M, p)))
## Semiperfect gas
print('--------------------------SemiperfectGas--------------------------')
air = SemiperfectIdealGas('Air')
isent = IsentropicFlow(air)
##
h = 15000
T = isa.temperature_isa(h)
p = isa.pressure_isa(h)
rho = p / air.Rg / T
v = 500 # m/s
a = isent.sound_speed(T)
M = isent.mach_number(v, T)
class Nozzle(ControlVolume):
"""
Nozzle:
-------
Defines a generic nozzle stage control volume, between one entrance and one
exit to the control volume. the nozzle may be solved considering:
+ Adapted discharge
+ Critical, convergent nozzle
+ Critical, con-di (Laval) nozzle
+ Generic nozzle
Contents:
---------
+ initialize_nozzle: initializes the control volume.
+ solve_basic_properties: partially solves basic thermodynamic properties of the nozzle
+ solve_adapted_nozzle: Completes the solution considering adapted discharge of the nozzle
+
+
A total of 34 variables of a control volume are defined:
+ 12 thermodynamic properties at the entrance of the CV:
+ Static properties:
+ p_e, T_e, rho_e, h_e (enthalpy)
+ Stagnation properties
+ p_et, T_et, rho_et, h_et (enthalpy)
+ Other:
+ vel_e (flow velocity), mach_e, ec_e (kin. energy), mflow_e (mass flow)
+ 12 thermodynamic properties at the exit of the CV
+ Static properties:
+ p_s, T_s, rho_s, h_s (enthalpy)
+ Stagnation properties
+ p_st, T_st, rho_st, h_st (enthalpy)
+ Other:
+ vel_s (flow velocity), mach_s, ec_s (kin. energy), mflow_s (mass flow)
+ 6 variables of the CV:
+ specific power:
+ q_se (heating/cooling power along the CV), w_se (mechanical power along the CV)
+ adiab_efficiency, A_e (entrance area), A_s (exit area), delta_massflow (mass flow variation along CV)
+ 4 properties at the nozzle throat, considering choked nozzle:
+ A_star, p_star, T_star
"""
def __init__(self, fluid, stage=None):
"""
"""
# Stage of the power plant:
self.stage = stage
# Initialize superclass methods
super().__init__(fluid)
# Isentropic flow:
if not(isinstance(fluid, PerfectIdealGas) or isinstance(fluid, SemiperfectIdealGas)):
# Check the flow is a Perfect or a Semiperfect gas fom pyturb
raise TypeError("Object must be PerfectIdealGas, SemiperfectIdealGas. Instead received {}".format(fluid))
self.isent_flow = IsentropicFlow(self.fluid)
return None
# **************************
# *** Entrance of the CV ***
# **************************
# Static thermodynamic properties:
@property
def p_e(self):
"""
Static pressure at the entrance of the CV. [Pa]
"""
return self._p_e
@property
def T_e(self):
"""
Static temperature at the entrance of the CV. [K]
"""
return self._T_e
@property
def rho_e(self):
"""
Static density at the entrance of the CV. [kg/m**3]
"""
return self._rho_e
@property
def h_e(self):
"""
Specific static enthalpy at the entrance of the CV. [W/kg/s]
"""
return self._h_e
# Stagnation thermodynamic properties
@property
def p_et(self):
"""
Stagnation pressure at the entrance of the CV. [Pa]
"""
return self._p_et
@property
def T_et(self):
"""
Stagnation temperature at the entrance of the CV. [K]
"""
return self._T_et
@property
def rho_et(self):
"""
Stagnation density at the entrance of the CV. [kg/m**3]
"""
return self._rho_et
@property
def h_et(self):
"""
Specific stagnation enthalpy at the entrance of the CV. [W/kg/s]
"""
return self._h_et
# Velocity and kinetic energy:
@property
def vel_e(self):
"""
Flow velocity at the entrance of the CV. [m/s]
"""
return self._vel_e
@property
def mach_e(self):
"""
"""
return self._mach_e
@property
def ekin_e(self):
"""
Specific kinetic energy at the entrance of the CV. [W/kg/s]
"""
return self._ekin_e
# Mass flow and area:
@property
def mflow_e(self):
"""
Mass flow at the entrance of the CV. [kg/s]
"""
return self._mflow_e
@property
def A_e(self):
"""
Mass flow at the entrance of the CV. [kg/s]
"""
return self._A_e
# **********************
# *** Exit of the CV ***
# **********************
# Static thermodynamic properties:
@property
