Optimizing the rotated arc mixer

Abstract

in Wiley InterScience (www.interscience.wiley.com).Using the mapping method an efficient methodology is developed for mixing analysis in the rotated arc mixer (RAM). The large parameter space of the RAM leads to numerous situations to be analyzed to achieve best mixing, and hence, it is indeed a challenging task to fully optimize the RAM. Two flow models are used to study mixing: one based on the full three-dimensional (3-D) flow field, and a second one based on a simplified 2.5-D model, where an analytical solution is used for transverse velocity components in combination with a Poiseuille profile for the axial velocity component. Detailed 3-D velocity field analyses reveal locally significant deviations from the Poiseuille profile e.g., presence of back-flow, but only minimal differences in mixing performance is found using both flow models (3-and 2.5-D) in the RAM designs that are candidates for accomplishing chaotic mixing. Despite the computational advantage of the 2.5-D approach over the 3-D approach, it is still cumbersome to analyze mixing for large number of designs using techniques based on particle tracking, e.g., Poincareś ections, dye traces, stretching distributions. Therefore, in this respect the mapping method provides an engineering tool able to tackle this optimization problem in an efficient way. On the basis of mixing evaluations, both in qualitative and quantitative sense, for the whole range of parameter space, the optimum set of design and kinematical parameters in the RAM is obtained to accomplish the best mixing.

Spectral analysis of mixing in chaotic flows via the mapping matrix formalism: Inclusion of molecular diffusion and quantitative eigenvalue estimate in the purely convective limit

“…Equation (12) corresponds to the computation of the Ulam's matrix using a swarm of N m particles to approximate the measures entering the numerator and the denominator of Eq. (14).…”

“…The mapping method, 8,9 based on the distribution matrices, offers an efficient way to investigate the kinematics of mixing for generic mixing protocols in time and spatial periodic flows. A variety of two-and three-dimensional prototypes of flows and mixers has been studied by using the mapping method, 10 including the Kenics and other static mixers, [11][12][13] the rotated arc mixer, 14 micromixers, 15 various extruders, 16 etc. In these works, the evolution of a scalar field is studied by the iterative application of the the mapping matrix to the vector describing the initial/inlet concentration distribution.…”

Eigenmode analysis of scalar transport in distributive mixing

“…In a range of studies the mapping matrix has been very successfully applied to optimize prototypical and industrial mixing flows. [14][15][16][17] The elegance of the method is that a set of matrices is only created once, and then multiplied to a vector describing the concentration distribution in the domain. This way a large number of mixing protocols can be fairly easy evaluated and compared by changing the order of the matrices.…”

Lagrangian transport characteristics of a class of three-dimensional inline-mixing flows with fluid inertia

“…Macroscopic industrial systems include the well-known Kenics mixer, [14][15][16][17] the multi-flux mixer, 18 the SMX mixer, 19 and the Rotated Arc Mixer (RAM). [20][21][22] The inline-mixing concept admits downscaling 7,8 and has found application in an array of compact and micro-fluidic counterparts such as the microKenics mixer, 23 the staggered herringbone mixer, 24,25 and the serpentine micro-channel. 26,27 These configurations have been the subject of investigation in numerous studies.…”

“…However, both transition and inertia may, depending on design and operating conditions, significantly affect flow and transport. 20,22 The underlying changes in Lagrangian mechanisms remain unclear, though. The 2.5D system possesses a well-defined Hamiltonian structure, causing the Lagrangian transport to be governed by Hamiltonian mechanics.…”