MODELING OF H2/O2 SINGLE-ELEMENT ROCKET THRUST CHAMBER COMBUSTION AT SUB- AND SUPERCRITICAL PRESSURES WITH DIFFERENT COMPUTATIONAL FLUID DYNAMICS TOOLS

This paper derives from the cooperation between DLR and Airbus DS within the work package ¤CFD Modeling of Combustion Chamber Processes¥ conducted in the frame of the Propulsion 2020 project. In a joint strategy, DLR Gottingen and Airbus DS Ottobrunn have identi¦ed a number of test cases with gradually growing complexity where adequate test data are available for proper successive validation of the computational §uid dynamics (CFD) tools to be used in an industrial environment. This work highlights the simulation results for the Mascotte A-10 and A-60 test cases as presented at the 2nd International Workshop on Rocket Combustion Modeling in Lampoldshausen 2001 by ONERA and SNECMA [1]. These two test cases are characterized by di ̈erent chamber pressures (10 and 60 bar) and, consequently, by oxygen injection conditions which are subcritical in one case and transcritical in the other case. The test cases are treated with three di ̈erent CFD codes: the DLR TAU Code (only A-60 case), the Airbus DS in-house tool Roc§am3, and the commercial CFD tool ANSYS CFX incorporating several modeling extensions by Airbus DS. To the knowledge of the authors, this paper is the ¦rst one which covers both the A-10 and the A-60 test cases.


INTRODUCTION
The main target of the cooperation between DLR and Airbus DS within Propulsion 2020 is extending knowledge and competence in the area of rocket propulsion combustion devices, particularly, with regard to test, modeling, and simulation capabilities.One of the work packages is focused on CFD modeling of the hot gas §ow and the hot gas-side heat transfer in rocket thrust chambers.This work package is executed in close cooperation between the DLR Institute of Aerodynamics and Flow Technology and Airbus DS.The ¦rst results emanating from this cooperation have been published by Ivancic et al. [2].They cover the numerical simulation of the well-known Penn State test case which deals with the combustion of preburned, i. e., gaseous, hydrogen, and oxygen in a single-element combustion chamber under supercritical conditions.Thereby, very good agreement could be achieved between the three applied CFD tools and the available wall heat §ux test data.In the second step, these CFD tools are now used for simulating the Mascotte test cases A-10 and A-60 (see [1] for o©cial test case descriptions) where two very similar combustion chambers (see section 2 for details) are operated in the sub-and supercritical pressure regime, respectively.In order to be applicable for the simulation of combustion and §ow in real rocket thrust chambers, a simulation tool must be able to cope with these conditions.
The three applied CFD tools are the Airbus DS in-house tool Roc §am3, the commercial code ANSYS CFX (equipped with several modeling extensions implemented by Airbus DS via the User Fortran interface), and the DLR TAU code.Further details on these codes and on the used models are given in section 3. The main goal of performing analog Reynolds-average NavierStokes (RANS) simulations with three di¨erent tools is to provide a broad spectrum of data for the assessment of the applied modeling methodologies regarding their suitability for rocket thrust chamber simulations.
In the end, the developed CFD tools with their speci¦c models and methods will be applicable in the design and optimization processes of real rocket thrust chamber hardware.Hence, each tool must comprise a package of models enabling it to simulate multiinjector full-scale combustors in a reasonable time frame thereby encompassing the driving mechanisms such as propellant disintegration, combustion, and heat transfer.Performing single-element combustor simulations as addressed in this paper is considered a valuable milestone for the validation of the CFD tools.Thereby, it should always be kept in mind that the elaborated settings must be transferable to multiinjector simulations since only the latter can support engine layout and contribute to reduce development time and cost (see Knab et al. [3]).

