Effect of aspect ratio of elliptical stirred vessel on mixing time and flow field characteristics in the absence of baffles

Abstract

Elliptical tanks were used as an alternative to circular tanks in order to improve mixing efficiency and reduce mixing time in unbaffled stirred tanks (USTs). Five different aspect ratios of elliptical vessels were designed to compare their mixing time and flow field. Computational fluid dynamics (CFD) simulations were performed using the k–e model to calculate the mixing time and simulate turbulent flow field features, such as streamline shape, velocity distribution, vortex core region distribution, and turbulent kinetic energy (TKE) transfer. Visualization was also carried out to track the tinctorial evolution of the liquid phase. Results reveal that elliptical stirred tanks can significantly improve mixing performance in USTs. Specifically, the mixing time at an aspect ratio of 2.00 is only 45.3% of the one of a circular stirred tank. Furthermore, the secondary flow is strengthened and the vortex core region increases with the increase of aspect ratio. The axial velocity is more sensitive to the aspect ratio than the circumferential and radial velocity. Additionally, the TKE transfer in elliptical vessels is altered. These findings suggest that elliptical vessels offer a promising alternative to circular vessels for enhancing mixing performance in USTs.

1. Introduction

The circular unbaffled stirred tank (C-UST) is a commonly used stirred equipment that has various applications, such as preventing cell damage during fermentation, reducing grain wear during crystallization, eliminating dead zone in high viscosity fluid mixing, and reducing energy consumption during solid–liquid suspension [1–7]. However, in the C-UST, the formation of a central vortex leads to highly circumferential fluid motion, with minimal movement in the radial and axial directions [8]. Consequently, the axial and radial mixing in the stirred tank without baffles remains insufficient even under large Reynolds numbers. Additionally, the mixing time in the C-UST is typically longer than in baffled tanks, leading to lower mixing efficiency [9]. These limitations arise because the C-UST has an arbitrary profile symmetry, which tends to produce symmetry and periodic flow fields. To address these limitations, researchers have explored to break the symmetry and periodicity of flow field, investigating issues related spatial symmetry and time stability.

In terms of temporal behavior, it is noteworthy that the stirring speed changes over time instead of maintaining a constant speed. However, the changing function of the variation is crucial to improve the mixing efficiency. Recent studies have indicated that the chaotic wave function exhibits superior performance in enhancing the mixing effect when compared to sine wave, sawtooth wave, and forward and backward mode [10]. Additionally, a comparison of two experimental conditions, namely chaotic speed and constant speed, has suggested that the chaotic speed can effectively increase the mixing performance [11]. These findings underscore the significance of the time-varying function of stirring speed in achieving optimal mixing efficiency.

To improve the mixing performance in C-USTs, various approaches have been investigated, including spatial structure change and eccentric stirring systems. Baffles are commonly added to break the symmetry in space, which improves mixing performance [12]. Although the core of this topic is to discuss the unbaffled stirred tank, the way of adding baffles can also be summarized as the spatial structure change. Moreover, eccentric stirring systems have been widely studied to enhance the mixing performance. Clear findings confirmed that an eccentric stirring system can enhance both laminar and turbulent mixing performance, and the optimal eccentricity was found to be 0.42 [13,14]. Karcz et al. [15] investigated the mixing time in an eccentric stirred system and found that it can shorten the mixing time by about 50%, while the mathematical model for connection between mixing time and eccentricity indicated that eccentricity directly affects the mixing time. Montante et al. [16] used a combination of particle image velocimetry (PIV) experiment and numerical simulation to investigate the turbulence characteristics of eccentric stirred system in a C-UST and found that eccentric stirred system can increase axial and radial velocity while destroying the symmetrical double-ring flow field structure. Galletti and Brunazzi [17] used laser Doppler anemometry (LDA) to study the eddy current in an eccentric stirred tank without baffles and found that eccentric system can enhance turbulence through increase macroscopic instability. Woziwodzki