def plot_condensation_curve(AR_min, AR_max, p_c, fp, T_ref):
gamma = fp.get_specific_heat_ratio(T=T_ref,
p=p_c) # [-] Specific heat ratio
# Determine maximum Mach number at exit
M_exit_max = IRT.Mach_from_area_ratio(
AR=AR_max, gamma=gamma) # [-] Max. Mach number at exit
M_exit_min = IRT.Mach_from_area_ratio(
AR=AR_min, gamma=gamma) # [-] Min. Mach number at exit
M_exit = np.linspace(start=M_exit_min, stop=M_exit_max,
num=50) # [-] Range of exit Mach numbers to evalulate
# Determine pressure at exit
PR_exit = IRT.pressure_ratio(M=M_exit,
gamma=gamma) # [-] Pressure ratio at exit
p_exit = p_c / PR_exit # [-] Exit pressure
# Determine saturation temperature at exit
T_sat_exit = fp.get_saturation_temperature(
p=p_exit) # [K] Saturation temperature at exit
# print(p_exit)
# print(T_sat_exit)
TR_exit = IRT.temperature_ratio(
M=M_exit, gamma=gamma) # [-] Temperature ratio at exit
T_chamber = T_sat_exit * TR_exit # [K] Chamber temperature that would result precisely in saturation temperature at nozzle exit
AR = IRT.area_ratio(
M=M_exit, gamma=gamma
) # [-] Area ratios corresponding to all specified mach numbers
plt.plot(
AR,
T_chamber,
label="$p_c ={:2.0f}$ bar , $T_c={:3.0f}$ K, $\\gamma={:1.3f}$".format(
p_c * 1e-5, T_ref, gamma))
def test_TRP_example(self):
# Slide 57-51 from Ideal Rocket Motor lecture from Thermal Rocket Propulsion course are used as example (Zandbergen)
F_expected = 401.8e3
u_exit_expected = 3021
m_dot_expected = 132.9
gamma = 1.3
R = 390.4
p_chamber = 5.6e6
p_back = 6.03e3
T_chamber = 3400
AR_exit = 49
d_exit = 1.6
A_exit = 0.25 * math.pi * d_exit**2
A_throat = A_exit / AR_exit
NS = "isentropically expanded (margin: 0.01)"
res = IRT.get_engine_performance(p_chamber=p_chamber,
T_chamber=T_chamber,
A_throat=A_throat,
AR_exit=AR_exit,
p_back=p_back,
gamma=gamma,
R=R)
self.assertAlmostEqual(res['thrust'], F_expected, -3)
self.assertAlmostEqual(res['m_dot'], m_dot_expected, 0)
self.assertAlmostEqual(res['u_exit'], u_exit_expected, -1)
self.assertEqual(res['nozzle_status'], NS)
def test_simple_input(self):
# Expected exit velocity and mass flow
# Should be sonic throat too, due to vacuum at exit
u_exit_expected = 1.0801234497346432
m_dot_expected = 0.6847314563772704 # Should be equal to Gamma(1.4) (vandankerkhove function)
p_exit = 0.5282817877171743 # Should be exit pressure for M=1
AR_exit = 1
T_chamber = 1
R = 1
gamma = 1.4
p_chamber = 1
A_throat = 1
AR_exit = 1
p_back = 0
# Expected thrust
F_expected = m_dot_expected * u_exit_expected + p_exit * A_throat * AR_exit
res = IRT.thrust(p_chamber=p_chamber,
T_chamber=T_chamber,
A_throat=A_throat,
AR_exit=AR_exit,
p_back=p_back,
gamma=gamma,
R=R)
self.assertEqual(res, F_expected)
def test_simple_input(self):
u_exit_expected = 1.0801234497346432
m_dot_expected = 0.6847314563772704 # Should be equal to Gamma(1.4) (vandankerkhove function)
p_exit = 0.5282817877171743 # Should be exit pressure for M=1
AR_exit = 1
T_chamber = 1
R = 1
gamma = 1.4
p_chamber = 1
A_throat = 1
AR_exit = 1
p_back = 0
# Expected thrust
F_expected = m_dot_expected * u_exit_expected + p_exit * A_throat * AR_exit
# Since the throat is M=1 and the back pressure is vacuum, it is clearly underexpanded
NS = "underexpanded"
res = IRT.get_engine_performance(p_chamber=p_chamber,
T_chamber=T_chamber,
A_throat=A_throat,
AR_exit=AR_exit,
p_back=p_back,
gamma=gamma,
R=R)
self.assertEqual(res['thrust'], F_expected)
self.assertEqual(res['m_dot'], m_dot_expected)
self.assertEqual(res['u_exit'], u_exit_expected)
self.assertEqual(res['nozzle_status'], NS)
def test_table_from_TRP(self):
