Numerical Simulation on Enhanced Heat Transfer and Flow Characteristics in Direct-Contact Heat Exchanger: A Novel Kenics Static Mixer

Zhao, Shuang; Zhang, Xia; Wang, Hua; Zhang, Hao; Huang, Junwei

doi:https://doi.org/10.1155/2023/4959962

International Journal of Energy Research

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Abstract Introduction Experimental Results Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 4959962 | https://doi.org/10.1155/2023/4959962

Numerical Simulation on Enhanced Heat Transfer and Flow Characteristics in Direct-Contact Heat Exchanger: A Novel Kenics Static Mixer

Shuang Zhao,¹Xia Zhang,¹Hua Wang,^2,3,4Hao Zhang ,¹and Junwei Huang¹

Academic Editor: Zhien Zhang

Received02 Sept 2022

Revised18 Jan 2023

Accepted24 Jan 2023

Published27 Mar 2023

Abstract

In this paper, a novel Kenics static mixer applied in a direct-contact heat exchanger (DCHE) was proposed in order to enhance the heat transfer efficiency. The computational fluid dynamics (CFD) simulation method was adopted to investigate the effect of the continuous phase and dispersed phase on direct-contact heat transfer (DCHT) in the Kenics static mixer. The perforation index (PI) was introduced to depict the performance of the Kenics static mixer, and the effect of different numbers of openings at three initial heat transfer temperature differences (at the inlet of the continuous and dispersed phases) was studied. The simulation results showed that under the same working conditions, a larger initial temperature difference would result in greater differences in the fluid uniformity index (UI), turbulence intensity, and time evolution of a gaseous working substance. The increase of hole numbers and decrease of hole diameters can optimize the DCHT. Under three initial temperature differences, the heat transfer efficiency for the 6-hole and 9-hole Kenics DCHEs was about 20% higher than the Kenics DCHE without holes.

1. Introduction

With the rapid development of the global economy, some problems such as energy shortage and environmental pollution have become increasingly serious, and the disparity between energy supply and demand has become increasingly prominent. The primary goal and basic requirement of energy system management is to develop and utilize energy resources rationally [1].

A heat exchanger is an important piece of equipment for improving energy utilization. Therefore, it is very necessary to improve the efficiency of heat exchange and reduce the heat loss in heat exchange processes. Heat exchangers are mainly divided into two types: surface heat exchangers and direct-contact heat exchangers (DCHEs). The heat transfer coefficient of DCHEs is higher than that of surface heat exchangers, and it does not easily cause problems such as corrosion and scaling [2]. DCHEs can be applied in different industrial applications such as seawater desalination, solar energy applications, and low-grade energy production including geothermal energy [3, 4]. Direct-contact heat transfer (DCHT) technology has been widely studied in various heat exchange processes. Kulkarni and Ranade [5] injected n-pentane into a hot viscous liquid and evaluated bubble dimensions, its rise velocity, distance from the detachment point, fraction of vapour, and the liquid phases in the evaporating drop. Wijeysundera et al. [6] developed an ice slurry generation system with DCHT between water and the coolant (Fluorinert FC-84) and found that the efficiency of ice fabrication increased by about 40 percent. Barabash et al. [7] introduced the DCHT technology in cooling towers and for cooling gas flow; they declared that the presence of DCHT can obviously improve the heat transfer efficiency. Mahood et al. [2] investigated the heat transfer efficiency, and hence the cost of a three-phase direct-contact condenser, and found that its investment expenses were 30 times lower than those of the corresponding surface condenser (shell-and-tube condenser). However, problems that hinder the outstanding performance of DCHEs still exist; for example, the mixing of fluids is not uniform enough in the DCHE, which affects the heat exchange capacity and restricts the heat exchange efficiency between fluids.

