G A Tirskii

Efficient numerical method for simulation of supersonic viscous flow past a blunted body at a small angle of attack

Abstract For solving the three-dimensional (3-D) full viscous shock-layer (FVSL) equations in a body-oriented coordinate system, an asymptotic method is used with the angle of attack as a small parameter. In using a small parameter method, the (3-D) FVSL system is separated into an axisymmetric set and a linear 2-D set of equations. The method of global iterations was used to solve both the axisymmetric and linearized sets of equations. Global iterations were carried out on the pressure gradient tangential component and on the shock wave tangle. The method is used uniformly for both the blunted and conic parts of the body. The shock wave angle was found by using the Rankine-Hugoniot boundary condition for the normal component of the velocity. A computational grid adapted to the solution was used in solving both systems of equations. The comparison of this approach with 3-D implicit time-marching methods shows that the time neccessary for the calculation in the 3-D case is about 100 times less, while the accuracy of the calculations is essentially the same. Also, the small parameter method enables one to find a one-parameter family of solutions; the parameter in question is the angle of attack.

NUMERICAL SIMULATION OF THE FLOW OVER A BODY FLYING THROUGH A THERMAL IN A STRATIFIED ATMOSPHERE

Abstract The three-dimensional supersonic viscous flow over a blunted body flying horizontally through a cloud of hot gas (a thermal) is studied numerically. It is assumed that the cloud was formed as the result of a powerful explosion in the Earths atmosphere. Consideration is given to the late stage of the explosion, corresponding to the vortex ring formation time. A complete problem is unstable. However, the air flow near the body at every point of the flight trajectory can be considered as a quasi-stationary flow, in view of the fact that the ratio of the characteristic time scale in the shock layer to the thermal characteristic time scale is 10 −5 . The aerodynamic and heat transfer characteristics of the flying body are studied.

A thermally non-equilibrium viscous shock layer past slender blunted cones

Abstract Physical-chemical processes in a shock layer past a slender spherically blunted body at high supersonic velocities are investigated. Using a gas-dynamic model, defined by the complete viscous shock-layer equations [1], the steady laminar axisymmetric flow of viscous, heat-conducting, partially dissociated and ionized air under chemical and thermal non-equilibrium is considered throughout the region between the body and the required thin shock wave. Attention is concentrated on the non-equilibrium chemical, ionization, and relaxation kinetics at large distances from the leading stagnation point. Multicomponent diffusion and the reverse influence of dissociation-recombination on the relaxation of vibrational quantum states, i.e. coupling vibration-dissociation-vibration (CVDV), are taken into account. A new model is used to describe dissociation-relaxation process [2]. The model includes the effect of non-equilibrium excitation of vibrations and the equilibrium excitation of rotational molecular modes on the dissociation rate constants. Comparisons with experimentally verified calculations and calculations within the scope of the chemically equilibrium full viscous shock-layer model indicate that the model is physically adequate. The calculations highlighted physical effects in the non-equilibrium viscous shock layer past a slender spherically blunted cone at various distances from the stagnation point.

Influence of second-order boundary layer effects in hypersonic flow over slender blunt cones

The aim of this study is to determine the influence of second-order effects in the aggregate on supersonic axisymmetric flow over slender blunt cones and also to determine the region of applicability of approximate methods of taking into account the strongest of these second-order effects — entropy layer absorption. A system of complete viscous shock layer equations containing all the terms of the gas dynamic Euler equations and all the second-order terms of asymptotic boundary layer theory is chosen as the gas-dynamic model. Within the calculation domain the problem is solved in a unified manner.

Application of the small-parameter method to the problem of the spatial flow of a viscous gas past bodies

Abstract The solution of the problem of the spatial hypersonic flow of a viscous gas past spherically blunted bodies is considered using the system of equations of a complete viscous shock layer (CVSL). The use of the small-parameter method (SPM) in conjunction with the method of global iterations enables one to reduce the computer time required by a factor of approximately 100 compared with the time needed to calculate similar problems in a strictly spatial formulation by establishment methods [1]. The flow past blunt cones and bicones of long length at low angles of attack is considered as well as the flow past a body, which differs slightly from an axisymmetric one, at zero angle of attack. The applicability of the SPM is confirmed by comparison with experimental and computed data.

Effects of second-approximation of boundary layer theory in three-dimensional flow over bodies with a large aspect ratio at small angles of incidence

The influence of the second-approximation effects of laminar boundary layer theory on the heat transfer in three-dimensional hypersonic flow over blunt cones with a large aspect ratio is investigated numerically.

Study of turbulent hypersonic flow past elongated blunt-nosed cones

Axisyrmnetdc turbulent hypersonic perfect-gas flow past slightly blunted cones is considered. The influence of the absorption of the entropy layer, developing on an elongated body, on friction and heat transfer to the body surface is studied using the viscous shock layer model. Correlations are established for the heat flux and the friction coefficient along the cone surface at large distances from the forward stagnation point. The results are presented together with their correlations in the framework of the viscous shock layer model and an approximate model of the boundary layer type, taking into account the entropy layer absorption. A generalization of the Reynolds analogy is obtained. There are many paper.s dealing with the calculation of the friction and heat transfer in flow past blunt bodies within the framework of the classical theory of the turbulent boundary layer (see [1]). The absorption of the entropy layer by the boundary layer may be regarded as the principal second-order effect in boundary layer theory. Approximate methods have been developed to take this effect into account (see [2--6]). It should be noted that the entropy layer is absorbed more rapidly by a turbulent than by a laminar boundary layer, due to the greater boundary layer thickness; in this case the absorption length is 5--50 bluntness radii. In [2--4] the effect of the absorption of the entropy layer by the boundary layer was taken into account by means of additional calculations for the flow parameters at the outer edge of the boundary layer, using the mass flow rate global balance method. The authors of [5] and [6] have proposed a technique based on the mass-average method. All these approaches enable the entropy layer absorption to be taken into account without solving a set of equations more intricate than that of boundary layer theory. All these approaches need theoretical or experimental verification. The similitude criteria for turbulent boundary layers on blunt-nosed cones were analyzed in [4, 6]. In [4] the similitude parameters determining the heat transfer to the cone surface were established for the entropy layer absorption regime over the following ranges of the governing parameters: cone half-angle 0k= 10 deg, Reynolds number Re~ =1.0-105--3.1-105, Mach number Mo. =6--8, temperature factor tw=0.40--0.52 (here, tw=Tw/To, T w being the wall temperature and T O -- the stagnation temperature). The similitude criteria governing hypersonic flow past slender blunt bodies in the turbulent boundary layer regime were determined in [6]. Our aim is to study numerically the problem of hypersonic turbulent flow past blunt-nosed cones using the viscous shock layer model; to estimate the errors of the various approximate theories; and to establish the similitude criteria for the heat transfer at large distances from the bluntness and for the friction at both large and intermediate distances.