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Aerothermodynamics for reusable launch systems
Aerospace Science and Technology 8 (2004) 101–110 www.elsevier.com/locate/aescte
Aerothermodynamics for reusable launch systems ✩ Aerothermodynamik wiederverwendbarer Raumtransportsysteme C. Weiland a,∗ , J. Longo b , A. Gülhan c , K. Decker d a EADS-ST, 81663 München, Germany b DLR Institute of Aerodynamics and Flow Technology, 38108 Braunschweig, Germany c DLR Institute of Aerodynamics and Flow Technology, 51170 Köln, Germany d Lehrstuhl für Fluidmechanik TU München, 85748 Garching, Germany
Received 24 February 2003; received in revised form 30 July 2003; accepted 8 September 2003
Abstract The development of modern spacecrafts (launch and re-entry vehicles), either fully reusable or partly reusable needs powerful tools for the design of the aerodynamic shape with a guarantee for reliable flight and controllability along the complete ascent and descent trajectories. Experimental and numerical tools are available these days and for improving the reliability of vehicle design their capability has to be improved step by step. In the frame of the German TETRA Program very detailed technology work was carried out to reach this goal. The growth of the efficiency of these methods is demonstrated by some specific aerothermodynamic problems which are reported in this paper. 2003 Elsevier SAS. All rights reserved. Zusammenfassung Die Entwicklung moderner Raumtransportsysteme, die entweder teilweise oder vollständig wiederverwendbar sind, erfordert leistungsfähige Simulationswerkzeuge, sowohl auf dem experimentellen als auch dem theoretisch/numerischen Sektor. Dadurch soll gewährleistet werden, dass der aerodynamische Entwurf dieser Vehikel einen zuverlässigen und kontrollierbaren Flug sowohl während des Aufstieges als auch des Abstieges aus dem Orbit ermöglicht. Die experimentellen und numerischen Simulationswerkzeuge, die heute vorhanden sind, müssen Schritt für Schritt weiter verbessert werden, um dem oben beschriebenen Ziel näher kommen zu können. Um dieses Ziel zu erreichen sind im Rahmen des deutschen Technologieprogrammes TETRA Technologiearbeiten formuliert und durchgeführt worden, worüber in dieser Veröffentlichung berichtet wird. 2003 Elsevier SAS. All rights reserved. Keywords: Reusable launch vehicles; Hypersonic flow; Aerothermodynamics; High enthalpy windtunnel experiments; Numerical simulations
1. Introduction In the last fifteen years there has been a considerable progress in Europe in the field of aerothermodynamics not only on the theoretical/numerical side but also on the experimental side. The activities started with the beginning of the European Hermes Project and were continued in the CRV, MSTP, X-CRV and FESTIP programmes. On the national German side there was additionally intensive aerothermodynamic technology work in the Sänger project (hyper✩
This article was presented at the German Aerospace Congress 2002.
* Corresponding author.
E-mail address: [email protected] (C. Weiland). 1270-9638/$ – see front matter 2003 Elsevier SAS. All rights reserved. doi:10.1016/j.ast.2003.09.003
sonic technology programme) and more recently within the TETRA/X-38 and ASTRA programmes. Aerothermodynamics is a key technology for the successful design of new space transportation vehicles, where a safe access to space should be guaranteed under the requirements of reducing uncertainties in existing aerodynamic data bases and by that margins of the vehicle design. This process is done step by step with the goal of gaining decreased weight and operational costs. Aerothermodynamics essentially defines the shape of the vehicle and strong interactions exist between this discipline and the vehicle lay-out, the GNC (⇒ flight mechanics) and the propulsion system, furthermore the disciplines of structures, materials and thermal protection systems need the aerothermodynamic data as input.
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Nomenclature s arc length L length CRV Crew Return Vehicle Re Reynolds number MSTP Manned Space Transportation Programme Reynolds number built with x-coordinate Re x TETRA Technologien für zukünftige Raumtransportsysteme k turbulent kinetic energy FESTIP Future European Space Transportation ω dissipation rate Investigation Programme ε emissivity factor ASTRA Ausgewählte Systeme und Technologien für α angle of attack zukünftige Raumtransportsystem-Anwendungen η angle of control flap deflection GNC Guidance, Navigation and Control R&D Research and Development Subscripts RCS Reaction Control System eff effective IR Infrared o total SST Shear Stress Transport Model bf body flap LC Liquid Crystal w wall Symbols ref reference cog center of gravity M Mach number ∞ infinity T temperature Abbreviations
Within the frame of the TETRA program an extensive numerical and experimental research program was established under the lead of DLR with participation of ASTRIUM, DLR R&D Institutes and the Universities of Stuttgart and München. The program focused on the improvement of the experimental and theoretical prediction capabilities for the following aerothermodynamic problems: • Local aerothermodynamic flows. • High enthalpy flows including radiation cooling (by means of view factor approach). • Wall catalycity. • Advanced turbulence modeling. • RCS-jet/external airflow interaction. • Laminar-turbulent flow-transition and Görtler vortices. • Dynamic stability derivatives. Where possible the same problems were modeled numerically, by CFD, and also simulated in windtunnels. In some cases, good to excellent agreement could be identified but in others there are still open questions. In the paper some outstanding results achieved during the TETRA program will be presented and the novelties will be highlighted and discussed.
phenomena have to be considered. Fig. 1 shows a typical reentry trajectory for the X-38 vehicle. In hypersonic flows viscous effects are very important. Viscous effects mean diffusive transport effects of mass, momentum and energy along and mainly across streamlines. These effects cannot be neglected and have to be accounted for. There is a strong coupling between the various diffusive effects. So the existence of a classical boundary layer means always that a thermal boundary layer exists, which is thicker for airflow than the viscous boundary layer since the Prandtl number is usually lower than 1 for air. Normally the boundary layers are turbulent in hypersonic flight for altitudes below approximately 55 km and hence the transition laminar-turbulent occurs also in that regime. The transition laminar-turbulent in hypersonic boundary layers is influenced by many flow parameters and properties: Reynolds number, Mach number, velocity field, thermal wall condition, entropy layer, surface roughnesss, etc., but
2. Flow physics along flight trajectory Since the goal of aerothermodynamics is both to define shapes of space vehicles, which can flight mechanically be controlled along complete trajectories and safely landed, and to determine the mechanical and thermal loads particularly in critical regimes of these vehicles, the relevant physical
Fig. 1. Physical phenomena along typical re-entry trajectory.