Mascotte A-10 Test Case
The Mascotte A-10 test case has been described in detail by Vingert and Habiballah [4].Therefore, only a short description is given here.In this case, the Mas-Figure 1 Sketch of the Mascotte combustor (taken from [4]) cotte H 2 /O 2 combustor works at a subcritical chamber pressure of 10 bar and a mixture ratio of 2.11.The chamber has one shear-coaxial injector located on the center axis.Liquid oxygen (LOx) is injected in the core of the injector with a temperature of 85 K whereas the surrounding hydrogen is injected in gaseous state at 287 K. Liquid nitrogen is used to cool down the oxygen before injection.The oxygen mass §ow rate is 50 g/s and the hydrogen mass §ow rate is 23.7 g/s.The diameter of the oxygen tube is 5 mm and the diameters of the hydrogen annulus are 5.6 and 12 mm.This results in a momentum ratio of J = 15.4 and a velocity ratio of 146.3 between fuel and oxidizer.A sketch of the Mascotte combustor is shown in Fig. 1.The chamber has a square cross section with an edge length of 50 mm.The distance between the injection plane and the throat is 478 mm.The throat diameter is 15 mm.For the purpose of optical diagnostics, the chamber is equipped with helium-cooled quartz windows on two sides.The helium cooling mass §ow rate is not given in the test case description and, consequently, is not taken into account by the simulations.Nevertheless, one must be aware of the nonquanti¦ed inaccuracy which is introduced due to this simpli¦cation when comparing simulation and experiment.
Furthermore, it is noticeable that neither the operation point (combination of chamber pressure and mixture fraction) of the Mascotte A-10 test case nor the geometry of the chamber is representative for common rocket engines.The area contraction ratio between chamber and throat is ε c = 14.1 and the characteristic chamber length (quotient of chamber volume and throat area) is = 6.6 m.Both values are notably higher than they are for common rocket engines like, for example, the space shuttle main engine, Vulcain, and HM7.For those engines, contraction ratios of the order of 2.5 ≤ ε c ≤ 3 and characteristic lengths of 0.7 ≤ l * ≤ 0.8 m can be found.Nevertheless, the A-10 test case is a very interesting and well reported test case to investigate the combustion of cryogenic propellants which is the reason why it has been chosen for this work.
Several authors have published experimental data resulting from the Mascotte A-10 case.The experimental data which are used for comparison with the numerical results in this work originate from two publications: there are an Abel-transformed emission image and mean temperature pro¦les published by Candel et al. [5] as well as additional mean temperature pro¦les published by Grisch et al. [6].The emission images are shown in Fig. 2.
Figure 2a shows the average emission image whereas Fig. 2b shows the Abeltransformed emission image which is suited to be compared with contour plots of the OH * radiation computed from numerical simulations.Note that the Abel transformation acts on the assumption of an axisymmetric §ame shape which is not necessarily applicable for the Mascotte combustor that has a square cross section.For the available CFD results, the evaluation of the OH * radiation is performed according to the a posteriori method proposed by Fiala and Sattelmayer [7].The aforementioned temperature measurements have been obtained by coherent anti-Stokes Raman scattering (CARS) thermometry.The mean temperature values, the measurement locations, the standard deviations, and the validation rates can be found in the cited publications [5,6].While Candel et al. [5] only show test data based on H 2 concentrations, Grisch et al. [6] also show test data based on H 2 O concentrations.Both are used for comparison with the simulation results (see subsection 4.1).Although being highly turbulent, the combustion process is said to be stationary in both cited publications which is a main requirement for the RANS simulations presented in this work.

Mascotte A-60 Test Case
The Mascotte A-60 test case has been described in detail by Thomas and Zurbach [8].A short description highlighting the di¨erences to the A-10 test case is given here.In this case, the Mascotte combustor works at a chamber pressure of 60 bar (supercritical for both H 2 and O 2 ) and a mixture ratio of 1.4.While the chamber pressure is representative for common rocket thrust chambers, the mixture ratio is not.The injection temperatures are the same as for the A-10 test case (85 K for O 2 and 287 K for H 2 , i. e., O 2 is injected transcritical and H 2 supercritical), but the propellant mass §ow rates are higher: the oxygen mass §ow rate is 100 g/s and the hydrogen mass §ow rate is 70 g/s.The diameter of the oxygen tube is again 5 mm but the diameters of the hydrogen annulus are 5.6 and 10 mm, i. e., the outer diameter of the hydrogen annulus is reduced by 2 mm compared to the A-10 test case.This results in a momentum ratio of J = 13.8 and a velocity ratio of 54.3 between fuel and oxidizer, i. e., while the momentum ratio is comparable to A-10, the velocity ratio is signi¦cantly lower.The throat diameter is 6 mm smaller than for the A-10 case and thus amounts to 9 mm.
