def gg_dump_isp(p_o, p_te, p_ne, T_o, eta, gamma, c_p, m_molar):
'''Get the specific impulse of a Gas Generator turbine exhaust dump.
Arguments:
p_o: turbine inlet stagnation pressure [units: pascal].
p_te: turbine exit pressure [units: pascal].
p_ne: Dump nozzle exit pressure [units: pascal].
T_o: turbine inlet stagnation temperature [units: kelvin].
eta: turbine efficiency.
gamma: working gas ratio of specific heats [units: none].
c_p: working gas heat capacity at const pressure
[units: joule kilogram**-1 kelvin**-1].
m_molar: working gas molar mass [units: kilogram mole**-1].
'''
T_te = turbine_exit_temperature(p_o, p_te, T_o, eta, gamma, c_p)
# Dump nozzle thrust coefficient and characteristic velocity.
# Assume optimal expansion.
C_f = nozzle.thrust_coef(p_c=p_te, p_e=p_ne, gamma=gamma)
c_star = nozzle.c_star(gamma=gamma, m_molar=m_molar, T_c=T_te)
# Dump nozzle specific impulse [units: second]
Isp = c_star * C_f / 9.81
return Isp
def burn_and_throat_area(F, p_c, p_e, a, n, rho_solid, c_star, gamma):
"""Given thrust and chamber pressure, and propellant properties, find the burn area and throat area.
Assumes that the exit pressure is matched (:math:`p_e = p_a`).
Arguments:
F (scalar): Thrust force [units: newton].
p_c (scalar): Chamber pressure [units: pascal].
p_e (scalar): Nozzle exit pressure [units: pascal].
a (scalar): Propellant burn rate coefficient [units: meter second**-1 pascal**-n].
n (scalar): Propellant burn rate exponent [units: none].
rho_solid (scalar): Solid propellant density [units: kilogram meter**-3].
c_star (scalar): Propellant combustion characteristic velocity [units: meter second**-1].
gamma (scalar): Exhaust gas ratio of specific heats [units: dimensionless].
Returns:
tuple: tuple containing:
A_b (scalar): Burn area [units: meter**2].
A_t (scalar): Throat area [units: meter**2].
"""
C_F = nozzle.thrust_coef(p_c, p_e, gamma)
A_t = F / (C_F * p_c)
A_b = A_t * burn_area_ratio(p_c, a, n, rho_solid, c_star)
return (A_b, A_t)
def test_hh_1_3(self):
"""Test against example problem 1-3 from Huzel and Huang."""
# Inputs
T_c = 3633 # = 6540 R
p_c = 6.895e6 # = 1000 psia
p_e = 67.9e3 # = 9.85 psia
p_a = 101e3 # = 14.7 psia
m_molar = 22.67e-3
gamma = 1.2
er = 12
# Correct results from Huzel and Huang
C_F_hh = 1.5918
C_F = nozzle.thrust_coef(p_c, p_e, gamma, p_a, er)
self.assertTrue(abs(C_F - C_F_hh) < 0.01)
def test_hh_1_3(self):
"""Test against example problem 1-3 from Huzel and Huang."""
# Inputs
T_c = 3633 # = 6540 R
p_c = 6.895e6 # = 1000 psia
p_e = 67.9e3 # = 9.85 psia
p_a = 101e3 # = 14.7 psia
m_molar = 22.67e-3
gamma = 1.2
er = 12
# Correct results from Huzel and Huang
C_F_hh = 1.5918
C_F = nozzle.thrust_coef(p_c, p_e, gamma, p_a, er)
self.assertTrue(abs(C_F - C_F_hh) < 0.01)
"""Estimate specific impulse, thrust and mass flow."""
