Reducing the Flow Maldistribution in Heat Exchangers through a Novel Polymer Manifold: Numerical Evaluation ^†

Abstract

The maldistribution of working fluid is one of the issues in heat exchangers that causes a reduction in performance of not only the heat exchanger but also the entire HVAC system. One of the methods to reduce such maldistribution is to improve manifold design to evenly distribute the flow. In the present work, an advanced maldistribution reduction manifold, which was based on a preliminary maldistribution reduction manifold, was designed to further improve the flow distribution in the heat exchanger. In the design, spiral baffles are used to create vortices in the tubes to regulate the flow in each tube. The design also keeps the tubes away from the manifold inlet to avoid direct flow from the inlet. Due to the complexity, the design of the advanced maldistribution reduction manifold is for AM only, which cannot be fabricated by traditional manufacturing. To evaluate the design, a computational fluid dynamic model is developed to study flow distribution in heat exchanger manifolds. The simulation results reveal that the relative standard deviation of the tubes in the advanced maldistribution reduction design is half of the preliminary maldistribution reduction design and about 1/20 of the reference design.

1. Introduction

A heat exchanger (HX) is a device that transfers heat (or cooling capacity) between a source and a working fluid. As one of the key components in both cooling and heating processes, HXs are widely used in heating, ventilation, air conditioning, and refrigeration systems [1,2], energy storage systems [3], and chemical plants [4], etc. According to the flow arrangement, HXs can be classified primarily into three types: parallel-flow, counter-flow, and crossflow. To enhance heat transfer in all three types of HXs, the working fluid is usually separated into small streams flowing into parallel tubes to enlarge the heat transfer contact areas. A manifold is essential to distribute this flow to HX tubes.

In the HX design, it is usually assumed that the manifold makes the working fluid flow distribution uniform through the HX. However, this assumption is not realistic, based on actual HX operation. Because of the HX shape and complex operating conditions, the flow distribution of each single tube is significantly different; this is called flow maldistribution [5,6,7]. Flow maldistribution is one of the factors that significantly influences the performance of HXs, leading to a reduction of heat transfer efficiency. As a result, the efficiency of an entire system using the HX will decrease. Therefore, studies have been conducted to find methods to reduce flow maldistribution [8,9]. They designed a baffle construction to regulate the flow and reduced the maldistribution in the plate-fin HX. Chu et al. [10] designed four different shapes of manifolds. Their evaluation of fluid flow in each shape revealed that hyperbolic manifolds obtain the best flow uniformity. Tong et al. [11] summarized eight strategies to reduce the flow maldistribution in HXs. They discovered that the nonlinear conical manifold can effectively reduce flow maldistribution in HXs. Kumaran et al. [12] revealed that the combination of a triangular-shaped manifold and a C-shaped inlet/outlet configuration can lead to good flow uniformity. Ma et al. [13] developed a novel mathematical framework to model flow distribution in the tubes based on the hydraulic loss network diagram. Their modeling results indicated that the longer channel could provide a better flow uniformity.

Computational fluid dynamics (CFD) plays a very important role in maldistribution reduction HX designs. Due to its flexibility and economy, CFD is widely used in the maldistribution reduction HX manifold designs. Wen and Li and Wen et al. [14,15] developed a CFD model to investigate flow distribution in the entrance of a plate-fin HX. Using the model, they designed a baffle construction to reduce maldistribution in a plate-fin heat exchanger. Wasewar et al. [16] employed CFD modeling to investigate the flow distribution in their modified manifold design for a plate-fin heat exchanger. The CFD results revealed an efficiency improvement of their modified manifold compared to that of the conventional heat exchanger. Zhou et al. [17], on the other hand, utilized CFD simulations to optimize the manifold parameters of central-type compact parallel flow HXs by studying flow distribution in the manifold. Their study revealed the important manifold parameters in the HXs impacting the flow distribution in the manifold. Dharaiya et al. [18] employed a CFD model to evaluate a tapered manifold configuration for maldistribution reduction in HXs. Jordaan et al. [19] developed a CFD method coupling one dimensional and three dimensional approaches to conduct thermal analysis with flow maldistribution. They implemented the method to a shell-and-tube heat exchanger and found that the new method can significantly reduce the computational expense. With the assistance of CFD modeling, Peng et al. [20] designed a new inlet manifold for plate-fin HXs by using splitter plates to improve the flow distribution in the manifold. Their new design is able to decrease flow maldistribution degree by 91.5% compared to the traditional manifold design for plate-fin HXs. Their results also indicated that adding splitter plates to the manifold can obtain a better maldistribution reduction effect than using splayed perforated wing panels in the manifold. Huang et al. [21] developed an effectiveness-NTU (number of transfer units) based co-simulation approach for flow maldistribution analysis in microchannel heat exchanger manifolds. The approach combined both CFD manifold simulation model and a fast and robust effectiveness NTU based segmented heat exchanger model to assist designing better microchannel manifolds for maldistribution reduction. Using this approach, Panda et al. [22] successfully improved the designs of the manifolds in microchannel heat exchangers to reduce the maldistribution.