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unfortunately in three dimensional flow the transition criteria today available are completely unsatisfactory. Somewhat better is the situation for turbulence modelling, where for classes of problems appropriate two equation models give acceptable results within a certain Mach number range. Wall heat transfer affects all hypersonic viscous effects. It is governed by the state of the boundary layer (laminar, transitional or turbulent), by interaction phenomena (shock/boundary layer/vortex), real gas effects (chemical and thermal non-equilibrium), catalytic walls, heat radiation of walls etc. It should be mentioned that it is nearly impossible to measure flight-realistic wall heat fluxes in windtunnels for hypersonic velocities, since the surfaces of the models are usually cold and the windtunnel nozzles produce flows which are in a thermodynamic transition phase between frozen and non-equilibrium, which contrasts to the equilibrium free-stream to perfect gas during flight. With the help of Fig. 1 an overview is given about the gas behaviour for spacecraft flying with hypersonic Mach numbers in different altitudes. During the first part of a re-entry trajectory where the atmosphere is rarefied and the velocity of the space vehicle is large chemical, thermal and to some extent radiative non-equilibrium real gas effects occur. At these larger altitudes the decrease of freestream density causes an increase of reaction time. Since the freestream velocity is also growing in higher altitudes the characteristic reaction length becomes of the same order of magnitude as the typical vehicle reference length and hence the thermodynamic state of the air is in non-equlibrium. The temperature behind a bow shock is very high and leads to excitation of vibrations, dissociations of molecules of air, formations of other chemical species, ionisation and radiation of the gas moving around the vehicle surface. At lower altitudes the characteristic time of the reaction (vibrational, chemical, ionisational) is much shorter than the flight time of a fluid element travelling along the vehicle surface with the consequence that the gas can be regarded as being in local equilibrium. Further for corresponding low Mach numbers (M∞ 4) a perfect gas approach is appropriate.
3. Local aerothermodynamic flows During re-entry and hypersonic flight, space vehicles experience a strong increase of surface temperature (hot surfaces) due to the heat transfer from the flow side. As well known some of this heat will be radiated from the wall in the ambient. In case that the complete contour is of the convex type the radiation is not hampered, but for nonconvex (concave) configurations there are surface elements which “see” each other which induce complicate absorption and emission of radiated heat on such elements, leading to an increase of the wall temperature. This phenomenon can be treated by the view factor approach, where a visibility
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Fig. 2. Effective emissivity coeffients on X-38 shape; εeff = ε (εo = 0.85, s, T = 1000 K).
coefficient for every surface element is computed. Further by using this visibility coefficients a fictitious emissivity factor εeff can be derived, which can be found in [9,21]. This is a function of the emissivity of the material, the temperature and the visibility coefficients. A good example for this approach is the X-38 vehicle, where the fictitious emissivity factor are computed. Fig. 2 shows the result for εeff = ε (εo = 0.85, s, T = 1000 K). As expected εeff is considerably low in the cavity regime and on the leeward side in the rear part between fuselage and winglet. Certain shapes of space vehicles generate geometrical areas where local flow phenomena occur, for example: • deflected flaps and rudders with local change of boundary layer state influencing the efficiency of controls, • gaps and steps between deflected flaps and rudders leading to local overheating, • gaps between TPS tiles producing high enthalpy sneak flow with the tendency to create overheating. In the frame of the TETRA program a generic configuration (ramp with a gap at the junction to the ramp) was designed for investigating the basic flow phenomena occuring on deflected aerodynamic controls with gap along hinge lines in high enthalpy flow [1]. In DLR’s L3K plasma tunnel experiments were conducted (Fig. 3) and in parallel numerical simulation cases were defined and computed for revealing the influence of the level of physical modelling and the geometrical setting of the gap on the results. The following figures give a selection of the computed flow cases which were performed by using ASTRIUM’s DAVIS-VOL code [15,17]. Fig. 4 gives an overview of the configuration and the fictitious emissivity factor distribution (εeff ) where it can clearly be observed that inside the gap the effective heat radiation tends to zero. The general flow field is drawn in Fig. 5, where for an open gap the pressure contours are shown (M∞ = 7.27, α = 15◦ , chemical nonequilibrium, laminar).
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Fig. 6. IR image of flap model with open gap. Fig. 3. Flap model in arc heated facility L3K.
are comparable with the temperatures on the flap. The size of the separation bubble is smaller than that of the model with closed gap [8].
4. High enthalpy flows
Fig. 4. Geometry of generic test model; effective emissivity coefficients on εeff .
Fig. 5. Pressure contours of generic shape with open gap (M∞ = 7.27, α = 15◦ , chemical non-equilibrium real gas, laminar).
The 2D surface temperature distribution measured with an IR-camera in L3K provides clear information about the flow field and the heat flux rate distribution. Based on these data and comparisons with numerical results, the influence of the coupling between the flow and structure can be analysed. The IR image of the model with an open gap slot (Fig. 6) shows that the gap temperature reaches levels that
Within the X-38 program the aerodynamic and aerothermodynamic environment of the X-38/CRV is defined based on close cooperations between ground based testing and Computational Fluid Dynamics (CFD) calculations. This strategy is based on the fact that it is mandatory to validate the complex models required in CFD codes to describe high temperature effects such as chemical- and thermal non-equilibrium or the laminar to turbulent transition of the boundary layer using dedicated experimental investigations before they are used for computations at high Mach number re-entry conditions. The investigations of the 1:24 scale Model E of X-38 in the High Enthalpy Shock Tunnel Göttingen (HEG) of the German Aerospace Center (DLR) represent the first experiments of this configuration in the high enthalpy flow regime up to 22 MJ kg−1 , corresponding to a flight velocity of 6000 m s−1 , for pressure and heat transfer rate measurements. Parallel to these experimental investigations CFD rebuilding was employed using the DLR Navier–Stokes solver CEVCATS-N. CEVCATS-N is a multi-block finite volume flow solver for the stationary Euler and Navier–Stokes equations in integral form [13]. The normalized measured and computed heat flux distribution on the windward side of the X-38 fore body and the 20◦ and 30◦ deflected body flap is shown in Fig. 7 using HEG condition I (22 MJ kg−1 ). Overall, the comparison between experiment and CFD assuming a fully laminar flow is good for the 20◦ body flap deflection. However, when the body flap deflection is increased to 30◦ , the unexpected result was obtained that the measured body flap heat flux is approximately twice as high as predicted by laminar CFD. The high heat transfer level on the 30◦ body flap could be reproduced by performing a computation with laminar fore body flow and fixed transition in front of the hinge line. From an engineering point of view this is a very important result indicating that in spite of the fact that the unit free-stream Reynolds number of the high enthalpy
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Fig. 9. Temperature distribution on the lower side of the fuselage (εo = 0.80 right; ε = ε (εo , s, T ) left). Fig. 7. Normalized measured and computed heat flux on X-38 for the 20◦ and 30◦ deflected body flap.
