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Sonderforschungsbereich/Transregio 40 – Annual Report 2015
311
Comparison of Single Element Rocket
Combustion Chambers with Round and
Square Cross Section
By S. Silvestri, H. Riedmann†, O. Knab† and O. J. Haidn
Lehrstuhl für Flugantriebe, Technische Universität München
Boltzmannstr. 15, 85748 Garching b. München
Today’s high performance liquid propellant rocket engines for transfer into orbit and
space exploration are mostly based on well-established cryogenic propellant combinations like liquid oxygen/liquid hydrogen (LOX/LH2), due to their high specific impulse.
The potential of using hydrocarbon as propellant, in particular methane instead of hydrogen, is under active consideration since it could be a solution for the high operational
costs. The design and optimization of liquid rocket engines using methane require a
detailed knowledge and understanding of the dominating physical phenomena of propellant injection, combustion and heat transfer. In the context of the national research
program Transregio SFB/TRR-40, sub-project K1, the Institute of Flight Propulsion (LFA)
of the Technische Universität München (TUM) and the System Analysis Department of
Airbus DS carry out experimental and numerical investigations on heat transfer and injector characterization at application-relevant combustion pressures and temperatures.
Two multi-injector combustion chambers are designed for gaseous oxygen (GOX) and
gaseous methane (GCH4). A high pressure combustion chamber developed under the
sub-project K1, and a combustion chamber with rectangular cross section for low pressure ranges, developed under the sub-project D9. Before the multi-elements chambers
are tested, two single-element combustion chambers having round and quadratic cross
section have been tested using several scaling procedures. The commonalities between
the combustion chambers in terms of geometries and operating conditions are analyzed
in detail and the experimental results, keeping the same combustion chamber pressure
and mixture ratio, are presented for the two chamber configurations tested. Airbus DS
is accompanying the experimental work with numerical simulations using the in-house
CFD tool Rocflam3 as well as the commercial code ANSYS CFX. In the last year, the
numerical activities have focused on the single-element chamber with quadratic cross
section. Thereby, special emphasis is put on the elaboration of a suitable approach for
methane combustion modeling in an industrial tool environment. A brief overview of the
current state is given in this report.
1. Introduction
Already in the ’80s, oxygen/methane propellant combinations have been examined
for high chamber pressure boost phase engine applications [1], and this fluid combination has been studied by several research teams in the US Space program [2] as
† Airbus DS GmbH, München, Germany
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S. Silvestri, H. Riedmann, O. Knab & O. J. Haidn
well in as Russia [3] and in Europe [4]. Recently, the interest in this propellant combination has arisen again. European and Russian industries [5] cooperate to conceive a
LOX/CH4 engine for booster applications. Jaxa [6] conducts hot-firing test on a LOX/CH4
rocket engine for an upper stage system. Purdue University [7] focuses the attention on
LOX/CH4 expander cycle engines. However, the new propellant combination brings new
challenges and the knowledge in oxygen/methane combustion, flame stabilization and
injector design criteria need a wide range of experimental and analytical database.
In the context of the national research program Transregio SFB/TRR-40 on “Technological Foundations for the Design of Thermally and Mechanically Highly Loaded
Components of Future Space Transportation Systems”, two multi-injector combustion
chambers are designed for gaseous oxygen (GOX) and gaseous methane (GCH4). The
high pressure combustion chamber (operating from 40 bar to 100 bar), equipped with a
round pattern of seven injectors [8], developed under the sub-project K1, and a combustion chamber with rectangular cross section for low pressure ranges (10 bar to 40 bar)
housing a line of five injector elements, developed under the sub-project D9 [9]. A key
aspect of the project is to improve the knowledge on heat transfer processes and cooling methods at representative engine-like conditions, focusing on injector-injector and
injector-wall interactions. For this purpose, classical measurement techniques together
with inverse methods are used to reconstruct the temperature field in the chamber wall
material and the heat flux profile. Furthermore, the low pressure chamber is equipped
with a quartz window to allow optical diagnostic techniques. The flat window and the
rectangular cross section of the hardware will allow full optical access to the flame interaction, avoiding, compared to a round chamber, the distortion due to the curvatures
and the flow disturbances caused by the presence of window corners.
In order to profit from the results coming from the optical measurements also for
the high pressure level, the two chambers feature the same performance and design
parameters, in this way a scalability criterion of the injector can be established. As a first
attempt in this direction, two single element capacitive chambers, having either round or
quadratic cross section, are built and tested at the Institute of Flight Propulsion. Since
the injection element has the greatest influence on the characteristics of performance,
heat transfer, combustion stability and ignition, it has been chosen to be the same for
the single element combustion chambers as well as for the multi-element chambers.
