Accepted Manuscript Numerical investigation of shell-side performance for shell and tube heat exchangers with two different clamping type anti-vibration baffles Chulin Yu, Zhiwen Ren, Min Zeng PII: DOI: Reference:
S1359-4311(17)34154-6 https://doi.org/10.1016/j.applthermaleng.2018.01.029 ATE 11683
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
20 June 2017 18 December 2017 9 January 2018
Please cite this article as: C. Yu, Z. Ren, M. Zeng, Numerical investigation of shell-side performance for shell and tube heat exchangers with two different clamping type anti-vibration baffles, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/j.applthermaleng.2018.01.029
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Unmarked Manuscript for Applied Thermal Engineering (ATE-2017-3543-R1)
Numerical investigation of shell-side performance for shell and tube heat exchangers with two different clamping type anti-vibration baffles Chulin Yu, Zhiwen Ren, Min Zeng * Key Laboratory of Thermo-Fluid Science and Engineering, MOE, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, P.R. China *Corresponding author: Tel & Fax: +86-29-82665581, E-mail:
[email protected]
HIGHLIGHTS (1) A new type of hexagon clamping anti-vibration baffle (HCB) is proposed. (2) The flow structure and heat transfer performances of two different clamping type anti-vibration baffles are compared. (3) The effect of geometry parameters on the thermo-hydraulic characteristics is numerically investigated.
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ABSTRACT Inspired by curve-rod baffle shell and tube heat exchanger (CRB-STHX), a new type of hexagon clamping anti-vibration baffle shell and tube heat exchanger (HCB-STHX) is proposed to overcome the vibration vulnerability of round rod baffle shell and tube heat exchanger (RRB-STHX). The assembling processes of HCB-STHX and CRB-STHX are illustrated. The flow and heat transfer characteristics on shell side are compared and analyzed numerically by CFD method. The effects of several factors such as velocity, baffle distance, baffle width, baffle profile, and baffle layout on thermal-hydraulic performance are investigated in full developed turbulence regime with Reynolds numbers ranging from 10,849 to 32,547. The results indicate that HCB is more suitable for large and heavy tube bundle due to its better rigidity; HCB has a better heat transfer enhancement but a poorer overall performance (indexed by PEC) than CRB; the baffle distance has a significant effect on thermal-hydraulic performance while the baffle width does not; with PEC concerned, the shape of the profile of CRB is superior to that of HCB; compared with baffle in parallel layout, baffle in perpendicular layout can enhance heat transfer, while the former is convenient for manufacturing and assembling. Keywords: Rod baffle heat exchangers; Thermal-hydraulic performance; Clamping type; Anti-vibration; Baffles
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Nomenclature A
Area, mm2
Ain
Flow cross-section area, mm2
Ao
Heat transfer surface area of tube, mm2
Ap
Area of profile of HCB/CRB, mm2
a
Length , mm
b
Baffle width , mm
c
Length, mm
cp
Specific heat capacity, J/(kg·K)
do
Outer tube diameter, mm
Dh
Hydraulic diameter, mm
f
Average friction factor
h
Convection heat transfer coefficient, W/(m2·K)
k
Turbulence kinetic energy
L
The unit duct length along the flow direction , mm
Lb
Baffle distance, mm
p
Pressure, Pa
Pt
Tube pitch, mm
Pr
Prandtl number
PEC
Performance evaluation criterion
Δp
Pressure drop, Pa
Re
Reynolds number
T
Log-mean temperature difference, K
T
Temperature, K
tb
Baffle thickness, mm
u
Velocity, m·s-1
Vin
Inlet velocity, m·s-1
y+
Non dimensional distance from wall
Greek symbols ρ
Density, kg·m-3
μ
Dynamic viscosity, kg/(m·s)
λ
Thermal conductivity, W/(m·K)
ε
Turbulence kinetic energy dissipation rate
Subscripts eff
Effective term
3
in
Inlet
i,j
Tensor
out
Outlet
R
Rod
w
Wall
Abbreviations CRB
Curved rod baffle
HCB
Hexagon clamping baffle
RRB
Round rod baffle
TKE
Turbulence kinetic energy
1. Introduction The intensification of heat transfer is an important societal challenge in terms of energy saving and materials, sustainable development, thermal control, compactness, etc. [1]. As for the heat transfer enhancement of shell and tube heat exchanger (STHX) [2], many different baffles, such as, single segmental baffle [3], trefoil-hole baffle [4], helical baffle [5], and round rod baffle (RRB) [6] have been proposed. Single segmental baffle heat exchanger (SG-STHX) has many disadvantages, such as high pressure drop, flow induced vibration, flow dead zone, and so on. Trefoil-hole baffle heat exchanger (TH-STHX) is widely used in nuclear power system. The shell side fluid flows longitudinally through the gaps between the orifice edges and tube walls [7]. It has good thermal-hydraulic performance while being less liable to foul, eliminates stagnant recirculation zones and avoids flow induced vibration. Helical baffle heat exchanger (HL-STHX) has led to some advantages such as high heat transfer efficiency and low flow resistance [8]. Nevertheless, it is difficult to manufacture the trefoil-hole and helical baffle. Round rod baffle heat exchanger (RRB-STHX)
proposed
by
Phillips
Petroleum 4