Fig. 8. Flow details inside the cavity between deflected bodyflap and fuselage M∞ = 17.5, α = 40◦ , ηbf = 20◦ .
test flow would suggest that the flow should be laminar, the separated flow at the body flap hinge line may be governed by transitional or turbulent flow. Consequently the measured overheating must be taken into account when developing a design database for X-38/CRV. The X-38 vehicle creates in case of a deflection of the body flaps a cavity between the leeward side of the flaps and the fuselage where the flow is of interest for the correct design of the hot structures in this area. Here the radiation cooling of the walls is significantly reduced by different hot surfaces facing one another. Therefore a view factor approach was used in the Navier–Stokes computations. Due to this model, the effective emissivity factor εeff = ε (εo , s, T ) of the walls inside the cavity approach values close to zero and significant temperature differences on the leeward side of the body flap and the cavity ceiling of approximately 500 K when comparing with a computation assuming a constant emissivity factor of εo = 0.8 were found [7,18] (see Figs. 8, 9).
5. Advanced turbulence modelling One of the most challenging flow phenomena is given by the turbulence. Turbulent flows either in attached boundary layers, separated flow bubbles, in globally separated boundary layers or free mixing layers influence the mechanical and thermal loads very severely. Therefore it is well known that the wall heat fluxes and the effectiveness of deflected aerodynamic controls as well as base flows of space transportation vehicles are considerably affected by turbulence. During the design and validation process of shapes for space vehicles CFD methods play an increasing role, particularly in industry. Thus the turbulence has to be described on the one hand with methods which are relatively fast and not too expensive and which on the other hand achieve results which are accurate and reliable enough for industrial processes. With these provisos two equation turbulence models on the basis of Wilcox’ k–ω model are investigated as a reasonable compromise between algebraic and Reynolds stress models. They are independent on an algebraic length scale and take naturally into account history effects through transport equations. The models are developed for incompressible flows which have been adapted for compressible flows by considering the variable density effects through changes in the mean density. This method might be justified for Mach numbers M∞ < 5, but for larger Mach numbers compressibility correction models which affect the structure of the turbulence has to be taken into account. The objective of this study was to investigate the behaviour of three variants of the standard k–ω model, namely Wilcox’ low Reynolds number version, Menter’s Shear Stress Transport version and a realizable version. Further some compressible correction models in conjunction with the standard k–ω approach were tested [20]. The models were investigated in super- and hypersonic flat plate boundary layers, on a compression ramp at M∞ = 9.22 and on a hypersonic flow over the X-38 vehicle at M∞ = 6, where windtunnel data are available from NASA Langley Research Center. The complete issue of the numerical simulations using ASTRIUM’s DAVIS-VOL
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Fig. 10. Flow configuration for compression ramp.
Fig. 11. Mach number distribution on compression ramp.
Fig. 13. Influence of compressible corrections on pressure (above) and heat flux (below).
Fig. 12. Influence of turbulence model on heat flux.
code are reported in [19]. Here a selection of these results will be given. Figs. 10 and 11 show the flow situation for the compression ramp and the Mach number distribution. The shock induced flow separation can be clearly identified. For the five different turbulence models Fig. 12 gives an insight into the heat flux distributions at the compression corner and compares these results with experimental data [4]. None of these models predict the separation bubble correctly, but it seems that the potential of the SST- and the realizable models is higher than for the others. Adding the compressibility corrections “length scale” and “rapid compression” proposed in [3] the separation bubble is predicted correctly and the pressure and heat flux distribution show the most promising behaviour (Fig. 13). The flow around the X-38 shape is calculated for the conditions of the NASA Langley windtunnel (M∞ = 6.0, α = 40◦ , Re = 3.57 × 106 , ηbf = 20◦). Detailed heat flux measurement for the windward side exist, where a transition tripping device was fixed at 25% of Lref from the nose. In the computation using the SST model transition was triggered at 25% of Lref , too.
Fig. 14. Heat fluxes on X-38 windward side M∞ = 6.0, α = 40◦ , Re = 3.57 × 106 , ηbf = 20◦ .
The comparison of the experimental and theoretical data shows excellent agreement in the laminar and turbulent regimes, in particular in the area in front of the bodyflaps and on the bodyflaps themselves (Fig. 14). An evaluation of the heat fluxes along the red line (Fig. 14) is given in Fig. 15, where besides three different turbulence models (Note: these computations have assumed fully turbulent flow!) the SST model including the transition onset (simple switch from laminar to turbulent modelisation) at 25% Lref was drawn. As one can see the agreement in the laminar regime, at the transition point, the turbulent regime up to the body flap and on the body flap itself is really very promising.
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Fig. 16. LC visualisation and computed turbulent heat flux distribution. Fig. 15. Heat flux distribution (along the red line of Fig. 14); comparison of different turbulence models.
6. Transition laminar-turbulent Traditionally the prediction of flap peak heating for re-entry vehicles falls short of actual magnitudes in the case of a reattachment line of a separated boundary layer, especially in the transitional regime and in the presence of shock boundary layer interaction. The current practise of performing fully turbulent computations and multiplying the results by a constant uncertainty factor has obvious disadvantages. For this reason an investigation of transitional and separated flow phenomena at the X-38 flaps with experimental as well as numerical tools has been started at DLR. For the windtunnel testing two models were manufactured for various measurements and visualisations in the Ludwieg tube facility Göttingen under flow conditions of M∞ = 6 and a Reynolds number range of 2.1–8.8 × 106 . In addition the main analysis was carried out by the DLR CFD code CEVCATS-N, which was validated in a broad range of sub-, trans- and hypersonic flow cases for a variety of flow conditions and configurations. Examples are given in [2]. For the separated turbulent flow the compressible extended one-equation Spalart–Allmares model [14] was chosen. Windtunnel investigations have been carried out on a brass model for pressure and heat flux measurements, and a low cost model, manufactured in rapid prototyping technique for liquid crystal (LC) thermo-visualisations. For pressure and heat flux measurements CFD and windtunnel data have shown good agreement [10]. An example of LC visualisation in comparison with a simulated heat flux distribution under fully turbulent flow conditions (Re = 8.8 × 106 ) is given in Fig. 16. At the reattachment line of compressible separated boundary layers, spanwise periodic heat flux peaks, generated by counter-rotating streamwise vortices, similar to the well known Görtler vortices in concave curved boundary layers, are a typical phenomenon [11]. Within the numerical investigations it was possible to simulate such vortices on the X-38 flaps under laminar as well as transitional flow conditions by using significantly refined span-
Fig. 17. Heat loads on X-38 flap and visualisation of streamwise vortices.
wise computational grids of the flap region derived from the entire grid of the whole vehicle-flow field [12]. In Fig. 17 the heat flux on the flap surface, generated by the vortices is shown for a laminar case together with contour surfaces of the streamwise perturbation velocity in the boundary layer, which is an indicator for the appearance of vortexdisturbances. For a better view the boundary layer was thickened artificially in the visualisation. With this investigation the capability of streamwise vortex simulation in separated boundary layers for realistic hypersonic cases by CEVCATS-N was shown.
