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CFD simulation for the effect of the header match on the flow distribution in a central-type parallel heat exchanger
Accepted Manuscript Title: CFD simulation for the effect of the header match on the flow distribution in a central-type parallel heat exchanger Authors: Jian Zhou, Ming Ding, Haozhi Bian, Yinxing Zhang, Zhongning Sun PII: DOI: Reference:
S0263-8762(18)30235-1 https://doi.org/10.1016/j.cherd.2018.04.047 CHERD 3168
To appear in: Received date: Revised date: Accepted date:
12-3-2018 27-4-2018 30-4-2018
Please cite this article as: Zhou, Jian, Ding, Ming, Bian, Haozhi, Zhang, Yinxing, Sun, Zhongning, CFD simulation for the effect of the header match on the flow distribution in a central-type parallel heat exchanger.Chemical Engineering Research and Design https://doi.org/10.1016/j.cherd.2018.04.047 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
CFD simulation for the effect of the header match on the flow distribution in a central-type parallel heat exchanger
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Jian Zhou, Ming Ding, Haozhi Bian, Yinxing Zhang, Zhongning Sun*
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Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Heilongjiang, 150001, China Corresponding author. Tel./fax:+86 451 82569655.
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E-mail address: [email protected] (Z. Sun), [email protected] (J. Zhou).
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Highlights The flow distribution in parallel manifolds has been numerically investigated. Three types of flow distribution have been analyzed. The effect of the header match on the flow distribution have been investigated. The best choice of DCR for different types of flow distribution are given.
Abstract
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The present study numerically investigates the effect of the header match on the flow distribution in a central-type heat exchanger. Past studies have shown that the
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appropriate choice in two different header diameters (header match) will significantly help improve the flow distribution in the Z-type and U-type parallel heat exchangers. Under this circumstance, investigations are carried out on the central-type heat
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exchangers. According to our previous work on the effect of the geometric parameters on the flow distribution in a central-type exchanger[14], three different types flow distribution have been pointed out. Considering the differences in characteristics among three types of the flow distribution. The investigations have been separately made on each type of flow distribution. The results indicate that for the different types of the flow distribution, the best choice of the cross-sectional area ratio of dividing
header to combining header (DCR) is different. Besides, for all of three types of the flow distribution, when the DCR values less than 1, a great deal of flow maldistirbution will be brought. The present study is intended to figure out the effect of the header match on the flow distribution and provide constructive suggestions for the design of a central-type heat exchanger.
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Keywords: Flow distribution; Header match; Central-type parallel heat exchanger.
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Nomenclature
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DCR ε ρ u σk, σε μt
Header diameter Tube diameter Number of tubes Mass flow rate The pitch between the tubes at the center The flow area ratio Combining header diameter Dividing header diameter Turbulent kinetic energy Cross-sectional area ratio of dividing header to combining header Turbulent energy dissipation rate Density of the working fluid Velocity Turbulent constants turbulent dynamic viscosity
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Dh Dt N 𝑚̇ Dpt AR Dc Dd k
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1. Introduction Parallel manifolds have been widely applied in various fields such as heat
exchangers in chemical engineering, solar collectors, fuel cells and the passive removal heat exchanger in PCCS (passive containment cooling system), etc. The previous studies all showed that the uniformity of the flow distribution in manifolds will greatly influence the heat transfer performance of the device. Besides, in some conditions that the environmental temperature is higher than the saturation, there is
great possibility that tubes in which little coolant flows explodes because of the overheating. Therefore, the uniform flow distribution is significant for the guarantee of good performance of the heat exchanger and the safety of the system operation. Many investigations have been analytically and numerically conducted on the characteristics of the flow distribution in manifolds. Acrivos et al.[1] founded that the flow maldistribution is caused by the pressure maldistribution, and bigger coss section
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area of both dividing header and combining header will contribute to a better flow
distribution. Gandhi et al.[2] have done a large amount of work on the effect of the
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geometrical parameters on the flow distribution. The results show that the increase in the number of tubes will increase the flow maldistribution and the decrease of tube diameter will help improve the flow distribution.
Wang et al.[3] have done the experimental investigations on both Z-type and
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U-type parallel heat exchangers. The results show that the flow distribution in U-type
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heat exchanger is better than that in Z-type. Besides, the influence of gravity is
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negligible. In another work of Wang et al.[4], five modified headers with baffle tube,
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blocker and baffle plate installed inside have been applied in a U-type parallel heat exchanger. The results show that the modified headers all produce a better uniform
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flow distribution and the baffle tube yields the best flow distribution for it removed the vortex flow. The modified headers is applicable for all the flow rates. Sparrow et al.[5] have developed a fully validated quasianalytical method for
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determining the fluid flow in a multi-inlet collection manifold. The predicted results show a good agreement with numerical simulation results and this method is
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applicable to design a manifold which can produce a uniform flow distribution. Besides, Sparrow et al.[6] has also done the numerical investigations on the fluid flow in a system with separate laminar and turbulent zones. Three turbulent models
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(standard k-ε, k-ω and SST (shear stress transport) ) are chosen for the investigation, and results show that the k-ω and SST model perform well. Tong et al.[7] have applied a valve-like obstruction in each manifold. With the adjustment of the obstruction, the uniform flow distribution can be achieved. In another work by Tong et al.[8], eight proposed geometry strategies have been numerically investigated for evaluating their performance of producing uniform flow distribution. The results
show that they all can yields positive results and the simplest one for application is believed to be the direct enlargement of the distribution manifold. Wei et al.[9] have applied a inserted perforated baffle inside the dividing header and successfully achieved target flow distribution in parallel channels. Besides, the principle of the adjustment of the width of each hole has been given. Wang et al.[10, 11] have done great jobs on the discrete model for design of flow distribution in
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manifolds. The discrete method for both U-type and Z-type manifolds have been
developed. The results show that the flow distribution in U-type is more uniform than
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that in the Z-type manifolds. Besides, the analytic model provides the useful tool to
evaluate the flow distribution in manifolds and offers guidelines for the geometry design.
Past studies consist of numerical or experimental investigations on the geometry,
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analytic discrete model and the geometry modifications. Lots of useful results have
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been obtained and applied in the actual design procedure. In the present work, the
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attention is focused on the effect of the geometrical parameters on the flow
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distribution. For most investigations on the geometrical parameters, the diameters of the dividing header and the combining header are the same. However, the width ratio
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of the dividing header to the combining header greatly influences the flow distribution in manifolds. Choi et al.[12] numerically investigated the effect of the width ratio of the combining header to the dividing header (Dc/Dd) on the flow distribution for
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Z-type parallel channels. The results indicate that a larger Dc/Dd would produce a more uniform flow distribution. For the effect of the width ratio (Dc/Dd) in U-type
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parallel channels, Bi et al.[13] found that the Dc/Dd should be more than 1, thus obtaining a uniform flow distribution. However, for the central-type parallel manifolds, no literature has been found in the effect of the width ratio or
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cross-sectional area ratio of two headers. To fill this scientific gap, the numerical investigations on the effect of DCR (cross-sectional area ratio of dividing header to combining header) have been made in the present study. In our previous work of investigations on the flow distribution in a central-type parallel heat exchanger[14], the results show that the pitch between the central tubes (Dpt) and the header diameter (Dh) combine together to influence the flow distribution.