company
exhibits
good
thermal-hydraulic performance [8]. It is found a broad application with advantages of higher heat transfer efficiency, lower pressure loss, and better anti-fouling performance and so on compared to SG-STHX. However, the RRB-STHX also has some drawbacks. It was reported that several RRB-STHXs encountered in tube leakage problem just as shown in figure 1 [9]. Efforts were then made to find the cause. It was found that micro vibration wear may be one of the most important factors to contribute the above problem, because the rod could not give a sufficient support for the tube. Take the RRB-STHX with square tube layout as an example, the rod arrangement design is shown in figure 2. Some failure explanation can be made based on the two facts: on one hand, one rod baffle supports the tube in a single direction by point contact, which is prone to fretting; on the other hand, natural frequency used in flow induced vibration calculation will be decreased to a large extent if one or two support lose function because of inevitable manufacture deviation. In order to solve the problems of RRB mentioned above, a curve-rod baffle (CRB) with better vibration-preventing performance was proposed by Li et al. [10] and Yan et al. [11]. It was found that the CRB not only can provide a full support for the tube bundle, but also enhance the heat transfer in the low Reynolds. However, the effects of baffle width, baffle profile, and baffle layout on the thermal-hydraulic performance have not been clarified yet. A new anti-vibration baffle called round rod with arc cuts baffle (RRACB) on the basis of conventional RRB was numerically studied by You et al. [12]. It was found that the RRACB could improve the
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thermal-hydraulic performance. However, it is still difficult and time-consuming to manufacture RRACB in factory as the arc cuts need to be machined with high precision in order to keep a good contact with the tube. Inspired by the fixed strip of economizer used in boiler, a new type of hexagon clamping anti-vibration baffle (HCB) is proposed. Its sketch is shown in figure 3. For a typical tube bundle in the non-staggered alignment supported by CRB or HCB, the assembling process is shown in figure 4 (a) and (b) respectively. From figure 4, an obvious difference can be found that HCB has a more assembling process than CRB, which is “welding two triangle shape strip to form HCB”. This process gives an extra stiffness to HCB compared with that of CRB. As a result, it makes the HCB more suitable for large and heavy tube bundle whose diameter dimension in the range of 3600 mm and weight in the range of 100 tons. For a typical tube bundle in the non-staggered alignment, the profiles of CRB and HCB are shown in figure 5 (a) and (b) respectively. Corresponding structural parameters are defined as follows: tb=3 mm, do=25 mm, Pt=32 mm, a=10 mm, c=10 mm, R1=11.5 mm, R2=8.5 mm). It can be seen from figure 5 that CRB gives a surface contact with the tube, while the HCB gives a line contact with the tube. The force between the tube and the CRB or the HCB can be decreased as the contact area is larger compared with that of RRB which supports the tube only by point contact, thus the abrasion between the tube and the CRB or the HCB can be eased. It is worth noting that the CRB has a better anti-vibration effect than the HCB, as the contact area of the CRB is much larger that of the HCB. This means that the CRB can be used
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in the environment with high risk of tube vibration failure. Although experimental investigation of thermal-hydraulic performance of STHXs is considered to be convincing and accurate, the experiments are costly and time-consuming. It is not always practical and necessary to conduct a great number of experiments. On the contrary, numerical simulation by CFD is convenient and efficient. In the past decades, many researches numerically studied different STHXs based on CFD and obtained many inspiring results. Yang et al. [13] systemically compared four modelling approaches used for numerical simulation of RRB-STHX: the unit model, the periodic model, the porous model and the whole model. Dong et al. [14] simulated a flow unit channel model of RRB-STHX and compared their results with both correlations and experiments. Liu et al. [15] applied a unit model for a new longitudinal flow STHX called the rod-vane compound baffle heat exchanger and compared with the rod-baffle heat exchanger. Their results demonstrated that the unit model ignores the impingent effects on the tube bundle caused by the inlet flow on the shell-side. However, unit model can get a good balance between precision and computer resources. The thermal-hydraulic performance of CRB-STHX and HCB-STHX may be quite different due to their different structure. The designer may be facing the problem that how to decide between these two types. However, to the best of the author’s knowledge, there are not any open literatures to discuss this problem. In the present study, the steady flow numerical models of CRB-STHX and HCB-STHX are established to investigate the shellside heat transfer and pressure drop characteristics.
