AIAA JOURNAL Vol. 39, No. 11, November 2001 Shock-Wave/Turbulent Boundary-Layer Interactions in Nonequilibrium Flows Francesco Grasso ¤ University of Rome “La Sapienza,” 00184 Rome, Italy Marco Marini † Centro Italiano Ricerche Aerospaziali, 81043 Capua, Italy Giuliano Ranuzzi ‡ and Simone Cuttica ‡ University of Rome “La Sapienza,” 00184 Rome, Italy and Bruno Chanetz § ONERA, 92190 Meudon, France Shock-wave/turbulent boundary-layer interactions in the presence of thermal and chemical nonequilibrium phenomena are analyzed. The approach relies on a linear eddy viscosity two-equation turbulence modeling that accounts for the coupling of turbulence with chemistry and vibration, and it employs a total variation diminishing nite volume numerical methodology. The capability of the model has rst been assessed for a cylinder are con guration, and results have been compared with experiments. The model has then been applied to assess the aerodynamic performance of control surfaces of a reusable launch vehicle. In particular, the effects of wall temperature and ap de ection on the separation, aerothermal loads, and ap ef ciency have been studied. The analysis shows that turbulence becomes important for ap de ection angles greater than a critical value [O (15 deg)], thus avoiding the crisis of the ap ef ciency that is observed under laminar conditions and extending the operating capabilities of the control surface. The study also shows that the wall temperature affects signi cantly the ef ciency and the operating envelope of the ap primarily under turbulent conditions. Introduction S HOCK-WAVE/boundary-layer interactions in high-speed ows have a large impact on the design of hypersonic vehicles for the presence of extended recirculation regions and intense local heat- ing. Indeed, the occurrence of such interactions may deteriorate the aerodynamic ef ciency of the control surfaces, making critical the ight control and the structural integrity of the vehicle. 1 In particu- lar, the position of primary separation has the greatest importance in determining the location of the shock con guration that affects the aerodynamic quantities. The complexity of the phenomenon and its importance in the design of aerodynamic shape and thermal protec- tion system of a hypersonic vehicle require the understanding of the controlling effects and their quantitative characterization. In the past few decades several studies dealing with the shock- wave/boundary-layer interaction phenomena were conducted, ei- ther for laminar or turbulent conditions, mainly for cold hypersonic ows, that is, for low enthalpy. Extensive reviews describing the physical phenomena of shock-wave/boundary-layer interaction in hypersonic regime and some correlation laws for incipient sepa- ration conditions, characteristic pressures, separation extent, and peak heating can be found in the works of Needham and Stollery, 2 Holden, 3 and Delery. 4 Experimental studies of both laminar and turbulent shock-wave/boundary-layer interactions from supersonic through hypersonic regime were conducted by Holden, 3 who has investigated the effects of Mach and Reynolds numbers, ramp an- gle, and leading-edge bluntness on the ow eld in terms of up- stream in uence, separation extent, and peak heating. In Ref. 3 it Received 14 April 2000; revision received 1 April 2001; accepted for publication 8 May 2001. Copyright c ° 2001 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. ¤ Professor, Department of Mechanics and Aeronautics, Via Eudossiana 18. Associate Fellow AIAA. † Research Scientist, Aerothermodynamics Laboratory, Via Maiorise. ‡ Aeronautical Engineer, Department of Mechanics and Aeronautics, Via Eudossiana 18. § Head of Hypersonic Project, Fundamental and Experimental Aerody- namic Department, Rue des Vertugadins. was established that upstream in uence increases with ramp an- gle and decreases with Mach number, and it is affected also by the Reynolds number (only weakly in a fully turbulent regime), whereas bluntness reduces pressure and thermal loads because the interaction for a blunt leading edge occurs in (a locally) supersonic regime. Delery 4 has experimentally shown that upstream in uence and separation length increase with ramp angle for a given Mach and Reynolds number and decrease with Mach number for a given ramp angle and Reynolds number. In Ref. 4 it was also shown that the main ow features remain similar in laminar and turbulent con- ditions, the differences being the extent of the interaction, that is, the characteristic scale, and the pressure and thermal loads. Grasso and Marini 5 have studied hypersonic viscous ows dominated by strong shock-wave/laminar boundary-layer interactions over wing– ap and wing– fuselage junction con gurations and have assessed the effects of the control surface de ection angle, leading-edge shape, and viscous interaction parameter. Scaling laws for the up- stream in uence, peak heating, and aerodynamic coef cients have been established by means of numerical simulations and theoretical considerations. Grasso et al. 6 have characterized the different con- trolling mechanisms of the shock-wave/boundary-layer interaction phenomena and have critically reviewed the various correlation for- mulas (skin friction, Stanton number, characteristic pressures, and peak heating) applicable in the different regions. Under reentry conditions, the gas may not always be treated as an ideal gas, and real gas effects such as vibrational excitation and chemical reactions affect signi cantly such phenomena; their in u- ence (and coupling with turbulence) must be necessarily accounted for. Grasso and Leone 7 have studied the in uence of chemical re- actions under the assumption of thermal and chemical equilibrium for shock-wave/laminar boundary-layer interactions over compres- sion ramps. In Ref. 7 it is shown that due to dissociation reactions (in equilibrium) the temperature is lowered and the shock waves are weakened, as well as their interaction with the boundary layer. The results of Ref. 7 show a reduction of the separation extent due to real gas effects; however, the peak heating (on the ramp) still correlates with the inviscid pressure jump across the shock. Re- cently, Mallinson et al. 8 have conducted high-enthalpy compression 2131