Thermochemistry
Contents
Thermochemistry¶
# this line makes figures interactive in Jupyter notebooks
%matplotlib inline
from matplotlib import pyplot as plt
import numpy as np
from scipy.optimize import root_scalar
from scipy import constants
from pint import UnitRegistry
ureg = UnitRegistry()
Q_ = ureg.Quantity
# for convenience:
def to_si(quant):
'''Converts a Pint Quantity to magnitude at base SI units.
'''
return quant.to_base_units().magnitude
# these lines are only for helping improve the display
import matplotlib_inline.backend_inline
matplotlib_inline.backend_inline.set_matplotlib_formats('pdf', 'png')
plt.rcParams['figure.dpi']= 300
plt.rcParams['savefig.dpi'] = 300
plt.rcParams['mathtext.fontset'] = 'cm'
# define some constants
Ru = Q_(constants.R, 'J/(K*mol)')
g0 = Q_(constants.g, 'm/s^2')
The thermochemical performance of a rocket is primarily represented using the characteristic velocity:
(6)¶\[
c^* = \frac{p_c A_t}{\dot{m}} = \sqrt{\frac{\mathcal{R}_u T_c}{\textrm{MW} \, \gamma} \left( \frac{\gamma + 1}{2} \right)^{\frac{\gamma+1}{\gamma-1}} } \;,
\]
which depends on the (combustion) chamber temperature \(T_c\), gas molecular weight \(\textrm{MW}\), and gas specific heat ratio \(\gamma\). The thrust coefficient \(C_F\) mainly represents the performance of the nozzle, but it also depends on the specific heat ratio \(\gamma\).
Up to this point, we have been provided or assumed these values, but they are actually a function of
propellant(s)
ratio of oxidizer to fuel
Given a propellant or combination of propellants and heating (due to combustion, nuclear reactions, or electricity), the gas in the chamber and moving into the nozzle will form a mixture of chemical species at the state of chemical equilibrium. At this state, the forward and reverse rates of all chemical reactions are balanced, and the species remain at a fixed composition (as long as the temperature and/or pressure remain constant).
The amounts of the chemical species at the equilibrium are unknown, but can be determined based on the initial conditions using methods based on reaction equilibrium constants or the minimization of Gibbs free energy. If the temperature is not known/fixed, then it is also an unknown and must be found.
Fortunately, we can use software tools such as NASA’s CEA or Cantera to find the equilibrium state for us. We’ll focus on CEA here.
def get_area_ratio(pressure_ratio, gamma):
'''Calculates area ratio based on specific heat ratio and pressure ratio.
pressure ratio: chamber / exit
area ratio: exit / throat
'''
return (
np.power(2 / (gamma + 1), 1/(gamma-1)) *
np.power(pressure_ratio, 1 / gamma) *
np.sqrt((gamma - 1) / (gamma + 1) /
(1 - np.power(pressure_ratio, (1 - gamma)/gamma))
)
)
def root_area_ratio(pressure_ratio, area_ratio, gamma):
''' Returns zero for a given area ratio, pressure ratio, and gamma.
pressure ratio: chamber / exit
area ratio: exit / throat
'''
return area_ratio - get_area_ratio(pressure_ratio, gamma)
def get_thrust_coeff(pressure_ratio, gamma):
'''Calculates thrust coefficient for optimum expansion.
pressure ratio: chamber / exit
area ratio: exit / throat
'''
return np.sqrt(
2 * np.power(gamma, 2) / (gamma - 1) *
np.power(2 / (gamma + 1), (gamma + 1)/(gamma - 1)) *
(1 - np.power(1.0 / pressure_ratio, (gamma - 1)/gamma))
)
def get_cstar(Tc, MW, gamma):
'''Calculates cstar using chamber properties.'''
return (
np.sqrt(Ru * Tc / (gamma * MW)) *
(2 / (gamma + 1))**(-0.5*(gamma + 1)/(gamma - 1))
)
Fixed temperature and pressure¶
Let’s first consider the problem where the pressure and temperature of the combustion/heating chamber are fixed and known, and determine the equilibrium composition of chemical species. This problem is relevant to an isothermal process, or where temperature is a design variable, such as in nuclear thermal or electrothermal rockets.
For example, say we have an arcjet operating on gaseous hydrazine (N2H4) as a propellant, with a chamber temperature of 5000 K and pressure of 50 psia. The nozzle area ratio is 100, and the arcjet will operate in vacuum. For this system, determine the equilibrium composition, the average molecular weight, ratio of specific heats \(\gamma\), and then use these to get \(c^*\), \(C_F\), and \(I_{\textrm{sp}}\).
In CEA, this is a tp problem, or fixed temperature and pressure problem.
We should expect that, at such high temperatures, the equilibrium state will have mostly one- and two-atom
molecules, based on the elements present: N2, H2, H, N, and HN.
The CEA plaintext input file looks like:
prob tp
p,psia= 50 t,k= 5000
reac
name N2H4 mol 1.0
output siunits
end
and the output is (with the repeated input removed):
*******************************************************************************
NASA-GLENN CHEMICAL EQUILIBRIUM PROGRAM CEA2, FEBRUARY 5, 2004
BY BONNIE MCBRIDE AND SANFORD GORDON
REFS: NASA RP-1311, PART I, 1994 AND NASA RP-1311, PART II, 1996
*******************************************************************************
THERMODYNAMIC EQUILIBRIUM PROPERTIES AT ASSIGNED
TEMPERATURE AND PRESSURE
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
NAME N2H4 1.0000000 0.000 0.000
O/F= 0.00000 %FUEL= 0.000000 R,EQ.RATIO= 0.000000 PHI,EQ.RATIO= 0.000000
THERMODYNAMIC PROPERTIES
P, BAR 3.4474
T, K 5000.00
RHO, KG/CU M 5.5368-2
H, KJ/KG 42058.0
U, KJ/KG 35831.8
G, KJ/KG -103744.4
S, KJ/(KG)(K) 29.1605
M, (1/n) 6.677
(dLV/dLP)t -1.04028
(dLV/dLT)p 1.4750
Cp, KJ/(KG)(K) 11.1350
GAMMAs 1.2548
SON VEL,M/SEC 2795.1
MOLE FRACTIONS
*H 0.74177
*H2 0.04573
*N 0.00806
*NH 0.00021
*N2 0.20422
So, CEA not only provides the equilibrium composition in terms of mole fraction (\(X_i\)), but also the mean molecular weight of the mixture \(MW\); thermodynamic properties and derivatives density \(\rho\), enthalpy \(h\), entropy \(s\), \(\left(\partial \log V / \partial \log P\right)_T\), \(\left(\partial \log V / \partial \log T\right)_P\), specific heat \(C_p = \partial h / \partial T)_P\), the ratio of specific heats (\(\gamma\)), and the sonic velocity (i.e., speed of sound) \(a\). Some of these quantities are not particularly interesting to us right now, but we can use these quantities to find our quantities of interest.
area_ratio = 100
Tc = Q_(5000, 'K')
Pc = Q_(50, 'psi')
# output from CEA
MW = Q_(6.677, 'kg/kmol')
gamma = 1.2548
First, we need to find the exit pressure of the nozzle based on the area ratio:
# initial guesses for Pc / Pe
root = root_scalar(root_area_ratio, x0=1000, x1=2000, args=(area_ratio, gamma))
Pc_Pe = root.root
Pe = Pc / Pc_Pe
print(f"Exit pressure = {Pe.to('psi'): .2e~P}")
cstar = get_cstar(Tc, MW, gamma)
print(f"Cstar = {cstar.to('m/s'): .1f~P}")
CF0 = get_thrust_coeff(Pc_Pe, gamma)
# ambient pressure is zero in vacuum
CF = CF0 + (1/Pc_Pe) * area_ratio
print(f"C_F = {CF: .3f}")
Exit pressure = 2.54e-02 psi
Cstar = 3786.6 m/s
C_F = 1.884
Isp = CF * cstar / g0
print(f"Isp = {Isp.to('s'): .1f~P}")
Isp = 727.4 s
Adiabatic combustion¶
For chemical rockets, the temperature in the combustion chamber is unknown, and is a function of the propellant combination, oxidizer/fuel ratio, and chamber pressure.
Consider the Space Shuttle Main Engine (SSME, also known as the RS-25), which uses liquid oxygen and liquid hydrogen as propellants, at an O/F ratio of 6.0 and with a chamber pressure of 2870 psia. The engine nozzle has an area ratio of 68.8.
Find the chamber temperature, mole fractions of equilibrium products, specific heat ratio, average molecular weight, \(c^*\), \(C_F\), and specific impulse at sea level.
In CEA, this is an hp type problem (assigned enthalpy and pressure), where the enthalpy of the initial mixture is known based on the propellants and combustion is assumed to be adiabatic.
The CEA plaintext input file (with some comments removed) looks like:
prob hp
# Pressure (1 value):
p,psia= 2870
# Oxidizer/Fuel Wt. ratio (1 value):
o/f= 6.0
reac
fuel H2(L) wt%=100.0000
oxid O2(L) wt%=100.0000
output short
output siunits
end
and the output is (with the repeated input removed):
*******************************************************************************
NASA-GLENN CHEMICAL EQUILIBRIUM PROGRAM CEA2, FEBRUARY 5, 2004
BY BONNIE MCBRIDE AND SANFORD GORDON
REFS: NASA RP-1311, PART I, 1994 AND NASA RP-1311, PART II, 1996
*******************************************************************************
THERMODYNAMIC EQUILIBRIUM COMBUSTION PROPERTIES AT ASSIGNED
PRESSURES
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 6.00000 %FUEL= 14.285714 R,EQ.RATIO= 1.322780 PHI,EQ.RATIO= 1.322780
THERMODYNAMIC PROPERTIES
P, BAR 197.88
T, K 3594.37
RHO, KG/CU M 9.0105 0
H, KJ/KG -986.31
U, KJ/KG -3182.40
G, KJ/KG -62790.6
S, KJ/(KG)(K) 17.1948
M, (1/n) 13.608
(dLV/dLP)t -1.01921
(dLV/dLT)p 1.3335
Cp, KJ/(KG)(K) 7.3661
GAMMAs 1.1472
SON VEL,M/SEC 1587.2
MOLE FRACTIONS
*H 0.02575
HO2 0.00003
*H2 0.24744
H2O 0.68555
H2O2 0.00002
*O 0.00207
*OH 0.03694
*O2 0.00220
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
From the output, we see that the chamber temperature is 3594.37 K, the average molecular weight is 13.608 g/mol, and the specific heat ratio \(\gamma\) is 1.1472. We also see that the equilibrium mixture contains mostly H\(_2\), H\(_2\)O, OH, H, and with some trace amounts of O, O\(_2\), and H\(_2\)O\(_2\). We can use this information to find the quantities of interest:
area_ratio = 68.8
Pc = Q_(2870, 'psi')
# sea level
Pa = Q_(1, 'atm')
# output from CEA
Tc = Q_(3594.37, 'K')
MW = Q_(13.608, 'kg/kmol')
gamma = 1.1472
# initial guesses for Pc / Pe
root = root_scalar(root_area_ratio, x0=500, x1=1000, args=(area_ratio, gamma))
Pc_Pe = root.root
Pe = Pc / Pc_Pe
print(f"Exit pressure = {Pe.to('psi'): .2f~P}")
cstar = get_cstar(Tc, MW, gamma)
print(f"Cstar = {cstar.to('m/s'): .1f~P}")
print('at sea level:')
CF0 = get_thrust_coeff(Pc_Pe, gamma)
CF = CF0 + (1/Pc_Pe + Pa/Pc) * area_ratio
print(f"C_F = {CF.to_base_units(): .3f~P}")
Isp = CF * cstar / g0
print(f"Isp = {Isp.to('s'): .1f~P}")
Exit pressure = 3.81 psi
Cstar = 2322.5 m/s
at sea level:
C_F = 2.350
Isp = 556.5 s
Rocket problem¶
CEA can also calculate performance quantities specific to rockets, such as the effective velocity (C-star, \(c^*\)), thrust coefficient (\(C_F\)), and specific impulse (\(I_{\text{sp}}\)).
