Effect of annular ribs in heat exchanger tubes on the performance of phase‐change regenerative heat exchangers

Optimizing the efficiency of conventional heat exchangers is critical for improving the performance of various processes. This study proposed increasing the heat dissipation buffer space of heat exchangers by filling the gap between the heat exchanger and the shell with phase‐change materials for optimizing phase‐change heat exchangers. Comparative simulation analyses were performed by investigating the difference between the internal and external diameters of the inner ring ribs of the heat exchanger, the flow rate of the cooling liquid, the spacing distance, and the number of the inner ring ribs as independent variables. The results revealed that the heat transfer efficiency of heat exchangers can be improved by adding the inner ring rib structure to the heat exchange copper tube. The difference between the inner and outer diameters of the inner ring rib considerably influences heat dissipation. Furthermore, a sensitivity coefficient of 0.2457 can be obtained. The distance and number of inner ring ribs and the flow rate of cooling liquid exhibit certain effects on the heat transfer efficiency of the heat exchanger. The sensitivity coefficients were 0.1477 and 0.0935. The heat dissipation efficiency of the coil heat exchanger was improved by 3.8% by adding inner ring ribs in the coil heat exchanger channel.

conventional heat exchangers is crucial for improving energy utilization.
Yuande et al. 1 introduced dimensionless entropy generation number NS for representing the thermal perfection of the heat exchanger. They analyzed the performance entropy generation and characteristic parameters of heat exchangers. The results of the study have been used as a reference in subsequent studies. Studies have revealed that the distribution of the flow field in the heat exchanger considerably influences the performance of heat exchangers. Xueliang et al. 2 verified the correctness of the field synergy theory. The results revealed that the field synergy theory is not only suitable for the parabolic flow but also suitable for complex elliptic flow with backflow. Gu et al. 3 calculated the flow resistance and heat transfer process in the corrugated channel with different heights on the air side through simulations and concluded that the corrugated height considerably influences the flow resistance and heat transfer process of air in the corrugated channel. Xian et al. 4 analyzed the enhanced heat transfer in chaotic convection. The analysis of the synergetic relationship between the flow field and the temperature field in the section of the chaotic flow passage revealed that the chaotic flow passage changes the distribution of the velocity field of the fluid in the flow passage, and the change of the flow field affects the distribution of the temperature field, which considerably improves the synergetic effect of two fields.
Xiangli et al. 5 simulated convection and heat source conduction for investigating the convective heat transfer mechanism. Hua-xin et al. 6 analyzed the mechanism of convective heat transfer enhancement of latent heat functional thermal fluids and investigated the influence of various factors on laminar heat transfer enhancement in a constant heat flux circular tube. Furthermore, they evaluated laminar heat transfer in the hot inlet area of a circular tube with variable surface heat flux boundary conditions. The results revealed that the heat transfer coefficient was closely related to the wall temperature gradient along the tube axis. 7 Additionally, the structure of the heat exchanger considerably affects its heat transfer efficiency. Guo et al. 8 revealed that the heat storage and release rate of the heat storage exchanger with an elliptical inner tube is higher than that of the circular inner tube model. Furthermore, the elliptical tube is suitable for heat storage heat exchangers. Yongqing et al. used fluent software to simulate the working condition of heat exchangers. The results revealed that when the heat exchanger tube is square and arranged in the second staggered manner, the comprehensive heat transfer performance of the heat exchanger is the best. 9 Zhu and others introduced the structure of the new heat exchanger and the strengthening mechanism of the heat transfer effect and concluded that the quadruple tube has more heat transfer advantages than the triple tube. When the pitch of the spiral tube changes with the temperature gradient, the tube has superior temperature uniformity. Shell and tube heat exchangers exhibit an excellent heat exchange effect, simple structure, and extensive industrial application prospects. 10 Numerous studies have been performed on the internal structure of heat exchange tubes and a series of reasonable structural assumptions have been devised experimentally. In the Journal of Thermal Science, a baffle structure with higher energy utilization efficiency is used for improving the heat exchange efficiency of heat exchangers. 11 Qi et al. designed three types of serrated fins as the inner core of the cold plate for cooling electronic equipment. 12 Zhang 13 analyzed the four factors of rib height, rib width, rib spacing, and pipe material of ring rib-shaped phase-change heat exchanger, and the results revealed that the rib height is the primary factor affecting heat storage and release efficiency. Liangdong et al. 14 analyzed the influence of flow characteristics on heat transfer and revealed that when the ratio of rib spacing to the pipe diameter is 8, the resistance coefficient and Nusselt number reached the maximum. However, the influence of the design of an annular inner rib and the setting of relevant parameters on the heat transfer efficiency of the liquid-cooled heat exchanger is yet to be investigated.
In this study, comparative simulation was performed to study the influence of the inner ring ribs of the heat exchange tube on the performance of phase-change heat storage heat exchangers by using the difference between the inner and outer diameters of the inner ring ribs of the heat exchanger, the flow rate of cooling liquid, the spacing distance and the number of the inner ring ribs as variables. The effects of these factors on the performance of heat storage heat exchangers filled with phase-change materials were investigated. This provides theoretical support for the application of heat storage heat exchangers in building energy conservation and other aspects.

