39th AIAA Fluid Dynamics Conference
22 - 25 June 2009, San Antonio, Texas
AIAA 2009-4038
CFD SIMULATION OF MIXING AND COMBUSTION
IN LOX/CH4 SPRAY UNDER SUPERCRITICAL
CONDITIONS
Maria Grazia De Giorgi 1, and Alessio Leuzzi 2
University of Salento –Dep. Engineering for Innovation , Lecce, Italy, I-73100
Future launchers will use rocket propulsion systems burning CH4/LOx at supercritical conditions.
Despite this new trend there are a lack in experimental data and numerical studies in literature using
methane-oxygen combustion at these extreme conditions. Until now, only H2/LOx injection and
combustion has been investigated deeply. The aim of this investigation is the numerical study of the
CH4/LOx injection, mixing and combustion in liquid rocket engines with shear coaxial injectors, at
supercritical conditions. A theoretical study on the great importance to account real gas effect at these
conditions has been done. Properties as isobaric specific heat and density have been calculated using
different equations of state, and they have been compared with ideal gas and NIST data. CFD simulations
have been also performed by using different approaches: the Soave Redlich-Kwong real gas model has
been implemented to model the physical properties of the species in the single step methane/oxygen
reacting mixture. An E.D.M. model describes the turbulence-chemical kinetics coupling. The use of real
gas equation of state is computational expensive so simulations have been also performed by the
implementation of NIST data at 15MPa in the material database. The two approaches have been
compared positively. The effect of activating LES model in cold flow simulations has been investigated.
Nomenclature
p
R
T
V
v
ω
H
Cp
Z
Cv
S
μ
Mw
k
Yi
pressure
gas constant
temperature
specific volume
molar volume
acentric factor
enthalpy
isobaric specific heat
compressibility factor
isochoric heat capacity
entropy
dynamic viscosity
molecular weight
thermal conductivity
mass fraction of species i
Superscripts
R real gas property
(0) reference state
Subscripts
c value at critical point
r reduced value
1
Assistant Professor, Department of Engineering for Innovation, Via per Monteroni I-73100 Lecce, Italy, AIAA
Member
2
Ph.D Student, Department of Engineering for Innovation, Via per Monteroni I-73100 Lecce, Italy, Copyright © 2009 by M.G. De Giorgi. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
I.
Introduction
Future launchers will use rocket propulsion systems burning CH4/LOx at supercritical conditions. Also the
FLPP Programme, launched by ESA in February 2004, has emphasized that the trend in spacecraft propulsion
systems are liquid rocket engines using methane and liquid oxygen. This kind of rocket has greater
performances compared to solid rocket engines, so it can carry a bigger payload, as satellites.
For these reasons a current problem is to understand the injection, mixing and combustion in typical liquid
rocket engines and combustion chambers conditions. An important help can be provided by numerical
modeling, therefore a considerable research effort is developing in this direction. Until now, only H2/LOx
injection and combustion has been investigated deeply, while there is a lack in experimental data and numerical
studies in literature on LOX/CH4 combustion, and it is not possible to transfer concepts design from LOX/H2
injector to LOX/CH4 injector. At typical injection conditions H2 is far in the supercritical region and shows in a
good approximation ideal gas behaviour. Methane however is near critical and some properties will show
significant deviations from ideal gas behaviour. At these operating conditions the pressure is above the critical
one, then complex flow phenomena appear especially near the injector, where besides the turbulent mixing
process and chemical reactions also real gas effects have to be considered. Above the critical pressure, liquid
and gaseous phases are no longer separated, some fluid properties are gas-like while others fluid properties are
liquid-like; in addition in a supercritical fluid surface tension doesn’t exist, due to non-existence of liquid-gas
bonds. Near the critical point small changes of state have great effects on transport properties and variables of
state, leading to huge gradients in the density and other thermodynamics variables during the mixing of two
overcritical fluids. Turbulent structures in the mixing layer can be seen in subcritical as well as supercritical
injections, but ligament and droplets develop only in subcritical injection.
