NAVWEPS OD-807-80  HIGH SPEED AERODkNAMlCS  will form on each surface of the wedge and the  inclination of the shock wave will be a func-  tion of the free stream Mach number and the  wedge angle.  As the free stream Mach number  increases, the shock wave angle decreases;  as  the wedge angle increases the shock wave  angle increases, and, if the wedge angle is in-  creased to some critical amount, the shock  wave will detach from the leading edge of the  wedge. It is important to note that detach-  ment of the shock wave will produce sub$onic  flow immediately after the central portion of  the shock wave. Figure 3.4 illustrates these  typical flow patterns and the effect of Mach  number and wedge angle.  When supersonic flow is clearly established,  all changes in velocity, pressure, density, flow  direction, etc., take place quite suddenly and  in relatively confined areas. The areas of flows  change are generally distinct and the phenom-  ena are referred to as “wave”  formations. All  compression waves occur suddenly and are  wasteful of energy. Hence, the compression  waves are distinguished by the sudden “shock”  type of behavior. All expansion waves are not  so sudden in their occurrence  and are not waste-  ful of energy like the compression  shock waves.  Various types of waves can occur in supersonic  flow and the nature of the wave formed depends  upon the airstream and the shape of the object  causing the flow change. Essentially, there  are three fundamental types of waves formed  in supersonic flow: (1) the oblip  shock wave  (compression), (2) the normal shock wave  (compression), (3) the expansion wave (no  shock).  ‘ I-YPICAL SUPERSONIC FLOW PATTERNS  The previous flow across a wedge in a  supersonic airstream would allow flow in ;UU  dimensions.  If a cone were placed in a super-  sonic airstream the airflow would occur in  three dimensions and there would be some  noticeable differences in flow characteristics.  Three-dimensional flow for the same Mach  number and flow direction change would pro-  duce a weaker shock wave with less change in  pressure  and density.  Also, this conical wave  formation allows changes in airflow that con-  tinue to occur past the wave front and the  wave strength varies with distance away from  the surface. Figure 3.5 depicts the typical  three-dimensional flow past a cone.  OBLIQUE SHOCK WAVE.  Consider the  case where a supersonic airstream is turned  into the preceding airflow.  Such would be  the case of a supersonic flow “into  a comer”  as shown in figure 3.3. A supersonic airstream  passing through the oblique shock wave will  experience  these changes:  (1) The airstream is slowed down; the  velocity and Mach number behind the wave  are reduced but the flow is still supersonic  (2) The flow direction is changed to flow  along the surface  (3) The static pressure of the airstrea:m  behind the wave is increased  (4) The density of the airstream behind  the wave is increased  (5) Some of the available energy of the  airstream (indicated by the sum of dynamic  and static pressure) is dissipated and turned  into unavailable heat energy. Hence, the  shock wave is wasteful of energy.  A typical case of oblique shock wave forma-  tion is that of a wedge pointed into a super-  sonic airstream. The oblique shock wave  NORMAL  SHOCK WAVE.  If a blunt-  nosed object is placed in a supersonic airstream  the shock wave which is formed will be de-  tached from the leading edge. This detached  Oblique shock waves can be reflected like  any pressure  wave and this effect is shown in  figure 3.5.  This reflection appears logical and  necessary  since the original wave changes the  flow direction toward the wall and the reflected  wave creates the subsequent flow change to  cause the flow to remain parallel to the wall  surface. This reflection phenomenon places  definite restrictions on the size of a model in a  wind tunnel since a wave reflected back to the  model would cause a pressure  distribution not  typical of free flight. 