Furthermore, to maintain the mean level of mixing in the developing combustion flow
field, the mean value of the Mach number and therefore the contraction ratio of the
hardware is kept identical.
Maintaining full combustion similarity in rocket flow systems is challenging, thus, a
partial modelling is necessary. Keeping the geometry similarity previously described,
different scaling approaches for the single element chambers are considered [10]. The
injector element mass flow can be kept the same for the two hardware. However, due
to the different cross sectional area and the same contraction ratio of the chambers, the
throat area is also different. This would result in a variation of the combustion chamber
pressure, as well as in a variation of the hot gas velocity in the chamber, which would
influence the boundary layer development. When instead the combustion parameters
in terms of pressure and mixture ratio are kept the same, the injection conditions are
subject to variations that could lead to different injector performances. If, as alternative,
the combustion chamber and the injection conditions should be preserved, the mixture
ratio or the contraction ratio of the two test hardware need to be modified. This would
affect the characteristic velocity in the chamber, hence the performance characteristics.
Single Element Rocket Combustion Chamber
(a) Round combustion chamber
313
(b) Rectangular combustion chamber
F IGURE 1. Combustion chamber schematics
In the following paragraphs the test results obtained maintaining the same combustion
chamber pressure and mixture ratio between the different hardware are described in
details. The experiments conducted on the quadratic combustion chamber are also accompanied by numerical simulations performed by the System Analysis Department of
Airbus DS, see section 4.
2. Test specimen and experimental configuration
All the experiments have been performed at the Institute of Flight Propulsion’s test
facility at the Technical University of Munich (TUM). The movable test bench allows experiments with gaseous methane and gaseous oxygen for designed interface pressures
up to 50 bar. In this section a description of the single element rocket combustion chambers, the injector geometry, the measurement equipment and data analysis procedures
is presented.
2.1. Hardware description
The investigations are performed using two modular capacitive cooled combustion chambers having round and square cross sections. The combustion chambers are designed
for a testing time of up to 4 s at a pressure of 20 bar and mixture ratio of 3.4.
The round combustion chamber, depicted in Fig. 1(a), features an inner diameter of
12 mm and a conical nozzle with a throat diameter of 7.6 mm. The rectangular chamber
instead, shown in Fig. 1(b), has an inner square cross section of 12 mm x 12 mm and a
truncated trapezoidal nozzle with a rectangular throat section of 4.8 mm x 12 mm. The
chamber height is kept identical in order to provide the same injector wall distance of
3 mm. As a consequence, the cylindrical cross section is smaller than the square cross
section requiring also a smaller throat cross section to yield the same contraction ratio.
A Mach number of 0.24, typical for rocket applications, is achieved by a contraction
ratio of 2.5 for both chambers. All chamber segments are made of oxygen-free copper
(Cu-HCP).
For the current study, a single shear coaxial injector element is used. More detailed
can be found in Silvestri et al. [10]
2.2. Experimental setup and operating conditions
Both hardware are equipped with standard instrumentation required to characterize the
operation of the combustion chamber. For a better understanding of the complex heat
transport processes, equally spaced pressure transducers on the side wall provide a
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S. Silvestri, H. Riedmann, O. Knab & O. J. Haidn
well resolved measurement of the wall pressure distribution p(z) along the chamber. To
characterize the injection conditions, thermocouples of type K with 0.5 mm diameter, and
pressure transducers are installed in the chamber manifolds. To determine the temperature field within the chamber material, type T thermocouples of 0.5 mm diameter are
mounted with a regular path along the center plane of both combustion chambers with
a distance of 1 mm from the hot wall. In both chambers the pressure transducers as well
as the thermocouples present the same axial pitch of 34 mm and 17 mm respectively.
Further information about the hardware setup for the rectangular and round combustion
chamber can be found in previous publications [11, 12].
The ignition of the chambers is achieved by a torch igniter using gaseous methane/
gaseous oxygen (OF = 2.5), which is mounted in a central axial position. The burning
time is kept constant for all the tests to 3 s and the same hot run sequence between
the test campaigns has been used. The combustion chamber pressure is maintained
constant for the two test set-ups. The tests are performed at 10 and 20 bar chamber
pressure and mixture ratios variation from 2.2 to 3.4.