Therefore, to illustrate the separate effect of each parameter, three types of flow distribution have been applied and different flow distribution types have different characteristics. For the type I flow distribution, it exists in heat exchangers with big flow area ratios (the ratio of the total cross-sectional area of tubes to the cross-sectional area of the header), the flow rates in central tubes are higher than the average flow. For the type II flow distribution, it exists in heat exchangers with
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medium flow area ratios, the flow rates in central tubes are less than the average flow. For the type III flow distribution, it exists in heat exchangers with small flow area
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ratios, the flow rates in central tubes are close to the average flow and with the decrease of the flow area ratio, the flow distribution in tubes tends to be uniform.
Considering different flow distribution types existed in a central-type parallel heat exchanger, the investigations on the effect of DCR (cross-sectional area ratio of
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dividing header to combining header) will be separately performed according to
Dd2 Dc2
(1)
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DCR
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individual flow distribution type. And the equation for the DCR is as followed:
Where the Dd and Dc separately represent the dividing header diameter and
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the combining header diameter.
2. Geometries and numerical solutions
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The numerical investigations were performed using Star-ccm+ and constraints described by the boundary of a given system have been applied to solve the control
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equations for mass and momentum. The resulting partial differential equations together with a suitable turbulence model are solved numerically.
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2.1. The description of the geometry The three-dimensional model and schematic diagram of the subject for this study
are shown in Fig. A1[14]. Fourteen C-tubes and two headers namely dividing header and combining header respectively make up a central-type heat exchanger. The CAD in the Star-ccm+ was used to create the geometry. The geometry modification are achieved in the form of varying the dividing header diameter for different DCR.
2.2. Governing equations In order to simulate the steady state flow distribution in tubes, the governing equations (continuity and momentum) need to be solved. In the present work, the standard k–ε turbulence model[15]was used. The steady-state continuity equation is written as
ui 0 xi
u j
ui u u j p [ t ( i )] x j xi x j x j xi
u u j ui k t k ( ) t ( i ) x j x j k x j x j xi x j
(3)
(4)
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u j
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The steady-state transport equation for k is written as
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The steady-state momentum conservation equation is written as
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(2)
u u j ui 2 ( ) C1t ( i ) C2 x j x j x j k x j xi x j k
M
u j
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The steady-state transport equation for ε is written as (5)
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Where the k and ε represent the turbulent kinetic energy and turbulent energy dissipation rate, respectively. ρ is the density of the working fluid, u is the velocity,
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turbulent constants σk=1.0 and σε=1.3 are used and μt means turbulent dynamic viscosity. Empirical constants C1 = 1.44, C2 = 1.92 are used.
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2.3. Boundary conditions
In the present study, the water is used as the working fluid and the volumetric
flow rate is set as 30m3/h. The system is operating over a range of total pressure up to
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0.15MPa. The inlet is set as the velocity-inlet, and the outlet is set as the pressure-outlet. Walls are set as no slip condition and rough. For that the flow belongs to turbulent flow, the standard k–ε model is applied. Because the present study focuses on the flow distribution in the heat exchanger, the flow is assumed to be isothermal, with no phase change or changes in density A dimensionless parameter Φ[3] has been utilized to evaluate the flow
maldistribution in the heat exchanger. The definition of Φ is described as followed: N
(m m i 1
i
av
)2
N M
(6)
Where the mi and mav represent the mass flow rate through the ith tube and the average mass flow rate respectively. The M represents the total flow rate and the N
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represents the tube number. Also, a dimensionless parameter βi has been utilized. m i i (7) M
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2.4. Grid details
In the present study, two different kinds of mesh have been applied in the mesh generation. For two headers and part of tubes, the polyhedral mesh is used. And the
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rest major part of tubes is meshed with generalized cylinder mesh. Besides, the prism
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layer model and the wall function is used at all of the geometry walls to solve the
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boundary conditions. Besides, the mesh refinement was made near the boundary for a
2.5 Grid independence
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more accurate simulation result as shown in Fig. 1.
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The grid independence tests have been completed for a less work and an accurate result. Four different ways have been applied to mesh the geometry. And the number
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of grids are 2,365,663; 2,941,239; 4,539,910; 7,925,274 and defined as mesh 1, mesh 2, mesh 3 and mesh 4 respectively. Because in this work, more attention are paid on
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the pressure drop and the flow distribution uniformity. Therefore, the evaluation standard for performance of the grid is based on the value of Φ and the pressure drop in numerical results. The simulation results of the mass flow rate through each tube
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with different number of grids are shown in Fig. A2. It can be seen that the there is no significant difference in results when the number of grids increase to mesh 2. Therefore, the number of grids is determined to 2,941,239. 2.6. Model validation The numerical results in present study is validated by comparing to the experimental results from Gandhi et.al[2]. They have used 10 tubes with a cylindrical
header and two nozzles respectively named inlet nozzle and outlet nozzle. Comparing to the geometry in the present study, 14 tubes, two headers, an inlet nozzle and an outlet nozzle are used. And the rest of the geometry is similar. Besides, the water is used as the working fluid in both studies. Apart from the experiments made by Gandhi et.al[2], they have also done the simulation work using Fluent on the condition of three different inlet velocities. The experimental results and numerical results made
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by Gandhi et.al[2] as well as the numerical results in present study are shown in Fig. A3. It is obviously that the simulation results in present study suit well and the future
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numerical results in present study are accurate and credible. 3. A brief description of the three types of flow distribution
Considering the different characteristic of the three different types of flow
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distribution, the work of the header match will be carried on separately according to
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each flow distribution type.
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For a central-type heat exchanger, with the decrease of the flow area ratio (AR) by increasing the header diameter, the type of the flow distribution will change from
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type I to type II then to type III. Besides, the flow uniformity coefficient (Φ) will be up and down with the decrease of the value of AR as shown in Fig. A4. And the
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detailed parameters for the heat exchanger are shown in the table. 1. The formula of AR is expressed here:
N t Dt2 Dh2
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AR
(8)
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It can be seen from the Fig. A4. that with the decrease of the AR, the Ф decrease
when 3.303
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the flow distribution type. For different flow distribution types, the relationships between Ф and AR are different. The pressure distribution inside the dividing header and the flow distribution in tubes are shown in Fig. A5. It can be seen from the Fig. A5.(A) that, with the increase of the header, the flow velocity in the header becomes smaller, therefore, the pressure recovery effect in the header is reduced. The type I flow distribution occurs when the AR is relatively small as shown in Fig. A5.(B). The
larger the AR is, the larger the flow velocity becomes as well as the pressure recovery effect, resulting in more flow rates through central tubes. And, the more flow rate through central tubes brings more maldistribution. With the decrease of the AR, the velocity in the header as well as the pressure recovery effect is reduced. Therefore, the flow rates in the central tubes are reduced and the flow distribution is improved as shown in Fig. A5.(B). However, with the continuous decrease of the AR and the
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pressure recovery effect, the flow rates in central tubes are less than the average flow
as shown in Fig. A5.(C). And the decrease of the flow rates in central tubes brought
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by the decrease of AR will produce more flow maldistribution. This kind of flow
distribution is denoted as type II flow distribution. As the AR continue to decrease, the velocity in the header continues to decrease and the pressure distribution is more uniform as shown in Fig. A5. (A). It can be seen from the Fig. A5. (D). As the AR
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decrease, the flow rates through tubes all tend to be close to the average flow. This
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kind of flow distribution is denoted as type III flow distribution.