Figure 3 shows the OH * emission images for the A-60 test case.These pictures have been obtained from [9].To the knowledge of the authors, no discrete temperature values from CARS measurements are available in literature for the A-60 load point exactly as it has been de¦ned by Thomas and Zurbach [8].However, there are CARS data available from Habiballah et al. [10] who refer to the A-60 load point as an operating point with a hydrogen mass §ow rate of 75 g/s which is 5 g/s more than Thomas and Zurbach [8] state for A-60.Nevertheless, these data will be used for comparison with the simulation results in subsection 4.2 whereby it has to be kept in mind that the load points from simulation and experiment not being identical introduces a further unknown deviation when comparing one with the other.An axial temperature distribution for the A-60 test case has been published by Poschner and P¦tzner [11] which is also used for comparison.Because the authors neither give detailed information about the origin of these data nor about the radial location where the values have been obtained, they are here interpreted as temperature values on the axis.

Roc §am3
The three-dimensional (3D) CFD tool Roc §am3 is currently under development at Airbus DS in Ottobrunn as designated successor of the two-dimensional (2D) / axisymmetric in-house code Roc §am-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 ¦nite-volume scheme for nonorthogonal, boundary-¦tted, and block-structured grids according to the semiimplicit method for pressure linked equations (SIMPLE) algorithm described by Patankar and Spalding [12].
The turbulence model used in this work is the standard kǫ model by Jones and Launder [13].In order to account for the interaction between turbulence and chemistry, an equilibrium-based presumed probability density function (PDF) approach is applied.Thereby, the thermodynamic and transport properties obtained for chemical equilibrium are superposed with a one-dimensional (1D) Beta-PDF for the mixture fraction and then integrated over the mixture fraction range.Therefore, additional transport equations are solved for the mixture fraction and its variance.The computed values for enthalpy, pressure, mixture fraction, and mixture fraction variance are used for a table lookup of the integrated quantities.These quantities are temperature, density, molar mass of the mixture, heat conductivity, speci¦c heat capacity, viscosity, species concentrations, and the derivative of pressure with respect to density at constant pressure which is used in the SIMPLE algorithm for the compressible NavierStokes equations.
Roc §am3 comprises several approaches to model the propellant injection.The most common one is the inlet boundary with prescribed mass §ow rate.This boundary condition is well suited for the injection of gaseous and supercritical propellants where a continuum exists.It has been chosen for the A-60 test case.
When it comes to the injection of liquid propellants, the propellants are assumed to form a spray of small droplets which deserves a special treatment.Therefore, the injection of liquid propellants can be modeled via a Lagrangian module for propellant droplet tracking and evaporation in Roc §am3.This model has been adopted from Roc §am-II.A detailed description can be found in the work by Kniesner et al. [14].It has been chosen for the A-10 test case.
The Lagrangian module is loosely coupled to the Euler module.Propellants injected in liquid state are tracked throughout the §ow ¦eld until they have vaporized.Thereby, mass, momentum, and enthalpy are released and are transferred to the gas phase via source terms in the conservation equations.
To keep the computational e¨ort low, not every single droplet of the injected propellant is tracked but only a certain number of representative trajectories are computed.Therefore, discrete diameters and injection angles are de¦ned and assigned with speci¦c probabilities.For the propellant droplet tracking procedure, an equation of motion must be solved for each of these representative trajectories.Droplet vaporization is approximated using the model by Abramzon and Sirignano [15].
For the A-10 test case, Vingert and Habiballah [4] propose the injection of the oxidizer droplets on a conical solid boundary resolved by the grid to represent the LOx core.This has not been done with Roc §am3 in order to keep the computational grid as simple as possible.The same methodology is also applied for multiinjector con¦gurations (see [16]) which are in the main focus of Roc §am3.As proposed by Vingert and Habiballah [4], the oxygen droplet size distribution is modeled using a RosinRammler distribution with a mean diameter of 130 µm.In the simulation, this distribution is approximated using 25 discrete droplet sizes.The injection velocity is 2.18 m/s as given by Vingert and Habiballah [4].The droplets enter the domain along 30 discrete vectors with o¨-axis angles between 0 • and 15 • .With these settings, the spray is modeled by 23,500 representative trajectories.The gaseous hydrogen is brought into the domain not via an inlet boundary but via source terms for mass, momentum, and enthalpy.
Figure 4 shows the numerical grid used for the 3D simulation of the A-10 test case.Both the faceplate and the liner walls are modeled as adiabatic no-slip walls.Symmetry boundary conditions are applied in the xz-and the xyplanes.A supersonic boundary condition is set on the outlet.The grid consists of a total number of about 1.6 • 10 6 grid cells.The grid which has been used for the 2D/axisymmetric computations has similar resolutions in both axial and radial directions.In order for the chamber cross section in the 2D/axisymmetric simulation to be equal to the real value, a diameter of 56.42 mm has been chosen.