7. Jet/external airflow interaction The effectiveness of jets of reaction control systems is influenced by the outer flow field and in contrary the jet itself affects the outer flow sometimes to such an extent that strong changes of the pressure and the heat fluxes at the wall occur. Changing the pressure field at the wall leads mostly to an amplification of the thrust effect of the jet which has to be determined. On the other hand the boundary layer of the external flow field may separate by the firing thruster and afterwards reattach where in hypersonic flows due to thinning of the boundary layer, growing heat fluxes (hot spots) may appear. For the controllability of space
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Fig. 18. Thruster position on X-38 shape.
Fig. 21. X-38 with 400 N thruster, M∞ = 17.5, α = 0◦ , Mach contours and streamlines.
Fig. 19. X-38 with 110 N thruster, M∞ = 17.5, α = 0◦ , Mach contours and streamlines.
Fig. 22. X-38 with 400 N thruster, M∞ = 17.5, α = 0◦ , temperature and streamlines at the wall.
Fig. 20. X-38 with 110 N thruster, M∞ = 17.5, α = 0◦ , temperature and streamlines at the wall.
transportation systems mainly during re-entry it is very important to quantify the above described phenomena. To investigate these effects two different thrusters were installed on the X-38 vehicle, one with a nominal thrust of 110 N and the other with 400 N (Fig. 18). For both thrusters computations with DAVIS-VOL were performed for M∞ = 17.5, α = 0◦ and 40◦ , where laminar and equilibrium real gas flow was assumed [22]. In front of the 110 N thruster a horse shoe vortex appears which leads along the trace where the flow reattaches the wall to a strong increase of the wall temperature (approx. 1000 K) compared to the non-firing case (Figs. 19, 20). A different situation
will be found in the flow field with the 400 N thruster. Here no vortex upstream of the firing thruster can be identified, but a more distinct one behind the jet, which has a trace of reattachment which obviously lies in the plane of symmetry (Figs. 21, 22). The wall temperature increase by this effect is approx. 500 K. Further in Fig. 22 the reduction of the wall temperature in the regime where flow separation occurs (due to the forming vortex) can be clearly seen.
8. Dynamic stability derivatives Dynamic stability derivatives are used in flight mechanics to describe instantaneous aerodynamic reactions on manoeuvering flight vehicles. Especially if the natural stability becomes small, like in the lateral directional modes of motion of X-38 at low supersonic Mach numbers, the availability of a proper set of dynamic derivatives is essential. The evaluation of dynamic derivatives still belongs to the challenging tasks of both experimental and numerical aerodynamics. The reason is the usually small underlying physical effects that have to be measured or accounted for.
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Fig. 24. Computed and measured damping-in-pitch-parameter versus Mach Number (different angles of attack). Fig. 23. X-38-model mounted on dynamic balance in windtunnel TMK.
In the frame of the TETRA program two numerical methods and an experimental one, covering the Mach number range from subsonic to hypersonic speeds, are applied for dynamic derivative analysis. The approach of evaluating the dynamic derivatives is comparable in all three cases. A harmonic analysis is applied, to determine the stability derivatives using the time history of force- and moment coefficients as a reaction to a given harmonic motion. Since the numerical methods allow to investigate arbitrary motions of the vehicle, it is possible to determine direct-, cross- and cross coupling derivatives from appropriate combinations of pure rotational and translational motions. First order dynamic derivatives were predicted by means of DLR’s unsteady Navier–Stokes solver FLOwer [6], which allows a numerical simulation including strongly nonlinear flow effects like shocks and separations. This code was validated with data available from X-24A and then applied to X-38. The Department of Fluid Mechanics of Technische Universität München (FLM) predicted dynamic derivatives based on the Euler equations [5]. This simulation covers an angle-of-attack range from 10◦ to 37◦ and includes a variation of the reduced frequency. Results were given as force- and moment coefficients versus instantaneous displacement and as real- and imaginary part of pressure distribution. The experimental method of small-amplitude forced oscillation with rigid coupling was established at DLR’s Trisonic Windtunnel Köln (TMK) [16]. A special lightweight model using aluminium high quality castings was fabricated. It was possible to measure direct derivatives in pitch and yaw. Test conditions and model configuration were chosen close to the reentry trajectory conditions. Fig. 23 is a picture of the 3.3% X-38 model mounted on the dynamic balance in windtunnel TMK. Fig. 24 shows results of pitch and incidence damping of X-38 obtained up to now. For comparison data of X-24A of different data bases were added. It is obvious that there are differences between the data sets. The reasons for that have to be
investigated. In general the numerical methods applied lead to smaller damping than experimental methods. It does not seem to be mainly due to errors in the different methods but to differences in the configurations tested and in the flow conditions applied in the windtunnel and in the numerical simulation. The first calculations were performed with a clean configuration. As shown in Fig. 24, if body-flaps and docking adapter are taken into account, the above mentioned differences decrease.
9. Conclusions In the last one and a half decade there has been a remarkable progress in the field of aerothermodynamics both for experimental tools and numerical simulation methods. The reason for that with respect to the theoretical side has been due to improvements of physical modelling, more robust and accurate discretisation methods and more sophisticated grid generation strategies and procedures. With respect to the experimental side progress has resulted from improvements in measurement systems and advanced windtunnel capabilities. The work recently performed in the German TETRA program has strongly contributed to this progress. Owing to these advancements and efforts the design of spacecrafts and re-entry vehicles could be made more reliable and the range of controllability be better predicted. Further, major contributions to the operability of spacecraft systems could be achieved.
Acknowledgements This paper represents work which has been conducted in the frame of the German Technology Programme TETRA. Because of this there are several contributions of colleagues who are not named in the author list. We are grateful for their results and the support they gave us.