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4. The detailed procedure for the present study
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According to our previous work, there are three types of flow distribution in a central-type flow parallel heat exchanger. And for each different flow distribution type,
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the influence of the variations of the geometry parameters are different. Therefore, it is necessary to make investigations on the effect of the header match on the flow
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distribution for each type of flow distribution separately. The detailed procedure of solution is that select different values of AR from different types of flow distribution.
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Then, for the current AR, choose the header diameter as the combining header diameter and change the DCR( the ratio of the cross section of dividing header to the combining header) by varying the dividing header diameters. Finally, draw the
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relationship lines between the Φ and the DCR. For different three types of flow distribution, three cases are selected for the
present study. For the type I flow distribution, the heat exchangers with the AR valued 4.496 and 3.303 are chosen for the case1 for investigations. For the type II flow distribution, the heat exchangers with the AR valued 2.529 and 1.998 are chosen for the case2 for investigations. While for the type III flow distribution the heat
exchangers with the AR valued 1.338 and 0.958 are chosen for the case3 for investigations. The different combining header diameters for the corresponding AR chosen from different types of flow distribution are listed in Table. 2. When the diameter valued as 60mm and 70mm, the flow distribution belongs to the type I flow distribution. When
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the diameter valued as 80mm and 90mm, the flow distribution belongs to the type II distribution. When the diameter valued as 110mm and 130mm, the flow distribution
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belongs to the type III flow distribution. 5. Results and discussions 5.1 Header match for the flow distribution type I.
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For the flow distribution type I, when the combining header diameter values
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60mm and 70mm separately, the values of the DCR are varied by varying the dividing
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header diameter. The curve of the relationship between Ф and DCR is shown in Fig. 2.
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It can be seen that the value of Ф becomes the smallest when the DCR=1. Besides, when DCR<1, the Ф increases greatly when the DCR decreases. Therefore, for the
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header match in the region of type I flow distribution, the diameter of dividing header should avoid being less than the combining header diameter. When the DCR>1, the
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amplitude of the increasing rate of Ф becomes less and less as DCR increases. And the value of Ф gradually tends to a stable value.
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When the combining header diameter values as 60mm, denoted as case1, the flow distributions under different values of DCR are shown in Fig. 3. It can be seen that as the value of DCR increases, the flow rates in central tubes increase
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significantly. For the flow distribution type I, the flow rates in central tubes are higher than the average flow. Therefore, when DCR>1, the increase of the flow rate through central tubes caused by the increase of DCR will bring more flow maldistribution. To figure out the influence of the variations of DCR on the flow rate through central tubes, three pressure distributions in the dividing header under three different values of DCR are displayed in Fig. 4, when the combining header diameter is 60mm.
The bigger the DCR is, the larger the dividing header diameter is. Therefore, the velocity in the dividing header is smaller, reducing the pressure loss at the header inlet tee junction. Besides, when the DCR is larger, the static pressure in front of central tubes is larger as well as the pressure drop between the tube inlet and the outlet, thus resulting in more flow rates through central tubes as shown in Fig. 5. Also, it can be
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seen that when the DCR=0.694, the static pressure varies greatest along the axial direction, because of the larger velocity comparing to that in conditions of bigger values of the DCR. And this is why when DCR<1, the value of Ф increases greatly
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when the DCR decreases a little. While DCR>1, the velocity in the dividing header
becomes smaller and smaller as the DCR increases, resulting in a more steady and uniform pressure distribution. Therefore, the value of Ф tends to be steady as the DCR
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increases.
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5.2 Header match for the flow distribution type II.
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For the flow distribution type II, when the combining header diameter values 80mm and 90mm respectively. The curve of the relationship between the Ф and DCR
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is shown in Fig. 6. Same to the flow distribution type I, when the DCR<1, for both of combining header diameters valued as 80mm and 90mm, the flow value of Ф
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increases greatly as the DCR decreases. Therefore, for the flow distribution type II, the dividing header diameter should avoid being less than the combining header
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diameter in the geometry design. When the 1.5>DCR>1, for both of two combining header diameters, the Φ decreases as the DCR increases. However, when the DCR>1.5, the results for two header diameters are different. For the Dc=80mm, the Φ
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increases as the DCR increase. While for the Dc=90mm, the Φ nearly keep constant as the DCR increases. For a deeper investigation on the relationship between the flow distribution and the variations of the DCR, the flow distribution in the heat exchanger with the combining header diameter as 80mm denoted as case2 is taken to analyzed and discussed with the variation of the DCR as shown in Fig. 7.
It can be obtained that from the Fig. 7. With the increase of the DCR, the flow rates in central tubes increase obviously. For the flow distribution type II, the flow rates in central tubes are less than the average flow rate. Therefore, the appropriate increase of DCR will improve the uniformity of the flow distribution. However, the continue increase of DCR leads to the flow rates through central tubes larger than the
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average flow and bring more flow maldistribution. On the contrary, for the Dc=90mm, which locates at the turning point between flow distribution type II and type III, the
continue increase does not increase the flow maldistribution, because the relatively
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larger combining diameter or large AR ensure a more uniform in the pressure
distribution. And especially when it comes to the flow distribution type III, the pressure distribution in the dividing header becomes more uniform and it will be
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discussed deeper in the subsequent discussions of the header match for the flow
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distribution type III.
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To figure out the influence of the variation of DCR on the flow rates through
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central tubes, three different pressure distributions in the dividing header under three different values of DCR are displayed in Fig. 8. It can be seen that as the DCR
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increases, the pressure drop near the inlet becomes smaller and the pressure distribution becomes more uniform. The reason is because of the decrease in the
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velocity of the fluid caused by the increase of the dividing header diameter. Besides, the less pressure drop contributes to higher static pressure at the first tube. Therefore,
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the pressure drop along the first tube will increase as shown in Fig. 9. And the larger pressure drop along the tube means more flow rate through the tube.
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5.3 Header match for the flow distribution type III. As for the flow distribution type III, the combining header diameters are
separately set as 110mm and 130mm. The relationship curves of the Φ and the DCR are shown in Fig. 10. As seen in the Fig. 10. that the Φ deceases with the increase of the DCR. Besides, the value of the Φ gradually tends to be nearly 0 with the constantly increase of the DCR. And this is different from that in the case1 and case2.
However, when the DCR<1, the Φ decreases significantly with the decrease of DCR and this is the same as that in the case1 and case2. Therefore, it can be concluded that for a central type heat exchanger, the dividing header diameter should avoid being smaller than the diameter of the combining header. For a deeper investigation on the relationship between the flow distribution and
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the variations of the DCR, the flow distribution in the heat exchanger with the combining header diameter as 110mm denoted as case3 is taken to analyzed and
discussed with the variation of the DCR as shown in Fig. 11. As is shown in the Fig.