Almost the same grid (only the throat diameter is di¨erent) is used for the A-60 test case.However, as mentioned earlier, the Lagrangian module is not applied in this case.Several studies have been conducted with Roc §am3 using the Lagrangian module for the injection of the transcritical oxygen in the A-60 test case, but while they all showed good convergence behavior and plausible results, the agreement with the characteristic §ame shape known from the experimental data (see Fig. 3) was not satisfactory.Instead, a mass §ow inlet boundary condition is prescribed for both fuel and oxidizer, i. e., a so-called dense gas approach is applied.For the simulations with this inlet boundary condition, the prescribed in §ow turbulence intensity has shown to have a great in §uence on the §ame shape: increasing the turbulence intensity leads to a shortening of the recirculation zone which develops between the injection element and the chamber wall and, thereby, moves the position where the §ame expands in upstream direction.

DLR TAU Code
The DLR TAU code is a hybrid (structured/unstructured) grid ¦nite-volume §ow solver for the compressible Euler and NavierStokes equations.Turbulence models ranging from RANS one-and two-equation models to detached and large eddy simulations are available in TAU.It has been validated for a range of steady and unsteady §ow cases [17,18] including combustion in a rocket preburner [2].
For the current work, a MAPS+ Riemann solver is used in a Godunov type framework to handle low Mach numbers and high density gradients.Spatial second order is reached by a MUSCL (monotonic upwind scheme for conservation laws) reconstruction.Stabilization, if necessary for the computation of high den-sity ratio shear layers, is carried out by reducing the spatial order to 1.95.In this way, the numerical damping is minimally increased while mass, momentum, and energy remain conserved.Turbulence is accounted for using the one-equation SpalartAllmaras [19] model.Chemical source terms are computed using Arrhenius reaction rates.Here, Jachimowski£s [20] [21] found practically no di¨erence in the temperature ¦eld when comparing laminar chemistry to a PDF model of turbulent combustion.Thus, while envisioned for future studies, no dedicated turbulencechemistry interaction model is employed here.
Cryogenic oxygen, as encountered in rocket engines, thermodynamically acts as a real gas.Following an Eulerian rather than Lagrangian approach to injection modeling, a new real gas mixture model has been developed and implemented in the DLR TAU code, which only treats oxygen as a real gas and all other species as ideal.This is consistent with physical ¦ndings [22,23].Cryogenic oxygen is treated as an Eulerian continuum.This is straightforward for A-60 where due to nonexistent latent heat and surface tension, droplets are not observed [24].Oxygen real gas properties are computed from the high ¦delity modi¦ed Benedict WebbRubin equation of state (EoS) of Younglove [25] and stored in a library during a preprocessing step.Thermodynamic state variables, such as pressure, enthalpy, heat capacities, speed of sound, etc., are all computed consistently from the real gas EoS.Real gas corrections to the transport coe©cients are evaluated following Lemmon and Jacobsen [26].For all other species, an ideal gas EoS is solved.The model is described in more depth in [2729].It has been veri¦ed and validated by §uid data comparison with NIST, zaro-dimensional vaporization of LOx, and 1D combustion.As the injection model is Eulerian, boundary conditions simply correspond to the physical in §ow conditions measured in the experiment.The numerical setup for the A-60 test case is illustrated in Figs. 5 and 6.The §ow ¦eld is modeled as axisymmetric with a cross section corresponding to the physical chamber, i. e., the model chamber diameter is 56.42 mm.The in §ow is treated with respective Dirichlet boundary conditions at the injector.Figure 5 shows the grid structure: the shear layer and the dense LOx core are resolved and enclosed in a structured subgrid A which is embedded in an unstructured grid B. A close up of this region can be seen in Fig. 6.Region C is a coarser unstructured grid in a §ow region where resolution requirements are relaxed.All walls are considered as inviscid Euler walls.The pressure is determined in the simulation by the §ow through the choked nozzle and not prescribed as a boundary condition.
The corresponding version of the present article included in the proceedings of 6th EUCASS conference includes preliminary results for the A-10 test case obtained with the aforementioned attempt.While we feel that these results represent an adequate contribution to a conference, the utilized approach requires a more detailed evaluation before it should be included in an archival publication.Therefore, the corresponding results are not included in the present article.

