Numerical investigation of thermal and chemical nonequilibrium flows past slender blunted cones

Chapter 1: Asymptotically Simplified Gas-Dynamic Models of Supersonic and Hypersonic Aerodynamics and Heat Transfer

“…The use of the VSL model made it possible to determine the influence of the second approximation effects in the laminar and turbulent flows around bodies with a large aspect ratio [81][82][83][84][85]. The following problems were solved within the framework of the VSL model: hypersonic airflow around bodies with a large aspect ratio with allowance for spatial transport of radiation and equilibrium reactions [86,87] with allowance for nonequilibrium thermal and chemical processes [81,88], supersonic nonuniform waketype flows around cones [89,90], and many others. Such numerical studies based on the full NS equations would not actually lead to any refinement of results, but would require much more computational resources.…”

Chapter 2: Generalized Equations of the Viscous Shock Layer with Slip Conditions on the Surface and Bow Shock Wave

“…As Chapter 2 deals with the construction of gas-dynamic models of supersonic and hypersonic flows around blunted bodies in various ranges of Reynolds (Knudsen) numbers, here we ignore the physical and chemical processes in the flow and on the body surface, which are inevitably inherent in problems of the flow around bodies with high supersonic velocities. The procedure for taking them into account has been well developed; it does not involve principal difficulties [6,15,16] (see Chapter 5) and does not change the basic conclusions concerning the construction of gas-dynamic models at various limiting values of the main governing parameters of the problem: free-stream Mach and Reynolds numbers, temperature factor, etc. Certainly, the allowance for physical and chemical processes will change quantitative results without changing the gas-dynamic models whose form and properties depend on the method of simplifying only the governing equations (2.2)-(2.4) and the equations of convective diffusion with allowance for chemical reactions and ionization reactions, which are added to these equations if diffusion, chemical reactions, and ionization reactions are taken into account [15].…”

“…These equations contain all terms of the Euler system, except for the approximation of the thin viscous shock layer (TVSL) where the approximation of a thin shock layer (SL) is used, and as a consequence, terms with the normal component of the velocity vector are omitted in inertial terms. Therefore, it becomes possible to solve stationary problems numerically by effective iterativemarching methods, which is particularly important in flow calculations with allowance for real physical and chemical processes in the shock layer and on the body surface [6,14,15].…”

Thermo-chemical ablation during reentrant and high altitude skipping flight

“…The transient heating and chemical evolution of the surface and interior of both carbon and silicon based materials experiencing atmospheric reentry remain subjects of vigorous inquiry 1,2,3,4,5,6,7,8 . Among these, material response calculations have been done using the heat-balance integral 1,2 (HBI), finite element 3 (FE) and finite volume 4 (FV) techniques.…”

“…Among these, material response calculations have been done using the heat-balance integral 1,2 (HBI), finite element 3 (FE) and finite volume 4 (FV) techniques. Coupled flow field calculations using viscous shock-layer 5 and full NavierStokes 6,7,8 techniques are not uncommon. Aspects of the operative surface thermochemistry are summarized in a fairly recent review 9 .…”