# Page 51 from the TRP reader has a table with in and outputs. It is used to verify the function here
in_out = ((1.05, 0.6177), (1.10, 0.6284), (1.12, 0.6325),
(1.19, 0.6466), (1.23, 0.6543), (1.31, 0.6691),
(1.38, 0.6813), (1.65, 0.7238))
for input, output in in_out:
res = IRT.vdk(input)
self.assertEqual(round(res, 4), output)
def test_Anderson_example(self):
# Example 10.5 from Anderson2016 (recalculated manually due to different formula, calculation approach)
expected_result = 586.1 # [kg/s]
res = IRT.mass_flow(p_chamber=3.03e6,
A_throat=0.4,
R=520,
T_chamber=3500,
gamma=1.22)
self.assertEqual(round(res, 1), expected_result)
def testAndersonTable(self):
# Test values from Appendix B from Anderson
gamma = 1.4
in_out = ((0.102e1, 0.1047e1, 3), (0.158e1, 0.2746e1, 3),
(0.345e1, 0.1372e2, 2), (0.61e1, 0.4324e2, 2), (0.36e2,
0.1512e4, 0))
for M, PR, places in in_out:
res = IRT.pressure_ratio_shockwave(M=M, gamma=gamma)
self.assertAlmostEqual(res, PR, places)
def test_TRP_example(self):
# Slide 57-51 from Ideal Rocket Motor lecture from Thermal Rocket Propulsion course are used as example (Zandbergen)
expected = 3021
gamma = 1.3
R = 390.4
T_chamber = 3400
AR_exit = 49
res = IRT.exit_velocity(AR_exit=AR_exit,
T_chamber=T_chamber,
R=R,
gamma=gamma)
self.assertAlmostEqual(
res, expected, -1) # 4 digits accuracy (-1, rounding difference)
def testAndersonTable(self): # Appendix A and B from Anderson2016
# For this case the pressure ratios of two tables must be multiplied. Accuracy unknown after multiplication
# Lets guess 1 digit loss is fine
gamma = 1.4
in_out = (
(0.1760e1, 0.8458e1, 0.4736e1, 3), # M = 2.05
(0.1395e2, 0.2247e3, 0.2140e2, 2) # M = 4.3
)
for AR, PR_exit, PR_shockwave, places in in_out:
res = IRT.exit_pressure_ratio_shockwave(exit_area_ratio=AR,
gamma=gamma)
self.assertAlmostEqual(res, PR_exit / PR_shockwave, places)
def plot_pressure_curve(AR_min, AR_max, p_c, fp, T_ref):
gamma = fp.get_specific_heat_ratio(T=T_ref,
p=p_c) # [-] Specific heat ratio
# Determine maximum Mach number at exit
M_exit_max = IRT.Mach_from_area_ratio(
AR=AR_max, gamma=gamma) # [-] Max. Mach number at exit
M_exit_min = IRT.Mach_from_area_ratio(
AR=AR_min, gamma=gamma) # [-] Min. Mach number at exit
M_exit = np.linspace(start=M_exit_min, stop=M_exit_max,
num=50) # [-] Range of exit Mach numbers to evalulate
# Determine pressure at exit
PR_exit = IRT.pressure_ratio(M=M_exit,
gamma=gamma) # [-] Pressure ratio at exit
p_exit = p_c / PR_exit # [-] Exit pressure
AR = IRT.area_ratio(
M=M_exit, gamma=gamma
) # [-] Area ratios corresponding to all specified mach numbers
plt.plot(AR,
p_exit * 1e-5,
label="{:2.0f} bar , $\\gamma={:1.2f}$".format(p_c * 1e-5, gamma))
def testAndersonTable(self):
# use Anderson2016 table Appendix for gamma-1.4 in order to verify function workings
in_out = (
(0.2894e2, 0.2e-1, False, 5),
(0.2708e1, 0.22e0, False, 4),
(0.1213e1, 0.58e0, False, 4),
#(0.1000e1, 0.98e0, False, 2), # Function is extremely insensitive to results close to M=1
#(0.1000e1, 0.102e1, True, 3),
(0.1126e1, 0.1420e1, True, 3),
(0.2763e1, 0.2550e1, True, 3),
(0.3272e3, 0.9e1, True, 3),
(0.1538e5, 0.2e2, True, 2))
for AR, expected_M, supersonic, M_places in in_out:
res_M = IRT.Mach_from_area_ratio(AR=AR,
gamma=1.4,
supersonic=supersonic)
self.assertAlmostEqual(res_M, expected_M, places=M_places)
def testAndersonTable(self):
# Using table from Anderon to test for different back pressures
# Taking line for M=0.5 first for subsonic test
p_chamber = 1.186e6
exit_area_ratio = 1.340
gamma = 1.4
p_exit = 1e6
