5th INTERNATIONAL SPACECRAFT PROPULSION CONFERENCE &
2nd INTERNATIONAL SYMPOSIUM ON PROPULSION FOR SPACE TRANSPORTATION, 5-8 May, HERAKLION
Comparison between Supercritical
Combustion Modelling for LO2-CH4 Rocket Engines at
15MPa and 16.5MPa
using Real and Ideal gas properties
A.Minotti∗ and C. Bruno*+
Department of Mechanics and Aeronautics, University of Rome “La Sapienza”,
Via Eudossiana 18, 00184, Rome, Italy
* +390644585272, [email protected]
*+ +390644585280, [email protected]
OVERVIEW
In this work mixing and combustion processes in LRE between ideal and real gases in supercritical regime
are studied. Three FANS simulations are presented: two deal with a LO2/CH4 coaxial reacting jet at
15MPa while the third is at 16.5MPa. All are performed with supercritical methane and supercritical
oxygen jet injection conditions. The first simulation is carried out using real gas properties while the
second simulation reproduces the first one but using ideal gas properties. The third is carried out using
real gas properties predicted at the highest chamber pressure found in the first simulation, that is 16.5MPa.
Real gas properties are reproduced using particular fitting polynomials, a single reaction is assumed and
combustion is modeled by the Eddy Dissipation concept. Simulations show how real and ideal gas
properties predict different maximum temperature and pressure and that particular attention must be taken
to the potential core length design parameter.
1.
INTRODUCTION
In [1] the differences between real and ideal gas behaviour have been analyzed and thermophysical properties have been
quantified. That work has shown that assuming ideal gas behaviour in transcritical conditions leads to large errors.
Therefore, accurate real gas properties modeling is mandatory to simulate Liquid Rocket Engines (LRE) in sub-trans
and supercritical conditions. These properties have been described by means of polynomials fits [1] based on:
1. experimental data (from NIST tables) and data obtained with the Lee-Kesler [2] equation of state (EOS), for
what concerns density and isobaric heat capacity;
2. experimental data (from NIST tables) and data obtained with the Chung et al. method [3], for what concerns
viscosity and thermal conductivity.
These polynomial fits have been introduced in a CFD software; it is not able to manage properties as function
simultaneously of two variables (pressure and temperature) but just of one (temperature). So, for every simulation, real
gas properties are predicted, and introduced in the CFD software, at the design chamber pressure.
These polynomial fits have been validated by simulating and comparing the results of N2 injection at supercritical
temperature in a N2 atmosphere chamber [4], and N2 injection at subcritical conditions in a N2 atmosphere chamber
[4,5]. After validation, two LO2/CH4 non-reacting coaxial jet simulations, at sub and supercritical conditions, have been
carried on and studied [1] and the results have been compared with Villermaux prediction theory [6,7] and with those in
[8]. The first two LO2/CH4 simulations, included here, are a reacting coaxial injection of LO2-CH4, with supercritical
CH4 injection and supercritical O2 injection carried out with, at first, real and, later, ideal gas properties; properties are
predicted at 15MPa and the simulations show that the chamber pressure is not uniform inside the chamber: in the
simulation with real gas properties the maximum reaches 16.5MPa.
By the light of this, the third simulation is carried out using real gas properties predicted at 16.5MPa in order to
understand if a CFD software able to manage properties as function of temperature and pressure is necessary.
Ideal gas properties are predicted using the ideal equation of state for the density, the NASA 400 CEA software
polynomials for the isobaric specific heat and the kinetic theory for the viscosity and the thermal conductivity.
The purpose of this study is to understand and quantify differences between ideal and real physical behaviour and to
investigate the mixing (length of the potential core) and combustion processes inside a combustion chamber in order to
have useful design indications.
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In literature there are other simulations of subcritical and supercritical problems: by Chehroudi [9,10], Mayer and
Tamura [11,12,13,14], and J. Oefelein and V. Yang [15,16,17,18,19] and N.O’Kongo, K. Harstad and J.Bellan [20,21].
Table 1 reports the critical conditions of the species analyzed in this study.
