# Shock Reduction through Opposing Jets--Aerodynamic Performance and Flight Stability Perspectives
## 3 Flow Physics of Opposing Jet
### Influence of Mach Number  
Free stream Mach is an important variable which effects the jet flow structure. A significant amount of drag reduction (up to 70%) is demonstrated in Figure 7. The percentage of reduction in drag coefficient (\(C_{d}\)) improves with the increase in free stream Mach number (\(M_{\infty}\) = 1.4 to 3.0). Pressure ratio, \(PR\) of 1.8 and Mach of jet, \(M_{j}\), equal to one were used to displace the shock wave from the nose of airfoil which primarily helps in the reduction of drag coefficient. However, the effectiveness of opposing jet at these PR and \(M_{j}\) decreases beyond \(M_{\infty}\) = 2.5 as shown in Figure 7.  
The Mach contours and the variation of pressure at stagnation point (0 in x-axis) and surface of airfoil (with and without jet) with the increase in free stream Mach number is illustrated in Figure 8. The comparison of Mach contours in Figure 8.-d clearly depicts that the smaller PR ratio is required at higher free stream Mach number to get the visible Mach disc. [PERSON] [46] also suggested that the increase in the free stream Mach number strengthens the bow shock and, as a result, the total pressure behind the shock decreases. The depletion in total pressure behind the shock minimize the pressure in the recirculating region so that the static pressure ratio of the jet enhances (at \(M_{\infty}\) = 2 & \(M_{\infty}\) = 3), where the pressure behind the shock is considerably low.  
\(M_{\infty}\) at 1.4 and 1.8, shows significantly higher drag. As a result, unstable flow structure was formed thereby exhibiting inferior performance of jet. At \(M_{\infty}\) = 2, the jet attains the \(SPM\) mode with visible Mach disc and appropriate re-circulation region as well as reduced drag coefficient. But at \(M_{\infty}\) = 3, the opposing jet seems to be more under-expanded as the Mach disc did not maintain its shape.  
In Figure 8.-d, the decrease in pressure values due the effects of counter flow jet at the stagnation point of airfoil are plotted. The stagnation point is displaced by means of opposing jet to an optimal distance from the leading edge of airfoil and creates a shock stand-off distance to reduce the drag. However, the graphical comparison of with and without jet raise a point which presumes that there was a sudden rise in pressure after the displacement of shock-wave.  
The re-circulation region collapses near (\(x/c\) = 0.02) and produce turning shocks along the surface of airfoil [20]. The abrupt change in pressure values take place after the turning shocks as shown in  
Figure 6: Comparison of stability derivatives with experimental data.  
Figure 7b and coalesce along the surface of airfoil. Similarly, these turning shocks are of compressive nature before maximum thickness position and expansive afterwards for no jet case as shown in Figure 7a. However the re-circulation region destroyed and evolved a new free stream boundary layer for different values of \(M_{\infty}\). This reattachment of free stream flow was another reason for the generation of turning shocks and increase in pressure. The hatched region in Figure 7c explains the difference of pressure between with and without jet curves; which were disturbed due to the generation of turning shocks.  
In the similar scenario by increasing the \(M_{\infty}\), pressure over surface of airfoil continuously decreases as depicted from Figure 7d. The main reason is movement of barrel shocks along the free stream and spreading of re-circulation region (dead-air region) over airfoil surface. So, it significantly decreases the force factors such as drag.  
Figure 7: Comparison of stream lines for Mach contours between with and without jet case.