Computation of Surface Heat Transfer Rate on Apollo CM Test Model in Free-Piston Shock Tunnel HIEST

Transcription

1 th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 9 - January, Nashville, Tennessee AIAA - Computation of Surface Heat Transfer Rate on Apollo CM Test Model in Free-Piston Shock Tunnel HIEST Tomoaki Ishihara, Yousuke Ogino, and Keisuke Sawada Tohoku University, Sendai, Miyagi, 9-9, Japan Hideyuki Tanno Japan Aerospace Exploration Agency, Kakuda Space Center, Kakuda, Miyagi, 9-, Japan Aeroheating on the Apollo CM test model placed in the free-piston shock tunnel HI- EST was measured. The obtained heat flux distributions were reasonably correlated when normalized by a product of Stanton number and the square-root of the Reynolds number for lower to moderate total enthalpy. However, for higher total enthalpy conditions, the heat flux distributions -% higher than those for other results conducted at lower total enthalpy. To clarify the possible causes of this phenomenon, we attempted to calculate heat flux around the Apollo CM test model. Obtained total heat flux considering radiated emission from driver gas agree well with measured heat flux. I. Introduction NASA decided the retirement of space shuttles in July, due to enormous maintenance costs and safety defects, and announced Multi-Purpose Crew Vehicle (MPCV) concept as the next-generation manned space vehicle. MPCV is an Apollo-like capsule space vehicle which aims asteroid probes and human explorations of Mars. Capsule space vehicles such as MPCV are now paid attention to, in the future, will play the principal role. When such a capsule vehicle enters into the atmosphere of a planet, a strong shock wave is formed around the capsule and it is exposed to severe aerodynamics heating in the shock layer. To protect the capsule from such heating environment, appropriate thermal protection system must be equipped. Therefore, it is critical to predict the heat fluxes accurately for the design of space vehicles. Recently, aerodynamic heating on the Apollo command-module AS- test model illustrated in Fig. placed in the free-piston shock tunnel HIEST illustrated in Fig. was measured by Tanno et al., The model was.%-scaled AS- command model made of SUS stainless steel and had a diameter of mm. To measure heat flux around the model, eighty-four miniature co-axial thermocouples were mounted on the forebody. The heat flux data were summarized along the centerline of the model for angles of attack of and degs as shown in Fig.. The stagnation enthalpy H and the stagnation pressure P were varied from MJ/kg to MJ/kg, and from MPa to MPa, respectively. Table summarizes the upstream conditions of the test section determined by an axis-symmetric nozzle code. The obtained heat flux distributions were reasonably correlated when normalized by a product of Stanton number and the square-root of the Reynolds number for lower to moderate total enthalpy. However, for higher total enthalpy conditions, the heat flux distributions differed considerably from the correlation plot. For example, the obtained heat flux distributions for the angle of attack of degs shown in Fig. -(a), three curves (Shot # and Shot # 9) are correlated reasonably well to yield single correlation curves, however, the obtained wall heat flux distributions for higher total enthalpy conditions (Shot # and Shot # ) exhibit significantly higher heating rate over the entire region. The reason of the higher wall heating rate is still unknown. For the angle of attack of deg. indicated in Fig. -(b), a similar trend was also observed. Graduate Student, Department of Aerospace Engineering, ishihara@cfd.mech.tohoku.ac.jp, AIAA Member Assistant Professor, Department of Aerospace Engineering, yogi@cfd.mech.tohoku.ac.jp, AIAA Member Professor, Department of Aerospace Engineering, sawada@cfd.mech.tohoku.ac.jp, AIAA Associate Fellow Associate Senior Researcher, Space Transportation Propulsion Research and Development Center, Space Transportation Mission Directorates, tanno.hideyuki@jaxa.jp, AIAA Member of Copyright by the, Inc. All rights reserved.

2 One can see that the heat flux distributions indicated in Shot # and # are significantly higher than that for Shot #. Similar results were also observed at the high-enthalpy shock tunnel T in Caltec. Such higher heat flux distributions, -% higher than those for other shots conducted at lower stagnation enthalpies obviously pose a critical issue over the existing design method of thermal protection system for entry capsules. For the reason of these heating anomalies, we believe it could be an important factor that (i) enhancement of thermal conductivities by turbulence transport, (ii) radiative heat transfer in the shock layer, (iii) radiated emission from the driver gas with diaphgram rapture in HIEST experiments (remarkable luminosities are observed). Therefore, we evaluate numerically the wall heating rate, accounting for several possible mechanisms in the HIEST experiments. In this study, we compute the flowfield over the forebody of the Apollo CM test model and evaluate the convective and radiative heat fluxes on the model surface in order to clarify the possible causes of significantly higher heating. (a) Side view Figure. Apollo CM test model. (b) Front view Table. Upstream parameters of Apollo CM test campaign at HIEST calculated with a JAXA in-house code. Shot P H T T v Pressure Density Velocity Mach Re No. [MPa] [MJ/kg] [K] [K] [kpa] [kg/m ] [m/s] [/m] of

