Logic-Based Active Control of Subsonic Cavity Flow Resonance

Abstract

We present the results of an experimental investigation for controlling a shallow cavity flow in the Mach number range 0.25-0.5. The flow exhibits the characteristic staging behavior predicted by the semi-empirical Rossiter formula with multiple modes in the Mach number range 0.32-0.38 and a single strong mode in other Mach numbers. A survey of the velocity at the exit of the zero net mass flow compression-driver actuator used for control reveals that its amplitude is frequency dependent and its behavior is little influenced by the main flow. Forcing the Mach 0.3 flow indicated that the actuator has good authority over a large range of frequencies, with reduction of spectral peaks observed at some forcing frequencies. We took advantage of this phenomenon to develop a logicbased controller that searches the frequency space and maintains the optimal forcing frequency for peak reduction at each Mach number. Optimal frequencies and the corresponding reduced resonance have been obtained for all of the flow conditions explored. The physics of optimal frequency forcing as well as some characteristics of the logic-based controller are discussed.

Modeling and Feedback Control for Subsonic Cavity Flows: A Collaborative Approach

“…The performance of the scaled feedback control law has been tested experimentally in design and off-design conditions, and compared with the results obtained using feed-forward control (specifically the open-loop periodic forcing approach of [12].) The design conditions refer to the Mach 0.3 baseline flow, whose parameters are given in Table 1, used for identification of the reduced-order model.…”

“…Further details on the actuator can be found in [12]. A more sophisticated mathematical model of the actuator dynamics, represented by an acoustic enclosure driven by the loudspeaker, is currently under development.…”

“…The uncontrolled flow at Mach 0.3 exhibits a single strong resonant tone at approximately 2900 Hz, which is very near the frequency of the third Rossiter mode. It has been shown from open-loop experiments that the actuator has sufficient authority to significantly alter the flow at this Mach number (see [12]). The voltage input to the actuator is computed from the commanded non-dimensionalized jet velocity Γ, which is the control input to the reduced-order model (10), by inverting the approximate linear relation Γ =K a V a , wherē…”

“…2 dt subject to (12), where the positive definite weighting functions for the state vector and the control signal are chosen respectively as…”

“…While feed-forward strategies have been attempted with various degrees of success [40,12], the most significant effort in recent years has been spent on feedback control (see [9,33] for a comprehensive review). In [47,34,35], a physically motivated linear model was proposed and used.…”