To do this, it has to make an assumption of whether to
For the above example, but choosing the rocket problem and specifying a (supersonic) nozzle area ratio
of 68.8, and leaving other options at their defaults, CEA provides this output:
*******************************************************************************
NASA-GLENN CHEMICAL EQUILIBRIUM PROGRAM CEA2, FEBRUARY 5, 2004
BY BONNIE MCBRIDE AND SANFORD GORDON
REFS: NASA RP-1311, PART I, 1994 AND NASA RP-1311, PART II, 1996
*******************************************************************************
### CEA analysis performed on Tue 08-Feb-2022 11:04:54
# Problem Type: "Rocket" (Infinite Area Combustor)
prob case=_______________8942 ro
# Pressure (1 value):
p,psia= 2870
# Supersonic Area Ratio (1 value):
supar= 68.8
# Oxidizer/Fuel Wt. ratio (1 value):
o/f= 6.0
# You selected the following fuels and oxidizers:
reac
fuel H2(L) wt%=100.0000
oxid O2(L) wt%=100.0000
# You selected these options for output:
# short version of output
output short
# Proportions of any products will be expressed as Mole Fractions.
# Heat will be expressed as siunits
output siunits
# Input prepared by this script:/var/www/sites/cearun.grc.nasa.gov/cgi-bin/CEARU
N/prepareInputFile.cgi
### IMPORTANT: The following line is the end of your CEA input file!
end
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 6.00000 %FUEL= 14.285714 R,EQ.RATIO= 1.322780 PHI,EQ.RATIO= 1.322780
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7688 1110.26
P, BAR 197.88 111.87 0.17823
T, K 3594.37 3276.93 980.79
RHO, KG/CU M 9.0105 0 5.5875 0 2.9742-2
H, KJ/KG -986.31 -2182.76 -9907.46
U, KJ/KG -3182.40 -4184.90 -10506.7
G, KJ/KG -62790.6 -58528.7 -26771.8
S, KJ/(KG)(K) 17.1948 17.1948 17.1948
M, (1/n) 13.608 13.608 13.608
Cp, KJ/(KG)(K) 3.7951 3.7416 2.7469
GAMMAs 1.1919 1.1952 1.2861
SON VEL,M/SEC 1617.9 1546.9 877.9
MACH NUMBER 0.000 1.000 4.812
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2289.4 2289.4
CF 0.6757 1.8450
Ivac, M/SEC 2841.2 4365.9
Isp, M/SEC 1546.9 4224.0
MOLE FRACTIONS
*H 0.02575 HO2 0.00003 *H2 0.24744
H2O 0.68555 H2O2 0.00002 *O 0.00207
*OH 0.03694 *O2 0.00220
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
The key properties include:
C-star of 2289.4 m/s (based on combustion chamber conditions)
throat pressure of 111.87 bar and temperature of 3276.93 K
exit pressure of 0.17823 bar, temperature of 980.79 K
at the nozzle exit, thrust coefficient = 1.8450, Isp = 4224.0 m/s
The reported specific impulse \(I_{\textrm{sp}}\) assumes that the ambient pressure is the same as the exit pressure, since CEA does not know the actual ambient pressure. (It also reports the specific impulse in vacuum, \(I_{\textrm{vac}}\).) The value is given in m/s and needs to be divided by the gravity constant to get our usual units of seconds:
Isp_cea = Q_(4224.0, 'm/s')
Isp = Isp_cea / g0
print(f"Isp = {Isp.to('s'): .1f~P}")
Isp = 430.7 s
The next thing to note is that CEA defaulted to assuming frozen mixture composition from the combustion chamber and throughout the nozzle; in other words, it is assuming that the equilibrium composition in the combustion chamber (based on chemical equilibrium) is the fixed composition throughout the whole nozzle.
However, in reality, the mixture composition will change because the temperature and pressure change throughout the nozzle. In the real system, these changes will be driven by chemical reactions occuring, but it is extremely challening to model these time-dependent effects. Instead, an approximate shifting equilibrium approach can be taken, based on the assumption that the chemical reactions occur infinitely fast, and, therefore, at every location in the nozzle, the mixture composition is the equilibrium composition based on the local temperature and pressure.
CEA can use this approximation by selecting the Equilibrium rocket problem option. This produces:
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 6.00000 %FUEL= 14.285714 R,EQ.RATIO= 1.322780 PHI,EQ.RATIO= 1.322780
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7401 960.27
P, BAR 197.88 113.71 0.20607
T, K 3594.37 3378.30 1234.47
RHO, KG/CU M 9.0105 0 5.5605 0 2.8330-2
H, KJ/KG -986.31 -2160.57 -10543.0
U, KJ/KG -3182.40 -4205.62 -11270.4
G, KJ/KG -62790.6 -60249.7 -31769.4
S, KJ/(KG)(K) 17.1948 17.1948 17.1948
M, (1/n) 13.608 13.735 14.111
(dLV/dLP)t -1.01921 -1.01432 -1.00000
(dLV/dLT)p 1.3335 1.2644 1.0000
Cp, KJ/(KG)(K) 7.3661 6.7421 2.9102
GAMMAs 1.1472 1.1484 1.2539
SON VEL,M/SEC 1587.2 1532.5 955.0
MACH NUMBER 0.000 1.000 4.578
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2322.1 2322.1
CF 0.6599 1.8827
Ivac, M/SEC 2867.0 4538.3
Isp, M/SEC 1532.5 4371.9
MOLE FRACTIONS
*H 0.02575 0.02063 0.00000
HO2 0.00003 0.00002 0.00000
*H2 0.24744 0.24496 0.24402
H2O 0.68555 0.70439 0.75598
H2O2 0.00002 0.00001 0.00000
*O 0.00207 0.00126 0.00000
*OH 0.03694 0.02734 0.00000
*O2 0.00220 0.00140 0.00000
With the key properties:
C-star of 2322.1 m/s (based on combustion chamber conditions)
exit pressure of 0.20607
at the nozzle exit, thrust coefficient = 1.8827, Isp = 4371.9 m/s
Isp_cea = Q_(4371.9, 'm/s')
Isp_eq = Isp_cea / g0
print(f"Isp (equilibrium) = {Isp_eq.to('s'): .1f~P}")
print(f"Difference: {100*np.abs(Isp_eq - Isp)/Isp: .2f~P}%")
Isp (equilibrium) = 445.8 s
Difference: 3.50%
The shifting equilibrium assumption typically overpredicts the real performance by 1–4%, while the frozen composition assumption underpredicts performance by 1–4%.
Oxidizer-to-fuel ratio¶
The thermochemical performance of a rocket, represented by \(c^*\), is a strong function of the oxidizer-to-fuel ratio, or \(r = \) O/F, and thus the overall performance (\(I_{\textrm{sp}}\)) also depends on the O/F ratio. For liquid rockets, this ratio can be controlled directly since the propellants are injected separately. CEA can help us identify the optimal O/F ratio.
For example, for the SSME considered above using liquid hydrogen and liquid oxygen, we can have CEA sweep over a range of O/F values, from 2 to 8 in increments of 0.25. This gives an input file of
prob case=_______________8942 ro equilibrium
# Pressure (1 value):
p,psia= 2870
# Supersonic Area Ratio (1 value):
supar= 68.8
# Oxidizer/Fuel Wt. ratio (25 values):
o/f= 2, 2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75, 4, 4.25, 4.5, 4.75, 5, 5.25, 5.5, 5
.75, 6, 6.25, 6.5, 6.75, 7, 7.25, 7.5, 7.75, 8
reac
fuel H2(L) wt%=100.0000
oxid O2(L) wt%=100.0000
output short
# Proportions of any products will be expressed as Mole Fractions.
# Heat will be expressed as siunits
output siunits
end
The output of CEA will be quite long, since there are 25 separate cases; the output is in the file cea_OF_ratio_out.txt. We can use Python to extract the desired information:
# Click the + to see the full contents of the output file
filename = 'cea_OF_ratio_out.txt'
print('Contents of ' + filename + ':')
with open(filename) as f:
file_contents = f.read()
print(file_contents)
Contents of cea_OF_ratio_out.txt:
NASA-GLENN CHEMICAL EQUILIBRIUM PROGRAM CEA2, FEBRUARY 5, 2004
BY BONNIE MCBRIDE AND SANFORD GORDON
REFS: NASA RP-1311, PART I, 1994 AND NASA RP-1311, PART II, 1996
*******************************************************************************
### CEA analysis performed on Tue 08-Feb-2022 16:53:23
# Problem Type: "Rocket" (Infinite Area Combustor)
prob case=_______________8942 ro equilibrium
# Pressure (1 value):
p,psia= 2870
# Supersonic Area Ratio (1 value):
supar= 68.8
# Oxidizer/Fuel Wt. ratio (25 values):
o/f= 2, 2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75, 4, 4.25, 4.5, 4.75, 5, 5.25, 5.5, 5