3. Experimental results and discussion
The main goal of the research is to characterize and compare the injector behavior in
terms of heat loads to the wall. In the present paragraph the pressure and temperature
load distribution along the combustion chambers main axis as well as the heat loads are
presented. The 20 bar OF =2.2 and OF =3.0 test results are chosen to be representative
of the whole test campaign.
3.1. Influence of combustion chamber geometry
One of the influencing parameter for the performance in the combustion chamber is
the geometry of the chamber itself. While comparing the two set-ups the difference in
geometries has to be taken into account. The two most important features of the combustion chamber are its length and its shape. In order to isolate the effects resulting from
the different shapes and to minimize the differences of the upcoming multi-element injector chambers, most of the geometry parameters are kept similar between the different
hardware. The length of the combustion chamber affects the overall vaporization efficiency, in case of liquid propellants, and the overall mixing efficiency. For mixing-limited
combustion, increasing the chamber length can increase the overall performance but
often at a much lower rate, depending on the injector element design. Injector elements
that have a higher initial interpropellant mixing, such as coaxial element patterns, show
little mixing improvement with increased chamber length [13]. As already described in
paragraph 2.1, the two chambers use the same injector design and have the same
contraction ratio. In this way, the mean level of the mixing process in the developing
combustion flow field is kept similar. Furthermore, a trade-off to keep similar characteristic and absolute characteristic chamber lengths, for which the residence time of the
propellants in the combustion chamber is determined, has been achieved. An overview
of the common parameters is given in Table 1. Moreover, the difference in the pressure
losses due to friction and heat losses to the chamber wall are minimized for the two
chambers by maintaining the same hydraulic diameter and the volume to surface ratio
(V /As ).
Although most of the geometric parameter are maintained similar, the main difference
between the two chambers is the thickness of the chamber walls and consequently the
mass of the combustion chambers. The rectangular chamber is almost two times heavier
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Single Element Rocket Combustion Chamber
Hydraulic diameter
Chamber cross section
Chamber length
Chamber characteristic length
Maximum chamber wall thickness
Volume to inner surface ratio
Contraction ratio
Throat area
dhyd
Ac
L′
L∗
w
V /As
ǫc
Ath
[m]
[m2 ]
[m]
[m]
[m]
[m]
[-]
[m2 ]
Rect. chamb.
12 · 10−3
113.10 · 10−6
290 · 10−3
724 · 10−3
36.5 · 10−3
3 · 10−3
2.5
45.24 · 10−6
Round cham.
12 · 10−3
144 · 10−6
285 · 10−3
749 · 10−3
19 · 10−3
3 · 10−3
2.5
57.60 · 10−6
TABLE 1. Common geometrical parameters of the hardware
than the round combustion chamber. The main effect coming from the bigger amount
of material is visible in the temperature readings. At the start-up, when the heat wave
has not reached the external surface yet, the difference in the slope of the temperature
profile depends only on the different surface available. Later on, the havier mass of the
rectangular chamber acts as a heat sink and decreases the steepness of the curve.
3.2. Similarity in combustion chamber pressure and mixture ratio
The two combustors feature the same propellant chemistry, flow mixture ratios and propellant inlet temperatures. Therefore, the Schmidt and the Prandtl numbers are kept
constant. Furthermore, having the same combustion chamber pressure, mixture ratio
and Mach number in the chamber results in identical hot gas velocities. With these hypotheses and combinig the Reynolds and the Damköhler numbers, it is possible to obtain a scalability criterion for the chemical conversion time. This approach, also followed
by Penner is known as “The Penner-Tsien Scaling Rule” [14]. The Reynolds number in
the combustion chamber depends mainly on the hot gas properties, the hot gas velocity
and the chamber length scale. Thus, the Reynolds number, for each hardware, would
differ only for the chamber length scale. Since for the case studied, as seen in section
3.1, the length scale, equal to the hydraulic diameter for the rectangular chamber and
to the geometrical diameter for the round chamber, is equal, also the Reynolds number
does not differ for the two compared chambers. By coupling the DaI number with the
Re number in Eq. 3.1 it is possible to conclude that the chemical reaction time in the
hardware setups is the same.
2
Lround
τi,round
=
=1
(3.1)
τi,rect.
Lrect.
