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Open Archive TOULOUSE Archive Ouverte (OATAO) OATAO is an open access repository that collects the ork o Toulouse researchers and makes it reely available over the eb here possible.

1 Open Archive TOULOUSE Archive Ouverte (OATAO) OATAO is an open access repository that collects the ork o Toulouse researchers and makes it reely available over the eb here possible. This is an author-deposited version published in : Eprints ID : 4576 To cite this version : Sourgen, Frédéric and Prévereaud, Ysolde and Vérant, Jean-Luc and Laroche, Emmanuel and Moschetta, Jean-Marc MUSIC/FAST, A PRE-DESIGN AND PRE-MISSION ANALYSIS TOOL FOR THE EARTH ATMOSPHERIC RE-ENTRY OF SPACECRAFT, CAPSULES AND DE-ORBITED SATELLITES. (05) In: Proceedings o 8th European Symposium on Aerothermodynamics or Space Vehicles, March 05-6 March 05 (Lisbonne, Portugal). Any correspondance concerning this service should be sent to the repository administrator: sta-oatao@listes-di.inp-toulouse.r

2 MUSIC/FAST, A PRE-DESIGN AND PRE-MISSION ANALYSIS TOOL FOR THE EARTH ATMOSPHERIC RE-ENTRY OF SPACECRAFT, CAPSULES AND DE-ORBITED SATELLITES F. Sourgen (), Y. Prévereaud (), J-L. Vérant (), E. Laroche (), J-M. Moschetta () () ONERA, Midi-Pyrénées Center, BP 7405 avenue Edouard Belin, FR-3055 Toulouse cedex 4, Frederic.sourgen@onera.r ABSTRACT The paper proposes an overvie o the physical models developed/selected and implemented in the ONERA aerothermodynamic (ATD) engineering code FAST. This tool is used to quickly determine the pressure and heat lux surace distribution at the all, as ell as aerodynamic orces and moments coeicients in hypersonic regime or ree-molecular, transitional and continuum los, or realistic designs o space vehicles ranging rom capsules to spacecrats and or generic shapes o orbital debris as ell. An original eature o the approach is that geometrical components o the object are not separately processed but are investigated by a global method taking into account geometrical eects and lo history (shado regions, surace heat lux propagation). Several application cases are displayed to rely on the engineering approach: ARD and AOTV capsules, Pre-X (an IXV-like vehicle) and CubeSat (a debris-like single object). The given results have been analysed by comparison ith experimental and CFD data. The limits o the approach are discussed, paving the ay or uture developments.. INTRODUCTION The transport to space is a major discipline in current aerospace activities. Deining the right trajectory o a re-entry vehicle is crucial or the mission success. Hoever, during the atmospheric re-entr a strong interaction exists beteen ATD mechanisms, light dynamics and vehicle shape. A predominant actor in designing a hypersonic re-entry vehicle is its shape: ranging rom a ballistic light design (e.g. Stardust, Mirca) providing aerodynamic stabilit to semi-ballistic (Apollo, ARD, AFE) including guidance and control, and inally spacecrat conigurations (Space Shuttle, PRE-X, IXV, HYPMOCES []) involving active trajectory and attitude control. Thereore, during pre-design phase o atmospheric reentry vehicles, several light points, vehicle geometries and many conigurations (rudders, ings positions and size, inlatable systems, laps size ) have to be explored. CFD computations being cost-consuming in terms o CPU time and man labour, their number is limited in many projects. In addition, their use during the pre-design phase can turn out inappropriate especially hen the shape is not yet ixed. Thereore, engineering methods that are able to quickly and accurately compute aerodynamic orces and moments coeicients and heat lux distribution at all are attractive tools. Since 006, ONERA has been developing a platorm so-called MUSIC/FAST, hich is the gathering o a multi-objects trajectory computation tool including GNC (MUSIC) [] and a geometric treatment and aerothermodynamic modelling tool (FAST). MUSIC/FAST demonstrates an alternative but eective approach to CFD and GNC to prepare the pre-design phase o atmospheric re-entry vehicles ithin reliable estimates o aerodynamic orces and moments coeicients and all heat lux distribution during 3DDL or 6DDL pre-lights ithin an attractive response time. This paper ocuses on the aerothermodynamics modelling perormed in the FAST code. First, the required geometrical treatment is described. Then, the olloing sections deal ith aerodynamic coeicients determination in hypersonic regime or ree-molecular, transitional and continuum los. Thirdl aerothermodynamic analysis (heating balance and heat lux models) is addressed. Then, three application cases are exhibited to rely on the engineering approach: ARD (Atmospheric Reentry Demonstrator) capsule, PRE-X, hich is a IXV-like vehicle and CubeSat, hich is an orbital debris-like single element. Along the paper, the given results are analysed by comparison ith experimental and CFD data regarding aerothermodynamics, and the limits o the approach ill be discussed, paving the ay or uture developments. Finall in the last section an overvie o an alternative model to the modiied Netonian method is proposed in the case o elliptic los representation.. CAD ANALYSIS Simple and more complex geometries can be designed and meshed ith any CAD sotare. Geometries must be meshed ith surace triangular mesh cells. From this, FAST computes automatically: - the reerence surace and length, used to compute aerodynamic orces and moments coeicients; - the local curvature radius used to compute the heat lux distribution at the all. The inertia matri the reerence mass, and the position