In order to improve the performance of the direct-contact experimental systems, researchers introduced some useful devices into the direct-contact experimental systems. Luo et al. [8] designed a new type of helical tube reactor and applied it to the experimental study of liquid-liquid dispersion. Jin et al. [9] applied Dixon rings in DCHT and found that the Dixon rings can have a positive effect through a series of experiments, and the heat transfer coefficient has almost doubled or even more. Li et al. [10] studied the falling film evaporation heat transfer of R134a-entrained 0.5% to 5.1% POE-type lubricating oil on the horizontal pipe. Experiments were carried out using test tubes with different surface structures. The experimental results showed that the heat transfer coefficient of the reinforced tube is higher than that of the smooth tube. Fu [11] used a pentane-water direct-contact evaporation heat transfer experiment to study the effect of the Kenics element on heat transfer performance. The results showed that the Kenics element reduces the evaporation height of the DCHE, and the volumetric heat transfer coefficient (VHTC) was more than two times larger than that of the DCHE without the Kenics element. It is worth mentioning that the Kenics static mixer is a typical type of static mixer. Its advantages are low energy consumption, low investment, high effect, and quick effect, and it is not easy to block. It is also suitable for high-viscosity fluids. Therefore, the Kenics-type static mixer is selected in this paper as a built-in enhanced heat exchange device for DCHE.

This paper wanted to find a way to further improve the performance of Kenics DCHE. The application of open-celled built-in inserts is proven to be an effective method of enhancing the heat transfer. Lei et al. [12] investigated the flow and heat transfer of fluids in staggered and twisted ribbon tubes with central holes using CFD methods. Compared with smooth tubes, the heat transfer rate of staggered and twisted ribbon tubes was increased by 34.1%-46.8%. The results of Thianpong et al. [13] showed that tubes with perforated twist tapes can increase the heat transfer rate by 27.4% compared to tubes without perforated twist tapes. Bhuiya et al. [14] reported that pipes fitted with perforated twisted tapes had better thermal properties than empty pipes, because the thermal performance coefficient increased by 28-59%. Yan et al. [15] applied crossed hollow twisted tapes with different hollow widths (6, 8, and 10 mm) in the heat exchange tubes and found that the heat transfer performance of twisted tapes with a hollow width of 6 mm was 93%-120% higher than that of ordinary tubes. Zhang et al. [16] studied the effects of continuous and discontinuous twisted band turbulators (perforated and nonperforated) inside the inner tube of a dual heat exchanger on thermal performance and finally concluded that the perforated dual-tube heat exchangers are preferred over nonporous double-tube heat exchangers. Meng et al. [17] conducted a numerical study on laminar and chaotic mixing characteristics of high-viscosity fluids in a staggered perforated helical-stage static mixer, and the results indicated that the porous structure could increase the secondary flow and enhance the mixing degree of the fluid. However, less research has been done on opening holes in Kenics static mixers to improve their mixing and heat transfer performance. Therefore, this paper will explore the heat transfer performance of perforated Kenics DCHE.

Due to the existence of mixing elements in the static mixer, the flow velocity field in the static mixer is very complex. The related research mainly adopts two methods: numerical simulations through CFD and experiments through flow measurement technology. With the increasing use of CFD methods in the treatment of water and other fluids [18], CFD software is also widely used in the treatment of water and other fluids [19]. CFD software has the advantages of simple simulation process, fast operation, visualization of results, and low cost [20]. Saatdjian et al. [21] used simulation and tracer technology to study the Kenics mixer. The research showed that the simulated pressure drop was basically consistent with the measured pressure drop, and the simulated flow field was consistent with the tracer results. Coroneo et al. [22] used CFD technology to study the main characteristics of the liquid flow in the corrugated static mixer and compared the simulation results at different locations with the tracer concentration data. The results showed that the data for simulation could accurately evaluate the velocity field. Yang et al. [23] proposed a new type of single-shot electric hemispherical vortex mixer and used simulation and experimental methods to study the rapid mixing process, and the mixing index was as high as 93%. It can be seen that the change of the flow field can be accurately simulated by using the CFD method. Therefore, in this paper, the CFD method is used for the experimental simulation of the heat exchanger.

In summary, more attention needs to be paid to the study of perforations on Kenics static mixers and their application in DCHEs. Therefore, based on the innovation of Fu [11], in which Kenics static mixers are applied to DCHT, openings based on the perforation index (PI) are made in Kenics static mixers to further improve the performance of DCHT in this paper. Moreover, the current fluids of DCHT are mainly water and air; there is little research on DCHT between liquid-liquid-gas where the phase change occurs. So the continuous phase fluid of DCHT in this paper selects the high boiling point heat transfer oil Therminol 62, and the dispersed phase adopts the low boiling point organic working substance R141b. This study focuses on investigating the effect of perforated Kenics static mixers on liquid-liquid-gas mixing uniformity, turbulence intensity, and VHTC in the DCHT process using the CFD method.