res = IRT.nozzle_status(p_chamber=p_chamber,
p_back=p_exit,
AR_exit=exit_area_ratio,
gamma=gamma)
self.assertEqual(res, 'subsonic')
p_chamber = 1.54e6 # Slight below value for which it will not have a shock in the nozzle
res = IRT.nozzle_status(p_chamber=p_chamber,
p_back=p_exit,
AR_exit=exit_area_ratio,
gamma=gamma)
self.assertEqual(res, 'shock in nozzle')
# Now test the same but with slightly higher pressure to see if it returns underexpanded
p_chamber = 1.55e6 # Slight above value for which it will not have a shock in the nozzle
res = IRT.nozzle_status(p_chamber=p_chamber,
p_back=p_exit,
AR_exit=exit_area_ratio,
gamma=gamma)
self.assertEqual(res, 'overexpanded')
# Now isentropic expansion (tolerance is set 0.01)
# Area ratio must be updated to a value present in Anderson table for M>1
# M = 2.1 is selected
exit_area_ratio = 1.837
p_chamber = 9.145e6
res = IRT.nozzle_status(p_chamber=p_chamber,
p_back=p_exit,
AR_exit=exit_area_ratio,
gamma=gamma)
self.assertEqual(res, 'isentropically expanded (margin: 0.01)')
# Same but with exit pressure slightly below margin set, so it is overexpanded
p_exit = 0.9899e6
res = IRT.nozzle_status(p_chamber=p_chamber,
p_back=p_exit,
AR_exit=exit_area_ratio,
gamma=gamma)
self.assertEqual(res, 'underexpanded')
# Same but slightly higher so it is underexpanded
p_exit = 1.01e6
res = IRT.nozzle_status(p_chamber=p_chamber,
p_back=p_exit,
AR_exit=exit_area_ratio,
gamma=gamma)
self.assertEqual(res, 'overexpanded')
def test_TRP_example(self):
# Slide 57-51 from Ideal Rocket Motor lecture from Thermal Rocket Propulsion course are used as example (Zandbergen)
expected = 401.8e3
gamma = 1.3
R = 390.4
p_chamber = 5.6e6
p_back = 6.03e3
T_chamber = 3400
AR_exit = 49
d_exit = 1.6
A_exit = 0.25 * math.pi * d_exit**2
A_throat = A_exit / AR_exit
res = IRT.thrust(p_chamber=p_chamber,
T_chamber=T_chamber,
A_throat=A_throat,
AR_exit=AR_exit,
p_back=p_back,
gamma=gamma,
R=R)
self.assertAlmostEqual(
expected, res,
-3) # Slight rounding error again and 1 digit accuracy less
def testOne(self):
# Mach is 1 input should return 1
expected = 1
res = IRT.pressure_ratio_shockwave(M=1, gamma=1.4)
self.assertEqual(res, expected)
fp = FluidProperties(td['propellant']) # Object to access fluid properties with
p_c = 5e5#td['p_inlet'] # [bar] Chamber pressure
T_c = 600#td['T_chamber_guess'] # [K] Chamber temperature
h_channel = td['h_channel'] # [m] Channel/nozzle depth
w_throat = td['w_throat'] # [m] Throat width
AR_exit = 10 #td['AR_exit'] # [-] Exit area ratio
p_back = 0# td['p_back'] # [Pa] Atmospheric pressire
print("Chamber temperature: {:3.2f} K".format(T_c))
# Calculate throat area, and propellant properties
A_throat = h_channel*w_throat # [m^2] Thrpat area
gamma = fp.get_specific_heat_ratio(T=T_c, p=p_c) # [-] Get gamma at specified gas constant
R = fp.get_specific_gas_constant() # [J/(kg*K)] Specific gas constant
ep = IRT.get_engine_performance(p_chamber=p_c, T_chamber=T_c, A_throat=A_throat, AR_exit=AR_exit, p_back=p_back, gamma=gamma, R=R)
print("\n --- IRT predictions --- ")
print("Isp: {:3.2f} s".format(ep['Isp']))
print("Gamma: {:1.3f} ".format(gamma))
print("Mass flow: {:2.3f} mg/s".format(ep['m_dot']*1e6))
print("Thrust: {:2.3f} mN".format(ep['thrust']*1e3))
zeta_CF = td['F']/ep['thrust']
Isp_real = td['F']/td['m_dot']/g0
zeta_Isp = Isp_real/ep['Isp']
discharge_factor = td['m_dot']/ep['m_dot']
print('\n --- Experimental values ---')
print("Isp: {:3.2f} s (zeta_Isp = {:1.3f})".format(Isp_real, zeta_Isp))
print("Mass flow: {:2.3f} mg/s (Cd = {:1.3f})".format(td['m_dot']*1e6, discharge_factor))
