REBUILDING THERMAL RESPONSE AND ABLATION RADIATION COUPLING FOR SUPERORBITAL RETURN

Transcription

1 REBUILDING THERMAL RESPONSE AND ABLATION RADIATION COUPLING FOR SUPERORBITAL RETURN Jérémy Mora-Monteros 1, Elise Fahy 2, Nikhil Banerji 1, Nathan Joiner 3, Georges Du a 4, and Pénélope Leyland 1 1 Interdisciplinary Aerodynamics Group, Ecole Polytechnique Fédérale de Lausanne, Switzerland, jeremy.mora-monteros@epfl.ch 2 Centre for Hypersonics, The University of Queensland, Australia 3 Fluid Gravity Engineering Ltd 4 Garéoult, France ABSTRACT The atmospheric entry or re-entry of super-orbital missions is a critical phase of the mission. The typical velocity of a capsule during an atmospheric entry is of the order of 1 km/s. The penetration of the capsule at this speed creates a strong bow shock in front of the heatshield. The shock layer is composed of a high temperature and strongly radiative plasma. The capsule therefore undergoes extreme conditions. In fact, the contributions of convective, di usive and radiative heat fluxes can sometimes make a total heat flux of around 1 MW/m 2. Lightweight ablators have therefore become part of the design of the Thermal Protection System (TPS) of atmospheric entry capsules. Heat is transferred to the capsule s surface via convection, di usion and radiation. Lightweight ablators are used to protect the aeroshell via dissipation of heat through radiation, ablation and pyrolysis. Neither the total heat flux nor the ablation phenomenons occur on their own. The study of ablation-radiation-flowfield coupling is therefore a key element to cfd model the hypersonic flow and better design the TPS. The evolutions of the temperature, the convective and radiative heat fluxes, the ablation rate are implicitly linked. The thermal response of a high speed re-entry capsule has a strong dependence on the freestream conditions, the surface material and the chemical reactions in the boundary layer. This work addresses simulation techniques for estimating such responses. Rebuilding ablation-radiation coupling for fast return missions requires a strategy for coupling trajectory evolving thermal response with the aerothermodynamics and radiating properties of the shock layer, the wall boundary layer together with the surface reactions. A particularly crucial analysis is required from the polyatomic radiative species, and the predominant role of VUV radiation. In the ESA TRP ARC, computational studies were performed with such a coupling strategy, using the PARADE radiation library of ESA developed by IRS and FGE, and an in-house ablation and thermal response tool for the Hayabusa mission trajectory, as well as the Apollo 4 mission. Figure 1. Illustration of aerothermodynamic processes occurring in the shock-layer and on the surface of a Stardust-type re-entry capsule at peak heating conditions[1] Key words: Hypersonic, ablation, radiation, thermal response code, PICA like materials, chemistry model, collision integrals. 1. INTRODUCTION Many space missions include atmospheric entries, like missions that come back to the Earth (Soyuz, ESA s ATV, Hayabusa, Apollo), missions that land on Mars or missions that enter other planets atmospheres (Huygens probe).