2. Experimental and Mathematical Methods

2.1. Geometric Modeling

The Design Modeler drawing tool of the Ansys Workbench 2021 software is applied to establish the system. The method of opening holes on the Kenics static mixer is to vertically penetrate the Kenics static mixer with a cylinder of corresponding diameter. For the preliminary exploratory experiments, in order to reduce the redundancy of the experiment, the arrangement angle of holes was designed with 90° or 180° distribution. According to the 180° longitudinal arrangement of the three holes in the Kenics static mixing element, obtaining a reasonable PI (0.2), which is used in the following experiments (it is worth mentioning that under the same PI, the following experiments can ensure that there is the same volume of continuous-phase fluid in the open-hole Kenics DCHE), the calculation formula is formula (1). The maximum number of holes when is 9 holes. As shown in Figure 1, when , it is reasonable and uniform to design five different open-hole Kenics DCHEs with the number of openings , 2, 3, 6, and 9 (the rotation angle of the Kenics static mixing element is 180° and the aspect ratio is 1 : 1).

(a)

(b)

The test part is a circular pipe, and the static mixer is placed in the pipe, as shown in Figure 1; the total length of the static mixer is 148 mm, the length of the main pipe is 140 mm, and the hydraulic diameter of the main pipe is 27 mm. The length of the inlet and outlet is 4 mm, and their hydraulic diameter is 9 mm. The liquid working substance flows into the DCHE from the lower inlet. Before that, the DCHE is equipped with heat transfer oil at a height of 115 mm. After the low-temperature liquid working substance is in contact with the high-temperature heat transfer oil, the liquid working substance is heated up by the heat transfer oil and turns into a gas. The gaseous working substance flows with the shape of the static mixer.

The perforation index is given by [24] where is the perforation area, is the number of holes, and is the total surface area of the static mixer.

2.2. Computational Fluid Dynamics

The numerical model of fluid flow and heat transfer in a DCHE is based on the following assumptions: (i)Body forces, thermal radiation, and viscous dissipation are ignored [25](ii)The liquids are fully turbulent and incompressible [25](iii)Ignore the microdissolution among the fluids and assume that the fluids are dispersed [26]

The volume fraction (VOF) model, which can capture the position of the gas-liquid interface and better observe the change of the gaseous working substance, is selected in this paper.

The continuity equation is where is the velocity tensor of the q-th phase, m/s; is the volume fraction of the q-th phase; is the mass transfer from the q-phase to the p-phase, kg/s; is the mass transfer from the p-phase to the q-phase, kg/s; and is the mass source term, kg/m³/s.

The momentum equation is where is the density, kg/m³; is the dynamic viscosity, kg/(m·s); is the velocity tensor, m/s; and is momentum source term, N/m.

The energy equations is where is the specific enthalpy of each phase and is the heat exchange intensity between the gaseous working substance and the heat transfer oil.

The k-ω SST turbulence model has shown better performance than the k-ε-type models in three-dimensional flows with a Kenics static mixer [27, 28]. Therefore, the steady-state 3D simulations were carried out using the k-ω SST turbulence model, which utilizes the transport equations for the specific turbulence dissipation rate, , and the turbulence kinetic energy, [29, 30].

The turbulent eddy viscosity, , is given as where and are closure coefficients. More information on the method for calculating various variables of this turbulence model can be found elsewhere [30].

The pressure-velocity coupling terms use the SIMPLE algorithm, the pressure equation uses the PRESTO! format, the volume fraction equation uses the Geo-Reconstruct format, and the rest use the second-order upwind format. Using the velocity inlet, the velocity is 0.1 mm/s, and the export boundary uses OUTFLOW. The simulation results are closer to the those of the actual situation.

ANSYS 2021 software was used for modeling and mesh generation. In order to reduce the calculation error caused by the grid, referring to [31], five different grid element sizes were selected to perform grid-independent analysis of the 2-hole Kenics DCHE. The results are shown in Table 1. When the number of grids reaches 560,805, the difference in the calculation results is very small, so it can be considered that the calculation results are independent of the grid. Considering the computational cost, after comprehensive evaluation, all models were generated with the same element size (1 mm) which generate 560,805 cells during the mesh independence analysis. The final meshes of 0 hole, 1 hole, 2 holes, 3 holes, 6 holes, and 9 holes are 464,048, 461,290, 560,805, 735,209, 1,438,418, and 2,161,876, respectively. Among them, the local calculation grid diagram generated by the 1-hole Kenics DCHE is shown in Figure 2.