print("Thrust: {:2.3f} mN (zeta_CF ={:1.3f})".format(td['F'], zeta_CF))
def run(F_desired, T_chamber, channel_amount, settings, x_guess):
""" Algorithm to determine the thruster with the best specific impulse for the given thrust and power requirements
Args:
F_desired (N): Required thrust
T_chamber (K): Chamber temperature determines mass flow and Isp and ideal power consumption
channel_amount (-): Amount of channels. Technically, this must be optmized, but using built-in optimization really doesn't work well for integers
In settings {dict}:
FDP (dict): Fixed design parameters
bounds (dict of 2-tuples): The constraints on the design parameters to be optimized
NR (dict of functions): Nusselt relations that are used in various phases in the channel (liquid, two-phase, dry-out,gas)
PDR (dict of functions): Pressure drop relations that are used in various phases in the channel (friction: liquid, two-phase, gas; contraction)
steps (dict of ints): Fidelity of the temperature-steps in the various sections of the channel
"""
print("\n ----- OPTIMIZING THRUSTER FOR POWER CONSUMPTION -----")
print("\n HIGH-LEVEL INPUTS")
print("--- Desired thrust: {:3.1f} mN".format(F_desired * 1e3))
print("--- Chamber temperature: {:4.1f} K".format(T_chamber))
## First determine ideal engine performance, and load settings for that
T_inlet = settings['FDP'][
'T_inlet'] # [K] Inlet temperature (at heating channel inlet manifold)
p_inlet = settings['FDP'][
'p_inlet'] # [Pa] Chamber pressure assumed equal to inlet pressure
AR_exit = settings['FDP']['AR_exit'] # [-] Exit area ratio of nozzle
p_back = settings['FDP']['p_back'] # [Pa]
assert p_back == 0 # Nozzle correction does not work for back pressure
fp = settings['FDP'][
'fp'] # [object] FluidProperties object containing thermodynamic parameters for propellant
print("--- Inlet pressure: {:2.1f} bar".format(p_inlet * 1e-5))
print("--- Exit area ratio {:2.1f}".format(AR_exit))
# Check if the inputs are correct
assert (T_chamber > T_inlet)
ep_ideal = IRT.engine_performance_from_F_and_T(F_desired=F_desired,
p_chamber=p_inlet,
T_chamber=T_chamber,
AR_exit=AR_exit,
p_back=p_back,
fp=fp)
# Calculate ideal power consumption
m_dot = ep_ideal['m_dot'] # [kg/s] Mass flow through chamber
Isp = ep_ideal['Isp'] # [s] Specific impulse
P_ideal = chamber.ideal_power_consumption( # [W] Ideal power consumption
mass_flow=m_dot,
T_inlet=T_inlet,
p_inlet=p_inlet,
T_outlet=T_chamber,
p_outlet=p_inlet,
fp=fp)
print("\n IDEAL PERFORMANCE")
print("--- Nozzle status: {}".format(ep_ideal['nozzle_status']))
print("--- Mass flow: {:3.2f} mg/s".format(m_dot * 1e6))
print("--- Isp: {:3.1f} s".format(Isp))
print("--- Power consumption: {:2.1f} W".format(P_ideal))
# Calculate pre-calculated values of heating channel that are constant through entire optimization
prepared_values = oneD.full_homogenous_preparation(
T_inlet=T_inlet, # [K] Inlet temperature of the channel
T_outlet=
T_chamber, # [K] Outlet of the channel is equal to chamber temperature in IRT
m_dot=m_dot / channel_amount, # [kg/s] Mass flow in a single channel
p_ref=
p_inlet, # [Pa] The pressure in the channel is assumed to be constant for heat flow calculation purposes
steps_l=settings['steps']
['steps_l'], # [-] Fidelity of simulation in liquid section of channel
steps_tp=settings['steps']
['steps_tp'], # [-] Fidelity of simulation in two-phase section of channel
steps_g=settings['steps']
['steps_g'], # [-] Fidelity of simulation in gas section of channel
fp=
fp, # [object] Object to access thermodynamic parameters of propellant with
)