2 The atmospheric entry or re-entry of such missions are critical phases. The typical velocity of a capsule during an atmospheric entry is of the order of 1 km/s. The penetration of the capsule at this speed creates a strong bow shock in front of the heatshield. The shock layer is composed of a high temperature and strongly radiative plasma. The capsule therefore undergoes extreme conditions. In fact, the contributions of convective, di usive and radiative heat fluxes can reach 1 MW/m 2. A thermal protection system is used to protect the capsule and its payload. There are di erent types of thermal protection systems. However, this work focuses on ablative thermal protection systems, made of phenolic impregnated carbon composites. Their principle is to dissipate the heat created by evaporating the resin into pyrolysis gases and by decomposing the carbon fibres. The gas created by these two processes created a layer that protects the capsule by reducing the incoming heat flux. The evolutions of the temperature, the convective and radiative heat fluxes, the ablation rate are implicitly linked. The thermal response of an high speed re-entry capsule has a strong dependence on the freestream conditions, the surface material and the chemical reactions in the boundary layer. This work addresses simulation techniques for estimating such responses and is a contribution to the European Space agency project called Ablation Radiation Coupling. First, this paper describes the di erent tools that were used to perform coupled simulations. The application of these tools to the Hayabusa capsule trajectory is presented. Finally, some results on the Apollo 4 equivalent sphere [2] are given. First this study, two trajectory points of Hayabusa, and three of Apollo 4 were studied. The conditions for Hayabusa are given in Table 1. Table 1. Hayabusa conditions used fl inf [kg/m 3 ] v inf [km/s] T wall [K] H e H e The conditions for Apollo 4 trajectory points are given in Table 2 Table 2. Apollo 4 conditions used fl inf [kg/m 3 ] v inf [km/s] T wall [K] A1 1.73e A2 3.41e A3 5.1e ABLATION RADIATION COUPLING 2.1. Flowfield Modelling The aerothermodynamics of the flow are estimated using the eilmer3 software. eilmer3 is the compressible flow computational fluid dynamics code developed at The University of Queensland, along with contributors from EPFL and other institutions worldwide. The basis of the solver is a cell-centred, finite-volume approach to the integral form of the Navier-Stokes equations (1) applied in two or three dimensions on structured grids. j ˆ UdV = ( ˆt F i F v ) ˆndA + QdV (1) V S V In this equation, U is the vector of conserved quantities, V the cell volume, F i the inviscid flux, F v the viscous flux, A the cell boundary area, and Q the vector of source terms from geometry, chemistry, thermal energy exchange and radiation. Of particular interest to this project are the inclusion of mass flux across boundaries through the flux vectors and the inclusion of radiation transport through the radiation source term. Details can be found in the eilmer3 theory book [3] and user guide [4] for a more detailed description of the theory behind the code and its operation Spectral modelling: PARADE Emission and absorption coe cients are computed with the Plasma Radiation Database (PARADE), a line-by-line radiation code. The species H2, C3 and C2H, were identified as missing from PARADE, as they could be potentially be important for VUV spectral studies of ablation products. These species were therefore added to the database. Spectroscopic constants, transition dipole moments and Frank Condon factors were readily found in the literature (NIST spectroscopic database and [1]) and implemented for the Lyman and Werner bands of H2. Line-by-line data for C3 and C2H was not found. An absorption cross-section look up was therefore added (a general look up method for any species). The model assumes that lines of these tri-atomic species are su ciently close that the spectra may be treated as a pseudo-continuum. The cross section database was populated from a number of sources including experimental data and other numerical tools Radiation transport modelling Transport modelling considers the way that radiative energy is transported through the flowfield, from emission at one location in the plasma to potential absorption at another location along a line of sight. The divergence of the radiative heat flux, the direct result of transport modelling, is the radiative source term taken into account by

3 the central equation of the flowfield solver, in cases of radiation-flowfield coupling. This term is consequently updated whenever the radiation transport is recalculated. eilmer3 s own radiation transport solver was used in this work simulations, radiation transport calculations were carried out using a monte-carlo ray tracing method for the hayabusa trajectory. In the case of the Apollo 4 trajectory, a tangent-slab method was used, as the simulations were only done for the equivalent sphere geometry. The radiative source term, Qrad is calculated using equation 2, taking into account emission and absorption coe cients: Conservation of mass The gas phase continuity equation that is solved to get the gas density profile in the material is: d fl g dv = Ê g dv fl g v g da (4) dt V V The model presented assumes that all the solid mass lost is transformed into gas, i.e. the volumetric mass production rate of gas Ê g is equal to the volumetric mass loss rate Ê s, and that the gas fills the entire free space in the porous medium. S Œ Œ Q rad =4fi j d Ÿ I dêd 4fi Emission Absorption (2) Conservation of momentum, Darcy s law Darcy s law is used to consider the conservation of momentum and close the system of equation. The velocity of the gas through a porous material is given by: 2.4. Material response code Joshi [5] developed a thermal response code sacram that is based the work of Amar [6]. The one-dimensional code, written in python, solves the conservation of mass, momentum and energy. The material decomposition, which is directly related to the mass loss, is modelled using Arrhenius equation [6]. The system of equations that describes the problem is defined using a control volume finite element spatial discretization method (CVFEM). A Newton iterative method is used to linearise the system by using the first order jacobian. The time integration is done with an implicit Euler scheme. Conservation of energy Both solid and gas energy equations can be reduced to the mixture energy equation: v g = Ÿ ÒP (5) µ The solving method and procedure are detailed in a previous work [7]. Material History To understand the behaviour of a TPS material at a chosen trajectory point, its thermochemical history needs to be taken into account. This is done by solving the material response from the start of re-entry until the trajectory point in question. Stagnation point heating results from previous Hayabusa simulations [8] are used to calculate the blowing rate ( m g ) and wall temperature at the stagnation point. The results are shown in figure 2. d fledv = dt V S Q da fl g h g v g da (3) S Where the di erent terms correspond to energy content, conduction, grid convection and gas flux. fl, e, and h are respectively the density, specific internal energy and specific enthalpy of the mixture. fl g, h g and v g are the density, specific enthalpy and velocity of the gas flowing through the porous media. v m is the velocity of the currently considered cell mesh. is the porosity of the material. Equation 3 has to be solved to calculate the temperature of the mixture, supposed identical in solid and gas. Figure 2. Material history of a PICA-like TPS material for a Hayabusa type re-entry trajectory.