2.3. Experimental Validation

In order to verify the effectiveness of the numerical simulation method, a smooth empty tube experimental platform was built, which is shown in Figure 3. The experimental equipment is mainly composed of two cycles, including the heat transfer oil-heating section cycle (yellow pipeline) and the gaseous working substance cycle (red pipeline).

Before the start of the experiment, the heat transfer oil Therminol 62 is firstly injected into the DCHE at the corresponding height, then the gear oil pump is turned on, and the heat transfer oil enters the heating section (the heating section is an electric heating device with four 5000 W electric heating rods), and the heating transfer oil flows back into the direct-contact heat exchanger, ready to enter the next cycle, until the heat transfer oil is heated to the specified temperature, and the heat transfer oil heating cycle is completed. Next, the heat transfer oil enters the condensation cycle of the gaseous working substance allowing the working substance pump to convert it into the working state. Opening the valve of the liquid storage tank of the liquid working substance R141b, the liquid working substance flows from the bottom of the direct-contact heat exchanger under the action of the working substance pump, and the liquid working substance is drawn into the heat exchanger. The liquid working substance obtains heat from the high-temperature heat transfer oil, then vaporizes and evaporates into the gaseous working substance, and finally rises and separates from the heat transfer oil. Several flow sensors, temperature sensors, and pressure sensors were installed on the experimental setup. The signal is transmitted to the computer through RS485 to achieve more precise control of the experiment and obtain accurate data. The relevant physical parameters of the two fluids are shown in Table 2.

The data obtained by the CFD simulation of the experimental condition are compared with the corresponding data obtained in the experiments. Figure 4 shows the five groups of temperatures measured according to the height of the temperature sensor on the DCHE in Figure 3. It can be clearly seen from the figure that the temperature obtained from the CFD simulation is consistent with the experimental data, and the maximum relative error was within 1.7%. The temperature trends at the outlet of the DCHE are different, mainly due to the heat loss during the experiment, and the largest heat loss is at the outlet of the heat exchanger.

2.4. Evaluation Method

2.4.1. Volumetric Heat Transfer Coefficient

In this simulation, the direct-contact evaporation heat transfer mainly occurs on the contact surface between the heat transfer oil and the organic working substance. The organic working substance R141b is heated and evaporated to form droplets consisting of both gas and liquid. R141b droplets take the form of bubbles in the heat exchange. It rises in the DCHE and is damaged or concentrated by various forces. It is difficult to obtain the heated area of a shell-and-tube heat exchanger. Therefore, the volume heat transfer coefficient is introduced to characterize the overall heat transfer performance of the DCHE, which can be calculated by the following equations: where is the volume of the continuous phase fluid, m³; is the heat transfer per unit time, kJ/s; is the logarithmic mean temperature difference; is the working substance evaporation mass flow, kg/s; is the working substance steam outlet enthalpy, kJ·kg; is the working substance inlet enthalpy, kJ/kg; is the heat transfer oil inlet temperature, K; is the heat transfer oil outlet temperature, K; is the working substance inlet temperature, K; and is the working substance steam outlet temperature, K.

2.4.2. Uniformity Index

After the heat transfer oil and the working substance enter the DCHE, the working substance exchanges energy and mass with the surrounding high-temperature heat transfer oil. Mixing, splitting, and recombination of two or more liquids occur under the action of the mixer [32], so that the distribution of the heat transfer oil and the working substance tends to be uniform. The uniformity index (UI) is introduced in order to study the mixing degree of the static mixer to the direct-contact evaporation heat transfer, which is the normalized root mean square of the difference between the representative cross-sectional areas and the mass-weighted averages of the gaseous working substance. According to the definition of uniformity index, the larger UI is, the better the degree of mixing is. When its value is 1, it indicates that the mixing is completely uniform [33]. The area-weighted UI for the gaseous working substance is calculated using the following formula: where is the facet index of a cross-sectional plane with facets and is the average value of the gaseous working substance volume fraction over the outlet boundary as follows:

