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TECHNICAL PAPERS

# Three-Dimensional Numerical Simulation and Performance Study of an Industrial Helical Static Mixer

[+] Author and Article Information
Ramin K. Rahmani

Department of Mechanical, Industrial and Manufacturing Engineering, The University of Toledo, Toledo, OH 43606rkhrahmani@yahoo.com

Theo G. Keith

Department of Mechanical, Industrial and Manufacturing Engineering, The University of Toledo, Toledo, OH 43606tkeith@eng.utoledo.edu

Anahita Ayasoufi

Department of Mechanical, Industrial and Manufacturing Engineering, The University of Toledo, Toledo, OH 43606aayasoufi@yahoo.com

J. Fluids Eng 127(3), 467-483 (Mar 01, 2005) (17 pages) doi:10.1115/1.1899166 History: Received November 16, 2003; Revised January 04, 2005; Accepted March 01, 2005

## Abstract

In many branches of processing industries, viscous liquids need to be homogenized in continuous operations. Consequently, fluid mixing plays a critical role in the success or failure of these processes. Static mixers have been utilized over a wide range of applications such as continuous mixing, blending, heat and mass transfer processes, chemical reactions, etc. This paper describes how static mixing processes of single-phase viscous 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 computational fluid dynamics code used here solves the Navier-Stokes equations for both laminar and turbulent flow cases. The turbulent flow cases were solved using $k-ω$ model and Reynolds stress model (RSM). The flow properties are calculated and the static mixer performance for different Reynolds numbers (from creeping flows to turbulent flows) is studied. A new parameter is introduced to measure the degree of mixing quantitatively. Furthermore, the results obtained by $k-ω$ and RSM turbulence models and various numerical details of each model are compared. The calculated pressure drop is in good agreement with existing experimental data.

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## Figures

Figure 2

(a) Computational domain across one helical surface is cut by a large number of parallel planes perpendicular to the flowfield centerline. (b) Cross-sectional mesh. (c) Volume mesh for one mixing element

Figure 5

Velocity contours (m∕s) and the vorticity contours (1∕s) for Re=5000 (using the kω model)

Figure 6

Images of particle distribution at second element for Re=1000 (for different released particles number, Np)

Figure 7

Velocity field at second, fourth, and sixth elements

Figure 8

Velocity field calculated by k–ω (left) and RSM (right) models

Figure 9

Particles’ locations at second, fourth, and sixth elements (Re=0.01)

Figure 10

Particles’ locations at second, fourth, and sixth elements (Re=0.1)

Figure 11

Particles’ locations at second, fourth, and sixth element (Re=1)

Figure 12

Particles’ locations at second, fourth, and sixth elements (Re=10)

Figure 13

Particles’ locations at second, fourth, and sixth elements (Re=100)

Figure 14

Particles’ locations at second, fourth, and sixth elements (Re=1000)

Figure 15

Particles’ locations at second, fourth, and sixth elements (Re=3000)k–ω model

Figure 16

Particles’ locations at second, fourth, and sixth elements (Re=5000)k—ω model

Figure 17

Particles’ locations calculated by k—ω (left) and RSM (right) models

Figure 18

G-value calculated for Re=0.01, 0.1, 1, 10, 100, 1000, 3000, and 5000

Figure 19

PDU values calculated for Re=0.01, 1, 10, 100, and 1000, at the second, fourth, and sixth mixing elements

Figure 20

PDU values for Re=0.01, 0.1, 1, 10, 100, 1000, 3000, and 5000 at the fourth mixing elements

Figure 21

PDU values at the end of even numbered mixing elements (Re=3000)

Figure 3

Residual curves for Re=0.01 (top), Re=10 (middle), and Re=1000 (bottom)

Figure 4

The obtained structure radius (left) and the computed pressure drop (right) for Re=100

Figure 1

A six-element static mixer

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