ANSYS CFX
The commercial ANSYS CFX software is a high-performance, general purpose 3D §uid dynamics program that has been applied to solve wide-ranging §uid §ow problems for over 20 years.The heart of ANSYS CFX is its advanced solver technology.The highly parallelized solver is the foundation for an abundant choice of physical models to capture many types of phenomena related to §uid §ow.Due to the fact that the model development of ANSYS CFX is focused on turbomachinery issues, important physical problems related to rocket combustors cannot be simulated with CFX directly.A customization of CFX is essential for the successful usage in rocket combustion simulations.Therefore, high e¨ort has been invested in the adaptation of the CFX solver for the usage under these extreme thermodynamic conditions.This means that some in-house model extensions and adaptations are necessary to achieve results with an acceptable quality.The modi¦cations 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 [2].
Apart from the investigation of the in §uence of the di¨erent turbulence models and turbulence intensities, the sensitivity of the combustion modeling was investigated.CFX can use the Flamelet model, eddy dissipation concept, and an equilibrium-based turbulent combustion model for the simulation of rocket combustion chambers.The equilibrium-based combustion model is not a CFX standard combustion model.It was developed and implemented via user de¦ned functions into CFX by Airbus DS.
As for the chemical equilibrium model, only two transport equations have to be solved for the CFX-Flamelet approach which leads to very low computational costs.The species composition for a certain mixture fraction is read from Flamelet tables which are generated in a preprocessing step.Unlike the equilibrium combustion model, the CFX-Flamelet approach also includes chemical nonequilibrium 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 §ame.The in §uence of turbulence on combustion is considered via presumed PDFs.A de¦ciency 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 §ame region, but close to strongly cooled walls or in nozzle extensions where the pressure drops, the inaccuracies are rising.
The §uid properties in CFX are extended with real gas data and sophisticated mixing rules for viscosity and heat conductivity are implemented also via user de¦ned functions.
The turbulence model in the CFX-simulations is the Shear Stress Transport (SST) model [28].It is a kω-based turbulence model, which has advantages for the near-wall treatment in the low Reynolds number region.In this region, the kω-based turbulence model is more accurate and robust compared to the kε turbulence model.In the free shear §ow region, the SST model switches with a blending function from the kω to the kε turbulence model which has here its strength.
For both Mascotte cases (A-10 and A-60, i. e., sub-and supercritical pressure regimes of a cryogenic LOx/H 2 injection), a two-phase §ow (particle-laden gas §ow) with subsequent spray combustion is an appropriate model description.In CFX, the two-phase §ow is simulated via a Lagrange approach for the droplets and an Euler description for the gas phase.The evaporating LOx droplets are accounted in the gas solution via source terms for mass, momentum, mixture fraction, and energy.When approaching the critical point, the two-phase regime transforms to a single-phase description.As shown in earlier publications (see, e. g., [31]), this regime can still be treated by a Lagrangian approach, taking special care of the fact that surface tension and evaporation enthalpy vanish above the critical point.In this Lagrangian approach, injection velocities, densities, and temperatures of the sub-and transcritical propellants are captured correctly.The hydrogen jet is completely described within the Euler equations (dense gas approach) and appropriate §uid property data bases are essential for accurate description of the mixing process of the cryogenic propellants (LOx droplets and dense hydrogen) with the surrounding hot gases.The thermodynamic and transport properties of the propellants are stored in real gas property tables down to cryogenic temperatures.For lower temperatures, i. e., below 700 K, these tables are generated with a §uid property data base to correctly capture real gas e¨ects.For higher temperatures, i. e., above 1000 K, ideal gas properties can be assumed.For the transition range between 700 and 1000 K, a blending function is implemented ensuring a smooth transition between both data sets (real to ideal gas properties).By this approach, it is ensured that also the subsequent combustion process at much higher temperatures is covered accurately.Moreover, validation studies revealed that the mixing laws are important in order to get satisfying results.Especially for a correct simulation of the mixing process and wall heat §uxes, a proper modeling of the gas mixture properties (like thermal conductivity) is essential.