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Aerothermodynamics for reusable launch systems ✩ Aerothermodynamik wiederverwendbarer Raumtransportsysteme C. Weiland a,∗ , J. Longo b , A. Gülhan c , K. Decker d a EADS-ST, 81663 München, Germany b DLR Institute of Aerodynamics and Flow Technology, 38108 Braunschweig, Germany c DLR Institute of Aerodynamics and Flow Technology, 51170 Köln, Germany d Lehrstuhl für Fluidmechanik TU München, 85748 Garching, Germany
Received 24 February 2003; received in revised form 30 July 2003; accepted 8 September 2003
Abstract The development of modern spacecrafts (launch and re-entry vehicles), either fully reusable or partly reusable needs powerful tools for the design of the aerodynamic shape with a guarantee for reliable flight and controllability along the complete ascent and descent trajectories. Experimental and numerical tools are available these days and for improving the reliability of vehicle design their capability has to be improved step by step. In the frame of the German TETRA Program very detailed technology work was carried out to reach this goal. The growth of the efficiency of these methods is demonstrated by some specific aerothermodynamic problems which are reported in this paper. 2003 Elsevier SAS. All rights reserved. Zusammenfassung Die Entwicklung moderner Raumtransportsysteme, die entweder teilweise oder vollständig wiederverwendbar sind, erfordert leistungsfähige Simulationswerkzeuge, sowohl auf dem experimentellen als auch dem theoretisch/numerischen Sektor. Dadurch soll gewährleistet werden, dass der aerodynamische Entwurf dieser Vehikel einen zuverlässigen und kontrollierbaren Flug sowohl während des Aufstieges als auch des Abstieges aus dem Orbit ermöglicht. Die experimentellen und numerischen Simulationswerkzeuge, die heute vorhanden sind, müssen Schritt für Schritt weiter verbessert werden, um dem oben beschriebenen Ziel näher kommen zu können. Um dieses Ziel zu erreichen sind im Rahmen des deutschen Technologieprogrammes TETRA Technologiearbeiten formuliert und durchgeführt worden, worüber in dieser Veröffentlichung berichtet wird. 2003 Elsevier SAS. All rights reserved. Keywords: Reusable launch vehicles; Hypersonic flow; Aerothermodynamics; High enthalpy windtunnel experiments; Numerical simulations
1. Introduction In the last fifteen years there has been a considerable progress in Europe in the field of aerothermodynamics not only on the theoretical/numerical side but also on the experimental side. The activities started with the beginning of the European Hermes Project and were continued in the CRV, MSTP, X-CRV and FESTIP programmes. On the national German side there was additionally intensive aerothermodynamic technology work in the Sänger project (hyper✩
This article was presented at the German Aerospace Congress 2002.
* Corresponding author.
E-mail address: [email protected] (C. Weiland). 1270-9638/$ – see front matter 2003 Elsevier SAS. All rights reserved. doi:10.1016/j.ast.2003.09.003
sonic technology programme) and more recently within the TETRA/X-38 and ASTRA programmes. Aerothermodynamics is a key technology for the successful design of new space transportation vehicles, where a safe access to space should be guaranteed under the requirements of reducing uncertainties in existing aerodynamic data bases and by that margins of the vehicle design. This process is done step by step with the goal of gaining decreased weight and operational costs. Aerothermodynamics essentially defines the shape of the vehicle and strong interactions exist between this discipline and the vehicle lay-out, the GNC (⇒ flight mechanics) and the propulsion system, furthermore the disciplines of structures, materials and thermal protection systems need the aerothermodynamic data as input.
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Nomenclature s arc length L length CRV Crew Return Vehicle Re Reynolds number MSTP Manned Space Transportation Programme Reynolds number built with x-coordinate Re x TETRA Technologien für zukünftige Raumtransportsysteme k turbulent kinetic energy FESTIP Future European Space Transportation ω dissipation rate Investigation Programme ε emissivity factor ASTRA Ausgewählte Systeme und Technologien für α angle of attack zukünftige Raumtransportsystem-Anwendungen η angle of control flap deflection GNC Guidance, Navigation and Control R&D Research and Development Subscripts RCS Reaction Control System eff effective IR Infrared o total SST Shear Stress Transport Model bf body flap LC Liquid Crystal w wall Symbols ref reference cog center of gravity M Mach number ∞ infinity T temperature Abbreviations
Within the frame of the TETRA program an extensive numerical and experimental research program was established under the lead of DLR with participation of ASTRIUM, DLR R&D Institutes and the Universities of Stuttgart and München. The program focused on the improvement of the experimental and theoretical prediction capabilities for the following aerothermodynamic problems: • Local aerothermodynamic flows. • High enthalpy flows including radiation cooling (by means of view factor approach). • Wall catalycity. • Advanced turbulence modeling. • RCS-jet/external airflow interaction. • Laminar-turbulent flow-transition and Görtler vortices. • Dynamic stability derivatives. Where possible the same problems were modeled numerically, by CFD, and also simulated in windtunnels. In some cases, good to excellent agreement could be identified but in others there are still open questions. In the paper some outstanding results achieved during the TETRA program will be presented and the novelties will be highlighted and discussed.
phenomena have to be considered. Fig. 1 shows a typical reentry trajectory for the X-38 vehicle. In hypersonic flows viscous effects are very important. Viscous effects mean diffusive transport effects of mass, momentum and energy along and mainly across streamlines. These effects cannot be neglected and have to be accounted for. There is a strong coupling between the various diffusive effects. So the existence of a classical boundary layer means always that a thermal boundary layer exists, which is thicker for airflow than the viscous boundary layer since the Prandtl number is usually lower than 1 for air. Normally the boundary layers are turbulent in hypersonic flight for altitudes below approximately 55 km and hence the transition laminar-turbulent occurs also in that regime. The transition laminar-turbulent in hypersonic boundary layers is influenced by many flow parameters and properties: Reynolds number, Mach number, velocity field, thermal wall condition, entropy layer, surface roughnesss, etc., but
2. Flow physics along flight trajectory Since the goal of aerothermodynamics is both to define shapes of space vehicles, which can flight mechanically be controlled along complete trajectories and safely landed, and to determine the mechanical and thermal loads particularly in critical regimes of these vehicles, the relevant physical
Fig. 1. Physical phenomena along typical re-entry trajectory.