As described earlier, the main strategy to reduce maldistribution is to modify the manifold design to regulate flow to achieve uniformity, which will increase the complexity of the manifold design. As a result, researchers evaluated whether the manifold design would be able to be fabricated by traditional manufacturing due to complexity of the manifold design, although the design can lead to a significant reduction in maldistribution. Recently, the rapid development of additive manufacturing (AM) techniques has expanded the feasibility of manufacturing complex designs; using AM, a complex geometry can be 3D printed with higher precision, lower cost, and shorter lead-time compared with a complex geometry produced via traditional manufacturing. AM techniques have been successfully implemented to manufacture HXs in various fields [23] and therefore offer a new opportunity to manufacture complex manifolds for maldistribution reduction using designs that were challenging to fabricate using traditional manufacturing [24,25,26]. For instance, an additively manufactured uniform fractal flow distributor and mixer were reported recently by Mazur et al. and Priyambodo et al., respectively [27,28].

In this paper, a novel maldistribution reduction manifold designed for AM is discussed. The novel design was based on the previous maldistribution reduction design [29] and improved the issue of high flow rates in the tubes close to the manifold inlet in the previous design. Different from previous studies, the novel maldistribution reduction manifold in the present work is suitable for AM only due to its complexity, which cannot be fabricated using traditional manufacturing. To evaluate the design, a CFD model was developed to study fluid flow and heat transfer of a manifold. The numerical results show a significant maldistribution reduction and temperature distribution improvement in the new manifold design compared with the previous maldistribution reduction design. The novel design and the model provide guidance for building HXs with reduced maldistribution using AM techniques.

2. Manifold Design

Figure 1 shows a typical heat exchanger with two rows of staggered tubes with their size noted. The 32 tubes are numbered as shown in the top view in Figure 1. The working fluid enters the manifold from the inlet, is separated by the manifold, and goes through the tubes to exchange heat. Figure 2 depicts a maldistribution reduction design, which has been preliminarily studied by our team [29]. To reduce the flow maldistribution in the manifold, spiral baffles are added between the manifold and the tubes. The baffle is a spiral piece surrounding a 3 mm diameter solid rod, with the length and pitch of each spiral piece measuring 2.5 mm and 5 mm, respectively. The spiral baffle regulates the fluid flow that enters the tube for even distribution. Previous studies revealed that the flow rates of tubes 16 and 17 are much higher than flow rates for the other tubes if spiral baffles are deployed [29] because tubes 16 and 17 are located just under the inlet. Therefore, it is necessary to make the flow rates in tubes 16 and 17 comparable to those of the other tubes. Because the high flow rates are due to the tubes’ entrance locations, it was decided to move the entrances to avoid direct flow from the manifold inlet. This led to an advanced maldistribution reduction design (Figure 3), in which the entrances of tubes 16 and 17, including the spiral baffles, are moved near the edges of the manifold. The distance between the tubes’ entrances for the two designs is 25.45 mm, resulting in the advanced maldistribution reduction design avoiding direct flows from the manifold inlet. Two S-shaped tube sections are employed to connect the entrances and the rest of tubes 16 and 17, which are otherwise the same as in previous designs. This paper discusses CFD models created for all three manifold designs: the reference, the maldistribution reduction, and the advanced maldistribution reduction.

3. Numerical Model and Validation

As described above, CFD models of all three designs have been developed. A commercial code, Ansys Fluent, is used to evaluate the fluid flow in the manifold [30]. Fluid flow and heat transfer are both included in the model to evaluate flow and temperature distributions. To simplify the model, this work considers only single-phase flow.

The continuity and momentum governing equations are included in the model,

$$\frac{\partial \rho }{\partial t}+\frac{\partial \left(\rho u_i\right)}{\partial x_i}=0$$

(1)

$$\frac{\partial \left(\rho u_i\right)}{\partial t}+\frac{\partial \left(\rho u_i{u}_j\right)}{\partial x_j}=-\frac{\partial p}{\partial x_i}+\frac{\partial }{\partial x_j}\left[\mu \left(\frac{\partial u_j}{\partial x_i}+\frac{\partial u_i}{\partial x_j}-\frac{2}{3}{\delta }_{ij}\frac{\partial u_k}{\partial x_k}\right)-\rho \overline{u_i^{’}{u}_j^{’}}\right]$$

(2)

in which u, ρ, p, and μ are fluid velocity vector, density, pressure, and dynamic viscosity, respectively.

