Greg Chini, Department of Mechanical Engineering, University of New Hampshire
Mixing Hot and Cold with Sound
The study of acoustic streaming, in which the nonlinear interaction of time-periodic sound waves of small amplitude 鈭� drives O(鈭�^2) time-mean flows, dates back to the work of Lord Rayleigh. Owing to their ability to effect a net transport of heat, mass, and momentum, acoustic streaming flows are employed in a range of modern technologies, e.g., to manipulate particles and cells in lab-on-a-chip devices, to improve the efficiency of chemical reactions, and for active irrigation in medical procedures. Surprisingly, when an acoustic wave interacts with a stratified fluid, a distinct, much stronger type of acoustic streaming can occur. This baroclinic acoustic streaming is investigated here via the derivation of a set of wave/mean-flow interaction equations for a system comprising a standing acoustic wave in a channel with walls maintained at differing temperatures. Unlike classical Rayleigh streaming, the resulting mean flow arises at O(鈭�) rather than at O(鈭坁2). Thus, fully two-way coupling between the waves and the mean flow is possible: the streaming is sufficiently strong to induce O(1) rearrangements of the imposed background temperature and density fields, which modifies the spatial structure and frequency of the acoustic mode on the streaming time scale. A novel WKBJ analysis is developed to average over the fast wave dynamics, enabling the coupled system to be integrated strictly on the slow time scale of the streaming flow. Numerical simulations of the asymptotically-reduced system are shown to reproduce results from prior numerical simulations of the full (instantaneous) compressible Navier-Stokes and heat equations with remarkable accuracy for a fraction of the computational expense. The reduced simulations shed light on the potential for baroclinic acoustic streaming to be used as an effective means to enhance heat transfer, particularly in micro-gravity environments, where weight often is a primary concern and natural convective flows are absent.