At such conditions the material properties can no longer be described as an ideal gas and real gas effects are to
be taking into account in the mixing process. The prediction of all thermodynamic properties depend on the
equation of state chosen. Thus, appropriate equations of state (EOS), and methods to determine transport
properties must be provided. Minotti and Bruno [1] conducted a study to analyze the thermo-physical properties
of methane and oxygen and their combustion products at high chamber pressure. They showed that highpressure effects significantly modify combustion regimes and so, to simulate mixing and combustion processes
at these conditions, high pressure effects must be described. In their study they analyzed the compressibility
factors of CH4, O2, CO2 and H2O at 15 MPa and they calculated the difference between ideal- and real-gas
thermophysical properties for these species in the temperature range in which experimental data are available
They showed that differences of thermo physical properties between ideal and real gases are large or very large,
so neglect real-gas behaviour could lead to significantly erroneous thermo-fluidynamic fields. Finally they
described thermo-physical properties at 15 MPa by polynomial fits. Ierardo, Congiunti and Bruno [2], starting
from optical diagnostic experimental observations, presented in their work a Large Eddy Simulation of a
CH4/LOx coaxial injector, at transcritical and supercritical conditions. They modelled high pressure conditions
using real gas transport and thermodynamic properties, and the Lee-Kesler equation of state. They used the
Eddy Dissipation Concept (EDC) combustion model. Poschner, Zimmermann and Pfitzner [3]focused their work
on the problem of how commercial CFD codes predict the extreme conditions of modern high performance
rocket combustion engines. They performed simulations on the H2/LOx Mascotte test case, using the RedlichKwong equation of state for material properties. In addition they compared Eddy Dissipation Model (EDM) and
Flamelet combustion model. They showed that considering ideal gas for hydrogen leads to an under-predicted
density and to an over-prediction in the injection velocity, leading to a dilatation of the flame compared to the
resulting from the Redlich-Kwong equation of state. In the present work a theoretical study on the great
importance to account real gas effect for LOx- CH4 spray at supercritical conditions has been done, comparing
different equations of state. Then the possibility of application of CFD codes for the simulation of combustion
of supercritical LOx- CH4 spray has been explored. The Soave-Redlick-Kwong real gas model has been
implemented in the simulations to model the physical properties of the species in the single step
methane/oxygen reacting mixture. . The use of this equation of state is computational expensive so simulations
have been also performed by the implementation of NIST table at 15MPa in the material database.
II.
Equations of state and thermodynamic properties
In this section a theoretical study has been done to clarify the great importance of real gas effects in the
calculation of species properties at supercritical pressure, typical of liquid rocket engine. Experimental data for
density and isobaric heat capacity are available in the National Institute of Standards and Technology (NIST)
tables. However, these data are available only for a range of temperature narrower than the one to be considered
in combustion simulations under supercritical conditions. The comparison between properties calculated with
ideal gas law and experimental data (from NIST) at 15 MPa, shows that the percentage differences near by the
critical point is very high. Fig. 1 and fig.2 show the methane density and isobaric specific heat calculated by
ideal gas law and compared with NIST data.
At lower temperatures it is evident an high difference between the two predictions. Even though these
differences reduce at high temperatures, they remain higher than 5% (a reasonable value below which real-gas
effects might be neglected) in almost the entire range of temperature of interest to liquid rocket engines.
