Role of acoustic waves and acoustic feedback in instability and aeroacoustics of shear flows

Context of the research
Most fluid flows in nature and engineering are in the form of shear flows. Moreover, they undergo transition from laminar states, which exhibit simple temporal and spatial patterns, to turbulent states, which are characterized by highly complex and apparently stochastic fluctuations in both time and space. The intrinsic reason of shear-layer transition is instability of the laminar state, but external factors such as ambient disturbances also play an important role. Transition involves a sequence of physical processes, starting with excitation of small-amplitude instability waves. This is followed by the linear stage, in which the excited instability waves grow exponentially, leading to the nonlinear regime, where mutual interactions take place between instability waves, or between instability waves and the non-modal response to the external disturbances. Transition is one of the outstanding nonlinear phenomena of great fundamental scientific significance. Understanding and predicting transition are also of crucial practical importance because it affects critically drag, aerodynamics heating at high speeds, mixing as well as noise generation.
Aims and objectives
Transition in shear flows is prone to external disturbances. In the supersonic regime, ambient acoustic waves are of particular importance. In laboratory conditions, acoustic waves come from the boundary layers along the tunnel walls, whereas in aerodynamical applications sound waves may be generated by other parts of the flow. In either case, acoustic waves impinge on the shear flow to change its instability and hence transition. On the other hand, supersonic shear flows may support the so-called radiating instabilities. The incident and spontaneously radiated sound waves may form an acoustic feedback loop thereby changing completely the instability and transition scenarios. The PhD project investigates the role of acoustic waves and acoustic feedback loop in instability and transition. We start with studying the interaction of an incident acoustic wave with a supersonic boundary layer and calculating the reflection coefficient as well as the signature of the forced response in the boundary layer. Next, we analyze the interaction of the forced response with instability waves and monitor its impact on the development of the latter. Particular attention will be directed to possible radiating instabilities, which manifest as resonant over-reflection. Formation of an acoustic feedback loop will be investigated in a twin-boundary-layer model pertaining to the wind tunnel experiments. The work will then be extended to twin jets.
Potential applications and benefits
With the effect of the incident sound waves on instability being quantified, the theoretical results will help 'extrapolate' wind tunnel data to the flight condition. The improved understanding gained will help develop flow control technique using acoustic actuation. The proposed research will lead to a better description of instability and acoustic radiation of twin jets.
Novelty of the research methodology
The research combines detailed asymptotic analysis and accurate numerical computations to probe into physical mechanisms, allowing for construction of relevant theoretical descriptions based on first principles.