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unfortunately in three dimensional flow the transition criteria today available are completely unsatisfactory. Somewhat better is the situation for turbulence modelling, where for classes of problems appropriate two equation models give acceptable results within a certain Mach number range. Wall heat transfer affects all hypersonic viscous effects. It is governed by the state of the boundary layer (laminar, transitional or turbulent), by interaction phenomena (shock/boundary layer/vortex), real gas effects (chemical and thermal non-equilibrium), catalytic walls, heat radiation of walls etc. It should be mentioned that it is nearly impossible to measure flight-realistic wall heat fluxes in windtunnels for hypersonic velocities, since the surfaces of the models are usually cold and the windtunnel nozzles produce flows which are in a thermodynamic transition phase between frozen and non-equilibrium, which contrasts to the equilibrium free-stream to perfect gas during flight. With the help of Fig. 1 an overview is given about the gas behaviour for spacecraft flying with hypersonic Mach numbers in different altitudes. During the first part of a re-entry trajectory where the atmosphere is rarefied and the velocity of the space vehicle is large chemical, thermal and to some extent radiative non-equilibrium real gas effects occur. At these larger altitudes the decrease of freestream density causes an increase of reaction time. Since the freestream velocity is also growing in higher altitudes the characteristic reaction length becomes of the same order of magnitude as the typical vehicle reference length and hence the thermodynamic state of the air is in non-equlibrium. The temperature behind a bow shock is very high and leads to excitation of vibrations, dissociations of molecules of air, formations of other chemical species, ionisation and radiation of the gas moving around the vehicle surface. At lower altitudes the characteristic time of the reaction (vibrational, chemical, ionisational) is much shorter than the flight time of a fluid element travelling along the vehicle surface with the consequence that the gas can be regarded as being in local equilibrium. Further for corresponding low Mach numbers (M∞ 4) a perfect gas approach is appropriate.
3. Local aerothermodynamic flows During re-entry and hypersonic flight, space vehicles experience a strong increase of surface temperature (hot surfaces) due to the heat transfer from the flow side. As well known some of this heat will be radiated from the wall in the ambient. In case that the complete contour is of the convex type the radiation is not hampered, but for nonconvex (concave) configurations there are surface elements which “see” each other which induce complicate absorption and emission of radiated heat on such elements, leading to an increase of the wall temperature. This phenomenon can be treated by the view factor approach, where a visibility
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Fig. 2. Effective emissivity coeffients on X-38 shape; εeff = ε (εo = 0.85, s, T = 1000 K).
coefficient for every surface element is computed. Further by using this visibility coefficients a fictitious emissivity factor εeff can be derived, which can be found in [9,21]. This is a function of the emissivity of the material, the temperature and the visibility coefficients. A good example for this approach is the X-38 vehicle, where the fictitious emissivity factor are computed. Fig. 2 shows the result for εeff = ε (εo = 0.85, s, T = 1000 K). As expected εeff is considerably low in the cavity regime and on the leeward side in the rear part between fuselage and winglet. Certain shapes of space vehicles generate geometrical areas where local flow phenomena occur, for example: • deflected flaps and rudders with local change of boundary layer state influencing the efficiency of controls, • gaps and steps between deflected flaps and rudders leading to local overheating, • gaps between TPS tiles producing high enthalpy sneak flow with the tendency to create overheating. In the frame of the TETRA program a generic configuration (ramp with a gap at the junction to the ramp) was designed for investigating the basic flow phenomena occuring on deflected aerodynamic controls with gap along hinge lines in high enthalpy flow [1]. In DLR’s L3K plasma tunnel experiments were conducted (Fig. 3) and in parallel numerical simulation cases were defined and computed for revealing the influence of the level of physical modelling and the geometrical setting of the gap on the results. The following figures give a selection of the computed flow cases which were performed by using ASTRIUM’s DAVIS-VOL code [15,17]. Fig. 4 gives an overview of the configuration and the fictitious emissivity factor distribution (εeff ) where it can clearly be observed that inside the gap the effective heat radiation tends to zero. The general flow field is drawn in Fig. 5, where for an open gap the pressure contours are shown (M∞ = 7.27, α = 15◦ , chemical nonequilibrium, laminar).
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Fig. 6. IR image of flap model with open gap. Fig. 3. Flap model in arc heated facility L3K.
are comparable with the temperatures on the flap. The size of the separation bubble is smaller than that of the model with closed gap [8].
4. High enthalpy flows
Fig. 4. Geometry of generic test model; effective emissivity coefficients on εeff .
Fig. 5. Pressure contours of generic shape with open gap (M∞ = 7.27, α = 15◦ , chemical non-equilibrium real gas, laminar).
The 2D surface temperature distribution measured with an IR-camera in L3K provides clear information about the flow field and the heat flux rate distribution. Based on these data and comparisons with numerical results, the influence of the coupling between the flow and structure can be analysed. The IR image of the model with an open gap slot (Fig. 6) shows that the gap temperature reaches levels that
Within the X-38 program the aerodynamic and aerothermodynamic environment of the X-38/CRV is defined based on close cooperations between ground based testing and Computational Fluid Dynamics (CFD) calculations. This strategy is based on the fact that it is mandatory to validate the complex models required in CFD codes to describe high temperature effects such as chemical- and thermal non-equilibrium or the laminar to turbulent transition of the boundary layer using dedicated experimental investigations before they are used for computations at high Mach number re-entry conditions. The investigations of the 1:24 scale Model E of X-38 in the High Enthalpy Shock Tunnel Göttingen (HEG) of the German Aerospace Center (DLR) represent the first experiments of this configuration in the high enthalpy flow regime up to 22 MJ kg−1 , corresponding to a flight velocity of 6000 m s−1 , for pressure and heat transfer rate measurements. Parallel to these experimental investigations CFD rebuilding was employed using the DLR Navier–Stokes solver CEVCATS-N. CEVCATS-N is a multi-block finite volume flow solver for the stationary Euler and Navier–Stokes equations in integral form [13]. The normalized measured and computed heat flux distribution on the windward side of the X-38 fore body and the 20◦ and 30◦ deflected body flap is shown in Fig. 7 using HEG condition I (22 MJ kg−1 ). Overall, the comparison between experiment and CFD assuming a fully laminar flow is good for the 20◦ body flap deflection. However, when the body flap deflection is increased to 30◦ , the unexpected result was obtained that the measured body flap heat flux is approximately twice as high as predicted by laminar CFD. The high heat transfer level on the 30◦ body flap could be reproduced by performing a computation with laminar fore body flow and fixed transition in front of the hinge line. From an engineering point of view this is a very important result indicating that in spite of the fact that the unit free-stream Reynolds number of the high enthalpy
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Fig. 9. Temperature distribution on the lower side of the fuselage (εo = 0.80 right; ε = ε (εo , s, T ) left). Fig. 7. Normalized measured and computed heat flux on X-38 for the 20◦ and 30◦ deflected body flap.
