Arshad Afzal

Multi-Objective Optimization of a Passive Micromixer Based on Periodic Variation of Velocity Profile

This paper presents a multi-objective optimization procedure for the design of a sigma micromixer. The procedure combines three-dimensional analyses of fluid flow and mixing, polynomial approximation of objective functions, and a multi-objective genetic algorithm (MOGA). MATLAB Optimization Toolbox (version 7.7, The Mathworks, Inc., MA, USA) was used to invoke MOGA for optimization. A brief discussion on the application of Toolbox is introduced in the paper. Three geometric design parameters concerning the shape of the sidewalls were exploited for optimization. Mixing index and non-dimensional pressure loss were selected as objective functions. For mixing analysis, steady Navier-Stokes equations with a convection-diffusion model for scalar transport were solved at the Reynolds number Re = 0.91. The design space was explored through parametric study, and the Latin hypercube sampling method was used as a design-of-experiment technique for selection of the design points in the design space. Surrogate modeling was performed for the objective functions using response surface approximation. Pareto-optimal solutions in the functional space lying on the Pareto-optimal curve were obtained.

Multiobjective Optimization of a Micromixer with Convergent–Divergent Sinusoidal Walls

A multiobjective optimization of a micromixer with convergent–divergent sinusoidal walls has been conducted using flow and mixing analyses, surrogate modeling, and multiobjective genetic algorithm. The ratios of amplitude to wavelength of the sinusoidal walls, throat width to depth of the convergent–divergent sections, and diameter of the inner circular wall to wavelength were chosen as the design variables for optimization. The full-factorial method was used to discretize the design space. The mixing index and nondimensional pressure loss were selected as objective functions. Radial basis neural network functions were used to train the objective functions. The optimization was carried out at a Reynolds number of 30. A concave Pareto-optimal front representing the trade-off between the two objective functions was obtained. The analysis of representative designs along the Pareto-optimal front showed significant variation in the ratio of throat width to depth of the convergent–divergent sections, whereas the ratio of amplitude to wavelength of the sinusoidal walls maintained a nearly constant value. The concept of mixing effectiveness was used to select the most efficient designs considering both the mixing performance and pressure drop.

Performance Analysis and Design Optimization of Gapped Pin-Fin in a Cooling Channel

ABSTRACT Performance analysis and optimization of a circular pin-fin with inside gaps in a rectangular cooling channel were performed at Reynolds number, 10,000, using three-dimensional Reynolds-averaged Navier–Stokes equations and a multi-objective genetic algorithm. The low-Reynolds-number version of the shear stress transport model was used as turbulence closure. A parametric study was also performed to identify the geometrical effects of the pin-fin on heat transfer and pressure drop. The straight and reference gapped pin-fins yielded better performances than those of the circular pin-fin without the gap in terms of both heat transfer and pressure drop. The objective of the optimization was to maximize the heat transfer and minimize the pressure loss, simultaneously. The area-averaged Nusselt number and pressure loss coefficient were considered as objective functions, and three design variables related to the geometry of the gapped pin-fin were chosen for the optimization. Twenty-seven design points were generated using Latin hypercube sampling in the design space, and response surface approximation models were constructed for the objective functions. The optimization results were analyzed using five representative solutions on the Pareto-optimal front. The objective functions were found to be significantly affected by variation in the design variables, especially, the width of front gap and the rear gap angle.

Three-objective optimization of a centrifugal pump with double volute to minimize radial thrust at off-design conditions:

Optimization of a centrifugal pump with double volute was performed using surrogate modeling and a multi-objective genetic algorithm to minimize the radial thrust at off-design conditions with minimal loss in hydraulic efficiency. Both steady and unsteady numerical analyses were conducted using three-dimensional Reynolds-averaged Navier–Stokes equations with a shear stress transport turbulent model. The three objective functions are hydraulic efficiency at the design flow rate, and radial thrust coefficient at 70% and 120% of the design flow rate. In addition, three geometric parameters related to the surface curve and the locations of both ends of the rib structure were selected as the design variables for optimization. The Latin hypercube sampling method was used to choose the design points in the design space. The three objective functions were approximated using response surface approximation models. Pareto-optimal solutions representing the trade-off between the objective functions were obtained using a genetic algorithm. Representative optimal designs show that the optimized double volutes significantly reduce both the radial force and the amplitude of the radial force fluctuation with small loss in hydraulic efficiency.

Shape Optimization of a Three-Dimensional Serpentine Split-and-Recombine Micromixer

Optimization of a three-dimensional split-and-recombine micromixer with serpentine structure was performed using Navier–Stokes analysis and optimization techniques. The optimization study was performed at a fixed Reynolds number of 15, with four dimensionless design variables, viz. the ratio of the subchannel width to the main channel width, the ratio of the subchannel length to the pitch length, the ratio of the subchannel depth to the main channel depth, and the ratio of the recombination channel width to the main channel width. The design space was investigated by a parametric study, and the design points within the design space were selected by the Latin hypercube sampling method. Two different objective functions, viz. the mixing index at the micromixer exit and mixing effectiveness, were used alternately for the single-objective optimizations. Mixing effectiveness was defined as the ratio of the mixing index to the pressure drop. A surrogate modeling technique based on a radial basis neural network was used to approximate the objective functions. Optimum configurations of the micromixer were found through the mixing-index and mixing-effectiveness optimizations. The optimum design of the micromixer obtained by the mixing-index optimization confirmed 33.0% relative increase in the mixing index compared with the reference micromixer. The mixing index, 0.86, which was achieved by the optimization of the micromixer, is much higher than those of the other split-and-recombine micromixers at the same mixing length and Reynolds number, and the optimized micromixer could be integrated with microfluidic systems including lab on a chip and micro total analysis system.

Parametric Study of a Micromixer with Convergent-Divergent Sinusoidal Walls

A Parametric study of a passive micromixer with convergent-divergent channel walls of sinusoidal variation is conducted numerically using combined Navier-Stokes equations and convection-diffusion model for a Reynolds number range, 10 ≤ Re ≤ 70. Water and ethanol are used as working fluids for mixing analysis. Mixing performance was used to compare different configurations (layout) of the micromixer. In comparison with previously published design, which was based on Dean vortices in the sub-channels, the new configurations offered Dean vortices in the sub-channels and recirculation zones in the recesses of the channel for effective mixing. The proposed configurations are competitive in terms mixing performance and pressure loss. Finally, effect of two geometrical parameters viz. the ratio of throat-width to diameter of circular wall and the ratio of diameter of circular wall to amplitude, on mixing performance was studied over a chosen Reynolds number range.