This means that using ideal-gas properties in CFD calculations will give incorrect gasdynamic fields, and this is
true at both low and high temperatures. Therefore it is necessary to find a complete and consistent description of
the species properties at conditions typical of liquid rocket combustion chambers. One could suggest to use
NIST data to provide species properties in a CFD code through an user defined database. Unfortunately NIST
tables provide experimental data for fluids properties only for a range of temperature narrower than the one to
be considered in combustion simulations. In addition, to use NIST tables is necessary to fix the value of pressure
and to take the values of some fluid properties (density, isobaric specific heat, viscosity, thermal conductivity,
etc.) in function of temperature. For these reasons, if the pressure in the computational domain is not constant,
or if the range of temperature change in the simulation is wider than the one available in NIST tables, as it
happens in combustion simulations, the use of a real gas equation of state is the only way to take account of real
gas effects.
There are a lot of equation of state for real gas available in literature, from the simplest to the most complicated;
nevertheless there is the necessity to understand which equation could tackle better mixing and combustion
phenomena modeling in the typical liquid rocket engine operating ranges. In this work a comparison among
three of the most common real gas equations of state at conditions of interest is presented. These equations are
the SRK (Soave-Redlick-Kwong), the PB (Peng-Robinson) and the LK (Lee-Kesler) equation of state:
SRK:
(1)
PR:
(2)
LK:
1
·
(3)
The SRK and PR equations are linear and cubic, therefore they are simple to solve and to implement in a CFD
code; instead LK equation is non linear, so its resolution is more complex and requires algorithms which would
make the code heavier.
A. Soave-Redlich-Kwong (SRK) equation of state
The Soave-Redlich Kwong equation of state takes the form in eq. (1). In eq.(1) the two parameter a and
accounting for the effects of attractive and repulsive forces among molecules, respectively, are calculated by:
0.42747
,
0.08664
(4)
The value of the exponent n are well correlated by the empirical equation [5], as a function of the acentric factor
ω:
0.4986
1.1735
0.475
(5)
To compute the density the SRK equation must be solved for the specific volume; for convenience, it can be
written as a cubic equation for specific volume, that :
0
where
(6)
(7)
Eq. (6) is solved with a standard algorithm for cubic equations [6]. The derivatives of specific volume with
respect to temperature and pressure can be easily determined from Eq. (1) using implicit differentiation. The
results are:
(8)
(9)
Where:
,
,
,
,
(10)
Analytical expressions for thermodynamic properties will be given in the following. Enthalpy can be written as:
1
ln
(11)
In the present case a fourth-order polynomial for the specific heat for a thermally perfect gas7 has been used:
(12)
The specific heat for the real gas can be obtained by differentiating Eq. (11) with respect to temperature (at
constant pressure):
(13)
1
(14)
Finally, the derivative of enthalpy with respect to pressure (at constant temperature) can be obtained using the
following thermodynamic relation:
(15)
The entropy can be expressed in the form:
,
,
ln
̀
ln
(16)
where the superscript 0 again refers to a reference state where the ideal gas law is applicable. Using the
polynomial expression for specific heat:
,
,
ln
(17)
where f(T0) is a constant, which can be absorbed into the reference entropy S(T0, p0). The dynamic viscosity of a
gas or vapour can be estimated using the following formula from Cheremisinoff [12]:
where
.
.
6.3 · 10
.
.
(18)
.
is the reduced temperature:
(19)
and M is the molecular weight of the gas. This formula neglects the effect of pressure on viscosity, which
usually becomes significant only at very high pressures. Knowing the viscosity, the thermal conductivity can be
estimated using the Eucken formula from Eckert and Drake [13]:
(20)
At the end, mixture properties are calculated by the real gas model using mass weighed mixing rules; for
example the mixture viscosity is determined by:
∑
B.
·
(21)
The Peng-Robinson ( PR) Equation of state
The Peng-Robinson (PR) equation has been shown in eq. (2). The parameter a is a function of the temperature
as:
1
1
/
0.45723553
0.37464
1.54226
0.077796074
0.26992
(22)
To compute the density the PR equation must be solved for the specific volume; as for the SRK EOS, it can be
written as a cubic equation for molar volume:
0
(23)
where
3
(24)
,
/
To calculate isobaric specific heat we must calculate
/
three derivatives must satisfy the “cyclical rule”, which may be written as
and
1
/
derivatives. These
(25)
Therefore, once we have values for any two of the three PVT derivatives, the third may be calculated from Eq.