.75, 6, 6.25, 6.5, 6.75, 7, 7.25, 7.5, 7.75, 8
# You selected the following fuels and oxidizers:
reac
fuel H2(L) wt%=100.0000
oxid O2(L) wt%=100.0000
# You selected these options for output:
# short version of output
output short
# Proportions of any products will be expressed as Mole Fractions.
# Heat will be expressed as siunits
output siunits
# Input prepared by this script:/var/www/sites/cearun.grc.nasa.gov/cgi-bin/CEARU
N/prepareInputFile.cgi
### IMPORTANT: The following line is the end of your CEA input file!
end
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 2.00000 %FUEL= 33.333333 R,EQ.RATIO= 3.968341 PHI,EQ.RATIO= 3.968341
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.8302 1683.07
P, BAR 197.88 108.12 0.11757
T, K 1797.77 1570.17 295.90
RHO, KG/CU M 8.0059 0 5.0085 0 2.9545-2
H, KJ/KG -1760.57 -3158.32 -10246.6
U, KJ/KG -4232.25 -5317.05 -10644.6
G, KJ/KG -50618.5 -45830.8 -18288.2
S, KJ/(KG)(K) 27.1769 27.1769 27.1769
M, (1/n) 6.048 6.048 6.182
MW, MOL WT 6.048 6.048 6.048
(dLV/dLP)t -1.00001 -1.00000 -1.30774
(dLV/dLT)p 1.0002 1.0000 6.5161
Cp, KJ/(KG)(K) 6.2443 6.0361 138.0837
GAMMAs 1.2825 1.2950 1.1183
SON VEL,M/SEC 1780.4 1672.0 667.1
MACH NUMBER 0.000 1.000 6.176
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2363.0 2363.0
CF 0.7076 1.7434
Ivac, M/SEC 2963.1 4216.3
Isp, M/SEC 1672.0 4119.7
MOLE FRACTIONS
*H 0.00002 0.00000 0.00000
*H2 0.74799 0.74800 0.74801
H2O 0.25199 0.25199 0.23019
H2O(L) 0.00000 0.00000 0.02180
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 2.25000 %FUEL= 30.769231 R,EQ.RATIO= 3.527415 PHI,EQ.RATIO= 3.527415
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.8214 1819.59
P, BAR 197.88 108.64 0.10875
T, K 1975.45 1736.00 298.69
RHO, KG/CU M 7.8927 0 4.9312 0 2.8689-2
H, KJ/KG -1656.35 -3067.04 -10461.5
U, KJ/KG -4163.45 -5270.18 -10840.6
G, KJ/KG -53103.6 -48278.2 -18240.5
S, KJ/(KG)(K) 26.0433 26.0433 26.0433
M, (1/n) 6.551 6.552 6.552
MW, MOL WT 6.551 6.552 6.552
(dLV/dLP)t -1.00002 -1.00000 -1.00000
(dLV/dLT)p 1.0006 1.0001 1.0000
Cp, KJ/(KG)(K) 5.9922 5.7929 4.6075
GAMMAs 1.2691 1.2806 1.3801
SON VEL,M/SEC 1783.7 1679.7 723.3
MACH NUMBER 0.000 1.000 5.802
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2389.0 2389.0
CF 0.7031 1.7566
Ivac, M/SEC 2991.3 4286.8
Isp, M/SEC 1679.7 4196.5
MOLE FRACTIONS
*H 0.00008 0.00002 0.00000
*H2 0.71644 0.71649 0.71651
H2O 0.28348 0.28349 0.28349
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 2.50000 %FUEL= 28.571429 R,EQ.RATIO= 3.174673 PHI,EQ.RATIO= 3.174673
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.8137 1739.44
P, BAR 197.88 109.11 0.11376
T, K 2144.07 1894.66 343.37
RHO, KG/CU M 7.8307 0 4.8865 0 2.8114-2
H, KJ/KG -1567.01 -2982.53 -10601.0
U, KJ/KG -4093.97 -5215.33 -11005.6
G, KJ/KG -55217.9 -50392.5 -19193.1
S, KJ/(KG)(K) 25.0229 25.0229 25.0229
M, (1/n) 7.055 7.055 7.056
MW, MOL WT 7.055 7.055 7.056
(dLV/dLP)t -1.00006 -1.00002 -1.00000
(dLV/dLT)p 1.0017 1.0005 1.0000
Cp, KJ/(KG)(K) 5.7811 5.5815 4.3324
GAMMAs 1.2570 1.2679 1.3736
SON VEL,M/SEC 1782.3 1682.6 745.5
MACH NUMBER 0.000 1.000 5.701
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2406.8 2406.8
CF 0.6991 1.7661
Ivac, M/SEC 3009.6 4345.8
Isp, M/SEC 1682.6 4250.6
MOLE FRACTIONS
*H 0.00024 0.00006 0.00000
*H2 0.68481 0.68496 0.68501
H2O 0.31494 0.31498 0.31499
*OH 0.00002 0.00000 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 2.75000 %FUEL= 26.666667 R,EQ.RATIO= 2.886066 PHI,EQ.RATIO= 2.886066
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.8066 1662.01
P, BAR 197.88 109.53 0.11906
T, K 2304.06 2046.61 390.80
RHO, KG/CU M 7.8060 0 4.8654 0 2.7699-2
H, KJ/KG -1489.58 -2903.81 -10707.7
U, KJ/KG -4024.54 -5155.02 -11137.5
G, KJ/KG -57021.2 -52230.3 -20126.6
S, KJ/(KG)(K) 24.1016 24.1016 24.1016
M, (1/n) 7.557 7.559 7.560
MW, MOL WT 7.557 7.559 7.560
(dLV/dLP)t -1.00016 -1.00005 -1.00000
(dLV/dLT)p 1.0038 1.0012 1.0000
Cp, KJ/(KG)(K) 5.6137 5.4018 4.0893
GAMMAs 1.2458 1.2564 1.3679
SON VEL,M/SEC 1777.1 1681.8 766.8
MACH NUMBER 0.000 1.000 5.600
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2418.3 2418.3
CF 0.6955 1.7755
Ivac, M/SEC 3020.4 4393.8
Isp, M/SEC 1681.8 4293.7
MOLE FRACTIONS
*H 0.00057 0.00017 0.00000
*H2 0.65305 0.65337 0.65351
H2O 0.34633 0.34645 0.34649
*OH 0.00005 0.00001 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 3.00000 %FUEL= 25.000000 R,EQ.RATIO= 2.645561 PHI,EQ.RATIO= 2.645561
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.8001 1587.44
P, BAR 197.88 109.93 0.12465
T, K 2455.55 2192.08 441.13
RHO, KG/CU M 7.8101 0 4.8623 0 2.7404-2
H, KJ/KG -1421.83 -2829.97 -10786.8
U, KJ/KG -3955.47 -5090.78 -11241.7
G, KJ/KG -58554.6 -53832.6 -21050.6
S, KJ/(KG)(K) 23.2668 23.2668 23.2668
M, (1/n) 8.058 8.062 8.064
MW, MOL WT 8.058 8.062 8.064
(dLV/dLP)t -1.00033 -1.00011 -1.00000
(dLV/dLT)p 1.0075 1.0028 1.0000
Cp, KJ/(KG)(K) 5.4926 5.2559 3.8780
GAMMAs 1.2351 1.2457 1.3622
SON VEL,M/SEC 1769.0 1678.2 787.2
MACH NUMBER 0.000 1.000 5.498
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2425.1 2425.1
CF 0.6920 1.7846
Ivac, M/SEC 3025.4 4432.9
Isp, M/SEC 1678.2 4327.8
MOLE FRACTIONS
*H 0.00116 0.00041 0.00000
*H2 0.62110 0.62169 0.62201
H2O 0.37759 0.37787 0.37799
*OH 0.00015 0.00004 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 3.25000 %FUEL= 23.529412 R,EQ.RATIO= 2.442056 PHI,EQ.RATIO= 2.442056
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7939 1516.04
P, BAR 197.88 110.31 0.13052
T, K 2598.47 2331.15 494.40
RHO, KG/CU M 7.8373 0 4.8737 0 2.7203-2
H, KJ/KG -1362.05 -2760.18 -10842.6
U, KJ/KG -3886.90 -5023.56 -11322.4
G, KJ/KG -59847.0 -55228.4 -21970.3
S, KJ/(KG)(K) 22.5075 22.5075 22.5075
M, (1/n) 8.557 8.563 8.567
MW, MOL WT 8.557 8.563 8.567
(dLV/dLP)t -1.00061 -1.00023 -1.00000
(dLV/dLT)p 1.0135 1.0057 1.0000
Cp, KJ/(KG)(K) 5.4192 5.1467 3.6969
GAMMAs 1.2248 1.2354 1.3559
SON VEL,M/SEC 1758.5 1672.2 806.6
MACH NUMBER 0.000 1.000 5.399
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2428.0 2428.0
CF 0.6887 1.7934
Ivac, M/SEC 3025.7 4464.6
Isp, M/SEC 1672.2 4354.4
MOLE FRACTIONS
*H 0.00208 0.00083 0.00000
*H2 0.58893 0.58987 0.59051
H2O 0.40862 0.40919 0.40949
*OH 0.00037 0.00011 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 3.50000 %FUEL= 22.222222 R,EQ.RATIO= 2.267624 PHI,EQ.RATIO= 2.267624
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7878 1448.16
P, BAR 197.88 110.68 0.13664
T, K 2732.68 2463.70 550.57
RHO, KG/CU M 7.8839 0 4.8972 0 2.7078-2
H, KJ/KG -1308.92 -2693.79 -10878.3
U, KJ/KG -3818.84 -4953.94 -11382.9
G, KJ/KG -60920.0 -56437.3 -22888.4
S, KJ/(KG)(K) 21.8141 21.8141 21.8141
M, (1/n) 9.052 9.063 9.071
MW, MOL WT 9.052 9.063 9.071
(dLV/dLP)t -1.00105 -1.00045 -1.00000
(dLV/dLT)p 1.0222 1.0103 1.0000
Cp, KJ/(KG)(K) 5.3937 5.0772 3.5431
GAMMAs 1.2149 1.2255 1.3490
SON VEL,M/SEC 1746.2 1664.3 825.1
MACH NUMBER 0.000 1.000 5.302
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2427.9 2427.9
CF 0.6855 1.8019
Ivac, M/SEC 3022.3 4490.1
Isp, M/SEC 1664.3 4374.8
MOLE FRACTIONS
*H 0.00341 0.00152 0.00000
*H2 0.55653 0.55788 0.55901
H2O 0.43928 0.44033 0.44099
*OH 0.00078 0.00026 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 3.75000 %FUEL= 21.052632 R,EQ.RATIO= 2.116449 PHI,EQ.RATIO= 2.116449
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7819 1383.89
P, BAR 197.88 111.05 0.14299
T, K 2858.04 2589.51 609.53
RHO, KG/CU M 7.9470 0 4.9312 0 2.7016-2
H, KJ/KG -1261.38 -2630.32 -10896.6
U, KJ/KG -3751.35 -4882.34 -11425.9
G, KJ/KG -61790.9 -57472.7 -23805.6
S, KJ/(KG)(K) 21.1787 21.1787 21.1787
M, (1/n) 9.544 9.561 9.575
MW, MOL WT 9.544 9.561 9.575
(dLV/dLP)t -1.00167 -1.00078 -1.00000
(dLV/dLT)p 1.0340 1.0173 1.0000
Cp, KJ/(KG)(K) 5.4147 5.0494 3.4134
GAMMAs 1.2054 1.2158 1.3412
SON VEL,M/SEC 1732.4 1654.7 842.5
MACH NUMBER 0.000 1.000 5.210
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2425.1 2425.1
CF 0.6823 1.8101
Ivac, M/SEC 3015.7 4510.4
Isp, M/SEC 1654.7 4389.8
MOLE FRACTIONS
*H 0.00515 0.00253 0.00000
*H2 0.52394 0.52571 0.52751
H2O 0.46942 0.47118 0.47249
*O 0.00001 0.00000 0.00000
*OH 0.00149 0.00057 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 4.00000 %FUEL= 20.000000 R,EQ.RATIO= 1.984171 PHI,EQ.RATIO= 1.984171
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7761 1323.39
P, BAR 197.88 111.41 0.14952
T, K 2974.45 2708.26 671.13
RHO, KG/CU M 8.0246 0 4.9745 0 2.7009-2
H, KJ/KG -1218.59 -2569.45 -10899.7
U, KJ/KG -3684.49 -4809.15 -11453.3
G, KJ/KG -62475.3 -58344.2 -24721.1
S, KJ/(KG)(K) 20.5943 20.5943 20.5943
M, (1/n) 10.029 10.054 10.079
MW, MOL WT 10.029 10.054 10.079
(dLV/dLP)t -1.00250 -1.00126 -1.00000
(dLV/dLT)p 1.0495 1.0272 1.0000
Cp, KJ/(KG)(K) 5.4801 5.0645 3.3046
GAMMAs 1.1964 1.2063 1.3327
SON VEL,M/SEC 1717.6 1643.7 858.9
MACH NUMBER 0.000 1.000 5.123
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2420.1 2420.1
CF 0.6792 1.8182
Ivac, M/SEC 3006.3 4526.1
Isp, M/SEC 1643.7 4400.2
MOLE FRACTIONS
*H 0.00728 0.00391 0.00000
*H2 0.49125 0.49338 0.49601
H2O 0.49883 0.50159 0.50399
*O 0.00002 0.00001 0.00000
*OH 0.00261 0.00112 0.00000