Because flow in the manifold is turbulence flow, a standard k-ε model is used. The Reynolds stress term in the k-ε model is

$$-\rho \overline{u_i^{’}{u}_j^{’}}={\mu }_t\left(\frac{\partial u_j}{\partial x_i}+\frac{\partial u_i}{\partial x_j}\right)-\frac{2}{3}(\rho k+{\mu }_t\frac{\partial u_k}{\partial x_k}){\delta }_{ij}$$

(3)

where μ_t is the turbulence dynamic viscosity calculated by turbulence kinetic energy k and turbulence dissipation rate ε. The following equations are for μ_t, k, and ε, respectively:

$${\mu }_t=\rho C_{\mu }\frac{k^2}{\epsilon }$$

(4)

$$\frac{\partial \left(\rho k\right)}{\partial t}+\frac{\partial \left(\rho k{u}_i\right)}{\partial x_i}=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_k}\right)\frac{\partial k}{\partial x_j}\right]-\rho \overline{u_i^{’}{u}_j^{’}}\frac{\partial u_j}{\partial x_i}-\rho \epsilon$$

(5)

$$\frac{\partial \left(\rho \epsilon \right)}{\partial t}+\frac{\partial \left(\rho \epsilon u_i\right)}{\partial x_i}=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_{\epsilon }}\right)\frac{\partial \epsilon }{\partial x_j}\right]-C_{1\epsilon }\frac{\epsilon }{k}\left(\rho \overline{u_i^{’}{u}_j^{’}}\frac{\partial u_j}{\partial x_i}\right)-C_{2\epsilon }\rho \frac{{\epsilon }^2}{k}$$

(6)

In Equations (4)–(6), the parameters c_μ = 0.09, c_1ε = 1.44, c_2ε = 1.92, σ_k = 1.0, and σ_ε = 1.3 are obtained from experimental data [31].

To obtain the temperature distribution, the energy equations are also solved in the model,

$$\frac{\partial }{\partial t}\left(\rho E\right)+\frac{\partial \left(\rho E{u}_i+p{u}_i\right)}{\partial x_i}=\nabla ·\left({\lambda }_{\mathrm{eff}}\nabla T\right),$$

(7)

where

$$E=h-\frac{p}{\rho }+\frac{v^2}{2},$$

(8)

and

$${\lambda }_{\mathrm{eff}}=\lambda +{\lambda }_t.$$

(9)

In Equation (9), λ is the thermal conductivity of water, and λ_t is the turbulent thermal conductivity. In the energy equations, T and h are the temperature and the enthalpy of the fluid, respectively, which are related with Equation (10),

$$h={{\displaystyle \int }}_{T_{ref}}^T{c}_{p}dT+\frac{p}{\rho },$$

(10)

where T_ref = 298.15 K and c_p is the specific heat of air.

To evaluate the flow maldistribution, maldistribution parameter S_n of the nth tube is defined as

$$S_n=\raisebox{1ex}{$\left(u_n-u_{ave}\right)$}\!\left/ \!\raisebox{-1ex}{$u_{ave}$}\right.,$$

(11)

where u_ave denotes the average velocity of all the tubes and n is the series number of the tube.

The relative standard deviation (RSD) of the velocity can be defined as

$$RSD=\sqrt{\frac{1}{n}\sum {\left(u_n-u_{ave}\right)}^2}/u_{ave}\ast 100\%.$$

(12)

The meshing size is about 0.5 mm in the CFD model, which is suggested by Peng et al. [20]. A mesh independent study was conducted by comparing results from the current meshing size to a refined mesh (0.35 mm). The comparison confirmed a consistency of the results from two meshing sizes, which indicates 0.5 mm meshing size is precise enough for the model in the present work.

In addition to the mesh independent study, the CFD model is also validated by comparing results from the present model with data from Wen and Li [14]. In their work, they studied flow distribution in the manifold of a plate-fin HX. There are 43 channels at the outlet of the manifold in the plate-fin HX. The flow enters the manifold from the inlet tube and leaves the manifold through the 43 channels. The maldistribution parameter of each channel was calculated in their study with different Re numbers, in which we selected the maldistribution parameters when Re = 10⁶ to validate our model. To conduct the validation, we duplicated the plate-fin HX manifold in their study in order to model the flow distribution in the manifold of a plate-fin HX with 43 channels at the outlet; we generated the mesh and ran the simulation using our CFD modeling method. Then, the maldistribution parameter of each channel from our model was calculated and compared with their results. The comparison results are shown in Figure 4; the green line and red circles represent results from the literature and the model from this paper, respectively. The comparison shows good agreement between the results from the present model and data from the literature, indicating that the CFD model can be used for maldistribution evaluation.