def p_s(self):
"""
Static pressure at the entrance of the CV. [Pa]
"""
return self._p_s
@property
def T_s(self):
"""
Static temperature at the entrance of the CV. [K]
"""
return self._T_s
@property
def rho_s(self):
"""
Static density at the entrance of the CV. [mg/m**3]
"""
return self._rho_s
@property
def h_s(self):
"""
Specific static enthalpy at the entrance of the CV. [W/kg/s]
"""
return self._h_s
# Stagnation thermodynamic properties
@property
def p_st(self):
"""
Stagnation pressure at the entrance of the CV. [Pa]
"""
return self._p_st
@property
def T_st(self):
"""
Stagnation temperature at the entrance of the CV. [K]
"""
return self._T_st
@property
def rho_st(self):
"""
Stagnation density at the entrance of the CV. [kg/m**3]
"""
return self._rho_st
@property
def h_st(self):
"""
Specific stagnation enthalpy at the entrance of the CV. [W/kg/s]
"""
return self._h_st
# Velocity and kinetic energy:
@property
def vel_s(self):
"""
Flow velocity at the entrance of the CV. [m/s]
"""
return self._vel_s
@property
def mach_s(self):
"""
Mach number at the entrance of the CV. [dimensionless]
"""
return self._mach_s
@property
def ekin_s(self):
"""
Specific kinetic energy at the entrance of the CV. [W/kg/s]
"""
return self._ekin_s
# Mass flow and area:
@property
def mflow_s(self):
"""
Mass flow at the entrance of the CV. [kg/s]
"""
return self._mflow_s
@property
def A_s(self):
"""
Area at the entrance of the CV. [m**2]
"""
return self._A_s
# ***************************
# *** Transfer variables: ***
# ***************************
@property
def w_se(self):
"""
Speficic mechanical power along the CV. [W/mg/s]
"""
return self._w_se
@property
def q_se(self):
"""
Speficic heating power along the CV. [W/mg/s]
"""
return self._q_se
@property
def delta_massflow(self):
"""
Mass flow variation along the CV. [W/mg/s]
"""
return self._delta_massflow
@property
def adiab_efficiency(self):
"""
Adiabatic efficiency along the CV. [dimensionless]
"""
return self._adiab_efficiency
## Critical conditions:
@property
def exit_regime(self):
"""
Flow regime at the exit of the nozzle.
"""
return self._exit_regime
@property
def T_s_star(self):
"""
Static temperature for choked nozzle throat.
"""
return self._T_s_star
@property
def p_s_star(self):
"""
Static temperature for choked nozzle throat.
"""
return self._p_s_star
@property
def A_star(self):
"""
Static temperature for choked nozzle throat.
"""
return self._A_star
@property
def pchoke(self):
"""
Static pressure to have a supersonic nozzle.
"""
return self._pchoke
@property
def padapt(self):
"""
Static pressure to have a supersonic, adapted nozzle.
"""
return self._padapt
## Initializes the nozzle with the exit properties of a CV:
def initialize_from_cv(self, cv):
"""
Initialize nozzle from the exit properties of last CV.
"""
# Isentropic flow:
if not(isinstance(cv, ControlVolume)):
# The control volume from which the nozzle has to be initialized is not a ControlVolume object
raise TypeError("Object must be of type ControlVolume, SemiperfectIdealGas. Instead received {}".format(cv))
self._mflow_e = cv.mflow_s
self._p_et = cv.p_st
self._T_et = cv.T_st
self._A_e = cv.A_s
self.solve_basic_properties()
return
## Collects basic inputs of a nozzle:
def initialize_nozzle(self, mflow_e, pet, Tet, Ae=None):
"""
Set basic inputs of a generic nozzle:
+ mflow_e: float. Mass flow at the entrance [kg/s]
+ pet: float. stagnation pressure at the entrance [Pa]
+ Tet: float. stagnation tmeperature at the entrance [K]
+ Ae: float. Area at the entrance. [m**2]. If no area is provided
related properties are set to np.nan in solve_basic_properties()
"""
self._mflow_e = mflow_e
self._p_et = pet
self._T_et = Tet
self._A_e = Ae
self.solve_basic_properties()
return None
def solve_basic_properties(self):
"""
Solves basic thermodyamic properties and CV variables at the entrance of
the nozzle.
