Transition effects on heating in the wake of a blunt body

A series of aerodynamic heating tests was conducted on a 70-deg sphere-cone planetary entry vehicle model in a Mach 10 perfect-gas wind tunnel at freestream Reynolds numbers based on diameter of 8.23x104 to 3.15x105. Surface heating distributions were determined from temperature time-histories measured on the model and on its support sting using thin-film resistance gages. The experimental heating data were compared to computations made using an axisymmetric/2D, laminar, perfect-gas Navier-Stokes solver. Agreement between computational and experimental heating distributions to within, or slightly greater than, the experimental uncertainty was obtained on the forebody and afterbody of the entry vehicle as well as on the sting upstream of the free-shear-layer reattachment point. However, the distributions began to diverge near the reattachment point, with the experimental heating becoming increasingly greater than the computed heating with distance downstream from the reattachment point. It was concluded that this divergence was due to transition of the wake free shear layer just upstream of the reattachment point on the sting. Nomenclature BC,H heating bias error CH Stanton number, q/ [ ρ 1 u 1 ( h 0 − h w ) ] d molecular diameter (m) h enthalpy (J/kg) Kn Knudsen number k thermal conductivity (W/m-K) M Mach number N number density (1/m3) PC,H heating precision error p pressure (N/m2) Q heat (J/m2) q heat transfer rate (W/m 2) R radius (m) Re Reynolds number S distance along model surface (m) T temperature (K) t time (sec) U∞ freestream velocity (m/sec) α thermal diffusivity (m2/sec) β thermal product, α / k (W-sec1/2/m2-K) ∆CH heating uncertainty λ correction factor (1/K) λMFP mean free path (m) ρ density (kg/m3) Subscripts: 0 stagnation 1 freestream 2 post-shock D diameter w wall Introduction Wake flow behavior is one of the important issues which must be considered in the design of planetary entry vehicles such as the Mars Pathfinder probe1. The nature of the wake flow dictates payload size, placement and shielding requirements. Accurate characterization of the wake flow behavior is becoming * Research performed as graduate research assistant. Presently National Research Council Research Associate, NASA Langley Research Center. AIAA Member. ** Professor of Mechanical and Aerospace Engineering. AIAA Associate Fellow Copyright ©1997 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved 1 American Institute of Aeronautics and Astronautics more important due to the increasing reliance in planetary mission planning on aerobraking, which produces much more severe aerothermodynamic loads on an entry vehicle. In this study, the effects of transition in the wake of a blunt body were investigated through heattransfer testing of a 70-deg sphere-cone entry vehicle configuration in a perfect-gas hypersonic wind tunnel. Other recent studies 2-15 have also addressed the effects of nonequilibrium thermochemistry, rarefaction, and transition to turbulence on wake flow behavior. Experiment Description Test Models The test model geometry was a 70-deg spherecone forebody of 1.0-in. radius with a 40-deg conefrustrum afterbody (Fig. 1). The forebody corner radius was 0.05 forebody radii, and the radius of the hemispherical nose was 0.5 forebody radii. The afterbody frustrum radius was 0.6 forebody radii. A heat-transfer test model was fabricated from Macor, a thermally-insulative, machinable glass-ceramic material. The model was instrumented with fastresponse (< 1 μsec) thin-film temperature resistance gages. There were a total of 37 gages on the forebody, afterbody and base of the model (Fig. 2). The support sting for this model was fabricated from stainless steel. A lengthwise slot into which a contoured Macor insert with 33 additional thin-film gages was fitted was machined into the sting (Fig. 2). The support sting was fitted to a sting adapter and the facility support barrel at a distance of 5.25 forebody radii downstream of the model. An additional uninstrumented model and sting were fabricated from aluminum for use in oil-flow tests. Facility Description Aerothermodynamic testing was conducted in the NASA Langley Research Center (LaRC) 31-Inch Mach 10 Air Tunnel 16 (Fig. 3). This facility is a conventional perfect-gas hypersonic blowdown wind tunnel in which air is used as the test gas. The 31-Inch Mach 10 Air Tunnel has been calibrated for operation at reservoir pressures of 0.86 MPa to 10 MPa at a reservoir temperature of 1000 K. These reservoir conditions produce freestream Reynolds numbers of from 1.62x106 m-1 to 6.20x106 m-1 at a nominal freestream Mach number of 10. Facility run times for the current series of heat-transfer tests were limited to 35 seconds in order to avoid violation of the semi-infinite heat transfer assumption 17, although much longer run times are possible for aerodynamic testing. Freestream conditions for this study are listed in Table 1. The runto-run