Wing in transonic range of speeds

Fig. 6.18.

Speeds corresponded to Mach numbers () are called transonic. All range can be divided on to: area of subsonic speeds (), area of supersonic speeds (), flow mode with Mach numbers .

Features of the aerodynamic characteristics in subsonic part of transonic speeds are determined by existence of mixed flow including subsonic (outside of the wing) and supersonic (on the wing and near to it) flow areas. The forward border of supersonic flow area represents the so-called sound line, along which the transition from subsonic to supersonic flow is occurred. The flow remains subsonic outside of zones limited by the sound line. Fig. 6.18 shows the approximate borders of supersonic zones at various Mach numbers . With increasing of Mach number the shock waves are originally formed on the upper surface and move to the trailing edge. Then the supersonic area is formed on the lower surface. The development of supersonic area on the airfoil lower surface proceeds more intensively, than on lower. The supersonic areas are finished by shock waves, which with increasing of numbers displace back and enlarge the extent in the vertical direction. At a shock wave is theoretically distributed into infinity, at that there is a head shock wave before the wing also in infinity. The further increasing of caused movement of a head shock wave and shock wave on the wing surface downwards of the flow. The supersonic wing flow mode comes at values , when the shock waves practically do not move any more, and reduce their angle of inclination with increasing of .

The appearance of transonic parameter of similarity , as a result of the non-linear theory, is characteristic for transonic area. Parameter influences onto changing of the aerodynamic characteristics so, that:

(Fig. 6.19);

(Fig. 6.20);

(Fig. 6.21).

At : the dimensionless parameters , , depend on , , shape of the airfoil and . Let's remind, that the taper continues to play a small role in changing of and , in some cases its influence can be neglected. However, the parameter plays an essential role for characteristic of aerodynamic center location, because it effects onto aerodynamic loading distribution wing spanwise.

For wings of arbitrary shape the influence of is investigated a little. More detail research is carried out on rectangular wings with rhomboid airfoil (, , or ). it was proved, that for such wings at and the value of . It can be explained that at reduced aspect ratio and we pass to the very low-aspect-ratio wing, for which . If , then the theory of transonic flows for a rectangular wing gives .

The analogous results are received for wave drag: at , at .

Fig. 6.19. Dependence on reduced aspect ratio

Fig. 6.20. Dependence on reduced aspect ratio

Fig. 6.21. Dependence of the aerodynamic center location on

It is necessary to note, that in the latter case , i.e. the wave drag grows with increasing of , though not so fast as in the supersonic flow, in which . Change of the aerodynamic center location dependently on is similar to changes of (Fig. 6.21). The more , then aerodynamic center changing by Mach numbers behaves more irregularly: drastic displacement forward in subsonic range is probable with the subsequent displacement backward into position corresponded to supersonic speeds (displacement of aerodynamic center for a triangular wing at passage from to is determined as ).

Main measures provided reduction of wing wave drag, improvement of its lifting properties and smooth change of aerodynamic center in supersonic range of speeds by Mach numbers are: reduction of and (decreasing of parameter value ) and increasing of .

6.6. Wing induced drag at with taking into account local supersonic flows.

Let's consider the problem on the account of additional drag occurred at values of and , outgoing of critical values (the approximate method of the account is offered by S. I. Kuznetsov). This drag is necessary for taking into account at construction of the wing polar for specified , .

Let's assumethat the dependence of critical Mach number on , i.e. or . Let's construct this dependence in a plane of , (Fig. 6.22).

Fig. 6.22 Fig. 6.23. Wing polar with the account of

Obviously, that all values of and , lying below the curve fall into subsonic speeds area. However if at specified will be , then the flow supersonic area closed by shock waves is formed on the wing. In this case there is an additional drag caused by lift (at ). If it assumes, that the growth of lift is not accompanied by growth of sucking force with increasing of angles of attack at (that at presence of the broad supersonic area on a wing is permissible), then for a flat wing we shall have or .

In addition adopting, that on transonic flow modes the proportion is executed, then finally we receive

.

This parameter is added to induced drag, and thus we have:

(6.22)

Wing polars take the form it shown in fig. 6.23.

Values of lift coefficients corresponded to the beginning of wave crisis at ; i.e. the dependence can be found from the formula ():

where the factors , , for a wing with a classical airfoil are equal , , ; for a wing with a supercritical airfoil - , , .

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