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The flow structure and field distribution are analyzed. The effects of baffle distance, baffle width, baffle profile, baffle layout, etc. are investigated in detail. 2. Numerical method 2.1 Physical model To simplify numerical simulation while still keep the basic characteristics of the process, following assumptions are made: (1) the shell-side fluid is water with constant thermal properties, the corresponding parameters are presented in Table 1; (2) the fluid flow and heat transfer processes are turbulent and in steady-state; (3) the leak flow between the baffle and the shell is neglected; (4) the heat exchanger is well insulated; (5) the viscous heating is neglected due to the limited fluid velocity and incompressible medium assumption; (6) the effect of gravity is negligible. It is worth noting that the baffle-shell leak flow can greatly reduce the average heat transfer and pressure drop for SG-STHX [16]. However, the ignoring leak flow will not have a significant effect on the thermal-hydraulic performance comparison results of RRB-STHX, CRB-STHX and HCB-STHX, as we assume that the leak flow passages of them are all the same. Based on the above assumption, a periodic flow unit channel of a non-staggered tube bundle is taken as the simplified model of the shell-side to perform numerical simulation. The schematic diagram of flow unit channel of RRB-STHX, CRB-STHX and HCB-STHX is shown in figure 6. The actual length of the computational domain is 4 times of the baffle distance plus 200 mm. That is, the domain is extended 100 mm for the entrance section to ensure the inlet uniformity, and at the exit, the domain is 8
extended 100 mm in order to make sure that the exit flow boundary has no flow recirculation [17]. For the RRB-STHX, the CRB-STHX and the HCB-STHX, the tube layout dimensions are all the same, which are given in above section. For the RRB-STHX, the outer diameter of round rod is 6 mm. The dimensionless equations for continuity, momentum and energy may be expressed in tensor notation as [17]:
( V ) ( g r ad )
(1)
S
In the above equation, the dependent variable, stands for the velocity components, temperature, k and ; and S represent the appropriate diffusion coefficients and the source terms, respectively. The commercial CFD software Fluent [18] is adopted for all the numerical simulations. The 3D, double-precision, pressure-based solver is used. The conservation equations are discreted with a finite volume formulation. The standard wall function method is adopted for the near-wall region, and the non-slip boundary condition is adopted on all solid surfaces. The surfaces of the baffles are set as adiabatic because the impact caused by thermal conduction of the baffles can be neglected, and taking the baffle surfaces as adiabatic allows for a coarser grid. The SIMPLE algorithm is used for pressure–velocity coupling, the second order upwind scheme is chosen to discrete momentum and energy equations, and the second order difference scheme is used for the pressure. The velocity inlet boundary condition is applied for the inlet and the pressure outlet boundary condition is applied for the outlet. The four boundary walls of the unit model are set as symmetry boundary
9
conditions. The other setting parameters adopt default settings according to user’s guide in Fluent. The upstream bulk temperature is set as 283.15 K. The temperature of tube wall is set as a constant, 350 K. All equations take the convergent criterions of relative residual of 10-4 except energy equation taking 5×10-7. In addition, the wall y+ is evaluated after the convergence to guarantee the requirement of the standard wall function [19]. Some formulas used in the post-processing are defined as: Re
Dh
DhVin
(2)
4( Pt 2 do 2 / 4) do
(3)
Tin Tout T T ln( in w ) Tout Tw
(4)
T
h
c p Vin Ain (Tin Tout ) A0 T
(5)
hDh
Nu
(6)
p pin pout f
(7)
Dh 2p ( ) L Vin 2
PEC
Tout
(8)
Nu / NuR ( f / f R )1/3
(9)
TdA
(10)
A
2.2 Grid independence and model validation The flow unit channel mesh of RRB-STHX, CRB-STHX and HCB-STHX is
10
shown in figure 7. As depicted by figure 7, hybrid mesh scheme is adopted. The mesh near the baffles is fine un-structural mesh while the mesh far away from the baffles is relative coarse structural mesh. In order to validate the solution independency of the grid, the grid-dependency is checked for three different grids: 2.2, 2.9, and 3.5 million cells, respectively. The error between the finest grid having 3.5 million cells and the grid having 2.2 million cells is less than 2% for the heat transfer coefficient and less than 3% for the friction coefficient. Therefore, the settings of the grid of the latter (3.5 million cells) are used for further investigations in the present study. To validate the reliability of present numerical model, the non-staggered tubes supported by RRB are simulated and compared with the data obtained by Dong et al. [14]. The results are listed in figure 8. It can be observed that the relative maximum deviation is within 16%. Considering that the unit duct model will underestimate the Nu compared with the whole model [13]. Such agreements show the reliability of the present physical model and numerical method. 