| Geometric model
Combining with the structural characteristics and application environment of the heat exchanger, the design model size is as follows: the length of the copper tube was 1000 mm, the inner diameter was 19 mm, the outer diameter was 21 mm, and the outer fin of the tube was 1 mm × 80 mm × 80 mm. In all, 34 pieces were spaced at intervals. The rest of the space was filled with paraffin, and the overall model was 100 mm × 100 mm × 1000 mm cuboid, as shown in Figure 1.
Paraffin, aluminum, and copper were used in the study. The parameters of the materials were presented in Table 1.

| Boundary condition
In this model, the fluid inlet and outlet surfaces and the external surface of paraffin wax were set as heat flux conditions, and the other noninternal contact surfaces were set as thermal insulation conditions. In the simulation process, heat transfer was conducted in the form of heat conduction. Therefore, the influence of the natural convection heat transfer process after the melting of phase-change materials was ignored.
The heat flux partially obeys the expression of convective heat flux as follows: The heat transfer coefficient satisfies h = 500 W/ (m 2 ·K) and the external temperature satisfies T = 293.15 K.
When establishing the computer fluid dynamics model, to digitize the model and simplify the calculation, the following assumptions were considered 15 : • Both air and phase-change materials were incompressible fluids. • Physical parameters of materials were fixed constants that do not change with temperature fluctuation. • The volume changes in phase-change materials during melting were ignored. • Radiant heat transfer is ignored.

| Simulation process
In this model, the following three factors that affect heat dissipation were considered: the difference between the inner and outer diameters of the inner ring rib, the flow rate of the cooling liquid, the distance between the inner rings, and the number of inner rings. In the experiment, the cooling process of the paraffin layer under the cooling fluid is simulated. The initial temperature of paraffin was assumed to be 343.15 K, the cooling fluid was 273.15 K, and the rest of the model was 293.15 K.
(1) Difference between internal and external diameters of the inner ring rib The inner diameter of the straight pipe model was 19 mm. The difference between the inner and outer diameters of the inner ring rib was the vertical distance from the top of the rib to the inner wall of the pipe. Acyclic refers to the absence of raised fins. Fins with various protrusions can produce various degrees of agitation in the cooling liquid flow process, which may affect heat dissipation results to some extent.
(2) Cooling liquid flow rate Water was used as the cooling liquid in this model. The flow process in the pipe can be adjusted by changing the normal flow velocity and analyzing its effect on heat dissipation results.
(3) Spacing distance and quantity of the inner ring rib When the tube length and inner ring rib size were unchanged, various numbers and spacing of inner ring ribs cause varying degrees of disturbance to the cooling fluid, which affects the heat dissipation effect of heat exchangers.
On the basis of the three factors, models were designed for simulation, and the best design and layout of inner ring ribs were obtained through comparison. The optimization scheme for the best design is determined by the simulation of the layout. The best design scheme is transplanted to the pipeline model and compared with the ordinary pipeline model for obtaining experimental conclusions. On the basis of the heat exchanger model, the simulation was performed. The specific process is shown in Figure 2.

