Acoustic response of turbulent cavity flow using resolvent analysis

Abstract

Fluid–acoustic interactions are important in a variety of applications and typically result in adverse effects. We analyze the influence of Mach number on such interactions and their input–output characteristics by combining resolvent analysis with Doak's momentum potential theory. The specific problem selected is the flow over an open cavity of L∕D = 6 at Re = 10 000 and M∞ = 0.6 and 1.4, respectively. The resolvent forcing and response modes are decomposed into their hydrodynamic, acoustic, and thermal components. Although the results depend quantitatively on Mach number, some trends remain consistent. In particular, at lower frequencies, the acoustic component appears primarily at the trailing edge of the cavity. When the frequency is increased, the acoustic response moves toward the leading edge and overlaps with its hydrodynamic component. Inspired by actual cavity flow control, the forcing is then localized to two regions—the leading edge and front wall of the cavity—and filtered to consider notional actuators that can separately introduce each component of velocity, density, and temperature forcing, respectively. Among these different types of actuation perturbations, regardless of Mach number, streamwise velocity forcing achieves the largest energy amplification at the leading edge. For both flows, beyond a certain forcing frequency threshold value, the nature of the acoustic vs hydrodynamic response becomes independent of the forcing type; however, the amplification continues to be strongly impacted by the forcing frequency. The present work provides an alternative approach to examine input–output flow–acoustic characteristics and evaluate the relative effectiveness of different types and locations of actuation.