Keywords: helical static mixer, laminar flow, turbulent flow, Large Eddy Simulation (LES), Newtonian fluid, non-Newtonian fluid, pseudo-plastic fluid.

Mixing is an essential component of nearly all industrial chemical processes, ranging from simple blending to complex multi-phase reaction systems for which the reaction rate, the yield and the selectivity are highly dependent upon the mixing performance. Consequences of improper mixing include non-reproducible processing conditions and lowered product quality, resulting in the need for more elaborate downstream purification processes and increased waste disposal costs.

Static mixers promote mixing of flowing fluid streams. One typical static mixer, the helical static mixer, consists of left- and right-twisting helical elements placed at a right angle to each other. Each element twists through an angle of 180^o. The range of Reynolds number of practical flows for helical static mixers in industry is usually from very small values (Re 0) to not very large values (e.g., Re = 5,000). It has been found that, the flow regime in helical static mixers is turbulent even for relatively low Reynolds numbers, compared to flow inside a pipe that contains no mixing elements.

Due to the industrial importance of static mixers, many studies have been undertaken in an attempt to characterize their performance. The way these mixers work is still not fully understood. This paper describes how static mixing processes of single-phase Newtonian (and non-Newtonian) liquids can be simulated numerically, presents the flow pattern through a helical static mixer, and provides useful information that can be extracted from the simulation results. The three- dimensional finite volume CFD code used here solves the Navier-Stokes equations for both laminar and turbulent flow cases. Turbulent flow case is solved using LES turbulent flow model [1]. The numerical simulation of the flow and the mixing in the helical static mixer has been performed via a two-step procedure. In the first step, the flow velocity (and pressure) is computed. These values are then used as input to the second step. In the second step the particle trajectory in the flow field is calculated. At the entry of the pipe inlet, a large number of particles are uniformly distributed over half of the flow field. This represents simplified model for diametrical feeding of the mixer with two liquids. Particle trajectories corresponding to only one of the fluids are calculated.

Using different tools, such as Residence Time Distribution (RTD) [2] and Particles Distribution Uniformity (PDU) [3], the performance of a six-element helical static mixer is studied.

It is shown that the Reynolds number has a major impact on the performance of a static mixer; for low Reynolds number flows most of fluid particles are separated, whereas for higher Reynolds number flows increased mixing of fluid particles occurs. For very low Reynolds numbers fluid mixing is virtually the same.

It is also shown that for the same flow Reynolds number, the performance of a helical static mixer is different for Newtonian and shear thinning, non-Newtonian, fluids in non-creeping flows. In the low Reynolds number flow regime, the mixing patterns are almost the same for both Newtonian and Non-Newtonian fluids. Fluid mixing increases more for non-Newtonian fluids by increasing the Reynolds number to 100. For a Reynolds number of 1,000, the distributions of particles for a Newtonian fluid and for a, shear thinning, non-Newtonian fluid appear to be almost the same, although for the case of Newtonian fluid, a higher degree of mixing was observed at the last mixing element.

It is shown that, for low Reynolds number flow conditions, the PDU values are nearly the same for both Newtonian and shear thinning fluids. The PDU value increases more for a non-Newtonian fluid over that of the Newtonian fluid by increasing the Reynolds number to 100. For a Reynolds number of 1,000, the helical static mixer manifests higher performance when the working fluid is Newtonian. Also, it is shown that the static mixer performance is low at a Reynolds number of 10 for both Newtonian and shear thinning fluids.

For the case of turbulent flow, significant increases in PDU values were observed at the end of each evenly numbered mixing element. This can be explained by considering the fact that mean vorticity magnitudes are larger at those elements. The averaged vorticity magnitude at the second mixing element is 1.15 times the averaged vorticity magnitude at the first element, and the averaged vorticity magnitude at the fourth mixing element is 1.04 times that at the third element.

1

A. Yakhot, S.A. Orszag, V. Yakhot, M. Israeli, "Renormalization Group Formulation of Large-Eddy Simulation", Journal of Scientific computing, 4, 139-158, 1989. doi:10.1007/BF01061499

2

E.B. Nauman, "On Residence Time and Trajectory Calculations in Motionless Mixers", The Chemical Engineering Journal, 47, 141-148, 1991. doi:10.1016/0300-9467(91)85019-R

3

R.K. Rahmani, T.G. Keith, A. Ayasoufi, "Three-Dimensional Numerical Simulation and Performance Study of an Industrial Helical Static Mixer", submitted to ASME Journal of Fluid Engineering, 2003. doi:10.1115/1.1899166

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