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Hydro-thermal shell-side performance evaluation of a shell and tube heat exchanger under different baffle arrangement and orientation
International Journal of Thermal Sciences 121 (2017) 138e149
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Hydro-thermal shell-side performance evaluation of a shell and tube heat exchanger under different baffle arrangement and orientation Mustapha Mellal a, *, Redouane Benzeguir a, Djamel Sahel a, Houari Ameur b a Laboratoire des Carburants Gazeux et Environnement, Facult e de G enie M ecanique, Universit e des Sciences et de la Technologie d’Oran, USTO-MB, BP1505, El-M’Naouer, Oran 31000, Algeria b ^ma), BP 66, 45000 Naa ^ma, Algeria Institut des Sciences et Technologies, Centre Universitaire Salhi Ahmed (Ctr Univ Naa
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 February 2017 Received in revised form 10 April 2017 Accepted 15 July 2017
In the present study, a three-dimensional numerical simulation of turbulent fluid flow and heat transfer in the shell side of a shell and tube heat exchanger (STHE) has been investigated. Two primordial parameters are tested: baffles spacing of 106.6, 80 and 64 mm and six baffles orientation angles of 45 , 60 , 90 , 120 , 150 and 180 . The investigations are performed with the CFD COMSOL Multiphysics 5.1 software using the finite elements method, for Reynolds number ranging from 3000 to 10 000. Some numerical results are validated with available experimental data and an adequate agreement is found. The numerical results show the important role of the studied parameters in the shell side thermal performance enhancement, where the case of baffle orientation angle of 180 , at 64 mm of baffle spacing is the best design that assures mixing flow, giving thus a highest value of thermal performance factor of 3.55 compared with STHE without baffles. © 2017 Published by Elsevier Masson SAS.
Keywords: Shell and tube heat exchanger CFD Turbulence Friction factor Baffle spacing
1. Introduction Over the time, it was proved that the shell-and-tube is the most widely used heat exchanger type in many engineering processes, such as food industry, oil and petrochemical industries, electric power generation, etc. The multi-purpose services and application possibilities provided by the STHXs make this device an essential component which plays a fundamental role in these industrial processes. For this context, the looking for their performance enhancement been an essential point and important factor in all the strategies followed to conserve and rationalize the energy consumption [1,2]. In this field, and because the shortage of the fundamental information concerning the flow patterns and associated heat transfer rates most of the research that has been done, has been focused on the heat exchanger shell side to improve their performance by testing several parameters to design a heat exchanger such as: shape, the metal used, the fluid used, etc. Baffles locations inside STHEs are an important technique to improve the thermal performance, they intense the turbulence of the fluid flow in the shell side across the tubes to ensure a high heat transfer coefficients and also to provide a mechanical resistance for
* Corresponding author. E-mail address: [email protected] (M. Mellal). http://dx.doi.org/10.1016/j.ijthermalsci.2017.07.011 1290-0729/© 2017 Published by Elsevier Masson SAS.
the tube bundle. Diverse baffles shapes are exploited to enhance the shell side thermal performance of the shell and tube heat exchangers. Mica et al. [3] by their experimental investigations of fluid flow and heat transfer in a shell-and-tube heat exchanger with one pass of warm water on the shell side and two passes of cold water in tube bundle, proved that the STHE's heat exchange performance is strongly depending on the shell side geometry parameters such as baffles number, baffle size, distance between baffles, the first and the last baffle position to inlet and outlet shell side, size of the constructive clearances. Baffles shape is also an important parameter where the most widely used type is the conventional segmental baffle which is a circle with a cut area called baffle cut, this baffle cause a change in the flow direction and augment the fluctuation velocity on the shell-side fluid across the tube bundle, this phenomenon enhance the thermal performance by improving the turbulence or local mixing on the shell-side, but unluckily increases also the shell side pressure loss which requires a huge pumping power and as a consequence, augments the energy consumption [4]. Nowadays, the use of the computational fluid dynamics (CFD) package becomes some indispensable and useful tools to study the hydro-thermal fluid behavior phenomena, by solving numerically the problems which represented by the governing equations. The CFD code can also gave us the opportunity to create a virtual
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Nomenclature A Bc Cp DS do Dh De f h GK Kf k L NB Nt Nu P
Total heat transfer surface area [m2] Baffle cut [%] Specific heat [J/(kg K)] Shell inside diameter [m] Tube outside diameter [m] Hydraulic diameter [m] diameter equivalent [m] Friction factor Heat transfer coefficient [W/(m2 K)] Turbulent kinetic energy production [kg/m s3] Thermal conductivity [W/(m K)] Turbulent kinetic energy [m2/s2] Heat exchanger length [m] Number of baffle Number of tube Nusselt number Pressure [Pa]