o the centre o gravity o complex objects must be ixed by the user. The local curvature radius model, developed at ONERA by Diallo [3], is based on the non-constraint divergentgradient method.

3 o the centre o gravity o complex objects must be ixed by the user. The local curvature radius model, developed at ONERA by Diallo [3], is based on the non-constraint divergentgradient method. The local surace can be approximated by a quadric equation as olloing: F( 0, () F( ax + by + cz + dxy + exz + yz + gx + hy + iz + l here z are the mesh surace coordinates. The coeicients rom a to l are the unknon o the quadric equation. They are determined using local coordinates o neighbouring nodes. Then, the local curvature C and the local curvature radius r can be computed: r C / r r r r F( n () F, nf F( z ) Eq. can be ritten or each node belongs to the irst and second circles o neighbouring nodes o the considered node. A linear system ith 0 unknons and i equations (equal to the number o neighbours nodes considered) is obtained. In practice, a suicient number o neighbouring nodes can alays be ound or the system to be solved. Figure displays the local curvature radius values computed on the ARD capsule olloing the abovementioned method. here λ is the mean ree path (m), L re the reerence length o the vehicle (m), T the temperature o the undisturbed lo (K), P the upstream pressure (Pa), R the ideal gas constant (J/mol.K), N A the Avogadro s number (mol - ), and σ the eective cross sectional area or spherical particles (m ). The ree-stream conditions are given by the US76 atmospheric model corrected by a Barlier model or altitudes above or equal to 0 km. 3.. Continuum lo (K n < 0.00) In the continuum lo domain, a computation o the shock layer characteristics at nation point is perormed under the thermochemical equilibrium hypothesis. Given the light point data, quoted 0 (or ) in the igure, the shock layer values (quoted ) are obtained using Rankine-Hugueniot generalized equations, hich can be ritten as olloing : P0 V0 P V (4) + ρ + 0 γ 0 ρ γ Gas are dierent upstream and donstream the shock (although they are assumed to be perect gas), so that a chemical equilibrium table should be used. In FAST, the equations o Srinivasan et al. [4], hich are valid or temperatures ranging beteen 0 and K, are used. Figure. The nomenclature or values behind the shock and at nation point [5]. Figure. Computed curvature radius or the ARD capsule meshed ith 3977 nodes. 3. AERODYNAMIC MODELLING Forces and moments are deduced rom local values o pressure and skin riction coeicients. Those depend on the lo regime, deined using the Mach number M and the Knudsen number K n. K n λ L re RT P in in N A σ (3) The nation point values ( ) are obtained assuming isentropic compression o the gas rom : P T + γ P M T γ + M γ γ (5) (6) Those values are used as reerence values in the olloing described models.

The local pressure coeicient is determined using the modiied Neton method (Eq. 7). C p, P P0 ρ0v0 C p C p, sin (7) Zero value is set or alls in the shado o the inlo (in blue on Figure 3).

θ here V γ s M ' c is the molecular speed rate (m/s) and T r the recovery te mperature (K).