### Define function to optimize here, and load settings into fixed design parameters
### IMPORTANT NOTE: if the order of arguments of f() is changed, the order of bounds must be changed too.
# The bounds are defined a bit early here, so one does not forgot this after changing either.
b = Bounds(
[ # Lower bounds
settings['bounds']['w_channel'][0],
settings['bounds']['w_channel_spacing'][0],
settings['bounds']['T_wall_superheat'][0] + T_chamber,
],
[ # Higher bounds
settings['bounds']['w_channel'][1],
settings['bounds']['w_channel_spacing'][1],
settings['bounds']['T_wall_superheat'][1] + T_chamber,
])
# Initial guess (just make it the higher bound (arbitary)) NOTE: SAME ORDER APPLIES ABOUNDS AND AS f() below
x0 = None # Set the first guess based on a guess being provided or not
if (x_guess is None):
x0 = [
settings['bounds']['w_channel'][0],
settings['bounds']['w_channel_spacing'][0],
settings['bounds']['T_wall_superheat'][0] + T_chamber,
]
else:
x0 = x_guess
# The function to optimize
def f(x,
return_full_results=False
): # NOTE: change bounds above if argument change
if (return_full_results):
print("Going to return full results.")
w_channel = x[0]
w_channel_spacing = x[1]
T_wall = x[2]
# Wall arguments need to be encapsulated in a dictionary so they can be conveniently passed to the section of code calcuating wall effects
# and the actual bottom wall temperature
wall_args = {
'kappa_wall': settings['FDP']
['kappa_wall'], # [W/(m*K)] Thermal conductivity of chip wall
'h_channel':
settings['FDP']['h_channel'], # [m] Channel depth, channel height
'w_channel': w_channel, # [m] Channel width
'w_channel_spacing':
w_channel_spacing, # [m] Spacing between channels/wall thickness
'emissivity_chip_bottom': settings['FDP']
['emissivity_chip_bottom'], # [m] Emissivity of the bottom of the chip
}
# Exit manifold length is zero based on existing VLM design, so should be zero in settings
assert settings['FDP'][
'l_exit_manifold'] == 0 # It is merely a remnant from previous code choices
# The function that returns the eventual power output
res_P = optim_P_total( # CAPITALIZED COMMENTS ARE FOR OPTIMIZED VARIABLES
channel_amount=channel_amount, # [-] AMOUNT OF CHANNELS
w_channel=w_channel, # [m] CHANNEL WIDTH
h_channel=settings['FDP']
['h_channel'], # [m] Channel depth, channel height
inlet_manifold_length_factor=settings['FDP']
['inlet_manifold_length_factor'], # [-] Linear factor to determine inlet manifold length
inlet_manifold_width_factor=settings['FDP']
['inlet_manifold_width_factor'], # [-] Linear factor to determine inlet manifold width
l_exit_manifold=settings['FDP']
['l_exit_manifold'], # [-] NOTE: old part of design. Is set to zero.
w_channel_spacing=
w_channel_spacing, # [m] SPACING BETWEEN CHANNELS/WALL THICKNESS
w_outer_margin=settings['FDP']
['w_outer_margin'], # [m] Margin around edge of heating channels, or nozzle width
T_wall=T_wall, # [K] WALL TEMPERATURE
p_ref=p_inlet, # [Pa] Pressure through channel
m_dot=m_dot, # [kg/s] Heat flow through channel
prepared_values=
prepared_values, # {dict} Dictionary with many parameters that are costly to calcuate but are cosntant throughout optimization
Nusselt_relations=settings[
'Nusselt_relations'], # {dict} Heat transfer relations used for optimization
pressure_drop_relations=settings[
'pressure_drop_relations'], # {dict} Pressure drops used for optimization
convergent_half_angle=settings['FDP']
['convergent_half_angle'], # [rad] Half-angle of convergent part of 2D-conical nozzle
divergent_half_angle=settings['FDP']
['divergent_half_angle'], # [rad] Half-angle of divergent part of 2D-conical nozzle
F_desired=
F_desired, # [N] Desired thrust. Still required to correct for pressure drop
p_back=
p_back, # [Pa] Back pressure. NOTE: Nozzle correction depends on this being 0.
