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Abstract

Following up ideas put forward by J.M. Ottino and colleagues, the possibility of designing a computational tool to optimize the mixing of viscous fluids in industrial devices is studied. It is shown that an efficient method to characterize and quantify a mixing process is to apply the statistical measures introduced by Danckwerts (e.g., intensity of segregation and scale of segregation) on the coarse-grained density distribution of points in Poincaré sections and advection patterns, that can be obtained by tracking the positions of marked fluid elements numerically. This method is not computationally excessively costly and, as is demonstrated here, can be applied easily to experimental dye advection studies. The model system used is the Stokes flow in a two-dimensional cavity transfer mixer: two rectangular cavities which are periodically driven by a solid wall and by the passage of the cavities over each other. This system shares with many industrial devices the complexity that the geometry of the flow is time-dependent. These changes in the geometry of the flow impose difficulties on the techniques of calculating the fluid velocity field (a boundary element method) and the advection of marked fluid elements. Ways of overcoming these difficulties are described.

Refractive Index-Matched PIV Experiments and CFD Simulations of Mixing in a Complex Dynamic Geometry

“…Their work found that the number of cavities per row and the dimensionless number k defined as the ratio between the axial and the tangential velocity of the fluid at the inlet are the two critical factors for the performance of the dynamic mixer. Many studies simplified dynamic mixers into two-dimensional approximations and conducted corresponding simulations. − Woering et al proposed a more specific and quantitative mixing analysis by investigating the interactions between two rectangular cavities . Recently, Grosso et al captured stretching-and-folding mixing actions inside the device and assessed the impact of geometrical and operational variables by a two-dimensional mixer model …”

“…10−13 Woering et al proposed a more specific and quantitative mixing analysis by investigating the interactions between two rectangular cavities. 10 device and assessed the impact of geometrical and operational variables by a two-dimensional mixer model. 11 Optical measurement techniques with laser light sources such as particle image velocimetry (PIV) have been used in various areas to investigate single-phase flow, two miscible fluid flow, and dilute two-phase flow.…”

Fluid Flow and Distributive Mixing Analysis in the Cavity Transfer Mixer

“…This length is called hereinafter displacement. Following Woering et al, a nondimensional displacement is defined as follows (see Figure )where S is the displacement and D the width of the cavity. Because we propose a 2D simplification of the real 3D geometry, in the definition of displacement we must also properly account for 3D effects.…”

“…This length is called hereinafter displacement. Following Woering et al, [25] a nondimensional displacement is defined as follows (see Figure 4)…”

“…The sequence of spherical cavities encountered along the path can then be approximated as a row of circumferential cavities. A similar approach was used by Woering et al in 1999, who proposed a study of mixing in a 2D CTM. In their case, however, the cavity shape was assumed to be rectangular, quite a simplification of the 3D spherical cavities of the device; we show in the following how even small differences in the cavity shape can give rise to differences in Poincaré maps ‐ see Section .…”