2.4.3. Turbulence Intensity

Turbulence intensity is caused by fluid disturbance, and turbulence intensity refers to the ratio of the root mean square of turbulent velocity fluctuations to the average velocity, which can also be expressed by Equation (14). When the turbulence intensity is less than 1%, it can be considered that the turbulence intensity is relatively low, and when the turbulence intensity is greater than 10%, it can be considered that the turbulence intensity is relatively high. In the mixing process, vortex diffusion and molecular diffusion coexist. Since the molecular diffusion speed is much greater than the vortex diffusion speed, the vortex diffusion plays a leading role in the mixing time. Turbulent flow can be seen as composed of vortex motions of different scales and intensities. Due to the formation of vortices and the increase of the heat dissipation rate, the magnitude of turbulent flow has a direct impact on the heat transfer performance. The enhancement of turbulence intensity can strengthen the heat transfer rate [34, 35]. where is the Reynolds number.

3. Results and Discussions

3.1. Effect of Pore Number on Mixing Uniformity

Concentration uniformity across the cross-section is represented by UI and is used to characterize the effectiveness of mixing in fluid dynamics. A UI of 0 indicates the presence of segregated regions of different concentrations, and a value of 1 indicates a uniform concentration. The volume fraction of the gaseous working substance obtained from the simulation of several configurations of DCHEs is plotted on multiple cross-sections in Figure 5. UI is almost 0 near the inlet (obvious red and blue regions can be observed in the contour plot shown in the figure), and then, UI increases along the length of the static mixer. It can be clearly observed in Figure 5 that when the gaseous working substance enters the first Kenics static mixing element, it is mainly distributed in the middle of the DCHE. Under the turbulent action of the Kenics static mixer, in the 0-hole Kenics DCHE, the distribution of the gaseous working substance gradually tends to be uniform in the third Kenics static mixing element. However, the time for the gaseous working substance distribution in the open-hole Kenics DCHE to become uniform is significantly less than that in the 0-hole Kenics DCHE. This shows that the mixing performance of the opening Kenics DCHE is better than that of the Kenics DCHE. In addition, if each part of the gaseous working substance volume fraction greater than 0 in Figure 5 is regarded as a bubble group, it can be seen that the size of the bubble group in the 6-hole and 9-hole Kenics DCHEs is significantly smaller than that in the DCHE without openings. The reason is that the open-cell Kenics static mixer speeds up the frequency of bubble separation by reducing the tendency of the bubbles to coalesce, which results in a reduction in the size of the bubble clusters.

In order to more clearly and accurately analyze the variation of mixing uniformity along the DCHE, the obtained data (uniformity coefficients of cross-section , 29, 56, 83, and 110) are plotted as a dot-line diagram in Figure 6. It can be clearly seen from the figure that under the three initial heat transfer temperature differences, the uniformity index of the gaseous working substance in the 6-hole and 9-hole Kenics DCHEs is relatively large. This shows that the gaseous working substance in the two devices has a relatively uniform distribution in the heat transfer oil. Taking the initial heat transfer temperature difference of 70°C as an example, from Figure 6, it can be seen that after passing through a static mixing element, the mixing uniformities in the 1-hole and 9-hole Kenics DCHEs are better. Starting from the second static mixing element, the mixing uniformity in the 9-hole Kenics DCHE performs the best and far outperforms the other models. The mixing uniformity of the open-hole Kenics DCHE is stronger than that of the Kenics DCHE at the time of the third mixing element. After entering the fourth Kenics mixing element, the mixing uniformities in the Kenics DCHE with 1 hole and 2 holes are worse than that of the Kenics DCHE. This shows that the small-aperture Kenics static mixer further optimizes the mixing performance of the Kenics static mixer. However, the larger aperture does not optimize the mixing performance of the Kenics DCHE. This conclusion can also be drawn from Figure 6.

