Two-Dimensional Supersonic Flow
When supersonic ?ow goes over a wedge or an expansion corner, it goes through an oblique shock or
expansion waves, respectively, to adjust to the change in surface geometry. Figure 3.7.11 shows the two
?ow situations. In Figure 3.7.11(a) an oblique shock abruptly turns the ?ow parallel to the wedge surface.
The Mach number behind the shock is less than ahead of it, whereas the pressure, temperature, and
density increase. In the case of an expansion corner, oblique expansion waves smoothly turn the ?ow
to become parallel to the surface downstream of the expansion corner. In this case, the Mach number
increases, but the pressure, temperature, and density decrease as the ?ow goes through the expansion
corner. Oblique shocks and expansion waves occur in two- and three-dimensional supersonic ?ows. In
this section, we will restrict ourselves to steady, two-dimensional supersonic ?ows only.
Oblique Shock Waves
The oblique shock can be treated in the same way as the normal shock by accounting for the additional
velocity component. If a uniform velocity v is superimposed on the ?ow ?eld of the normal shock, the
resultant velocity ahead of the shock can be adjusted to any ?ow direction by adjusting the magnitude
and direction of v. If v is taken parallel to the shock wave, as shown in Figure 3.7.12, the resultant
velocity ahead of the shock is w1 = and its direction from the shock is given by b = tan?1
(u1/v). On the downstream side of the shock, since u2 is less than u1, the ?ow always turns toward the
shock. The magnitude of u2 can be determined by the normal shock relations corresponding to velocity
u1 and the magnitude of v is such that the ?ow downstream of the shock turns parallel to the surface.
Since imposition of a uniform velocity does not affect the pressure, temperature, etc., we can use normal
shock relations with Mach number replaced in them to correspond to velocity u1 or u1/a1, which is
nothing but M1 sin b. Thus, oblique shock relations become
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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