(25). The first derivative in Eq. (21) is found by direct differentiation of Eq. (2):
(26)
The second derivative in Eq.(20) is also found by direct differentiation of Eq.(2):
′
(27)
where
′
(28)
/
To compute isobaric heat capacity we have to calculate the isochoric heat capacity for a real gas, given by
Walas [9], Carnahan [10] and Kyle [11]:
where
′′
√
√
√
(29)
′′
(30)
Then isobaric specific heat will be given by the sum of the ideal and real contributions:
(31)
From the general relationship between
and
we have at the end:
(32)
The comparison with ideal-gas and experimental (NIST tables) properties shows that the SRK and PR equations
of state well predict the real gas properties also near by the critical point: the percentage difference in the range
of interest is less than 5%, as shown in Fig. 1. Furthermore, the comparison among SRK, PR and LK [1] at 15
MPa, in a wide range of temperature typical of liquid rocket combustion chambers, emphasizes that isn’t so
convenient to increase computational difficult using LK equation in order to have only a small increase of
accuracy, as depicted in Fig. 2.
1200
500
400
Ideal
NIST
SRK
PR
1000
Ideal
NIST
SRK
O2 Density, kg/m3
CH4 Density, kg/m3
600
300
200
100
800
600
400
200
0
0
90
190
290
390
T (K)
490
590
80
280
680
880
O2 Isobaric Specific Heat, J/kgK
5400
CH4 Isobaric Specific Heat, J/kgK
480
T (K)
Nist
Ideal
SRK
PR
2500
4500
2000
3600
1500
2700
1800
1000
Nist
Ideal
SRK
PR
900
0
500
0
90
190
290
390
490
590
80
T (K)
280
480
T (K)
680
Figure 1 - CH4 and O2 density and isobaric specific heat comparison at 15 MPa.
880
12600
500
450
CH4 density [kg/m3]
350
CH4 isobaric specific heat [J/kgK]
Lee‐Kesler
SRK
PR
400
300
250
200
150
100
50
Lee‐Kesler
SRK
PR
10600
0
8600
6600
4600
2600
0
1000
2000
3000
T [K]
4000
5000
6000
0
2000
4000
6000
T [K]
Figure 2 – Comparisons between different real gas equations for the prediction of CH4 density and
isobaric specific heat at 15 MPa
III.
CFD Modeling
Numerical simulations have been done by using the two commercial CFD codes Ansys CFX and Fluent
12.0. The test case is a methane-oxygen coaxial liquid rocket injector at supercritical conditions [2]. The
operating conditions are described in table 1.
Four different cases have been simulated, and can be divided in supercritical cold flow injection (case A, B,C ),
transcritical cold flow injection (case D) and supercritical combustion (case A). The oxygen is injected from a
central duct while methane enters the chambers from annular coaxial duct. Fig. 3 shows the computational
domains used in CFX and in Fluent, respectively. In CFX case, a periodic 45° 3D sector characterized by a
structured grid with 133152 cells has been used, with rotational periodic boundary conditions for the interfaces,
velocity inlet and pressure outlet, while wall boundary conditions have been used for the other faces. In Fluent a
two-dimensional structured axisymmetric grid with 160000 cells and the spacing and boundary conditions has
been used.
The CFD codes model the mixing and transport of chemical species by solving conservation equations
describing convection, diffusion, and reaction sources for each component species. Multiple simultaneous
chemical reactions can be modelled, with reactions occurring in the bulk phase (volumetric reactions) and/or on
wall or particle surfaces, and in the porous region.
