The dynamics of the coupled Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instability (referred to as KHRT instability or KHRTI) is studied using statistically steady experiments performed in a multi-layer gas tunnel. Experiments are performed at four density ratios ranging in Atwood number $A_{t}$ from 0.035 to 0.159, with varying amounts of shear and $\unicode[STIX]{x0394}U/U$ ranging from 0 to 0.48, where $\unicode[STIX]{x0394}U$ is the speed difference between the two flow streams being investigated and $U$ is the mean velocity of these two streams. Three types of diagnostics – back-lit visualization, hot-wire anemometry and particle image velocimetry (PIV) – are employed to obtain the mixing widths, velocity field and density field. The flow is found to be governed by KH dynamics at early times and RT dynamics at late times. This transition from KH-instability-like to RT-instability-like behaviour is quantified using the Richardson number. Transitional Richardson number magnitudes obtained for the present KHRT flows are found to be in the range 0.17–0.56 similar to the critical Richardson numbers for stably stratified free shear flows. Comparing the evolution of density and velocity mixing widths, the density mixing layer is found to be approximately two times as thick as the velocity mixing layer. Scaling of velocity fluctuations is attempted using combinations of KH and RT scales. It is found that the proposed KHRT velocity scale, obtained using the combined mixing-layer growth equation, is appropriate for intermediate stages of the flow when both KH and RT dynamics are comparable. Probability density functions (p.d.f.s) for different fluctuating quantities are presented. Multiple peaks in p.d.f.s are qualitatively explained from the development of coherent KH roll-ups and their subsequent transition into turbulent pockets. The evolution of energy spectra indicates that density fluctuations start to show an inertial subrange from earlier times compared to velocity fluctuations. The spectra exhibit a slightly steeper slope than the Kolmogorov–Obukhov five-thirds law.
In the present work, effects of compressibility on the dynamic stall of NACA 0012 airfoil, pitching sinusoidally from 5.03° to 24.79°, are investigated computationally using implicit large eddy simulations in a finite difference framework. Simulations of two-dimensional (2D), high Reynolds number, compressible flows are carried out without any transition or turbulence model to capture the physics of the dynamic stall process. The problem is formulated in a body-fixed, rotating, non-inertial frame. High accuracy, dispersion relation preserving optimized upwind compact scheme is used to compute convective flux derivatives, and an optimized three-stage Runge-Kutta method is used for time integration. Results are presented for free stream Mach number M∞ = 0.283, 0.4, and 0.5, where the Mach number is varied independent of the Reynolds number. The computations have been quite successful in capturing the essential features of the dynamic stall mechanism. It is observed that dynamic moment and lift stalls occur at smaller angles of attack as the Mach number increases. Reduction in the size of airload hysteresis loops and maximum attainable load coefficients are observed with increasing Mach number. Weak shock waves are observed near the leading edge (LE) at M∞ = 0.4, and lambda-shock is formed near the LE for M∞ = 0.5. It is observed that with increasing Mach number, the impact of dynamic stall on the aerodynamic loads (Cl, Cd, and Cm) becomes less dramatic as the maximum value attained by these aerodynamic loads decreases with an increase in the Mach number. An increase in positive damping area in the hysteresis loop is observed with an increase in the Mach number, inhibiting possible vulnerability to stall flutter.
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