4. Results and Discussion

The CFD models of the three designs (reference, maldistribution reduction, and advanced maldistribution reduction) have been simulated in steady state. In the simulations, the working fluid is assumed to be water, which is injected to the HX manifolds with two inlet velocities, 2.5 m/s and 5 m/s; the water temperature is 10 °C. The tubes are assumed to be heated by a stream of 40 °C hot air, with a fixed convective heat transfer coefficient of 2000 W/(m²⋅K).

Figure 5 shows the maldistribution parameters S_n from the reference, maldistribution reduction, and advanced maldistribution reduction designs when inlet velocity is 2.5 m/s. The figure shows that the maldistribution parameters from the reference model (blue triangles) change significantly. Maldistribution parameters S₁₆ and S₁₇ are about five and the highest, respectively. According to Equation (11), flow rates in tubes 16 and 17 are about six times higher than the average flow rate because these tubes are directly facing the inlet of the manifold. Figure 6a shows the fluid flow concentrates in tubes 16 and 17. Because tubes 15 and 18 are close to the inlet, their flow rates are also higher than the average value for all the tubes. Figure 7a depicts the streamlines of the reference design; near tubes 13, 14, 19, and 20, the fluid flows horizontally, which is generated by the flow concentrates in the center tubes, leading to low flow rates in those tubes although they are close to the inlet. Because of the mass balance—except for tubes 15, 16, 17, and 18—the maldistribution parameters in the rest of the tubes are negative (i.e., the individual flow rates are lower than the average flow rate). Therefore, the fluid flow in the reference manifold concentrates at the four tubes closest to the manifold inlet. The RSD of the velocities in the reference manifold tubes is 136.1%, revealing a dramatic maldistribution in the reference manifold.

The green squares in Figure 5 represent the maldistribution parameters of each tube from the maldistribution reduction design. Owing to the regulation created by the spiral baffles, the maldistribution parameters of most tubes are much lower than those of the reference design. Figure 7b depicts the streamlines from the manifold to the tubes of the maldistribution reduction design, which shows how the spiral baffle helps regulate fluid flow in the manifold. Comparing Figure 7a,b, the spiral baffle creates vortices in the tubes that are not present in the reference design. The vortices create local pressure differences to blend the fluid flow in the manifold. The RSD of the velocities in the maldistribution reduction manifold tubes is 13.7%, showing a significant reduction of maldistribution. However, the green squares also indicate that S₁₆ and S₁₇ are still very high, with S₁₇ as high as 0.8. As discussed above, the high unevenness of tubes 16 and 17 is due to the tube entrance locations directly facing the inlet of the manifold. The flow velocity profile of the maldistribution reduction design is shown in Figure 6b, which clearly demonstrates that the velocities in tubes 16 and 17 are much higher than those of the other tubes.

The red circles in Figure 5 indicate the maldistribution parameters of each tube from the advanced maldistribution reduction design. Because the entrances of tubes 16 and 17 have been moved away from facing the manifold inlet, the inlet flow does not directly flush to the two tubes.

As a result, S₁₈ and S₁₅ become the two highest maldistribution parameters (0.165 and 0.145, respectively); S_n is very low in other tubes, including tubes 16 and 17. The result reveals an better flow distribution in the tubes compared to the results of the baffle construction from Wen and Li [14], in which the highest maldistribution parameter is more than 0.3. Figure 6c shows the velocity profiles of each tube. Comparing Figure 6b,c, the flow concentration disappears in the advanced maldistribution reduction design. Moreover, because the entrances of tubes 16 and 17 on the manifold have been moved, no tubes directly face the manifold inlet. As shown in Figure 7c, the spiral baffle is still working in the advanced maldistribution reduction design but owing to the location change of the entrances of tubes 16 and 17, all the tubes have a relatively equal chance to absorb fluid flow to them. The RSD of the velocities in the advanced maldistribution reduction manifold tubes is 5.3%, indicating a significant reduction of maldistribution in the new design compared with the other two designs.