*O2 0.00001 0.00000 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 4.25000 %FUEL= 19.047619 R,EQ.RATIO= 1.867455 PHI,EQ.RATIO= 1.867455
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7705 1266.63
P, BAR 197.88 111.77 0.15623
T, K 3081.92 2819.66 735.18
RHO, KG/CU M 8.1149 0 5.0260 0 2.7049-2
H, KJ/KG -1179.87 -2510.98 -10889.4
U, KJ/KG -3618.34 -4734.72 -11466.9
G, KJ/KG -62988.0 -59059.4 -25633.4
S, KJ/(KG)(K) 20.0550 20.0550 20.0550
M, (1/n) 10.509 10.543 10.583
MW, MOL WT 10.509 10.543 10.583
(dLV/dLP)t -1.00357 -1.00194 -1.00000
(dLV/dLT)p 1.0689 1.0404 1.0000
Cp, KJ/(KG)(K) 5.5875 5.1228 3.2139
GAMMAs 1.1879 1.1972 1.3235
SON VEL,M/SEC 1702.0 1631.6 874.3
MACH NUMBER 0.000 1.000 5.040
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2413.0 2413.0
CF 0.6762 1.8262
Ivac, M/SEC 2994.5 4537.8
Isp, M/SEC 1631.6 4406.7
MOLE FRACTIONS
*H 0.00973 0.00564 0.00000
*H2 0.45860 0.46094 0.46451
H2O 0.52733 0.53137 0.53549
*O 0.00005 0.00001 0.00000
*OH 0.00427 0.00202 0.00000
*O2 0.00002 0.00001 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 4.50000 %FUEL= 18.181818 R,EQ.RATIO= 1.763707 PHI,EQ.RATIO= 1.763707
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7651 1213.50
P, BAR 197.88 112.11 0.16306
T, K 3180.53 2923.45 801.47
RHO, KG/CU M 8.2164 0 5.0850 0 2.7131-2
H, KJ/KG -1144.68 -2454.73 -10867.1
U, KJ/KG -3553.02 -4659.40 -11468.2
G, KJ/KG -63342.7 -59625.4 -26540.6
S, KJ/(KG)(K) 19.5559 19.5559 19.5559
M, (1/n) 10.980 11.025 11.087
MW, MOL WT 10.980 11.025 11.087
(dLV/dLP)t -1.00490 -1.00283 -1.00000
(dLV/dLT)p 1.0924 1.0574 1.0000
Cp, KJ/(KG)(K) 5.7347 5.2241 3.1387
GAMMAs 1.1802 1.1885 1.3139
SON VEL,M/SEC 1685.9 1618.7 888.7
MACH NUMBER 0.000 1.000 4.962
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2404.1 2404.1
CF 0.6733 1.8342
Ivac, M/SEC 2980.7 4545.9
Isp, M/SEC 1618.7 4409.6
MOLE FRACTIONS
*H 0.01239 0.00768 0.00000
*H2 0.42615 0.42852 0.43301
H2O 0.55472 0.56033 0.56699
*O 0.00011 0.00003 0.00000
*OH 0.00658 0.00341 0.00000
*O2 0.00005 0.00002 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 4.75000 %FUEL= 17.391304 R,EQ.RATIO= 1.670881 PHI,EQ.RATIO= 1.670881
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7600 1163.87
P, BAR 197.88 112.43 0.17002
T, K 3270.40 3019.42 869.78
RHO, KG/CU M 8.3280 0 5.1506 0 2.7251-2
H, KJ/KG -1112.55 -2400.72 -10834.3
U, KJ/KG -3488.62 -4583.60 -11458.2
G, KJ/KG -63552.4 -60048.7 -27440.6
S, KJ/(KG)(K) 19.0924 19.0924 19.0924
M, (1/n) 11.444 11.501 11.591
MW, MOL WT 11.444 11.501 11.591
(dLV/dLP)t -1.00651 -1.00396 -1.00000
(dLV/dLT)p 1.1204 1.0787 1.0000
Cp, KJ/(KG)(K) 5.9203 5.3682 3.0772
GAMMAs 1.1731 1.1803 1.3040
SON VEL,M/SEC 1669.5 1605.1 902.0
MACH NUMBER 0.000 1.000 4.889
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2393.5 2393.5
CF 0.6706 1.8422
Ivac, M/SEC 2965.1 4551.0
Isp, M/SEC 1605.1 4409.5
MOLE FRACTIONS
*H 0.01513 0.00996 0.00000
*H2 0.39411 0.39627 0.40151
H2O 0.58080 0.58825 0.59849
*O 0.00020 0.00008 0.00000
*OH 0.00964 0.00540 0.00000
*O2 0.00012 0.00004 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 5.00000 %FUEL= 16.666667 R,EQ.RATIO= 1.587337 PHI,EQ.RATIO= 1.587337
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7553 1117.54
P, BAR 197.88 112.73 0.17707
T, K 3351.71 3107.44 939.87
RHO, KG/CU M 8.4487 0 5.2221 0 2.7406-2
H, KJ/KG -1083.09 -2348.82 -10792.0
U, KJ/KG -3425.22 -4507.58 -11438.1
G, KJ/KG -63628.9 -60336.3 -28330.9
S, KJ/(KG)(K) 18.6609 18.6609 18.6609
M, (1/n) 11.899 11.968 12.095
MW, MOL WT 11.899 11.968 12.095
(dLV/dLP)t -1.00841 -1.00537 -1.00000
(dLV/dLT)p 1.1532 1.1047 1.0000
Cp, KJ/(KG)(K) 6.1433 5.5554 3.0276
GAMMAs 1.1667 1.1727 1.2937
SON VEL,M/SEC 1653.0 1591.1 914.3
MACH NUMBER 0.000 1.000 4.820
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2381.6 2381.6
CF 0.6681 1.8503
Ivac, M/SEC 2947.9 4553.2
Isp, M/SEC 1591.1 4406.6
MOLE FRACTIONS
*H 0.01783 0.01237 0.00000
*H2 0.36268 0.36436 0.37001
H2O 0.60538 0.61490 0.62999
*O 0.00036 0.00015 0.00000
*OH 0.01351 0.00811 0.00000
*O2 0.00023 0.00010 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 5.25000 %FUEL= 16.000000 R,EQ.RATIO= 1.511749 PHI,EQ.RATIO= 1.511749
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7509 1074.30
P, BAR 197.88 113.01 0.18419
T, K 3424.61 3187.41 1011.52
RHO, KG/CU M 8.5778 0 5.2992 0 2.7593-2
H, KJ/KG -1055.99 -2298.95 -10741.1
U, KJ/KG -3362.87 -4431.60 -11408.7
G, KJ/KG -63582.5 -60494.7 -29209.6
S, KJ/(KG)(K) 18.2580 18.2580 18.2580
M, (1/n) 12.343 12.427 12.599
MW, MOL WT 12.343 12.427 12.599
(dLV/dLP)t -1.01063 -1.00709 -1.00000
(dLV/dLT)p 1.1909 1.1359 1.0000
Cp, KJ/(KG)(K) 6.4028 5.7865 2.9882
GAMMAs 1.1609 1.1657 1.2834
SON VEL,M/SEC 1636.5 1576.7 925.6
MACH NUMBER 0.000 1.000 4.755
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2368.3 2368.3
CF 0.6657 1.8583
Ivac, M/SEC 2929.3 4552.8
Isp, M/SEC 1576.7 4401.2
MOLE FRACTIONS
*H 0.02035 0.01476 0.00000
HO2 0.00001 0.00000 0.00000
*H2 0.33208 0.33303 0.33851
H2O 0.62830 0.64006 0.66149
H2O2 0.00001 0.00000 0.00000
*O 0.00061 0.00029 0.00000
*OH 0.01822 0.01163 0.00000
*O2 0.00044 0.00021 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 5.50000 %FUEL= 15.384615 R,EQ.RATIO= 1.443033 PHI,EQ.RATIO= 1.443033
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7469 1033.87
P, BAR 197.88 113.27 0.19140
T, K 3489.25 3259.25 1084.58
RHO, KG/CU M 8.7147 0 5.3815 0 2.7811-2
H, KJ/KG -1030.98 -2251.00 -10682.3
U, KJ/KG -3301.62 -4355.85 -11370.5
G, KJ/KG -63422.3 -60529.7 -30075.6
S, KJ/(KG)(K) 17.8810 17.8810 17.8810
M, (1/n) 12.777 12.875 13.103
MW, MOL WT 12.777 12.875 13.103
(dLV/dLP)t -1.01318 -1.00914 -1.00000
(dLV/dLT)p 1.2337 1.1728 1.0000
Cp, KJ/(KG)(K) 6.6967 6.0622 2.9559
GAMMAs 1.1557 1.1593 1.2733
SON VEL,M/SEC 1619.9 1562.1 936.1
MACH NUMBER 0.000 1.000 4.693
PERFORMANCE PARAMETERS
Ae/At 1.00000 68.800
CSTAR, M/SEC 2354.0 2354.0
CF 0.6636 1.8664
Ivac, M/SEC 2909.5 4550.1
Isp, M/SEC 1562.1 4393.5
MOLE FRACTIONS
*H 0.02257 0.01702 0.00000
HO2 0.00001 0.00001 0.00000
*H2 0.30253 0.30252 0.30702
H2O 0.64939 0.66350 0.69298
H2O2 0.00001 0.00000 0.00000
*O 0.00096 0.00050 0.00000
*OH 0.02374 0.01603 0.00000
*O2 0.00079 0.00042 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 5.75000 %FUEL= 14.814815 R,EQ.RATIO= 1.380293 PHI,EQ.RATIO= 1.380293
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7433 995.99
P, BAR 197.88 113.51 0.19867
T, K 3545.79 3322.91 1158.90
RHO, KG/CU M 8.8590 0 5.4686 0 2.8056-2
H, KJ/KG -1007.82 -2204.91 -10616.2
U, KJ/KG -3241.46 -4280.49 -11324.4
G, KJ/KG -63155.9 -60446.5 -30928.6
S, KJ/(KG)(K) 17.5273 17.5273 17.5273
M, (1/n) 13.199 13.311 13.607
MW, MOL WT 13.199 13.311 13.607
(dLV/dLP)t -1.01605 -1.01155 -1.00000
(dLV/dLT)p 1.2815 1.2156 1.0000
Cp, KJ/(KG)(K) 7.0207 6.3821 2.9306
GAMMAs 1.1511 1.1535 1.2634
SON VEL,M/SEC 1603.5 1547.3 945.9
MACH NUMBER 0.000 1.000 4.635
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2338.5 2338.5
CF 0.6617 1.8746
Ivac, M/SEC 2888.7 4545.2
Isp, M/SEC 1547.3 4383.7
MOLE FRACTIONS
*H 0.02439 0.01901 0.00000
HO2 0.00002 0.00001 0.00000
*H2 0.27425 0.27307 0.27552
H2O 0.66851 0.68501 0.72448
H2O2 0.00001 0.00001 0.00000
*O 0.00144 0.00081 0.00000
*OH 0.03002 0.02128 0.00000
*O2 0.00135 0.00079 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 6.00000 %FUEL= 14.285714 R,EQ.RATIO= 1.322780 PHI,EQ.RATIO= 1.322780
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7401 960.27
P, BAR 197.88 113.71 0.20607
T, K 3594.37 3378.30 1234.47
RHO, KG/CU M 9.0105 0 5.5605 0 2.8330-2
H, KJ/KG -986.31 -2160.57 -10543.0
U, KJ/KG -3182.40 -4205.62 -11270.4
G, KJ/KG -62790.6 -60249.7 -31769.4
S, KJ/(KG)(K) 17.1948 17.1948 17.1948
M, (1/n) 13.608 13.735 14.111
MW, MOL WT 13.608 13.735 14.111
(dLV/dLP)t -1.01921 -1.01432 -1.00000
(dLV/dLT)p 1.3335 1.2644 1.0000
Cp, KJ/(KG)(K) 7.3661 6.7421 2.9102
GAMMAs 1.1472 1.1484 1.2539
SON VEL,M/SEC 1587.2 1532.5 955.0
MACH NUMBER 0.000 1.000 4.578
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2322.1 2322.1
CF 0.6599 1.8827
Ivac, M/SEC 2867.0 4538.3
Isp, M/SEC 1532.5 4371.9
MOLE FRACTIONS
*H 0.02575 0.02063 0.00000
HO2 0.00003 0.00002 0.00000
*H2 0.24744 0.24496 0.24402
H2O 0.68555 0.70439 0.75598
H2O2 0.00002 0.00001 0.00000
*O 0.00207 0.00126 0.00000
*OH 0.03694 0.02734 0.00000
*O2 0.00220 0.00140 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 6.25000 %FUEL= 13.793103 R,EQ.RATIO= 1.269869 PHI,EQ.RATIO= 1.269869
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7373 926.38
P, BAR 197.88 113.90 0.21360
T, K 3635.16 3425.40 1311.32
RHO, KG/CU M 9.1688 0 5.6569 0 2.8633-2
H, KJ/KG -966.28 -2117.95 -10462.8
U, KJ/KG -3124.47 -4131.38 -11208.8
G, KJ/KG -62333.1 -59943.7 -32599.7
S, KJ/(KG)(K) 16.8815 16.8815 16.8815
M, (1/n) 14.005 14.145 14.615
MW, MOL WT 14.005 14.145 14.615
(dLV/dLP)t -1.02257 -1.01743 -1.00000
(dLV/dLT)p 1.3885 1.3185 1.0000
Cp, KJ/(KG)(K) 7.7176 7.1313 2.8934
GAMMAs 1.1438 1.1440 1.2447
SON VEL,M/SEC 1571.2 1517.7 963.6
MACH NUMBER 0.000 1.000 4.523
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2304.9 2304.9
CF 0.6585 1.8908
Ivac, M/SEC 2844.3 4529.3
Isp, M/SEC 1517.7 4358.1
MOLE FRACTIONS
*H 0.02662 0.02179 0.00000
HO2 0.00005 0.00003 0.00000