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11. that when the DCR decrease from 1, the flow rates through central tubes decrease significantly. However, when the DCR>1, the flow rates through central tubes do not
increase with the increase of the DCR like that in the case1 and case2. On the contrary,
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the flow rates through central tubes keep nearly constant as the DCR increases.
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Besides, the flow distribution in tubes becomes more uniform and this is consistent
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with the characteristic of the flow distribution type III.
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Three pressure distributions in the dividing header for different values of DCR is shown in Fig. 12. As the same in that for the case1 and case2, the larger DCR and
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larger dividing header diameter bring less pressure drop and more uniform pressure distribution. And it should be noticed that when the DCR>1, the pressure show no
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obvious upward trend or downtrend overally. It means that the increase of pressure caused by the pressure recovery and the decrease of the pressure caused by the
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frictional resistant are nearly equivalent. Therefore, with the increase of the DCR and the decrease of the flow velocity in the header, the pressure distribution and the flow distribution will be more and more uniform as shown in Fig. 12 and Fig. 13. And this
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is why the value of Φ keeps decreasing with the continuous increase of the DCR. 6. Conclusions The present study focuses on the effect of the header match on the flow distribution in a central-type heat exchanger. Considering the three different flow distributions existed in central-type heat exchanger according to our previous
work[14]. In the present study, these three different flow distribution types are separately investigated. The results are concluded as follows: 1. For all of three different flow distributions in a central-type heat exchanger, when the DCR<1, the little decrease of the DCR will greatly reducing the flow rates through central tubes thus bring significant flow maldistribution. 2. When the DCR>1, for the flow distribution type I, of which the flow rates
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through central tubes are larger than the average flow rate, the increase of the DCR will further increase the flow rates through central tubes and bring more flow
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maldistribution. Therefore, for the flow distribution type I, the DCR=1 is the best choice of the header match.
3. When the DCR>1, for the flow distribution type II, of which the flow rates
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through central tubes are less than the average flow rate, the appropriate increase of the DCR will result in proper increase of the flow rates through central tubes and
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produce uniform flow distribution. However, when the flow rates in central tubes are
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increased up to the average flow, then the continuous increase of the DCR will bring
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flow maldistribution. Besides, according to our results, the DCR is suggested as 1.5. 4. When the DCR>1, for the flow distribution type III, the large header diameter
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means more uniform pressure and flow distribution than that in the flow distribution type I and type II. Therefore, the increase of the DCR will enhance the uniformity of the pressure and flow distribution. And the DCR is suggested as 2.5 because the
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continuous increase of the DCR shows weakened effect on the improving the uniformity of the flow distribution.
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Ackonwledgments
Support of Fundamental Science on Nuclear Safety and Simulation Technology
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Laboratory gratefully acknowledged.
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[4]. Wang, C.C., et al., Characteristics of flow distribution in compact parallel flow heat exchangers, part II: Modified inlet header. Applied Thermal Engineering, 2011. 31(16): p. 3235-3242.
[5]. Sparrow, E.M., J.C.K. Tong and J.P. Abraham, A Quasi-Analytical Method for Fluid Flow in a Multi-Inlet Collection Manifold. Journal of Fluids Engineering, 2007. 129(5): p. 579-586.
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[6]. Sparrow, E.M., J.C.K. Tong and J.P. Abraham, Fluid Flow in a System with Separate Laminar and Turbulent Zones. Numerical Heat Transfer Part A Applications, 2008. 53(4): p. 341-353.
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p. 1186-1192.
[8]. Tong, J.C.K., E.M. Sparrow and J.P. Abraham, Geometric strategies for attainment of identical
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outflows through all of the exit ports of a distribution manifold in a manifold system. Applied Thermal Engineering, 2009. 29(17-18): p. 3552-3560.
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[9]. Wei, M., et al., CFD-based evolutionary algorithm for the realization of target fluid flow
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distribution among parallel channels. Chemical Engineering Research & Design, 2015. 100: p. 341-352. [10]. Wang, J., Pressure drop and flow distribution in parallel-channel configurations of fuel cells: Z-type arrangement. International Journal of Hydrogen Energy, 2010. 35(11): p. 5498-5509.
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[11]. Wang, J. and H. Wang, Discrete method for design of flow distribution in manifolds. Applied Thermal Engineering, 2015. 89: p. 927-945. [12]. Choi, S.H., S. Shin and Y.I. Cho, The effects of the Reynolds number and width ratio on the flow
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distribution in manifolds of liquid cooling modules for electronic packaging. International Communications in Heat & Mass Transfer, 1993. 20(5): p. 607-617. [13]. Bi, W., J. Li and Z. Lin, Flow uniformity optimization for large size planar solid oxide fuel cells
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with U-type parallel channel designs. Journal of Power Sources, 2010. 195(10): p. 3207-3214. [14]. Zhou, J., et al., CFD simulation for flow distribution in manifolds of central-type compact parallel flow heat exchangers. Applied Thermal Engineering, 2017. 126. [15] Jones, W.P., and Launder, B.E. 1972. “The Prediction of Laminarization with a Two-Equation
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Model of Turbulence”, Int. J. Heat and Mass Transfer, 15, pp. 301-314.
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PT
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A
N
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Fig. 1 The mesh for the configurat
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PT
ED
M
A
N
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Fig. 2. The relationship between the Φ and DCR for the flow distribution type I.
Fig. 3. The flow distributions under different values of DCR for the flow distribution
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type I.
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Fig. 4. The pressure distributions in the dividing header for different values of the
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PT
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M
A
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DCR.
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Fig. 5. The pressure drop through tubes for different values of the DCR.
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PT
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A
N
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Fig. 6. The relationship between the Φ and DCR for the flow distribution type II.
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Fig. 7. The flow distributions under different values of DCR for the flow distribution type II.
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PT
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M
A
N
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Fig. 8. The pressure distributions in the dividing header for different values of the DCR.
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Fig. 9. The pressure drop through tubes for different values of the DCR.
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PT
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M
A
N
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Fig. 10. The relationship between the Φ and DCR for the flow distribution type III.
Fig. 11. The flow distributions under different values of DCR for the flow distribution
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type III.
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PT
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M
A
N
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Fig. 12. The pressure distributions in the dividing header for different values of the DCR.
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Fig. 13. The pressure drop through tubes for different values of the DCR.
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Appendix
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M
A
N
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Fig. A1. The three-dimensional model and schematic diagram of the subject (A) schematic diagram of the subject (B) side view of the subject (C) the three-dimensional model[14].
Fig. A2 Grid independence test[14].
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PT
ED
M
A
N
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Fig. A3. The validation of the simulation results[14].
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Fig. A4. The relationship between Φ and AR[14].
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A
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PT
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M
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Fig. A5. (A) The static pressure distribution in the half of the header (B) The flow distribution of AR=6.474, 4.496,3.303 (C) The flow distribution of AR=3.303, 2.529, 1.998 (D) The distribution of AR=1.998, 1.618, 0.719, 0.405[14].