Tc
[K]
Pc[atm
]
O2
154.6
49.8
CO2
304.2
72.8
H2
O
647.3
217.6
CH4
190.4
46
Table 1: Critical properties of species assumed of interest to LRE
2.
OXYGEN/METHANE COAXIAL JET REACTING SIMUALTIONS
Two reacting simulations of an axial symmetry reacting LO2/CH4 coaxial jets are presented. All use the same geometry
(see fig. 1), computational mesh (32600 cells) and boundary conditions: inlet mass flow imposed, constant temperature
on the walls, adiabatic heat flux on the post tip, slip wall at the outer boundary and constant pressure at the outlet.
Simulations reproduce a supercritical CH4 jet that reacts with a supercritical O2, using real gas and ideal gas properties.
Both use time dependent FANS equation with a k-ε turbulence model and the simulations reach stationary conditions.
One single global reaction is assumed:
(1)
CH4+2O2 → CO2+ 2H2O
The subsequent over-estimated maximum temperature is managed by a modified methane formation enthalpy: ∆H’fCH4=1.3×108 [J/kgmol] [22].
The source term (Ri,r) of the i-specie production is modelled by means of an Eddy-Dissipation model
[23,24,25,26,27,28]:
(2)
Ri , r = ν i', r M w,i Aρ
 Y
min ℜ  ' ℜ
ν M
k
 i , r w,ℜ
ε




where
Yℜ≡ mass fraction of the reactant ℜ;
A ≡ empirical constant, 4.0;
ε
≡ reverse of turbulent time scale;
k
ν’i,r ≡ stechiometric coefficient of the i-species in reaction r;
The key point of this model is that chemical times are much shorter than those of turbulence and that thus each reaction
velocity is controlled by the rate of turbulent mixing.
5th INTERNATIONAL SPACECRAFT PROPULSION CONFERENCE &
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2.1.
Supercritical CH4 reacting with supercritical O2 using real gas properties
The operating conditions of the case analyzed with real gas properties are reported in Table 2, pressure and temperature
are supercritical for both the reactants.
Pressure [MPa]
Temperature [K]
Mass flow [kg/s]
Velocity [m/s]
Molecular Viscosity [kg/m-s]
Density [kg/m3]
Reynolds number
Isobaric Specific Heat
[J/kgK]
O2
15
300
0.386
49.4
2.74×10-5
200
2524000
CH4
15
300
0.114
31.8
1.23×10-5
117
302000
1166.3
3379.8
Table 2: LO2/CH4 with real gas properties, operating conditions
Results reported below show a steady flow simulation snapshot. Figure 2 shows the axial pressure that is not constant
along the axis, with the highest value around 16.5MPa (1.5MPa higher than the exhaust pressure). Figure 3 reports the
axial O2 mass fraction : as in the non reacting simulation [22], the O2 mass fraction never reaches, along the combustion
chamber axis, the reference value defined to estimate the length of the potential core, equal to 0.9 [22] . Figure 4 reports
the radial temperature at different axial sections (the maximum temperature is around 3770K) ; figures 5 to 8 show the
reactants and products radial mass fraction at different axial sections, respectively fig. 5 for O2, fig. 6 for CH4, fig. 7 for
CO2 and fig. 8 for H2O.
2.2.
Supercritical CH4 reacting with supercritical O2 using ideal gas properties
This analysis is about the supercritical reacting O2/CH4 coaxial injector carried on using ideal gas properties at the same
boundary conditions of the previous case : this has been done in order to asses the effect of the compressibility factors
Z≠1, which at these operating conditions are equal to ZCH4=0.8 and ZO2=0.9 [22]. Comparing Table 2 with Table 3 the
first differences can be shown : ideal gas properties [29,30,31,32] lead to different densities and viscosities, so providing
different Oxygen and Methane Reynolds numbers and different inlet velocities.
