Continuum models in problems of the hypersonic flow of a rarefied gas around blunt bodiest

Continuum models of rarefied gas flows in problems of hypersonic aerothermodynamics

“…The Navier-Stokes equations in the chosen system of coordinates have been derived in the literature many times both for a perfect gas, 30,31,41 and for a multicomponent gas with chemical reactions. 41 To reduce the effect of the density on the coefficients of the equations, to facilitate finding a solution and deriving the different asymptotically simplified equations both for high and low Reynolds numbers, it is convenient to convert to new independent Dorodnitsyn variables in the Lees form , (Refs 30,31):…”

“…we neglect terms O( 2 ), O() and O() taking only terms O(1) into account, the Navier-Stokes equations reduce to "local" Stokes equations (quasi-two-dimensional, when there are no derivatives of the longitudinal coordinates) for Reynolds' problem 38 with vanishing inertia and pressure forces, which are called the vanishing viscous shock layer equations. 30,31 The solution of these equations is obtained in analytical form for an arbitrary power dependence of the coefficient of viscosity on the temperature; the velocity and temperature profiles in the shock layer around the windward surface of the body, the stream function and the external boundary of the shock layer are obtained. This solution gives values of the drag coefficient and the heat transfer coefficient that are identical with their free-molecule limits with an energy accommodation coefficient of unity.…”

The applicability of continuum models in the transitional regime of hypersonic flow over blunt bodies

“…They are discussed in Ref. 5. To investigate the justification for using these models at low Re numbers, an asymptotic analysis of the Navier-Stokes equations was carried out 1 for a shypersonic viscous shock layer over a blunt body at low Re numbers and it was shown that the two models are correct, i.e., they are asymptotically strictly derived from the Navier-Stokes equations not only for high Re numbers but also for low Re numbers, assuming the parameter introduced is small.…”

Generalized viscous shock layer equations with slip conditions on a surface in a flow field and on a head shock

“…7 Assuming that the contour of a plane or axisymmetric body is fairly smooth (at each point of the contour, only one definite tangent plane or normal to the contour can be constructed with a possible discontinuity of the curvature of the contour), we will consider the translational steady supersonic gas flow over it with a velocity V ∞ along the axis of symmetry Oz of the body (Fig. 1), in an orthogonal curvilinear system of coordinates connected to its surface.…”

“…In the asymptotic sense, they will thus be of the third order, and they are omitted in the classical viscous shock layer equations. 7 However, retaining them does not alter the mathematical nature of system of equations (4.1)-(4.4) at either high or moderate Reynolds numbers (Re). When they are taken into account, the solution will be refined and will approximate to the solution of the complete Navier-Stokes equations.…”