SECTIONS IN SUPERSONIC FLOW

In order to appreciate the effect of these various wave forms on the aerodynamic char­acteristics in supersonic flow, inspect figure 3.8. Parts (a) and (b) show the wave pattern and resulting pressure distribution for a thin flat plate at a positive angle of attack. The air – stream moving over the upper surface passes through an expansion wave at the leading edge and then an oblique shock wave at the trailing edge. Thus, a uniform suction pressure exists over the upper surface. The airstream moving underneath the flat plate passes through an oblique shock wave at the leading edge then an expansion wave at the trailing edge. This pro­duces a uniform positive pressure on the under­side of the section. This distribution of pres­sure on the surface will produce a net lift and incur a subsequent drag due to lift from the in­clination of the resultant lift from a perpen­dicular to the free stream.

Parts (c) and (d) of figure 3.8 show the wave pattern and resulting pressure distribu­tion for a double wedge airfoil at zero lift. The airstream moving over the surface passes through an oblique shock, an expansion wave, and another oblique shock. The resulting pressure distribution on the surfaces produces no net lift, but the increased pressure on the forward half of the chord along with the de­creased pressure on the aft half of the chord produces a “wave” drag. This wave drag is caused by the components of pressure forces which are parallel to the free stream direction. The wave drag is in addition to the drag due to friction, separation, lift, etc., and can be a very considerable part of the total drag at high supersonic speeds.

Parts (e) and (f) of figure 3.8 illustrate the wave pattern and resulting pressure distribu­tion for the double wedge airfoil at a small positive angle of attack. The net pressure

distribution produces an inclined lift with drag due to lift which is in addition to the wave drag at zero lift. Part (g) of figure 3.8 shows the wave pattern for a circular arc air­foil. After the airflow traverses the oblique shock wave at the leading edge, the airflow undergoes a gradual but continual expansion until the trailing edge shock wave is en­countered. Part (h) of figure 3-8 illustrates the wave pattern on a conventional blunt nose airfoil in supersonic flow. When the nose is blunt the wave must detach and become a normal shock wave immediately ahead of the leading edge. Of course, this wave form produces an area of subsonic airflow at the leading edge with very high pressure and density behind the detached wave.

The drawings of figure 3-8 illustrate the typical patterns of supersonic flow and point out these facts concerning aerodynamic surfaces in two dimensional supersonic flow:

(1) All changes in velocity, pressure, density and flow direction will take place quite suddenly through the various. wave forms. The shape of the object and the required flow direction change dictate the type and strength of the wave formed.

(2j) As always, lift results from the distri­bution of pressure on a surface and is the net force perpendicular to the free stream direc­tion. Any component of the lift in a direc­tion parallel to the wind stream will be drag due to lift.

(3) In supersonic flight, the zero lift drag of an airfoil of some finite thickness will include a "wave drag.” The thickness of the airfoil will have an extremely powerful effect on this wave drag since the wave drag varies as the square of the thickness ratio— if the thickness is reduced 50 percent, the wave drag is reduced 75 percent. The lead­ing edges of supersonic shapes must be sharp or the wave formed at the leading edge will be a strong detached shock wave.

(4) Once the flow on the airfoil is super­sonic, the aerodynamic center of the surface

will be located approximately at the 50 per­cent chord position. As this contrasts with the subsonic location for the aerodynamic center of the 25 percent chord position, sig­nificant changes in aerodynamic trim and stability may be encountered in transonic flight.