Pressure [MPa]
Temperature [K]
Mass flow [kg/s]
Velocity [m/s]
Molecular Viscosity
[kg/m-s]
Density [kg/m3]
Reynolds number
Isobaric Specific Heat [J/kgK]
O2
15
300
0.386
46.5
CH4
15
300
0.114
38.3
2.06×10-5
1.12×10-5
216
3430000
918.3
108
331000
2229.1
Table 3: LO2/CH4 with ideal gas properties, operating conditions
The different values shown in the two previous tables are quantified in percentage, (((ideal-real)/ideal)*100), in the
following table 4.
Velocity
O2
6.2 %
CH4
16.97 %
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Molecular Viscosity
Density
Reynolds number
Isobaric Specific
Heat
-33 %
7.4 %
26.4 %
9.8 %
-8.3 %
8.7 %
-27 %
-51 %
Table 4: reactants properties % differences beteween real and ideal behaviour
Is evident that, despite the fact that both the reactants are injected at supercritical conditions, both for temperature and
pressure, differences are not negligible and in fact they lead to the different final results shown below.
The supercritical reacting simulation reaches steady state conditions with ideal properties too. Figure 9 reports the axial
pressure ; also in this case pressure is not constant and the maximum value is around 17MPa, 2MPa higher than the
exhaust pressure and 0.5MPa higher than corresponding simulation carried on with real gas properties. The potential
core, see fig. 10, is longer than the axial combustion chamber extension; the same happens also in the non reacting
simulation [22].
The maximum temperature is 4320K, i.e. it’s higher by 500K than the maximum temperature obtained with real gas
properties : this is due to the reactants different isobaric specific heat behaviours at low temperature, see fig. 16 and fig.
17. Figure 11 shows the radial tempertaure at different axial sectons while figures 12 to 15 show the reactants and
products radial mass fractions at different axial sections, i.e. fig. 12 for O2, fig. 13 for CH4, fig. 14 for CO2 and fig. 15
for H2O. Table 5 shows the comparison between the results obtained with the two methodologies.
Non Reacting Potential Core Length [22]
Ideal
x/d > 15
Real
x/d > 15
Reacting Potential core length
x/d > 15
x/d > 15
Reacting Simulation
Maximum Temperature
Steady State
4320K
Steady State
3770K
Maximum Pressure
16.9MPa
16.4MPa
Table 5: Ideal and real gas properties: results comparison
2.3.
Supercritical CH4 reacting with supercritical O2 using real gas properties predicted at 16.5MPa
This analysis reproduces the first simulation with only one difference: real gas properties are predicted at 16.5MPa, that
is the highest chamber pressure found in the previous real simulation (section 2.1).
This has been done because the CFD software is not able to manage properties as simultaneous function of pressure and
temperature but just on temperature and we would know if is necessary a CFD software able to manage properties as
function of 2 variables.
The following Table 6 reports the operating conditions with properties predicted at the two reference pressure values:
15MPa and 16.5MPa. It is evident that differences are not very important so we expect that results are comparable with
ones obtained using real gas properties predicted at 15MPa.
Maximum temperature and maximum pressure at 16.5MPa are very close to the those at 15MPa: 3800K against 3770K,
and 16.4MPa against 16.5MPa, see fig. 18.
The potential core length is longer than combustion chamber just as in the case at 15MPa, see fig. 19 and compare it
with fig. 3: both predict an axial oxygen mass fraction at the exist plane greater than 0.9 (the reference value used in the
Villermaux theory).
According to these results, a difference of 1.5MPa in real gas predictions doesn’t change significantly the global
flowfield simulations carried out with methane and oxygen reacting at supercritical conditions. The same difference has
instead a much larger impact in comparisons between ideal and real gas simulations. This result enables LRE
simulations at supercritical injection conditions with properties function only of temperature but defined at design
pressure; thus making possible to reduce problem complexity and especially computational effort.
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Pressure [MPa]
Prediction Properties Pressure [MPa]
Temperature [K]
Mass flow [kg/s]
Velocity [m/s]
Molecular Viscosity [kg/m-s]
Density [kg/m3]
Reynolds number
Isobaric Specific Heat [J/kgK]
O2
15
15
300
0.386
49.4
2.74×10-5
200
2524000
1166.3
CH4
15
15
300
0.114
31.8
1.23×10-5
117
302000
3379.8
O2
15
16.5
300
0.386
44.9
2.46×10-5
223.4
2860000
1187.9
CH4
15
16.5
300
0.114
28.8
1.72×10-5
119
215000
3454.3
Table 6: LO2/CH4 with real gas properties, operating conditions at 15MPand 16.5MPa
3.