AR_exit=
AR_exit, # [-] Exit area ratio to correct nozzle after pressure drop
emissivity_top=settings['FDP']
['emissivity_chip_top'], # [-] Emissivity of top chip (black-body-radiation)
fp=
fp, # [object] Object to access thermodynamic parameters of propellant with
wall_args=
wall_args, # {dict} Arguments about wall design. See aboves
)
# Return the total power consumption. The variable of interest
P_total = P_ideal + res_P['P_loss']
#print(x)
if math.isnan(P_total):
#print("A constraint violated.")
# Punish the objective function by outputting high power consumptions for invalid solutions
# The punishment must however not be constant, or it will converge at the boundary where it is invalid.
# Since the punishment stems from the pressure drop being higher than the initial p_chamber value, the lower the negative final pressure is the higher the punishment
if return_full_results:
print("Converged on invalid result!")
print(res_P['pressure_drop_punishment'])
return (P_ideal * (2 + 1 * res_P['pressure_drop_punishment'])
) * settings['function_scaling']
else:
#print("P_total: {:2.5f} W".format(P_total))
# Scipy minimize can't handle multiple returns for the objective function, so the extensive final results must be pulled out afterwards
if return_full_results:
print("Returning full results!")
print(res_P['P_loss'])
return res_P
else:
return P_total * settings['function_scaling']
## OPTIMIZATION ALGORITHM
# First bounds must be set in the same order that arguments are given in f()
# The order is: channel_amount, w_channel,w_channel_spacing,T_wall
optimization_method = 'L-BFGS-B'
optimization_options = {
'ftol': 2.220446049250313e-20,
'gtol': 1e-10,
'disp': False,
}
# Pressure drop constraint
con_pressure_drop = NonlinearConstraint(f, 0, 2 * P_ideal)
minimize_results = minimize(fun=f,
x0=x0,
bounds=b,
method=optimization_method,
options=optimization_options)
#
print(minimize_results.x)
print(minimize_results.success)
print(minimize_results.status)
print(minimize_results.message)
print(minimize_results.nit)
print("Trying to return full results")
res_final = f(minimize_results.x, return_full_results=True)
print(res_final['P_loss'])
optim_results = {
#'full_res': res_final['res'],
#'full_prepared_values': res_final['prepared_values'],
'minimize_results': minimize_results,
'w_channel': minimize_results.x[0],
'w_channel_spacing': minimize_results.x[1],
'T_wall_top': minimize_results.x[2],
'P_total': minimize_results.fun / settings['function_scaling'],
'P_loss': res_final['P_loss'],
'P_ideal': P_ideal,
'l_channel': res_final['l_channel'],
'h_channel': res_final['h_channel'],
'hydraulic_diameter': res_final['hydraulic_diameter'],
'l_inlet': res_final['l_inlet'],
'l_total': res_final['l_total'],
'A_chip': res_final['A_chip'],
'l_outlet': res_final['l_outlet'],
'l_convergent': res_final['l_convergent'],
'l_divergent': res_final['l_divergent'],
'l_channel_l': res_final['l_channel_l'],
'l_channel_tp': res_final['l_channel_tp'],
'l_channel_g': res_final['l_channel_g'],
'T_wall_bottom': res_final['T_wall_bottom'],
'w_total': res_final['w_total'],
'w_channels_total': res_final['w_channels_total'],
'w_nozzle': res_final['w_nozzle'],
'w_inlet': res_final['w_inlet'],
'pressure_drop': res_final['pressure_drop'],
'Re_channel_l': res_final['Re_channel_l'],
'Re_channel_tp': res_final['Re_channel_tp'],
'Re_channel_g': res_final['Re_channel_g'],
'M_channel_exit_after_dP': res_final['M_channel_exit_after_dP'],
'Re_channel_exit_after_dP': res_final['Re_channel_exit_after_dP'],
'm_dot': ep_ideal['m_dot'],
'Isp': ep_ideal['Isp'],
'p_inlet': p_inlet,
'w_throat_new': res_final['w_throat_new'],
'Re_throat_new': res_final['Re_throat_new'],
}
#print(optim_results)
return optim_results
def test_zero_two(self):
expected_result = 0.769800358919501
res = IRT.mass_flow(p_chamber=1, A_throat=1, R=1, T_chamber=1, gamma=2)
self.assertEqual(res, expected_result)
def test_simple_input(self):
expected = 1.0801234497346432 # Manually calculated
# area ratio of 1 means the mach number is 1
res = IRT.exit_velocity(AR_exit=1, T_chamber=1, R=1, gamma=1.4)
self.assertEqual(res, expected)
def testAreaRatioOne(self):
expected_result = 1.0
input = 1
res = IRT.Mach_from_area_ratio(AR=input, gamma=1.4)
self.assertEqual(res, expected_result)