*H2 0.22229 0.21844 0.21252
H2O 0.70042 0.72145 0.78748
H2O2 0.00002 0.00001 0.00000
*O 0.00285 0.00185 0.00000
*OH 0.04431 0.03407 0.00000
*O2 0.00343 0.00236 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 6.50000 %FUEL= 13.333333 R,EQ.RATIO= 1.221028 PHI,EQ.RATIO= 1.221028
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7350 894.01
P, BAR 197.88 114.05 0.22134
T, K 3668.40 3464.22 1389.59
RHO, KG/CU M 9.3336 0 5.7575 0 2.8964-2
H, KJ/KG -947.59 -2076.97 -10375.4
U, KJ/KG -3067.67 -4057.88 -11139.6
G, KJ/KG -61791.0 -59533.8 -33422.8
S, KJ/(KG)(K) 16.5858 16.5858 16.5858
M, (1/n) 14.387 14.540 15.119
MW, MOL WT 14.387 14.540 15.119
(dLV/dLP)t -1.02598 -1.02076 -1.00000
(dLV/dLT)p 1.4438 1.3758 1.0000
Cp, KJ/(KG)(K) 8.0531 7.5284 2.8795
GAMMAs 1.1410 1.1403 1.2361
SON VEL,M/SEC 1555.3 1502.9 971.9
MACH NUMBER 0.000 1.000 4.468
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2286.8 2286.8
CF 0.6572 1.8988
Ivac, M/SEC 2821.0 4518.3
Isp, M/SEC 1502.9 4342.3
MOLE FRACTIONS
*H 0.02699 0.02246 0.00000
HO2 0.00007 0.00004 0.00000
*H2 0.19896 0.19376 0.18102
H2O 0.71307 0.73607 0.81898
H2O2 0.00003 0.00002 0.00000
*O 0.00378 0.00260 0.00000
*OH 0.05193 0.04126 0.00000
*O2 0.00516 0.00380 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 6.75000 %FUEL= 12.903226 R,EQ.RATIO= 1.175805 PHI,EQ.RATIO= 1.175805
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7331 862.80
P, BAR 197.88 114.18 0.22935
T, K 3694.44 3494.93 1469.55
RHO, KG/CU M 9.5045 0 5.8621 0 2.9325-2
H, KJ/KG -930.11 -2037.62 -10280.3
U, KJ/KG -3012.05 -3985.29 -11062.4
G, KJ/KG -61172.3 -59026.7 -34243.1
S, KJ/(KG)(K) 16.3062 16.3062 16.3062
M, (1/n) 14.754 14.920 15.623
MW, MOL WT 14.754 14.920 15.623
(dLV/dLP)t -1.02924 -1.02410 -1.00000
(dLV/dLT)p 1.4961 1.4328 1.0001
Cp, KJ/(KG)(K) 8.3450 7.9006 2.8684
GAMMAs 1.1388 1.1373 1.2279
SON VEL,M/SEC 1539.8 1488.3 980.0
MACH NUMBER 0.000 1.000 4.413
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2268.1 2268.1
CF 0.6562 1.9066
Ivac, M/SEC 2797.0 4505.2
Isp, M/SEC 1488.3 4324.4
MOLE FRACTIONS
*H 0.02690 0.02263 0.00001
HO2 0.00010 0.00006 0.00000
*H2 0.17756 0.17112 0.14951
H2O 0.72351 0.74817 0.85047
H2O2 0.00004 0.00002 0.00000
*O 0.00483 0.00349 0.00000
*OH 0.05957 0.04865 0.00000
*O2 0.00750 0.00586 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 7.00000 %FUEL= 12.500000 R,EQ.RATIO= 1.133812 PHI,EQ.RATIO= 1.133812
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7317 832.37
P, BAR 197.88 114.27 0.23773
T, K 3713.70 3517.88 1551.63
RHO, KG/CU M 9.6811 0 5.9704 0 2.9717-2
H, KJ/KG -913.72 -1999.86 -10176.3
U, KJ/KG -2957.69 -3913.80 -10976.3
G, KJ/KG -60486.8 -58431.7 -35066.7
S, KJ/(KG)(K) 16.0414 16.0414 16.0414
M, (1/n) 15.107 15.282 16.127
MW, MOL WT 15.107 15.282 16.127
(dLV/dLP)t -1.03210 -1.02717 -1.00001
(dLV/dLT)p 1.5416 1.4846 1.0003
Cp, KJ/(KG)(K) 8.5656 8.2078 2.8604
GAMMAs 1.1371 1.1350 1.2200
SON VEL,M/SEC 1524.6 1473.9 987.9
MACH NUMBER 0.000 1.000 4.357
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2248.7 2248.7
CF 0.6554 1.9140
Ivac, M/SEC 2772.4 4490.0
Isp, M/SEC 1473.9 4304.1
MOLE FRACTIONS
*H 0.02640 0.02236 0.00002
HO2 0.00013 0.00008 0.00000
*H2 0.15814 0.15065 0.11801
H2O 0.73179 0.75775 0.88196
H2O2 0.00004 0.00003 0.00000
*O 0.00598 0.00449 0.00000
*OH 0.06699 0.05597 0.00001
*O2 0.01053 0.00868 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 7.25000 %FUEL= 12.121212 R,EQ.RATIO= 1.094715 PHI,EQ.RATIO= 1.094715
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7306 802.41
P, BAR 197.88 114.34 0.24660
T, K 3726.77 3533.62 1636.45
RHO, KG/CU M 9.8627 0 6.0820 0 3.0141-2
H, KJ/KG -898.32 -1963.66 -10061.9
U, KJ/KG -2904.66 -3843.61 -10880.1
G, KJ/KG -59745.1 -57760.5 -35902.0
S, KJ/(KG)(K) 15.7903 15.7903 15.7903
M, (1/n) 15.444 15.628 16.630
MW, MOL WT 15.444 15.628 16.630
(dLV/dLP)t -1.03434 -1.02966 -1.00002
(dLV/dLT)p 1.5771 1.5264 1.0007
Cp, KJ/(KG)(K) 8.6941 8.4134 2.8578
GAMMAs 1.1359 1.1334 1.2124
SON VEL,M/SEC 1509.7 1459.7 995.9
MACH NUMBER 0.000 1.000 4.298
PERFORMANCE PARAMETERS
Ae/At 1.00000 68.800
CSTAR, M/SEC 2228.9 2228.9
CF 0.6549 1.9207
Ivac, M/SEC 2747.6 4472.1
Isp, M/SEC 1459.7 4281.0
MOLE FRACTIONS
*H 0.02556 0.02170 0.00005
HO2 0.00017 0.00011 0.00000
*H2 0.14070 0.13240 0.08651
H2O 0.73803 0.76491 0.91342
H2O2 0.00005 0.00003 0.00000
*O 0.00718 0.00557 0.00000
*OH 0.07397 0.06292 0.00003
*O2 0.01433 0.01236 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 7.50000 %FUEL= 11.764706 R,EQ.RATIO= 1.058224 PHI,EQ.RATIO= 1.058224
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7300 772.31
P, BAR 197.88 114.38 0.25622
T, K 3734.29 3542.88 1725.10
RHO, KG/CU M 1.0049 1 6.1962 0 3.0606-2
H, KJ/KG -883.83 -1928.95 -9933.55
U, KJ/KG -2853.07 -3774.94 -10770.7
G, KJ/KG -58958.8 -57027.1 -36762.0
S, KJ/(KG)(K) 15.5518 15.5518 15.5518
M, (1/n) 15.767 15.958 17.133
MW, MOL WT 15.767 15.958 17.133
(dLV/dLP)t -1.03583 -1.03136 -1.00005
(dLV/dLT)p 1.6005 1.5547 1.0016
Cp, KJ/(KG)(K) 8.7223 8.4972 2.8668
GAMMAs 1.1351 1.1323 1.2045
SON VEL,M/SEC 1495.1 1445.8 1004.2
MACH NUMBER 0.000 1.000 4.237
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2208.9 2208.9
CF 0.6545 1.9260
Ivac, M/SEC 2722.6 4451.1
Isp, M/SEC 1445.8 4254.3
MOLE FRACTIONS
*H 0.02447 0.02076 0.00009
HO2 0.00021 0.00014 0.00000
*H2 0.12519 0.11633 0.05502
H2O 0.74238 0.76983 0.94480
H2O2 0.00006 0.00004 0.00000
*O 0.00839 0.00668 0.00000
*OH 0.08036 0.06927 0.00009
*O2 0.01893 0.01696 0.00000
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 7.75000 %FUEL= 11.428571 R,EQ.RATIO= 1.024088 PHI,EQ.RATIO= 1.024088
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7296 741.25
P, BAR 197.88 114.41 0.26695
T, K 3736.98 3546.53 1819.13
RHO, KG/CU M 1.0238 1 6.3127 0 3.1123-2
H, KJ/KG -870.17 -1895.69 -9783.56
U, KJ/KG -2802.99 -3707.99 -10641.3
G, KJ/KG -58139.5 -56246.3 -37661.7
S, KJ/(KG)(K) 15.3250 15.3250 15.3250
M, (1/n) 16.076 16.271 17.634
MW, MOL WT 16.076 16.271 17.634
(dLV/dLP)t -1.03654 -1.03219 -1.00016
(dLV/dLT)p 1.6118 1.5686 1.0057
Cp, KJ/(KG)(K) 8.6565 8.4612 2.9273
GAMMAs 1.1347 1.1317 1.1944
SON VEL,M/SEC 1480.9 1432.2 1012.2
MACH NUMBER 0.000 1.000 4.171
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2188.7 2188.7
CF 0.6543 1.9290
Ivac, M/SEC 2697.6 4425.3
Isp, M/SEC 1432.1 4222.2
MOLE FRACTIONS
*H 0.02322 0.01963 0.00013
HO2 0.00026 0.00017 0.00000
*H2 0.11150 0.10232 0.02371
H2O 0.74505 0.77274 0.97573
H2O2 0.00007 0.00004 0.00000
*O 0.00957 0.00775 0.00000
*OH 0.08602 0.07487 0.00041
*O2 0.02432 0.02247 0.00003
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 8.00000 %FUEL= 11.111111 R,EQ.RATIO= 0.992085 PHI,EQ.RATIO= 0.992085
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7295 724.92
P, BAR 197.88 114.41 0.27297
T, K 3735.56 3545.45 1867.79
RHO, KG/CU M 1.0430 1 6.4310 0 3.1702-2
H, KJ/KG -857.26 -1863.82 -9607.65
U, KJ/KG -2754.51 -3642.94 -10468.7
G, KJ/KG -57298.3 -55432.5 -37828.4
S, KJ/(KG)(K) 15.1091 15.1091 15.1091
M, (1/n) 16.371 16.569 18.036
MW, MOL WT 16.371 16.569 18.036
(dLV/dLP)t -1.03655 -1.03223 -1.00078
(dLV/dLT)p 1.6123 1.5696 1.0265
Cp, KJ/(KG)(K) 8.5137 8.3263 3.2227
GAMMAs 1.1345 1.1315 1.1764
SON VEL,M/SEC 1467.1 1418.8 1006.4
MACH NUMBER 0.000 1.000 4.157
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2168.7 2168.7
CF 0.6543 1.9290
Ivac, M/SEC 2672.8 4389.2
Isp, M/SEC 1418.8 4183.4
MOLE FRACTIONS
*H 0.02187 0.01838 0.00006
HO2 0.00031 0.00021 0.00000
*H2 0.09946 0.09019 0.00270
H2O 0.74624 0.77392 0.99041
H2O2 0.00008 0.00005 0.00000
*O 0.01067 0.00876 0.00003
*OH 0.09091 0.07964 0.00198
*O2 0.03047 0.02886 0.00482
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
mixture_ratios = np.arange(2, 8.1, 0.25)
with open('cea_OF_ratio_out.txt', 'r') as f:
lines = f.readlines()
cstars = []
specific_impulses = []
specific_impulses_vac = []
for line in lines:
# ignore blank lines
if not line.strip():
continue
words = line.split()
if words[0] == 'CSTAR,':
cstars.append(float(words[3]))
elif words[0] == 'Isp,':
specific_impulses.append(float(words[3]))
elif words[0] == 'Ivac,':
specific_impulses_vac.append(float(words[3]))
cstars = Q_(np.array(cstars), 'm/s')
specific_impulses = Q_(np.array(specific_impulses), 'm/s') / g0
specific_impulses_vac = Q_(np.array(specific_impulses_vac), 'm/s') / g0
# just checking that things line up
assert len(mixture_ratios) == len(cstars)
assert len(mixture_ratios) == len(specific_impulses)
assert len(mixture_ratios) == len(specific_impulses_vac)
fig, axes = plt.subplots(3, 1)
axes[0].plot(mixture_ratios, to_si(cstars))
axes[0].set_ylabel('$c^*$ (m/s)')
axes[0].grid(True)
axes[1].plot(mixture_ratios, to_si(specific_impulses))
axes[1].set_ylabel('$I_{\mathrm{sp}}$ (s)')
axes[1].grid(True)
axes[2].plot(mixture_ratios, to_si(specific_impulses_vac))
axes[2].set_xlabel('O/F ratio')
axes[2].set_ylabel('$I_{\mathrm{vac}}$ (s)')
axes[2].grid(True)
plt.tight_layout()
plt.show()
This allows us to determine the mixture ratio for optimal performance, although in practice something slightly off-optimal might be used for other reasons (e.g., combustion stability, reducing peak temperature).