A perectly smooth all avours a specular relection, hereas rough an irregular surace avours a diuse relection. τ T he local skin riction coeicient C is deined by P Bird [7] as: 0 s 3.

4 The local pressure coeicient is determined using the modiied Neton method (Eq. 7). C p, P P0 ρ0v0 C p C p, sin (7) Zero value is set or alls in the shado o the inlo (in blue on Figure 3). An advanced method to compute the shado zones has been developed in [6] and successully applied to ATV, PRE-X and baseline vehicle (Figure 3). θ here V γ s M ' c is the molecular speed rate (m/s) and T r the recovery te mperature (K). ε is the raction o molecules having a specular relection, hile ( - ε) represents the raction o diuse relection. ε depends on the all surace characteristics. A perectly smooth all avours a specular relection, hereas rough an irregular surace avours a diuse relection. τ T he local skin riction coeicient C is deined by P Bird [7] as: 0 s 3.3. Transitional lo (0-3 < K n < 00) A sin-square bridging unction derived rom Blanchard [8] is used to compute the pressure ( p ) and riction ( ) coeicients in transitional regime (quoted tr ), i.e. beteen continuum (noted cont ) and ree molecular (noted m ) lo domains. C m cont ( C C ) tr cont p, C p, + ( K n ) p, p, (0) Figure 3. Shado areas computations or the baseline coniguration o the HYPMOCES project [], or 35 o angle o attack and -5 o side slip angle. In blue: regions in the shade. The local skin riction coeicient is not computed in the case o a hypersonic continuum lo. 3.. Free molecular lo (K n > 00) (a) Specular relection (b) diuse relection Figure 4. Surace accommodation. In the case o a ree molecular lo (K n > 00), the Bird ormula are used [7] to compute the pressure distribution at the all: ith : n ( K n ) sin [ π ( a + a log0 Kn )] () The values o a, a, a 3 and n have been calibrated by comparison ith numerical data issued rom literature or various objects (sphere, cylinder, AFE, stardust). The complete validation strategy and cases can be ound in [6]. cont m The reerence coeicients values ( C p, and C p, ) correspond to altitude values (pressure and temperature values in the atmosphere table) alloing to achieve K n 0-3 and K n 00 or a given object, respectively. The pressure coeicient at nation point o a sphere is compared ith data rom [9] on Figure 5. The pressure coeicient decrease rom. to.9 rom reemolecular regime to continuum regime respectively. In ree-molecular regime, the exact value is obtained ith FAST, hereas in continuum regime, a deviation o.6% is obtained ith CFD. The maximal discrepancy (5.9%) is reached or K n 0. A satisactory agreement is observed beteen DSMC data and FAST ones or the sphere. C p P P 0 s

5 .069 P conv 3.79 Ht h q R N rtre here R n, is the nose radius (m) and ΔH (4) H h rt * t. H tot is total enthalpy at ree-stream conditions, h is all enthalp T re 73.5 K and r 87 J/kg/K (air gas). It has to be noticed that the convective heat lux given by equation (4) assumes a ully catalytic all. re Figure 6. Comparison beteen the pressure coeicient at nation point obtained ith FAST and the data rom [9] or a sphere. Aerodynamic orces and moments, and their corresponding coeicients, are computed by integration o pressure and riction coeicients on the object surace or dierent lo regimes (continuum, reemolecular and transitional). 4. AEROTHERMODYNAMICS MODELLING In the case o vehicles and capsules, the equation controlling the temperature o the system is ritten taking into account the convective heat lux (q conv ), the radiative heat lux rom the shock layer (q rad,g ) and the all radiative cooling (q rad, ): q T ) q q ( T ) 0 () conv ( + rad, g rad, The all radiative cooling is given by the olloing equation, hatever the lo regime: q 4 rad, ( T ) εσt (3) here T is the all temperature (K), ε the material emissivity and σ the Stean-Boltzmann constant (W/m².K 4 ). 4.. Continuum lo In the continuum lo domain, the convective heat lux at nation point can be computed by one o the olloing equations: - Detra equation [0]; - Vérant-Lepage equation [], [7]; - Vérant-Sagnier equation []. The Verant-Sagnier ormulation is based on experimental measurements perormed by [3] ho have pointed out that the ratio q conv (R n /P )/(H t - h ) is almost constant at nation point o a sphere or a ide range o reestream conditions and nose radius values. The Verant-Sagnier [] ONERA correlation used in FAST is ritten as olloing: q The radiative heat lux at nation point coming rom the radiative shock layer (q rad,g ) can be computed ith Tauber model [4] or ith Martin model [5]. In continuum regime, the 3D heat lux distribution at the all is computed rom the reerence heat lux at nation point thanks to Vérant-Lerançois model [6], [7]: total R R( ( (, ) N P x z q re, β 0.8 R( P (5) here R( is the local curvature radius (m), R n is the nose curvature radius (m), P is the local pressure value (Pa). The reerence heat lux value at nation point is given by: total conv rad g q q q + q (6) re β poer is determined using spheres as calibration cases hereas α is a unction o local curvature radius hich has been determined using numerical simulations database [8]. A most important point is that suraces are assumed to behave as ully catalytic alls, hich means that convective heat lux is going to be overestimated. Thereore, in the case o orbital debris, ground damage is going to be under-estimated. In a model like harmonic oscillator (vibrational levels o molecules are excited), all enthalpy can be ritten as olloing: θ0 T θ 0 e Cp ( ) T + (7) θ0 T T e θ K h ( T ) Cp ( T ) T (8) α RN β The all temperature T is obtained by solving the radiative equilibrium equation. 4.. Free molecular and transitional los In the case o ree molecular lo (K n > 00), the Bird s ormula or the heat lux are used [7].