"""
# Mass flow
self._mflow_s = self.mflow_e # By definition
self._delta_massflow = 0 # By definition
# Enthalpies:
self._T_st = self.T_et # All nozzles isoenthalpic
self._h_et = self.fluid.cp(self.T_et) * self.T_et
self._h_st = self.fluid.cp(self.T_st) * self.T_st
# By definition, no work/heat is done
self._q_se = 0
self._w_se = 0
if self.A_e is None:
# If the area at the entrance is not provided all area-related properties are set to nan
self._T_e = np.nan
self._p_e = np.nan
self._rho_e = np.nan
self._rho_et = np.nan
self._vel_e = np.nan
self._h_e = np.nan
self._ekin_e = np.nan
self._mach_e = np.nan
else:
# If the area is provided, the mach number is calculated
gamma_to = self.fluid.gamma(self.T_et)
# Solve mach at the entrance with variable size iterator:
# Subsonic solution:
var_aux = self.mflow_e/self.A_e*np.sqrt(self.fluid.Rg/gamma_to) * np.sqrt(self.T_et)/self.p_et
expon = -(gamma_to+1)/(gamma_to-1)/2
mach_func = lambda M: M*(1+(gamma_to-1)/2*M**2)**(expon) -var_aux
mach_solution, _, _ = num_iters.variable_step_roots(x0=0, func=mach_func, dxmax=.2, verbosity=True)
self._mach_e = mach_solution
# Static properties at the entrance:
self._T_e = self.isent_flow.stat_temp_from_mach(self.mach_e, self.T_et)
self._p_e = self.isent_flow.stat_pressure_from_mach(self.mach_e, self.p_et, self.T_et)
self._rho_e = self.p_e / self.T_e / self.fluid.Rg
self._rho_et = self.isent_flow.stag_density_from_mach(self.mach_e, self.rho_e, self.T_e)
self._vel_e = self.isent_flow.vel_from_mach(self.mach_e, self.T_e)
self._h_e = self.fluid.cp(self.T_e) * self.T_e
self._ekin_e = 0.5 * self.vel_e**2
return
def solve_from_static_exit_pressure(self, ps, As=None, adiab_efficiency=1, nozzle_type='con-di'):
"""
Solve nozzle with static discharge pressure known (exit section).
The nozzle is assumed to be adiabatic.
+ If As is None, the discharge area is calculated with the provided
adiabatic efficiency
+ If As is provided, the corresponding adiabatic efficiency is
calculated. If the efficiency is impossible a warning is raised
Inputs:
-------
ps: float. Static pressure at the exit section (stage #9). [Pa]
As: float. Area of the exit section (stage #9) of a nozzle. If no area is
provided, it is calculated assuming the adiabatic efficiency set in
initialize_nozzle. Otherwise the efficiency is recalculated. A warning
is raised if the adiabatic efficiency is unfeasible.
adiab_effiency: float. Adiabatic efficiency of the nozzle. If the exit area is
not provided, isentropic nozzle is assumed. Otherwise it is calculated
nozzle_type: string. May be 'con-di' for Laval/convergent-divergent nozzle or
'convergent' for a convergent nozzle. By default 'con-di' is selected.
"""
# Nozzle type
if nozzle_type.lower()=='condi' or nozzle_type.lower()=='laval':
nozzle_type = 'con-di'
elif nozzle_type.lower()=='con' or nozzle_type.lower()=='conv':
nozzle_type = 'convergent'
elif not nozzle_type.lower() in ['con-di', 'convergent']:
warnings.warn('Unknown nozzle type: {}. Nozzle will be set to con-di (default)'.format(nozzle_type))
# Store static pressure
self._p_s = ps
gamma_to = self.fluid.gamma(self.T_et)
if As is None:
# Calculate discharge area assuming adapted nozzle with a given adiabatic efficiency
self._adiab_efficiency = adiab_efficiency
Ts_Tet =(1 + self.adiab_efficiency*((self.p_s/self.p_et)**((gamma_to-1)/gamma_to)- 1))
self._T_s = self.T_et * Ts_Tet
if self.T_s <= 2/(gamma_to + 1)*self.T_st:
self._exit_regime = 'supersonic'
self._T_s_star = self.isent_flow.stat_temp_from_mach(1, self.T_st)
self._p_s_star = self.isent_flow.stat_pressure_from_mach(1, self.p_st, self.T_st)
self._A_star = self.A_s*self.mach_s*((gamma_to+1)/2/(1+(gamma_to-1)/2*self.mach_s**2))**((gamma_to+1)/2/(gamma_to-1))
else:
self._exit_regime = 'subsonic'
self._T_s_star = np.nan
self._p_s_star = np.nan
self._A_star = np.nan
self._vel_s = self.isent_flow.vel_from_stag_temp(self.T_st, self.T_s)
self._mach_s = self.isent_flow.mach_number(self.vel_s, self.T_s)
self._p_st = self.isent_flow.stag_pressure_from_mach(self.mach_s, self.p_s, self.T_s)
self._rho_s = self.p_s / self.fluid.Rg / self.T_s
self._A_s = self.mflow_s / self.rho_s / self.vel_s
self._rho_st = self.isent_flow.stag_density_from_mach(self.mach_s, self.rho_s, self.T_s)
self._ekin_s = 0.5 * self.vel_s**2
self._h_s = self.h_st - self.ekin_s
else:
# As is provided, check the adiabatic efficiency
self._A_s = As
# Solve static temperature from mass flow 2nd order equation:
aux_var = 2*self.fluid.cp(self.T_st)*(self.p_s*self.A_s/self.fluid.Rg/self.mflow_s)**2
T9 = (-aux_var + np.sqrt(aux_var**2 + 4*aux_var*self.T_st))/2
self._T_s = T9
if self.T_s <= 2/(gamma_to + 1)*self.T_st:
self._exit_regime = 'supersonic'
self._T_s_star = self.isent_flow.stat_temp_from_mach(1, self.T_st)
self._p_s_star = self.isent_flow.stat_pressure_from_mach(1, self.p_st, self.T_st)
self._A_star = self.A_s*self.mach_s*((gamma_to+1)/2/(1+(gamma_to-1)/2*self.mach_s**2))**((gamma_to+1)/2/(gamma_to-1))
else:
self._exit_regime = 'subsonic'
self._T_s_star = np.nan
self._p_s_star = np.nan
self._A_star = np.nan
self._vel_s = self.isent_flow.vel_from_stag_temp(self.T_st, self.T_s)
self._mach_s = self.isent_flow.mach_number(self.vel_s, self.T_s)
self._p_st = self.isent_flow.stag_pressure_from_mach(self.mach_s, self.p_s, self.T_s)
self._rho_s = self.p_s / self.fluid.Rg / self.T_s
self._rho_st = self.isent_flow.stag_density_from_mach(self.mach_s, self.rho_s, self.T_s)
self._ekin_s = 0.5 * self.vel_s**2
self._h_s = self.h_st - self.ekin_s
# Recalculate adiabatic efficiency
adiab_eff = (self.T_s/self.T_et-1)/((self.p_s/self.p_et)**((gamma_to-1)/gamma_to)-1)
self._adiab_efficiency = adiab_eff
if not 0<=adiab_eff<=1:
warnings.warn('Unfeasible nozzle adiabatic efficiency (ad_eff={0}) for adapted nozzle (ps={1}) and fixed area (As={2})'.format(self.adiab_efficiency, self.p_s, self.A_s), UserWarning)
if self.exit_regime=='supersonic':
if nozzle_type=='convergent':
# Recalculate solution assuming critical, convergent nozzles
self.solve_critical_convergent_nozzle(self.ps, adiab_efficiency=self.adiab_efficiency)
else:
# Calculate nozzle regime. Solution is iterated:
expon = (gamma_to+1)/(2*(gamma_to-1))
area_rela = self.A_star/self.A_s
# Mach function
mach_func = lambda M: M*((gamma_to + 1)/2/( 1+(gamma_to-1)/2*M**2 ))**(expon) - area_rela
# Subsonic solution (pressure at wich choking occurs)
subsonic_mach, _, _ = num_iters.variable_step_roots(x0=0.5, func=mach_func, dxmax=.2, verbosity=True)
# Supersonic solution (pressure at wich supersonic nozzle is adapted).
supersonic_mach, _, _ = num_iters.variable_step_roots(x0=1.5, func=mach_func, dxmax=.2, verbosity=True)
self._pchoke = self.isent_flow.stat_pressure_from_mach(subsonic_mach, self.p_st, self.T_st)
self._padapt = self.isent_flow.stat_pressure_from_mach(supersonic_mach, self.p_st, self.T_st)
return
def solve_critical_convergent_nozzle(self, ps=None, As=None, adiab_efficiency=1):
"""
Critical nozzle (choked) with convergent geometry (thus critical area is
the discharge area A_s). Solves the nozzle assuming critical conditions and:
+ ps: If ps is provided, the discharge area and adiabatic efficiency are
calculated
+ As: if As is provided, the corresponding adiabatic efficiency and static
pressure are calculated. If the efficiency is impossible a warning is raised
+ adiab_efficiency: If no ps nor As are provided, the adiabatic efficiency is
used to calculate the nozzle. By default the nozzle is assumed isentropic.