3 / # H =9. [MJ/kg] Re=. # H =. [MJ/kg] Re=. [/m] # H =. [MJ/kg] Re=. [/m] #9 H =. [MJ/kg] Re=. [/m] [/m] (a) AOA deg. Figure. / 9 # H =.9 [MJ/kg] Re=. [/m] # H =. [MJ/kg] Re=. [/m] # H =. [MJ/kg] Re=. [/m] (b) AOA deg. Measured heat flux distribution along the centerline of the model. HIEST Specifications Compression tube Bore:φ mm, Length: m Stagnation enthalpy to MJ/kg Shock tube Bore:φ mm, Length: m Stagnation pressure to MPa Piston mass to kg Test time ms or longer Nozzle Conical: exit diameter φ. m Contoured: exit diameterφ. m Figure. Free-piston shock tunnel HIEST II. Numerical Methods The numerical method is based on the cell-center finite volume discretization. For calculation at AOA deg., we solve the axi-symmetric Navier-Stokes equations for the Earth atmosphere accounting for thermochemical nonequilibrium effects in the shock layer. We employ Park s two-temperature thermochemical model in which five chemical species (O, N, NO, N, O) are considered. The convective numerical flux is calculated by SLAU. We employ MUSCL approach for attaining a second order spatial accuracy. In the time integration, the Euler explicit method is employed. On the other hand, for AOA deg., we solve the three-dimensional Navier-Stokes equations accounting for thermochemical nonequilibrium. The convective numerical flux is calculated by SLAU. We use the LU-SGS implicit method 9 for time integration. For improving the stability in the integration of source terms, the diagonal point implicit method is utilized. The radiative transfer equation is solved one-dimensionally in the direction normal to the wall. The absorption coefficients are calculated using the multi-band model. O, N, NO, O, and N are considered as contributors to radiation. Absorption coefficients of each contributors are evaluated at, wavelength points assuming to be in local thermodynamic equilibrium. They are constructed for the wavelength region from to, Å. In this work, radiative heat transfer calculation is uncoupled with flowfield. III. Numerical Condition Upstream conditions are equal to experimental value in Tab., and mass fractions of upstream calculated by NENZF are listed in Tab.. We assume that wall boundary condition is isothermal and fully-catalytic wall. We have generated grids adapted to the shock wave front to estimate heat flux appropriately. A typical example of the computational grid for axi-symmetric calculation is shown in Fig. -(a), that for threedimensional calculation is shown in Fig. -(b). These grids have points in the wall normal direction and of

4 in the direction along the wall. The grid for three-dimensional calculation has points in circumferential direction. The distance between the first layer and the wall surface, that means grid resolution for temperature boundary layer, is set to order which is determined from grid convergence property of wall heat flux. The geometry of test model is same as the experimental model. Table. Mass fraction of upstream Shot C O C N C NO C O C N Y Y Z X X Z (a) AA deg. Figure. (b) AA deg. Solution-adaptive grids for Apollo CM test model. IV. Results and Discussion IV.A. Convective heat flux without turbulence and radiation We have calculated three cases: Shot #, #, and #. The computed pressure and translational temperature contours for each case are shown in Fig.. One can find that a bow shock wave is developed in front of the body. By the use of shock adapted grid, we capture shock wave sharply and obtain the smooth pressure and temperature contours along the wall surface. Figure shows the temperature distributions along the stagnation streamline for Shot # (lower enthalpy) and # (higher enthalpy). Horizontal axis shows the distance from stagnation point normalized by nose radius. Results of translational temperature is up to, K behind the shock wave, and vibrational temperature quickly equilibrates with the transnational temperature in the shock layer. Figure shows the calculated convective heat flux under each condition with experimental results. Relatively high heating near the shoulder region ( =.) arises from recombination processes of N and of