Frozen vs. shifting equilibrium¶
We have already seen how assuming the mixture composition either remains frozen from the combustion chamber or follows a shifting equilibrium model leads to different calculations of performance. Frozen equilibrium underpredicts, while shifting equilibrium overpredicts. We can use these together to estimate the true actual performance as somewhere in between, such as 40% of the difference between the two results.
We already have results for shifting equilibrum, and can similarly extract the specific impulse for frozen equilibrium calculations saved in CEA_OF_ratio_frozen_out.txt:
# Click the + to see the full contents of the output file
filename = 'CEA_OF_ratio_frozen_out.txt'
print('Contents of ' + filename + ':')
with open(filename) as f:
file_contents = f.read()
print(file_contents)
Contents of CEA_OF_ratio_frozen_out.txt:
NASA-GLENN CHEMICAL EQUILIBRIUM PROGRAM CEA2, FEBRUARY 5, 2004
BY BONNIE MCBRIDE AND SANFORD GORDON
REFS: NASA RP-1311, PART I, 1994 AND NASA RP-1311, PART II, 1996
*******************************************************************************
### CEA analysis performed on Tue 08-Feb-2022 17:38:43
# Problem Type: "Rocket" (Infinite Area Combustor)
prob case=_______________8942 ro frozen
# Pressure (1 value):
p,psia= 2870
# Supersonic Area Ratio (1 value):
supar= 68.8
# Oxidizer/Fuel Wt. ratio (25 values):
o/f= 2, 2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75, 4, 4.25, 4.5, 4.75, 5, 5.25, 5.5, 5
.75, 6, 6.25, 6.5, 6.75, 7, 7.25, 7.5, 7.75, 8
# You selected the following fuels and oxidizers:
reac
fuel H2(L) wt%=100.0000
oxid O2(L) wt%=100.0000
# You selected these options for output:
# short version of output
output short
# Proportions of any products will be expressed as Mole Fractions.
# Heat will be expressed as siunits
output siunits
# Input prepared by this script:/var/www/sites/cearun.grc.nasa.gov/cgi-bin/CEARU
N/prepareInputFile.cgi
### IMPORTANT: The following line is the end of your CEA input file!
end
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 2.00000 %FUEL= 33.333333 R,EQ.RATIO= 3.968341 PHI,EQ.RATIO= 3.968341
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.8302 1903.04
P, BAR 197.88 108.12 0.10398
T, K 1797.77 1570.06 256.50
RHO, KG/CU M 8.0059 0 5.0087 0 2.9485-2
H, KJ/KG -1760.57 -3158.31 -10281.4
U, KJ/KG -4232.25 -5316.91 -10634.1
G, KJ/KG -50618.5 -45827.6 -17252.3
S, KJ/(KG)(K) 27.1769 27.1769 27.1769
M, (1/n) 6.048 6.048 6.048
Cp, KJ/(KG)(K) 6.2372 6.0346 4.9115
GAMMAs 1.2828 1.2950 1.3887
SON VEL,M/SEC 1780.6 1672.0 699.8
MACH NUMBER 0.000 1.000 5.899
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2362.9 2362.9
CF 0.7076 1.7471
Ivac, M/SEC 2963.0 4213.6
Isp, M/SEC 1672.0 4128.2
MOLE FRACTIONS
*H 0.00002 *H2 0.74799 H2O 0.25199
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 2.25000 %FUEL= 30.769231 R,EQ.RATIO= 3.527415 PHI,EQ.RATIO= 3.527415
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.8216 1819.86
P, BAR 197.88 108.63 0.10873
T, K 1975.45 1735.58 298.56
RHO, KG/CU M 7.8927 0 4.9318 0 2.8696-2
H, KJ/KG -1656.35 -3067.06 -10459.2
U, KJ/KG -4163.45 -5269.74 -10838.1
G, KJ/KG -53103.6 -48267.3 -18234.7
S, KJ/(KG)(K) 26.0433 26.0433 26.0433
M, (1/n) 6.551 6.551 6.551
Cp, KJ/(KG)(K) 5.9708 5.7872 4.6075
GAMMAs 1.2699 1.2809 1.3802
SON VEL,M/SEC 1784.3 1679.7 723.2
MACH NUMBER 0.000 1.000 5.802
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2388.7 2388.7
CF 0.7032 1.7566
Ivac, M/SEC 2991.1 4286.2
Isp, M/SEC 1679.7 4195.9
MOLE FRACTIONS
*H 0.00008 *H2 0.71644 H2O 0.28348
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 2.50000 %FUEL= 28.571429 R,EQ.RATIO= 3.174673 PHI,EQ.RATIO= 3.174673
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.8141 1740.26
P, BAR 197.88 109.08 0.11371
T, K 2144.07 1893.51 342.93
RHO, KG/CU M 7.8307 0 4.8879 0 2.8133-2
H, KJ/KG -1567.01 -2982.64 -10594.9
U, KJ/KG -4093.97 -5214.30 -10999.0
G, KJ/KG -55217.9 -50363.8 -19176.0
S, KJ/(KG)(K) 25.0229 25.0229 25.0229
M, (1/n) 7.055 7.055 7.055
Cp, KJ/(KG)(K) 5.7303 5.5651 4.3324
GAMMAs 1.2589 1.2687 1.3737
SON VEL,M/SEC 1783.6 1682.6 745.1
MACH NUMBER 0.000 1.000 5.703
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2405.9 2405.9
CF 0.6994 1.7661
Ivac, M/SEC 3008.9 4344.3
Isp, M/SEC 1682.6 4249.2
MOLE FRACTIONS
*H 0.00024 *H2 0.68481 H2O 0.31494
*OH 0.00002
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 2.75000 %FUEL= 26.666667 R,EQ.RATIO= 2.886066 PHI,EQ.RATIO= 2.886066
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.8075 1664.05
P, BAR 197.88 109.47 0.11891
T, K 2304.06 2044.01 389.64
RHO, KG/CU M 7.8060 0 4.8680 0 2.7739-2
H, KJ/KG -1489.58 -2904.19 -10693.9
U, KJ/KG -4024.54 -5153.03 -11122.6
G, KJ/KG -57021.2 -52168.0 -20085.0
S, KJ/(KG)(K) 24.1016 24.1016 24.1016
M, (1/n) 7.557 7.557 7.557
Cp, KJ/(KG)(K) 5.5118 5.3633 4.0892
GAMMAs 1.2494 1.2581 1.3681
SON VEL,M/SEC 1779.7 1682.0 765.8
MACH NUMBER 0.000 1.000 5.603
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2416.6 2416.6
CF 0.6960 1.7754
Ivac, M/SEC 3019.0 4390.5
Isp, M/SEC 1682.0 4290.5
MOLE FRACTIONS
*H 0.00057 *H2 0.65305 H2O 0.34633
*OH 0.00005
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 3.00000 %FUEL= 25.000000 R,EQ.RATIO= 2.645561 PHI,EQ.RATIO= 2.645561
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.8018 1591.73
P, BAR 197.88 109.82 0.12432
T, K 2455.55 2187.03 438.50
RHO, KG/CU M 7.8101 0 4.8668 0 2.7477-2
H, KJ/KG -1421.83 -2830.82 -10760.3
U, KJ/KG -3955.47 -5087.40 -11212.7
G, KJ/KG -58554.6 -53716.1 -20962.7
S, KJ/(KG)(K) 23.2668 23.2668 23.2668
M, (1/n) 8.058 8.058 8.058
Cp, KJ/(KG)(K) 5.3122 5.1785 3.8778
GAMMAs 1.2411 1.2488 1.3625
SON VEL,M/SEC 1773.2 1678.7 785.2
MACH NUMBER 0.000 1.000 5.504
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2422.1 2422.1
CF 0.6931 1.7843
Ivac, M/SEC 3022.9 4426.4
Isp, M/SEC 1678.7 4321.7
MOLE FRACTIONS
*H 0.00116 *H2 0.62110 H2O 0.37759
*OH 0.00015
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 3.25000 %FUEL= 23.529412 R,EQ.RATIO= 2.442056 PHI,EQ.RATIO= 2.442056
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7968 1523.98
P, BAR 197.88 110.13 0.12984
T, K 2598.47 2322.40 489.08
RHO, KG/CU M 7.8373 0 4.8803 0 2.7323-2
H, KJ/KG -1362.05 -2761.89 -10796.8
U, KJ/KG -3886.90 -5018.48 -11272.0
G, KJ/KG -59847.0 -55033.2 -21804.6
S, KJ/(KG)(K) 22.5075 22.5075 22.5075
M, (1/n) 8.557 8.557 8.557
Cp, KJ/(KG)(K) 5.1291 5.0085 3.6960
GAMMAs 1.2337 1.2407 1.3567
SON VEL,M/SEC 1764.9 1673.2 802.9
MACH NUMBER 0.000 1.000 5.410
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2423.3 2423.3
CF 0.6905 1.7926
Ivac, M/SEC 3021.9 4453.3
Isp, M/SEC 1673.2 4343.9
MOLE FRACTIONS
*H 0.00208 *H2 0.58893 H2O 0.40862
*OH 0.00037
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 3.50000 %FUEL= 22.222222 R,EQ.RATIO= 2.267624 PHI,EQ.RATIO= 2.267624
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7924 1461.43
P, BAR 197.88 110.40 0.13540
T, K 2732.68 2449.88 540.79
RHO, KG/CU M 7.8839 0 4.9062 0 2.7260-2
H, KJ/KG -1308.92 -2696.73 -10805.9
U, KJ/KG -3818.84 -4946.91 -11302.6
G, KJ/KG -60920.0 -56138.8 -22602.8
S, KJ/(KG)(K) 21.8141 21.8141 21.8141
M, (1/n) 9.052 9.052 9.052
Cp, KJ/(KG)(K) 4.9605 4.8511 3.5406
GAMMAs 1.2272 1.2336 1.3503
SON VEL,M/SEC 1755.1 1666.0 819.0
MACH NUMBER 0.000 1.000 5.322
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2420.9 2420.9
CF 0.6882 1.8002
Ivac, M/SEC 3016.7 4472.2
Isp, M/SEC 1666.0 4358.2
MOLE FRACTIONS
*H 0.00341 *H2 0.55653 H2O 0.43928
*OH 0.00078
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 3.75000 %FUEL= 21.052632 R,EQ.RATIO= 2.116449 PHI,EQ.RATIO= 2.116449
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7885 1404.32
P, BAR 197.88 110.64 0.14091
T, K 2858.04 2569.27 592.97
RHO, KG/CU M 7.9470 0 4.9427 0 2.7276-2
H, KJ/KG -1261.38 -2634.87 -10789.9
U, KJ/KG -3751.35 -4873.26 -11306.5