Inputs:
-------
ps: float. Static discharge pressure [Pa]
As: float. Discharge, critical area [m**2]
adiab_efficiency: float. Adiabatic efficiency of the nozzle. By default is 1 (isentropic)
"""
gamma_to = self.fluid.gamma(self.T_et)
# Exit mach number and static temperature:
self._mach_s = 1
self._exit_regime = 'supersonic'
self._T_s = self.isent_flow.stat_temp_from_mach(1, self.T_st)
self._vel_s = self.isent_flow.sound_speed(self.T_s)
if (As is None) and not (ps is None):
# Store static pressure
self._p_s = ps
# Calculate the critical discharge area given the adiabatic efficiency
self._p_st = self.isent_flow.stag_pressure_from_mach(self.mach_s, self.p_s, self.T_s)
self._rho_s = self.p_s / self.fluid.Rg / self.T_s
self._A_s = self.mflow_s / self.rho_s / self.vel_s
self._rho_st = self.isent_flow.stag_density_from_mach(self.mach_s, self.rho_s, self.T_s)
self._ekin_s = 0.5 * self.vel_s**2
self._h_s = self.h_st - self.ekin_s
# Recalculate adiabatic efficiency
adiab_eff = (self.T_s/self.T_et-1)/((self.p_s/self.p_et)**((gamma_to-1)/gamma_to)-1)
self._adiab_efficiency = adiab_eff
if not 0<=adiab_eff<=1:
warnings.warn('Unfeasible nozzle adiabatic efficiency (ad_eff={0}) for adapted nozzle (ps={1}) and fixed area (As={2})'.format(self.adiab_efficiency, self.p_s, self.T_s), UserWarning)
elif not (As is None) and (ps is None):
# As is provided
self._A_s = As
self._rho_s = self.mflow_s / self.A_s / self.vel_s
self._rho_st = self.isent_flow.stag_density_from_mach(self.mach_s, self.rho_s, self.T_s)
self._p_s = self.rho_s * self.fluid.Rg * self.T_s
self._p_st = self.isent_flow.stag_pressure_from_mach(self.mach_s, self.p_s, self.T_s)
self._rho_st = self.isent_flow.stag_density_from_mach(self.mach_s, self.rho_s, self.T_s)
self._ekin_s = 0.5 * self.vel_s**2
self._h_s = self.h_st - self.ekin_s
# Recalculate adiabatic efficiency
adiab_eff = (self.T_s/self.T_et-1)/((self.p_s/self.p_et)**((gamma_to-1)/gamma_to)-1)
self._adiab_efficiency = adiab_eff
if not 0<=adiab_eff<=1:
warnings.warn('Unfeasible nozzle adiabatic efficiency (ad_eff={0}) for adapted nozzle (ps={1}) and fixed area (As={2})'.format(self.adiab_efficiency, self.p_s, self.T_s), UserWarning)
elif (As is None) and (ps is None):
# Calculate ps form adiabatic efficiency
self._adiab_efficiency = adiab_efficiency
# Static pressure
self._p_s = self.p_et * (1 + (self.T_s/self.T_et -1)/self.adiab_efficiency)**(gamma_to/(gamma_to-1))
self._rho_s = self.p_s / self.fluid.Rg / self.T_s
self._A_s = self.mflow_s / self.rho_s / self.vel_s
self._rho_st = self.isent_flow.stag_density_from_mach(self.mach_s, self.rho_s, self.T_s)
self._p_st = self.isent_flow.stag_pressure_from_mach(self.mach_s, self.p_s, self.T_s)
self._ekin_s = 0.5 * self.vel_s**2
self._h_s = self.h_st - self.ekin_s
else:
warnings.warn('If the nozzle is critical, the area and the static pressure at the discharge section cannot be set at the same time. The static pressure at the discharge section will be dismissed and recalculated.')
# As is provided
self._A_s = As
self._rho_s = self.mflow_s / self.A_s / self.vel_s
self._rho_st = self.isent_flow.stag_density_from_mach(self.mach_s, self.rho_s, self.T_s)
self._p_s = self.rho_s * self.fluid.Rg * self.T_s
self._p_st = self.isent_flow.stag_pressure_from_mach(self.mach_s, self.p_s, self.T_s)
self._rho_st = self.isent_flow.stag_density_from_mach(self.mach_s, self.rho_s, self.T_s)
self._ekin_s = 0.5 * self.vel_s**2
self._h_s = self.h_st - self.ekin_s
# Recalculate adiabatic efficiency
adiab_eff = (self.T_s/self.T_et-1)/((self.p_s/self.p_et)**((gamma_to-1)/gamma_to)-1)
self._adiab_efficiency = adiab_eff
if not 0<=adiab_eff<=1:
warnings.warn('Unfeasible nozzle adiabatic efficiency (ad_eff={0}) for adapted nozzle (ps={1}) and fixed area (As={2})'.format(self.adiab_efficiency, self.p_s, self.T_s), UserWarning)
# Critical conditions:
self._p_s_star = self.p_s
self._T_s_star = self.T_s
self._A_star = self.A_s
if self.A_s>=self.A_e:
warnings.warn('Exit area must be smaller than entry area in a convergent, critical nozzle. Results may be unfeasible')
return
def solve_generic_nozzle(self, ps=None, As=None, adiab_efficiency=1, nozzle_type='con-di'):
"""
Generic nozzle solver.