Case Units Flight point Flight point Exp. S4 Exp. S4 M 5 M 4 P 0 85 bar P 0 5 bar Altitude [km] 5.53 65.83 Velocity [m/s] 4905.537 7.43 484 454 Density [kg/m 3 ] 9. x 0-4.5869 x 0-4.3 x 0-4.

6 Case Units Flight point Flight point Exp. S4 Exp. S4 M 5 M 4 P 0 85 bar P 0 5 bar Altitude [km] Velocity [m/s] Density [kg/m 3 ] 9. x x x x 0-3 Temperature [K] Pressure [Pa] Wall conditions 500 K ixed Fully catalytic 300 K ixed Fully catalytic Table. Free-stream values and experimental conditions used or LORE computations and S4 ind tunnel measurements, respectively. Figure 6. Comparison o the heat lux coeicient obtained ith FAST at nation point o a sphere ith data rom literature [9]. In the transitional lo domain (0-3 < K n < 00), the bridging unction used is similar to the one presented above (Eq. 0 and ); only the values o the coeicients n, a, a have been modiied. The comparison o the nation point heat lux coeicient o a sphere obtained ith FAST results ith DSMC computations rom [9] shos a good agreement beteen the to approaches (Figure 6). 5. APPLICATION TO SPACE VEHICLES 5.. ARD vehicle Atmospheric re-entry o the ARD vehicle (Figure 7) as the irst European Union successul re-entry light. Perect gas and real gas Navier-Stokes computations have been perormed by Walpot [9] using the ESA code LORE. Heat lux and pressure measurements along a body in ind tunnel have also been perormed at the ONERA S4 ind tunnel and rebuilt by Walpot [9] using LORE computations. Flight points data used or LORE computations and S4 experimental conditions are given in Table. Computations and experiments have been conducted or 0 o angle o attack (α) and 0 o side slip angle (β). Figure 8. Dierence (in %) beteen the pressure distribution computed by FAST and LORE or M 5. The local pressure coeicient computed ith FAST and LORE is compared in Figure 8 and Figure 9 or M 5, α 0 and β 0. A good agreement is observed, except in the elliptic lo region. Close to the shoulder, the inormation rom the lo expansion goes back to the lo through the subsonic boundary layer. This is a characteristic problem o local method. Figure 9. Comparison o pressure coeicient obtained ith FAST and LORE in the ARD symmetry plane (y 0) and or (M 5; α 0, β 0 ). Figure 7. ARD vehicle geometry [9]. The maximum heat lux computed ith LORE and observed experimentally is not located at the nation point (nation pressure), but on the trailing edge, here the accelerated lo induces a decrease o the boundary layer, and thus, a strong increase o the temperature gradient and then heat lux. FAST underestimates the heat lux obtained ith LORE. Hoever, Walpot [9] revealed the presence o a carbuncle phenomenon, inluencing the shock capture. So, the LORE computation seems to over-estimate the peak o

heat lux (Figure 0) in the vicinity o trailing edge. Figure 0.Comparison o LORE and FAST heat lux distribution in the ARD symmetry plane (y 0) and or (M 5;

. Pre-X (IXV-like vehicle) Since the early 000s, ONERA has been involved in experimental and numerical investigations perormed to build the aerothermodynamic database or the IXV and Pre-X vehicles.