The CFX simulations shown here are quasi-2D/axisymmetric simulations assuming rotation symmetry of the geometry.The model chamber diameter is 56.42 mm, i. e., the cross section is equal to the original value.The LOx droplet injection is realized via a cone at the LOx inlet representing the LOx core, where the droplets are released with correct mass §ow, momentum, and energy but with assumed droplet size distributions and velocity angles ¡ just as proposed by Vingert and Habiballah [4] for the A-10 test case.The same approach is applied for the A-60 test case, but the droplet size distribution mean diameter is reduced to 80 µm.Figure 7 shows the numerical mesh for the 2D/axisymmetric CFX simulations.

Mascotte A-10 Test Case
Before comparing the simulation results from Roc §am3 and CFX, attention will be attracted to the temperature ¦elds computed by Roc §am3 in a 3D and The §ame is much longer in the 3D case.In addition to that, the 3D simulation reveals that the quadratic chamber geometry has a signi¦cant in §uence on the §ame shape via the recirculation zones in the four corners.This is visualized in Fig. 9 where the temperature ¦elds for three slices at distinct axial locations are shown for the Roc §am3 simulation.(Note that 360 • are shown here while the actual Roc §am3 domain covers only 90 • .)This result shows that it is worthwhile to make some e¨orts towards the 3D simulation capability even for this simple single element con¦guration.Therefore, all following ¦gures show Roc §am3 3D results.Figure 10 shows the computed OH* molar concentrations (for details on the a posteriori computation, see [7]) in comparison to the experimental OH* emission images from Candel et al. [5].It should be noted that the experimental data are time-averaged data, whereas the CFD results stem from the solution of time-and density-averaged equations.To further assess this, it would be interesting to compare them with simulation results from time-accurate CFD, which are, however, not available here.While in comparison with the test data both the Roc §am3 3D simulation and the axisymmetric CFX simulation reproduce the §ame shape quite well, they unveil completely di¨erent §ame lengths.The OH * emission image unfortunately does not give an information about the §ame length as it only covers a part of the §ame.The absolute levels of the OH * concentrations are di¨erent for the two simulations, but the experiment does not give a reference value.Thereby, CFX predicts a higher OH * concentration than Roc §am3.
At this point, it is important to emphasize again that the Roc §am3 3D simulation, which has been performed on a quarter segment of the square cross section, does not show an axisymmetric §ame shape (see Fig. 9) as assumed by both the 2D/axisymmetric simulations and the Abel transformation which has been applied to the test data in order to generate the shown OH * emission images.This suggests that the comparison with the OH * emission image should not be exaggerated ¡ a more or less good agreement with the OH * emission image might be as much as can be concluded from this comparison.
Figure 11 shows the temperature ¦elds from Roc §am3 and CFX.In the recirculation region, which is located in the upper left corner of the domain, CFX computes lower temperatures than Roc §am3.Looking at the cold oxygen-rich cores, CFX shows a very long and broad cold core thereby indicating a weak mixing normal to the main §ow direction.The maximum temperatures computed by Roc §am3 and CFX are 3112 and 3254 K, respectively.Due to turbulence chemistry interaction, they are lower than the stoichiometric combustion temperature of 3380 K at 10 bar (computed with CEA2 (Chemical Equilibrium with Applications v.2) [32]).
In order to further assess the agreement of the simulations with the available test data, attention is now attracted to the quantitative comparison with the discrete temperature values from CARS measurements as shown in Fig. 12. Figure 12 is divided into four charts, each showing the axial temperature pro¦les at a distinct radial location (0, 5, 10, and 15 mm).It should be noted that the 3D Roc §am3 simulation results are shown in the form of temperature pro¦les evaluated in the xy-plane.
The Roc §am3 temperatures show very satisfactory agreement with the CARS data in all four charts.There are only a few measuring points where Roc §am3 exceeds the standard deviation range around the measured mean value.The CFX results unveil too low temperature values on the axis (y = 0 mm) in the ¦rst part of the chamber indicating that the computed cold and dense core might be too long in this simulation.However, the agreement with both Roc §am3 and the CARS data becomes better with increasing radial distance from the axis.According to the CEA2 code [32], the chamber temperature for the A-10 case is around 2118 K, a value which is approached by both Roc §am3 and CFX at the end of the cylindrical part.