repeatability of the facility flow conditions was investigated, and it was found that the freestream conditions were repeatable to within less than ±2%. Data Reduction Heat-transfer rate time-histories were computed from thin-film gage temperature time-histories using the 1DHEAT data reduction code 18. Heating timehistories were determined from the temperature timehistories by two methods: the Kendall-Dixon method 19, which is a closed-form analytical scheme; and a numerical solution of the one-dimensional heatconduction equation. Both methods are based on the assumption of one-dimensional heat conduction within the model substrate 17. In the Kendall-Dixon method, the total heat energy added as a function of time is first computed by: Q ( t n ) = β π n 3 i = 1 ( T i − T1 ) + ( T i − 1 − T1 ) t n − ti + t n − ti − 1 ∆ t (1) After the total heat added has been computed, the heattransfer rate is computed from 20: q ( t n ) = dQ ( t n ) dt = − 2 Q n − 8 − Qn − 4 + Qn + 4 + 2 Q n + 8 40∆ t (2) It is assumed in the derivation of the KendallDixon method that the thermal properties of the model remain constant. However, the thermal properties of Macor are functions of temperature. Curve fits to experimental thermal properties data 18 re given by: ρ = 2543 (kg/ m 3 ) (3) k = 0 . 33889 + 7 . 4682x 10 3 T − 1 . 6118x 10 5 T 2 + 1 . 2376x 10 8 T 3 ( W / m − K ) (4) α = 1 . 3003x 10 6 − 2 . 2523x 10 9 T + 1 . 8571x 10 12 T 2 ( m 2 / sec) (5) The results from the Kendall-Dixon method are adjusted to account for the temperature dependence 2 American Institute of Aeronautics and Astronautics through an empirical correction given by 18: q var = qconst 1 + λ ‡ T w − 300Ž (6) where the correction factor λ is given by: λ = 7 . 380x 10 4 − 4 . 604x 10 7 ‡ T w − 300Ž (7) This empirical correction can be avoided through the use of the numerical method, in which the variation of thermal properties with temperature is included in the formulation of the method. In this numerical method, the one-dimensional heat conduction equation: ρ c p M T M t = M M x Š ‹ k M T M x ‘ ’ (8) is solved through a time-implicit, finite-volume discretization given by: − k i − 1 / 2 ‡ T n i − T n i − 1 Ž ‡ x i − x i − 1 Ž − − k i + 1 / 2 ‡ T n i + 1 − T n i Ž ‡ x i + 1 − x i Ž = ‡ ρ c p Ž i ‡ T n i − T n− 1 i Ž ∆ t ‡ x i + 1 / 2 − x i − 1 / 2 Ž (9) The Kendall-Dixon method was used for rapid initial analysis of the experimental data. The validity of the empirical correction in this method was later verified by re-reducing the data using the finite-volume method. Experimental Results The 70-deg sphere-cone heat-transfer model was tested in the 31-Inch Mach 10 Air Tunnel at diameterbased freestream Reynolds numbers of 8.23x10 4, 1.62x105, and 3.15x105. The experimental data are reported in terms of the Stanton number which is defined by: C H = q ρ 1 U 1 ‡ h 0 − hw Ž (10) The Stanton number remains nominally constant during a test, whereas the heat-transfer rate decreases as the wall surface temperature and enthalpy increases. Stanton number distributions normalized by the measured stagnation point values from tests at each of the three Reynolds number test points are plotted in Figs. 4 and 5. The complete distributions are shown on a log scale in Fig. 4, while the details of the forebody and wake distributions are shown separately on linear scale plots in Fig. 5. The Reynolds number had no effect on the normalized forebody heating distribution, but had a strong influence on the heating distribution in the wake, where the normalized heating was an increasing function of Reynolds number. The peak heating on the model sting varied from 8% of the forebody stagnation point heating at the lowest Reynolds number to 15% at the highest Reynolds number. Relative peak sting heating rates of this level are consistent with turbulent wakes 6,7,14, whereas relative laminar peak sting heating levels are in the 45% range12-15. Several surface oil flow tests were also carried out using the uninstrumented aluminum model. From inspection of oil flow photographs from these tests, it was possible to identify the boundary-layer separation point on the afterbody and the free-shear-layer reattachment point on the sting. A sample surface oil flow photograph is shown in Fig. 6. It was found that the reattachment point on the sting moved a small distance upstream toward the model as the Reynolds number was increased. This behavior is typical of increasing turbulence in the free shear layer. As the turbulence increases, momentum dissipation causes its thickness to increase, and the thicker turbulent free shear layer then comes into contact with the sting further upstream than a laminar free shear layer would. Experimental Uncertainty Two primary sources of experimental uncertainty were considered: precision error, PC,H, due to run-to-run repeatability of flow conditions and test data, and bias error, BC,H, due to uncertainty in the thermal properties of the Macor models. From these two sources, t