Table shos corresponding light points data. coeicients. Results obtained or Mach number 7.75 are shon in Figure and Figure 3, respectively.

7 heat lux (Figure 0) in the vicinity o trailing edge. Figure 0.Comparison o LORE and FAST heat lux distribution in the ARD symmetry plane (y 0) and or (M 5; α 0, β 0 ). 5.. Pre-X (IXV-like vehicle) Since the early 000s, ONERA has been involved in experimental and numerical investigations perormed to build the aerothermodynamic database or the IXV and Pre-X vehicles. Figure exhibits Navier-Stokes chemical non-equilibrium computations o the lo around the Pre-X vehicle perormed at to light points using the ONERA CFD code CELHyO. Table shos corresponding light points data. coeicients. Results obtained or Mach number 7.75 are shon in Figure and Figure 3, respectively. Table 3 and Table 4 allo to perorm a comparison o the pressure coeicient and heat lux at nation point or the to light points considered (M 7.75 and 5). A good agreement has been obtained at nation point or both light points beteen FAST and Navier-Stokes computations. Mach Cp (CELHyO) Cp (FAST) Error (%) % 0% Table 3. Comparison o pressure coeicient at nation point obtained ith FAST and CELHyO3D. M 7.75 M 5 q (CELHyO) W/m² q (FAST) W/m² Error (%).3% % Table 4. Comparison o convective heat lux at nation point obtained ith CELHyO and FAST (Vérant-Sagnier equation). Figure. Navier-stokes computations or the Pre-X vehicle perormed ith the ONERA code CELHyO3D or Mach 7.75 and Mach 5. Mach [-] Altitude [km] Velocity [m/s] Density [kg/m 3 ].579 x x 0-5 Temperature [K] Pressure [Pa] Wall conditions rad. Equilibrium Fixed at ε K Table. Flight point data (PRE-X, phase A), α 40, β 0, laps delection 5. Those Navier-Stokes simulations, hich are accurate but time-consuming, have been compared to FAST computations or the local pressure and heat lux Figure. Comparison o pressure distribution obtained ith FAST and CELHyO or PRE-X phase A, M Figure 3. Comparison o heat lux distribution obtained ith FAST (Vérant-Sagnier equation) and CELHyO or PRE-X phase A, M 7.75

Figure and Figure 3 conirm that both pressure coeicient and heat lux values are matched pretty ell all over the large blunted region o the vehicle.

Hoever, strong discrepancies appear in the transverse lo regions, near the separation zone and on the laps.

In the particular case o the laps, both shock-boundary layer interaction and separation modelling ould require much higher level representation. at corners and trailing edges.

8 Figure and Figure 3 conirm that both pressure coeicient and heat lux values are matched pretty ell all over the large blunted region o the vehicle. In the centre part o the indard side and upstream o the separation zone, dierences loer than 5 % are still obtained or the heat lux value hich is an acceptable number. Hoever, strong discrepancies appear in the transverse lo regions, near the separation zone and on the laps. It has to be noticed that errors rom the modiied Neton method have impacted the heat lux computation since the local pressure value is then used. In the particular case o the laps, both shock-boundary layer interaction and separation modelling ould require much higher level representation. at corners and trailing edges. Since the connexion beteen elements o a satellite can be a junction exposed to high heat lux levels (characteristic o a trailing edge), engineering methods should aim to improve heat lux prediction in such regions in uture ork CubeSat (debris-like object) In the rame o the QB50 project, ISAE and ONERA have been equipping a CubeSat dedicated to in-light measurements characteristic o the atmospheric re-entry o an orbital debris single shape. A smooth coniguration or the cubesat has been computed using FAST and compared to non equilibrium lo simulations using the Navier-Stokes code CEDRE (ONERA). Since many aces o the cubesat are lat plates, the cubesat has been divided in several domains : - The heat lux value on lat plates is computed ith FAST using eective nose radius as a unction o the bluntness parameters. - The heat lux value on other suraces is computed using Eq. (4) and (5). Figure 5. Navier-Stokes computation o the Mach number using CEDRE Figure 6. Navier-Stokes computation o the surace heat lux using CEDRE (W/cm²) Figure 4. ISAE-ONERA cubesat EntrySat or the QB50 project The light point z 70 km and V 669 m/s has been under investigation since this is a critical altitude or the cubesat hich is to be destroyed beore. Navier-Stokes results are pictured on Figures 5 & 6. FAST computation o the surace heat lux is shon in Figure 7. A good agreement has been ound or the exposed ace o the cubesat but the heat lux value is underestimated Figure 7. Navier-Stokes computation o the surace heat lux using FAST (W/cm²)