CONCLUSIONS
This study has focused on the mixing and combustion processes differences between ideal and real gas properties of a
supercritical LO2/CH4 coaxial injector, two at 15MPa and one at 16.5MPa. Purposely calculated polynomials to define
real gas properties have been used [1,22]. Compared results are provided in Table 4. All the simulations (using real and
ideal gas properties) predict pressure as not uniform inside the chamber, exactly ideal gas simulations provide a higher
chamber pressure (17MPa) than predicted using real gas (16.5MPa): this is due to the higher temperature predicted in
the “ideal combustion chamber” by the different isobaric specific heat behaviours, fig. 16 and fig. 17. In both cases,
combustion provides a length of the potential core longer than the computational domain axial extension. In summing up
if ideal gas properties are used, to simulate supercritical real gas conditions, we will overestimate temperature and
pressure parameters and the length of the potential core will be underestimated; all of them are important design
parameter.
The third simulation reproduces the first one but using real gas properties predicted at 16.5MPa, that is the highest
chamber pressure found in the first real simulation (section 2.1).
This has been done to understand if is necessary a CFD software able to manage properties as function simultaneously
of 2 variables (temperature and pressure) because the CFD software, which has been used, is not able to do it (it
manages properties as function only of temperature). Results show little differences, therefore they enable LRE
simulations at supercritical injection conditions with properties function only of temperature but defined at the design
pressure. This leads to a reduced problem complexity and especially a reduced computational effort.
4. FIGURES
CH4
0.0011m
0.005m
O2
0.0035m
0.0055m
0.1m
Figure 1: LO2/CH4 schematic diagram of the computational domain
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1.66E+07
1.01
1.64E+07
1
1.62E+07
0.99
O2 mass fraction
pressure, Pa
1.60E+07
1.58E+07
1.56E+07
0.98
0.97
0.96
1.54E+07
0.95
1.52E+07
0.94
1.50E+07
1.48E+07
0.93
0
0.02
0.04
0.06
0.08
0.1
0
0.01
0.02
0.03
0.04
axis, m
0.05
0.06
0.07
0.08
0.09
0.1
axis, m
Figure 2: Real gas: axial pressure
Figure 3: Real gas: O2 axial mass fraction
4000
1.2
3500
1
3000
2000
1500
O2 mass fraction
temperature, K
0.8
xd1
xd11
xd13
xd3
xd5
xd7
xd9
2500
0.6
xd1
xd11
xd13
xd3
xd5
xd7
xd9
0.4
1000
0.2
500
0
0
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
0.005
0
0.0005
0.001
0.0015
0.002
radius, m
0.0025
0.003
0.0035
0.004
0.0045
raggio, m
Figure 4: Real gas: radial temperature
at different axial sections
Figure 5: Real gas: O2 radial mass fraction
at different axial sections
4.50E-01
1.20E+00
4.00E-01
1.00E+00
3.50E-01
xd1
xd11
xd13
xd3
xd5
xd7
xd9
6.00E-01
3.00E-01
CO2 mass fraction
CH4 mass fraction
8.00E-01
xd1
xd11
xd13
xd3
xd5
xd7
xd9
2.50E-01
2.00E-01
1.50E-01
4.00E-01
1.00E-01
2.00E-01
5.00E-02
0.00E+00
0.00E+00
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
0
0.005
0.0005