The modelling of species transport and reactions has been done using the Eddy Dissipation Model (EDM) in
both the CFD codes. In this model reaction rates are assumed to be controlled by the turbulence, so expensive
Arrhenius chemical kinetic calculations can be avoided. The model is computationally cheap, but, for realistic
results, only one or two step heat-release mechanisms should be used. In all cases, the κ - ω turbulence model
has been used, even if in case 1 a comparison also with Large Eddy Simulation (LES) has been done.
The Soave-Redlick-Kwong real gas model has been implemented in the simulation to model the physical
properties of the species in the single step methane/oxygen reacting mixture. Density and isobaric specific heat
for the single species are calculated with the procedures and equations used to solve the SRK equation of state
(Eqs. 4-21). The use of this equation of state is computational expensive so simulations have been also
performed by the implementation of the piecewise-linear interpolation of the NIST database properties at 15
MPa.
Table 1 – Injection methane‐oxygen conditions and combustion chamber pressure. CASE
VCH4
VO2
TCH4
TO2
Combustion Chamber Pressure
A
70 m/s
20 m/s
300 K
300 K
150 bar
B
100 m/s
20 m/s
300 K
300 K
150 bar
C
115 m/s
20 m/s
300 K
300 K
150 bar
D
93 m/s
10 m/s
300 K
100 K
150 bar
Figure 3 – Computational domain used in CFX and in Fluent 6.3.
IV.
Results and discussion
The simulations have been done to study the typical methane-oxygen shear coaxial injector geometry under
supercritical conditions, following a step-by-step procedure: first cold flow simulations, without reactions and
combustion, are performed. Then, starting from cold flow convergent solutions, reactions and combustion are
activated, increasing problem complexity.
A.
Cold flow simulations with κ - ε standard turbulence model
Different approaches have been compared in this section. Ansys CFX performs real gas properties with SoaveRedlich-Kwong equation of state, yet implemented in the code. Cold flow simulations show a well prediction in
the mass fraction contours (Fig. 4) in good agreement with the results obtained by Fluent 12.0. Simulations have
been done also by implementing the piecewise-linear interpolation of the NIST database properties at 15 MPa
in the material database, since pressure variations in the computational domain is small. However in this last
case the species mixing is different from the simulations with real gas model. Figs. 5 - 6 show the species radial
profiles at three different axial positions, predicted by three different modelling approaches : ideal gas , SRK
real gas model with pressure based solver and piecewise-linear interpolation of the NIST database properties at
15 MPa. Looking to the supercritical cases, large differences between ideal gas simulation and real gas model is
evident in particular in the case of high methane velocity, at highest distance from the nozzle exit (X/D=5.0).
Then using the same coaxial injector configuration the oxygen injection temperature have been lowered to 100
K in case D, to evaluate the effects of larger density gradients and to simulate the presence of a transcritical
transformation. Also in this case the ideal gas predictions are different from the simulation that use NIST and
SRK. Discrepancies are present also for the prediction of the potential core length, defined as the axial position
where the oxygen mass fraction is equal to 0.9. In case A, the prediction length in function of the jet diameter D,
is 6.24D by ideal gas simulation, 6D by SRK and 5.5D for the simulation by NIST database. In case B, the
prediction length is 3.17D by ideal gas simulation, 2.94D by SRK and 2.64D for the simulation by NIST
database. In case C, the prediction core length is 3.06D by ideal gas simulation, 2.65D by SRK and 2.12D for
the simulation by NIST database. So the ideal gas predicted length is higher than the SRK prediction, that is
similar to the value by simulation with NIST database. Also in the transcritical case the length of the potential
core, is higher for the ideal gas, equal to 2.47D, than the real gas model SRK equal to 2.11D, while the value
with NIST is 0.42D. In this case the discrepancies between the real gas model and the NIST database is evident.
This is in accordance with the comments about fig.1, given in the previous sections.
CFX - SRK REAL GAS MODEL
FLUENT SRK REAL GAS MODEL
FLUENT NIST DATABASE
Figure 4 – Methane mass fraction contours using different approaches (case A).