Fig. 8. Flow details inside the cavity between deflected bodyflap and fuselage M∞ = 17.5, α = 40◦ , ηbf = 20◦ .
test flow would suggest that the flow should be laminar, the separated flow at the body flap hinge line may be governed by transitional or turbulent flow. Consequently the measured overheating must be taken into account when developing a design database for X-38/CRV. The X-38 vehicle creates in case of a deflection of the body flaps a cavity between the leeward side of the flaps and the fuselage where the flow is of interest for the correct design of the hot structures in this area. Here the radiation cooling of the walls is significantly reduced by different hot surfaces facing one another. Therefore a view factor approach was used in the Navier–Stokes computations. Due to this model, the effective emissivity factor εeff = ε (εo , s, T ) of the walls inside the cavity approach values close to zero and significant temperature differences on the leeward side of the body flap and the cavity ceiling of approximately 500 K when comparing with a computation assuming a constant emissivity factor of εo = 0.8 were found [7,18] (see Figs. 8, 9).
5. Advanced turbulence modelling One of the most challenging flow phenomena is given by the turbulence. Turbulent flows either in attached boundary layers, separated flow bubbles, in globally separated boundary layers or free mixing layers influence the mechanical and thermal loads very severely. Therefore it is well known that the wall heat fluxes and the effectiveness of deflected aerodynamic controls as well as base flows of space transportation vehicles are considerably affected by turbulence. During the design and validation process of shapes for space vehicles CFD methods play an increasing role, particularly in industry. Thus the turbulence has to be described on the one hand with methods which are relatively fast and not too expensive and which on the other hand achieve results which are accurate and reliable enough for industrial processes. With these provisos two equation turbulence models on the basis of Wilcox’ k–ω model are investigated as a reasonable compromise between algebraic and Reynolds stress models. They are independent on an algebraic length scale and take naturally into account history effects through transport equations. The models are developed for incompressible flows which have been adapted for compressible flows by considering the variable density effects through changes in the mean density. This method might be justified for Mach numbers M∞ < 5, but for larger Mach numbers compressibility correction models which affect the structure of the turbulence has to be taken into account. The objective of this study was to investigate the behaviour of three variants of the standard k–ω model, namely Wilcox’ low Reynolds number version, Menter’s Shear Stress Transport version and a realizable version. Further some compressible correction models in conjunction with the standard k–ω approach were tested [20]. The models were investigated in super- and hypersonic flat plate boundary layers, on a compression ramp at M∞ = 9.22 and on a hypersonic flow over the X-38 vehicle at M∞ = 6, where windtunnel data are available from NASA Langley Research Center. The complete issue of the numerical simulations using ASTRIUM’s DAVIS-VOL
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Fig. 10. Flow configuration for compression ramp.
Fig. 11. Mach number distribution on compression ramp.
Fig. 13. Influence of compressible corrections on pressure (above) and heat flux (below).
Fig. 12. Influence of turbulence model on heat flux.
code are reported in [19]. Here a selection of these results will be given. Figs. 10 and 11 show the flow situation for the compression ramp and the Mach number distribution. The shock induced flow separation can be clearly identified. For the five different turbulence models Fig. 12 gives an insight into the heat flux distributions at the compression corner and compares these results with experimental data [4]. None of these models predict the separation bubble correctly, but it seems that the potential of the SST- and the realizable models is higher than for the others. Adding the compressibility corrections “length scale” and “rapid compression” proposed in [3] the separation bubble is predicted correctly and the pressure and heat flux distribution show the most promising behaviour (Fig. 13). The flow around the X-38 shape is calculated for the conditions of the NASA Langley windtunnel (M∞ = 6.0, α = 40◦ , Re = 3.57 × 106 , ηbf = 20◦). Detailed heat flux measurement for the windward side exist, where a transition tripping device was fixed at 25% of Lref from the nose. In the computation using the SST model transition was triggered at 25% of Lref , too.
Fig. 14. Heat fluxes on X-38 windward side M∞ = 6.0, α = 40◦ , Re = 3.57 × 106 , ηbf = 20◦ .
The comparison of the experimental and theoretical data shows excellent agreement in the laminar and turbulent regimes, in particular in the area in front of the bodyflaps and on the bodyflaps themselves (Fig. 14). An evaluation of the heat fluxes along the red line (Fig. 14) is given in Fig. 15, where besides three different turbulence models (Note: these computations have assumed fully turbulent flow!) the SST model including the transition onset (simple switch from laminar to turbulent modelisation) at 25% Lref was drawn. As one can see the agreement in the laminar regime, at the transition point, the turbulent regime up to the body flap and on the body flap itself is really very promising.
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Fig. 16. LC visualisation and computed turbulent heat flux distribution. Fig. 15. Heat flux distribution (along the red line of Fig. 14); comparison of different turbulence models.
6. Transition laminar-turbulent Traditionally the prediction of flap peak heating for re-entry vehicles falls short of actual magnitudes in the case of a reattachment line of a separated boundary layer, especially in the transitional regime and in the presence of shock boundary layer interaction. The current practise of performing fully turbulent computations and multiplying the results by a constant uncertainty factor has obvious disadvantages. For this reason an investigation of transitional and separated flow phenomena at the X-38 flaps with experimental as well as numerical tools has been started at DLR. For the windtunnel testing two models were manufactured for various measurements and visualisations in the Ludwieg tube facility Göttingen under flow conditions of M∞ = 6 and a Reynolds number range of 2.1–8.8 × 106 . In addition the main analysis was carried out by the DLR CFD code CEVCATS-N, which was validated in a broad range of sub-, trans- and hypersonic flow cases for a variety of flow conditions and configurations. Examples are given in [2]. For the separated turbulent flow the compressible extended one-equation Spalart–Allmares model [14] was chosen. Windtunnel investigations have been carried out on a brass model for pressure and heat flux measurements, and a low cost model, manufactured in rapid prototyping technique for liquid crystal (LC) thermo-visualisations. For pressure and heat flux measurements CFD and windtunnel data have shown good agreement [10]. An example of LC visualisation in comparison with a simulated heat flux distribution under fully turbulent flow conditions (Re = 8.8 × 106 ) is given in Fig. 16. At the reattachment line of compressible separated boundary layers, spanwise periodic heat flux peaks, generated by counter-rotating streamwise vortices, similar to the well known Görtler vortices in concave curved boundary layers, are a typical phenomenon [11]. Within the numerical investigations it was possible to simulate such vortices on the X-38 flaps under laminar as well as transitional flow conditions by using significantly refined span-
Fig. 17. Heat loads on X-38 flap and visualisation of streamwise vortices.
wise computational grids of the flap region derived from the entire grid of the whole vehicle-flow field [12]. In Fig. 17 the heat flux on the flap surface, generated by the vortices is shown for a laminar case together with contour surfaces of the streamwise perturbation velocity in the boundary layer, which is an indicator for the appearance of vortexdisturbances. For a better view the boundary layer was thickened artificially in the visualisation. With this investigation the capability of streamwise vortex simulation in separated boundary layers for realistic hypersonic cases by CEVCATS-N was shown.
