Analysis of Wall Jet Flow in EAPG with Super-Lift Coefficient

This paper presents the findings of a 2D numerical study of flows in Extreme Adverse Pressure Gradients (EAPG) enabled by Co-Flow Jet (CFJ) Active Flow Control (AFC). We define an EAPG to be an adverse pressure gradient that is at least ten times larger than the maximum adverse pressure gradient sustainable by the non-controlled flow of a baseline case at the same conditions. The flow field is solved using a set of 2D one-equation Spalart-Allmaras turbulence model. A CFJ cylinder and CFJ airfoil with EAPG and attached flow are studied at Mach number 0.063, and Reynolds numbers 5.62x10^5 -- 1.69x10^6. The CFJ cylinder achieves time-averaged lift coefficients up to C_L = 26.718 with C_mu = 10.0, and the CFJ airfoil shows time-averaged lift coefficients up to C_L = 13.411 with C_mu = 12.0. The injection jet remains subsonic for both the cylinder and the airfoil, reducing the power required compared to previous studies, which reach supersonic injection jet speeds. The CFJ cylinder measures a maximum streamwise pressure gradient 14 times the strength of its baseline, while the the CFJ airfoil reports a much higher adverse pressure gradient that is 879 times greater than its baseline counterpart. Such extraordinary lift generation and adverse pressure gradient ratios motivate this effort to investigate how the implementation of the CFJ can achieve this effect. The exceptional lift coefficients presented exceed the classically defined limit for C_L_max, and are termed ``Super-Lift Coefficients" (SLCs). Supporting spatial mesh and time step refinement studies, conducted subsequently, show nearly identical results. Evaluating boundary layer flow attachment via the turbulent wall jet momentum equation, this study finds that the turbulent eddy viscosity diffusion near the wall is the most significant factor offsetting the adverse pressure gradient to maintain attached flow. The turbulence diffusion near the wall has a degree of uncertainty due to the use of the S-A RANS turbulence model. To ensure the EAPG phenomenon is captured within RANS models' uncertainty, a CFJ cylinder case with C_L of 22.89 is simulated using the two-equation k-omega SST model, which gives a C_L of 20.365, only differed by 11% and is acceptable for RAND models. Further studies with high fidelity simulation of LES, DNS, and experiment to verify the EAPG phenomenon are desirable.