RU2558498C2 - Construction of optimum airfoil for hypersonic aircraft - Google Patents

Abstract

FIELD: aircraft engineering.

SUBSTANCE: proposed method comprises subjecting the aircraft airfoil to effects with application of optimisation criterion. The latter represents the relationship between the factors of lift and drag wherefrom optimum aircraft airfoil is derived to solve the problem of deviation from collision with application of numerical methods of the solution of complete equations of Navier-Stocks. Note here that rational arrangements of structural surfaces and aircraft nose shape are defined for minimum heat loads.

EFFECT: optimised deviation from collision.

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Description

The claimed invention relates to rocket and space technology and can be used to determine the optimal surface shape of a hypersonic aircraft designed to save the crew from the board of a space station in an accident.

It is known to build the surface of a hypersonic gliding aircraft using the form optimality criterion as the maximum condition for the aerodynamic quality of the synthesized product (K → max), which is a certain limitation due to the neglect of evasion [1].

The closest solution to the claimed is a method of constructing the optimal aerodynamic surface of a hypersonic aircraft, which consists in exposure using an optimization criterion associated with maximizing the aerodynamic drag coefficient [2].

A disadvantage of the known solution is the limited capabilities of the method due to the inability to ensure optimal collision avoidance.

The objective is to propose the definition of collision avoidance criteria and a method for constructing the optimal surface of a hypersonic aircraft to ensure optimal collision avoidance.

, по которому формируют оптимальную поверхность летательного аппарата для решения задачи уклонения от столкновения, с использованием численных методов решения полных уравнений Навье-Стокса, для чего определяют рациональное расположение несущих поверхностей и форму носовой части аппарата с минимальными тепловыми нагрузками, гдеThe solution of this problem is provided by the fact that in the method of constructing the optimal aerodynamic surface of a hypersonic aircraft, including the impact on its surface using the optimization criterion, the ratio of the degrees of the lift and drag coefficients is used as the optimization criterion $$P=\raisebox{1ex}{$C_{ya}^a$}\!\left/ \!\raisebox{-1ex}{$C_{xa}^b$}\right.$$

using which the optimal surface of the aircraft is formed to solve the collision avoidance problem using numerical methods for solving the complete Navier-Stokes equations, which determine the rational location of the bearing surfaces and the shape of the nose of the vehicle with minimal thermal loads, where

P is the ratio of the degrees of the coefficients of the lifting force and the drag force, which characterizes the efficiency indicator obtained as a result of the numerical solution of the differential quality game,

- коэффициент подъемной силы, определяемый как отношение подъемной силы к скоростному напору и характерной площади, $$C_{ya}^a$$

- the coefficient of lifting force, defined as the ratio of the lifting force to the pressure head and the characteristic area,

- коэффициент силы лобового сопротивления, определяемый как отношение силы лобового сопротивления к скоростному напору и характерной площади. $$C_{xa}^b$$

- drag coefficient of force, defined as the ratio of drag to velocity pressure and characteristic area.

The invention is illustrated by the following example.

A diagram of a conflict situation on avoiding a collision of two aircraft (two players with opposing (antagonistic) interests) is presented in Fig. 1. Player P seeks to get closer to player E by the minimum distance, player E seeks to maximize the minimum distance. The game ends with victory P if the PE segment turns out to be less than l, and defeat P if player E passes the area of convergence closer than l.

The differential game of quality was solved numerically in the coordinate system associated with the player P, provided that player E was superior in speed and the players were initially placed on the opposite courses. A schematic diagram of a differential game in a coordinate system associated with a minimizing player is shown in FIG. The maneuverability of player E was limited by the minimum turning radius (the value of the coefficient of lift), and his speed was reduced quadratically with a proportionality coefficient associated with the aerodynamic drag coefficient.

