Nonequilibrium ionization accompanying hypersonic flow of carbon dioxide gas over blunt bodies

A study is made of the nonequilibrium ionization in the shock layer when carbon dioxide gas flows over cones with spherical noses at velocity 4–7 km/sec, the density of the oncoming flow being 10^–8-10^–5 g/cm³. The influence of admixtures of nitrogen and sodium on the electron concentration is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 183–186, January–February, 1981.     

Estimates of nonequilibrium radiative heating of blunt bodies in a hypersonic flow of carbon dioxide gas

The solution to the problem of hypersonic nonequilibrium flow over cones with rounded noses [1, 2] is used to estimate the radiative heating of the surfaces of the bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 158–160, November–December, 1979.     

Similitude of hypersonic flows of low-density gas over blunt bodies

Laws of similitude of hypersonic flows of monatomic gases have been obtained earlier from asymptotic analysis of the equations as S and confirmed by experimental data and numerical results [1], For diatomic gases, dimensionless numbers have not been deduced by analyzing the equations but by general arguments based on analogy with monatomic gases; they were used to compare experimental and calculated results in [1–3]. In the present paper, dimensionless numbers are derived on the basis of model kinetic equations for a diatomic gas, and limits of their applicability are established. Numerical calculations confirm the exact and approximate laws of similitude and permit a comparison with experimental results. The influence of the laws of viscosity on the drag for a sphere as a function of the Reynolds number Re₀ determined using the viscosity at the stagnation point is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 130–135, March–April, 1981.     

Supersonic flow of dusty gas over blunt bodies

The results are given of a numerical investigation of the flow of dusty gas over the complete front surface of a sphere. The flow conditions are varied over a wide range in which the state of the gas suspension in the shock layer changes from a frozen to an equilibrium state. The phenomenological approach [5] is used to derive the system of equations describing the behavior of the two-phase medium. The system of conservation equations for the gas—solid-particle mixture is closed by means of relations that generalize the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 73–77, May–June, 1982.     

Shock layers over blunt and conical bodies in hypersonic non-equilibrium flow

It is well known that the flow-field over blunt and pointed bodies is sensitive to the non-equilibrium phenomena characteristic of high enthalpy hypersonic flows. Till date, most experiments and modelling were related to flows essentially dominated by the dissociation rate. However, in practical cases of a re-entry low density flow, the aerodynamic quantities such as the shock shape and location may also be strongly influenced by vibrational relaxation coupled with dissociation and chemical reactions. Thus, the flow about various bodies such as spheres, hemisphere–cylinders and cones is recomputed using a chemical model recently proposed by the authors and by taking into account the coupling between the vibrational relaxation and the chemical kinetics. Then, the computed shock shapes in air flow are compared to recent experimental results obtained in a ballistic range for flight velocities between 2,500 and 4,000 m/s, and in a shock tunnel for enthalpies close to 5 and 10 MJ/kg. The computed density field around hemispherical bodies is also compared to the experimental one. A good agreement, within 5%, between computed and measured results is observed. A few comparisons are also proposed with the results obtained with another well-known (empirical) model. A comparison is also made between the flow quantities along the stagnation line obtained over cylindrical and spherical bodies using the present model and those coming from a quasi-one-dimensional model recently developed, showing also a satisfactory agreement.     

Approximate analytical solutions for heat fluxes in three-dimensional hypersonic flow over blunt bodies

Analytical expressions for the heat flux divided by its value at the stagnation point which depend on the geometric parameters invariant with respect to the choice of the coordinate system, as well as expressions depending on the geometry and the pressure on the surface which have a wider applicability range are obtained in the problem of three-dimensional hypersonic flow over blunt bodies at large and moderate Reynolds numbers. These formulas are derived by solving the thin viscous shock layer equations for a perfect gas using the integral method of successive approximations developed by the author. The accuracy and the range of applicability of the analytical solutions are estimated by comparing them with numerical solutions. On the basis of comparisons with numerical solutions for multicomponent chemically nonequilibrium air at altitudes from 90 to 50 km of the spacecraft reentry trajectory in the Earth’s atmosphere it is shown that the formulas obtained can be used for calculations of the heat flux on an ideal catalytic surface of bodies in hypersonic chemically reacting gas flow.     

Three-dimensional hypersonic gas flow over wings

The results of the theory of three-dimensionai hypersonic flow over a wing based on the use of the thin shock layer method are reviewed.Based on paper read at the Seventh Congress on Theoretical and Applied Mechanics, Moscow, August 1991. Presented by V. Ya. Neiland.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 148–161, September–October, 1992.     

Entropy effects in hypersonic flow over blunt delta wings

The problem of hypersonic flow over blunt delta wings is considered. It is shown that in the case of large wing lengths x -100, where x is the longitudinal coordinate measured in blunt nose radii, extremal flow regimes characterized by an essentially nonuniform distribution of the gas dynamic parameters (density, entropy, Mach number) may be realized in the shock layer near the windward surface of the wing. The location of the zones of flow convergence or divergence on the surface of a delta wing with sweep angle x=75° is established. For the same wing the ranges of Mach numbers M and angles of attack leading to extremal flow regimes are indicated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, 178–181, March–April, 1991.     