4 2.5. Coupling The Radiation-Flowfield and Ablation-Flowfield coupling algorithms are described in [7]. Figure 3 shows the Ablation-Radiation-Flowfield coupling algorithm that was used to run coupled simulations for this work. PARADE T t,r, T v,e, ρ j ν,κ ν,λ T t,r, T v,e, ρ e3rad F SACRAM e3mpi F ' 1 e3rad F 1 1 F 1 ' T t,r, T v,e, ρ e3rad n-1 PARADE F n-1 ' j ν,κ ν,λ F ' SACRAM F 1 ' + m g, + m g,1 F n-1 ' + SACRAM m g,n-1 e3mpi n F n PARADE j ν,κ ν,λ ABLATION RADIATION Figure 3. Ablation-Radiation-flowfield coupling with eilmer3. The degree of radiation-flowfield coupling can be estimated through the evaluation of the Goulard number,, which is the conversion of the freestream energy flux to incident radiative energy flux as shown in equation 6 below, = 2Q rad 1 2 fl Œu 3 Œ (6) The rule of thumb for Goulard number evaluation is that radiation-flowfield coupling should be considered for >.1, although it can still be important for <.1, especially for scaled flows. For most flight vehicle simulations, a Goulard number of.1 or below indicates that uncoupled analysis is su cient. The Goulard numbers for H1 and H2, using the radiative heat transfer at the stagnation point from a tangent-slab calculation, are given in Table 3. It is clear that strong coupling is not required for the two Hayabusa trajectory points studied. Regarding Apollo 4 (Table 4), strong coupling is relevant for the first two trajectory points. 3. APPLICATION TO HAYABUSA TRAJECTORY This work focused on two points of the Hayabusa trajectory. The first trajectory point corresponds to the peak convective heating condition, the second to the peak radiative heating. However, the results presented in this paper concern the first trajectory point (H1) only. Refer to a previous work [7] to see results for the second trajectory point. All the results presented here were obtained using a loose coupling of ablation, radiation and flowfield. This section shows the e ect of coupling on the results. As previously said, the coupling for the two studied trajectory point is clearly not strong. However, this aspect of the problem was checked. In fact, simulations have been performed while updating the radiative source term every 1 steps and every body-length. There was not any noticeable di erence. Therefore, the coupled simulations presented here were done with an update of the radiative source term every body-length. Temperature profiles Figure 4 shows the evolution of the translation-rotational temperature profile on the stagnation line over 5 radiation-flowfield coupling steps. Overall, the amplitude remains the same, except for an increase of about 2K at the shock. Moreover, the shock is slightly shifted towards the wall. This temperature profile is stable from the first coupling step. Table 3. points. Goulard number for Hayabusa trajectory Condition H1 H2 Goulard number.93.1 Table 4. Goulard number for Apollo 4 trajectory points. Condition A1 A2 A3 Goulard number Figure 4. Evolution of the translation-rotational temperature profile on the stagnation line over 5 radiation-flowfield coupling steps. The same change in the shock stand-o distance can be observed on Figure 5, which displays the evolution of the vibrational-electron-electronic temperature profile on the stagnation line over 5 radiation flowfield coupling steps. A decrease can can be