def Rajeev_complete(p_chamber, T_chamber, w_throat, h_throat, throat_roc,
AR_exit, p_back, divergence_half_angle,
fp: FluidProperties, is_cold_flow):
""" Function that implements all corrections proposed by Makhan2018
Args:
p_chamber (Pa): Chamber pressure
T_chamber (K): Chamber temperature
w_throat (m): Throat width
h_throat (m): Throat heigh (or channel depth)
throat_roc (m): Throat radius of curvature
AR_exit (-): Area ratio of nozzle exit area divided by throat area
p_back (Pa): Back pressure
divergence_half_angle (rad): Divergence half angle of nozzle
fp (FluidProperties): Object to access fluid properties
is_cold_flow (bool): Reynolds number is adjusted depending on whether the chamber is heated or cooled
Raises:
ValueError: Is raised for hot flow, since no verification is done yet on that equation
"""
# Get the (assumed to be) constant fluid properties
gamma = fp.get_specific_heat_ratio(T=T_chamber,
p=p_chamber) # [-] Specific heat ratio
R = fp.get_specific_gas_constant() # [J/kg] Specific gas constant
# Report calculated values for verification and comparison purposes
print("Gamma: {:1.4f}".format(gamma))
print("R: {:3.2f} J/kg\n".format(R))
# Calculate basic peformance parameters
A_throat = w_throat * h_throat # [m] Throat area
## IDEAL PERFORMANCE
# First get ideal performance, and check if the nozzle is properly expanded.
ep = IRT.get_engine_performance(p_chamber=p_chamber,
T_chamber=T_chamber,
A_throat=A_throat,
AR_exit=AR_exit,
p_back=p_back,
gamma=gamma,
R=R)
# Report ideal performance
print("Thrust: {:.2f} mN".format(ep['thrust'] * 1e3))
print("Isp_ideal: {:.1f} s".format(ep['thrust'] / ep['m_dot'] / 9.80655))
print("Mass flow: {:.3f} mg/s".format(ep['m_dot'] * 1e6))
m_dot_ideal = ep['m_dot'] # [kg/s] Ideal mass flow
#F_ideal = ep['thrust'] # [N] Ideal thrust
## CALCULATING THE CORRECTION FACTORS
# Calculate the divergence loss and report it
CF_divergence_loss = divergence_loss_conical_2D(
alpha=divergence_half_angle)
print("\n -- DIVERGENCE LOSS for {:2.2f} deg divergence half-angle".format(
math.degrees(divergence_half_angle)))
print(
" Divergence loss (2D concical): {:.5f} ".format(CF_divergence_loss))
# Calculate the viscous loss
# To determine the Reynolds number at the throat, the hydraulic diameter at the throat and nozzle conditions must be determined
# Get hydraulic diameter of the nozzle from the wetted perimeter and nozzle area
wetted_perimeter_throat = 2 * (w_throat + h_throat
) # [m] Wetted perimeter throat
Dh_throat = hydraulic_diameter(A=A_throat,
wetted_perimeter=wetted_perimeter_throat
) # [m] Hydraulic diameter at throat
p_throat = p_chamber / IRT.pressure_ratio(
M=1, gamma=gamma) # [Pa] pressure in throat
T_throat = T_chamber / IRT.temperature_ratio(
M=1, gamma=gamma) # [K] Temperature in throat
viscosity_throat = fp.get_viscosity(T=T_throat, p=p_throat)
# Throat reynolds based on ideal mass flow?
Re_throat = reynolds(m_dot=m_dot_ideal,
A=A_throat,
D_hydraulic=Dh_throat,
viscosity=viscosity_throat)
if is_cold_flow:
Re_throat_wall = Reynolds_throat_wall_cold(reynolds_throat=Re_throat)
else:
Re_throat_wall = Reynolds_throat_wall_hot(reynolds_throat=Re_throat)
print("\n-- THROAT CONDITIONS --")
print(" p = {:2.4f} bar, T = {:4.2f} K".format(
p_throat * 1e-5, T_throat))
print(" mu = {:2.4f} [microPa*s] Dh = {:3.4f} [microm]".format(
viscosity_throat * 1e6, Dh_throat * 1e6))
print(" Reynolds: {:6.6f} ".format(Re_throat))
CF_viscous_loss = viscous_loss(area_ratio=AR_exit,
reynolds_throat_wall=Re_throat_wall)
print(" CF_viscous_loss: {:1.5f}".format(CF_viscous_loss))
# Calculating throat boundary layer loss, which causes a reduction in effective throat area/mass flow
Cd_throat_boundary_loss = throat_boundary_loss(gamma=gamma,
reynolds_throat=Re_throat,
throat_radius=0.5 *
Dh_throat,
throat_roc=throat_roc)
print("\n-- DISCHARGE FACTOR --")
print(" Throat boundary layer: {:1.4f}".format(Cd_throat_boundary_loss))
## APPLYING THE CORRECTION FACTORS
# Now all these loss factors must be combined into a new "real" thrust
# The divergence loss only applies to the jet/momentum thrust and not the pressure, so jet thrust is needed
# This is equal to the exit velocity times corrected mass flow. The returned exit velocity does not include pressure terms!
