A.J.S. Rodrigo

On the optimization of mixing protocol in a certain class of three-dimensional Stokes flows

Mixing in a special class of three-dimensional, non-inertial periodic flows is studied numerically. In the type of flow considered here, the cross-sectional velocity components are independent of the axial flow and the axial flow is independent of the axial coordinate. Using the eccentric helical annular mixer as a prototype, we consider the counter-rotating case with steady rotation of the outer cylinder and sinusoidal modulation of the inner one. Apart from the mixer geometry, the behavior of the system is governed by two dimensionless parameters obtained by scaling the cross-sectional stirring protocol with respect to the characteristic residence time of the fluid in the mixer. The first parameter is related to the average number of turns of the outer cylinder and the second one is related to the average number of modulation periods of the inner cylinder. The convection-diffusion equation is solved numerically, with temperature as a passive scalar, at high Peclet number. For a given three-dimensional mixer geometry and axial flow rate we show that there is an optimum modulation frequency for which the exit standard deviation of the temperature field is a minimum. Lagrangian simulations at infinite Peclet number and the use of other tools to study mixing, such as stretching calculations and tracer tracking methods, confirm that the optimized protocol does result in very effective mixing.

Heat-Transfer Enhancement by Chaotic Advection in the Eccentric Helical Annular Flow

Chaotic advection in the eccentric helical annular heat exchanger is investigated as a means to enhance its thermal efficiency. Chaotic streak lines are generated by steadily rotating one boundary while the other is counter-rotated with a time-periodic angular velocity. The effects of the eccentricity ratio and modulation frequency on the heat-transfer rate are analyzed by numerically solving the 3D convection-diffusion equation for a broad range of parameter values. For the frequency range over which chaotic advection can be effectively promoted, the efficiency of the heat exchanger is enhanced over that obtained for steady boundary rotation. Other tools, such as stretching field calculations and streak-line plots, applicable for dissipative dynamical systems, are implemented. These tools qualitatively confirm the quantitative heat-transfer results obtained.

MIXING ENHANCEMENT BY FREQUENCY-SELECTIVE CHAOTIC ADVECTION IN A 3-D TIME-PERIODIC STOKES FLOW

ABSTRACT A new 3-D periodic Stokes flow has been imagined and realized experimentally. It consists of axial Poiseuille flow superimposed on the 2-D tangential motion between two confocal ellipses that glide circumferentially so that the geometry is invariant. Chaotic streak lines obtained experimentally are compared to numerical simulations of this time-periodic flow. We next turn our attention to the problem of determining how to move the boundaries in order to obtain the most efficient mixing. Using a numerical experiment to study the advection of a passive scalar, we show that for a given 3-D mixer geometry and flow rate there is an optimum modulation frequency of the boundary displacement protocol for which the mixing process is most efficient. Furthermore, it is shown that chaotic advection can be regarded as a frequency-selective amplifier. This behavior is similar to that of fluid instability where external perturbations are amplified for a certain frequency range. For values above or below this range, perturbations are damped and the system is stable.

Optimization of mixing protocol in a 3-d time-periodic stokes flow

Abstract A new 3-D periodic Stokes flow has been imagined and realized experimentally. It consists of axial Poiseuille flow superimposed on the 2-D tangential motion between two confocal ellipses that glide circumferentially so that the geometry is invariant. Using a numerical experiment to study the advection of a passive scalar, we show that for a given 3-D mixer geometry and flow rate there is an optimum modulation frequency of the boundary displacement protocol for which the mixing process is most efficient. Furthermore, it is shown that chaotic advection can be regarded as a frequency-selective amplifier. This behavior is not unlike that of fluid stability where external perturbations are amplified for a certain frequency range. For values above or below this range, perturbations are damped and the system is stable.