Shell and tube heat exchanger optimization using new baffle and tube configuration

Applied Thermal Engineering 157 (2019) 113736

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Research Paper

Shell and tube heat exchanger optimization using new baffle and tube configuration

T

⁎

Ali Akbar Abbasian Arania, , Reza Moradia,b a b

Mechanical Engineering Department, University of Kashan, Kashan, Iran Department of Mechanical Engineering, Faculty of Enghelabe Eslami Branch, Technical and Vocational University (TVU), Tehran, Iran

H I GH L IG H T S

baffle STHE optimization with combined baffle and ribbed tube is studied. • Segmental and circular ribbed tubes are employed for STHE optimization. • Triangular of DB-TR and CSDB-TR are 27% and 32% higher than DB-CR and CSDB-CR, respectively. • hHighest performance belong to disk baffle and longitudinal triangular ribbed tube. • Disk baffle Performance with triangular ribbed tube is 39% over conventional STHE. •

A R T I C LE I N FO

A B S T R A C T

Keywords: Shell and tube heat exchanger (STHE) Combined segmental-disk baffle (CSDB-STHE) Optimization Baffle Ribbed Tube PEC

This research focus on the fluid flow and heat transfer of water inside the segmental baffle shell and tube heat exchanger (SB-STHE) optimization using combined baffle and longitudinal ribbed tube configuration. Triangular and circular ribbed tubes are employed with disk baffle shell and tube heat exchanger (DB-STHE) and combined segmental-disk baffle shell and tube heat exchanger (CSDB-STHE). The fluid domain is simulated by SOLIDWORKS Flow Simulation (Ver. 2015). Obtained results are compared with experimental data and numerical results available in literature. Based on the obtained results under maximum mass flow rates (2 kg/s), the average value of shell-side heat transfer coefficient of DB-TR and CSDB-TR are 26.6% and 31.9% higher than DB-CR and CSDBCR, respectively. To evaluate the performance, Q/ΔP is selected at the same flow rate. A 42.8%, 40.5%, 24.2% and 7.12% difference over conventional baffles are represented by DB-TR, CSDB-TR, CSDB-CR and DB-CR respectively. In another criterion named as Performance evaluation criterion a 39%, 37%, and 13% performance difference over conventional baffles are represented by disk baffle shell and tube heat exchanger with longitudinal triangular ribbed tube (DB-TR), combined segmental-disk baffle shell and tube heat exchanger with longitudinal triangular ribbed tube (CSDB-TR), and combined segmental-disk baffle shell and tube heat exchanger with longitudinal circular ribbed tube (CSDB-CR) respectively.

1. Introduction Heat exchangers are an inseparable part of the industries such as: power plants, process industries, oil refining and so on. Meanwhile, the shell and tube heat exchangers (STHE) have 40% share apparatus of the different industry. Therefore, focus on this apparatus is needed to improve the performance of this device. Baffles and tube configuration and their arrangement have a profound effect on the performance of this kind of heat exchanger. One can refer to common segmental baffle problems as: creation of fouling in dead zone, producing high pressure drop because of dead zones, remarkable flow streams between shell and

⁎

baffle, tube and baffle because of construction tolerance and decreasing the lifetime of the heat exchanger due to the vibration caused by the fluid flow across the tube bundle [1,2]. Gao et al. [3] studied the discontinuous baffle with different angles experimentally. Their result show that 40° helix angle is the best among the other studied helix angles [3]. In an industrial research project in Tabriz, Zeyninejad Movassag et al. [4], using helical baffle as an alternative of segmental baffle, improved the performance of the conventional shell and segmental baffle STHE by reducing the pressure drop and fouling. In another investigation, Nemati Taher et al. [5] studied numerically the impact of baffle space for the helical baffle

Corresponding author. E-mail address: [email protected] (A.A. Abbasian Arani).

https://doi.org/10.1016/j.applthermaleng.2019.113736 Received 17 January 2019; Received in revised form 9 April 2019; Accepted 4 May 2019 Available online 06 May 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

