Unsteady shock-wave reflection and interaction in viscous flow with thermal and chemical nonequilibrium

Introduction Steady shock/boundary layer interactions and self-sustained unsteady type IV shock-shock interference heating problems with nonequilibrium real gas effects were studied by numerical simulations. The emphasis of the investigation was on the effects of internal thermo-chemical excitation on surface heating rates, skin friction, and flow field unsteadiness of the viscous shock interactions. The multicomponent Navier-Stokes equations with nonequilibrium rotational, vibrational, and chemical models for fivespecies air were solved by a finite-volume secondorder TVD scheme together with a new third-order semi-implicit Runge-Kutta scheme. For the steady shock/boundary layer interaction on a flat plate, it was found that the real gas effects reduce the size of the shock induced separation bubble and the magnitude of the surface heating rates. For the unsteady shock-shock interference heating of a pure N2 flow over a cylinder, the results showed that type-IV shock-shock interference heating flows with real gas effects are inherently unsteady. The degree of the unsteadiness is related to the location of the jet impingement on the cylinder relative to the stagnation point. For certain impingement positions, vortices are generated and shed off near the jet impingement point. This periodic shedding of the vortices contributes to the self-substained oscillations of both the jet and other parts of the flow fields. In addition, the real gas effects reduce the level of peak surface heating and peak surface pressure in the case of endothermic internal-mode excitations. 'Graduate Student Researcher, Department of Mechanical and Aerospace Engineering, Student Member AIAA t Assistant Professor, Department of Mechanical and Aerospace Engineering, Member AIAA ^Graduate Student, Department of Mechanical and Aerospace Engineering. Copyright ©1996 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Understanding unsteady shock/boundary layer and shock-shock interference heating phenomena is vital for the design of hypersonic vehicles. Such interactions occur in many external and internal flow fields around steady and maneuvering hypersonic vehicles, such as the one shown in Figure 1. The interactions strongly affect the magnitudes of surface heating rates and skin friction. Two types of shock interactions, shock/boundary layer interactions and type IV shock interference heating, were examined in this study. The first class of shock interactions is the shock/boundary layer interaction, where an incident oblique shock is reflected by a surface. Interaction between the incident and reflected shock waves and the boundary layer occurs. Figure 2 shows a schematic of a steady shock-wave reflection interaction with the viscous boundary layer. The large adverse pressure gradient due to the incident shock hitting the wall causes the boundary layer to separate. When the boundary layer reattaches, a reattachment compression shock is formed. The second class of hypersonic shock interactions is the type IV shock interference interaction. Figure 3 shows a type IV interaction which is caused by an impinging oblique shock intersecting the free stream bow shock ahead of a body. This interaction creates a transmitted shock which then impinges upon the lower bow shock (due to the flow behind the initial impinging oblique shock). Behind this transmitted shock, which is weaker than either bow shock, a supersonic jet is formed in the surrounding subsonic flow. This jet impinges on the body, ending in a terminating strong shock. At the jet impingement point, extremely high surface pressures and heating rates are encountered''' ''. As the jet flow is expanded over the surface, it once again becomes supersonic. This creates a shear layer along the body between the flow from the jet and the subsonic bulk flow behind the bow shock. This type of interaction has been shown to be inherently unstable ' ' in ideal gas flows. To date most studies of the shock interactions have been limited to ideal gas flows for both shock/boundary layer interaction ' ', and type IV shock interference heating. The ideal gas type IV problem has been extensively studied experimentally and analytically t' "1, and numerically!''' "I However, due to the high temperatures found in these interactions, real gas effects need to be considered for many of these flow studies. Real gas effects have a noticeable impact on flow structure, such as the reduction of the shock stand off distance in a blunt body flow' ',and parameters such as surface heating rates, which can be either reduced or enhanced depending on the nature of the chemical nonequilibrium. Because of their importance, real gas effects have recently been the focus of several studies. For steady shock/boundary layer interactions, Ballaro and Andersen'', and Grumet et of.'' have performed numerical studies of flow at a scramjet inlet with real gas effects. In their cases, they assumed a partially dissociated freestream to simulate conditions at an inlet behind the bow shock of a vehicle. They found that the recombination of species at the wall enhanced the surface heat flux. Type IV interactions were studied numerically by Prabhu, et al. '' for equilibrium chemistry. More recently, Sanderson'' experimentally and analytically examined the effects of nonequilibrium on type IV flows. A real gas numerical study was done by Briick'' which looked at the effects of nonequilibrium and impinging shock location on flow structure and surface pressure and heat flux. These real gas studies, however, have only addressed the issue of steady flows. Though ideal gas shock interference has been found to be unsteady and the unsteadiness has strong effects on surface heating rates, so far, no work in studying real gas effects in unsteady shock interactions, such as those around a maneuvering hypersonic vehicle, has been done, to the authors' knowledge. Therefore, the objective of our work is to study viscous and nonequilibrium effects in steady shock wave reflections and unsteady type IV shock interference heating problems using numerical simulations. The present paper focuses on work done in studying the fluid mechanics and real gas effects in unsteady viscous shock reflection and interaction flow fields. Specifically, we have numerically studied the effects of thermo-chemical nonequilibrium on the flow characteristics by using currently available thermal and chemical nonequilibrium models. The viscous flows are modeled by the multicomponent Navier-Stokes equations with a three temperature model and nonequilibrium rotational, vibrational, and chemical modes. Though rotational nonequilibrium is only important in the low density regime, it is included in the present model for use in planned future studies at lower densities. At present, air flow in the temperature regime below 8000 9000°^ is considered. This allows ionization of the gas to be neglected for simplicity. The models follow those of Candler'', Gokgen'', and Park''. The numerical method is a secondorder TVD scheme with Roe's approximate Riemann solver as extended to nonequilibrium flows by Grossman and Cinella''. The source terms are computed using the Additive Semi-implicit RungeKutta method derived by Zhong'l