# First we must know the corrected mass flow
m_dot_real = ep['m_dot'] * Cd_throat_boundary_loss # [kg/s]
# Secondly, we must know the pressure thrust to add to the jet thrust again
F_pressure = IRT.pressure_thrust(p_chamber=p_chamber,
p_back=p_back,
A_throat=A_throat,
AR=AR_exit,
gamma=gamma)
F_divergence = m_dot_real * ep[
'u_exit'] * CF_divergence_loss + F_pressure # [N] Thrust decreased by divergence loss, pressure term must be added again, since divergence only applies to jet thrust
# This jet thrust is then again corrected by viscous losses, which are subtracted from the current CF
CF_jet_divergence = F_divergence / (
p_chamber * A_throat
) # [-] Thrust coefficient after taking into account discharge factor and divergence loss
CF_real_final = CF_jet_divergence - CF_viscous_loss # [-] The final thrust coefficient, also taking into account viscous loss
F_real = CF_real_final * p_chamber * A_throat # [N] Real thrust, after taking into account of all the three proposed correction factors
# Report "real" results
print("\n === CORRECTED PERFORMANCE PARAMETERS === ")
print(" Real mass flow: {:3.4f} mg/s".format(m_dot_real * 1e6))
print(" CF with divergence loss {:1.5f}".format(CF_jet_divergence))
print(" Real CF: {:1.5f}".format(CF_real_final))
print(" Real thrust: {:2.4f} mN".format(F_real * 1e3))
print(" Real Isp: {:3.2f}".format(F_real / m_dot_real / 9.80655))
return {
'm_dot_real': m_dot_real,
'm_dot_ideal': ep['m_dot'],
'F_real': CF_real_final
}
def testOne(self):
# Should return pressure ratio for M=1, as shockwave is infinitely weak
# Value taken from Anderson2006 Appendix A again
expected = 0.1893e1
res = IRT.exit_pressure_ratio_shockwave(exit_area_ratio=1, gamma=1.4)
self.assertAlmostEqual(res, expected, 3)
def test_one(self):
# Mach number is 1 in the throat so area ratio must be 1.
expected_result = 1
res = IRT.area_ratio(M=1, gamma=1.4)
self.assertEqual(res, expected_result)
mu_throat = np.zeros_like(m_dot) # [Pa*s] Dynamic viscosity in the throat
# Results to check condensation in nozzle exit
T_exit = np.zeros_like(m_dot) # [K]
p_exit = np.zeros_like(m_dot) # [Pa]
it_AR = np.nditer(AR_exit, flags=['c_index'])
# Iterate over all possible combinations of area ratio and chamber temperature to find the mass flow and area ratio that finds according to basic IRT
for AR in it_AR:
it_T = np.nditer(T_chamber, flags=['c_index'])
for T in it_T:
# Store mass flow, throat area and other results
ep = IRT.engine_performance_from_F_and_T(F_desired=F,
p_chamber=p_chamber,
T_chamber=float(T),
AR_exit=float(AR),
p_back=p_back,
fp=fp)
m_dot[it_AR.index][it_T.index] = ep['m_dot'] # [kg/s] Mass flow
A_throat[it_AR.index][it_T.index] = ep['A_throat'] # [m^2] Throat area
Isp[it_AR.index][it_T.index] = ep['Isp'] # [s] Specific impulse
h_chamber[it_AR.index][it_T.index] = fp.get_enthalpy(
T=float(T), p=p_chamber) # [J/kg] Enthalpy at chamber inlet
# Throat stuff
T_throat[it_AR.index][it_T.index] = ep[
'T_throat'] # [K] Throat temperature
p_throat[it_AR.index][it_T.index] = ep[
'p_throat'] # [Pa] Throat pressure
u_throat[it_AR.index][it_T.index] = ep[
'u_throat'] # [K] Throat velocity
Pr_throat[it_AR.index][it_T.index] = fp.get_Prandtl(