G, KJ/KG -61790.9 -57048.5 -23348.2
S, KJ/(KG)(K) 21.1787 21.1787 21.1787
M, (1/n) 9.544 9.544 9.544
Cp, KJ/(KG)(K) 4.8046 4.7050 3.4078
GAMMAs 1.2215 1.2272 1.3435
SON VEL,M/SEC 1744.0 1657.4 833.1
MACH NUMBER 0.000 1.000 5.240
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2415.5 2415.5
CF 0.6862 1.8073
Ivac, M/SEC 3007.9 4483.8
Isp, M/SEC 1657.4 4365.4
MOLE FRACTIONS
*H 0.00515 *H2 0.52394 H2O 0.46942
*O 0.00001 *OH 0.00149
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 4.00000 %FUEL= 20.000000 R,EQ.RATIO= 1.984171 PHI,EQ.RATIO= 1.984171
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7851 1352.84
P, BAR 197.88 110.85 0.14627
T, K 2974.45 2680.39 644.88
RHO, KG/CU M 8.0246 0 4.9884 0 2.7359-2
H, KJ/KG -1218.59 -2575.92 -10751.4
U, KJ/KG -3684.49 -4798.03 -11286.0
G, KJ/KG -62475.3 -57776.8 -24032.2
S, KJ/(KG)(K) 20.5943 20.5943 20.5943
M, (1/n) 10.029 10.029 10.029
Cp, KJ/(KG)(K) 4.6600 4.5690 3.2938
GAMMAs 1.2164 1.2217 1.3363
SON VEL,M/SEC 1731.9 1647.6 845.2
MACH NUMBER 0.000 1.000 5.166
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2407.6 2407.6
CF 0.6844 1.8136
Ivac, M/SEC 2996.3 4488.9
Isp, M/SEC 1647.6 4366.4
MOLE FRACTIONS
*H 0.00728 *H2 0.49125 H2O 0.49883
*O 0.00002 *OH 0.00261 *O2 0.00001
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 4.25000 %FUEL= 19.047619 R,EQ.RATIO= 1.867455 PHI,EQ.RATIO= 1.867455
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7821 1306.86
P, BAR 197.88 111.04 0.15142
T, K 3081.92 2783.21 695.81
RHO, KG/CU M 8.1149 0 5.0423 0 2.7503-2
H, KJ/KG -1179.87 -2519.58 -10692.9
U, KJ/KG -3618.34 -4721.70 -11243.5
G, KJ/KG -62988.0 -58337.0 -24647.5
S, KJ/(KG)(K) 20.0550 20.0550 20.0550
M, (1/n) 10.509 10.509 10.509
Cp, KJ/(KG)(K) 4.5256 4.4419 3.1954
GAMMAs 1.2119 1.2167 1.3291
SON VEL,M/SEC 1719.0 1636.9 855.4
MACH NUMBER 0.000 1.000 5.099
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2397.5 2397.5
CF 0.6828 1.8194
Ivac, M/SEC 2982.2 4488.1
Isp, M/SEC 1636.9 4361.9
MOLE FRACTIONS
*H 0.00973 *H2 0.45860 H2O 0.52733
*O 0.00005 *OH 0.00427 *O2 0.00002
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 4.50000 %FUEL= 18.181818 R,EQ.RATIO= 1.763707 PHI,EQ.RATIO= 1.763707
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7794 1266.10
P, BAR 197.88 111.20 0.15629
T, K 3180.53 2877.75 745.14
RHO, KG/CU M 8.2164 0 5.1033 0 2.7700-2
H, KJ/KG -1144.68 -2465.62 -10616.9
U, KJ/KG -3553.02 -4644.68 -11181.1
G, KJ/KG -63342.7 -58742.4 -25188.7
S, KJ/(KG)(K) 19.5559 19.5559 19.5559
M, (1/n) 10.980 10.980 10.980
Cp, KJ/(KG)(K) 4.4002 4.3228 3.1095
GAMMAs 1.2079 1.2124 1.3219
SON VEL,M/SEC 1705.6 1625.4 863.6
MACH NUMBER 0.000 1.000 5.040
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2385.6 2385.6
CF 0.6813 1.8245
Ivac, M/SEC 2966.0 4482.1
Isp, M/SEC 1625.4 4352.5
MOLE FRACTIONS
*H 0.01239 *H2 0.42615 H2O 0.55472
*O 0.00011 *OH 0.00658 *O2 0.00005
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 4.75000 %FUEL= 17.391304 R,EQ.RATIO= 1.670881 PHI,EQ.RATIO= 1.670881
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7771 1230.20
P, BAR 197.88 111.35 0.16085
T, K 3270.40 2964.08 792.29
RHO, KG/CU M 8.3280 0 5.1707 0 2.7944-2
H, KJ/KG -1112.55 -2413.86 -10525.7
U, KJ/KG -3488.62 -4567.37 -11101.3
G, KJ/KG -63552.4 -59005.2 -25652.3
S, KJ/(KG)(K) 19.0924 19.0924 19.0924
M, (1/n) 11.444 11.444 11.444
Cp, KJ/(KG)(K) 4.2830 4.2111 3.0338
GAMMAs 1.2043 1.2085 1.3149
SON VEL,M/SEC 1691.6 1613.2 870.0
MACH NUMBER 0.000 1.000 4.987
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2372.2 2372.2
CF 0.6801 1.8291
Ivac, M/SEC 2948.1 4471.6
Isp, M/SEC 1613.3 4338.9
MOLE FRACTIONS
*H 0.01513 *H2 0.39411 H2O 0.58080
*O 0.00020 *OH 0.00964 *O2 0.00012
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 5.00000 %FUEL= 16.666667 R,EQ.RATIO= 1.587337 PHI,EQ.RATIO= 1.587337
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7749 1198.77
P, BAR 197.88 111.49 0.16507
T, K 3351.71 3042.34 836.77
RHO, KG/CU M 8.4487 0 5.2440 0 2.8230-2
H, KJ/KG -1083.09 -2364.06 -10421.4
U, KJ/KG -3425.22 -4490.01 -11006.1
G, KJ/KG -63628.9 -59136.8 -26036.3
S, KJ/(KG)(K) 18.6609 18.6609 18.6609
M, (1/n) 11.899 11.899 11.899
Cp, KJ/(KG)(K) 4.1732 4.1061 2.9662
GAMMAs 1.2011 1.2051 1.3082
SON VEL,M/SEC 1677.3 1600.6 874.6
MACH NUMBER 0.000 1.000 4.941
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2357.5 2357.5
CF 0.6789 1.8332
Ivac, M/SEC 2928.8 4457.0
Isp, M/SEC 1600.6 4321.6
MOLE FRACTIONS
*H 0.01783 *H2 0.36268 H2O 0.60538
*O 0.00036 *OH 0.01351 *O2 0.00023
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 5.25000 %FUEL= 16.000000 R,EQ.RATIO= 1.511749 PHI,EQ.RATIO= 1.511749
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7731 1171.41
P, BAR 197.88 111.60 0.16892
T, K 3424.61 3112.63 878.18
RHO, KG/CU M 8.5778 0 5.3227 0 2.8556-2
H, KJ/KG -1055.99 -2316.21 -10306.0
U, KJ/KG -3362.87 -4412.94 -10897.5
G, KJ/KG -63582.5 -59146.7 -26339.8
S, KJ/(KG)(K) 18.2580 18.2580 18.2580
M, (1/n) 12.343 12.343 12.343
Cp, KJ/(KG)(K) 4.0701 4.0071 2.9050
GAMMAs 1.1983 1.2021 1.3019
SON VEL,M/SEC 1662.6 1587.6 877.6
MACH NUMBER 0.000 1.000 4.901
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2341.7 2341.7
CF 0.6780 1.8368
Ivac, M/SEC 2908.3 4438.7
Isp, M/SEC 1587.6 4301.2
MOLE FRACTIONS
*H 0.02035 HO2 0.00001 *H2 0.33208
H2O 0.62830 H2O2 0.00001 *O 0.00061
*OH 0.01822 *O2 0.00044
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 5.50000 %FUEL= 15.384615 R,EQ.RATIO= 1.443033 PHI,EQ.RATIO= 1.443033
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7715 1147.76
P, BAR 197.88 111.70 0.17240
T, K 3489.25 3175.08 916.16
RHO, KG/CU M 8.7147 0 5.4063 0 2.8918-2
H, KJ/KG -1030.98 -2270.11 -10181.0
U, KJ/KG -3301.62 -4336.31 -10777.2
G, KJ/KG -63422.3 -59043.8 -26562.8
S, KJ/(KG)(K) 17.8810 17.8810 17.8810
M, (1/n) 12.777 12.777 12.777
Cp, KJ/(KG)(K) 3.9731 3.9137 2.8488
GAMMAs 1.1959 1.1994 1.2961
SON VEL,M/SEC 1647.8 1574.3 879.0
MACH NUMBER 0.000 1.000 4.867
PERFORMANCE PARAMETERS
Ae/At 1.00000 68.800
CSTAR, M/SEC 2325.0 2325.0
CF 0.6771 1.8399
Ivac, M/SEC 2886.7 4417.2
Isp, M/SEC 1574.3 4277.8
MOLE FRACTIONS
*H 0.02257 HO2 0.00001 *H2 0.30253
H2O 0.64939 H2O2 0.00001 *O 0.00096
*OH 0.02374 *O2 0.00079
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 5.75000 %FUEL= 14.814815 R,EQ.RATIO= 1.380293 PHI,EQ.RATIO= 1.380293
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7700 1127.47
P, BAR 197.88 111.79 0.17551
T, K 3545.79 3229.81 950.44
RHO, KG/CU M 8.8590 0 5.4946 0 2.9314-2
H, KJ/KG -1007.82 -2225.66 -10047.7
U, KJ/KG -3241.46 -4260.26 -10646.5
G, KJ/KG -63155.9 -58835.5 -26706.3
S, KJ/(KG)(K) 17.5273 17.5273 17.5273
M, (1/n) 13.199 13.199 13.199
Cp, KJ/(KG)(K) 3.8815 3.8253 2.7964
GAMMAs 1.1937 1.1971 1.2908
SON VEL,M/SEC 1632.9 1560.7 879.1
MACH NUMBER 0.000 1.000 4.837
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2307.5 2307.5
CF 0.6763 1.8427
Ivac, M/SEC 2864.3 4392.8
Isp, M/SEC 1560.7 4252.0
MOLE FRACTIONS
*H 0.02439 HO2 0.00002 *H2 0.27425
H2O 0.66851 H2O2 0.00001 *O 0.00144
*OH 0.03002 *O2 0.00135
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 6.00000 %FUEL= 14.285714 R,EQ.RATIO= 1.322780 PHI,EQ.RATIO= 1.322780
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7688 1110.26
P, BAR 197.88 111.87 0.17823
T, K 3594.37 3276.93 980.79
RHO, KG/CU M 9.0105 0 5.5875 0 2.9742-2
H, KJ/KG -986.31 -2182.76 -9907.46
U, KJ/KG -3182.40 -4184.90 -10506.7
G, KJ/KG -62790.6 -58528.7 -26771.8
S, KJ/(KG)(K) 17.1948 17.1948 17.1948
M, (1/n) 13.608 13.608 13.608
Cp, KJ/(KG)(K) 3.7951 3.7416 2.7469
GAMMAs 1.1919 1.1952 1.2861
SON VEL,M/SEC 1617.9 1546.9 877.9
MACH NUMBER 0.000 1.000 4.812
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2289.4 2289.4
CF 0.6757 1.8450
Ivac, M/SEC 2841.2 4365.9
Isp, M/SEC 1546.9 4224.0
MOLE FRACTIONS
*H 0.02575 HO2 0.00003 *H2 0.24744
H2O 0.68555 H2O2 0.00002 *O 0.00207
