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Edited by: Muhammad Zubair, University of Sharjah, United Arab Emirates

Reviewed by: Yen-Shu Chen, Institute of Nuclear Energy Research (INER), Taiwan; Luteng Zhang, Chongqing University, China; Arash Mirabdolah Lavasani, Islamic Azad University Central Tehran Branch, Iran; Xiaowei Li, Tsinghua University, China

This article was submitted to Nuclear Energy, a section of the journal Frontiers in Energy Research

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Passive containment cooling system (PCCS) is widely applied in a new generation of nuclear power plants. The initial heat exchanger is the most improtant heat transfer device in the PCCS. Past studies show that the flow distribution has a great influence on the heat transfer performance of a heat exchanger. And a lot of work has been done on improving the flow distribution uniformity of the heat exchanger such as the geometry modification, proper choice of the geometry parameters. However, little work has been done on the tube arrangement. For a heat exchanger applied in the industry, the number of tubes are huge, and it is unrealistic to arrange all the tubes in a row on the one side of the heat exchanger. Therefore, more work should be paid on the influence of the tube arrangement on the flow distribution in the heat exchanger. The present study numerically investigated the effect of the tube arrangement on the flow distribution in a Central-type parallel heat exchanger. Six different kinds of tube arrangement have been investigated on the flow distribution and the pressure loss characteristics of the heat exchanger. The obtained results show that the tube arrangement has a great influence on the flow distribution and the staggered tube arrangement provides a better flow distribution than the aligned tube arrangement.

For the new generation of nuclear power plants, passive containment cooling system (PCCS) is commonly applied in the system. The initial heat exchanger is the most important heat transfer device and it has a great effect on the heat transfer performance of the PCCS. Therefore, it is neccesary to pay more attention on the initial heat exchanger. In the PCCS, the initial heat exchangers are usually compact parallel flow heat exchangers.

Compact parallel flow heat exchanger has been widely used in many industrial systems such as the reheater and electric heater in the power station boiler system, radial flow reactor in chemical applications, plate heat exchanger or plate fin heat exchanger, solar collector, etc.

However, ununiform flow distribution in the heat exchanger always exists and greatly affects the normal operation of the heat exchanger. For example, ununiform flow distribution reduces the performance of the heat exchanger. And for some tubes with very little liquid flow, they may be more likely to boil under overheating, threatening the safety of the heat exchanger. In addition, due to the ununiform flow distribution, the heat transfer performance is degraded, and the heat exchanger may not meet the design performance requirements in practical applications. Therefore, the attention is focused on the study of the flow distribution in heat exchangers. In this study, the goal was to provide some simple and feasible inlet and header designs numerically, which can significantly reduce the flow maldistribution in the heat exchanger.

There are some works focused on the modification of heat exchanger design for a more uniform flow distribution. _{i}/_{i} = 0.05Re_{i}. Besides, they found that the Tee-type bifurcation is better than the Circular-type. For the two-phase flow distribution,

For parallel channels,

In our previous work (

In previous studies, a lot of work has been done on the reducing flow maldistribution in parallel manifolds or micro channels, and a lot of valuable results have been obtained. For the PCCS initial heat exchanger, the compact parallel manifolds with two headers are chosen for the basic geometry. Except for the basic part of the geometry, the tube arrangement is one of the most important part of the heat exchanger design. The tube arrangement makes a great influence on the flow distribution in the heat exchanger, and the flow distribution will influence the whole natural circulation of the PCCS. Therefore, a uniform flow distribution will help establish a steady natural circulation of the PCCS. However, little work has been done on tube arrangement. A approritate choice of the tube arrangement will help improve the flow distribution, besides, the tube arrangement is also important for a heat exchanger with large number of tubes because of the limitation of the space occupation and the reduction of the material.

For the Central-type manifolds of heat exchanger, there is still more work to be done on the tube arrangement. With the appropriate tube arrangement, improving the flow distribution may be easier and more convenient. In the present study, six kinds of tube arrangement have been investigated for their effects on the flow distribution through tubes.

In the present study, the aim is to investigate the influence of the tube arrangement on the flow maldistribution existed in a Central-type heat exchanger. Therefore, six different kinds of tube arrangements have been applied for a central-type heat exchanger and investigated on their influence on the flow maldistribution through tubes. For the configuration model, there are two headers namely dividing header and combining header, respectively, and sixteen C-tubes are connected to the headers. Six different test cases with different tube arrangement have been under investigations, respectively. And three cases are denoted case1, case2, case3,case4, case5, and case6. For the case1, the tube arrangement is a common tube arrangement and all parallel tubes are arranged at one side of the heat exchanger as shown in

The three dimensional geometry of six different tube arrangements for the central-type heat exchanger.