5 noticed on this temperature profile in a region comprised between about 2 and 6 mm from the wall. More details can be observed on Figure 6. However this shows that the di erence is small. Figure 8 shows that ablation increases the radiative heat flux of about 14% in the stagnation point region, which is significant. Otherwise, the evolution of the radiative heat around the surface of the aeroshell is similar. Again, this arises the importance of considering ablation for the simulation of heat fluxes around such a capsule. Figure 5. Evolution of the vibrational-electronelectronic temperature profile on the stagnation line over 5 radiation-flowfield coupling steps. Figure 7. Evolution of the convective heat flux around the aeroshell over 5 radiation flowfield coupling steps. Figure 6. Evolution of the vibrational-electronelectronic temperature profile on the stagnation line over 5 radiation-flowfield coupling steps. Heat fluxes Figure 7 shows changes in the convective heat flux in three cases (ablation only, radiation-flowfield coupling, ablation-radiation-coupling). The introduction of ablation slightly reduces the convective heat flux at the stagnation point. However, it is significantly increased in the region close to the shoulder of the aeroshell. Ablation radiation coupling is therefore important for the design of a TPS. However, these convective heat fluxes are di erent from what was presented in Figure 2. This means that the method used to compute heat fluxes in the present work is probably not adequate. Therefore, some improvements are needed. Figure 8. Evolution of the radiative heat flux around the aeroshell over 5 radiation flowfield coupling steps. Radiation Figure 9 gives the divergence of the radiative heat flux along the stagnation line. Note that the surface boundary condition is a surface energy balance, with a surface emissivity of.9. The green (respectively blue) curve corresponds to the case without ablation (respectively with ablation). It can be noticed on this graph that the absorption is increased (negative divergence of radiative heat flux) in the region between.7 and 2 mm from the wall. On the contrary, the emission is increased in the layer between the wall and.7 mm from the

6 wall (positive divergence of radiative heat flux). Figure 9. Divergence of radiative heat flux along the stagnation line, with and without ablation. Figure 1 compares the spectral flux over wavelengths between 5 and 12 nm. The di erence between the two spectral flux profiles denotes a strong influence of ablation on the radiation in the shock layer. As the flow around such a capsule is known to be highly energetic, the VUV (vacuum-ultra-violet) part of the spectrum represents a significant contribution to the total spectrum (approximately 25%). However, the spectral flux displayed shows the lack of obvious contributions in the UV/visible from CN, C2 and C3. This can be explained by the probably very low quantities of these species in the flow during the simulations. That can be seen in the mole fraction plots (Figure 11). Especially with CN, which seems to form at the surface, and to dissociate straight away. These are all areas that need more investigation, since this is really the first time these simulations have been possible in eilmer3, so refining of the physics, chemistry and coupling is needed. Figure 1. Spectral flux and cumulative heat flux obtained with and without ablation. The wavelength range is 5-12 nm Figure 11. Mole fractions of ablative species on the stagnation line 4. APOLLO 4 EQUIVALENT SPHERE SIMULATIONS Some results were presented by Papadopoulou [9]. The aforementioned work used photaura, eilmer3 s own radiation library. The results presented here were obtained using PARADE, as previously said. As the flowfield results are coming from simulations made on the Apollo 4 equivalent sphere [2], a tangent-slab model was utilised. In fact, simulations on the equivalent sphere reproduce correctly the profiles on the stagnation line as well as the shock stand-o distance. A tangent-slab method applied on the stagnation line of the equivalent sphere gives a good approximation of the radiative heat flux. Figures 12, 13 and 14 show the spectral flux over a wavelength range from 5 nm to 12 nm, as well as the integrated radiative heat flux, for the three Apollo 4 trajectory points. The second trajectory point corresponds to the peak radiative heat flux. It is therefore expected that the integrated radiative heat is the highest of the three. However, the Vacuum-Ultra-Violet (VUV) contributions for the first two trajectory points are similar in absolute values (3.2 MW/m 2 vs 3.46 MW/m 2 ), even if the one for the second trajectory point remains slightly bigger. In relative values, the VUV contribution is bigger for the first point (17.2% vs 15.6 %) than for the second. The main di erence between these first two points is made in the Near-Infrared (NIR) region. Finally, the relative contribution of VUV for the third trajectory point is equivalent to the one for the second trajectory point (15.4% vs 15.6%).