9 6. PERSPECTIVES Figure 9. Global method or D los. It is ell knon that modiied Netonian method is not suitable or many cases such as elliptic los, high angle sphere-cones or delected laps. In the case o elliptic los, a global method has been tested. The principle and the used variables are deined on Figure. The shock curvature is assumed to be knon. Many approximations based on the curvature radius value can be ound [6], here an equation rom Love et al. [8] has been used in the case o the AOTV vehicle. The object is assumed to be approximately D axisymmetrical. The global mass conservation through the control volume pictured on Figure 9 can be ritten as olloing: On igure 0 and, the results are compared to experimental measurements perormed by Wells et al. [0]. A signiicant improvement can be observed compared to the modiied Neton method. Hoever, Figures 6 and 7 sho that the method is sensitive to the shock curve location accuracy. Although that global approach has not been generalized to any 3D lo yet, it can use all other developments perormed in FAST. δ y ρ V rs ρu cos( θ ) + dy r r y 0 Assuming that ρu is constant along the section 4, it comes: ρ V rs u (rδ + δ cos( θ )) ρ Pressure is then obtained by isentropic expansion rom nation point : γ γ γ u γ P P + M u,m u, a au + u a u ith M u u/a and a a u + (γ - )/ u Figure 0. Global method or pressure determination (AOTV vehicle). A Love s ormulation has been used or the shock curve location. Figure 8. AOTV vehicle Figure. Global method or pressure determination (AOTV vehicle). A D Navier-stokes computation has been used or the shock curve location. 7. CONCLUSIONS The main aerothermodynamics models implemented in the ONERA FAST code have been described. An original eature is that geometrical components o the object are not separately processed but they are investigated by a global method taking into account