Applied Thermal Engineering 157 (2019) 113736

A.A. Abbasian Arani and R. Moradi

STHE, as producing the better local mixing and increasing the turbulence intensity [25], due to creating the zigzag pattern among the tube bundle. However, there are some undesirable effects on fluid flow and heat transfer as forming the fouling rear of baffle plates in the stagnation zone and near the shell wall, producing a large pressure drop and creating separation flow near the baffle edge. Due to recent effect more pumping power is needed for the same heat load. Another problem of baffles related to the providing bypass streams and leakage streams and tube vibrations [2,26]. Therefore, it is essential to present an investigation on the baffles to amplify the positive effect and lessen the negative effect. Son and Shin [27] reported that the performance of STHE with helical baffles is superior to that of a conventional STHE due to better fluid contacts with the tubes and reducing the shell side stagnation zones. In addition to presented investigation, one can found an investigation that deal with entropy generation minimization concepts in heat exchangers in order to enhance the heat exchanger performance [28]. Rashidi et al. [29] presented a three-dimensional, numerical thermo-hydrodynamic and second low analysis of nanofluid flow inside a square duct equipped with transverse twisted-baffles. They found that the baffles geometry and situation provide the maximum value of heat transfer coefficient and the minimum pressure drop. They also reported that the entropy generation decreases by inserting the baffles inside the duct. In an another work that used from second law of thermodynamics, Tahery et al. [30] present a study for performance analysis of a STHE by using hydraulic network modeling in order to enhance the performance of the heat exchanger. Tahery et al. [30] focus on the effect of using different tube count, tube layout and tube diameter at different baffle sections on the heat transfer, pressure drop and exergy destruction rate of STHEs with segmental baffles. They reported that the modified heat exchanger, even though the number of tubes is reduced compared to the conventional design version, has better thermo-hydraulic performance, improving the original design heat transfer performance, and having lower exergy destruction rate. The results of the present investigation showed that the heat transfer performance (hs/ΔPs) increased about 25–48% by elimination the window-section baffles. Using from exergy analysis (second law of thermodynamics), He and Li [31] conducted a numerical study on the double-tube-pass shell-and-tube heat exchanger (DTP-STHE) to improve the recovered heat quality from the point of exergy analysis. Results of referred investigation reveal that the heat quality in DTPSTHE is twice as that in single-tube-pass shell-and-tube heat exchanger (STP-STHE). They compared the thermo-hydraulic performances of three kinds of DTP-STHEs with segmental, helical and flower baffles under the same conditions. Obtained results show that flower baffles produce the lowest pressure drop and lowest heat transfer coefficient. For comparing the economic performance, the heat transfer rate per effective pumping power (i.e., QH/P0) are evaluated and showed that the flower baffle is the highest and the segmental baffle is the lowest. Salahuddin et al. [32], presented a review on the major investigation done on helical baffles applied for improving the STHE performance. In referred work a comparison between the helical and segmental baffles are presented. They reported that the helical baffles are more advantageous than the segmental baffles. In addition, discontinuous, folded, sextant helical baffles, 40° baffle inclination angle as well as low baffle spacing will give the best results when incorporated in some combination, while the continuous helical baffles eliminate dead regions. Dong et al. [33] presented an investigation on the thermo-hydraulic performance of five trisection helical baffle heat exchangers with different inclination angles, baffle shapes, or connection patterns, and one segmental baffle heat exchanger. By obtaining the pressure loss characteristics and flow field distributions, they presented a comprehensive explanation about thermo-hydraulic performance of heat exchanger with different inclination angles of baffles. They reported that the three sector baffle with inclination angles of 10° has the highest shell-side Nusselt number and shell-side pressure loss, and can be selected only when the heat transfer capability is very

STHE. They used baffles with angle of 20-degree. In the new approach by You et al. [6], they studied the computationally based on the porosity and permeability concept in the range of Reynolds numbers from 6,813 to 22,326. Wang et al. [7] presented flower baffled STHE in an experimental investigations and compared its performance with common segmental baffle. Wang et al. [7] compared thermo-hydraulic characteristics of STHE with different type of helical baffle to reduce triangle zones. Helical baffle was introduced to remove the defects of segmental baffle. This was first presented by Lutcha and Nemcansky [8]. Ozden and Tari [9] conducted a study on small STHE in order to investigate the effect of baffle spacing, baffle cut and shell diameter dependencies of the heat transfer coefficient and the pressure drop. They found good agreement between obtained results and the Bell–Delaware method results. Lei et al. [10] studied numerically and experimentally three STHE with different baffle types such as current segmental baffle, single helical baffle and two-layer helical baffle. Based on the obtained results, at the same pressure drop, the two-layer helical baffle show better performance than others. Zhang et al. [11] investigated the angle of helix baffle on STHE with the experimental test while Nemati et al. [5] did it numerically. Many articles was devoted to the structure of the helical baffles for example: continuous helical baffles [12], combined helical baffles [13], and combined multiple shell-pass helical baffles [14]. Gorman et al. [15] used a corrugated structure in an inner tube of double tube heat exchanger. Ahmed et al. [16] in the numerical research showed the behavior of finned tube with different configuration in a STHE. Based on their data, wavy fin configuration showed better performance than others [16]. El Maakoul et al. [17] used helical baffle to optimize the double pipe heat exchanger. Amini et al. [18] investigated the effect of helical and segmental tube sheet on the performance of STHE. There are a number of investigation that focus on baffles and tubes simultaneously. Liu et al. [19] presented a numerical simulation of the shell side flow in rodbaffle heat exchangers with spirally corrugated tubes. Results are compared with those in rod-baffle heat exchanger with plain tubes. Obtained results showed that the thermo–hydraulic performance in spirally corrugated tubes are much higher that the rod-baffle heat exchanger with plain tubes. Chen et al. [20] examined the effect of surface roughness on the performance of a conventional heat exchanger, and found that the system's performance is slightly improved. In the study of Ibrahim et al. [21], the thermal-fluid behavior of the elliptical tube was investigated in a crossover flow for the aspect ratio of 0.25, 0.33, 0.5 and 1. Swain et al. [22] compared the heat transfer coefficient and pressure drop over the flat and elliptical tubes. In referred study, the elliptical tube bundles show better performance than the flat tubes from the heat transfer viewpoint. In a similar investigation, He et al. [23] conducted an investigation on flow characteristic in the shell side of a vertical STHE having combined helical baffles with elliptic tubes. Obtained results showed that the heat transfer rate, Nusselt number, friction factor and thermal performance factor of the elliptic tubes are 14.7–%-16.4%, 11.4–16.6%, 29.2–36.9% and 30–35%, higher than those of the circular tubes respectively. Heat exchanger, and the shell side friction factor is lower by 29.2–36.9%. Referred work demonstrates that the elliptic tube can effectively improve the heat transfer performance of non-Newtonian fluid flowing in the helical baffle heat exchanger when compared to the circular tube. Shrikant et al. [24] presented a study on the effects of different baffles configurations, including single, double, triple segmental, helical and flower baffle, inside STHE. Based on obtained results, baffles increased the heat transfer and pressure drop. For the same mass flow rate of shell side, heat transfer rate, heat transfer coefficient and pressure drop are found to be the best for single segmental baffles. In addition, zero stagnation zones are detected in helical baffles, leading to reduction in fouling. Baffles have an important role, as tubes support, providing shell-side desirable velocity distribution, and preventing from the tubes vibrating. In addition to assemblage effects, it can provide an important effects on fluid flow and heat transfer in shell side of 2