3.2. The Effect of the Number of Holes on the Turbulence Intensity

Figure 7 shows scatter plots of the turbulence intensity along the length of the heat exchanger tube; it can be seen from the figure that the turbulence intensity of the fluid in the six devices will be enhanced with the increase of the initial heat transfer temperature difference. When the initial heat transfer temperature difference is 70°C, the change of turbulence intensity is the most obvious. When the initial heat transfer temperature difference is 30°C, the turbulence intensity of several devices is not much different, but the frequency of the turbulence intensity value greater than 5% in the 6-hole and 9-hole Kenics DCHEs is larger than that in other devices. Among them, the turbulence intensity in the 6-hole Kenics DCHE is up to 11.49%. When the initial heat transfer temperature difference is 50°C, the turbulence intensities in the 3-hole, 6-hole, and 9-hole Kenics DCHEs are obviously greater than those in other devices. Among them, the average turbulence intensity of the 6-hole and 9-hole Kenics DCHEs is the largest, and the frequency of the turbulence intensity greater than 10% of the 3-hole and 9-hole Kenics DCHEs is the highest. When the initial heat transfer temperature difference is 70°C, the turbulence intensity in the 9-hole Kenics DCHE is significantly higher than that in other devices, and the turbulence intensity can reach up to 19.35. In addition, it can also be found that a higher turbulence intensity generally occurs within perforated Kenics DCHEs compared to the results of existing studies of Kenics DCHE, and mixing elements still have a large effect on the turbulence intensity after more than three Kenics static mixing elements.

(a)

(b)

(c)

3.3. Time Evolution Analysis

As shown in Figure 8, it can be obtained that the larger the initial heat transfer temperature difference, the shorter the time for the generated gaseous working substance to reach the DCHE; the reason is that the larger initial heat transfer temperature difference increases the intensity of the direct-contact reaction and accelerates the reaction time. The speed of the phase change may also increase the turbulence intensity of the fluid to a certain extent, so that the gaseous working substance can flow out of the DCHE at a faster rate. Under each initial heat transfer temperature difference condition, the influence of Kenics static mixers with different openings on the DCHT time is not the same.

The initial heat transfer temperature difference of 70°C is taken as an example. The gaseous working substance began to flow out from the outlet of all devices at about 2 s. And the volume fraction of the gaseous working substance at the outlet of all devices reached 1 at about 2.5 s, which means that the vacuum space above the heat transfer oil in the DCHE will be occupied by the generated gaseous working substance in just 2.5 s, and the gaseous working substance will have filled the entire upper part of the DCHE. After about 2.5 s, the volume fraction of the outlet gaseous working substance becomes 1 and gradually becomes stable. Among them, the 2-hole Kenics DCHE is the one in which the gaseous working substance initially flows out of, which means that the residence time of the gaseous working substance in it is short. This may cause the gaseous working substance to receive less heat in the 2-hole Kenics DCHE than in other units. The gaseous working substance flows out of the outlet of the 6-hole Kenics DCHE the last. Contrary to the 2-hole Kenics DCHE, the heat exchange time of the gaseous working substance in it is longer. This may improve the heat transfer effect of the DCHE to a certain extent.

The residence time of the gaseous working substance is mainly determined by both the flow velocity and the path of the fluid, which means that the longer residence time of the gaseous working substance may be determined by both the lower turbulence intensity and the longer path it flows through within the DCHE. Compared with the existing studied Kenics DCHE, the residence time of the fluid in the 6-hole Kenics DCHE is greater than that in the Kenics DCHE at three different initial heat transfer temperature differences. Furthermore, the turbulence intensity and UI of the fluid in the 6-hole Kenics DCHE are better, which would predict that the better heat transfer will be achieved in the 6-hole Kenics DCHE. However, the effectiveness of heat transfer does not completely determine the length of the residence time of the gaseous working substance.