| Calculation process
After importing the geometric models into software, the specific calculation process typically depends on COMSOL software. For observing the real-time temperature changes, the transient response is selected for analysis. The calculation formula used is as follows: (1) Solid heat transfer equation (2) Fluid heat transfer equation (3) Convection equation where ρ represents the self-density of the solid or liquid (kg/m 3 ), C p represents the constant pressure heat capacity of the solid or liquid (J/(g·C)), T represents the temperature of the temperature field (K), Q represents the thermal load (W/m 2 ), k represents the solid heat transfer coefficient (W/(m·K)), h represents the convective heat transfer coefficient (W/(m 2 ·K)), and q representative heat transfer rate (J/s). To ensure the simulation results were close to those in practice, the software gridded the geometric model, solved each F I G U R E 2 Simulation analysis process. grid in turn, and finally obtained the simulation results through integration.

| Difference between internal and external diameters of the inner ring rib
The length of the straight pipe was set to be 1000 mm, the thickness of the inner ring rib was 3 mm, and the number as 50, spaced 20 mm apart. The difference between the inner and outer diameters of the inner ring rib was a variable. The difference between the inner and outer diameters of the inner ring rib was set to be 2, 3, and 4 mm, and no inner ring rib, which was then simulated. Under the same initial temperature, the relationship between wax temperature and time was obtained, as shown in Figure 3.
To quantify the temperature change when the variable changes, the calculation quantity was introduced to reflect the cooling amplitude. The calculation method is as follows: According to Figure 3, the heat exchanger exhibited the best heat dissipation effect when the internal and external diameter difference of the inner ring rib was 3 mm. After calculation, the temperature drop of the paraffin layer could reach 13.28% within 18 s.

| Cooling liquid flow rate
According to the simulation results in Section 3.1.1, the difference between the inner and outer diameters of the inner ring ribs in this model was 3 mm, and the spacing distance and the number of the inner ring ribs remained unchanged. Under the condition that the initial temperature was the same, the cooling fluid flow rates of 2, 3.5, 5, and 6.5 m/s were selected for simulation for studying their effects on the heat dissipation effect of the heat exchanger, and the change curve of the paraffin temperature with time is shown in Figure 4.
According to Figure 4, when the flow rate of cooling liquid was 3.5 m/s, the heat dissipation effect of the model was the best. Because the heat dissipation effect of the heat exchanger could not be distinguished on the diagram in four cases, the simulation data were calculated. When the flow rates of the cooling fluid were 2, 3.5, 5, and 6.5 m/s, the temperature drop amplitudes of the paraffin layer within 18 s were 11.86%, 12.99%, 12.40%, and 12.72%, respectively.
When the overall differentiation is not obvious, the time is refined, and the temperature change within 1 s is selected to draw the chart as shown in Figure 5.
In 1 s, when the flow rate of cooling fluid was 2 m/s, the cooling rate of the paraffin layer was considerably slower than that of other groups. When the flow rate of cooling fluid was 3.5 m/s, the cooling rate was the fastest,

| Spacing distance and quantity of the inner ring rib
According to the simulation results of the first two factors, the difference between the inner and outer diameters of the inner ring rib of this model was determined to be 3 mm, and the flow rate of cooling liquid was 3.5 m/s. The spacing of inner ring ribs was 5, 10, and 15 mm, and the number of corresponding inner ring ribs was 200, 100, and 66, respectively. These variables were simulated and the relationship between paraffin temperature and time was obtained as follows. Figure 6 reveals that the spacing distance and the number of inner ring ribs have a limited influence on the heat dissipation effect of heat exchangers. When the inner ring rib spacing was 5, 10, 15, and 20 mm, respectively, the temperature drop amplitudes of the paraffin layer within 18 s were 12.99%, 13.04%, 13.41%, and 13.09%, respectively.