Applied Thermal Engineering 157 (2019) 113736

A.A. Abbasian Arani and R. Moradi

There is no defined criterion to provide the optimum baffle spacing, while baffle spacing is a very important factor which affects the capital costs as well as the operating of the heat exchanger. Wen et al. [45] proposed an improved structure STHE with helical baffles. The numerical results showed that the temperature distribution are more uniform than conventional STHE. In addition, the thermal performance factor enhances by 18.6–23.2%. Wang et al. [46] proposed n new kind of STHE. Obtained results show that both the Nusselt number and shellside pressure drop increase with the decrease of helical angle and shellside inlet velocity, and increase with the increasing overlapped degree. Dong et al. [47] presented a study on trisection helical baffle in comparison with conventional segmental baffles STHE. The results show that the heat transfer performance and comprehensive performance evaluation indexes of the proposed STHE are much better than those of the segmental baffles. Chamoli et al. [48] presented a multi-objective optimization on heat exchanger for Nu number ratio and friction factor ratio as a function of Reynolds number (Re), pitch ratio (PR), twist ratio (TR), and twisted tape number (N). According to the presented research, it can be concluded that there are few articles that point out to the optimization of heat exchangers by changing the baffles and tubes simultaneously. In this research two kind of baffles and longitudinal ribbed tube is proposed in order to improve the thermal performance of STHE. For fulfill of this propositions the fluid flow and heat transfer in three dimensional domain are simulated numerically using SOLIDWORKS Flow Simulation (Ver. 2015). By numerical simulation of flow domain in the shell side of STHE the best model is selected.

important in an engineering application. Pal et al. [34] presented an investigation on the heat transfer coefficient in a STHE by introduction the baffles. They reported that, baffles increase the turbulence level in the flow, hence the Reynolds number increases thus the heat transfer coefficient increase. Based on referred study the chosen unbaffled heat exchangers were quite large in diameter. Lei et al. [35] conducted an investigation on the two novel STHEs with louver baffles. Obtained results showed that, new proposition decrease and eliminate the dead spaces and augment the local heat transfer due to creating the oblique flow produced in the shell side of the STHEs with louver baffles. The numerical results of Lei et al. [35] showed that the heat transfer coefficient per pressure drop of both new proposed STHEs with louver baffles are higher than that of the STHE with segmental baffles. Recent results implies that at the same amount of heat transfer, the required pumping power of the STHEs with louver baffles is lower than that of the STHE with conventional segmental baffles. Naqvi et al. [36] presented a study on the helical baffles used in shell side of STHEs providing increase the heat transfer efficiency, lessen the pressure losses, avoiding the flow induced vibrations and eliminating the stagnant recirculation zones. For referred aims a new design, clamping anti-vibration baffles with square twisted tubes, helical baffles with cylindrical tubes and conventional segmental baffle with cylindrical tubes are proposed and simulated numerically. Based on obtained results, the performance of the heat exchanger with clamping anti-vibration baffles with square twisted tubes has higher heat transfer coefficient than segmental baffles with cylindrical tubes (SGCT-STHE) and less pressure drop than both helical baffle with cylindrical tube (HBCT-STHE) and segmental baffle with cylindrical tubes (SGCT-STHE), while its comprehensive performance is higher than SGCT-STHE and slightly less than HBCT-STHE. Bichkar et al. [37] carried out a numerical simulations on the fluid flow and heat transfer inside the STHE considering different baffles i.e. single segmental, double segmental and helical baffles. Their results showed that, single segmental baffles provided the formation of dead zones resulting increase in heat transfer. The helical baffles showed an elimination of dead zones resulting a decrease in pressure drop and increasing the heat transfer. The comparative results show that helical baffles are more advantageous than other two studied baffles. For evaluation of STHE, thermal performance and pressure drop are considered as major factors. Both, thermal performance and pressure drop are dependent on the path of fluid flow and types of baffles in different orientations respectively. Increasing the complexity of baffles enhances the heat transfer which also results in higher pressure drop which means higher pumping power is required. This reduces the system efficiency. The less dead zones result in better heat transfer. The lower pressure drop results in lower pumping power, which in turn increases the overall system efficiency. The key factors affecting the STHE performance are attributed to turbulence, pressure drop, heat transfer coefficient, fouling, length of heat exchanger and type of baffles … [32]. Baffles, aside from the providing a support for the tube bundles, maintain desirable velocity for shell side, create turbulence and resist vibrations to enhance the fluid velocity as well as the heat transfer coefficient. Segmental, flower, ring, trefoil hole, disc and doughnut type and helical are various baffles types that used in STHEs [38]. It is worth to note that traditional STHEs with segmental baffles showed large pressure drop accompanied with low heat transfer efficiency [39,40]. Baffle shape is one of the important factors affecting the STHE performance. Baffles shape effect have been investigated widely. Continuous and discontinuous baffle are also generally employed in STHEs. As examples there are the investigations [41–43] that reports the superiority of discontinuous baffles to that of the continuous baffles due to the elimination of dead region in discontinuous baffles STHE. One of the other factor affecting the STHE performance is baffles spacing. Increasing the baffle spacing increases the flow velocity, which leads to the heat transfer enhancement due to a reduction in leakage through baffle-shell clearance [44].