"""
# Nozzle type
if nozzle_type.lower()=='condi' or nozzle_type.lower()=='laval':
nozzle_type = 'con-di'
elif nozzle_type.lower()=='con':
nozzle_type = 'convergent'
elif not nozzle_type.lower() in ['con-di', 'convergent']:
warnings.warn('Unknown nozzle type: {}. Nozzle will be set to con-di (default)'.format(nozzle_type))
gamma_to = self.fluid.gamma(self.T_et)
if (As is None) and (ps is None):
warnings.warn("Exit area or exit static pressure must be provided to solve a generic nozzle.")
elif (As is None) and not (ps is None):
# Calculate discharge area assuming known adiabatic efficiency and static pressure
self._adiab_efficiency = adiab_efficiency
self._p_s = ps
self.solve_from_static_exit_pressure(self.p_s, adiab_efficiency=self.adiab_efficiency)
elif not (As is None) and (ps is None):
# As is provided
self._A_s = As
T_s_function = lambda T_s: self.p_et * (1+ (T_s/self.T_et-1)/self.adiab_efficiency)**(gamma_to/(gamma_to-1)) - self.mflow_s*self.fluid.Rg*T_s/self.A_s/np.sqrt(2*self.fluid.cp(self.T_st - T_s))
T_s_solution, _, _ = num_iters.variable_step_roots(x0=220, func=T_s_function, dxmax=5, verbosity=True)
p_s = self.mflow_s*self.fluid.Rg*T_s_solution/self.A_s / self.isent_flow.vel_from_stag_temp(self.T_st, T_s_solution)
self._p_s = p_s
self._T_s = T_s_solution
self._vel_s = self.isent_flow.vel_from_stag_temp(self.T_st, self.T_s)
self._mach_s = self.isent_flow.mach_number(self.vel_s, self.T_s)
if self.T_s <= 2/(gamma_to + 1)*self.T_st:
self._exit_regime = 'supersonic'
self._T_s_star = self.isent_flow.stat_temp_from_mach(1, self.T_st)
self._p_s_star = self.isent_flow.stat_pressure_from_mach(1, self.p_st, self.T_st)
self._A_star = self.A_s*self.mach_s*((gamma_to+1)/2/(1+(gamma_to-1)/2*self.mach_s**2))**((gamma_to+1)/2/(gamma_to-1))
else:
self._exit_regime = 'subsonic'
self._T_s_star = np.nan
self._p_s_star = np.nan
self._A_star = np.nan
self._rho_st = self.isent_flow.stag_density_from_mach(self.mach_s, self.rho_s, self.T_s)
self._ekin_s = 0.5 * self.vel_s**2
self._h_s = self.h_st - self.ekin_s
if self.exit_regime=='supersonic':
if nozzle_type=='convergent':
# Recalculate solution assuming critical, convergent nozzles
self.solve_critical_convergent_nozzle(self.ps, adiab_efficiency=self.adiab_efficiency)
else:
# Calculate nozzle regime. Solution is iterated:
expon = (gamma_to+1)/(2*(gamma_to-1))
area_rela = self.A_star/self.A_s
# Mach function
mach_func = lambda M: M*((gamma_to + 1)/2/( 1+(gamma_to-1)/2*M**2 ))**(expon) - area_rela
# Subsonic solution (pressure at wich choking occurs)
subsonic_mach, _, _ = num_iters.variable_step_roots(x0=0.5, func=mach_func, dxmax=.2, verbosity=True)
# Supersonic solution (pressure at wich supersonic nozzle is adapted).
supersonic_mach, _, _ = num_iters.variable_step_roots(x0=1.5, func=mach_func, dxmax=.2, verbosity=True)
self._pchoke = self.isent_flow.stat_pressure_from_mach(subsonic_mach, self.p_st, self.T_st)
self._padapt = self.isent_flow.stat_pressure_from_mach(supersonic_mach, self.p_st, self.T_st)
return
class Intake(ControlVolume):
"""
Intake:
-------
Defines a generic intake stage control volume, between one entrance and one
exit to the control volume.
Contents:
---------
+ initialize_intake: initializes the control volume with the minimum number
of thermodynamic properties and variables needed to solve the intake.
+ solve_intake: solves all thermodynamic properties and variables involved
in the control volume.
A total of 30 variables of a control volume are defined:
+ 12 thermodynamic properties at the entrance of the CV:
+ Static properties:
+ p_e, T_e, rho_e, h_e (enthalpy)
+ Stagnation properties
+ p_et, T_et, rho_et, h_et (enthalpy)
+ Other:
+ vel_e (flow velocity), mach_e, ec_e (kin. energy), mflow_e (mass flow)
+ 12 thermodynamic properties at the exit of the CV
+ Static properties:
+ p_s, T_s, rho_s, h_s (enthalpy)
+ Stagnation properties
+ p_st, T_st, rho_st, h_st (enthalpy)
+ Other:
+ vel_s (flow velocity), mach_s, ec_s (kin. energy), mflow_s (mass flow)
+ 6 variables of the CV:
+ specific power:
+ q_se (heating/cooling power along the CV), w_se (mechanical power along the CV)
+ adiab_efficiency, A_e (entrance area), A_s (exit area), delta_massflow (mass flow variation along CV)
"""
def __init__(self, fluid, stage=None):
"""
Initializes Intake and ControlVolume.