7 Spectral flux, q λ (W/m 2 -m) 1x1 15 1x1 14 1x1 13 1x1 12 1x1 11 1x1 1 1x1 9 1x1 8 1x Wavelength (nm) q λq 2.5x1 6 2x x1 6 1x1 6 5 Figure 12. Spectral flux and integrated radiative heat flux for the first trajectory point Spectral flux, q λ (W/m 2 -m) 1x1 14 1x1 13 1x1 12 1x1 11 1x1 1 1x1 9 1x1 8 1x Wavelength (nm) q λq 2.5x1 6 2x x1 6 1x1 6 5 Figure 13. Spectral flux and integrated radiative heat flux for the second trajectory point Spectral flux, q λ (W/m 2 -m) 1x1 15 1x1 14 1x1 13 1x1 12 1x1 11 1x1 1 1x1 9 1x1 8 1x Wavelength (nm) q λq 2.5x1 6 2x x1 6 1x1 6 5 Figure 14. Spectral flux and integrated radiative heat flux for the third trajectory point 5. CONCLUSION This work presented the methodology and tools used to perform coupled simulations of flows around Integrated Flux, q (W/m 2 ) Integrated Flux, q (W/m 2 ) Integrated Flux, q (W/m 2 ) aeroshells during atmospheric entries. The di usion modelling was updated to make the simulations more accurate. An existing material response was also updated to include the gas phase continuity and momentum equation. Ablation-Radiation coupling is an iterative and complex process. The Goulard number allows to determine how strong the coupling needs to be. For the two Hayabusa s trajectory points studied in this work, a loose coupling was su cient. The results obtained for the peak convective heat flux trajectory point (H1) showed that radiation-flowfield coupling has an influence on the temperature profiles along the stagnation line, and on the convective and radiative heat fluxes. This e ect remains small in the results presented in this work. However, the introduction of the ablation phenomena modifies significantly the radiation results. The ablation species change the radiative properties of the plasma in the near wall boundary layer. The emission of the plasma is increased in a layer of about.7 mm near the wall, and the absorption is increased in the layer between.7 and 2 mm from the wall. The e ect of ablation on the spectral flux (Figure 1) is significant. Nevertheless, a lack of obvious contribution of ablative species can be observed. The reason for this is probably the relatively low quantities of ablation species observed in the flowfield. In fact, even for the species created in significant amounts, they react almost directly with the flowfield. These observations prove that the coupling of ablation and radiation to the flowfield is important to simulate realistically hypersonic flows. Some more work on the material response code should be done. The development of a multi-dimensional version is one direction. Further investigations on the internal radiation in the TPS should give a better description of internal material properties. 6. ACKNOWLEDGEMENTS This work has been partially supported by ESA-TRP ARC" under contract No:416422/12/NL/AF. The authors would like to thank Dr. Gennady Plyushchev for his help with the update of the di usion model. REFERENCES [1] Daniel F Potter. Modelling of radiating shock layers for atmospheric entry at Earth and Mars. PhD thesis, The University of Queensland, 211. [2] R.C. Jr. Ried, W.C. Rochelle, and J.D. Milhoan. Radiative Heating to the Apollo

8 Command Module: Engineering Prediction and Flight Measurement. Technical report, NASA, Manned Spacecraft Center, Houston, Texas, [3] P.A. Jacobs, R.J. Gollan, A.J. Denman, B.T. O Flaherty, D.F. Potter, P.J. Petrie-Repar, and I.A. Johnston. Eilmer s Theory Book : Basic Models for Gas. Technical report, Centre for Hypersonics, Brisbane, Queensland Australia, 212. [4] P.A. Jacobs, R.J. Gollan, and D.F. Potter. The Eilmer3 Code : User Guide and Example Book 214 Edition. Technical report, Centre for Hypersonics, Brisbane, Queensland Australia, 214. [5] Ojas Joshi. Fluid-structure thermal coupling and ablation e ects in atmospheric entry. PhD thesis, Ecole Polytechinque Federale de Lausanne, 213. [6] Adam Joseph Amar. Modeling of One-Dimensional Ablation with Porous Flow Using Finite Control Volume Procedure. Master s thesis, North Carolina State University, 26. [7] Jeremy Mora-Monteros, Elise Fahy, Nikhil Banerji, and Penelope Leyland. Ablation Radiation Coupling for the Hayabusa Trajectory. In 6th International Workshop on Radiation of High Temperature Gases in Atmospheric Entry, St Andrew, UK, 214. [8] Michael Winter, Ryan McDaniel, Yih-Kanq Chen, Yen Liu, David Saunders, and Petrus Jenninskens. Radiation Modeling for the Reentry of the Hayabusa Sample Return Capsule. In 5th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, pages 1 21, Reston, Virigina, January 212. American Institute of Aeronautics and Astronautics. [9] Ermioni Papadopoulou, Nikhil Banerji, and Penelope Leyland. Ablation Radiation Coupling for the Apollo Command Module Filght Missions. In 6th International Workshop on Radiation of High Temperature Gases in Atmospheric Entry, number 1, St Andrew, UK, 214. [1] U. Fantz and D. Wünderlich. Franck-Condon factors, transition probabilities, and radiative lifetimes for hydrogen molecules and their isotopomeres. Technical report, 24.