from math import pi
from proptools import nozzle
# Declare engine design parameters
p_c = 10e6 # Chamber pressure [units: pascal]
p_e = 100e3 # Exit pressure [units: pascal]
gamma = 1.2 # Exhaust heat capacity ratio [units: dimensionless]
m_molar = 20e-3 # Exhaust molar mass [units: kilogram mole**1]
T_c = 3000. # Chamber temperature [units: kelvin]
A_t = pi * (0.1 / 2)**2 # Throat area [units: meter**2]
# Predict engine performance
C_f = nozzle.thrust_coef(p_c, p_e,
gamma) # Thrust coefficient [units: dimensionless]
c_star = nozzle.c_star(
gamma, m_molar, T_c) # Characteristic velocity [units: meter second**-1]
I_sp = C_f * c_star / nozzle.g # Specific impulse [units: second]
F = A_t * p_c * C_f # Thrust [units: newton]
m_dot = A_t * p_c / c_star # Propellant mass flow [units: kilogram second**-1]
print 'Specific impulse = {:.1f} s'.format(I_sp)
print 'Thrust = {:.1f} kN'.format(F * 1e-3)
print 'Mass flow = {:.1f} kg s**-1'.format(m_dot)
from matplotlib import pyplot as plt
import skaero.atmosphere.coesa as atmo
from proptools import nozzle
p_c = 10e6 # Chamber pressure [units: pascal]
gamma = 1.2 # Exhaust heat capacity ratio [units: dimensionless]
p_e_1 = 100e3 # Nozzle exit pressure, 1st stage [units: pascal]
exp_ratio_1 = nozzle.er_from_p(p_c, p_e_1, gamma) # Nozzle expansion ratio [units: dimensionless]
p_e_2 = 15e3 # Nozzle exit pressure, 2nd stage [units: pascal]
exp_ratio_2 = nozzle.er_from_p(p_c, p_e_2, gamma) # Nozzle expansion ratio [units: dimensionless]
alt = np.linspace(0, 84e3) # Altitude [units: meter]
p_a = atmo.pressure(alt) # Ambient pressure [units: pascal]
# Compute the thrust coeffieicient of the fixed-area nozzle, 1st stage [units: dimensionless]
C_F_fixed_1 = nozzle.thrust_coef(p_c, p_e_1, gamma, p_a=p_a, er=exp_ratio_1)
# Compute the thrust coeffieicient of the fixed-area nozzle, 2nd stage [units: dimensionless]
C_F_fixed_2 = nozzle.thrust_coef(p_c, p_e_2, gamma, p_a=p_a, er=exp_ratio_2)
# Compute the thrust coeffieicient of a variable-area matched nozzle [units: dimensionless]
C_F_matched = nozzle.thrust_coef(p_c, p_a, gamma)
plt.plot(alt * 1e-3, C_F_fixed_1, label='1st stage $\\epsilon_1 = {:.1f}$'.format(exp_ratio_1))
plt.plot(alt[0.4 * p_a < p_e_2] * 1e-3, C_F_fixed_2[0.4 * p_a < p_e_2],
label='2nd stage $\\epsilon_2 = {:.1f}$'.format(exp_ratio_2))
plt.plot(alt * 1e-3, C_F_matched, label='matched', color='grey', linestyle=':')
plt.xlabel('Altitude [km]')
plt.ylabel('Thrust coefficient $C_F$ [-]')
plt.title('Effect of altitude on nozzle performance')
plt.legend()
"""Estimate specific impulse, thrust and mass flow."""