Considering that the residence times of the propellants in the chamber are almost
identical due to the similar characteristic lengths, the combustion processes and in particular the heat release should be alike and consequenthly the pressure decay along the
combustion chamber axis is also similar. Fig. 2 shows the comparison of the wall pressure distribution for the round and the rectangular chamber at 20 bar. On the left side,
the comparison is shown for a mixture ratio of 2.2. The plot on the right side shows the
comparison for a mixture ratio of 3.0. The pressure signal is normalized with the mean
chamber pressure in the chamber of each test and its repetition.
Due to the combustion processes, the injected mixture accelerates from the injection
velocity to the hot gas velocity for a full combusted flow. Consequently, the wall pressure
decreases along the chamber axis and the pressure gradient tends to flatten when the
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S. Silvestri, H. Riedmann, O. Knab & O. J. Haidn
1.05
Round. chamb. 20 bar, OF=2.2
Rect. chamb. 20 bar, OF=2.2
1.04
Rect. chamb. 20 bar, OF=3.0
Round chamb. 20 bar, OF=3.0
1.04
Normalized Pressure [−]
Normalized Pressure [−]
1.06
1.02
1
0.98
1.03
1.02
1.01
1
0.99
0.98
0.96
0
0.05
0.1
0.15
0.2
Axial Position [m]
(a) OF =2.2
0.25
0.3
0.97
0
0.05
0.1
0.15
0.2
0.25
0.3
Axial Position [m]
(b) OF =3.0
F IGURE 2. Pressure distribution along the chamber axis at pc =20 bar
completeness of combustion is reached [15]. A pressure gradient of up to 5% is visibile
for both the chambers until the combustion process is accomplished, shortly before the
nozzle section. No considerable difference could be seen in the pressure decay for the
different pressures and mixture ratios. In the region close to the faceplate a drop in wall
pressure, linked to the presence of a recirculation zone, is observable. The stagnation
point, shown by the pressure peak, occurs for both the hardware at the same axial
position. For the rectangular combustion chamber, where the presence of the corners
leads to a bigger volume and the injected velocity is slightly higher, the effect appears
to be stronger and a higher initial rise of the pressure can be seen. For lower mixture
ratio cases, when the velocity and the momentum flux for the methane is greater, the
difference in the recirculation zone seems to be amplified. In the region close to the
injector, the influence of a round flame in a rectangular chamber is more evident, since
the flame is not yet complitely adapted to the rectangular shape. This could also cause
the flatter shape of the pressure profile along the chamber axis in the first third part of
the chamber.
The characteristic of an injector element is mainly defined by the heat loads to the hot
wall. The mixing mechanisms in the near injector region determine the flow conditions
and influence the flame behavior. Because of the different cross sectional areas of the
chamber and the identical contraction ratio, leading to different throat areas Ath the
injected mass flow needs to be scaled proportional according to Eq. 3.2, to achieve
the same combustion chamber pressure level. This however leads to different injection
mass flow conditions in the two chambers.
pc · At
(3.2)
ṁ =
c∗
Due to the gaseous form of the propellants, the variation in the injector velocities
is moderate. A maximum difference in velocity of 14% higher for the rectangular combustion chamber is reached. Additionally, the values of the velocity ratio (V R) and the
momentum flux ratio (J) vary with OF in small ranges and there is no significant difference for the two chambers. Table 2 gives an overview of the actual variation of V R
and J at 20 bar for the different mixture ratios tested. Since for a shear coaxial injector
the mixing process improves with fuel to oxidizer momentum flux ratio, similar injector
performance has to be expected in both configurations.
Single Element Rocket Combustion Chamber
VR
Mixture ratio (OF )
2.2 2.6 3.0 3.4
Rectangular comb. chamb. 1.12 1.03 0.96 0.93
Round comb. chamb.
1.22 1.05 0.96 0.93
317
J
2.2 2.6 3.0 3.4
0.74 0.56 0.46 0.39
0.80 0.58 0.46 0.40
TABLE 2. Velocity ratio and momentum flux ratio for 20 bar case test conditions
Despite a different total amount of propellant is injected, the energy per unit volume
introduced in the systems remains constant since compensated by the difference in
volume of the hardware. The heat transfer, driven by the convection mechanism in the
chamber, is similar as long as the Re number and the P r number are kept constant.
Consequently, the rate of heat addition per unit volume by chemical reaction and the
rate of heat removed by the convection of the enthalpy are in the same relation and the
Damköhler number of the third group is also preserved. Keeping of complete chemical
and reaction kinetic similarity in the gas stream automatically satisfies the boundary
conditions for heat transfer to the chamber wall. For the underlying physical phenomena,
the heat flux in the two combustion chambers, is expected to be comparable.
