Hydraulic Characteristics, Residence Time Distribution, and Flow Field of Electrochemical Descaling Reactor Using CFD
Bolin Hu 1 , Xiaoqiang Zhang 1, *, Zhaofeng Wang 2 , Zixian Wang 1 and Yuanfan Ji 1
1 College of Environment and Resources, Xiangtan University, Xiangtan 411100, China;
email@example.com (B.H.); firstname.lastname@example.org (Z.W.); email@example.com (Y.J.)
2 College of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo 454000, China;
* Correspondence: firstname.lastname@example.org
Abstract: This paper uses computational fluid dynamics (CFD) to simulate flow field distribution inside an electrochemical descaling reactor in three dimensions. First, the reactor flow field was obtained by steady‐state simulation, and the grid independence was verified. Then, the steady state of the flow field was judged to ensure the accuracy of the simulation results. Transient simulations were performed on the basis of steady‐state simulations, and residence time distribution (RTD) curves were obtained by a pulse‐tracing method. The effects of plate height and plate spacing on reactor hydraulic characteristics (flow state and backmixing) were investigated using RTD curves, and the results showed that increasing the plate height and decreasing the plate spacing could make the flow more similar to the plug flow and reduce the degree of backmixing in the reactor. The flow field details provided by CFD were used to analyze the reactor flow field and were further verified to obtain the distribution patterns of dead and short circuit zones. Meanwhile, information regard‐
ing pressure drops was extracted for different working conditions (490, 560, and 630 mm for pole plate height and 172.6, 129.45, and 103.56 mm for pole plate spacing), and the results showed that increasing the pole plate height and decreasing the pole plate spacing led to an increased drop in pressure. In this case, a larger pressure drop means higher energy consumption. However, increas‐
ing the pole plate height had a smaller effect on energy consumption than decreasing the pole plate spacing.
Keywords: CFD; residence time distribution; reactor; hydraulic characteristics; flow field analysis;
The circulating cooling water is used primarily for cooling equipment, dust removal, and the cooling of shower products in the industry. This process consumes large quanti‐
ties of water. According to some statistics , industrial water consumption in China in 2019 was 121.76 billion cubic meters, accounting for 20% of total water consumption. In terms of industrial water, industrial cooling water accounted for about 60–70% of total industrial water consumption. Due to the exchange and transfer of heat, a scale will grad‐
ually form on the surface of heat‐exchange equipment after accumulation. This scale causes higher energy consumption and equipment corrosion and, in severe cases, it may even explode. Several studies have documented that a scale of 3 mm in thickness can cause 20% of extra energy consumption, while a 9 mm‐thick scale can cause 60% of extra energy consumption . Therefore, to ensure production safety and decrease the treat‐
ment of energy consumption, the descaling of heat‐exchange equipment is essential. Until recently, the method of adding chemicals has been widely used due to its low treatment costs and efficient effects. However, problems such as environmental pollution and sec‐
ondary treatment of effluent also make it difficult to satisfy the needs of an environmen‐
Citation: Hu, B.; Zhang, X.; Wang, Z.; Wang, Z.; Ji, Y. Hydraulic Char‐
acteristics, Residence Time Distribu‐
tion, and Flow Field of Electrochemi‐
cal Descaling Reactor Using CFD.
Processes 2021, 9, 1896.
Academic Editor: Alessandro D’Adamo
Received: 20 September 2021 Accepted: 21 October 2021 Published: 23 October 2021
Publisher’s Note: MDPI stays neu‐
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This article is an open access article distributed under the terms and con‐
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been favored by researchers for its clean, non‐polluting, and low‐energy consumption fea‐
At present, many scholars have examined the descaling mechanism of electrochemi‐
cal technology and have worked to improve its descaling efficiency. In 2021, Guo et al. 
points out that the current magnitude can directly affect the descaling efficiency of an electrochemical system. In addition, it has been shown that the removal efficiency of both hardness and alkalinity increases with the increasing current. In 2019, Luan et al.  de‐
signed multi‐meshes coupled cathodes—which produce a self‐synergy effect based on their unique multilayer structure—that significantly improved descaling efficiency and further reduced energy consumption. In 2011, David Hasson  designed a novel descal‐
ing system that was characterized by the fact that the cathode and anode of the system were separated by a cationic ion exchange membrane and equipped with a separate reac‐
tor, thus avoiding the problem of cathode descaling. Furthermore, it can significantly in‐
crease the precipitation rate of CaCO3, significantly reduce the required electrode area, and overcome the fact that the conventional equipment is limited by the current limit. All of the above studies have made great contributions to the progress of electrochemical treatment technology, in which they offer something new in terms of improvements to electrical parameters and the development of new equipment. However, there is not a great deal of focus on the hydraulic characteristics of equipment, including internal water flow state, backmixing, etc.
Many scholars have conducted theoretical studies on the flow phenomena of fluids by developing universal mathematical models to guide and enable the intensification of flow processes [12–14]. However, whenever fluid flow is involved, the structure of the reactor is also an important factor that affects hydraulic flow characteristics . The hy‐
draulic characteristics of equipment have significant effects on improvements in descaling efficiency, equipment optimization, etc. One of the main approaches to the study of reac‐
tor mixing performance and hydraulic properties is the theory of residence time distribu‐
tion. This concept was first proposed in 1935 by MacMullin and Weber for application in analytical chemical reactors and developed into a more explicit form through Danckwerts and Levenspiel et al. [16–18].
At the same time, flow field analysis is also an important mean for the study of the hydraulic characteristics of a reactor. However, the complicated nature of fluid motion has made it almost impossible to examine the flow field characteristics simply by direct field measurements or laboratory experiments. However, since the introduction of CFD in 1970, it has been easy to obtain complete flow field characteristics. Therefore, this method has been widely used in a variety of continuous flow systems. In 2010, Ding et al.
 conducted a three‐dimensional CFD simulation of a biohydrogen reactor. The authors derived reactor parameters with both performance and economy by optimizing its impel‐
ler structural parameters and analyzing the flow patterns of different types and speeds of the impeller. In 2017, Das et al.  performed two‐dimensional simulations of multiphase flow in modified up‐flow anaerobic sludge blanket (MUASB) and up‐flow anaerobic sludge blanket (UASB) reactors. In addition, the authors compared and analyzed their hydrodynamic characteristics. The results showed that the mixing performance of MUASB was superior. Moreover, in the MUASB reactor, the appropriate baffle length and angle were more conducive to the mixing of materials. In the field of reactor design, CFD is a relatively mature research method [21–23], but few studies have used CFD to study the hydraulic characteristics of electrochemical descaling reactors.
In this paper, the internal structure of an electrochemical reactor is taken as the influ‐
encing factor, and the CFD method is adopted to simulate an electrochemical reactor in
three dimensions with different structures. In Section 2, the RTD theory and numerical
simulation scheme are described. In Section 3, results of the residence time distribution
(RTD) and the reactor internal flow fields are presented from simulations. Moreover, this
section analyzes the influence of structural changes to the reactor hydraulic characteristics
and provides the theoretical basis for the design of electrochemical reactors with good
hydraulic characteristics. In Section 4, the findings of our study are summarized and the concluding remarks are presented.
2.1. Methods of RTD
In an actual industrial reactor, due to the uneven flow rate of the reaction material or the influence of internal components, the reactor exists in a trench flow, dead zone, etc.
This leads the reactor outlet material to have a different residence time in the reactor. Ac‐
cording to the probability theory, the residence time distribution density function can be used to quantitatively describe the residence time distribution of the material in the reac‐
tor. This function can be written as:
E t C t
C t dt