5 O with adiabatic expansion of flowfield. We can confirm that convective heat flux distributions normalized by St Re /,D are almost same, but is lower than experimental one. Although previous our results could obtain very good agreements with Fay-Ridell s theoretical solution and Gökçen s computation, measured heat fluxes are significantly high, and do not obey St Re /,D manner. These heating anomalies are critical issue for thermal protection system. In addition, We have calculated four cases at AOA deg.: Shot #, # (under higher enthalpy condition), #, and # 9 (under lower enthalpy condition). Figure shows the pressure and translational temperature distribution, and Fig. 9 shows the wall heat flux distributions at Shot # (the highest enthalpy condition) as a typical example. Due to using shock adaptive grid, we can capture shock sharply and obtain reasonable heat flux distributions in spite of three dimensional calculation. Figure shows calculated heat flux distributions on xy-plane with experimental results. Note that, in Fig. and, a numerical error shown around the center of body is caused by singularity of grids. This numerical error doesn t effect heat flux to wall so much, so in this study, more appropriate treatment to this singular point is out of scope. Under all condition, the calculated heat flux normalized by St Re /,D are correlated reasonably well to yield single correlation curve, but less than experimental one. IV.B. Effects of turbulent transfer to convective heat flux We investigate the effect of turbulence heat transport, since there are still experimental uncertainties in disturbance of free stream, surface roughness of test model and so on. Then, we compute the flowfield coupled with the algebraic turbulence model: model assumed fully turbulence, so as to examine the upper limit of wall heating by turbulent mixing. Figure shows the normalized convective heat flux distributions assuming fully turbulence at AOA deg. Under lower enthalpy condition (Shot # ), the calculated heat fluxes come close to the experimental one, in contrast with under higher enthalpy conditions (Shot # and ) our results don t agree with the value of experiments, because Reynolds number is lower. Figure (a)-(d) show the normalized convective heat flux distributions assuming fully turbulence at AOA deg. for each experimental measurement. In all results, heat flux increases as it goes down stream, since the magnitude of the vorticity increases in down stream. The calculated values come closer to experimental results especially in lower enthalpy case. There is a possibility of laminar-turbulence transition, but it s not a dominant factor of the heating anomalies. IV.C. Effects of radiative heat transfer In the HIEST experiment, driver gas is compressed by the heavy piston mass, the pressure and temperature in the reservoir rise up to atm and K, respectively. Thus, the driver gas has potential to emit intense radiation. In this computation, when we solve the radiative transfer equation utilizing tangent slab approximation, we set black-body radiation determined by driver gas temperature for the outer boundary condition of wall-ward radiative intensities. Figure shows normalized total heat flux with radiation from driver gas at AOA deg. Blue dashed line shows the heatflux without radiated emission from driver gas. Red solid line shows the one including radiated emission from driver gas. Under Shot #, calculated heat fluxes are in same range of experimental ones, if the temperature of driver gas is set to, K. For Shot # and #, our estimated temperatures became, K and, K, respectively. One can find that the radiation from driver gas greatly contributes to radiative heat flux to the wall surface. Because the temperature in shock layer is about, K at most even for higher enthalpy condition, then absorption coefficients are relatively small. Therefore, the radiated emission from driver gas is hardly absorbed in the shock layer and directly heat the test model. Figure (a)-(d) show normalized total heat flux including radiated emission from driven gas. For results of Shot # and # 9 as shown in Fig. -(a) and (b), good agreements with measured heat fluxes are obtained, if estimated radiative temperatures of driver gas are, K and, K, respectively. The driver gas temperature for shot # is higher than it for # 9, since the freestream enthalpy is higher. For Shot # and # as those shown in Fig. (c) and (d), calculated heat fluxes with radiative temperature set to, K agree well with experimental ones near the stagnation region. On the leeward, calculated heat flux is larger, because all same values of black-body intensities are assumed for the outer boundary condition of radiative transfer equation. of