CASE A
CASE B
s
Figure 5 - Species radial profiles at X/D=0.3, X/D=0.5 and X/D=5.0 in the case A and case B, simulations
with Ideal Gas, NIST and SRK properties.
CASE C
CASE D
Figure 6 - Species radial profiles at X/D=0.3, X/D=0.5 and X/D=5.0 in the case C and case D, simulations
with Ideal Gas, NIST and SRK properties.
B. Cold Flow simulations with LES
The implementation of real gas model involve more difficulties in the use of others turbulence models, as LES;
some experimental observations obtained through non-intrusive optical techniques show the formation of
turbulent vortices at the two jets interface, which make easy the mixing between methane and oxygen (Fig.7).
These vortices can’t be correctly predicted by the more robust κ-ε turbulence model. The use of NIST tables
allows the use of LES without particular difficulties. The activation of LES model in cold flow simulations
really shows eddies formation at the methane-oxygen interface: the jet surfaces exhibit tiny instability waves
immediately downstream of the injector. These waves then grow and roll-up into a succession of ring vortices.
The resultant large-scale vertical motion facilitates the mixing of the jet with the ambient flow and causes the
entrainment of warmer and irrotational fluid into the jet.
Numerical
Experimental observation
Figure 7 – Methane mass fraction contours with LES, compared with experimental observations [14].
C. Reacting flow simulations
Then, starting from a convergent cold flow solution, reactions can be activated: the eddy dissipation model
(EDM) is used to compute the reacting flow for the case A. This model assume that chemical reactions are
infinitely fast with a single step global mechanism (no production of radicals and intermediate species); even
though this is a very crude model, in a real liquid rocket engine thrust chamber, due to the high pressure and
temperature environment, chemical reactions take place at very small characteristic times, a suitable condition
for a fast chemistry assumption.
2
2
(33)
Simulations results by SRK real gas model, emphasizes that the flame shape is well predicted (see Fig. 8) and
similar to others numerical observations available in literature (see Fig. 9), even if few experimental data are
present in literature in particular in the case of LOX/CH4 injector. However the highest temperature is over
predicted in comparison of the typical methane-oxygen combustion one at supercritical condition. This is
probably due to the use of the EDM model and so to the absence of radicals and intermediate species that
develop in a real combustion and that are predicted by others more accurate but more complex combustion
models, as the Flamelet Model.
Fig. 10 shows the species radial profiles at X/D=0.3, X/D=0.5 and X/D=5.0, calculated in the simulation, where
d is the oxygen inlet diameter, x the axial coordinate: proceeding towards downstream, the reaction zone
becomes thicker, the reactants mass fraction decreases, while the products mass fraction increases.
The species mass fraction field predicted by this simulation are different than that computed with ideal gas
equation, in particular at highest distance from the nozzle exit. As mentioned before the differences of thermo
physical properties between ideal and real gases are large or very large. The differences are so high that to
neglect real-gas behaviour could lead to significantly erroneous thermofluidynamic fields Therefore the use of
the SRK real gas equation of state is better recommended.
SRK REAL GAS MODEL
IDEAL GAS
Figure 8 - Contours of temperature by using SRK and IDEAL GAS equation of state.
M. Oschwald, F. Cuoco, B. Yang, M. De
Rosa experimental observations with
LOX/CH4 [15]
M. Poschner, I. Zimmermann, M. Pfitzner
numerical results with LOX/H2 [3]
C. Cheng, Farmer, numerical results
with LOX/H2 [16]
Figure 9 –Numerical and experimental observations available in literature.