10 geometrical eects and lo history or the all heat lux distribution prediction. A major advantage is that the approach remains lo time-consuming compared to Navier-Stokes simulations and it can easily be coupled to a computational dynamic light. The modelling developed or FAST allos computing a complete trajectory rom its entry point since continuum, ree molecular and transitional lo have been addressed. Comparisons have been perormed on a list o vehicles (but representatives o atmospheric re-entry activities in European Union) that have pointed out some eak and strong points in the present modelling. Elliptic lo regions, mainly encountered by capsules thermal shields or manoeuvring suraces like laps, cannot be correctly described by a Netonian approach but it has been shon that results could be signiicantly improved by using non-local methods. The diiculty relies on their implementation or any investigated 3D objects. It has also been noticed that boundary layer thickness could play a signiicant role or local heat lux assessment at trailing edges or instance. Thereore a boundary layer modelling might be considered to address such issue. A prime important point concerning application to orbital debris risk assessment is the development o corrected las taking account o partial catalycity at all according to non metallic materials. Otherise the heat luxes values should be overestimated as the addressed risk at ground. Speciic eatures such as tumbling o the object (unsteady heat lux process), strong curvature radius variations (due to the object design, tumbling, all ablation) require additional modelling or aerothermodynamics. Multi-physics phenomena such as heat transer inside the object (conduction [6] [7], radiation, pyrolysis), breaking up, possible interaction beteen ragments [6], [] require speciic developments as ell. Reerences. Laroche, E., Prévereaud, Y., Vérant, J-L., Sourgen, F., Bonetti, D. (05). Aerothermodynamics analysis o the Spaceliner Cabin Escape System modiied via a morphing system. 8 th Europ. Symp. Aerothermodyn. Space Veh., to be published, -6 th march 05, Lisbon, Portugal.. Jouhaud, F. (0). Atmospheric and Space Flight Mechanics: collection o models, Technical Rapport NT 4/763 DCSD, ONERA (in French). 3. Diallo, A. (005). Automatic Surace Heating Description in Hypersonic Continuum Regime. Master Thesis, ISAE and Politecnico di Torino. 4. Srinivasan, S., Tannehill, J.C. & Weilmuenster, K.J. (987). Simpliied Curve Fits or the Thermodynamic Properties o Equilibrium Air, Tech. Rep. NASA-RP Bertin, J.J. (938). Hypersonic Aerothermodynamics. AIAA Education Series. 6. Prévereaud, Y. (04). Development o models or the atmospheric re-entry o space debris, Ph.D. Thesis, Toulouse Universit Toulouse, France (in French). 7. Bird, G.A. (994). Molecular Gas Dynamics and the Direct Simulation o Gas Flos. Oxord Science Publications, Oxord Engineering Scienc Series number 4. 8.Blanchard, R.C. (99). Rareied-Flo Aerodynamics Measurement Experiment on the Aeroassist Flight Experiment Vehicle. J. Space. Rockets 8 (4), Glass, C.E., Moss, J.N. (00). Aerothermodynamic Characteristics in the hypersonic Continuum- Rareied transitional Regime. 35 th AIAA thermophys. Con. Anaheim, USA. 0. Detra, R.W., Kemp, N.H. & Riddell, F.R. (957). Addendum to 'Heat Transer to Satellite Vehicle Re-entering the Atmosphere', Jet Prop. 7 (), Lepage, Y. (005). Correlation du lux de chaleur convecti au point d arrêt lors d une rentrée atmospherique terrestre. Master Thesis, Ecole Polytecnique, Paris (In French).. Sagnier, P. & Vérant, J-L. (998). Flo Characterization in the ONERA F4 high enthalpy ind tunnel, AIAA J. 36 (4), Sutton, K. & Graves, R.A. (97). A general nation point convective heating equation or arbitrary gas mixtures. NASA Technical report TR Tauber, M.E. & Sutton, K. (99). Stagnation-Point Radiative Heating Relations or Earth and Mars Entries, J. Space. Rockets 8 (), Martin, J.J. (966). Atmospheric Reentr an introduction to its science and engineering. Prentice-Hall international series in space technology. 6. Lerançois, R. (006). Calcul avant-projet du lux de chaleur lors d une rentrée atmosphérique. Projet d Initiation à la Recherche, ISAE, Toulouse. 7. Prevereaud, Y. Vérant, J-L. & Balat-Pichelin, M. (04). Orbital Debris Atmospheric Re-entry Prediction. In Proc. 65th International Astronautical Congress, IAC-4-A6.9.0, Toronto, Canada (submitted or publication). 8. Sourgen, F., Prévereaud, Y., Vérant, J-L.,

11 Moschetta, J-M., Manuel mathematique, ONERA report RF /0874, Dec. 0 (in rench) 9. Walpot, L. (00). Development and Application o Hypersonic Flo Solver. Ph.D Thesis. Det Technical Universit The Netherlands. 0. Wells, William L., Measured and Predicted Aerodynamic Coeicients and Shock Shapes or Aeroassist Flight Experiment Coniguration, NASA TP-956, 990. Prévereaud, Y., Vérant, J-L., Moschetta, J-M., Sourgen, F. (03). Debris Aerodynamic interaction and its Eect on re-entry risk Assessment. 6 th Europ. Con. Space Debris, Darmstadt, Germany.

8th European Symposium on ATD for Space Vehicle, Lisbon, 2-6 March 2015

8th European Symposium on ATD for Space Vehicle, Lisbon, 2-6 March 2015 1 FAST a Pre-Design Tool for the Atmospheric Re-entry of Space Vehicles and Debris F. Sourgen (*) Y. Prévereaud J-L. Vérant E. Laroche J-M. Moschetta (*) frederic.sourgen@onera.fr Onera Midi Pyrénées Center