Enhanced mixing at inertial microscales using flow-induced flutter

Numerical simulations are used to explore the use of flow-induced flutter of a membrane as a mechanism for effective mixing at inertial microscales. A simple two-dimensional model of mixing in a channel is employed and fluid-structure interaction modeling with an immersed boundary method-based solver is used to explore the flow physics, flutter dynamics, and scalar mixing of these flutter mixers. The performance of the mixers is characterized in terms of a mixing index and a nondimensional head loss, and the effect of Reynolds and Schmidt numbers, as well as the membrane length on these performance indices, is examined. Simulations indicate that flow-induced flutter is capable of significantly enhancing mixing for channel Reynolds numbers as low as 15 and the relatively low associated pressure loss might make these flutter mixers a viable alternative for such applications.

Figure 1

Schematic diagram of the computational domain (not to scale) showing the geometry and boundary conditions.

Figure 2

Flapping amplitude and Strouhal number vs Reynolds number, measured from the maximum $y$ component of the tip position.

Figure 3

Contour plots of spanwise vorticity (top) and scalar concentration (bottom) for $L=W/2$ membrane at Reynolds numbers of 25, 50, 100, 200. The images to the left of the contour plots show the motion envelopes for the membrane through one cycle.

Figure 4

Plots of time averaged mixing index (left) and head loss (right) as a function of downstream location for the $L=W/2$ cases. The solid lines are the flapping membrane cases, and the dashed lines are the empty channel baseline cases for comparison. Only three selected cases are shown in the head loss plot. The shaded vertical bands represent the region occupied by the membrane.

Figure 5

Flutter amplitude $(y_{max}/W)$ and envelopes for the $L=W/2, W$, and $2W$ cases for low Reynolds numbers.

Figure 6

Spanwise vorticity $\left({\omega }_z\right)$ and scalar concentration (ϕ) for the $L=2W, \mathrm{Re}=15$ case.

Figure 7

Performance comparison in terms of pressure drop and mixing index for the various cases studied in this paper. The Reynolds number for each case is noted on the plot. The point corresponding to the cylinder is discussed in a later section.

Figure 8

Contour plots show instantaneous snapshots of the scalar concentration field $\varphi$ for $\mathrm{Sc}=1$, 10, 100, 1000.

Figure 9

Plots of time-averaged mixing index vs downstream location for $\mathrm{Re}=200$ and $\mathrm{Sc}=1$, 10, 100, 1000. Shaded areas depict the extent of the membrane.

Figure 10

Comparison of a cylinder and the $L=W/2$ membrane case with snapshots of (a) the spanwise vorticity $\omega$, (b) the scalar field $\varphi$, as well as plots of the (c) the average mixing index and (d) the head loss for the $\mathrm{Re}=100, \mathrm{Sc}=100$ cases.