Numerical analysis of aerodynamic characteristicsof non-circular cones in supersonic flow

Abstract

Numerical modeling of viscous gas flows around non-axisymmetric lifting bodies streamlined at an angle of attack is one of the urgent problems of modern aerodynamics. Such bodies have high aerodynamic quality and are promising in the creation of maneuverable aircraft.
The paper considers the problem of supersonic flow of a viscous gas around a sharp cone with an arbitrary smooth cross-section. It was assumed that the effect of viscosity is con-centrated in a thin layer near the solid surface, and the entire flow region between the body surface and the shock wave can be divided into an inviscid flow and a boundary layer.
The flow regimes considered were when the shock wave formed in front of the cone is attached to its top and the inviscid flow around it is conical. The integration of the system of differential equations of Euler was carried out using a stationary analogue of the Godunov method, using the principle of establishing a solution along the longitudinal coordinate. To solve the boundary layer problem, the Petukhov finite-difference method was used. As a result of solving the specified boundary value problems, the velocity and pressure fields in the boundary layer and in the inviscid flow region, as well as the integral aerodynamic coeffi-cients, were found.
Based on the proposed methodology, calculations of aerodynamic coefficients for bi-elliptical cones were performed. The surface shape of these bodies is specified by three geo-metric parameters δ1, δ2, θk (θk is the half-angle of the cone in the plane of the major semi-axis, δ1 and δ2 are the ellipticity coefficients of the lower and upper semi-ellipses).
Numerical analysis of aerodynamic characteristics showed that taking into account the influence of the boundary layer leads to a significant increase in drag and a decrease in aer-odynamic quality. The contribution of viscous components to the lift and longitudinal moment is insignificant. The shape of the cone cross-section has a significant effect on the value of its aerodynamic coefficients.