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_simple_input(self):
M = 1
gamma = 2
expected_temperature_ratio = 1.5
expected_pressure_ratio = 2.25
res_temperature_ratio = IRT.temperature_ratio(M=M, gamma=gamma)
res_pressure_ratio = IRT.pressure_ratio(M=M, gamma=gamma)
self.assertEqual(expected_temperature_ratio, res_temperature_ratio)
self.assertEqual(expected_pressure_ratio, res_pressure_ratio)
def test_anderson_table(self):
# Table in back of Anderson book gives values for gamma=1.4
gamma = 1.4
in_out = ((0.2e-1, 0.1e1, 3, 0.1e1,
3), (0.24e0, 0.1041e1, 3, 0.1012e1,
3), (0.56e0, 0.1237e1, 3, 0.1063e1,
3), (1, 0.1893e1, 3, 0.12e1,
3), (1.64e0, 0.4511e1, 3, 0.1538e1, 3),
(2.45e0, 0.1581e2, 2, 0.22e1, 3), (50, 0.2815e10, -6,
0.5010e3, 1))
for M, expected_PR, PR_places, expected_TR, TR_places in in_out:
res_PR = IRT.pressure_ratio(M=M, gamma=gamma)
res_TR = IRT.temperature_ratio(M=M, gamma=gamma)
self.assertAlmostEqual(res_PR, expected_PR, PR_places)
self.assertAlmostEqual(res_TR, expected_TR, TR_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 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
}