Figure 8 shows the maldistribution parameters S_n from the reference, maldistribution reduction, and advanced maldistribution reduction designs when the inlet velocity is 5 m/s. A comparison of Figure 5 and Figure 8 shows that the maldistribution parameters S_n of the same tubes are very close, although the inlet velocity is doubled from Figure 5, Figure 6, Figure 7 and Figure 8. In addition, the manifold effect on the velocity distribution does not change when the velocity changes from 2.5 m/s to 5 m/s, a finding also supported by results in the literature [14]. This conclusion can also be obtained by comparing the velocity profiles and streamlines in Figure 6 and Figure 9 and Figure 7 and Figure 10, respectively (i.e., except for the velocity value, the distributions of the flow paths are very close to the corresponding cases). The RSD of the velocities from the reference, maldistribution reduction, and advanced maldistribution reduction designs are 128.6%, 15.0%, and 7.0%, respectively.

The influence of the designs on heat transfer is also evaluated using the model. It is assumed that the manifold inlet temperature is 10 °C, and the tubes are assumed to be heated by a stream of hot air with 40 °C. Figure 11 shows the outlet temperatures for all tubes from all three designs when the inlet velocities are (a) 2.5 m/s and (b) 5 m/s, respectively. Figure 11a reveals that in the reference design, due to the high velocities in tubes 15–18, the outlet temperatures of the four tubes are much lower than the outlet temperatures of the other tubes, most of which are higher than 15 °C. On the other hand, for the maldistribution reduction design, the higher maldistribution parameters of tubes 16 and 17 make the outlet temperatures of those two tubes lower than those of the other tubes. The outlet temperatures of the other tubes are lower than temperatures in the same tubes in the reference case because the fluid velocities are higher in the maldistribution reduction design than in the reference case (Figure 6). Finally, for the advanced maldistribution reduction design, the outlet temperatures deviation is low, within 1 °C due to the low maldistribution parameters of all the tubes. Figure 11b shows the temperature distributions of the outlets when the inlet velocity is 5 m/s. The trends are close to Figure 11a because the maldistribution parameters are very close with two velocities. However, the outlet temperatures in Figure 11b are about 2 °C lower than those in Figure 11a because the velocity is doubled in Figure 11b.

Although the advanced maldistribution reduction manifold can significantly reduce the flow maldistribution in the manifold compared to the other two designs, it does have the pressure drop penalty. Therefore, future work will be focusing on improving the advanced maldistribution reduction manifold design to eliminate the pressure drop penalty.

5. Conclusions

An advanced maldistribution reduction manifold has been designed based on the design of a maldistribution reduction manifolds. In the advanced maldistribution reduction design, spiral baffles are used to create vortices in the tubes, so the fluid flow will be regulated into each tube for even distribution in the manifold. In addition to the spiral baffles, the entrances of tubes 16 and 17 are located away from the manifold inlet to avoid direct flow from the inlet, which resulted in higher flow rates in tubes 16 and 17 in previous designs. Therefore, the advanced maldistribution reduction manifold design was improved from the maldistribution reduction manifold by moving the tubes 16 and 17 away from the manifold inlet but kept spiral baffles in the maldistribution reduction manifold.

CFD models have been developed to model the reference, maldistribution reduction, and advanced maldistribution reduction designs to evaluate flow and temperature distributions. A series cases of hot air outside heating cold water in the HXs were simulated using the CFD models with different water velocities. The maldistribution parameter of each tube was calculated based on the CFD simulations’ results to evaluate the flow distribution in the manifold. The RSD was also calculated for each design to reveal the maldistribution reduction of each manifold design. In addition to the statistic results, the flow pathlines and velocity distribution in each manifold design were visualized after postprocessing CFD simulations’ results, which offers a straightforward approach to analyze the mechanisms to reduce the maldistribution in manifolds. Moreover, the tube outlet temperature distributions were plotted to exam the effect of maldistribution reduction on heat transfer performance of HXs.

The results show that the advanced maldistribution reduction design regulates the flow distribution in the manifold better than the other two designs. The spiral baffles create the vortices to regulate flow distribution in the manifold. In addition, flow rates in tubes 16 and 17 are improved by locating the entrances away from the manifold inlet. As a result, the highest maldistribution parameter in the advanced maldistribution reduction design is less than 0.2, which is much smaller than the ones in the reference design (5) and the maldistribution reduction design (0.8). As a result, the simulation results indicate that the RSD of the tubes in the advanced maldistribution reduction design is very small compared with the other two designs: half of the maldistribution reduction design and about 1/20 of the reference design. Therefore, the advanced maldistribution reduction design provides a significant improvement to reduce maldistribution in the manifold comparing to the other two designs. Moreover, the inlet velocity has a limited impact on maldistribution reduction parameters, according to the results. Therefore, the advanced maldistribution reduction design can also provide an evenly distributed outlet temperature.