3.2.1. Axial heat flux and temperature distribution
Due to the capacitive design of the hardware, heat fluxes can only be calculated
from wall temperature measurements. Several methods to calculate the heat fluxes are
investigated at the Institute of Flight Propulsion. In this section an Inverse method using
Finite Difference Scheme is briefly described and the test results are analyzed. Detailed
information about the heat flux calculation methods can be found in Celano et al. [16].
For the calculation of the heat flux based on the thermocouple measurements, an inverse computational method has been employed. The applied tool relies on an iterative
regularization method, which aims to minimize a residual function [17]. In this case, the
residual function is defined as the difference between measured and calculated temperature values. To achieve that, the code takes advantage of the variational formulation
of the heat diffusion PDEs, leading to a constrained minimization of the residual function. The boundary condition in the chamber wall is represented by the unknown heat
flux (over time and position). By using the boundary condition as a necessary optimality requirement, Lagrange multipliers are introduced for the formulation of the residual
gradient. Finding the optimal solution corresponds to the minimization of the residual
gradient and for this task, the conjugate gradient approach is utilized. This updates the
values of the heat flux in each node for the next iteration step. A numerical implementation using the Finite Difference Scheme has been carried out and the tool has been
optimized for the combustion chamber geometries. For the round combustion chamber,
the modeling domain is defined as a 3D cylinder, whereas for the rectangular one, the
domain is modeled by a cave square prism. Each computational node is assigned with
a value of temperature and heat flux. Since the method involves an iterative solution, the
direct problem is solved each time with the new heat flux as boundary condition. Upon
convergence, a complete time dependant profile for the heat flux and the temperature is
obtained for all points in the domain. The results obtained for the 20 bar case, OF =2.2,
on the left, and OF =3.0, on the right, at the evaluation time are reported in Fig. 3.
The wall heat flux versus axial location profile shows, for both combustion chambers,
a relatively slow, but steady rise up to a maximum of 6 MW/m2 just close to the nozzle
section. As already seen in previous studies, using a single element rocket combustion
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S. Silvestri, H. Riedmann, O. Knab & O. J. Haidn
6
7
x 10
7
5
4
3
2
Round chamb. 20 bar, OF=2.2
Rect. chamb. 20 bar, OF=2.2
1
0
0
6
6
Heat flux [W/m2]
Heat flux [W/m2]
6
x 10
0.05
0.1
0.15
0.2
0.25
5
4
3
2
Round chamb. 20 bar, OF=3.0
Rect. chamb. 20 bar, OF=3.0
1
0
0
0.05
0.1
0.15
Axial length [m]
Axial length [m]
(a) OF =2.2
(b) OF =3.0
0.2
0.25
F IGURE 3. Axial heat flux distribution at pc =20 bar
chamber with LOX/GCH4 [2], the peak in wall heat flux for shear coaxial injector show-up
in a far downstream position. Different behavior instead has been encountered for a swirl
coaxial injector, where the heat flux peak is more close to the injector faceplate. Although
the maximum heat flux level is comparable for the different hardware configurations,
the heat flux of the rectangular chamber (red line in Fig. 3) presents a slightly lower
heat flux in the second third of the chamber, this could be attributed to a lower mixing
efficiency due to the presence of the corners and to the different recirculation zones.
This discrepancy, in fact, seems to be stronger for the lower mixture ratio case, where
the impact of the recirculation zone is bigger in the rectangular chamber, already visible
in the pressure profile in Fig. 2. The recirculation zone affects the local mixing in the near
injection region. The burned propellants are transported towards the gaseous methane
entering the chamber through the outer injector annulus and have a strong influence
on the gas composition near the walls. Therefore the local mixture ratio and the heat
conductivity of the gas are not equal to the other chamber anymore. The heat flux, in
this region, is then dominated by the creation of recirculation vortices amplified by the
bigger volume of the the rectangular chamber. The better mixing in the recirculation zone
appears, nevertheless, to be only local and the mixing of the remaining species could
lead to a smaller heat flux level in a further downstream position. Furthermore, a non
uniform distribution of the heat flux profile in circumferential direction could decrease the
annular average level for this chamber configuration, shown in Fig. 3. With increasing
mixture ratio, a slight increase in the heat flux can be noticed for both the combustion
chambers. The small heat flux peak, in the round chamber, located at z=0.1875 m, is
considered to be due to a characteristic behavior of the temperature sensor located at
this axial position. Analysis of other tests has led to the conclusion that this peak is
independent of the pressure level and the mixture ratios used. The error bars, placed
at each measurement position, represent the relative deviation of the calculated heat
flux. It is based on a direct solution from a CFD analysis, for which the residual of the
calculated and measurement temperature are taken into account.