Mascotte A-60 Test Case
Before comparing the simulation results from Roc §am3, TAU, and CFX for the A-60 test case, attention will again be attracted to the temperature ¦elds computed by Roc §am3 in a 3D and a 2D/axisymmetric simulation visualized in Fig. 13.In contrast to the A-10 test case, where major di¨erences between the 2D and 3D results are given, they are much more similar here ¡ primarily, the positions of the §ame shoulder are slightly di¨erent.The probable main reason for this is that the Roc §am3 3D simulation of the A-60 test case computes a §ame shape which is almost axisymmetric (not shown here).This is not the case for the A-10 test case, i. e., the axisymmetric modeling in Roc §am-II is a better approximation for the A-60 case than for the A-10 case.This also leads to the fact that the application of the Abel transformation for the processing of the OH * emission images seems to be better suited in this case.Nevertheless, all following ¦gures show Roc §am3 3D results.
Figure 14 shows a qualitative comparison of the numerically determined OH * molar concentrations (for details on the applied a posteriori method, see [7]) with the experimental OH * emission image.The emission images again give only qualitative information.The OH * comparison shows that all three codes compute qualitatively similar §ame shapes ¡ just as for the A-10 test case: the TAU §ame is the shortest and CFX produces the longest shape.As the §ame is not fully captured in the measurement, it remains unclear how long it actually is ¡ just as for the A-10 test case.Nonetheless, TAU seems to underestimate the §ame length somewhat.While the axial position of maximal radial §ame spread (¤shoulder¥) is captured quite well by all methods, the three simulations show OH * concentration maxima at di¨erent locations.The experimental OH * inten- In comparison to the A-10 test case, the A-60 case features a smaller §ame opening angle and the §ame shoulder is located further downstream, but the computed §ame lengths are not that di¨erent.There is obviously a correlation between the propellant injection momentums (notably higher for A-60) and the §ame shape, which to be reproduced by the here.
Figure 15 visualizes the temperature ¦elds computed in the three simulations.The maximum temperature distribution follows the §ame shape shown in the OH * concentration plots in Fig. 14.Injected hydrogen and oxygen are seen as cold streams entering the chamber, the §ame develops between both streams.Consistent with the classical literature, the §ame is seen to isolate oxygen and hydrogen stream in all computations.TAU predicts the coldest recirculation zone but the hottest §ame: the adiabatic §ame temperature of stoichiometric H 2 /O 2 combustion at 60 bar of approximately 3623 K (computed with CEA2 [32]) is slightly overestimated by TAU, whereas Roc §am3 and CFX give maximum temperatures of 2840 and 3490 K, respectively.This discrepancy is caused by di¨erent levels of turbulence in the §ame region.The di¨erence is much stronger than in the A-10 test case.Going along with the shortest and hottest §ame, the shortest cold core is in the TAU computation.The maximum §ame temperature computed by Roc §am3 for the A-60 test case is lower than the value computed for the A-10 test case.This is due to high in §ow turbulence which had to be prescribed in Roc §am3 in order to reproduce the characteristic §ame shape for the A-60 test case.
It is interesting to evaluate the length of the cold core when the density, visualized in Fig. 16, is taken into account as well.Roc §am3 and TAU model the injected oxygen as an Eulerian continuum, the high LOx core density of 1100 3  hence, re §ected in the contour plot.The CFX simulation employs a Lagrangian treatment of LOx droplets, the high density is thus present in the disperse Lagrangian phase instead of the Eulerian carrier phase and is due to that not visible in Fig. 16.So, while CFX predicts the longest cold core, TAU predicts oxygen core with the highest density.
Figures 17 and 18 show a comparison of experimentally obtained temperature pro¦les with simulation results.Figure 17 shows radial pro¦les and Fig. 18 shows an axial one.All simulation results in Fig. 17a, which shows the radial temperature pro¦les at the axial position x = 50 mm, exhibit a distinct peak close to the injector before §attening out to a plateau closer to the chamber wall.As before, TAU predicts the highest peak temperatures, whereas Roc §am3 and CFX predict lower peak temperatures due to the in §uence of turbulencechemistry interaction taken into account by these two simulations.The experimental data does not exhibit a peak at all but remains rather level, the value lying between Roc §am3 and TAU outside of the peak.The experimental data not showing a peak at all here is misleading as the OH * emission image clearly shows that the §ame is present at the axial position x = 50 mm (see Fig. 14).This suggests that there must be a temperature peak which is obviously not resolved by the CARS measurements here.