"""
# Stage of the power plant:
self.stage = stage
# Initialize superclass methods
super().__init__(fluid)
# Isentropic flow:
if not (isinstance(fluid, PerfectIdealGas)
or isinstance(fluid, SemiperfectIdealGas)):
# Check the flow is a Perfect or a Semiperfect gas fom pyturb
raise TypeError(
"Object must be PerfectIdealGas, SemiperfectIdealGas. Instead received {}"
.format(fluid))
self.isent_flow = IsentropicFlow(self.fluid)
return None
# **************************
# *** Entrance of the CV ***
# **************************
# Static thermodynamic properties:
@property
def p_e(self):
"""
Static pressure at the entrance of the CV. [Pa]
"""
return self._p_e
@property
def T_e(self):
"""
Static temperature at the entrance of the CV. [K]
"""
return self._T_e
@property
def rho_e(self):
"""
Static density at the entrance of the CV. [kg/m**3]
"""
return self._rho_e
@property
def h_e(self):
"""
Specific static enthalpy at the entrance of the CV. [W/kg/s]
"""
return self._h_e
# Stagnation thermodynamic properties
@property
def p_et(self):
"""
Stagnation pressure at the entrance of the CV. [Pa]
"""
return self._p_et
@property
def T_et(self):
"""
Stagnation temperature at the entrance of the CV. [K]
"""
return self._T_et
@property
def rho_et(self):
"""
Stagnation density at the entrance of the CV. [kg/m**3]
"""
return self._rho_et
@property
def h_et(self):
"""
Specific stagnation enthalpy at the entrance of the CV. [W/kg/s]
"""
return self._h_et
# Velocity and kinetic energy:
@property
def vel_e(self):
"""
Flow velocity at the entrance of the CV. [m/s]
"""
return self._vel_e
@property
def mach_e(self):
"""
"""
return self._mach_e
@property
def ekin_e(self):
"""
Specific kinetic energy at the entrance of the CV. [W/kg/s]
"""
return self._ekin_e
# Mass flow and area:
@property
def mflow_e(self):
"""
Mass flow at the entrance of the CV. [kg/s]
"""
return self._mflow_e
@property
def A_e(self):
"""
Mass flow at the entrance of the CV. [kg/s]
"""
return self._A_e
# **********************
# *** Exit of the CV ***
# **********************
# Static thermodynamic properties:
@property
def p_s(self):
"""
Static pressure at the entrance of the CV. [Pa]
"""
return self._p_s
@property
def T_s(self):
"""
Static temperature at the entrance of the CV. [K]
"""
return self._T_s
@property
def rho_s(self):
"""
Static density at the entrance of the CV. [mg/m**3]
"""
return self._rho_s
@property
def h_s(self):
"""
Specific static enthalpy at the entrance of the CV. [W/kg/s]
"""
return self._h_s
# Stagnation thermodynamic properties
@property
def p_st(self):
"""
Stagnation pressure at the entrance of the CV. [Pa]
"""
return self._p_st
@property
def T_st(self):
"""
Stagnation temperature at the entrance of the CV. [K]
"""
return self._T_st
@property
def rho_st(self):
"""
Stagnation density at the entrance of the CV. [kg/m**3]
"""
return self._rho_st
@property
def h_st(self):
"""
Specific stagnation enthalpy at the entrance of the CV. [W/kg/s]
"""
return self._h_st
# Velocity and kinetic energy:
@property
def vel_s(self):
"""
Flow velocity at the entrance of the CV. [m/s]
"""
return self._vel_s
@property
def mach_s(self):
"""
Mach number at the entrance of the CV. [dimensionless]
"""
return self._mach_s
@property
def ekin_s(self):
"""
Specific kinetic energy at the entrance of the CV. [W/kg/s]
"""
return self._ekin_s
# Mass flow and area:
@property
def mflow_s(self):
"""
Mass flow at the entrance of the CV. [kg/s]
"""
return self._mflow_s
@property
def A_s(self):
"""
Area at the entrance of the CV. [m**2]
"""
return self._A_s
# ***************************
# *** Transfer variables: ***
# ***************************
@property
def w_se(self):
"""
Speficic mechanical power along the CV. [W/mg/s]
"""
return self._w_se
@property
def q_se(self):
"""
Speficic heating power along the CV. [W/mg/s]
"""
return self._q_se
@property
def delta_massflow(self):
"""
Mass flow variation along the CV. [W/mg/s]
"""
return self._delta_massflow
@property
def adiab_efficiency(self):
"""
Adiabatic efficiency along the CV. [dimensionless]
"""
return self._adiab_efficiency
## Collects basic inputs of an intake
def initialize_intake(self, pe, Te, ve, Ae, adiab_efficiency=1, As=None):
"""
Sets basic inputs of a generic intake (diffuser) control volume:
+ Static pressure, static temperature and flow velocity at the entrance
+ Adiabatic efficiency of the diffuser (by default the intake is considered
to be isentropic)
+ Exit area of the intake (if no exit area is provided, properties dependent
on the area are set to np.nan).