Table. 1. The detailed geometric parameters for the heat exchanger. Dt
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Dh
AR
values
34mm
14
50mm~200mm
0.405-6.474
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PT
ED
M
A
N
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Parameters
AR chosen from different types of flow Case 2
Case 3
Type II
Type III
2.529
1.998
1.338
0.958
80
90
110
130
A
CC E
PT
ED
M
A
N
U
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Table .2. The corresponding Dh for the distribution. Case Case 1 Flow distribution Type I type 4.496 3.303 AR Dh (mm) 60 70
S0263-8762(18)30235-1 https://doi.org/10.1016/j.cherd.2018.04.047 CHERD 3168
To appear in: Received date: Revised date: Accepted date:
12-3-2018 27-4-2018 30-4-2018
Please cite this article as: Zhou, Jian, Ding, Ming, Bian, Haozhi, Zhang, Yinxing, Sun, Zhongning, CFD simulation for the effect of the header match on the flow distribution in a central-type parallel heat exchanger.Chemical Engineering Research and Design https://doi.org/10.1016/j.cherd.2018.04.047 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
CFD simulation for the effect of the header match on the flow distribution in a central-type parallel heat exchanger
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Jian Zhou, Ming Ding, Haozhi Bian, Yinxing Zhang, Zhongning Sun*
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Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Heilongjiang, 150001, China Corresponding author. Tel./fax:+86 451 82569655.
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E-mail address: [email protected] (Z. Sun), [email protected] (J. Zhou).
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Highlights The flow distribution in parallel manifolds has been numerically investigated. Three types of flow distribution have been analyzed. The effect of the header match on the flow distribution have been investigated. The best choice of DCR for different types of flow distribution are given.
Abstract
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The present study numerically investigates the effect of the header match on the flow distribution in a central-type heat exchanger. Past studies have shown that the
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appropriate choice in two different header diameters (header match) will significantly help improve the flow distribution in the Z-type and U-type parallel heat exchangers. Under this circumstance, investigations are carried out on the central-type heat
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exchangers. According to our previous work on the effect of the geometric parameters on the flow distribution in a central-type exchanger[14], three different types flow distribution have been pointed out. Considering the differences in characteristics among three types of the flow distribution. The investigations have been separately made on each type of flow distribution. The results indicate that for the different types of the flow distribution, the best choice of the cross-sectional area ratio of dividing
header to combining header (DCR) is different. Besides, for all of three types of the flow distribution, when the DCR values less than 1, a great deal of flow maldistirbution will be brought. The present study is intended to figure out the effect of the header match on the flow distribution and provide constructive suggestions for the design of a central-type heat exchanger.
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Keywords: Flow distribution; Header match; Central-type parallel heat exchanger.
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Nomenclature
N
A M
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PT
ED
DCR ε ρ u σk, σε μt
Header diameter Tube diameter Number of tubes Mass flow rate The pitch between the tubes at the center The flow area ratio Combining header diameter Dividing header diameter Turbulent kinetic energy Cross-sectional area ratio of dividing header to combining header Turbulent energy dissipation rate Density of the working fluid Velocity Turbulent constants turbulent dynamic viscosity
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Dh Dt N 𝑚̇ Dpt AR Dc Dd k
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1. Introduction Parallel manifolds have been widely applied in various fields such as heat
exchangers in chemical engineering, solar collectors, fuel cells and the passive removal heat exchanger in PCCS (passive containment cooling system), etc. The previous studies all showed that the uniformity of the flow distribution in manifolds will greatly influence the heat transfer performance of the device. Besides, in some conditions that the environmental temperature is higher than the saturation, there is
great possibility that tubes in which little coolant flows explodes because of the overheating. Therefore, the uniform flow distribution is significant for the guarantee of good performance of the heat exchanger and the safety of the system operation. Many investigations have been analytically and numerically conducted on the characteristics of the flow distribution in manifolds. Acrivos et al.[1] founded that the flow maldistribution is caused by the pressure maldistribution, and bigger coss section
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area of both dividing header and combining header will contribute to a better flow
distribution. Gandhi et al.[2] have done a large amount of work on the effect of the
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geometrical parameters on the flow distribution. The results show that the increase in the number of tubes will increase the flow maldistribution and the decrease of tube diameter will help improve the flow distribution.
Wang et al.[3] have done the experimental investigations on both Z-type and
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U-type parallel heat exchangers. The results show that the flow distribution in U-type
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heat exchanger is better than that in Z-type. Besides, the influence of gravity is
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negligible. In another work of Wang et al.[4], five modified headers with baffle tube,
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blocker and baffle plate installed inside have been applied in a U-type parallel heat exchanger. The results show that the modified headers all produce a better uniform
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flow distribution and the baffle tube yields the best flow distribution for it removed the vortex flow. The modified headers is applicable for all the flow rates. Sparrow et al.[5] have developed a fully validated quasianalytical method for
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determining the fluid flow in a multi-inlet collection manifold. The predicted results show a good agreement with numerical simulation results and this method is
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applicable to design a manifold which can produce a uniform flow distribution. Besides, Sparrow et al.[6] has also done the numerical investigations on the fluid flow in a system with separate laminar and turbulent zones. Three turbulent models
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(standard k-ε, k-ω and SST (shear stress transport) ) are chosen for the investigation, and results show that the k-ω and SST model perform well. Tong et al.[7] have applied a valve-like obstruction in each manifold. With the adjustment of the obstruction, the uniform flow distribution can be achieved. In another work by Tong et al.[8], eight proposed geometry strategies have been numerically investigated for evaluating their performance of producing uniform flow distribution. The results
show that they all can yields positive results and the simplest one for application is believed to be the direct enlargement of the distribution manifold. Wei et al.[9] have applied a inserted perforated baffle inside the dividing header and successfully achieved target flow distribution in parallel channels. Besides, the principle of the adjustment of the width of each hole has been given. Wang et al.[10, 11] have done great jobs on the discrete model for design of flow distribution in
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manifolds. The discrete method for both U-type and Z-type manifolds have been
developed. The results show that the flow distribution in U-type is more uniform than
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that in the Z-type manifolds. Besides, the analytic model provides the useful tool to
evaluate the flow distribution in manifolds and offers guidelines for the geometry design.
Past studies consist of numerical or experimental investigations on the geometry,
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analytic discrete model and the geometry modifications. Lots of useful results have
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been obtained and applied in the actual design procedure. In the present work, the
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attention is focused on the effect of the geometrical parameters on the flow
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distribution. For most investigations on the geometrical parameters, the diameters of the dividing header and the combining header are the same. However, the width ratio
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of the dividing header to the combining header greatly influences the flow distribution in manifolds. Choi et al.[12] numerically investigated the effect of the width ratio of the combining header to the dividing header (Dc/Dd) on the flow distribution for
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Z-type parallel channels. The results indicate that a larger Dc/Dd would produce a more uniform flow distribution. For the effect of the width ratio (Dc/Dd) in U-type
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parallel channels, Bi et al.[13] found that the Dc/Dd should be more than 1, thus obtaining a uniform flow distribution. However, for the central-type parallel manifolds, no literature has been found in the effect of the width ratio or
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cross-sectional area ratio of two headers. To fill this scientific gap, the numerical investigations on the effect of DCR (cross-sectional area ratio of dividing header to combining header) have been made in the present study. In our previous work of investigations on the flow distribution in a central-type parallel heat exchanger[14], the results show that the pitch between the central tubes (Dpt) and the header diameter (Dh) combine together to influence the flow distribution.
Therefore, to illustrate the separate effect of each parameter, three types of flow distribution have been applied and different flow distribution types have different characteristics. For the type I flow distribution, it exists in heat exchangers with big flow area ratios (the ratio of the total cross-sectional area of tubes to the cross-sectional area of the header), the flow rates in central tubes are higher than the average flow. For the type II flow distribution, it exists in heat exchangers with
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medium flow area ratios, the flow rates in central tubes are less than the average flow. For the type III flow distribution, it exists in heat exchangers with small flow area
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ratios, the flow rates in central tubes are close to the average flow and with the decrease of the flow area ratio, the flow distribution in tubes tends to be uniform.
Considering different flow distribution types existed in a central-type parallel heat exchanger, the investigations on the effect of DCR (cross-sectional area ratio of
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dividing header to combining header) will be separately performed according to
Dd2 Dc2
(1)
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DCR
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individual flow distribution type. And the equation for the DCR is as followed:
Where the Dd and Dc separately represent the dividing header diameter and
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the combining header diameter.
2. Geometries and numerical solutions
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The numerical investigations were performed using Star-ccm+ and constraints described by the boundary of a given system have been applied to solve the control
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equations for mass and momentum. The resulting partial differential equations together with a suitable turbulence model are solved numerically.
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2.1. The description of the geometry The three-dimensional model and schematic diagram of the subject for this study
are shown in Fig. A1[14]. Fourteen C-tubes and two headers namely dividing header and combining header respectively make up a central-type heat exchanger. The CAD in the Star-ccm+ was used to create the geometry. The geometry modification are achieved in the form of varying the dividing header diameter for different DCR.
2.2. Governing equations In order to simulate the steady state flow distribution in tubes, the governing equations (continuity and momentum) need to be solved. In the present work, the standard k–ε turbulence model[15]was used. The steady-state continuity equation is written as
ui 0 xi
u j
ui u u j p [ t ( i )] x j xi x j x j xi
u u j ui k t k ( ) t ( i ) x j x j k x j x j xi x j
(3)
(4)
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u j
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The steady-state transport equation for k is written as
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The steady-state momentum conservation equation is written as
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(2)
u u j ui 2 ( ) C1t ( i ) C2 x j x j x j k x j xi x j k
M
u j
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The steady-state transport equation for ε is written as (5)
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Where the k and ε represent the turbulent kinetic energy and turbulent energy dissipation rate, respectively. ρ is the density of the working fluid, u is the velocity,
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turbulent constants σk=1.0 and σε=1.3 are used and μt means turbulent dynamic viscosity. Empirical constants C1 = 1.44, C2 = 1.92 are used.
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2.3. Boundary conditions
In the present study, the water is used as the working fluid and the volumetric
flow rate is set as 30m3/h. The system is operating over a range of total pressure up to
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0.15MPa. The inlet is set as the velocity-inlet, and the outlet is set as the pressure-outlet. Walls are set as no slip condition and rough. For that the flow belongs to turbulent flow, the standard k–ε model is applied. Because the present study focuses on the flow distribution in the heat exchanger, the flow is assumed to be isothermal, with no phase change or changes in density A dimensionless parameter Φ[3] has been utilized to evaluate the flow
maldistribution in the heat exchanger. The definition of Φ is described as followed: N
(m m i 1
i
av
)2
N M
(6)
Where the mi and mav represent the mass flow rate through the ith tube and the average mass flow rate respectively. The M represents the total flow rate and the N
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represents the tube number. Also, a dimensionless parameter βi has been utilized. m i i (7) M
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2.4. Grid details
In the present study, two different kinds of mesh have been applied in the mesh generation. For two headers and part of tubes, the polyhedral mesh is used. And the
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rest major part of tubes is meshed with generalized cylinder mesh. Besides, the prism
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layer model and the wall function is used at all of the geometry walls to solve the
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boundary conditions. Besides, the mesh refinement was made near the boundary for a
2.5 Grid independence
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more accurate simulation result as shown in Fig. 1.
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The grid independence tests have been completed for a less work and an accurate result. Four different ways have been applied to mesh the geometry. And the number
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of grids are 2,365,663; 2,941,239; 4,539,910; 7,925,274 and defined as mesh 1, mesh 2, mesh 3 and mesh 4 respectively. Because in this work, more attention are paid on
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the pressure drop and the flow distribution uniformity. Therefore, the evaluation standard for performance of the grid is based on the value of Φ and the pressure drop in numerical results. The simulation results of the mass flow rate through each tube
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with different number of grids are shown in Fig. A2. It can be seen that the there is no significant difference in results when the number of grids increase to mesh 2. Therefore, the number of grids is determined to 2,941,239. 2.6. Model validation The numerical results in present study is validated by comparing to the experimental results from Gandhi et.al[2]. They have used 10 tubes with a cylindrical
header and two nozzles respectively named inlet nozzle and outlet nozzle. Comparing to the geometry in the present study, 14 tubes, two headers, an inlet nozzle and an outlet nozzle are used. And the rest of the geometry is similar. Besides, the water is used as the working fluid in both studies. Apart from the experiments made by Gandhi et.al[2], they have also done the simulation work using Fluent on the condition of three different inlet velocities. The experimental results and numerical results made
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by Gandhi et.al[2] as well as the numerical results in present study are shown in Fig. A3. It is obviously that the simulation results in present study suit well and the future
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numerical results in present study are accurate and credible. 3. A brief description of the three types of flow distribution
Considering the different characteristic of the three different types of flow
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distribution, the work of the header match will be carried on separately according to
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each flow distribution type.
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For a central-type heat exchanger, with the decrease of the flow area ratio (AR) by increasing the header diameter, the type of the flow distribution will change from
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type I to type II then to type III. Besides, the flow uniformity coefficient (Φ) will be up and down with the decrease of the value of AR as shown in Fig. A4. And the
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detailed parameters for the heat exchanger are shown in the table. 1. The formula of AR is expressed here:
N t Dt2 Dh2
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AR
(8)
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It can be seen from the Fig. A4. that with the decrease of the AR, the Ф decrease
when 3.303
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the flow distribution type. For different flow distribution types, the relationships between Ф and AR are different. The pressure distribution inside the dividing header and the flow distribution in tubes are shown in Fig. A5. It can be seen from the Fig. A5.(A) that, with the increase of the header, the flow velocity in the header becomes smaller, therefore, the pressure recovery effect in the header is reduced. The type I flow distribution occurs when the AR is relatively small as shown in Fig. A5.(B). The
larger the AR is, the larger the flow velocity becomes as well as the pressure recovery effect, resulting in more flow rates through central tubes. And, the more flow rate through central tubes brings more maldistribution. With the decrease of the AR, the velocity in the header as well as the pressure recovery effect is reduced. Therefore, the flow rates in the central tubes are reduced and the flow distribution is improved as shown in Fig. A5.(B). However, with the continuous decrease of the AR and the
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pressure recovery effect, the flow rates in central tubes are less than the average flow
as shown in Fig. A5.(C). And the decrease of the flow rates in central tubes brought
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by the decrease of AR will produce more flow maldistribution. This kind of flow
distribution is denoted as type II flow distribution. As the AR continue to decrease, the velocity in the header continues to decrease and the pressure distribution is more uniform as shown in Fig. A5. (A). It can be seen from the Fig. A5. (D). As the AR
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decrease, the flow rates through tubes all tend to be close to the average flow. This
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kind of flow distribution is denoted as type III flow distribution.
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4. The detailed procedure for the present study
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According to our previous work, there are three types of flow distribution in a central-type flow parallel heat exchanger. And for each different flow distribution type,
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the influence of the variations of the geometry parameters are different. Therefore, it is necessary to make investigations on the effect of the header match on the flow
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distribution for each type of flow distribution separately. The detailed procedure of solution is that select different values of AR from different types of flow distribution.
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Then, for the current AR, choose the header diameter as the combining header diameter and change the DCR( the ratio of the cross section of dividing header to the combining header) by varying the dividing header diameters. Finally, draw the
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relationship lines between the Φ and the DCR. For different three types of flow distribution, three cases are selected for the
present study. For the type I flow distribution, the heat exchangers with the AR valued 4.496 and 3.303 are chosen for the case1 for investigations. For the type II flow distribution, the heat exchangers with the AR valued 2.529 and 1.998 are chosen for the case2 for investigations. While for the type III flow distribution the heat
exchangers with the AR valued 1.338 and 0.958 are chosen for the case3 for investigations. The different combining header diameters for the corresponding AR chosen from different types of flow distribution are listed in Table. 2. When the diameter valued as 60mm and 70mm, the flow distribution belongs to the type I flow distribution. When
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the diameter valued as 80mm and 90mm, the flow distribution belongs to the type II distribution. When the diameter valued as 110mm and 130mm, the flow distribution
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belongs to the type III flow distribution. 5. Results and discussions 5.1 Header match for the flow distribution type I.
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For the flow distribution type I, when the combining header diameter values
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60mm and 70mm separately, the values of the DCR are varied by varying the dividing
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header diameter. The curve of the relationship between Ф and DCR is shown in Fig. 2.
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It can be seen that the value of Ф becomes the smallest when the DCR=1. Besides, when DCR<1, the Ф increases greatly when the DCR decreases. Therefore, for the
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header match in the region of type I flow distribution, the diameter of dividing header should avoid being less than the combining header diameter. When the DCR>1, the
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amplitude of the increasing rate of Ф becomes less and less as DCR increases. And the value of Ф gradually tends to a stable value.
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When the combining header diameter values as 60mm, denoted as case1, the flow distributions under different values of DCR are shown in Fig. 3. It can be seen that as the value of DCR increases, the flow rates in central tubes increase
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significantly. For the flow distribution type I, the flow rates in central tubes are higher than the average flow. Therefore, when DCR>1, the increase of the flow rate through central tubes caused by the increase of DCR will bring more flow maldistribution. To figure out the influence of the variations of DCR on the flow rate through central tubes, three pressure distributions in the dividing header under three different values of DCR are displayed in Fig. 4, when the combining header diameter is 60mm.
The bigger the DCR is, the larger the dividing header diameter is. Therefore, the velocity in the dividing header is smaller, reducing the pressure loss at the header inlet tee junction. Besides, when the DCR is larger, the static pressure in front of central tubes is larger as well as the pressure drop between the tube inlet and the outlet, thus resulting in more flow rates through central tubes as shown in Fig. 5. Also, it can be
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seen that when the DCR=0.694, the static pressure varies greatest along the axial direction, because of the larger velocity comparing to that in conditions of bigger values of the DCR. And this is why when DCR<1, the value of Ф increases greatly
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when the DCR decreases a little. While DCR>1, the velocity in the dividing header
becomes smaller and smaller as the DCR increases, resulting in a more steady and uniform pressure distribution. Therefore, the value of Ф tends to be steady as the DCR
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increases.
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5.2 Header match for the flow distribution type II.
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For the flow distribution type II, when the combining header diameter values 80mm and 90mm respectively. The curve of the relationship between the Ф and DCR
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is shown in Fig. 6. Same to the flow distribution type I, when the DCR<1, for both of combining header diameters valued as 80mm and 90mm, the flow value of Ф
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increases greatly as the DCR decreases. Therefore, for the flow distribution type II, the dividing header diameter should avoid being less than the combining header
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diameter in the geometry design. When the 1.5>DCR>1, for both of two combining header diameters, the Φ decreases as the DCR increases. However, when the DCR>1.5, the results for two header diameters are different. For the Dc=80mm, the Φ
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increases as the DCR increase. While for the Dc=90mm, the Φ nearly keep constant as the DCR increases. For a deeper investigation on the relationship between the flow distribution and the variations of the DCR, the flow distribution in the heat exchanger with the combining header diameter as 80mm denoted as case2 is taken to analyzed and discussed with the variation of the DCR as shown in Fig. 7.
It can be obtained that from the Fig. 7. With the increase of the DCR, the flow rates in central tubes increase obviously. For the flow distribution type II, the flow rates in central tubes are less than the average flow rate. Therefore, the appropriate increase of DCR will improve the uniformity of the flow distribution. However, the continue increase of DCR leads to the flow rates through central tubes larger than the
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average flow and bring more flow maldistribution. On the contrary, for the Dc=90mm, which locates at the turning point between flow distribution type II and type III, the
continue increase does not increase the flow maldistribution, because the relatively
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larger combining diameter or large AR ensure a more uniform in the pressure
distribution. And especially when it comes to the flow distribution type III, the pressure distribution in the dividing header becomes more uniform and it will be
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discussed deeper in the subsequent discussions of the header match for the flow
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distribution type III.
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To figure out the influence of the variation of DCR on the flow rates through
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central tubes, three different pressure distributions in the dividing header under three different values of DCR are displayed in Fig. 8. It can be seen that as the DCR
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increases, the pressure drop near the inlet becomes smaller and the pressure distribution becomes more uniform. The reason is because of the decrease in the
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velocity of the fluid caused by the increase of the dividing header diameter. Besides, the less pressure drop contributes to higher static pressure at the first tube. Therefore,
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the pressure drop along the first tube will increase as shown in Fig. 9. And the larger pressure drop along the tube means more flow rate through the tube.
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5.3 Header match for the flow distribution type III. As for the flow distribution type III, the combining header diameters are
separately set as 110mm and 130mm. The relationship curves of the Φ and the DCR are shown in Fig. 10. As seen in the Fig. 10. that the Φ deceases with the increase of the DCR. Besides, the value of the Φ gradually tends to be nearly 0 with the constantly increase of the DCR. And this is different from that in the case1 and case2.
However, when the DCR<1, the Φ decreases significantly with the decrease of DCR and this is the same as that in the case1 and case2. Therefore, it can be concluded that for a central type heat exchanger, the dividing header diameter should avoid being smaller than the diameter of the combining header. For a deeper investigation on the relationship between the flow distribution and
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the variations of the DCR, the flow distribution in the heat exchanger with the combining header diameter as 110mm denoted as case3 is taken to analyzed and
discussed with the variation of the DCR as shown in Fig. 11. As is shown in the Fig.
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11. that when the DCR decrease from 1, the flow rates through central tubes decrease significantly. However, when the DCR>1, the flow rates through central tubes do not
increase with the increase of the DCR like that in the case1 and case2. On the contrary,
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the flow rates through central tubes keep nearly constant as the DCR increases.
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Besides, the flow distribution in tubes becomes more uniform and this is consistent
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with the characteristic of the flow distribution type III.
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Three pressure distributions in the dividing header for different values of DCR is shown in Fig. 12. As the same in that for the case1 and case2, the larger DCR and
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larger dividing header diameter bring less pressure drop and more uniform pressure distribution. And it should be noticed that when the DCR>1, the pressure show no
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obvious upward trend or downtrend overally. It means that the increase of pressure caused by the pressure recovery and the decrease of the pressure caused by the
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frictional resistant are nearly equivalent. Therefore, with the increase of the DCR and the decrease of the flow velocity in the header, the pressure distribution and the flow distribution will be more and more uniform as shown in Fig. 12 and Fig. 13. And this
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is why the value of Φ keeps decreasing with the continuous increase of the DCR. 6. Conclusions The present study focuses on the effect of the header match on the flow distribution in a central-type heat exchanger. Considering the three different flow distributions existed in central-type heat exchanger according to our previous
work[14]. In the present study, these three different flow distribution types are separately investigated. The results are concluded as follows: 1. For all of three different flow distributions in a central-type heat exchanger, when the DCR<1, the little decrease of the DCR will greatly reducing the flow rates through central tubes thus bring significant flow maldistribution. 2. When the DCR>1, for the flow distribution type I, of which the flow rates
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through central tubes are larger than the average flow rate, the increase of the DCR will further increase the flow rates through central tubes and bring more flow
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maldistribution. Therefore, for the flow distribution type I, the DCR=1 is the best choice of the header match.
3. When the DCR>1, for the flow distribution type II, of which the flow rates
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through central tubes are less than the average flow rate, the appropriate increase of the DCR will result in proper increase of the flow rates through central tubes and
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produce uniform flow distribution. However, when the flow rates in central tubes are
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increased up to the average flow, then the continuous increase of the DCR will bring
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flow maldistribution. Besides, according to our results, the DCR is suggested as 1.5. 4. When the DCR>1, for the flow distribution type III, the large header diameter
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means more uniform pressure and flow distribution than that in the flow distribution type I and type II. Therefore, the increase of the DCR will enhance the uniformity of the pressure and flow distribution. And the DCR is suggested as 2.5 because the
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continuous increase of the DCR shows weakened effect on the improving the uniformity of the flow distribution.
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Ackonwledgments
Support of Fundamental Science on Nuclear Safety and Simulation Technology
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Laboratory gratefully acknowledged.
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[4]. Wang, C.C., et al., Characteristics of flow distribution in compact parallel flow heat exchangers, part II: Modified inlet header. Applied Thermal Engineering, 2011. 31(16): p. 3235-3242.
[5]. Sparrow, E.M., J.C.K. Tong and J.P. Abraham, A Quasi-Analytical Method for Fluid Flow in a Multi-Inlet Collection Manifold. Journal of Fluids Engineering, 2007. 129(5): p. 579-586.
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[6]. Sparrow, E.M., J.C.K. Tong and J.P. Abraham, Fluid Flow in a System with Separate Laminar and Turbulent Zones. Numerical Heat Transfer Part A Applications, 2008. 53(4): p. 341-353.
[7]. Tong, J.C.K., E.M. Sparrow and J.P. Abraham, Attainment of Flowrate Uniformity in the Channels That Link a Distribution Manifold to a Collection Manifold. Journal of Fluids Engineering, 2007. 129(9):
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p. 1186-1192.
[8]. Tong, J.C.K., E.M. Sparrow and J.P. Abraham, Geometric strategies for attainment of identical
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outflows through all of the exit ports of a distribution manifold in a manifold system. Applied Thermal Engineering, 2009. 29(17-18): p. 3552-3560.
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[9]. Wei, M., et al., CFD-based evolutionary algorithm for the realization of target fluid flow
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distribution among parallel channels. Chemical Engineering Research & Design, 2015. 100: p. 341-352. [10]. Wang, J., Pressure drop and flow distribution in parallel-channel configurations of fuel cells: Z-type arrangement. International Journal of Hydrogen Energy, 2010. 35(11): p. 5498-5509.
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[11]. Wang, J. and H. Wang, Discrete method for design of flow distribution in manifolds. Applied Thermal Engineering, 2015. 89: p. 927-945. [12]. Choi, S.H., S. Shin and Y.I. Cho, The effects of the Reynolds number and width ratio on the flow
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distribution in manifolds of liquid cooling modules for electronic packaging. International Communications in Heat & Mass Transfer, 1993. 20(5): p. 607-617. [13]. Bi, W., J. Li and Z. Lin, Flow uniformity optimization for large size planar solid oxide fuel cells
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with U-type parallel channel designs. Journal of Power Sources, 2010. 195(10): p. 3207-3214. [14]. Zhou, J., et al., CFD simulation for flow distribution in manifolds of central-type compact parallel flow heat exchangers. Applied Thermal Engineering, 2017. 126. [15] Jones, W.P., and Launder, B.E. 1972. “The Prediction of Laminarization with a Two-Equation
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Model of Turbulence”, Int. J. Heat and Mass Transfer, 15, pp. 301-314.
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Fig. 1 The mesh for the configurat
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Fig. 2. The relationship between the Φ and DCR for the flow distribution type I.
Fig. 3. The flow distributions under different values of DCR for the flow distribution
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type I.
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Fig. 4. The pressure distributions in the dividing header for different values of the
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DCR.
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Fig. 5. The pressure drop through tubes for different values of the DCR.
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Fig. 6. The relationship between the Φ and DCR for the flow distribution type II.
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Fig. 7. The flow distributions under different values of DCR for the flow distribution type II.
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Fig. 8. The pressure distributions in the dividing header for different values of the DCR.
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Fig. 9. The pressure drop through tubes for different values of the DCR.
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Fig. 10. The relationship between the Φ and DCR for the flow distribution type III.
Fig. 11. The flow distributions under different values of DCR for the flow distribution
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type III.
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Fig. 12. The pressure distributions in the dividing header for different values of the DCR.
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Fig. 13. The pressure drop through tubes for different values of the DCR.
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Appendix
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Fig. A1. The three-dimensional model and schematic diagram of the subject (A) schematic diagram of the subject (B) side view of the subject (C) the three-dimensional model[14].
Fig. A2 Grid independence test[14].
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Fig. A3. The validation of the simulation results[14].
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Fig. A4. The relationship between Φ and AR[14].
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Fig. A5. (A) The static pressure distribution in the half of the header (B) The flow distribution of AR=6.474, 4.496,3.303 (C) The flow distribution of AR=3.303, 2.529, 1.998 (D) The distribution of AR=1.998, 1.618, 0.719, 0.405[14].
Table. 1. The detailed geometric parameters for the heat exchanger. Dt
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Dh
AR
values
34mm
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50mm~200mm
0.405-6.474
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Parameters
AR chosen from different types of flow Case 2
Case 3
Type II
Type III
2.529
1.998
1.338
0.958
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90
110
130
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Table .2. The corresponding Dh for the distribution. Case Case 1 Flow distribution Type I type 4.496 3.303 AR Dh (mm) 60 70