SRK REAL GAS MODEL
X/D = 0.3
IDEAL GAS
X/D = 0.3
0.8
O2
O2, CH4, CO2, H2O
O2, CH4, CO2, H2O
1
CH4
H2O
0.6
CO2
0.4
0.2
0
0
0.005
r [m]
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
O2
CH4
H2O
CO2
0.000
0.01
X/D = 0.5
0.010
X/D = 0.5
1.0
1
0.9
0.8
0.8
O2
O2, CH4, CO2, H2O
O2, CH4, CO2, H2O
0.005
r [m]
CH4
0.6
H2O
CO2
0.4
0.2
O2
0.7
CH
4
H2
O
0.6
0.5
0.4
0.3
0.2
0.1
0
0.0
0
0.005
0.01
0.000
0.005
r [m]
r [m]
X/D = 5
X/D = 5
1
O2, CH4, CO2, H2O
O2, CH4, CO2, H2O
0.8
O2
0.6
CH4
H2O
0.4
CO2
0.2
0
0
0.005
r [m]
0.01
O2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.000
0.010
CH4
H2O
CO2
0.005
0.010
r [m]
Figure 10 - Species radial profiles at X/D=0.3, X/D=0.5 and X/D=5.0 in the simulation with SRK equation
of state, on the left, and IDEAL GAS, on the right, (reactive flow, case A).
V.
Conclusions
The present work has been focused on the numerical study of injection, mixing and combustion of methaneoxygen shear coaxial injectors in typical liquid rocket engine combustion chambers under supercritical
conditions. These extreme conditions can not be predicted accurately by commercial CFD codes yet, because at
such conditions the material properties can no longer be described as an ideal gas and real gas effects are
thermodynamically not treated correctly by the codes available today. A theoretical study to clarify the great
importance to account the real gas effect in the CFD calculation of species properties has been presented. The
comparison between properties calculated with ideal gas law and experimental data at 15 MPa demonstrate that
using ideal-gas properties in CFD calculations will give completely wrong fluid dynamic fields. If the change of
pressure in the computational domain can’t be neglected, or if the range of temperature change in the simulation
is wider than the one available in NIST tables, as it happens in combustion simulations, the use of a real gas
equation of state is mandatory to take account of real gas effects. In this paper a comparison among three of the
most common real gas equations of state at conditions of interest has been presented. The comparison with
ideal-gas and experimental properties has shown that the SRK and PR equations of state well predict the real gas
properties also near by the critical point, so it isn’t convenient to increase problem accuracy using LK equation
in order to have only a small increase of accuracy.
The second part of the present work has been focused on modelling of cold and reactive flow with different
modelling approaches: ideal gas equation, implementing the piecewise-linear interpolation of the NIST database
properties, and SRK real gas model in commercial CFD codes. Ansys CFX and Fluent 12.0 perform real gas
properties with Redlich-Kwong equation of state. The cold flow simulations show that large differences between
ideal gas simulation and SRK real gas model is evident in particular in the case of cold supercritical injection
(case A) at highest distance from the nozzle exit. In particular in the transcritical case the SRK predictions of the
potential core length are different from the simulation that use NIST database, this is in agreement with the
theoretical analysis, that empathizes that the properties calculated by SRK real gas equation for lower
temperature (also at 100 K) at 15 MPa are not well predicted, if compared with the NIST data . Using the SRK
real gas equation the reactive flow simulations have been performed. The simulation has predicted well the
flame shape qualitatively similar to others numerical observations available in literature, but the combustion
model used seems to ovepredict the highest temperature due to the absence of radicals and intermediate species.
The analysis stresses the necessity to use a real gas model in the CFD simulations of mixing and combustion in
LOx/CH4 spray under supercritical conditions, instead the ideal gas equation, because the differences of thermophysical properties between ideal and real gases are large or very large. The differences are so high that to
neglect real-gas behaviour could lead to significantly erroneous thermofluidynamic fields
References
1
A. Minotti, C. Bruno, “Subtranscritical and Supercritical Properties for LO2-CH4 at 15 MPa”, Journal of
Thermophysics and Heat Transfer, Vol. 21, No. 4, October-December 2007.
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