3.4. The Effect of the Number of Holes on the Volumetric Heat Transfer Coefficient

As mentioned above, the high continuous phase temperature means that more heat is available in the DCHE to satisfy the evaporation of the working substance. Under the assumption that no heat is lost in the DCHE, the law of conservation of energy implies a higher heat transfer rate between the two phases in the DCHE. As shown in Figure 9, by changing the number of openings on the Kenics static mixer, the temperature of the continuous phase significantly affects the VHTC. From the figure, we can see the variation of the VHTC of different devices under the three initial heat transfer temperature differences; the initial heat transfer temperature difference acts as the driving force for heat transfer. The larger the initial heat transfer temperature difference, the more intense the heat exchange reaction, the greater the turbulence intensity, and the more uniform the distribution of the gaseous working substance in the DCHE. However, it can be seen from the simulation results that in the DCHT, the VHTC decreases with the increase of the initial heat transfer temperature difference; that is, the efficiency of the DCHT is higher at a small initial heat transfer temperature difference. Under three different initial heat transfer temperature differences, the VHTC within the perforated Kenics DCHE is generally greater than that in the existing Kenics DCHEs studied, and with the increase of the number of holes on the Kenics static mixer, the VHTC of the DCHT generally shows an increasing trend. Among them, under three different initial heat transfer temperature differences, the heat transfer effect of the 6-hole and 9-hole Kenics static mixers is about 20% higher than that of Kenics static mixers for direct contact. Under the three initial heat transfer temperature differences, the number of openings on the Kenics static mixer has different effects on the VHTC of DCHT. Among them, when the initial heat transfer temperature difference is 30°C, the 6-hole and 9-hole Kenics static mixers have similar enhancement effects on DCHT. Under the initial heat transfer temperature difference of 50°C, the heat exchange efficiency of the 9-hole Kenics DCHE is the better than others. On the contrary, under the initial heat transfer temperature difference of 70°C, the heat exchange efficiency of the 6-hole Kenics DCHE is the best.

4. Conclusions

In this paper, under the same PI, Kenics static mixers with a different hole diameter and different number of holes are designed. Through CFD simulation, the data obtained from the simulation results were sorted and analyzed. The key conclusions are as follows: (1)It was found that the UI and turbulence intensity of several perforating devices decrease with the decrease of the initial heat transfer temperature difference under three different low initial heat transfer temperature differences. Among them, the advantages of Kenics DCHE with a smaller hole diameter and more holes are more obvious(2)The monitoring of the outlet gaseous working substance at the same flow rate shows that the greater the initial heat transfer temperature difference, the greater the difference in the time it takes for the gaseous working substance to reach the outlet. This means that the greater the initial heat transfer temperature difference, the more significant the advantage of perforation(3)At the same initial heat transfer temperature difference, the VHTC tends to increase with an increasing number of holes. The most significant increase in VHTC is found in the 6- and 9-hole Kenics DCHEs, with a maximum increase in VHTC of 20% compared to the Kenics DCHE(4)Compared to the Kenics DCHE, the flow and heat transfer characteristics in the perforated Kenics DCHE are improved. It also saves material in the manufacturing equipment and meets the requirements for energy saving and emission reduction. This would be a fruitful area for further work, which would be to study the way in which perforations are distributed in different locations

Nomenclature

:	Perforation area (m²)
:	Total surface area of the static mixer (m²)
:	Momentum source term (N/m)
:	Working substance steam outlet enthalpy (kJ/kg)
:	Facet index of a cross-sectional plane with facets
:	Turbulence kinetic energy
:	Mass transfer from the q-phase to the p-phase (kg/s)
:	Mass transfer from p-phase to q-phase (kg/s)
:	Number of hole
:	Heat transfer per unit time (kJ/s)
:	The heat exchange intensity between the gaseous working substance and the heat transfer oil
:	Working substance evaporation mass flow (kJ/s)
:	Reynolds number
:	Mass source term (kg/m³/s)
:	Heat transfer oil inlet temperature (K)
:	Heat transfer oil outlet temperature (K)
:	Working substance inlet temperature (K)
:	Working substance steam outlet temperature (K)
:	Volume heat transfer coefficient (kW·m^-3·K)
:	Volume of continuous phase fluid (m³)
:	The specific enthalpy of each phase
:	Working substance inlet enthalpy (kJ/kg)
:	Working substance steam outlet enthalpy (kJ/kg).

Greek Symbols

:	The volume fraction of the q-th phase
:	Logarithmic mean temperature difference
:	Inlet of the continuous and dispersed phases
:	Turbulent eddy viscosity
:	Velocity tensor (m/s)
:	Velocity tensor of the q-th phase (m/s)
:	Dynamic viscosity (kg/(m·s))
:	Density (kg/m³)
:	Average value of the gaseous working substance volume fraction over the outlet boundary
:	Specific turbulence dissipation rate.

Abbreviations

DCHE:	Direct-contact heat exchanger
DCHT:	Direct-contact heat transfer
CFD:	Computational fluid dynamics
PI:	Perforation index
UI:	Uniformity index
VHTC:	Volumetric heat transfer coefficient.

Data Availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (No. 52166010, No. 51706195) and the Yunnan Provincial Project Fund (No. 202101AT070202).

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Copyright © 2023 Shuang Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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