Due to the combustion process, the temperature increases continously along the
chamber axis until the accomplishment of the reaction process. The temperature distribution along the chamber axis (∆T (z)) for the complete set of thermocouples positioned
at 1 mm distance from the hot gas is shown in Fig.4 for both configurations. In a heat sink
319
Single Element Rocket Combustion Chamber
160
Temperature difference [K]
Temperature difference [K]
160
140
120
100
80
60
Round chamb. 20 bar, OF= 2.2
Round chamb. 20 bar, OF= 2.2
Rect. chamb. 20 bar, OF= 2.2
Rect. chamb. 20 bar, OF= 2.2
40
20
0
0
140
120
100
80
60
20
0
0.05
0.1
0.15
0.2
0.25
0.3
Round chamb. 20 bar, OF= 3.0
Round chamb. 20 bar, OF= 3.0
Rect. chamb. 20 bar, OF= 3.0
Rect. chamb. 20 bar, OF= 3.0
40
0
0.05
0.1
0.15
0.2
Axial length [m]
Axial length [m]
(a) OF =2.2
(b) OF =3.0
0.25
0.3
F IGURE 4. Wall temperature distribution at pc =20 bar
hardware, higher initial temperature of the test would lead, for the same test duration, to
higher levels of temperature. For this reason, only the temperature difference between
the signal at the evaluation time (t1 ) and at the initial time (t0 ) is taken into account. All
curves present a steady rise along the chamber axis until z=0.240 m and a short plateau
is identified in the last section, close to the nozzle, as indication of end of the reaction
process. Although any visible change on the tendency between the chambers for mixture ratio or pressure variations is observed, the temperature level increases for both
cases, as already seen for the heat flux analises with increasing mixture ratios.
Due to the different heat capacity of the chambers, an equal heat rate distributed on
the hot gas surface would lead to a higher temperature level for the chamber having
less mass to disperse the heat, if an equal heat up of the chamber wall material is considered. Therefore, a higher temperature level would have been expected for the round
combustion chamber. From the experimental results, instead, a different tendency has
been observed. The temperature level of the rectangular chamber (in red) is higher than
the one of the round chamber. This behavior can be explained by considering the difference between the internal goemetry of the chambers. For a similar heat flux distribution,
the difference in cross sectional area would lead to higher heat rate in the rectangular
chamber, since a larger hot gas surface has to be taken into account. The higher heat
rate leads, due to the same material properties, to higher temperature level in the rectangular chamber. Furthermore the effect of having a round flame in a square cross section
can not be neglected. The heat flux profile will have a maximum on the symmetry plane,
where the flat walls are closest to the injector element. Since the thermocouple positions are located on the symmetry plane, this would cause higher temperature readings
for the rectangular chamber. This hypothesis is confirmed by having a closer look to the
inner surface of the rectangular chamber after the test campaign. The color of the inner
wall in circumferential direction is not uniform. The central parts are brighter than the
color in the four corners, which corresponds to a higher level of the temperature color
scale. CFD simulations, ongoing at the Institute, have already confirmed this behavior.
Moreover, the non uniform distribution of the heat flux results in a smaller average heat
flux value for the rectangular combustion chamber, when compared to the average heat
flux of the round chamber.
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S. Silvestri, H. Riedmann, O. Knab & O. J. Haidn
F IGURE 5. 3D view of the square cross section chamber colored with the temperature field from
CFD
4. CFD Activities at Airbus DS
4.1. Modeling approach
Airbus DS has accompanied the experimental work with numerical simulations of the
square cross section chamber using the in-house CFD tool Rocflam3 as well as the
commercial code ANSYS CFX. Figure 5 shows a 3D view of the square cross section
chamber colored with the temperature field from CFD. The 3D CFD tool Rocflam3 is
currently under development at Airbus DS in Ottobrunn as designated successor of the
2D/axisymmetric in-house code Rocflam-II. The continuous gas phase is treated using
an Euler description solving the Favre-averaged conservation equations for mass, momentum and enthalpy in three spatial dimensions. The equations are discretized with
a Finite-Volume scheme for non-orthogonal, boundary-fitted and block-structured grids
according to the pressure based SIMPLE algorithm. The turbulence model used in this
work is the standard k-ǫ model by Jones & Launder. The commercial ANSYS CFX software is a high-performance, general purpose 3D fluid dynamics program that has been
applied to solve wide-ranging fluid flow problems for over 20 years. However, a customization of CFX is essential for the successful usage in rocket combustion simulations. This means that some in-house model extensions and adaptations are necessary
to achieve results with an acceptable quality. The modifications are attached to CFX e.g.
by the User Fortran Interface. The adaption process and the status of the Airbus DS tool
development are shown in Ivancic et al. [18].