"""
self._A_e = Ae
self._p_e = pe
self._T_e = Te
self._vel_e = ve
self._adiab_efficiency = adiab_efficiency
self._A_s = As
self.solve_intake()
return None
## Solves the intake at the entrance:
def solve_intake(self):
"""
Solves the thermodynamic properties and variables of the intake.
Note that the followwing variables and properties are solved only if an exit area
is provided in initialize_intake(), otherwise those variables are set to np.nan:
vel_s, p_s, T_s, rho_s, ekin_s, h_s, mach_s
If the exit area is provided, Sympy is used to solve the mach at the exit
of the intake.
"""
# Solve basic thermodyamic properties at the entrance:
self._rho_e = self.p_e / self.T_e / self.fluid.Rg
self._mach_e = self.isent_flow.mach_number(self.vel_e, self.T_e)
self._T_et = self.isent_flow.stag_temp_from_mach(self.mach_e, self.T_e)
self._p_et = self.isent_flow.stag_pressure_from_mach(
self.mach_e, self.p_e, self.T_e)
self._rho_et = self.isent_flow.stag_density_from_mach(
self.mach_e, self.rho_e, self.T_e)
# Mass flow along the control volume
self._mflow_e = self.rho_e * self.A_e * self.vel_e
# TODO: If the intake is used with a fan, bypass ratio may be obtained here
self._mflow_s = self.mflow_e
self._delta_massflow = self.mflow_s - self.mflow_e
# Enthalpies:
self._h_e = self.fluid.cp(self.T_e) * self.T_e
self._ekin_e = 0.5 * self.vel_e**2
self._h_et = self.h_e + self.ekin_e
self._h_st = self.h_et
# Thermodynamic properties at the exit fo the CV
self._T_st = self.T_et
gamma_d = self.fluid.gamma(self.T_et)
self._p_st = self.p_e * (
(self.T_st / self.T_e - 1) * self.adiab_efficiency +
1)**(gamma_d / (gamma_d - 1))
self._rho_st = self.rho_e * (
(self.T_st / self.T_e - 1) * self.adiab_efficiency +
1)**(1 / (gamma_d - 1))
# By definition, no work/heat is applied in a diffuser cv
self._w_se = 0
self._q_se = 0
if self.A_s is None:
# Is exit area is not provided:
self._vel_s = np.nan
self._p_s = np.nan
self._T_s = np.nan
self._rho_s = np.nan
self._ekin_s = np.nan
self._h_s = np.nan
self._mach_s = np.nan
else:
# With the exit area, solve the mach number at the exit
var_aux = self.mflow_s / self.A_s * np.sqrt(
self.fluid.Rg / gamma_d) * np.sqrt(self.T_st) / self.p_st
var_aux = var_aux**(-2 * (gamma_d - 1) / (gamma_d + 1))
Ms = symbols('Ms')
ec1 = Eq(var_aux, (Ms + (1 + (gamma_d - 1) / 2 * Ms**2)))
# Dismiss negative solutions
M_s = solveset(ec1, Ms, domain=S.Reals)
M_s_ = list(M_s)
M_s_.sort(reverse=True)
mach_s_value = M_s_[0] if M_s_[0] > 0 else None
if mach_s_value is None:
raise ValueError(
"Mach number at exit of the CV is not possitive: {0}".
format(mach_s_value))
else:
self._mach_s = float(mach_s_value)
# Calculate static properties at the exit of the CV
self._T_s = self.isent_flow.stat_temp_from_mach(
self.mach_s, self.T_st)
self._p_s = self.isent_flow.stat_pressure_from_mach(
self.mach_s, self.p_st, self.T_st)
self._vel_s = self.isent_flow.vel_from_mach(self.mach_s, self.T_s)
self._rho_s = self.p_s / self.T_s / self.fluid.Rg
self._ekin_s = 0.5 * self.vel_s**2
self._h_s = self.fluid.cp(self.T_s) * self.T_s
return