2. Geometry of the studied model The laboratory scale of shell and tube heat exchangers with combined segmental-disk, disk baffle and segmental baffle are depicted in Figs. 1–3 respectively. In addition, three different used tubes are presented in Fig. 4. The dimensions of the respective heat exchanger are shown in Table 1. The geometric dimension of studied shell and tube is same for all models. In fact, the tube length and diameter and shell diameter are same for all studied configurations. To facilitate the simulation process while the basic characteristics of the analysis still keep, some assumption is considered: The temperature of the walls was maintained at 400 K. There is no leak between the connection (shell and baffle connection, baffle and tube connection). The thermal flux of shell is considered to be zero. The fluid properties are considered to be constant. 3. Governing equations For turbulent flow modelling, the k − ε turbulence model is adopted for the calculation process. The governing equations for continuity, momentum, energy, k and ε in the computational domain are shown as

Fig. 1. Shell and tube heat exchanger with combined segmental-disk baffle, (CSDB-STHE). 3

Applied Thermal Engineering 157 (2019) 113736

A.A. Abbasian Arani and R. Moradi

Table 1 Geometrical dimensions of studied shell and tube heat exchanger.

Fig. 2. Shell and tube heat exchanger with disk baffle, (DB-STHE).

Geometry

Size

Shell diameter Tube diameter Number of tubes Heat exchanger length, Shell side inner diameter Shell side outer diameter Angle of inclined baffle Baffle cut Central baffle spacing

90 mm 30 mm 7 mm 600 mm 30 mm 30 mm 200 36% 86 mm

called k - ε model. The adopted model meets accuracy and reliability requirements in the considered fluid flow and heat transfer study, Palumbo et al. [49]. In SolidWorks Flow Simulation the classical twoequation k- ε empirical model for simulating turbulence effects in fluid flow CFD simulation is used as it requires the minimum amount of additional information to calculate the flow, Wilcox [50]. The modified k - ε turbulence model with damping functions describes laminar, turbulent, and transitional flows of homogeneous fluids consisting of the following turbulence conservation laws, Lam and Bremhorst [51], Sobachkin and Dumnov [52]. Turbulent kinetic energy: Fig. 3. Shell and tube heat exchanger with segmental baffle, (SB-STHE).

μt ⎞ ∂k ⎞ ∂ ∂ ∂ ⎛⎛ (ρk ) + (ρui k ) = ⎜ μ + ⎟ + Sk σk ⎠ ∂x i ⎠ ∂t ∂x i ∂x i ⎝ ⎝ ⎜

follows: Continuity:

⎟

(4)

Turbulence dissipation energy:

∂ (ρui ) = 0 ∂x i

μt ⎞ ∂ε ⎞ ∂ ∂ ∂ ⎛⎛ (ρε ) + (ρui ε ) = ⎜ μ + ⎟ + Sε σε ⎠ ∂x i ⎠ ∂t ∂x i ∂x i ⎝ ⎝ ⎜

(1)

Momentum:

⎟

(5)

where the source terms Sk and Sɛ are defined as

∂ ∂P ∂ ⎛ ∂uk ⎞ (ρui uk ) = − μ + ∂x i ∂x i ∂x i ⎝ ∂x i ⎠ ⎜

Sk = τijR

⎟

(2)

Energy:

∂ ∂ ⎛ ∂T k ⎞ (ρui T ) = ∂x i ∂x i ⎝ ∂x i cP ⎠ ⎜

∂ui − ρε + μt PB ∂x j

ρε 2 ε ∂u Sε = Cε1 ⎛⎜f1 τijR i + μt CB PB ⎞⎟ − Cε 2 f2 k k⎝ ∂x j ⎠

⎟

(3)

(6)

(7)

here PB represents the turbulent generation that is due to buoyancy force and can be written as, using the Boussinesq assumption:

3.1. Turbulence modeling

PB = − Taking into account expected application of the developed fluid flow and heat transfer, the fluid flow inside the shell side of heat exchanger is considered as turbulent. In the flow simulation module, the Favre-averaged Navier-Stokes equations are employed, where timeaveraged effects of the flow turbulence on the flow parameters are considered. To close this system of equations, transport equations for the turbulent kinetic energy and its dissipation rate is used, the so-

gi 1 ∂ρ σB ρ ∂x i

(8)

where gi is the gravitational acceleration component in xi direction, the constants Cμ , Cε1, Cε2 , σk and σε are defined empirically. In Flow simulation the following typical values are used: Cμ = 0.09, Cε1 = 1.44 , Cε2 = 1.92 , σk = 1, σε = 1.3. Where Lewis number Le = 1.the constant σB = 0.9, and constant CB is defined as: CB = 1 when PB > 0, and 0 for otherwise; and, following the Boussinesq assumption, the Reynolds-

Fig. 4. Tubes with different longitudinal rib types, (a) circular rib, (b) triangular rib and (c) without rib. 4

Applied Thermal Engineering 157 (2019) 113736

A.A. Abbasian Arani and R. Moradi

stress tensor for Newtonian fluids has the following form:

Table 2 Thermo-physical properties of working fluid in shell side of STHE, 300 K.

∂uj ∂u 2 ∂u 2 − δij k ⎞⎟ − δij ρk τijR = μ ⎛⎜ i + ∂ ∂ ∂ x x x 3 3 j i k ⎝ ⎠

(9)

here δij is refer to the Kronecker delta function (it is equal to unity when i = j, and zero otherwise), μ is the dynamic viscosity coefficient, k is the turbulent kinetic energy and μt is the turbulent eddy viscosity coefficient, which is determined from:

μt = fμ

μ * 103 Pa.s

k W/m.K

cp kJ/kg.K

β * 106 K−1

997.0

0.855

0.613

4179

276.1

And the heat transfer coefficient of shell side fluid flow is calculated using the fallowing formulation:

cμ ρk 2

hs =

(10)

ε

ρ kg/m3

Q̇ A0 ΔTm

here fμ is a turbulent viscosity factor. It is defined by the expression

Ao = Nt . πdo L

20.5 ⎞ fμ = (1 − e−0.0165Ry ). ⎛1 + , RT ⎠ ⎝

ΔTm =

⎜

⎟

(11)

The distance from the point to the wall is y and Lam and Bremhorst’s damping functions are determined from 3

⎛ 0.05 ⎞ f1 = 1 + ⎜ f ⎟ ⎝ μ ⎠

(12)

f2 = 1 − exp(−RT2)

(13)

u τw ρ

∫0

y+

(

η

1 + 4K 2η2 1 − e− Av

)

⎜

(22)

ΔTmin = Ts, out − Tw

(23)

Nu/ Nun (f / fn )1/3

(24)

where Nun and Nu Nuav,0 are the averaged Nusselt number for STHE which is equipped with the new baffles and tube configuration and the commonly STHE, respectively. Also, f and fn are the friction factor for STHE which is equipped with the new baffles and tube configuration and the commonly STHE, respectively. 3.3. Boundary conditions The used boundary condition for fluid flow and heat transfer simulation are summarized as follows: 1. All the solid walls are set with momentum boundary condition of no slip. 2. The thermal boundary condition of zero heat flux is set for the shell wall. 3. The heat transfer between the water and the baffles is neglected. 4. The fluid temperature is kept constant at the shell side inlet. 5. The walls of tubes have the thermal boundary condition of coupling heat transfer. 6. The inlet to the shell is set as mass flow inlet. 7. The shell outlet is said to be a pressure outlet with pressure so that the inlet pressure is equal to the pressure drop.

2

(14)

here K = 0.4504 is the Karman constant and the Van Driest coefficient is Aν = 26. The diffusive heat flux is defined as:

μ ∂h μ i = 1, 2, 3 qi = ⎛ + t⎞ σC ⎠ ∂x i ⎝ Pr

(21)

ΔTmax = Ts, in − Tw

PEC =

2dη 1+

(20)

where Ao is the heat exchange area (outer area of tubes). The number of tubes is shown with Nt, Tw is the tube walls temperature and the subscripts s and t show shell side and tube side, respectively. The performance evaluation criteria index (PEC) is used to compare the thermal and fluid-dynamic performances of STHE which is equipped with new baffles and tube configuration to evaluate the heat transfer enhancement. It is calculated using the predicted Nusselt numbers and friction factor as:

Lam and Bremhorst’s damping functions fμ, f1, f2 decrease turbulent viscosity and turbulence energy and increase the turbulence dissipation rate when the Reynolds number Ry based on the average velocity of fluctuations and distance from the wall becomes too small. When fμ = 1, f1 = 1, f2 = 1 the approach obtains the original k - ε model. To simulate the fluid boundary layer effects near the solid walls, solve the Navier-Stokes equations with a two-equation k – ε turbulence model and evaluate skin friction in these regions a “wall function” approach is utilized in the Flow Simulation module, Launder and Spalding [53]. But SolidWorks Flow Simulation employs Van Driest’s profiles instead of a logarithmic profile. Additionally, a “two-scale wall functions” (2SWF) approach is employed to describe a turbulent boundary layer and fit a fluid’s boundary layer profile relative to the main flow’s properties, Driest [54]. When the number of cells across the boundary layer is sufficient (more than ∼ 10) the simulation of laminar boundary layers is done via Navier-Stokes equations as part of the core flow calculation. For turbulent boundary layers proceeding from the Van Driest mixing length, Driest [54], SolidWorks Flow Simulations uses following dependency of the dimensionless longitudinal velocity u+ on the dimensionless wall distance y+.

u+ =

ΔTmax − ΔTmin ln(ΔTmax /ΔTmin )

(19)

⎟

(15)

The standard wall functions was employed for the near wall region to accurately simulate the thermo hydraulic performance. The governing equations mentioned above were discretized by the finite volume method with SIMPLE pressure–velocity coupling algorithm. QUICK scheme was applied for both the convective and diffusive terms in the numerical simulation. The convergence criterion were taken as 10−4 for the flow equations and 10−8 for the energy equation.

here the constant σc = 0.9, Pr refer to the Prandtl number, and h is the thermal enthalpy. It is worth to note that presented equations describe both turbulent and laminar flows regimes. In addition, moves from one regime to another regime and back are possible. The parameters k and μt are zero for purely laminar flows. 3.2. Heat transfer and pressure drop

3.4. Thermo-physical properties of shell side fluid of STHE

Heat transfer rate of shell side fluid flow is presented as follow:

̇ ps (Ts, in − Ts, out ) Q̇ = mC

The inlet fluid temperature of shell side of STHE is fixed at 300 K, while the inlet fluid pressure of shell side is fixed at 100 kPa. In

(18) 5

Applied Thermal Engineering 157 (2019) 113736

A.A. Abbasian Arani and R. Moradi

Table 3 Validation results. Present study

0.5 1.0 2.0

Q 84,494 163,940 298,975

Bell-Delaware p 1457 5776 23,226

Q 91,766 157,501 368,312

Ozden & Tari p 1251 4616 18,700

Q 93,851 160,103 240,506

p 1522 6168 24,963

Diff. with Bell-Delaware

Diff. with Ozden & Tari

Q diff. 7.9% −4.1% 19%

Q diff. 10% −2.4% −24%

p diff. −16% −25% −24%

p diff. 4.3% 6.3% 7.0%

Fig. 7. Heat transfer coefficient vs mass flow rate for five studied types of baffles and tubes combination, CSDB-TR, CSDB-CR, DB-TR, DB-CR and SBSTHE.

Fig. 5. Mesh independency for temperature.

Fig. 6. Mesh independency for pressure drop. Fig. 8. Heat transfer vs mass flow rate for five studied types of baffles and tubes combination, CSDB-TR, CSDB-CR, DB-TR, DB-CR and SB-STHE.

addition, the thermo-physical properties of water is presented in Table 2. It must point out that

correlations, is used for calculating the shell-side pressure drop and heat transfer coefficient. In recent method presumed that all the shellside fluid flowed across the tube bundle without leakage and bypass flow. And then the effect of bypassing streams, leakage, baffle configuration and adverse temperature gradient in the flow are applied by a correction factor. Three grid numbers are used for obtaining the temperature (Fig. 5) and pressure drop (Fig. 6) considering a = 57384, b = 178092 and c = 239881 elements. The difference between the results of the three configuration is very small, less than 5 percent. By comparing the results and taking into account the time of calculations, the model B is the best choice. In fact, a grid number whose results are not sensitive to grid numbers is preferred.

3.5. Mesh generation The unstructured tetrahedral grid is selected for the commutative domain due to the complex space of fluid flow between the baffles and tubes. By comparing the numerical results with results of Ozden and Tari [9] and Bell-Delaware method in Table 3, it can be concluded that the simulation accuracy is acceptable for the aforementioned shell and tube heat exchanger. It is worth to note that different methods, in order to calculating the pressure drop and shell-side heat transfer coefficient, based on experimental data, was developed for typical heat exchanger. One of these methods is named as Kern [55] method that used from the experimental correlations. Another method which is often referred as the Bell-Delaware method [56] is also based on the empirical 6

