Construction and performance characterisation of the low-cost regenerators for travelling-wave thermoacoustic engines

A threerdimensional CFD study of the tworphase flow field in a GasrLiquid Cylindrical Cyclone (GLCC) using the finite volumerbased finite element method is presented. The numerical analysis was made for airrwater mixtures at near atmospheric conditions, while both liquid and gas flow rates were changed. The tworphase flow behavior is modeled using an EulerianrEulerian approach, considering both phases as an interpenetrating continuum. This method computed the interrphase phenomena by including a source term in the momentum equation to consider the drag between the liquid and gas phases. The gasrliquid flow is modeled using an inhomogeneous mixture model, in order to capture the interfacial effects associated to the general complex interfacial boundaries. Results are compared to experiments and to results from a birmodal inhomogeneous particle model. The CFD technique here proposed, demonstrates to satisfactorily reproduce important features not easily depicted in experiments and not computed when using the particle model. Results show phase distributions and velocity profiles inside the GLCC, as well as the computed gas carryrunder for different operating conditions. Thursday 11:15 11:30 23 Vortices II Billant, P Non-linear evolution of a vortex pair in a stratified fluid Axel Deloncle∗, Paul Billant∗ and Jean-Marc Chomaz∗ We have performed high-resolution direct numerical simulations of the nonlinear evolution of a pair of counter-rotating vertical vortices in a stratified fluid for various high Reynolds numbers Re and low Froude numbers Fh. As observed experimentally, the vortices are bent by the zigzag instability producing high vertical shear (figure 1). We have found that there is no nonlinear saturation so that the exponential growth is stopped only when the viscous dissipation by vertical shear is of the same order as the horizontal transport, i.e. when Z max = O(Re) where Z h max is the maximum horizontal enstrophy nondimensionalized by the vortex turn-over frequency. The zigzag instability therefore transfers directly the energy from large scales to the small dissipative vertical scales. However, for high Reynolds number, the vertical shear created by the zigzag instability is so intense that the minimum local Richardson number Ri decreases below a threshold around 1/4 and small-scale Kelvin-Helmholtz instabilities develop (figure 1). We show that this can only occur when ReF 2 h > 340. LadHyX, CNRS, École Polytechnique, F–91128 Palaiseau Cedex, France A. Deloncle et al., J. Fluid Mech. 599, 229 (2008). P. Billant and J.-M. Chomaz J. Fluid Mech. 418, 167 (2000). Figure 1: Vertical vorticity isosurfaces of the simulation for Fh = 0.66 and Re = 3180. The two vortices, initially columnar, are bent by the zigzag instability (t = 50). By t = 70, Kelvin-Helmholtz instabilities develop in the highly sheared region and produce small-scales structures (t = 105). Smooth pancake vortices are eventually produced (t = 160). Red and blue contours represent ±60% of the vertical average of the maximum vertical vorticity in each horizontal plane. Transparent isosurfaces are the same for a 10% level. Monday 15:15 15:30 24 Interfacial Waves Billingham, J The initial flow caused by an inclined, accelerating wavemaker John Billingham, David J. Needham, Peter G. Chamberlain We consider the initial, two-dimensional flow generated by the horizontal motion of a plane, rigid wavemaker into an initially stationary layer of inviscid fluid. The most interesting flows occur when the wavemaker is inclined towards the fluid. Using the method of matched asymptotic expansions for small times, we find that the flow develops in an inner and an outer region, with a jet forming in the inner region, but that this solution only exists when the wavemaker is sufficiently close to the vertical. At inclinations beyond a critical value, we include the effect of surface tension, with coefficient σ, in order to investigate how the solution breaks down as σ → 0. We find that when the contact angle is such that the initial free surface is horizontal, capillary waves form, and pinch off a bubble at a finite time. For other contact angles, we have uncovered a rich asymptotic structure, one feature of which is the formation of a breaking gravity wave, unaffected by surface tension at leading order, that owes its existence purely to the initial curvature of the free surface and its effect on the subsequent flow. Another interesting feature is a finite waiting time, which occurs for contact angles less than 45o, during which the contact line is stationary before starting to move up the wavemaker. School of Mathematical Sciencess, University of Nottingham. School of Mathematics, University of Birmingham. Department of Mathematics, University of Reading. Tuesday 16:15 16:30 25 Free Surface Flow Blount, M Bending at the base of a dragged-out viscous thread M. J. Blount∗, J. R. Lister∗ We consider steady flow of a slender viscous thread falling from a nozzle onto a moving horizontal belt. We analyse steady solutions in the asymptotic limit of a very slender thread. Previous analysis of the problem has assumed the dominant force balance to be between gravity and viscous stretching, and has neglected the resistance that the thread has to bending. While the bending resistance is small for a slender thread, we show that its inclusion gives rise to a boundary-layer structure in which bending stresses become important only near the belt, where they support a vertical stress and allow the velocity and rolling conditions to be satisfied. The outer solution is analogous to a viscous catenary, with velocity fixed at the belt and at the nozzle. There are three asymptotic regimes, with distinct structures, corresponding to the cases that the belt speed is larger than, smaller than, or close to the velocity of a freely falling thread. The stability of the solutions within each regime is discussed, and the implications for the onset of meanders in the ‘fluid-mechanical sewing machine’ are explored. ∗ITG, DAMTP, University of Cambridge. Chiu-Webster, S. & Lister, J. R., J. Fluid Mech. 569, 89 (2006). Wednesday 14:00 14:15 26