6 V. Conclusions In this study, we computed heat fluxes for the forebody of Apollo CM test model to clarify the possible causes of heating anomalies measured in HIEST experiments. For the reasons of it we examined (i) enhancement of thermal conductivities by turbulence transport, (ii) radiative heat transfer in the shock layer, (iii) radiated emission from the driver gas. From results of turbulence transport analysis, heat flux was larger than it in laminar flow, especially under lower enthalpy condition. However, calculated heat flux distribution could not reproduce experimental tendency. It is hard to say that the heating anomalies caused by turbulence heat transport. We also investigated effects of radiative transfer in the shock layer and radiation from driver gas. From our computations, we could obtain very good agreements with experimental heat fluxes. Therefore, we can say that the radiation from driver gas is as the possible reason for the heating anomalies. Since radiative heat flux in the shock layer is relatively small, we should correct the measured values by the driver gas radiation. References Tanno, H., Kodera, M., Komuro, T., Sato, K., Takahashi, M., and Itoh, K., Aeroheating Measurements on A Reentry Capsule Model in Free-Piston Shock Tunnel HIEST, AIAA Paper -,. Tanno, H., Komuro, T., Sato, K., Itoh, K., Yamada, T., Sato, N., and Nakano, E., Heat Flux Measurement of Apollo Capsule Model in The Free-piston Shock Tunnel HIEST, AIAA Paper 9-, 9. Takahashi, M., Kodera, M., Itoh, K., Sato, K., and Tanno, H., Influence of Thermal Non-equilibrium on Nozzle Flow Condition of High Enthalpy Shock Tunnel HIEST, AIAA Paper 9-, 9. Eric, M., Stuart, L., and Hans, G., Apollo-Shaped Capsule Boundary Layer Transition at High-Enthalpy in T, AIAA Paper -,. Candler, G. V. and Nompelis, I., Computation Fluid Dynamics for Atmospheric Entry, Von Karman Institute for Fluid Dynamics Lecture Series, RTO-EN-AVT-, 9. Perry, K. M. and Imlay, S. T., Blunt-Body Flow Simulations, AIAA Paper -9, 99. Park, C., Nonequilibrium Hypersonic Aerothermodynamics, John Wiley and Sons Inc., New York, 99. Kitamura, K. and Shima, E., A New Pressure Flux for AUSM-Family Schemes for Hypersonic Heating Computations, AIAA Paper -,. 9 Yoon, S. and Jameson, A., An Lu-ssor Scheme for The Euler and Navier-Stokes Equations, AIAA Paper -, 9. Van Leer, B., Towards the Ultimate Conservation Difference Scheme V. A Second-Order Sequel to Goudnov s Method, Journal of Computational Physics,, 99, pp. -. Eberhartdt, S. and Imalay, S., Diagonal Implicit Scheme for Computing Flows with Finite Rate Chemistry, Journal of Thermophysics and Heat Transfer,, 99, pp. -. Vincenti, W. G. and Kruger, C. H., Introduction of Physical Gas Dynamics, John Wiley and Sons Inc., New York, 9. Park, C. and Milos, F. S., Computational Equations for Radiating and Ablating Shock Layers, AIAA Paper 9-, 99. Lordi, J. A., Mates, R. E., and Mossele, J. R., Computer Program for Numerical Solution of Nonequilibrium Expansions of Reacting Gas Mixtures, NASA CR-, 9. Ishihara, T., Ogino, Y., Sawada, K., and Tanno, H., Computation of Surface Heat Transfer Rate on Apollo CM Test Model in Free-Piston Shock Tunnel HIEST, Conference proceedings of JSFM, Fay, J. A. and Ridell, F. R., Theory of stagnation point heat transfer in dissociated air, Journal of Aeronautical Sciences, (), -,, 9. Gökçen, T., Effects of Freestream Nonequilibrium on Con- vective Heat Transfer to A Blunt Body, AIAA Paper 9-, 99. Baldwin, B. S. and Lomax, H., Thin Layer Approximation and Algebric Model for Separated Turbulent Flows, AIAA Paper -, 9. of

7 Pressure [Pa] Pressure [Pa] Pressure [Pa] (a) Shot # Figure. (b) Shot # (c) Shot # Pressure and translational temperature distributions at AOA deg. T t T v T t T v Normalized distance along the stagnation stream line Normalized distance along the stagnation stream line (a) Shot # (b) Shot # Figure. Temperature distributions along the stagnation streamline at AOA deg. St Re,D / 9 Calc. # Calc. # Calc. #..... Exp. # Exp. # Exp. # Figure. Normalized convective heat flux at AOA deg. of

8 Y Y Z X Z X Pressure [Pa] 9 9 (a) (b) Figure. (a)pressure and (b)translational temperature distributions at AOA deg. (Shot # ) Figure 9. Convective heat flux distribution at AOA deg. (Shot # ) / Exp. # Exp. # Exp. # Exp. #9 Calc. # Calc. # Calc. # Calc. # Figure. Normalized convective heat flux at AOA deg. of

9 / (a) Shot # / (b) Shot # Figure. / (c) Shot # Normalized convective heat flux assuming fully turbulence at AOA deg. St Re, D / St Re, D / (a) Shot # (Re =.9 [/m]) (b) Shot # 9 (Re =. [/m])) St Re, D / St Re, D / (c) Shot # (Re =. [/m])) (d) Shot # (Re =. [/m])) Figure. Normalized convective heat flux assuming fully turbulence flow at AOA deg. 9 of

10 / with radiation driver gas w/o radiation driver gas..... (a) Shot # (driver gas temperature:, K) / / with driver gas radiation w/o driver gas radiation..... (b) Shot # (driver gas temperature:, K) Figure. with driver gas radiation w/o driver gas radiation..... (c) Shot # (driver gas temperature:, K) Normalized total heat flux with radiated emission from driver gas at AOA deg. with radiation driver gas w/o radiation driver gas with driver gas radiation w/o driver gas radiation / / (a) Shot # (driver gas temperature:, K) (b) Shot # 9 (driver gas temperature:, K) with driver gas radiation w/o driver gas radiation with driver gas radiation w/o driver gas radiation / / (c) Shot # (driver gas temperature:, K) (c) Shot # (driver gas temperature:, K) Figure. Normalized total heat flux with radiated emission from driver gas at AOA deg. of