3. Results and discussion 3. 1 Thermal-hydraulic performance analysis For Re in the range of 10,849 ~ 32,547, the thermal-hydraulic performance comparisons of HCB-STHX, CRB-STHX and RRB-STHX are shown in figure 9 when the baffle width is 10 mm and the baffle distance is 200 mm. It can be seen from figure 9 (a) that the Nu of HCB-STHX, CRB-STHX and RRB-STHX increases with increasing Re. The Nu of HCB-STHX is larger than that of RRB-STHX by a percentage value that varies from 13.9% to 29.3% as the inlet Re
11
increases from 10,849 to 32,547. The Nu of CRB-STHX is larger than that of RRB-STHX by a percentage value that varies from 6.6% to 19.6%. The Nu of HCB-STHX is on average 7.6% larger than that of CRB-STHX. This means that HCB-STHX can provide a better heat transfer performance compared with CRB-STHX; alternatively, RRB-STHX presents a low heat transfer capacity. It can be seen from figure 9 (b) that the f-factor decreases with increasing Re. The f-factor of HCB-STHX is larger than that of RRB-STHX by a percentage value that varies from 187% to 281%. The f-factor of CRB-STHX is larger than that of RRB-STHX by a percentage value that varies from 117% to 181%. The f-factor of HCB-STHX is on average 34.4% larger than that of CRB-STHX. Therefore, the HCB-STHX has a higher value of power consumption than that of the CRB-STHX. In contrast, RRB presents a considerable lower pressure drop which makes it suitable to STHX design that has a very high pressure drop requirement. Figure 9 (c) shows that the PEC of HCB-STHX and CRB-STHX is all smaller than 1.0. This means that the overall thermal-hydraulic performance of RRB-STHX is better than that of HCB-STHX and CRB-STHX. The reason is that the shape of RRB is more close to streamline shape. Furthermore, figure 9 (c) shows that the PEC of CRB-STHX is larger than that of HCB-STHX by a percentage value that varies from 2.4% to 2.7%. This means that the overall thermal-hydraulic performance of CRB-STHX is better than that of HCB-STHX. The reason is that the increase of pressure drop is more quickly than the increase of heat enhancement for HCB-STHX. 3.2 Flow structure analysis
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To analyze the physical mechanism, the flow structures of RRB-STHX, CRB-STHX and HCB-STHX are shown in figure 10 when the inlet Re is 10,849, the baffle width is 10 mm and the baffle distance is 200 mm. In figure 10, the streamline is colored by absolute value of velocity. Three cross-sections of the unit duct at position Z=0.2 m, Z=0 m and Z=-0.2 m are selected to show the streamline changing tendency along the flow direction. Meanwhile, the temperature variations at these three cross-sections are plotted in figure 11. It can be seen from figure 10 that, when the fluid crosses over the baffle, the baffle continues to shear and comminute the streamline flow along the horizontal and vertical directions in the unit duct. The continuity and stability of the fluid are destroyed. For RRB-STHX, at cross-section Z= 0.2 m, some vortices are established and their position and magnitude are significantly altered relative to those at cross-section Z=0 m. Subsequently, the vortices continuously alter their position and magnitude at cross-section Z=-0.2 m. A similar vortices evolution progress can be found for CRB-STHX and HCB-STHX. However, the vortices position and magnitude are quite different at the same cross-section. From figure 11, it can be found that the temperature of the three cross-sections undergoes different variation. For RRB-STHX, at cross-section Z=0.2 m, the bulk temperature of the water is nearly at a constant value of 283.15 K. At cross-section Z=0 m, the temperature of the water near the heated tube rises rapidly while an inner core region is still not heated. At cross-section Z=-0.2 m, the temperature of the whole cross-section rises. For CRB-STHX, a similar temperature variation can be found
13
except that a relative smaller low temperature inner region at cross-section Z=0 m and Z=-0.2 m. For HCB-STHX, the temperature of the whole region undergoes a faster increasing and the inner region also has a relative higher temperature. The reason can be partly found from the partial enlarged view of AA and BB shown in figure 10. We can find that the fluid experiences an acceleration progress when passing the baffle. At the same time, a strong swirling flow is generated at the back of the baffle. The velocity
and
swirling
magnitude
of
the
flow
follows
an
order
of
RRB-STHX