In the noted formulation, the differential game was described by a system of ordinary differential equations:

,

,

,

,

,

,

,

,

where x and y are geometric coordinates (of the evading player E in the coordinate system associated with player P);

w ₁ and w ₂ are the speeds of the players P and E;

R ₁ and R ₂ are the minimum radii of curvature of the trajectories P and E;

θ is the orientation of the velocity vector (w ₂ ) of the evading player E;

φ and ψ are the parameters for controlling the movement of players P and E, -1≤φ, ψ≤1;

, $$C_N^{(2)}$$

- коэффициенты нормальных сил игроков Р и Е; $$C_N^{(\mathrm{one})}$$

, $$C_N^{(2)}$$

- the coefficients of the normal forces of the players P and E;

k is the scaling factor for the allocation of dimensionless aerodynamic coefficients taking into account the flight altitude, the mass of the players and their characteristic area;

- коэффициент тангенциальной силы игрока Е, $$C_{\tau }^{(2)}$$

is the tangential force coefficient of player E,

with the initial conditions on the terminal surface at the point of contact with the barrier surface, shown in Fig.3.

The problem was solved numerically by the methods of Euler and Runge-Kutta, the reliability of the results was confirmed by the convergence of processes in mathematical time (in the number of iterations) and in the grid of control parameters. As an independent test, we considered a comparison of the numerical and analytical solutions of the “driver-killer” problem proposed by R. Isaacs [3], as shown in Fig. 4.

Numerical calculations ended at the control point — the intersection by the barrier of the symmetry plane of the differential game, corresponding to the starting point of maneuvering and, accordingly, of some linear measure of optimal evasion. The terminal surface and the surface of the barriers of the 4-dimensional phase space are presented in figure 5.

.The approximation of the results of parametric studies and their further analysis made it possible to establish the law of degrees for the efficiency indicator of the aerodynamic layout of a hypersonic aircraft: $$P=\raisebox{1ex}{$C_{ya}^a$}\!\left/ \!\raisebox{-1ex}{$C_{xa}^b$}\right.$$

.

The surface of the hypersonic aircraft of the optimal shape was constructed numerically by the method of local variations with the objective function: P → max and the initial surface shape of the aircraft in the form of a cone of a limited length and midsection section blunted over a sphere and a structured grid of quadrangular cells on its surface, shown in Fig. 6 .

The numerical solution of the variational problem of constructing the optimal surface of the aircraft was obtained for 3000 iterations, the dependence of the corresponding efficiency indicator is shown in Fig.7. The value of the efficiency indicator P for the optimal layout with restrictions on the shape of the toe and bottom cut, the length of the apparatus and the dimensions of the compartments for the payload was 1.5, and its shape is shown in Fig. 8 (a - front view, b - top view, c - side view).

The form of the aircraft shown in Fig. 8 contains technical solutions for limiting maximum thermal loads, manufacturability of an assembly with an accelerating carrier, and the possibility of using critical CALS technologies. The shape of the winged hypersonic aircraft was obtained with constant internal volumes with a payload, invariance of the fore and aft parts of the aircraft. The fixed shape of the bow allowed us to provide the necessary balancing angle of attack, and the aft was unified for location on the booster stage of the launch vehicle.

Thus, the claimed invention allows to solve the problem of determining the optimal shape of the evading hypersonic aircraft, which can ensure the salvation of the crew from the board of the space station in an accident, as well as solving the problem of avoiding a collision of high-speed civil aviation aircraft.

Bibliography

1. Fofonov D.M. Optimization of the aerodynamic layout of hypersonic aircraft. // Cosmonautics and rocket science. - 2010 .-- 17 p.

2. Petrov K.P. Aerodynamics of space transport systems. - M.: Editorial URSS, 2000 .-- 368 p.

3. Isaacs R. Differential games. - M .: Mir, 1967 .-- 315 p.

Claims (1)

A method of constructing the optimal aerodynamic surface of a hypersonic aircraft, including the impact on its surface using the optimization criterion, characterized in that the ratio of the degrees of the lift and drag coefficients is used as the optimization criterion

using which the optimal surface of the aircraft is formed to solve the collision avoidance problem using numerical methods for solving the complete Navier-Stokes equations, which determine the rational location of the bearing surfaces and the shape of the nose of the vehicle with minimal thermal loads, where
P is the ratio of the degrees of the coefficients of the lifting force and the drag force, which characterizes the efficiency indicator obtained as a result of the numerical solution of the differential quality game,

- the coefficient of lifting force, defined as the ratio of the lifting force to the pressure head and the characteristic area,

- drag coefficient of force, defined as the ratio of drag to velocity pressure and characteristic area.

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