For the numerical simulations of the single element methane combustion chamber,
main focus has been set on the investigation and comparison of different chemistry
modeling approaches regarding their suitability for methane combustion simulation in
an industrial environment. In a first step an equilibrium based mixture fraction PPDF approach which gives very good results for hydrogen combustion [19] has been applied for
methane combustion modeling. As is known, the chemical reaction speed of methane
combustion is significantly lower than for hydrogen so that non-equilibrium effects gain
increasing importance. The neglect of these effects in the equilibrium based model has
shown to lead to a strong overestimation of the wall heat flux. For this reason a global
chemistry scheme based on Westbrook & Dryer [20] has been derived for the combustion of methane. As another alternative, a freezing technique for the equilibrium based
chemistry model has been introduced, where the gas composition within the chemistry
table is kept constant below a certain temperature, so that recombination at lower temperatures is prevented. The three mentioned approaches are explained in detail in [21].
While these combustion models have been tested with Rocflam3, another approach
- the well-known Flamelet model - has been tested with ANSYS CFX. Thereby, the adiabatic Flamelet tables were generated based on the ANSYS C1 mechanism. Unlike
Single Element Rocket Combustion Chamber
321
F IGURE 6. Axial wall pressure profile - comparison between simulation results and test data
the equilibrium based combustion model used in Rocflam3, the CFX Flamelet approach
also includes chemical non-equilibrium conditions, characterized by the scalar dissipation rate. For high scalar dissipation rates or shear strain the Flamelet model accounts
also for possible (local) extinction of the flame. The influence of turbulence on combustion is considered via presumed PDFs. A deficiency of the current implementation of the
Flamelet model is that the chemistry table only depends on the mixture fraction, mixture
fraction variance and scalar dissipation rate, but not on the enthalpy (for constant mixture fraction) or pressure. This means that strictly speaking the species composition is
only correct for constant pressure and adiabatic conditions. This is more or less accurate
enough in the flame region, but close to strongly cooled walls or in nozzle extensions
where the pressure drops, the inaccuracies are rising.
4.2. Simulation results
The CFD results discussed here are valid for the load point which has been specified as
the "Transregio SFB/TRR40 Test Case 1", i.e. combustion chamber pressure of 20 bar
and mixture ratio of 2.6. Fig. 6 shows a comparison between the simulation results
obtained with Rocflam3 for the three different combustion models, CFX Flamelet and
experimental data for the wall pressure. The measured pressure level is underestimated
significantly by all available simulations - just as it has been observed in the SFB/TRR40
summer program: not a single CFD simulation matches the measured pressure level.
Of course, this disagreement not only questions the quality of the simulation results but
also the method of test case set-up. The fact that the capacitive hardware is not in a
steady state during the test data evaluation interval makes the use of these data for a
steady state test case at least arguable. Since a steady state computation cannot follow
the local temporal flow evolution and hence the history of the material heat-up, it is
questionable if the wall temperature and heat flux measurements during a transient can
fit to a steady flow field simulation. The data which will be obtained for the calorimetric
multi-element chamber during the upcoming year may provide valuable information in
this context as a steady state will be reached there.
Fig. 7 shows a comparison between the available Airbus DS simulation results and the
322
S. Silvestri, H. Riedmann, O. Knab & O. J. Haidn
F IGURE 7. Axial wall heat flux profile - comparison between simulation results and test data
experimental data for the specific wall heat flux. Despite the underestimation of the measured pressure profile the agreement is quite well for the CFX Flamelet approach while
the wall heat flux is significantly overestimated both by the Rocflam3 global chemistry
approach and by the equilibrium based PPDF approach. The freezing technique for the
PPDF chemistry leads to a strong reduction of the computed wall heat flux compared to
the standard PPDF approach bringing simulation and test closer together but the shape
of the profile does not compare well with the experimental data. A very important deficiency of the global chemistry approach is that it leads to a strong overestimation of
the flame temperature (not shown here). This is most probably due to the very small
mechanism (7 species, 3 reactions) which is applied here.
Two tasks result from these observations: First, the applied global chemistry mechanism must be revised in order to achieve a more realistic temperature field. Second,
the freezing technique must be improved in order to affect the simulation results only
in regions where it is intended to. This is where Airbus DS will put its further efforts in
order to be able to deliver valuable simulation results for the multi-element chamber with
Rocflam3 and with ANSYS CFX.
5. Conclusion
In the context of the national research program Transregio SFB/TRR-40 on “Technological Foundations for the Design of Thermally and Mechanically Highly Loaded
Components of Future Space Transportation Systems”, two single element chambers
using gaseous oxygen and gaseous methane are experimentally tested and compared
at relevant rocket engine conditions. The two chambers mainly differ in their cross section, round and rectangular, and in their chamber wall thickness. Several parameters
are maintained constant between the two combustion chambers to assure similarity of
the combustion process. Since the injector element has the biggest influence on the
performance and heat flux characteristics, in both combustion chamber configurations
the injector element is kept the same. Tests are performed maintaining the combustion
chamber pressure in the different configurations. Although similar heat flux levels are
Single Element Rocket Combustion Chamber
323
reached, the integral heat flux level, obtained for the rectangular chamber, is slightly
lower compared to the round combustion chamber. This can be attributed to the effects given by the presence of the corners and the stronger recirculation zone in the
rectangular chamber. On the numerical side represented by Airbus DS, the work on
methane combustion modeling is not yet completed. Based on the experience for the
single-element chamber with square cross section, the Flamelet approach seems to be
well suited for the industrial application while there are open tasks for the combustion
models used in Rocflam3. In addition to that, it is necessary to investigate several combustion chamber configurations for a proper tool validation. Therfore, the simulations
will take advantage of the experiments performed with the multi-element water cooled
combustion chambers that will follow.
Acknowledgments
Financial support has been provided by the German Research Foundation (Deutsche
Forschungsgemeinschaft – DFG) in the framework of the Sonderforschungsbereich
Transregio 40.
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Sonderforschungsbereich/Transregio 40 – Annual Report 2015
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Experimental Flow Separation Study in Stiff
Ovalized Rocket Nozzles
By C. Génin, D. Schneider, A N D S. Jack†
German Aerospace Center, DLR, Institute of Space Propulsion
Langer Grund, 74219 Lampoldshausen, Germany
Nozzle ovalization is a highly complex problem involving flow structure interaction. The
numerical investigations conducted until now often lack reliable experimental data for
validation. A step-by-step investigation of the ovalization problem, both experimentally
and numerically, has been started as a cooperation regrouping different institutes of the
German Aerospace Center (DLR). The work presented in this study concentrates on the
experimental aspect, conducted at the Institute of Space Propulsion in the framework of
the SFB Transregio 40. For this purpose, three nozzle geometries were deformed and
tested under cold flow conditions. Each test specimen was equipped with several pressure ports in order to measure the pressure distribution along various axial lines. In addition to the pressure measurements, the exhaust flow shock system was recorded with
Schlieren optics. The nozzles were rotated around their own axis in 45◦ steps in order
to observe the flow from different points of view and reconstruct the three-dimensional
shock system. The data generated in this work will be used in the future to validate
numerical simulation of separated flow in deformed nozzles.
1. Introduction
Rocket nozzle structural deformation can result from small exhaust flow fluctuations,
combustion chamber pressure variation or irregularity in the nozzle structure. Initially,
two flow conditions must be differentiated depending on the nozzle pressure ratio (NPR,
ratio of total over ambient pressure). For high NPR values the nozzle is full flowing
(nominal operation conditions) and the supersonic flow attaches the wall over the entire
inner nozzle surface. For low NPR the nozzle flow is separated: the flow detaches from
the nozzle wall, resulting in a back flow region downstream to the separation position,
with sucked in ambient flow under nearly ambient pressure conditions. The last flow
condition is present during the transient start-up and shut-down of a rocket engine under
sea-level conditions and is therefore of special interest.
In case of a full flowing nozzle an inward bended nozzle wall increases the recompressing characteristic of the wall. As a result the pressure difference, which causes
the bending force, decreases (Fig. 1, left). The deformation tends to disappear and the
bending is damped.
However if the flow separates inside the nozzle, the same structure deformation is
reinforced by the nozzle flow. An outward bending of the contour shifts the separation
position upstream, increasing the local wall pressure, and hence the structure deforma† Institut of Aerodynamics and Flow Technology, Braunschweig, Germany