At the axial position of x = 100 mm as shown in Fig. 17b, the three temperature pro¦les from the simulations again show similar general shapes while the absolute values partly di¨er considerably.The pro¦les from CFX and Roc §am3 almost coincide for a radial position farther than 5 mm from the centerline and agree su©ciently well with the measurements.Towards the centerline, all three codes predict a cold core, while the experimental results show a higher temperature at the axis.However, the validation rate of 5% of the CARS data is rather low here.This is probably due to the fact that the CARS data have been obtained based on H 2 molecules which might not occur at the axis quite often.It should also be kept in mind that the CARS data by Habiballah et al. [10] are valid for a slightly di¨erent load point (see subsection 2.2).
Finally, Fig. 18 compares the CFD results with an axial CARS temperature pro¦le which is ¡ due to missing information ¡ assumed to contain values measured on the axis.Three regions may be distinguished: a cool core at the beginning, the hot §ame with a peak in the center, and a plateau in the chamber behind the §ame.The plateau approaches the value of ∼ 1600 K, which is the adiabatic §ame temperature that CEA2 [32] computes for this test case inside the chamber.The temperature pro¦les from the simulations are again similar in shape, but di¨er regarding absolute values and also regarding the axial position of the maximum temperature peak.Interestingly, the three codes predict di¨erent parts well: CFX captures the low temperature in the core; TAU the position and magnitude of the peak; and Roc §am3 the plateau behind Figure 18 Temperature pro¦les along the x axis and comparison to available test data [11]; see top picture (Roc §am3 result) for orientation: 1 ¡ Roc §am3; 2 ¡ TAU; 3 ¡ CFX; and 4 ¡ text data the §ame.The main reason why CFX shows higher temperatures in the core than Roc §am3 and TAU is that the Lagrangian approach is applied in CFX.It must be noted that Habiballah et al. [10] give a temperature of ∼ 2100 K for x = 100 mm on the center axis (see Fig. 17b) while Poschner and P¦tzner [11] give a value of ∼ 3500 K for the same position (see Fig. 18).This is indeed a bit confusing and cannot be ¦nally assessed here.It stands out that the value given by Poschner and P¦tzner [11] is the only one which is close to the adiabatic §ame temperature for stoichiometric combustion inside a di¨usion §ame at 60 bar.However, turbulence is expected to reduce the §ame temperature here.

CONCLUDING REMARKS
This paper provides a comparison between the three di¨erent codes: Roc §am3, CFX, and TAU, being applied to the Mascotte A-10 and A-60 test cases, which operate in the sub-and supercritical pressure regimes of cryogenic coaxial injection.
The 3D Roc §am3 as well as the 2D/axisymmetric CFX simulation results (both EulerLagrange) show very good agreement for the A-10 test case both with the OH * emission image and with the available temperature values from CARS measurements.
For the high-pressure case, it is interesting to note that the three codes, which might be considered validated when comparing experimental OH * intensity and numerical OH * molar concentration, show very distinctly di¨erent §ame lengths and temperature distributions.Based on these results, one may conclude that a comparison between simulation and experiment on the basis on the OH * emission images alone is of minor signi¦cance.This is mainly due to the facts that the emission images do not give any quantitative information, that they only cover a small section of the chamber, and that they are based on the assumption of an axisymmetric §ame shape.One should de¦nitely include the CARS measurements for comparison with discrete temperatures.However, detailed information regarding the CARS method and the data evaluation procedure must be known such that simulation results can be compared in a reasonable manner.Also, very important is to be sure about the origin and the validity of the used test data.Especially for the A-60 test case, one can ¦nd several di¨erent OH * emission images in the literature and due to the fact that no CARS data have been presented alongside with the test case description, also, di¨erent temperature pro¦les have been published by di¨erent authors.Therefore, special attention is necessary here.
As already seen in previous cooperative work [2], the comparison between di¨erent CFD tools proves to be a valuable practice to review the characteristics of each modeling package.Regarding the proceeding validation of the applied modeling approaches, it must be emphasized that both Mascotte test cases are not representative for real rocket thrust chambers.Therefore, from an industrial point of view, no further e¨orts shall be put into the improvement of the agreement between simulation and experiment for these test cases.Instead, focus will be put on the transferability of the elaborated approaches on more relevant con¦gurations (for more information on the Airbus DS modeling philosophy, see [3]).

Figure 5 Figure 6
Figure 5 TAU grid structure

Figure 7
Figure 7 Numerical mesh for the CFX simulations of the Mascotte A-10 test case

Figure 10 OH
Figure 10 OH * radiation ¦elds for the Mascotte A-10 test case (comparison between simulation results and emission image from test [5], exponential color scale): (a) Roc §am3 3D; and (b) CFX