from math import pi
from proptools import nozzle
# Declare engine design parameters
p_c = 10e6 # Chamber pressure [units: pascal]
p_e = 100e3 # Exit pressure [units: pascal]
gamma = 1.2 # Exhaust heat capacity ratio [units: dimensionless]
m_molar = 20e-3 # Exhaust molar mass [units: kilogram mole**1]
T_c = 3000. # Chamber temperature [units: kelvin]
A_t = pi * (0.1 / 2)**2 # Throat area [units: meter**2]
# Predict engine performance
C_f = nozzle.thrust_coef(p_c, p_e, gamma) # Thrust coefficient [units: dimensionless]
c_star = nozzle.c_star(gamma, m_molar, T_c) # Characteristic velocity [units: meter second**-1]
I_sp = C_f * c_star / nozzle.g # Specific impulse [units: second]
F = A_t * p_c * C_f # Thrust [units: newton]
m_dot = A_t * p_c / c_star # Propellant mass flow [units: kilogram second**-1]
print 'Specific impulse = {:.1f} s'.format(I_sp)
print 'Thrust = {:.1f} kN'.format(F * 1e-3)
print 'Mass flow = {:.1f} kg s**-1'.format(m_dot)
"""Effect of expansion ratio on thrust coefficient."""
import numpy as np
from matplotlib import pyplot as plt
from proptools import nozzle
p_c = 10e6 # Chamber pressure [units: pascal]
p_a = 100e3 # Ambient pressure [units: pascal]
gamma = 1.2 # Exhaust heat capacity ratio [units: dimensionless]
p_e = np.linspace(0.4 * p_a, 2 * p_a) # Exit pressure [units: pascal]
# Compute the expansion ratio and thrust coefficient for each p_e
exp_ratio = nozzle.er_from_p(p_c, p_e, gamma)
C_F = nozzle.thrust_coef(p_c, p_e, gamma, p_a=p_a, er=exp_ratio)
# Compute the matched (p_e = p_a) expansion ratio
exp_ratio_matched = nozzle.er_from_p(p_c, p_a, gamma)
plt.plot(exp_ratio, C_F)
plt.axvline(x=exp_ratio_matched, color='grey')
plt.annotate('matched $p_e = p_a$, $\epsilon = {:.1f}$'.format(exp_ratio_matched),
xy=(exp_ratio_matched - 0.7, 1.62),
xytext=(exp_ratio_matched - 0.7, 1.62),
color='black',
fontsize=10,
rotation=90
)
plt.xlabel('Expansion ratio $\\epsilon = A_e / A_t$ [-]')
plt.ylabel('Thrust coefficient $C_F$ [-]')
plt.title('$C_F$ vs expansion ratio at $p_c = {:.0f}$ MPa, $p_a = {:.0f}$ kPa'.format(
p_c *1e-6, p_a * 1e-3))
plt.show()
"""Effect of expansion ratio on thrust coefficient."""
import numpy as np
from matplotlib import pyplot as plt
from proptools import nozzle
p_c = 10e6 # Chamber pressure [units: pascal]
p_a = 100e3 # Ambient pressure [units: pascal]
gamma = 1.2 # Exhaust heat capacity ratio [units: dimensionless]
p_e = np.linspace(0.4 * p_a, 2 * p_a) # Exit pressure [units: pascal]
# Compute the expansion ratio and thrust coefficient for each p_e
exp_ratio = nozzle.er_from_p(p_c, p_e, gamma)
C_F = nozzle.thrust_coef(p_c, p_e, gamma, p_a=p_a, er=exp_ratio)
# Compute the matched (p_e = p_a) expansion ratio
exp_ratio_matched = nozzle.er_from_p(p_c, p_a, gamma)
plt.plot(exp_ratio, C_F)
plt.axvline(x=exp_ratio_matched, color='grey')
plt.annotate(
'matched $p_e = p_a$, $\epsilon = {:.1f}$'.format(exp_ratio_matched),
xy=(exp_ratio_matched - 0.7, 1.62),
xytext=(exp_ratio_matched - 0.7, 1.62),
color='black',
fontsize=10,
rotation=90)
plt.xlabel('Expansion ratio $\\epsilon = A_e / A_t$ [-]')
plt.ylabel('Thrust coefficient $C_F$ [-]')
plt.title('$C_F$ vs expansion ratio at $p_c = {:.0f}$ MPa, $p_a = {:.0f}$ kPa'.
format(p_c * 1e-6, p_a * 1e-3))
plt.show()