| Straight pipe simulation analysis
During simulation, the cooling liquid inlet and outlet were set to ensure the flow of the cooling liquid. The realtime temperature at the inlet and outlet was obtained by inserting temperature probes at the inlet and outlet, and the temperature difference at the inlet and outlet reflects the heat dissipation of the heat exchanger laterally. If the temperature difference at the inlet and outlet can reach a high peak in a short time, then the heat dissipation effect of this parameter improved.
Therefore, according to the simulation results, the factor of the difference between the inner and outer diameters of the inner ring rib was considered for analyzing the time when the inlet and outlet reach the peak temperature difference and the peak temperature difference, and Figure 7 is drawn. The peak time and peak temperature difference were recorded as presented in the table.
According to Figure 7 and Table 2, when the difference between the inner diameter and the outer F I G U R E 5 Temperature change process after the refining time.
F I G U R E 6 Spacing distance and number of inner ring ribs.
F I G U R E 7 Change in temperature difference at the inlet and outlet when the difference between internal and external diameters differed considerably. diameter was 3 mm, the temperature difference at the inlet and outlet reached the peak value of 11.65 K, and the time required was the shortest, 0.53054 s, which indicated, consistent with previous conclusions, that this structure was conducive to the heat exchange of the heat exchanger.
To investigate the factors that simultaneously affect the cooling range of the heat exchanger, further sensitivity analysis was conducted on the obtained data.
The first behavior in the table is the control group. The calculation expression involved is as follows: T A B L E 2 Comparison between the peak time and peak temperature difference.  Table 3 reveals that the sensitivity coefficients corresponding to each factor were between 0 and 1, indicating that the difference between internal and external diameters, the flow rate of cooling liquid, the spacing distance, and the number of internal ring ribs exhibit distinct effects on the cooling amplitude of the heat exchanger simultaneously. Analysis of the calculation results reveals that the average sensitive factors of the three influencing factors were 0.2457, 0.1477, and 0.0935. This result indicates that the difference between the internal and external diameters of the inner ring rib exhibits the largest effect on the heat transfer efficiency of the heat exchanger among the three factors, and the flow rate of cooling liquid exhibits the smallest effect on the heat transfer efficiency of the heat exchanger.
3.2.2 | Simulation results of heat dissipation before and after adding fins to heat exchange tube Adding a fin structure to the heat exchange tube helps improve the heat transfer efficiency of the heat exchanger. Therefore, adding fins on the basis of straight pipes is closer to the actual application and exhibits a higher reference value. The structure is shown in Figure 8.
For the pipe without an inner ring rib, the simulation results revealed that the temperature drop amplitude was 10.73% within a given 10 s. Combined with the summarized rules, 66 inner ring ribs with a difference of 3 mm could be added between the internal and external diameters. These rings were spaced 15 mm apart to the pipe, and the model with the cooling liquid flowing was simulated at a speed of 3.5 m/s. The cooling range of the pipe with an inner ring rib reached 11.14% within 10 s, which was 3.8% higher than that without an inner ring rib. The relationship between the paraffin temperature and time in the two groups of models is shown in Figure 9. Figure 9 reveals that the cooling rate and range improved to a certain extent after the internal ring rib was added to the pipe. This result indicated that the addition of the internal ring rib of this size positively affects the heat dissipation effect.

| CONCLUSION
The factors affecting the heat dissipation performance of phase-change liquid-cooled heat exchangers were analyzed, and the following conclusions were obtained: • Adding annular inner ring ribs can effectively enhance the heat dissipation of heat exchangers. The results revealed that under the same environment, the temperature drop of the paraffin layer in the heat exchanger with an annular inner ring fin was 3.8% higher than that without an annular inner ring fin in 10 s. • The heat dissipation effect of the model was the highest when the flow rate of the cooling fluid was 3.5 m/s. The temperature drop amplitude of the paraffin layer within 1 s was 3.61%, and the temperature drop amplitude of the paraffin layer within 18 s was 12.99%. • The difference between the inner and outer diameters of the inner ring rib and the spacing and quantity of the inner ring rib exhibit a certain effect on the heat exchange efficiency of the heat exchanger. The results revealed that when the internal and external diameter difference of the inner ring ribs was 3 mm and the spacing between the inner ring ribs was 10 mm, the temperature drop range of the paraffin layer of the heat exchanger was 13.41% within 18 s.

NOMENCLATURE
C p constant pressure heat capacity h convective heat transfer coefficient (W/(m 2 ·K)) K solid heat transfer coefficient (W/(m·K)) PCM phase-change material q heat transfer rate Q heat load (W/m 2 ) q 0 heat flux T initial temperature (K) T text external temperature (K) contributions. We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.