Hypersonic flow of nonequilibrium air over blunt bodies

A numerical method is described for computing nonequilibrium three-dimensional supersonic flow of a gas in the shock layer over the forward surface of blunt bodies with discontinuities of shape. The basic idea is to divide the original system of differential equations into two subsystems, which are solved in succession: first for the gasdynamic variables, the velocity components and the pressure, and then for the relaxation parameters and the enthalpy. To calculate the velocity components and the pressure we use the iterative marching method [1, 2] in the form given in [3]. The relaxation equations and the enthalpy equation are integrated numerically along the stream lines. A discussion is given of the effect of nonequilibrium of physical and chemical reactions on the distribution of parameters in the inviscid shock layer and on the aerodynamic coefficients of blunt bodies in hypersonic air flow. The unsteady aerodynamic coefficients are calculated by the curved body method [4]. The computational algorithm takes the form of a program in “ALGOL-60” for the BéSM-6 computer.     

Entropy layer in the problem of hypersonic flow over thin blunt bodies which are close to two-dimensional

In the problem of the hypersonic flow of a nonviscous thermally nonconducting gas over thin blunt bodies which are close to two-dimensional the solution is constructed in the entropy layer. The construction is achieved by a generalization of the method developed ia [1] in application to bodies close to two-dimensional. The use of an approximate model identifying the effect of the blunting on the gas with the effect of a concentrated force distributed over the edge is important in the construction. The solution is represented in the form of asymptotic expansions. The equations of the hypersonic theory of small perturbations, which is the null approximation in the process of construction of the solution in the form of a series in powers of a small parameter determined as the square of the relative thickness of the body or the relative width of the perturbed region, are obtained in the null approximation in this case. The surface of the blunt body proves to be singular for the null approximation, since the entropy function p/?^x grows without limit as the surface is approached. The attempt to construct the succeeding approximations leads to strengthening of the singularity. This necessitates the use of the method of deformed coordinates (the PLG method). Basic to the latter is the removal of the singularity, which is not inherent to the exact solution of the problem, through asymptotic expansions with respect to a small parameter not only of the unknown variables, but also of the independent variables, with the subsequent determination of the deformation of the independient variables on the basis of the “quenching” of the singularity. Use of the PLG method allows one to construct a solution which is uniformly applicable in the entire stream, including the entropy layer. In practice, the construction of such a solution leads to the determination of the displacement of the streamlines near the surface of the body, as a result of which the singularity is “absorbed” by the body and the solution outside the body proves to be freed of the singularity. In the null approximation this displacement of the streamlines can be determined in closed form.     

Three-dimensional hypersonic rarefied gas flow round bodies of revolution

A proposed method of studying three-dimensional rarefied gas flow around a body of revolution is based on the numerical solution of model kinetic equations. By way of example, the problem is considered of hypersonic flow round an ellipsoid of revolution whose velocity vector forms an angle of ₀ with the axis of symmetry of the body and is located in the plane of symmetry. A study is made of the effect of the angle of attack, surface temperature and Knudsen number on the aerodynamic characteristics of the body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti 1 Gaza, No. 1, pp. 184–186, January–February, 1986.     

Nonequilibrium hypersonic flow of gas past a wing of small aspect ratio

It is well known [1] that nonequilibrium physicochemical processes taking place in gases at high temperature influence the gas-dynamic parameters and aerodynamic characteristics of bodies in hypersonic flight. In the present paper, the thin shock layer method [2–4] is used to consider the problem of nonequilibrium hypersonic flow of gas past a wing of small aspect ratio at an angle of attack. It is shown that the flow component of the vorticity is conserved along the streamlines, and this property is exploited to obtain an analytic solution of the equations of the three-dimensional nonequilibrium shock layer. The influence of the disequilibrium on the thickness of the shock layer and the pressure distribution is investigated.     

Numerical investigation of the structure of nonequilibrium three-dimensional hypersonic flow past blunt bodies

Three-dimensional dissociating air flow past blunt bodies is investigated within the framework of the parabolized Navier-Stokes equations in the thin layer approximation. Multicomponent diffusion, barodiffusion and homogeneous chemical reactions, including dissociation-recombination and exchange reactions, are taken into account. The boundary conditions are assigned in the free stream and at the surface of the body with allowance for heterogeneous catalytic reactions and slip effects. The problem of flow at zero angle of attack past blunt bodies possessing two planes of symmetry is investigated numerically for flow patterns varying from smeared layer structure to almost ideal flow (Re=50-10⁵). The flow conditions corresponded to the motion of a body with lift along a re-entry trajectory [1]. The contribution of the chemical reactions in the shock wave as compared to the diffusion flux at the edge of the shock wave was estimated. The edge of the shock wave is assumed to correspond to the point at which the density profile has the greatest slope. The influence of slip effects and barodiffusion on the flow characteristics is demonstrated. The results of the calculations are compared with calculations based on the thin viscous shock layer model [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 143–150, September–October, 1987.The author wishes to express his thanks to G. A. Tirskii and V. V. Lunev for useful discussions and valuable advice.