On Shock Interactions And Reflections With High Temperature Non-equilibrium Effects

The high temperature in the shock layer of the hypersonic re-entry vehicle will in-duce various physical and chemical phenomena, such as the multi-mode internal energy excitation, dissociation and ionization, etc. As the density is very low in the upper atmo-sphere, these thermochemical processes are often in the non-equilibirum state with the energy exchanges between different internal energies and the chemical reactions. The effects of these thermochemical phenomena, which leading to nonuniform flow field and gas properties, are termed non-equilibrium effects. Non-equilibrium effects have an important influnence on the aerodynamic force and heating through changing the gas properties, shock location and shape, boundary layer separation, etc. Shock/shock inter-action and shock reflection are two common problems in the hypersonic vehicle internal and external flows, and have been extensively investigated and fruitful results have been achieved. However, most of the researches are based on the perfect gas model, and var-ious underlying fundamental mechanisms associated with non-equilibrium effects on shock/shock interactions and shock reflections are still unclear. In this paper, the shock interactions and reflections will be investigated, and the emphasis is placed on the non-equilibrium effects on the transition between different shock interaction types and the shock reflection hysteresis phenomena.Firstly, we outline various thermo-chemical non-equilibrium models, including the multi-mode internal energy, thermodynamic relations, energy change relaxation equa-tion, gas transport properties, chemical reaction rates, chemical and vibrational coupling and species mass production rate. The govern equations are established by combining Navier-Stokes equation with the non-equilibirum effects, and a new numerical program is developed to solve these equations. sevveral cases on the hypersonic flow around bodies are simulated including circular cylinder, sphere and compression ramp. With different free stream conditions including various species components and Mach num-ber, and considering three wall conditions adopting inviscid, isothermal and adiabatic assumptions respectively, the shock stand-off, physical quantity distributions along the stagnation, wall pressure, friction, heat flux, boundary layer thickness and seperation zone are focused on. By comparing with experiments or previous simulations, it is shown that the present numerical method has good reliability and precision, especially in the simulation of the shock wave and non-equilibrium relaxation process. For the viscous case, the flow properties in the boundary layer can been predicted reliably as well.Secondly, the theoretical analysis method for the shock interactions and reflections with non-equilibrium effects is developed. By dividing the process of the gas across a normal shock into frozen part and non-equilibrium relaxation part, and introducing a non-equilibrium relaxation length δneq to represent the relaxation process, a functional formula is established to reflect the physical quantities relationships before and behind a normal shock. The functional formula for a normal shock is then extended to the oblique shock situation. For the expansion waves, the functional formula is established by di-viding the expansion process into a group of isentropic and quasi-steady sub-expansion fans with small deflection angle and integrating these sub-expansion fans numerically. Referring to the perfect gas, the shock polar diagram considering the non-equilibrium effects is established from the functional formulas mentioned above. Moreover, a pre-liminary rule for choosing the suitable non-equilibrium relaxation length is proposed.Then the Type VI and V of inviscid shock interactions on a double-wedge geome-try and the transition critical conditions (the second wedge angle θ2) between these two types are investigated theoretically and numerically. The critical value of the second wedge angle can be predicted theoretically by the established shock polar method with a suitable non-equilibrium relaxation length estimated by evaluating the equilibrium relaxation length behind each oblique shock and the geometry size considered in the study. Referring to the theoretical results, numerical simulation is also used to capture the complete transition process and to obtain the second wedge angle span for this pro-cess. Comparing the theoretical results with the numerical results with Ma=11, it is found that the critical conditions and the local pressure obtained by the shock polar agree well with the numerical simulation, and the shock polar can predict the shock interaction tructure with a certain geometry condition. The comparison result declears that the shock polar method and the estimation of the non-equilibrium relaxation length are reasonable. It is also found that there are distinct differences on the critical transition condition between the perfect gas and non-equilibrium gas. The non-equilibrium gas effects lead to a larger second wedge angle for the transition and these effects become more significant with a larger Mach number of the inflow. It is interesting that the vari-ation of the transition wedge angle with the Mach number of inflow behaves oppositely for the calorically perfect gas and the non-equilibrium gas. In the Mach number range of7≤Mα≤18, the rangeability of the critical wedge angle is very small for the perfect gas, while is about4°℃for the non-equilibrium gas. The second wedge angle span for the complete transition process is basically the same for different Mach number, although the non-equilibrium effects influence the critical condition.At last, the reflection hysteresis between steady regular reflection and Mach re-flection is investigated theoretically and numerically considering the non-equilibrium effects. Both the numurical and theoretical results show that the non-equilibrium ef- fects lead to a larger value of von Neumann angle θN and detachment angle θD-The hysteresis domain also becomes bigger with a small change of θN and a large change of θD.The numerical simulation process and theoretical analysis approach establish the foundation for a further investigation of the shock reflection with non-equilibrium effects.