7. Jet/external airflow interaction The effectiveness of jets of reaction control systems is influenced by the outer flow field and in contrary the jet itself affects the outer flow sometimes to such an extent that strong changes of the pressure and the heat fluxes at the wall occur. Changing the pressure field at the wall leads mostly to an amplification of the thrust effect of the jet which has to be determined. On the other hand the boundary layer of the external flow field may separate by the firing thruster and afterwards reattach where in hypersonic flows due to thinning of the boundary layer, growing heat fluxes (hot spots) may appear. For the controllability of space
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Fig. 18. Thruster position on X-38 shape.
Fig. 21. X-38 with 400 N thruster, M∞ = 17.5, α = 0◦ , Mach contours and streamlines.
Fig. 19. X-38 with 110 N thruster, M∞ = 17.5, α = 0◦ , Mach contours and streamlines.
Fig. 22. X-38 with 400 N thruster, M∞ = 17.5, α = 0◦ , temperature and streamlines at the wall.
Fig. 20. X-38 with 110 N thruster, M∞ = 17.5, α = 0◦ , temperature and streamlines at the wall.
transportation systems mainly during re-entry it is very important to quantify the above described phenomena. To investigate these effects two different thrusters were installed on the X-38 vehicle, one with a nominal thrust of 110 N and the other with 400 N (Fig. 18). For both thrusters computations with DAVIS-VOL were performed for M∞ = 17.5, α = 0◦ and 40◦ , where laminar and equilibrium real gas flow was assumed [22]. In front of the 110 N thruster a horse shoe vortex appears which leads along the trace where the flow reattaches the wall to a strong increase of the wall temperature (approx. 1000 K) compared to the non-firing case (Figs. 19, 20). A different situation
will be found in the flow field with the 400 N thruster. Here no vortex upstream of the firing thruster can be identified, but a more distinct one behind the jet, which has a trace of reattachment which obviously lies in the plane of symmetry (Figs. 21, 22). The wall temperature increase by this effect is approx. 500 K. Further in Fig. 22 the reduction of the wall temperature in the regime where flow separation occurs (due to the forming vortex) can be clearly seen.
8. Dynamic stability derivatives Dynamic stability derivatives are used in flight mechanics to describe instantaneous aerodynamic reactions on manoeuvering flight vehicles. Especially if the natural stability becomes small, like in the lateral directional modes of motion of X-38 at low supersonic Mach numbers, the availability of a proper set of dynamic derivatives is essential. The evaluation of dynamic derivatives still belongs to the challenging tasks of both experimental and numerical aerodynamics. The reason is the usually small underlying physical effects that have to be measured or accounted for.
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Fig. 24. Computed and measured damping-in-pitch-parameter versus Mach Number (different angles of attack). Fig. 23. X-38-model mounted on dynamic balance in windtunnel TMK.
In the frame of the TETRA program two numerical methods and an experimental one, covering the Mach number range from subsonic to hypersonic speeds, are applied for dynamic derivative analysis. The approach of evaluating the dynamic derivatives is comparable in all three cases. A harmonic analysis is applied, to determine the stability derivatives using the time history of force- and moment coefficients as a reaction to a given harmonic motion. Since the numerical methods allow to investigate arbitrary motions of the vehicle, it is possible to determine direct-, cross- and cross coupling derivatives from appropriate combinations of pure rotational and translational motions. First order dynamic derivatives were predicted by means of DLR’s unsteady Navier–Stokes solver FLOwer [6], which allows a numerical simulation including strongly nonlinear flow effects like shocks and separations. This code was validated with data available from X-24A and then applied to X-38. The Department of Fluid Mechanics of Technische Universität München (FLM) predicted dynamic derivatives based on the Euler equations [5]. This simulation covers an angle-of-attack range from 10◦ to 37◦ and includes a variation of the reduced frequency. Results were given as force- and moment coefficients versus instantaneous displacement and as real- and imaginary part of pressure distribution. The experimental method of small-amplitude forced oscillation with rigid coupling was established at DLR’s Trisonic Windtunnel Köln (TMK) [16]. A special lightweight model using aluminium high quality castings was fabricated. It was possible to measure direct derivatives in pitch and yaw. Test conditions and model configuration were chosen close to the reentry trajectory conditions. Fig. 23 is a picture of the 3.3% X-38 model mounted on the dynamic balance in windtunnel TMK. Fig. 24 shows results of pitch and incidence damping of X-38 obtained up to now. For comparison data of X-24A of different data bases were added. It is obvious that there are differences between the data sets. The reasons for that have to be
investigated. In general the numerical methods applied lead to smaller damping than experimental methods. It does not seem to be mainly due to errors in the different methods but to differences in the configurations tested and in the flow conditions applied in the windtunnel and in the numerical simulation. The first calculations were performed with a clean configuration. As shown in Fig. 24, if body-flaps and docking adapter are taken into account, the above mentioned differences decrease.
9. Conclusions In the last one and a half decade there has been a remarkable progress in the field of aerothermodynamics both for experimental tools and numerical simulation methods. The reason for that with respect to the theoretical side has been due to improvements of physical modelling, more robust and accurate discretisation methods and more sophisticated grid generation strategies and procedures. With respect to the experimental side progress has resulted from improvements in measurement systems and advanced windtunnel capabilities. The work recently performed in the German TETRA program has strongly contributed to this progress. Owing to these advancements and efforts the design of spacecrafts and re-entry vehicles could be made more reliable and the range of controllability be better predicted. Further, major contributions to the operability of spacecraft systems could be achieved.
Acknowledgements This paper represents work which has been conducted in the frame of the German Technology Programme TETRA. Because of this there are several contributions of colleagues who are not named in the author list. We are grateful for their results and the support they gave us.
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