*OH 0.03694 *O2 0.00220
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 6.25000 %FUEL= 13.793103 R,EQ.RATIO= 1.269869 PHI,EQ.RATIO= 1.269869
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7678 1095.83
P, BAR 197.88 111.94 0.18057
T, K 3635.16 3316.59 1007.06
RHO, KG/CU M 9.1688 0 5.6847 0 3.0202-2
H, KJ/KG -966.28 -2141.30 -9761.22
U, KJ/KG -3124.47 -4110.35 -10359.1
G, KJ/KG -62333.1 -58130.2 -26761.9
S, KJ/(KG)(K) 16.8815 16.8815 16.8815
M, (1/n) 14.005 14.005 14.005
Cp, KJ/(KG)(K) 3.7133 3.6622 2.6992
GAMMAs 1.1903 1.1935 1.2820
SON VEL,M/SEC 1602.8 1533.0 875.5
MACH NUMBER 0.000 1.000 4.791
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2270.7 2270.7
CF 0.6751 1.8471
Ivac, M/SEC 2817.4 4336.6
Isp, M/SEC 1533.0 4194.0
MOLE FRACTIONS
*H 0.02662 HO2 0.00005 *H2 0.22229
H2O 0.70042 H2O2 0.00002 *O 0.00285
*OH 0.04431 *O2 0.00343
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 6.50000 %FUEL= 13.333333 R,EQ.RATIO= 1.221028 PHI,EQ.RATIO= 1.221028
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7669 1083.93
P, BAR 197.88 111.99 0.18256
T, K 3668.40 3349.01 1029.20
RHO, KG/CU M 9.3336 0 5.7861 0 3.0692-2
H, KJ/KG -947.59 -2101.22 -9610.08
U, KJ/KG -3067.67 -4036.71 -10204.9
G, KJ/KG -61791.0 -57647.2 -26680.2
S, KJ/(KG)(K) 16.5858 16.5858 16.5858
M, (1/n) 14.387 14.387 14.387
Cp, KJ/(KG)(K) 3.6358 3.5867 2.6528
GAMMAs 1.1890 1.1921 1.2785
SON VEL,M/SEC 1587.7 1519.0 872.1
MACH NUMBER 0.000 1.000 4.773
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2251.5 2251.5
CF 0.6747 1.8487
Ivac, M/SEC 2793.2 4305.2
Isp, M/SEC 1519.0 4162.3
MOLE FRACTIONS
*H 0.02699 HO2 0.00007 *H2 0.19896
H2O 0.71307 H2O2 0.00003 *O 0.00378
*OH 0.05193 *O2 0.00516
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 6.75000 %FUEL= 12.903226 R,EQ.RATIO= 1.175805 PHI,EQ.RATIO= 1.175805
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7662 1074.33
P, BAR 197.88 112.03 0.18419
T, K 3694.44 3374.49 1047.24
RHO, KG/CU M 9.5045 0 5.8915 0 3.1210-2
H, KJ/KG -930.11 -2062.48 -9455.13
U, KJ/KG -3012.05 -3964.12 -10045.3
G, KJ/KG -61172.3 -57087.6 -26531.7
S, KJ/(KG)(K) 16.3062 16.3062 16.3062
M, (1/n) 14.754 14.754 14.754
Cp, KJ/(KG)(K) 3.5623 3.5150 2.6077
GAMMAs 1.1879 1.1909 1.2757
SON VEL,M/SEC 1572.6 1504.9 867.7
MACH NUMBER 0.000 1.000 4.759
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2231.9 2231.9
CF 0.6743 1.8501
Ivac, M/SEC 2768.5 4272.1
Isp, M/SEC 1504.9 4129.2
MOLE FRACTIONS
*H 0.02690 HO2 0.00010 *H2 0.17756
H2O 0.72351 H2O2 0.00004 *O 0.00483
*OH 0.05957 *O2 0.00750
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 7.00000 %FUEL= 12.500000 R,EQ.RATIO= 1.133812 PHI,EQ.RATIO= 1.133812
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7657 1066.79
P, BAR 197.88 112.07 0.18549
T, K 3713.70 3393.46 1061.33
RHO, KG/CU M 9.6811 0 6.0004 0 3.1754-2
H, KJ/KG -913.72 -2025.03 -9297.52
U, KJ/KG -2957.69 -3892.75 -9881.67
G, KJ/KG -60486.8 -56461.0 -26322.8
S, KJ/(KG)(K) 16.0414 16.0414 16.0414
M, (1/n) 15.107 15.107 15.107
Cp, KJ/(KG)(K) 3.4925 3.4467 2.5637
GAMMAs 1.1871 1.1900 1.2734
SON VEL,M/SEC 1557.7 1490.8 862.5
MACH NUMBER 0.000 1.000 4.748
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2212.0 2212.0
CF 0.6740 1.8512
Ivac, M/SEC 2743.6 4237.5
Isp, M/SEC 1490.8 4094.8
MOLE FRACTIONS
*H 0.02640 HO2 0.00013 *H2 0.15814
H2O 0.73179 H2O2 0.00004 *O 0.00598
*OH 0.06699 *O2 0.01053
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 7.25000 %FUEL= 12.121212 R,EQ.RATIO= 1.094715 PHI,EQ.RATIO= 1.094715
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7652 1061.07
P, BAR 197.88 112.10 0.18649
T, K 3726.77 3406.45 1071.72
RHO, KG/CU M 9.8627 0 6.1125 0 3.2322-2
H, KJ/KG -898.32 -1988.88 -9138.45
U, KJ/KG -2904.66 -3822.77 -9715.42
G, KJ/KG -59745.1 -55777.7 -26061.2
S, KJ/(KG)(K) 15.7903 15.7903 15.7903
M, (1/n) 15.444 15.444 15.444
Cp, KJ/(KG)(K) 3.4262 3.3818 2.5206
GAMMAs 1.1864 1.1893 1.2716
SON VEL,M/SEC 1542.8 1476.9 856.5
MACH NUMBER 0.000 1.000 4.739
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2192.0 2192.0
CF 0.6738 1.8520
Ivac, M/SEC 2718.6 4201.7
Isp, M/SEC 1476.9 4059.6
MOLE FRACTIONS
*H 0.02556 HO2 0.00017 *H2 0.14070
H2O 0.73803 H2O2 0.00005 *O 0.00718
*OH 0.07397 *O2 0.01433
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 7.50000 %FUEL= 11.764706 R,EQ.RATIO= 1.058224 PHI,EQ.RATIO= 1.058224
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7649 1056.95
P, BAR 197.88 112.12 0.18722
T, K 3734.29 3414.08 1078.73
RHO, KG/CU M 1.0049 1 6.2274 0 3.2911-2
H, KJ/KG -883.83 -1954.01 -8979.12
U, KJ/KG -2853.07 -3754.38 -9547.97
G, KJ/KG -58958.8 -55049.1 -25755.2
S, KJ/(KG)(K) 15.5518 15.5518 15.5518
M, (1/n) 15.767 15.767 15.767
Cp, KJ/(KG)(K) 3.3632 3.3199 2.4785
GAMMAs 1.1860 1.1888 1.2703
SON VEL,M/SEC 1528.2 1463.0 850.1
MACH NUMBER 0.000 1.000 4.734
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2172.0 2172.0
CF 0.6736 1.8526
Ivac, M/SEC 2693.6 4165.1
Isp, M/SEC 1463.0 4023.8
MOLE FRACTIONS
*H 0.02447 HO2 0.00021 *H2 0.12519
H2O 0.74238 H2O2 0.00006 *O 0.00839
*OH 0.08036 *O2 0.01893
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 7.75000 %FUEL= 11.428571 R,EQ.RATIO= 1.024088 PHI,EQ.RATIO= 1.024088
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7647 1054.20
P, BAR 197.88 112.13 0.18771
T, K 3736.98 3417.04 1082.75
RHO, KG/CU M 1.0238 1 6.3445 0 3.3518-2
H, KJ/KG -870.17 -1920.42 -8820.66
U, KJ/KG -2802.99 -3687.77 -9380.68
G, KJ/KG -58139.5 -54286.6 -25413.9
S, KJ/(KG)(K) 15.3250 15.3250 15.3250
M, (1/n) 16.076 16.076 16.076
Cp, KJ/(KG)(K) 3.3033 3.2609 2.4374
GAMMAs 1.1856 1.1885 1.2694
SON VEL,M/SEC 1513.8 1449.3 843.1
MACH NUMBER 0.000 1.000 4.730
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2152.0 2152.0
CF 0.6735 1.8530
Ivac, M/SEC 2668.7 4128.0
Isp, M/SEC 1449.3 3987.6
MOLE FRACTIONS
*H 0.02322 HO2 0.00026 *H2 0.11150
H2O 0.74505 H2O2 0.00007 *O 0.00957
*OH 0.08602 *O2 0.02432
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
Pin = 2870.0 PSIA
CASE = _______________
REACTANT WT FRACTION ENERGY TEMP
(SEE NOTE) KJ/KG-MOL K
FUEL H2(L) 1.0000000 -9012.000 20.270
OXIDANT O2(L) 1.0000000 -12979.000 90.170
O/F= 8.00000 %FUEL= 11.111111 R,EQ.RATIO= 0.992085 PHI,EQ.RATIO= 0.992085
CHAMBER THROAT EXIT
Pinf/P 1.0000 1.7646 1052.61
P, BAR 197.88 112.14 0.18799
T, K 3735.56 3416.02 1084.22
RHO, KG/CU M 1.0430 1 6.4633 0 3.4139-2
H, KJ/KG -857.26 -1888.11 -8664.11
U, KJ/KG -2754.51 -3623.07 -9214.78
G, KJ/KG -57298.3 -53501.2 -25045.7
S, KJ/(KG)(K) 15.1091 15.1091 15.1091
M, (1/n) 16.371 16.371 16.371
Cp, KJ/(KG)(K) 3.2463 3.2048 2.3974
GAMMAs 1.1855 1.1883 1.2688
SON VEL,M/SEC 1499.7 1435.9 835.9
MACH NUMBER 0.000 1.000 4.727
PERFORMANCE PARAMETERS
Ae/At 1.0000 68.800
CSTAR, M/SEC 2132.2 2132.2
CF 0.6734 1.8532
Ivac, M/SEC 2644.2 4090.8
Isp, M/SEC 1435.9 3951.4
MOLE FRACTIONS
*H 0.02187 HO2 0.00031 *H2 0.09946
H2O 0.74624 H2O2 0.00008 *O 0.01067
*OH 0.09091 *O2 0.03047
* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS
with open('CEA_OF_ratio_frozen_out.txt', 'r') as f:
lines = f.readlines()
specific_impulses_frozen = []
for line in lines:
# ignore blank lines
if not line.strip():
continue
words = line.split()
if words[0] == 'Isp,':
specific_impulses_frozen.append(float(words[3]))
specific_impulses_frozen = Q_(np.array(specific_impulses_frozen), 'm/s') / g0
# just checking that things line up
assert len(mixture_ratios) == len(specific_impulses_frozen)
specific_impulses_act = specific_impulses_frozen + 0.4*(specific_impulses - specific_impulses_frozen)
plt.plot(mixture_ratios, to_si(specific_impulses), label='Shifting equilibrium')
plt.plot(mixture_ratios, to_si(specific_impulses_frozen), label='Frozen')
plt.plot(mixture_ratios, to_si(specific_impulses_act), '--', label='Actual')
plt.ylabel('$I_{\mathrm{sp}}$ (s)')
plt.xlabel('Mixture ratio')
plt.grid(True)
plt.legend()
plt.tight_layout()
plt.show()
