# Shock Reduction through Opposing Jets--Aerodynamic Performance and Flight Stability Perspectives
## 3 Flow Physics of Opposing Jet
### Pressure Ratio Effects  
The flow field in the vicinity of leading edge is significantly governed by pressure ratio. The impact of opposing jet on flow field and drag was analyzed for different values of pressure ratios (0.8-4.0) at \(M_{\infty}=1.4\) and \(M_{j}=1\). The variation in pressure ratio (PR) generate two distinct flow modes, LPM and SPM. LPM, unsteady and undesirable, exists at low PR values. SPM, steady and desirable, exist at higher PR, which is more beneficial for drag and heat flux reduction [47]. In between the oscillating/unstable LPM and stable SPM, a transition regime is also observed. The re-circulation region generated as a result of opposing jet is illustrated in Figure 9c. Interestingly, the pressure on the upper surface of airfoil remains same (while, moving towards the trailing edge) for with and without jet at zero degree angle of attack (as displayed in Figure 9a,b. Points A, B, and C in Figure 9d explain the peak pressure values for flow countered with and without jet. Point B is the stagnation point for no jet case that gets displaced through opposing jet to point A. Point A is the new stagnation point lying on the interface curve between disturbed shock wave and Mach disc of jet. Point C represent the pressure value of the jet at the leading edge of an airfoil that is significantly higher than the free stream total pressure. Figure 8: Comparison of stream lines for Mach contours with constant \(PR=1.8\), \(M_{j}=1\) and also includes the changes in pressure with increasing Mach number. The modes are shown in Figure 10a-l. For \(PR\) = 0.8, the total pressure in the jet reservoir is less than the stagnation pressure. Therefore, the jet ejection from the orifice do not take place. However, when \(PR\) is greater than one, the shock standoff distance amplifies with \(PR\). Moreover, the flow pattern of re-circulation zone in the vicinity of opposing jet is also significantly changed. The distinct LPM mode can be seen at \(PR\) of 1.9 and 2.4. The oscillatory behavior of pressure can be observed at these values. In LPM, the drag value is recorded enough due to the fluctuations that formulate a series of expansion and compression waves [19] at \(PR\) = 2.4 (as in Figure 10f). The pressure of re-circulation regions were significantly higher than the stagnation point in front of Mach disc. From \(PR\) of 2.8 and 3.0 onwards, a strong SPM mode is captured. The influence of opposing jet diminishes beyond 10% of the chord length (\(x/c\) = 0.1) as depicted in Figure 10a-l. Similarly, some minor fluctuations were observed for SPM at \(PR\) = 3 where pressure of re-circulation region was less than the stagnation point at different \(PR\) values. Figure 9: The comparison of drag reduction due to formation of recirculation regions. As the free-stream static pressure at the interface curve was greater than the counter flow jet, the stagnation point of interface stopped Mach disc of jet from further protrusion. With the increase  
Figure 10: The pressure distribution of free stream flow at constant \(M_{\infty}\) = 1.4 and increasing \(PR\) between 0.8 to 4.0.  
in PR value, the Mach disc also got enlarged thereby bending the barrel shocks. The bending of shockwaves along the free-stream flow also moved the re-circulation regions over the airfoil surface. That re-circulation region creates an imaginary body that reduces the skin friction coefficient from the leading edge of airfoil. Figure 10(a) empirically illustrate the flow field difference between no jet, unsteady LPM and steady SPM modes. The flow manifests the same trend as that of [PERSON] [48] who analyzed the flow modes on blunt body at free stream Mach 3.48. There is a transition region that coexists between LPM and SPM modes. At \(PR=4\), the Mach disc does not maintain its shape as depicted in Figure 10(b). The increment in \(PR\) increases the mass flow rate [8]. The increase in mass flow rate on small jet to body diameter ratio build more under-expanded jet and less jet stream passes through the barrel shock [49].