For the heat exchanger, the dividing and combining header diameter is 180 mm, the tube diameter is 44 mm, and the height of the heat exchanger is 1.7 m, the tube distance is 0.044 m, the tube length is 1.9 m, and the angles between the tube and the headers is 90 degree.

The heat exchanger three dimensional model is created by the CAD module in the Star-ccm+. And the grid processing is accomplished by the Star-ccm+.

For the boundary conditions, velocity-inlet is selected for the inlet, the pressure outlet selected for the outlet is set to zero gauge pressure, and the walls are set to no slip condition and rough. The k–ε turbulent model is chosen as the turbulence model. When all of the residuals are less than 1 × 10^{–4}, solutions are considered to be completely convergent.

For the evaluation of the flow distribution, two dimensionless parameters Φ and β have been utilized.

Where the _{i} and _{av} represent the mass flow rate through the _{i} stands for the ratio of the flow rate through

The governing equations are listed below.

The steady-state continuity equation is expressed as

The steady-state momentum conservation equation is expressed as

The steady-state transport equation for

The steady-state transport equation for ε is expressed as

Where

ε stands for turbulent energy dissipation rate;

_{t}

In this present work, no phase change happens. For the single-phase flow, the flow distribution in the heat exchanger is determined by the geometry of the heat exchanger and has little relationship with the heat transfer. Therefore, the heat transfer process is beyond the consideration.

For the grid independence test and the model validation, we have done detailed work in our previous study (

For six different kinds of tube arrangement, the flow maldistribution coefficient and the pressure loss are shown in

The flow distribution cofficient and the pressure loss for different tube arrangements.

For the tube arrangement of the case1, case2, and case3. They all belong to the single-row arrangement. Therefore, the flow distribution and the pressure distribution of case1, case2, and case3 will be analyzed together in this part. The

The

Comparing to the case1, the increase amplitude in pressure is bigger for the case4 and case5. And the difference in pressure distribution in the dividing header is mainly caused by the tube arrangement. Comparing to the case1, at each position of the tube, there are two tubes instead of one. And it means that the pressure recovery effect is bigger for the case4. For the case5, the staggered arrangement leads to a the smaller tube pitch than that for the case1. It means that along the direction of the main stream, the pressure will increase more quickly over unit distance. And it can be seen that in the

The

Comparing to the case1, the case2 and case3 brings more pressure loss. It is because that the diversion of fluid to both sides bring more local pressure loss. For the case4 and case5. The more densely tube arrangement contributes to a more local pressure loss at the inlet of tubes. Comparing to the case4, the staggered arrangement for the case5 brings less local pressure loss than the aligned arrangement. For the case6, the more densely tube arrangement comparing to the case4 and case5, making a shorter length of the dividing header and the combining header. And the frictional pressure loss is decreased, therefore, the pressure loss for the case6 is less than that in case4 and case5.

This study investigated the effects of six different tube arrangements on the flow distribution characteristics and pressure loss in the central-type heat exchanger. The conclusions are as follows:

Under the premise of fixed important geometrical dimensions such as header diameter, tube diameter, inlet and outlet diameter, etc., the tube arrangement has a significant effect on the flow distribution characteristics and resistance characteristics of the heat exchanger tubes.

Due to the larger header length for the case1, more frictional pressure drop is introduced to make the static pressure distribution in the header more uniform, and the flow distribution uniformity is the best among all cases.

For the single row arrangement on both sides of the heat exchanger, the pressure distribution is different from the classic pressure distribution theory for the compact heat exchanger with the tube arrangement at one side. The increase in pressure caused by the pressure recovery effect is less than the decrease in pressure caused by the local pressure loss. Therefore, the pressure decreases along the direction of the main stream rather than increase as in the classic pressure distribution theory for the compact heat exchanger with the tube arrangement at one side. And it shows that the discipline of the pressure distribution for compact heat exchanger will change with different tube arrangements.

For the case2 and the case3, the aligned and staggered tube arrangements show no apparent difference in flow distribution and the pressure loss of the heat exchanger.

For the double-row tube arrangement on one side of the heat exchanger such as case4 and case5, the staggered tube arrangement contributes to a more uniform flow distribution and the flow distribution coefficient has been decreased by 24%, comparing to the aligned tube arrangement.

For the double-row and three-row tube arrangement, the flow distribution is worse in outer tubes. Besides, the difference between the maximum flow and the minimum flow in outer tubes is larger than that in inner tubes.

Φ Evaluation parameter of flow maldistribution

ε turbulent energy dissipation rate

_{k}_{ε}

_{t}

The datasets generated for this study are available on request to the corresponding authors.

JZ finish this manuscript. ZM give some useful advice. ZS provide the guideline for the manuscript. All authors contributed to the article and approved the submitted version.

YY was employed by company Research and development Center, China Nuclear Power Engineering.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.