CONTINUUM MODELS IN PROBLEMS OF THE HYPERSONIC FLOW OF A RAREFIED-GASAROUND BLUNT BODIES

All possible continuum (hydrodynamic) models in the case of two-dimens ional problems of supersonic and hypersonic flows around blunt bodies in the two-layer model (a viscous shock layer and shock-wave structure ) over the whole range of Reynolds numbers, Re, from low values (free molecular and transitional flow conditions) up to high values (flow co nditions with a thin leading shock wave, a boundary layer and an exter nal inviscid flow in the shock layer) are obtained from the Navier-Sto kes equations using an asymptotic analysis. In the case of low Reynold s numbers, the shock layer is considered but the structure of the shoc k wave is ignored. Together with the well-known models (a boundary lay er, a viscous shock layer, a thin viscous shock layer, parabolized Nav ier-Stokes equations (the single-layer model) for high, moderate and l ow Re numbers, respectively), a new hydrodynamic model, which follows from the Navier-Stokes equations and reduces to the solution of the si mplified (''local'') Stokes equations in a shock layer with vanishing inertial and pressure forces and boundary conditions on the unspecifie d free boundary (the shock wave) is found at Reynolds numbers, and a d ensity ratio, k, up to and immediately after the leading shock wave, w hich tend to zero subject to the condition that (k/Re)(1/2) --> 0. Unl ike in all the models which have been mentioned above, the solution of the problem of the flow around a body in this model gives the free mo lecular limit for the coefficients of friction, heat transfer and pres sure. In particular, the Newtonian limit for the drag is thereby rigor ously obtained from the Navier-Stokes equations. At the same time, the Knudsen number, which is governed by the thickness of the shock layer , which vanishes in this model, tends to zero, that is, the conditions for a continuum treatment are satisfied. The structure of the shock w ave can be determined both using continuum as well as kinetic models a fter obtaining the solution in the viscous shock layer for the weak ph ysicochemical processes in the shock wave structure itself. Otherwise, the problem of the shock wave structure and the equations of the visc ous shock layer must be jointly solved. The equations for all the cont inuum models are written in Dorodnitsyn-Lees boundary layer variables, which enables one, prior to solving the problem, to obtain an approxi mate estimate of second-order effects in boundary-layer theory as a fu nction of Re and the parameter k and to represent all the aerodynamic and thermal characteristics in the form of a single dependence on Re o ver the whole range of its variation from zero to infinity. An efficie nt numerical method of global iterations, previously developed for sol ving viscous shock-layer equations, can be used to solve problems of s upersonic and hypersonic flows around the windward side of blunt bodie s using a single hydrodynamic model of a viscous shock layer for all R e numbers, subject to the condition that the limit (k/Re)(1/2)-->0 is satisfied in the case of small Re numbers. An aerodynamic and thermal calculation using different hydrodynamic models, corresponding to diff erent ranges of variation Re (different types of Bow) can thereby, in fact, be replaced by a single calculation using one model for the whol e of the trajectory for the descent (entry) of space vehicles and natu ral cosmic bodies (meteoroids) into the atmosphere. (C) 1998 Elsevier Science Ltd. All rights reserved.