Applied Thermal Engineering 157 (2019) 113736

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fluid, and the second is the introduction of additional turbulence due to using the rib that affect seriously the fluid flow and heat transfer distribution. It is worth to note that additional rib can affect (increase) the pressure drop also. In fact the performance evaluation criterion (PEC) or/and performance evaluation factor are the criterion that determine the real benefit of new configuration. As it is shown, CSDB has greater effect than the additional rib, and the triangular rib has greater effect that the circular rib. As can be seen CSDB has a stronger effect on the heat transfer coefficient than DB in STHE. Based on this effect, the CSDB-STHE heat transfer coefficient are greater that DB-STHE heat transfer coefficient. In addition, ribbed tube has another effect on the heat transfer coefficient. Furthermore, the triangular ribbed tube has greater effect than the circular ribbed tube on the heat transfer coefficient. Based on this reality the CSDB-TR has the maximum and the DB-CR has the minimum heat transfer coefficient between the four studied baffle and tube configurations. About the order of CSDB-CR and DB-TR, the significance of combined segmental-disk baffle than ribbed tube is determinant. The effect of triangular ribbed tube is greater than combined segmental-disk baffle. For referred reason the DB-TR heat transfer coefficient is greater than CSDB-CR. Pressure drop is considered as one of the essential parameters in the design of STHEs. The pressure drop with mass flow rate for five types of studied heat exchanger are presented in Fig. 9. Based on the obtained results in Fig. 9, the average pressure drop for the SB-STHE has the maximum pressure drop in comparison with others types. For the CSDB-CR and DB-TR, the pressure drop has the minimum value in comparison with others types and are followed by CSDB-TR and DB-CR. As expected from the obtained results, Fig. 9, the DB-STHEs (DB-TR and DB-CR) and combined segmental-disk baffle (CSDB-TR and CSDB-CR) eliminated zigzag fluid flow path, and the flow of fluid becomes in the longitudinal direction. So the pressure drop in proposed configurations is reduced. In common segmental shell and tube heat exchanger, SB-STHE, because of sudden change in fluid flow path (the dead zones) more pressure is needed to drive the fluid to the outlet, Figs. 10–12. Pathlines illustrate the path of fluid flow and it is dependent on the orientation of baffles types. For segmental baffles (SGSTHX), fluid follows a zigzag pattern which produces dead zones, eddy formation and back mixing of fluid particles. So the heat transfer cannot take place effectively. This also causes an increase in pressure drop leading to additional of pump power. This problem is solved by usage of

Fig. 9. Pressure drop vs mass flow rate for five studied types of baffles and tubes configurations, CSDB-TR, CSDB-CR, DB-TR, DB-CR and SB-STHE.

4. Results and discussion The heat transfer coefficient and heat transfer with mass flow rate are presented in Figs. 7 and 8 for five types of studied STHE. Figs. 7 and 8 shows the trends variation of shell-side heat transfer coefficient and the heat transfer rate for five types of STHE within the studied mass flow rates (between the 0.5 and 2.0 kg/s). Based on the obtained results from Fig. 7 under maximum mass flow rates (2 kg/s), the average value of shell-side heat transfer coefficient of DB-TR and CSDB-TR are 26.6% and 31.9% higher than DB-CR and CSDB-CR, respectively. In referred mass flow rate (2 kg/s), the average value of shell-side heat transfer of DB-TR and CSDB-TR are 24% and 19.5% higher than DB-CR and CSDB-CR, respectively. The average value of shell-side heat transfer coefficient and heat transfer of SB-STHE is 4.7% higher and 2.9% lower than CSDB-TR, respectively. In fact, using the longitudinal triangular rib increases the heat transfer coefficient and heat transfer in DB-STHE and CSDB-STHE. By adding the rib on the tube surface, two important factor affect the fluid flow and heat transfer distribution. The first one is the additional surfaces that improve the heat exchange between the tube and

Fig. 10. Velocity path line in combined segmental-disk baffle shell and tube heat exchanger, CSDB-STHE. 7

Applied Thermal Engineering 157 (2019) 113736

A.A. Abbasian Arani and R. Moradi

Fig. 11. Velocity path line in disk baffle shell and tube heat exchanger, DB-STHE.

Fig. 12. Velocity path line in segmental baffle shell and tube heat exchanger, SB-STHE.

segmental baffles which provided ineffective heat transfer zone and heat transfer weakening in the referred area. Referred phenomenon, changing sharply the path of flow, is observed with lower intensity in CSBD-STHE, Fig. 10, and DB-STHE, Fig. 11. On the other hand, as can be understood from Fig. 11, the path of fluid flows in DB-STHE are in oblique flow pattern that is diverse from the previous refereed type, SBSTHE type, Fig. 12. The cross flow paths are observed through the shell volume and the flow is strongly developed. In fact the flow structure in recent baffles types (DB-STHE, Fig. 11) shell side is flatter than that by SB-STHE. It must note that using the DB-STHE type caused to sweep the space which eliminate and decrease the dead spaces. This phenomenon improved meaningfully the local heat transfer in the region behind the baffles, Fig. 8. Fig. 13(a–e) show the temperature distribution of five studied combinations of baffle type and ribbed tube heat exchangers. For the DB-CR, temperature distribution, as displays in Fig. 13(c), is obviously non-uniform than other types along the shell side. In referred type, the temperature distribution just behind the baffles is very low and as a

