M. A. Kravtsova

An effective numerical method for solving viscous–inviscid interaction problems

This paper presents a new numerical method to solve the equations of the asymptotic theory of separated flows. A number of measures was taken to ensure fast convergence of the iteration procedure, which is employed to treat the nonlinear terms in the governing equations. Firstly, we selected carefully the set of variables for which the nonlinear finite difference equations were formulated. Secondly, a Newton–Raphson strategy was applied to these equations. Thirdly, the calculations were facilitated by utilizing linear approximation of the boundary-layer equations when calculating the corresponding Jacobi matrix. The performance of the method is illustrated, using as an example, the problem of laminar two-dimensional boundary-layer separation in the flow of an incompressible fluid near a corner point of a rigid body contour. The solution of this problem is non-unique in a certain parameter range where two solution branches are possible.

Receptivity of a Boundary Layer to External Sonic Waves

The effect of external acoustic perturbations on a two-dimensional laminar boundary layer is studied within the framework of the asymptotic theory. Essentially nonparallel regimes of the basic flow when flows with a separation zone develop are investigated.

Inviscid interaction in the thin shock layer at high mach numbers

Hypersonic perfect gas flow past the weakly curved end face of a circular cylinder is considered in the thin shock layer approximation. Regimes in which the shape of the end face is not a monotonic function of the radius but contains, for example, a central body of variable height are studied. It is found that, as the central body is extended, a break is formed in the slope of the shock. Smoothing takes place in a short zone of interaction between the main part of the thin shock layer, the shock, and the small near-wall potential jet. The solution, which depends continuously on a parameter, exists over a limited height range and bifurcates when a critical value is exceeded.

Effect of a Thin Longitudinal Inviscid Vortex on a Two-Dimensional Pre-Separation Boundary Layer

For large Reynolds numbers, an asymptotic solution of the Navier-Stokes equations describing the effect of a thin longitudinal vortex with a constant circulation on the development of an incompressible steady two-dimensional laminar boundary layer on a flat plate is obtained. It is established that, in a narrow wall region extending along the vortex filament, the viscous flow is described by the 3-D boundary layer equations. A solution of these equations for small values of the vortex circulation is studied. It is found that the solution of the two-dimensional pre-separation boundary layer equations collapses. This is attributable to the singular behavior of the 3-D disturbances near the zero-longitudinal-friction points.

Detachment of a supersonic boundary layer in front of the bottom edge of a contour of a body

Abstract The detachment of a supersonic flow in the neighbourhood of an angular point of the contour of a body is considered within the framework of the asymptotic theory of the interaction between a laminar boundary layer and the external non-viscous part of the flow.