Analysis of Circulation Control Jet Bi-Stability on a Wing Section at Transonic Speeds via Dynamic Mode Decomposition

Abstract

The phenomenon of stable lift oscillations occurring on an elliptic wing section utilizing circulation control at transonic speeds was evaluated using numerical simulations. As the momentum of the jet increases beyond a prescribed magnitude, periodic detachment occurs from the trailing-edge. This behavior conforms to a bi-stable state, consistent with prior experimental observations. Analysis by both steady and unsteady Reynolds-Averaged Navier-Stokes calculations showed that the effect is decoupled from the dominant upstream shockwave. This indicates that the jet can no longer augment the wing's circulation, marking the termination of circulation control. Furthermore, the results confirm that the absence of the downstream separation bubble acts as the catalyst for this detachment. Dynamic Mode Decomposition analysis revealed that the bi-stability is driven by a pressure feedback between the trailing-edge shockwave and a downstream pressure bubble. A secondary feedback governs the pressure redistribution during the detachment cycle. It was concluded that the pressure-dominant nature of the bi-stability allows it to be captured using relatively simple methods such as URANS, and even approximated through a Reduced Order Model comprising only 2% of the total modes, encapsulating 25% of the modal influence and reconstructing the pressure field with 98% accuracy.

Figures (18)

• Figure 1: Geometry of the modeled TDT experimental wing.
• Figure 2: Computational domain illustrating the relevant boundary conditions and cross-sections of the grid.
• Figure 3: Convergence of the mid-span lift and drag coefficients with increasing grid count for different mass flow inputs at an angle of attack of 3$^\circ$ and a free-stream Mach number of 0.8. $N = 1.3 \times 10^6$, $N = 1.9 \times 10^6$, $N = 2.7 \times 10^6$, $N = 4 \times 10^6$
• Figure 4: Pressure coefficient distribution at mid-span, validated against the TDT experimental data at a free-stream Mach number of 0.8 and angle of attack of $3^{\circ}$, as well as the respective Mach fields using the SA turbulence model. Spalart-Allmaras, $\;$$k-\omega$ SST, $\;$Chen et al. chenNumericalStudyLift2021, $\;$TDT tunnel data
• Figure 5: Effect of momentum addition on the mid-span lift enhancement at a free-stream Mach number of 0.8 and an angle of attack of $3^{\circ}$ and $0^{\circ}$. $\;$ CFD results $\alpha=3^\circ$, $\;$ TDT tunnel data $\alpha=3^\circ$, $\;$$\color{navyblue}{\blacktriangle}$$\;$ CFD results $\alpha=0^\circ$, $\color{navyblue}{\triangle}$$\;$ TDT tunnel data $\alpha=0^\circ$