0.001
0.0015
0.002
radius, m
0.0025
0.003
0.0035
0.004
0.0045
0.005
radius, m
Figure 7: Real gas: CO2 radial mass fraction
at different axial sections
Figure 6: Real gas: CH4 radial mass fraction
at different axial sections
4.00E-01
1.75E+07
3.50E-01
1.70E+07
1.65E+07
xd1
xd11
xd13
xd3
xd5
xd7
xd9
2.50E-01
2.00E-01
1.50E-01
pressure, MPa
H2O mass fraction
3.00E-01
1.60E+07
1.55E+07
1.00E-01
1.50E+07
5.00E-02
1.45E+07
0.00E+00
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
radius, m
Figure 8: Real gas: H2O radial mass fraction
at different axial sections
0.005
0
0.02
0.04
0.06
0.08
0.1
axis, m
Figure 9: Ideal gas, axial pressure
0.005
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1.01
4500
1
4000
x/d=1
x/d=3
x/d=5
x/d=7
x/d=9
x/d=11
x/d=13
0.99
3500
0.98
temperature, K
O2 mass fraction
3000
0.97
0.96
0.95
2500
2000
1500
0.94
1000
0.93
0.92
500
0.91
0
0
0.02
0.04
0.06
0.08
0.1
0
0.0005
0.001
0.0015
0.002
axis, m
1.2
1.20E+00
1
1.00E+00
0.8
8.00E-01
0.6
x/d=1
x/d=3
x/d=5
x/d=7
x/d=9
x/d=11
x/d=13
0.2
0.0035
0.004
0.0045
0.005
x/d=1
x/d=3
x/d=5
x/d=7
x/d=9
x/d=11
x/d=13
6.00E-01
4.00E-01
2.00E-01
0
0.00E+00
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
0.005
0
0.0005
0.001
0.0015
0.002
radius, m
0.0025
0.003
0.0035
0.004
0.0045
0.005
radius, m
Figure 12: Ideal gas: O2 radial mass fraction
at different axial sections
Figure 13: Ideal gas: CH4 radial mass fraction
at different axial sections
4.50E-01
4.00E-01
4.00E-01
3.50E-01
x/d=1
x/d=3
x/d=5
x/d=7
x/d=9
x/d=11
x/d=13
3.00E-01
2.50E-01
x/d=1
x/d=3
x/d=5
x/d=7
x/d=9
x/d=11
x/d=13
3.00E-01
H2O mass fraction
3.50E-01
CO2 mass fraction
0.003
Figure 11: Ideal gas: radial temperature
at different axial sections
CH4 mass fraction
O2 mass fraction
Figure 10: Ideal gas: O2 axial mass fraction
0.4
0.0025
radius, m
2.00E-01
2.50E-01
2.00E-01
1.50E-01
1.50E-01
1.00E-01
1.00E-01
5.00E-02
5.00E-02
0.00E+00
0.00E+00
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
0.005
0
0.0005
0.001
0.0015
radius, m
0.002
0.0025
0.003
0.0035
0.004
0.0045
0.005
radius, m
Figure 14: Ideal gas: CO2 radial mass fraction
at different axial sections
Figure 15: Ideal gas: H2O radial mass fraction
at different axial sections
2500
4900
2300
4400
CH4 Isobaric Specific Heat, J/kgK
O2 Isobaric Specific Heat, J/kgK
2100
Ideal
Real
1900
1700
1500
1300
Ideal
Real
3900
3400
2900
2400
1900
1100
1400
900
900
700
80
180
280
380
480
580
680
780
880
980
Temperature,K
Figure 16: O2 ideal and real isobaric specific heat, comparison
90
190
290
390
490
590
Temperature, K
Figure 17: CH4 ideal and real isobaric specific heat, comparison
5th INTERNATIONAL SPACECRAFT PROPULSION CONFERENCE &
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1.66E+07
1.01
1.64E+07
1
1.62E+07
0.99
O2 mass fraction
axial pressure, MPa
1.60E+07
1.58E+07
1.56E+07
0.98
0.97
0.96
1.54E+07
0.95
1.52E+07
0.94
1.50E+07
1.48E+07
0.93
0
0.02
0.04
0.06
0.08
0.1
axis, m
Figure 18: Real gas, 16.5MPa, axial pressure
0
0.02
0.04
0.06
0.08
0.1
radius, m
Figure 19: Real gas, 16.5MPa: O2 axial mass fraction
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