TY - JOUR

T1 - On Mathematical Modeling of a Hypersonic Flow Past a Thin Wing with Variable Shape

AU - Bogatko, V.I.

AU - Potekhina, E.A.

N1 - Bogatko V.I., Potekhina E.A. "On Mathematical Modeling of a Hypersonic Flow Past a Thin Wing with Variable Shape" Pleiades Publishing, Ltd., Vestnik St. Petersburg University, Mathematics, Ltd., 2021, Vol. 54, No. 4, pp. 395–399. © 2021.

PY - 2021

Y1 - 2021

N2 - This work is devoted to the further study of a spatial flow past a thin wing of variable shape by a hypersonic flow of a nonviscous gas. The head shock wave is considered to be attached to the leading edge of the wing. The use of the thin shock-layer method for solving the system of gas-dynamics equations allows constructing a mathematical model of the flow in question. Also note that the analysis of boundary conditions makes it possible to determine the structure of the expansion of sought values in a series and to construct approximate analytical solutions. In this case, in determining the first approximation corrections, two equations are integrated independently of other equations. The applicationof the Euler–Ampere transform allows constructing a solution depending on two arbitrary functions and an unknown shape of the front of the head shock wave. To determine these functions, the integrodifferential system of equations was obtained previously. This paper proposes a variant of the semi-inverse method for constructing a solution (of this system) such that the formula for one arbitraryfunction is given. This approach allows additional assignment of the equation for the leading edge of the wing, as well as (in the case in which the head wave is attached along the entire leading edge) the inclination of the wing surface on it. The variant of the semi-inverse method presented in this paper for the nonstationary spatial problem of flow makes it possible to obtain a particular solution, which is a model solution for various regimes of a flow past a wing. We obtain formulas to determine the shape of the front of the shock wave, the shape of the surface of the streamlined body, the distance between the shock wave and the surface of the body, and the flow parameters on the wing surface.

AB - This work is devoted to the further study of a spatial flow past a thin wing of variable shape by a hypersonic flow of a nonviscous gas. The head shock wave is considered to be attached to the leading edge of the wing. The use of the thin shock-layer method for solving the system of gas-dynamics equations allows constructing a mathematical model of the flow in question. Also note that the analysis of boundary conditions makes it possible to determine the structure of the expansion of sought values in a series and to construct approximate analytical solutions. In this case, in determining the first approximation corrections, two equations are integrated independently of other equations. The applicationof the Euler–Ampere transform allows constructing a solution depending on two arbitrary functions and an unknown shape of the front of the head shock wave. To determine these functions, the integrodifferential system of equations was obtained previously. This paper proposes a variant of the semi-inverse method for constructing a solution (of this system) such that the formula for one arbitraryfunction is given. This approach allows additional assignment of the equation for the leading edge of the wing, as well as (in the case in which the head wave is attached along the entire leading edge) the inclination of the wing surface on it. The variant of the semi-inverse method presented in this paper for the nonstationary spatial problem of flow makes it possible to obtain a particular solution, which is a model solution for various regimes of a flow past a wing. We obtain formulas to determine the shape of the front of the shock wave, the shape of the surface of the streamlined body, the distance between the shock wave and the surface of the body, and the flow parameters on the wing surface.

KW - mathematical modeling

KW - hypersonic flowing of bodies,

KW - unsteady flows

KW - partial differential equations

KW - small parameter

KW - mathematical modeling

KW - hypersonic flowing of bodies

KW - unsteady flows

KW - partial differential equations

KW - small parameter

M3 - Article

VL - 54

SP - 395

EP - 399

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -