Shell-side thermal-hydraulic performances of multilayer spiral-wound heat exchangers under different wall thermal boundary conditions

Applied Thermal Engineering xxx (2014) 1e12

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Shell-side thermal-hydraulic performances of multilayer spiral-wound heat exchangers under different wall thermal boundary conditions Xing Lu, Xueping Du, Min Zeng, Sen Zhang, Qiuwang Wang* Key Laboratory of Thermo-Fluid Science and Engineering, MOE, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, PR China

h i g h l i g h t s
Shell-side flow and heat transfer of a spiral-wound heat exchanger is experimentally studied.
Effects of three kinds of thermal boundary conditions are numerically investigated.
The constant temperature thermal boundary condition could be employed for simulation.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 January 2014 Accepted 20 February 2014 Available online xxx

The multilayer spiral-wound heat exchanger (SWHX) is used extensively in many industrial fields, but little research on the shell-side thermal-hydraulic performances in SWHXs has been performed. So an investigation on the shell-side flow and heat transfer performances of multilayer SWHXs under turbulent flow is implemented by using experimental and numerical methods. An experiment on the shell-side flow and heat transfer performance of a self-manufactured SWHX with three layers of coils is carried out under heat flux specified boundary condition (BC) to validate a numerical method. The results obtained by the simulations agree well with those from the experiment. Furthermore, to study the effects of different thermal BCs of the tube wall on the shell-side heat transfer performance in the multilayer SWHXs, numerical simulations are performed under the thermal BC of constant heat flux and constant temperature. Then the results are compared to those of the water-to-water conjugate heat transfer. It is found that the maximum relative deviation is 11.4% and 3.5%, respectively. Finally, the correlation of the , with shell-side Nusselt number, Nus is obtained by the Wilson plot method, which is Nus ¼ 0.179$Re0.862 s the available range of Res from 500 to 3500. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Multilayer spiral-wound heat exchanger Shell-side heat transfer performance Thermal boundary conditions

1. Introduction The spiral-wound heat exchangers (SWHXs) are widely applied in rectisol process [1], air separation plants, liquefied natural gas (LNG), chemical process [2], coal gasification and liquid nitrogen [3] due to their overwhelming advantages, including:
Highly compact structure According to Zhang [4], the SWHXs have large heat transfer area per unit volume. Generally in shell-and-tube heat exchangers, a straight tube with the diameter of 8 mme21 mm usually makes the

heat transfer area from 54 m2 m3 to 77 m2 m3, while a spiral pipe with the same diameter 100 m2 m3 to 170 m2 m3 [5].
High pressure endurance The stress intensity of the spiral-wound tubes in SWHXs which are usually made of copper, aluminium and stainless steel is quite high to endure high-pressure working fluid as high as around 20 MPa [5].
Good thermal compensation performance The free-ends of the spiral-wound tubes benefit for the heat exchanger a good response for thermal expansion [5].

* Corresponding author. Tel./fax: þ86 29 82665539. E-mail address: [email protected] (Q. Wang).


Multi-stream heat transfer

http://dx.doi.org/10.1016/j.applthermaleng.2014.02.053 1359-4311/Ó 2014 Elsevier Ltd. All rights reserved.

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X. Lu et al. / Applied Thermal Engineering xxx (2014) 1e12

Nomenclature Ai Ao As,min B cp Det Ds,i Ds,o Dt dt dp Gs H h k L Nc Nlay Nu P Pl Plr q qv

Heat transfer area of inner walls of coils, m2 Heat transfer area of outer walls of coils, m2 Minimum cross-section area in shell-side flow passage, m2 Thickness of space bar, mm Specific heat capacity in constant pressure, J kg1 K1 Dean number of helix pipe Outer diameter of centre cylinder, mm Inner diameter of shell, mm Outer diameter of spirally coiled pipes, mm Inner diameter of spirally coiled pipes, mm Pressure drop, Pa Mass flow rate of shell-side fluid, kg s1 Effective height for heat transfer, mm Heat transfer coefficient, W m2 K1 Turbulent kinetic energy, m2 s2 Tube length, mm Number of spirally wound pipes in one layer of coil Number of layer Nusselt number Pressure, Pa Helix pitch, mm Axial distance of two adjacent layers of coils, mm Heat flux, W m2 Volume flow rate of gas, m3 h1

The SWHXs are classified into mono-stream SWHXs and multistream SWHXs according to the species of tube-side working fluid [6]. The mono-steam SWHXs have one kind of fluid in the flow passages of the coils, while the multi-stream SWHXs have several different working fluids in different layers of coils. The structure of the multilayer SWHXs is quite complicated, with several layers of spirally coiled tubes inside a shell. Ever since Eustice [7] first observed a secondary flow inside a curved pipe in his experiment, lots of studies on flow and heat transfer inside curved pipes have been performed. Naphon and Wongwises [8] presented a literature review on heat transfer and flow characteristics of single-phase and two-phase flow in curved tubes which have been used as one of the passive heat transfer enhancement techniques in several heat transfer applications. They categorized the curved tubes into three kinds, including helically coiled tubes and spirally coiled tubes and other coiled tubes, to make classification discussion. To a large extent, the flow and heat transfer enhancement mechanisms in curved pipes have been investigated and clarified a lot since before, but the mechanisms of the shell-side fluid flow and heat transfer are not clear yet. In engineering fields, the manufacturing of multilayer SWHXs remains some problems on the characteristics and mechanisms of the shell-side flow and heat transfer performance, which needs to further investigate the shellside performance of SWHXs. However, there are only scattered reports on investigations of the shell-side thermal-hydraulic performance in SWHXs. Ho et al. [9] experimentally investigated a spiral coil heat exchanger consisted of horizontal layers of spirally wound, finned tubes connected to vertical manifolds at the inner and outermost turns of each coil, which is widely used in air conditioning and heat recovery. Charts of the effectiveness vs. NTU (Number of Transfer Units) suitable for the heat exchanger design were also presented.

Ra Re Sij T U vm vt x, y, z

Rayleigh number Reynolds number Mean rate of strain tensor, s1 Temperature, K Overall heat transfer coefficient, W m2 K1 Maximum velocity of shell-side fluid, m s1 Inlet velocity of tube-side fluid, m s1 Coordinates, m

Greek symbols Helix angle,  Temperature difference, K 3 Dissipation of turbulent kinetic energy, m2 s3 l Thermal conductivity, W m1 K1 m Dynamic viscosity, Pa s mt Turbulent viscosity, Pa s y Kinematic viscosity, m2 s1 r Density, kg m3 F Heat transfer rate, W

a DT

Subscripts a Averaged value Varieties using shell-side equivalent diameter as Deq characteristic scale s Shell-side t Tube-side w Wall

Naphon et al. [10] investigated the heat transfer characteristics under cooling and dehumidifying conditions in a spiral coil heat exchanger which is consisted of a steel shell and a six-layer spirally coiled tube unit. They developed a mathematical model based on mass and energy conservation to determine the heat transfer characteristics and the results obtained from the model were in reasonable agreement with their experimental data. Neeraas et al. [11] constructed a test plant for measurements of local heat-transfer coefficients and frictional pressure drops on the shell side of LNG SWHXs. The heat transfer coefficients from the experimental results were compared with those from the Gnielinski formula [12], with an average deviation of 5%. For frictional pressure drop, a modified method from Barbe et al. [13] was employed, with an average deviation of 3%. Neeraas et al. [14] also conducted an experiment of the shell-side liquid falling film in LNG SWHXs to measure the shear flow of single phase steam, liquid film and two-phase fluid. The experimental results of heat transfer coefficients for gravity dominated liquid falling film flow were validated against the method from Bays and McAdams [15], with an average deviation of 7%. Jayakumar et al. [16] numerically calculated the mixed convective heat transfer in a helix coiled heat exchanger to obtain correlations for tube-side Nusselt number. The helix coiled heat exchanger had one helical pipe with two turns inside the shell. Also, Jayakumar et al. [17] described the variation of local Nusselt number along the length and circumference at the wall of vertically oriented helical coils with the aid of numerical simulation. Geometrical parameters such as pitch circle diameter, tube pitch and pipe diameter were varied to study their influence on the heat transfer and obtain the correlations for prediction of Nusselt number. Gupta et al. [18] experimentally studied the pressure drop characteristics of the tube-side and shell-side flow of cryogenic cross-counter flow coiled finned tube heat exchangers. All

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experiments were performed at room temperature in the Reynolds number range of 3000 to 30,000 for the tube side and 25 to 155 for the shell side. They proposed new correlations based on the experimental data for predicting the friction factors for tube side and shell side. Ghorbani et al. [19] implemented an experimental study on mixed convective heat transfer under various Reynolds number, curvature ratio and pitch, and made a discussion on the influences of various geometrical parameters on heat transfer performance. Different definitions of characteristic length were analysed and the shell-side equivalent diameter was taken as the most reasonable one. The correlation using the shell-side equivalent diameter is: 0:3 NuDeq ¼ 0:0041Ra0:4533 Re0:2 Deq Deq Prs , where 120 < ReDeq < 1200, 1.2  107 < RaDeq < 3.2  108. Mirgolbabaei et al. [20] numerically investigated the mixed heat transfer performance in a monolayer shell and helical heat exchanger. The influences of Reynolds number, Rayleigh number and dimensionless pitch on the heat transfer performance under coupled wall boundary condition were studied. The model agrees well with Ghorbani’s results and numerical correlations were obtained. Fernández-Seara et al. [21] investigated the heat transfer performance in a vertical helical coil heat exchanger by establishing a numerical model. The helical coil was inside a fluid storage tank and natural convection was considered as boundary condition for the outer surface of coil. Their results show that the Nusselt number increases with the increase of tube diameter. Moawed et al. [22] investigated the influences of various curvature and torsion rate on outside heat transfer coefficient under constant heat flux wall thermal BC. The experiment model was a vertical heat exchanger whose coil was wound by the hollow pipe inserted with electric heating wire. The range of the curvature (the ratio of coil diameter and tube diameter) is from 7.086 to 16.142, the torsion rate (the ratio of pitch and outer-diameter of tube) from 1.81 to 3.205 and the Reynolds number from 660 to 2300. It is found that the outside Nusselt number increases with the increases of curvature and torsion rate under the same Reynolds number. Yang et al. [23] experimentally studied the heat transfer in convection cooling section of pressurized coal gasifier with the membrane helical coils under high pressure. They selected high pressure single gas (He or N2) and their mixture (He þ N2) as the test media with the test pressure range from 0.5 MPa to 3.0 MPa. It is found that the working pressure is the most significant influencing factor of the convection heat transfer coefficient of high pressure gas. Furthermore, Zhao et al. [24] numerically investigated the flow and heat transfer characteristics of synthesis gas in membrane helical-coil heat exchanger under different operating pressures, inlet velocities and pitches. The realizable k-3 model was adopted to simulate the turbulent flow and heat transfer in heat exchangers. Their numerically heat transfer coefficients for heat exchangers are in good agreement with experimental values in Ref. [23]. The numerical results indicated that the syngas tangential velocity in the membrane helical-coil heat exchanger increases along the axial direction and is independent of the gas pressure, increasing with the axial velocity and axial pitch rise and decreasing with the radial pitch rise. Li et al. [25] established a three-dimensional numerical model for the SWHXs to investigate the effects of main geometry parameters on shell-side flow and heat transfer performance under constant temperature BC. It is found that large number of layers enhances the heat transfer but brings difficulties in manufacture and transportation, and the decrease of space bar thickness causes significant increases of heat transfer coefficient as well as flow resistance. Also, the tube number has little effect on the flow and heat transfer performance when the shell-side flow is fully developed.

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Fig. 1. Structure of a multilayer spiral-wound heat exchanger (SWHX).

Jamshidi et al. [26] experimentally analysed the enhancement heat transfer performance in shell and helical tube heat exchangers. In their experiments, cold fluid flowed in tube-side passage and hot fluid in the shell-side passage. Shell-side and tube-side heat transfer coefficients were separated by Wilson plot method to determine the optimum structure parameters and working conditions. It was concluded that large tube diameter, large pitch and large mass flow rate are beneficial for the heat transfer enhancement. Ferng et al. [27] investigated the effects of different Dean number (De) and pitch size on the thermal-hydraulic characteristics in a helically coil-tube heat exchanger using the computational fluid dynamics (CFD) method. The complicated phenomena, including the flow acceleration and separation in the shell side, the turbulent wake around the rear of a coiled tube, the secondary flow within the tube, and the developing flow and heat transfer behaviours from the entrance region, occurred in the helically coiledtube heat exchanger was captured from the results. Considering the insufficient investigation on mechanisms of the shell-side flow and heat transfer performance in multilayer SWHXs, the present work focuses on the modelling for the investigation on the shell-side fluid flow and heat transfer performance in multilayer SWHXs by experimental and numerical methods. First, a selfdesigned and self-manufactured SWHX model, whose main geometrical parameters are selected within the industrial application ranges, is tested in the experiment by providing a steady electric power on the walls of coils. Then based on the numerical model validated though the experimental results, the effects of different wall thermal BCs on the shell-side heat transfer in SWHXs are numerically investigated. It includes the shell-side heat transfer under constant heat flux and constant temperature wall thermal BC, and the conjugate heat transfer which takes both the shell-side and the tube-side convection heat transfer as well as the heat conduction of the wall into consideration. 2. Characteristics of spiral-wound heat exchangers The SWHX is a typical shell-and-tube heat exchanger and has quite a complex structure. An outer shell tightly encloses several layers of spirally wound coils inside it. A centre cylinder is configured in the middle of the shell to fix the coils and support the weight of the coils. In industrial application, the diameter of the spirally coiled tubes is selected within a range of 8 mme12 mm. The metallic space bar is selected as 1 mme5 mm in thickness and a thickness of 2.5 mm or larger is commonly used to guarantee a better endurance for high pressure drop of the shell-side fluid. Fig. 1 portrays a brief configuration of a multilayer SWHX. For the SWHXs, the main component for the heat exchange is the spirally wound coils. Coils are wound in reverse directions between adjacent layers. That is, the direction of spiral in one layer of coils is left-hand, and then the adjacent layers of the coils are right-hand. The metallic space bars are utilized to fix the coils to avoid loose connection inside the shell. Taking coils with three layers for example, detailed structure of coils [28] is shown in Fig. 2.

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X. Lu et al. / Applied Thermal Engineering xxx (2014) 1e12 Table 1 Multilayer spiral-wound heat exchanger specifications. No. Ds,o/mm Ds,i/mm Dt/mm Dc/mm Pl/mm Turns Helix Nc Helix Angle/ direction 1 2 3

Fig. 2. Structure of spirally wound coils in a multilayer SWHX [27].

The tube-side fluid flows inside the coils and the shell-side fluid flows outside the coils, which is usually in the manner of counter flow pattern. The tube-side convection, the shell-side convection and the heat conduction through the walls of coils act simultaneously in the SWHX, which is regarded as the conjugate heat transfer in this paper.

243 243 243

159 159 159

10 10 10

175 201 227

20.85 19.16 18.03

3.6 3.1 2.8

8.53 8.53 8.53

4 5 6

Left Right Left

geometrical parameters is within the industrial application ranges. The geometrical parameters of the experimental model are shown in Table 1. The coils inside the self-designed and self-manufactured multilayer SWHX are shown in Fig. 4. The coils are bent using the material of copper electric heating pipes and are enclosed by a cylinder shell to provide a shell-side fluid passage. Via applying fixed electric power for the coils, the constant heat flux thermal BC is closely approached. In the present work, an electric power of 950 W is provided and the total area of the outer surface of the coils is 0.95 m2, which makes a constant heat flux of 1000 W m2 on the outer walls of coils.

3. Experimental system and procedure 3.2. Experimental system 3.1. Multilayer spiral-wound heat exchanger manufacturing Fig. 3 explains the basic geometry parameters of a multilayer SWHX. The spirally coiled pipe has an inner diameter of dt and an outer diameter Dt. The longitudinal distance between the two adjacent turns of a spirally coiled pipe is Pl, which is known as pitch. The horizontal distance between two longitudinal central axes of two adjacent layers of coils is Plr. The angle that projection of one turn of the coil makes with a plane perpendicular to the axis, is named as the helix angle, a. The space bar thickness is B. The coil has a diameter of Dc (measured between the centre axes). The outer diameter of the centre cylinder and the inner diameter of the shell are Ds,i and Ds,o, respectively. An effective height for the heat transfer, H, is defined when the height of an SWHX is needed. A set of multilayer SWHX is designed and manufactured. The effective height of the heat exchanger H is 300 mm, and the straightening length between the entrance and outlet is 100 mm. The present SWHX has 4 pipes in the innermost layer (the first layer, Nc ¼ 4), 5 pipes in the middle layer (the second layer, Nc ¼ 5) and 6 ones in the outermost layer (the third layer, Nc ¼ 6). The numbers of turns in each layer are 3.6, 3.1 and 2.8, respectively. In engineering applications, the space bar thickness ranges from 1 mm to 4 mm, the helix angle 5 e15 , the outer diameter of pipe 8 mme19 mm, and the pitch of coil 8 mme20 mm. The selection of

Fig. 3. Basic geometry parameters of a multilayer SWHX.

The experiment study is carried out in an open wind tunnel laboratory. The test section of SWHX is connected to an open system which is consisted of entrance, straightening section of inlet and prolongation section of outlet, blower and measure instruments, providing necessary flows through the shell of the system and the required measure facilities. The wind tunnel testing system is illustrated in Fig. 5. Air is employed as the shell-side working fluid. Nine copper-constantan thermocouples are evenly set on the inlet and outlet of the test system, respectively, to measure the inlet and outlet fluid temperature. A glass rotameter is employed to measure the volume flow rate of the air. Copper-constantan compensating conductors are connected to the data acquisition board and temperature-constant furnace is used to achieve the cold end compensation. Microbarometer with a minimum scale of 2 Pa at small flow rates and U-tube water column manometer at big flow rates are used to obtain the pressure data. The electric power applied for the pipes is measured by a wattmeter. A voltage regulator, whose range is 0 Ve220 V, is used for regulating the value of electric power. An ammeter is connected in the electric circuit to check whether the current is overload or not for the safety of the experiment system.

Fig. 4. Coils in the self-manufacturing SWHXs with three layers.

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5

Fig. 5. Experimental setup.

3.3. Experimental procedure Heat insulation cotton with a thickness of 2 cm is wrapped around the shell of the test section to minimise the heat loss. Much attention is paid to the heat balance to ensure the steady state of heat exchange before writing down the data during implementing the experiment. The energy gain of the air and the electric power are used to calculate the heat balance error, which is within 5% in each trials of the test. During the experiment process, the heat transfer rates of the pipes keep constant (1000 W m2) under a steady electric power, and the volume flow rate of the air varies from 60 m3 h1 to 160 m3 h1. More than 3 h is needed to attain a steady state at the beginning of the experiment and the steady states of the following trials are achieved within 2e3 h.


 v v vu vp m k  ðrui uk Þ ¼ vxi vxi vxk vui

(2)

Energy:


 l vT v v ðrui TÞ ¼ vxi vxi cp vxi

(3)

Transport equations for turbulent kinetic energy k, and energy dissipation rate 3 in the realizable k-3 model are: Turbulent kinetic energy:

v v ðrkui Þ ¼ vxi vxj




mþ



!

mt vk þ Gk  r3 sk vxj

(4)

Energy dissipation rate: 4. Numerical simulation Based on the simplified model validated by the experimental results, the numerical simulations under three different wall thermal BCs are performed to study the effects of the wall thermal BCs on the shell-side thermal-hydraulic performance. 4.1. Governing equations and numerical model The double precision segregated 3D version method has been employed to solve the governing equations. The SIMPLEC algorithm is used for pressureevelocity coupling with a skewness correction of 1. For momentum and energy equation, second order upwind scheme is used and turbulent kinetic energy, turbulent dissipation, power law scheme is used. The flow is considered to be steady and the thermal properties of fluids are assumed constant. The realizable k-3 turbulence model with standard wall functions is used for numerical simulations. In the present paper, a convergence criterion of 104 is used for continuity, 105 for x, y and z velocities. The convergence criterion for energy equation is 107, while that for the k and 3 is 104. The three-dimensional governing equations for mass, momentum and heat transfer differential equations in the SWHXs could be written in the Cartesian coordinate system as: Continuity:

v ðrui Þ ¼ 0 vxi Momentum:

(1)

v v ðr3 ui Þ ¼ vxi vxj

"




#

2 m v3 3 pffiffiffiffiffi mþ t þ rC1 S3  rC2 s3 vxj k þ y3

(5)

where

!   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h k 1 ui uj ; h ¼ S ; S ¼ 2Sij $Sij ; Sij ¼ C1 ¼ max 0:43; þ : hþ5 2 xj xi 3 In Equations (4) and (5), mt is determined by mt ¼ rCmk2/3 , where Cm is the is a function of the mean strain and rotation rates, the angular velocity of the system rotation and the turbulence fields [29]. Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients and is evaluated by Gk ¼ mt$S2. The model constants in the present study are set as C2 ¼ 1.9, sk ¼ 1.0 and s3 ¼ 1.2. Three different wall thermal BCs are investigated. It includes the shell-side heat transfer under the constant heat flux and constant temperature wall thermal BC, and the conjugate heat transfer which takes both the shell-side convection heat transfer and the tube-side heat transfer as well as the wall conduction into consideration. In the case of conjugate heat transfer calculation, the inner and outer walls of the coils are defined as a coupled wall BC for the energy transfer from the hot fluid (inside the tubes) to the cold fluid (in the shell). For momentum equation, they are treated as no-slip ones. The tube-side fluid inlet is velocity inlet BC, varying from 2.04 m s1 to 6.12 m s1, and the tube-side fluid outlet is set as pressure outlet BC.

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Fig. 6. Three-dimensional geometrical model of coils.

In the case of the constant temperature BC, the outer walls of the coils are set at a constant value of 353.15 K. In the case of the constant wall heat flux, the outer walls of the coils are varied at constant values of 40,000 W m2 to 70,000 W m2. For all the cases, the shell-side fluid inlet is taken as mass flow rate BC, varying from 0.18 kg s1 to 0.98 kg s1. And the shell-side fluid outlet is set as pressure outlet BC. The inner wall of the shell and outer wall of centre cylinder are taken as no-slip adiabatic ones. 4.2. Grid generation In this study, the geometrical parameters of the numerical model are the same as those of the experimental model. But the inlet and outlet are prolonged much longer than the test heat exchanger to avoid the entrance effect and reversed flow during the numerical simulations. Also, the wall thickness of pipes is considered under the coupled wall BC in order to calculate the conjugate heat exchange from the hot fluid inside the pipes to the cold fluid in the shell. Fig. 6 shows the coils of the geometrical model.
Mesh for shell-side domain In the numerical model, the unstructured mesh is generated for the shell-side fluid area due to its highly irregular structure. Four sets of meshes for shell-side volume are generated with the nodes number of 599,264, 760,668, 971,899 and 1,503,612, respectively. A grid independency of the model is studied for the shell-side domain. The optimum mesh is selected as the third one with 971,899 nodes, for the deviations of the shell-side heat transfer rate and pressure drop are below 0.3% and 4%, respectively, which is shown in Fig. 7.
Mesh for tube-side domain and hybrid mesh generation Structured meshes are generated for tube-side volume, both in solid domain within the wall thickness and fluid domain inside the pipes. Boundary layer meshes near the inner walls for tube-side fluid domain are considered. Grid refinements in the radial

direction (shown in Fig. 8(a)) and the longitudinal direction (shown in Fig. 8(b)) of the tube side are implemented to make a grid independency check. Fig. 9 shows the grids of the tube side for the numerical analysis domain and the enlarged details of meshes on the coils. Hybrid mesh is the combination of structured and unstructured grids, which is fit for complex physical structures with both regular and irregular parts. The grids on the interface between structured and unstructured mesh should correspond one to one for information exchange during numerical iterations. So much attentions should be paid to the quality of mesh on the interface between structured and unstructured ones. Conjugate heat transfer performance in the SWHXs is calculated by merging the grids of the shellside and tube-side domains in this study. And the mesh is shown in Fig. 10. The total number of nodes of hybrid meshes is 6,497,809. 4.3. Data reduction Since the tube configuration in the SWHX varies continuously between in-line which gives a minimum radial distance and staggered which gives a maximum one [11]. The minimum flow area of the shell-side in the multilayer SWHX, As,min, is suggested to calculate by Naphon P. et al. (2006) [8],

As;min ¼ p$




 Ds;i þ Ds;o $Nlay $B 2

(6)

Then the maximum shell-side fluid velocity, vm, could be calculated. Reynolds number of the shell-side fluid in this study is defined as,

Res ¼

r$vm $Dt m

(7)

Similar to Reynolds number for flow in pipes, Dean number is used to characterize the flow in a curved pipe. The Dean number, Det in this study is defined as,

r$vt $dt Det ¼ m

sffiffiffiffiffiffi dt Dc

(8)

According to Table 1, the coil diameters, Dc, of layer 1, layer 2 and layer 3 are 175 mm, 201 mm and 227 mm, respectively. Here, we define the averaged value of Dc ¼ 201 mm to calculate the Dean number of the multilayer spirally wound coils. The heat absorbed by the shell-side fluid, Fs can be calculated by the inlet and outlet temperature and mass flow rate. For the heat transfer experiment, the uncertainty of the shell-side heat transfer rate dependent on the precision of glass rotameter and thermocouples is less than 3% and pressure drop dependent on the precision of microbarometer and thermocouples is less than 0.5%.

Fig. 7. Grid independence check for shell-side domain.

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7

Fig. 8. Grid independency for tube-side domain.

For data reduction method in the numerical simulations of conjugate heat exchange, the average heat transfer rate of the heat absorbed by the shell-side fluid, Fs and the heat released by the tube-side fluid, Ft is calculated by,

Fa ¼

Fs þ Ft

(9)

2

The overall heat transfer coefficient based on the shell-side heat exchange area of coils is calculated by,

U ¼

Fa

(10)

Ao $LMTD

where LMTD is the logarithmic mean temperature difference of the multilayer heat exchanger.

LMTD ¼

ðDT2  DT1 Þ   T2 ln D DT

(11)

1

where DT2 is the temperature difference between hot fluid inlet and cold fluid outlet, DT1 is the temperature difference between hot fluid outlet and cold fluid inlet. The relationship among the overall heat transfer coefficient, the shell-side heat transfer coefficient and the tube-side heat transfer coefficient are as follows:

1 Ao Ao lnðDt =dt Þ 1 ¼ þ þ U hs Ai ht 2plL

Fig. 9. Grids of the tube-side domain (fluid and solid volume).

(12)

Fig. 10. Grids of multilayer SWHX.

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X. Lu et al. / Applied Thermal Engineering xxx (2014) 1e12

Fig. 12. Pressure drop of numerical vs. experimental results.

Fig. 11. Comparison between numerical simulations vs. experiment.

The Wilson plot method is employed to separate the tube-side and shell-side heat transfer coefficients for conjugate heat transfer analysis. It can be assumed that the heat transfer coefficient of the tube-side fluid is constant when the tube-side flow rate and mean temperature difference approximately keep constant. Then the shell-side heat transfer coefficient is assumed to have a relationship with shell-side velocity as,

hs ¼ Cvnmax

(13)

where the C and n are constant value to be determined. By submitting Equation (13) to (12), the unknown constants, C and n, could be determined by data fitting and the shell-side heat transfer coefficient can be calculated at last. The Nusselt number of the shell side is defined as follows,

Nus ¼

hs $Dt

l

(14)

5. Results and discussion 5.1. Numerical model validation with experiment results To determine whether the numerical method is credible to investigate the complex shell-side flow and heat transfer performance in the multilayer SWHXs, a numerical calculation is

implemented. The outer walls of the pipes are defined as the wall BC with a constant heat flux of 1000 W m2, which is the same as the electric power in the experiment. Air inlet flow rate and temperature are set the same value as the experiment value. Fig. 11(a) compares the temperature differences between the inlet and the outlet of the experiment with those of the numerical simulations and Fig. 11(b) compares the shell-side average heat transfer rate. The deviation of the temperature differences between the experiment and the simulation is within 6.4%, while that of the shell-side heat flux is 7.8%. The maximum deviation of the average heat transfer rate in shell side is 6%. As is shown in Fig. 12, the pressure drops from the numerical simulation are lower than those from the experiment. It could be caused by the other disturbing stuffs set inside the flow passage of the experimental model such as the thermocouples and casing gaskets. The maximum and average errors of the pressure drop between the numerical simulation and the experiment are 14.8% and 9.6%, respectively, which can be accepted in the engineering applications. Therefore, it can be considered that the numerical model agrees well with the experiment results and it can be adopted to do further analysis. 5.2. Characteristics of conjugate heat transfer in multilayer SWHXs The methodology of numerical analysis for conjugated heat transfer has been validated by calculating the water-to-water heat transfer performance through the metal tube walls of curved tube with two turns inside a water tank. The average deviation of the overall heat transfer coefficient between our calculation and Jayakumar’s experiment in their helically coiled heat exchanger is within 5% (as shown in Fig. 13). So the use of the numerical modelling for the study of conjugate heat transfer can be employed with confidence. In the present investigation, the working fluid in the conjugate heat transfer performance in the multilayer SWHXs is water. Cold water flows in the coils with an inlet temperature of 293.15 K and hot water in the shell with an inlet temperature of 353.15 K. The mass flow rates of the shell-side fluid are varied from 0.18 kg s1 to 0.98 kg s1. The tube-side fluid velocities vary within the range of 2.04 m s1 to 6.12 m s1, corresponding to the range of the tube-side Dean number from 4800 to 14,560. And the fluid inside the pipes is treated as in the turbulent region according to the critical value of Schmidt’s suggestion [30]. Take one of the cases (the hot inlet velocity is 3.06 m s1 and shell-side mass flow rate is 0.54 kg s1) as example, the features of the velocity, temperature and pressure are visualized as follows.

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X. Lu et al. / Applied Thermal Engineering xxx (2014) 1e12

Fig. 13. Numerical validation for conjugate heat transfer by experimental results in Ref. [16].

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Fig. 16. Velocity profile and temperature profile on the cross-section of coils (tube outlet, z ¼ 0 plane).

Fig. 17. Contours of temperature of shell-side fluid. Fig. 14. Pathlines in the multilayer SWHX.

Fig. 14 displays the pathlines with temperature of both the shellside fluid and the tube-side fluid. The directions of arrows in the image reveal the flow directions of hot and cold fluid. It can be seen that the hot water in the pipes flows spirally along the coils and the spiral flowing direction alternates from left to right among adjacent layers. The cold fluid enters the shell inlet from the opposite direction, flows across the confined flow passages outside the tube bank and gets heated by tube-side fluid. Fig. 15 shows the contours of velocity magnitude on z ¼ 0 plane. The profiles reveals that high velocities are occurred in the outer side of coils and low velocity in the inner side. The velocity and temperature profiles at the exit of the innermost coils (the position

Fig. 15. Contours of velocity magnitude of tube-side fluid (z ¼ 0 plane).

inside the small box in Fig. 15) of the tube-side fluid are shown in Fig. 16. It can be readily seen that comparing with the flows in the straight tubes, the velocity and the temperature of the helical tubes are larger on the outer side of the tube and relatively smaller on the inner side because of centrifugal force induced by helix structure. As is shown in Fig. 17, the cold water in the shell side is heated by hot fluid in the pipes through tube walls, so the temperature of shell-side fluid increases along the flow passage and temperature surround the tube walls is relatively high. Fig. 18 displays the

Fig. 18. Contours of static pressure of tube-side fluid.

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X. Lu et al. / Applied Thermal Engineering xxx (2014) 1e12

Fig. 19. Variation of average surface heat flux on inner and outer walls of coils with the increase of shell-side mass flow rate under different tube-side velocity.

Fig. 21. Variation of overall heat transfer coefficient with the increase of shell-side mass flow rate under different tube-side velocity.

contours of the static pressure of the tube-side fluid in the three layers of coils. The tube-side fluid flows into the heat exchangers from positive y direction to negative y direction with the hot fluid pressure drops along the flow passage by almost 4 MPa. Fig. 19 shows the average surface heat flux both on the inner walls and outer walls of the tubes. Under the specified shell-side mass flow rate, the average surface heat flux increases with the increase of the tube-side fluid velocity. Fig. 20 shows the variation of the average heat transfer rate with various shell-side mass flow rates and tube-side inlet velocities. Under the specified shell-side mass flow rate, the average heat transfer rate gets larger when tube-side velocity increases. Also, under larger tube-side velocities, the average heat transfer rate changes more rapidly with the increase of the shell-side mass flow rate. When the mass flow rate of shell-side fluid is 0.18 kg s1, the average heat transfer rate changes little with the increase of the tube-side velocity. As shown in Fig. 21, similar curves can be found in the variation of the overall heat transfer coefficients. But the increase of velocity in tube-side fluid can enlarge the overall heat transfer coefficient under the conditions when shell-side mass flow rate is 0.18 kg s1. Fig. 22 shows that the shell-side heat transfer coefficient changes linearly from 2800 W m2 K1 to 12,000 W m2 K1 with the shell-side Reynolds number ranging from 500 to 3500 and the tube-side Dean number from 4800 to 14,560. The corresponding Nusselt number is shown in Fig. 23. Based on the correlations available in the literature, it is proposed that the Nusselt number for heat transfer can be represented in the following form,

Nus ¼ a$Rebs

Fig. 20. Variation of average heat transfer rate with the increase of shell-side mass flow rate under different tube-side velocity.

(15)

where a and b are constants to be determined. By using Origin software, the following correlation is generated by linear fitting under logarithmic coordinates to estimate the shell-side Nusselt number with the assumption of the constant properties,

Nus ¼ 0:179$Re0:862 s

(16)

which is applicable for 500 < Res < 3500. 5.3. Effects of wall thermal BCs on heat transfer performance The shell-side heat transfer performance in multilayer SWHXs is numerically investigated under three thermal BCs on the tube wall: constant temperature BC, constant heat flux BC and coupled wall BC. Under constant temperature BC, the outer walls of the tubes are specified as 353.15 K (Tw ¼ 353.15 K). Under constant heat flux BC, the outer walls of the tubes are set as 40,000 W m2, 50,000 W m2, 60,000 W m2 and 70,000 W m2 (qw ¼ 50,000 W m2e80,000 W m2). Under the coupled wall BC, the solid domain on the walls, the tube-side fluid domain and the shell-side fluid domain are all considered. The calculation method of the heat transfer coefficient differs from each other among the three wall thermal BCs, which brings

Fig. 22. Variation of shell-side heat transfer coefficients with the increase of shell-side mass flow rate under different tube-side velocity.

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Fig. 23. Variation of shell-side Nusselt number with the increase of shell-side Reynolds number under different tube-side velocity.

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Fig. 25. Evaluation heat transfer rate vs. shell-side Reynolds number under three different wall thermal boundary conditions, including constant temperature BC (Tw ¼ 353.15 K), constant heat flux BC (qw ¼ 50,000 W m2e80,000 W m2) and coupled wall BC (vt ¼ 2.04 m s1e6.12 m s1).

different evaluation criterion. To determine the influence of different wall thermal BCs on the heat transfer performance in SWHXs, an evaluation heat transfer coefficient for the shell-side fluid is employed, where all the values used in the coefficient are from the shell-side variables.

heva ¼

F

s

Ao $ tw  ts;in

(17)

where tw is the average temperature on the outer wall of layer 1, layer 2 and layer 3; ts,in is the inlet temperature of the shell-side fluid, Ao is the heat transfer area of the outer walls. As is shown in Fig. 24(a), the evaluation heat transfer coefficients almost keep constant when the heat flux on the outer tube walls varies from 40 kW m2 to 70 kW m2. Also, as is shown in Fig. 24(b), the evaluation heat transfer coefficients have little variations when the inlet velocity of tube-side fluid varies from 2.04 m s1 to 6.12 m s1 under specified shell-side flow flux. The comparison of evaluation heat transfer coefficient among three wall thermal BCs is shown in Fig. 25. Take the heat transfer coefficients under the coupled wall BC as reference values, the maximum relative deviation between the results under the constant temperature BC and those under the coupled wall BC is 3.5%. The relative deviation between the results under the constant heat flux BC and those under the coupled wall BC reaches to 11.4% when the mass flow rate of shell-side fluid is 0.18 kg s1 (corresponding to the Reynolds number of 576.5), while no more than 4.3% when the Reynolds number of shell-side fluid increases from 1100 to 3200. Also, the value of the constant heat flux BC is larger than that of the coupled wall BC within 576.5 to 1730 of Res, while smaller after 1730 to 3138 of Res. Considering the variation trend and relative deviation, the constant temperature BC is better than the constant heat flux BC for simplifying the conjugate heat transfer model in the present working condition, and the relative deviations get smaller when tube-side velocity increases. 6. Conclusions

Fig. 24. Comparison between evaluation heat transfer coefficient.

This paper focuses on the shell-side fluid flow and heat transfer in multilayer SWHXs by the experimental and numerical methods. The experimental investigation on the shell-side fluid flow and heat transfer performances of a self-designed and self-manufacturing SWHX with 3-layer coil inside the cylinder shell is performed.

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X. Lu et al. / Applied Thermal Engineering xxx (2014) 1e12

Then the numerical simulation with the same specifications and working conditions as the experiment is implemented. Further, since both tube-side and shell-side convective heat transfer and wall conduction are considered, the grids number for conjugate heat transfer is massive, consuming large amount of computing costs. To investigate the effects of different wall thermal BCs on the shell-side heat transfer coefficient, the results of numerical investigations under constant temperature with wall temperature of 353.15 K and constant heat flux, varying from 50,000 W m2 to 80,000 W m2, are compared with those under the conjugate heat transfer situation. The deviations of the shell-side heat transfer coefficients under the constant temperature BC and under the constant heat flux BC are acquired. It is found that the constant temperature BC has a small deviation of 3.5%, while the maximum deviation of constant heat flux BC is 11.4%. Besides, the number of grids of numerical model in conjugate heat transfer is quite large and the influence of tube-side fluid on the shell-side heat transfer coefficient is relatively small. So the constant temperature wall BC can be employed to numerically study the thermal-hydraulic performance of the SWHX, considering the balance of improving the calculation accuracy and reducing the computing consumption. Acknowledgements This work is supported by the China National Funds for Distinguished Young Scientists (No. 51025623) and the National Natural Science Foundation of China (Grant No. 51276139). References [1] B. Sun, The spiral-wound heat exchangers in Linder rectisol facilitates, in: The Conference of Gas Purification Information Website, Proceedings, 2008. Chengde, China (in Chinese). [2] Y.L. Du, Y.D. Chen, X. Zhang, J.L. Wang, B. Chen, Domestic manufacturing research of large multi-stream spiral-wound heat exchanger, Press. Contain. 21 (2004) 26e29 (in Chinese). [3] J.W. Li, Design and manufacturing of high-pressure spiral-wound heat exchangers, in: The 11th Academic Conference Proceedings of National Mechanical Industry on Industrial Gas Separation Facilitate Technology, 1998, pp. 96e100 (in Chinese). [4] X. Zhang, Energy-saving and industrial example of the high-effected woundtube heat exchanger, Press. Contain. 25 (2008) 54e57 (in Chinese). [5] X. Zhang, Y.D. Chen, J.L. Wang, Engineering applications of wrap-round tubular heat exchangers, Large Scale Nitrogenous Fertil. Ind. 27 (2004) 9e11 (in Chinese). [6] H.Y. Kan, Design of the spiral tube heat exchangers, Large Scale Nitrogenous Fertil. Ind. 31 (2008) 145e148 (in Chinese). [7] J. Eustice, Experiment of streamline motion in curved pipes, Proc. Royal Soc. Lond. Ser. A 85 (1911) 119e131. [8] P. Naphon, S. Wongwises, A review of flow and heat transfer characteristics in curved tubes, Renew. Sustain. Energy Rev. 10 (2006) 463e490.

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Please cite this article in press as: X. Lu, et al., Shell-side thermal-hydraulic performances of multilayer spiral-wound heat exchangers under different wall thermal boundary conditions, Applied Thermal Engineering (2014), http://dx.doi.org/10.1016/j.applthermaleng.2014.02.053