other types of baffles as DB-STHE and/or CSDB-STHE. In DB-STHE and/ or CSDB-STHE cases, there is an improvement in the removal of dead zones. Due to this improvement, thermal performance increases to a greater extent. It is worth to note that, in SB-STHE the flow hits the baffle plate, and the direction of the flow is changed. Therefore, the shell space behind the baffle is not effectively used for cross flow and recirculation zones appear in these regions. When the flow is observed to be well developed (in DB-STHE and CSDB-STHE) the cross flow paths are established throughout the shell volume and the recirculation zones disappear. The velocity path line along the length of the STHE are depicted in Figs. 10–12 for CSDB-STHE, DB-STHE and SB-STHE respectively. As it is shown in Fig. 12, the zigzag flow pattern is made in the shell side of the SB-STHE. The path of flow is changed sharply when the fluid is moved inside the shell side of SB-STHE. Consequently, greater momentum changed and caused more pressure drop in shell side (as it is reported in Fig. 9). In addition, a key phenomenon can be obviously appeared is produce the recirculation zones and large dead spaces ahead the 8

Applied Thermal Engineering 157 (2019) 113736

A.A. Abbasian Arani and R. Moradi

Fig. 13. Temperature distribution in shell side of (a) CSDB-CR, (b) CSDB-TR, (c) DB-CR, (d) DB-TR, and (e) SB-STHE.

Fig. 14. Variation of performance evaluation factor vs mass flow rate for five studied types of baffles and tubes combination, CSDB-TR, CSDB-CR, DB-TR, DBCR, SB-STHE.

Fig. 15. Variation of performance evaluation coefficient (PEC) vs mass flow rate for five studied types of baffles and tubes combination, CSDB-TR, CSDB-CR, DB-TR, DB-CR, SB-STHE.

consequence the local heat transfer in the region is very poor. This phenomenon come from the existence of recirculation zones and the dead spaces region. It is worth to note that one can see the temperature distribution in DB-TR, Fig. 13d, are more uniform inside the shell side than other types that can significantly enhance the thermo-hydraulic performance of heat exchanger. From the viewpoint of the heat exchanger designers, the ratio of heat transfers to pressure drops is the determinant factor in selection of the optimal STHE. It is better to obtain maximum heat transfer rate at the lowest pressure drop at same condition. By comparing the obtained

results from the proposed models (Fig. 14), it can be concluded that the DB-TR, and CSDB-TR show the best performance than other models. A 42.8%, 40.5%, 24.2% and 7.12% difference over conventional baffles are represented by DB-TR, CSDB-TR, CSDB-CR and DB-CR respectively. Both pressure drop and heat transfer coefficient are critical merits of heat exchanger performance. Performance Evaluation Coefficient, PEC, gives the relative performance of a heat transfer enhancing device where two competing factors such as heat transfer coefficient and pressure drop are involved. In this investigation, the above declared 9

Applied Thermal Engineering 157 (2019) 113736

A.A. Abbasian Arani and R. Moradi

factor was applied as a comparison criterion. By this factor, the value of heat exchange at an equal pumping power condition was compared. When this value, PEC, is higher than 1.0, the overall improved heat exchanger performance is then enhanced, and higher value is preferred. The variation trend of performance evaluation coefficient (PEC) along with mass flow rate is shown in Fig. 15. It can be clearly observed that except DB-CR, the Performance evaluation coefficient (PEC) for all studied models are higher than 1.0, CSDB-TR, DB-TR, CSDB-CR. The average comprehensive performance of the proposed models increases 39%, 37%, 13% for DB-TR, CSDB-TR, and CSDB -CR in comparison with the SB-STHE, respectively. Therefore, the comprehensive performance of the improved STHE, DBTR, is enhanced significantly. The variations of heat transfer coefficient in Fig. 7, heat transfer in Fig. 8, pressure drop in Fig. 9, performance evaluation factor (Q/Δp) in Fig. 14, and performance evaluation criteria (PEC) in Fig. 15 are presented. Obtained results illustrate that the heat transfer coefficient, the heat transfer, and the pressure drop are increased with increasing the mass flow rate while the performance evaluation factor (Q/Δp) and the performance evaluation criteria (PEC) are decrease with increasing mass flow rate.

[12]

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[14]

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[16] [17]

[18]

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5. Conclusion [21]

In this research, CFD method is applied to study the thermohydraulic behavior of STHE with the new baffles and ribbed tube in a 3D geometry. The pressure drop decreases due to the directional movement of the fluid along the axis of the tubes. The outputs of this study show that the DB-STHE and CSDB-STHE significantly reduce the pressure drop of the shell side rather than common SB-STHE. With new tubes, heat transfer is also increased due to the promoting area of heat exchanging with this ribbed tube. To show the thermohydraulic behavior of presented baffles and ribbed tubes combinations, the ratio of net heat transfer to pressure drop of all proposed types are compered. Based on obtained results, among the proposed combinations the DB-TR show the best performance among the other combinations. This type of baffle and tube configuration can be a good choice instead of current SBSTHE, because of its application in energy optimization and increase the lifetime of the device.

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