prototype for the system investigated and test many parameters in a short time and with low cost. However, the misuse of these codes can lead to a wrong data and incorrect comprehension. In this field, it is worth mentioning that in the numerical simulation when we use the computational methods to study leakage and bypass flow characteristics and thermal performances of any heat exchangers type. It should be emphasized that if any heat transfer or friction factor correlation from the literature is used, the geometrical characteristics must be evaluated in the same manner as in the original source of the correlations [5]. In order to analyze the flow and heat transfer behaviors, a numerical investigation of fluid-solid coupled heat transfer with variable physical propriety in the LBEhelium heat exchanger is performed by Chen et al. [6]. They found that the performance of heat transfer can be appreciably enhanced by augmenting the mass flow rate of helium in the shell side. Helical baffles or helix-changer is another efficient arrangement in the shell side. The helical shape of baffles enhances the flow circulation and minimizes the principle weakness in design of the usual segmental baffles whereas the flow patterns produced by this shape are also much close to plug flow condition, which causes a diminution in shell-side pressure loss and enhances the heat transfer execution in heat exchangers [7e14]. Xiao et al. [15] simulated numerically the fluid flow and heat transfer characteristics for helical baffles heat exchanger with different Prandtl number (Pr) fluids and different helical tilt angle (b). By comparing heat exchangers with the same required heat transfer capacity, they found that the heat exchanger contained water as the shell side fluid achieves the best heat transfer coefficients when b is at 40 . However, for a shell side fluid with a higher Prandtl number, the small angle design is the optimal selection. Also, they concluded that the pressure drop provided by helical baffle is feeble compared with segmental baffles. Lei et al. [16] studied experimentally and numerically the characteristics of hydrodynamics and heat transfer of a heat exchanger with single-helical baffles by the comparison of the thermal performance of those three different heat exchangers designs: single-segment baffles, single-helical baffles and twolayer helical baffles. Their results show that the heat exchangers with helical baffles ensures a higher heat transfer rate with the same pressure drop than that with segmental baffles, and the configuration of the two-layer helical baffles has better
Pt Pr U T
139
Tube pitch [m] Prandtl number Velocity [m/s] Temperature [K]
Greek letters Baffles orientation angle (degree) Dynamic viscosity [kg/(m s)] Density [kg/m3] Thermal Performance Factor
a m rh
Subscript e f in out o t w 0
Equivalent Fluid Inlet Outlet Outer Tube Wall Base case (STHE without baffles)
Abbreviations STHE Shell and Tube Heat Exchanger
performance than that with single-helical baffles. The high heat transfer achieved in a shell and tube heat exchanger by using segmental baffles, still make this kind of heat exchanger the most widely used in the industry. However, the disadvantage of this type is the great pressure loss coming through zigzag flow manner in the shell-side [17e20]. Gay et al. [21] studied the heat transfer shell-side performance in double-segmental baffled cylindrical shell and tube heat exchangers, by using a plane through a diameter parallel to the baffle cut; this design creates a symmetrical geometry in order to allow the fluid flow distributes itself equally between the two halves of the bundle. They concluded that a double-segmental baffled exchanger cannot be viewed as two single segmental baffled exchangers back-toback, but the effects of this configuration are likely to be greater than those for single-segmental baffled units [22,23]. Roetzel et al. [24] investigated experimentally the thermal performance in a shell and tube heat exchanger with segmental baffles by changing five variables: stream flow direction, shell side flow rate, tube side flow rate, clearance between baffles and shell, and distance between baffles [25,26]. Emerson et al. [27] proposed empirical correlations for the shell side pressure drop and heat transfer of a segmental baffled shell and tube heat exchanger, by considering methods to estimate the magnitude of the non-effective fluid streams in the shell, so that the effective flow through the tube bundle may be determined [28e30]. Ozden et al. [31], by using a CFD package, studied the performance of a single shell and single tube pass heat exchanger with different number of segmental baffles and different turbulent flows for two baffle cut values. Their results indicate that the shell side flow and the temperature distribution are very sensitive to modeling choices such as mesh, order of discretization and turbulence modeling [32e36]. You et al. [37] proved the sensitivity of the shell side thermo-hydraulic performance about the baffle spacing parameters, by computing the shell side turbulent heat transfer enhancement in a small shell and tube heat exchanger using trefoil-hole baffles. In this paper, and in order to enchane the STHE performances, the effect of two parameters are considered: baffles orientation angles and baffles spacing on the hydro-thermal shell side performance of a shell and tube heat exchanger. A three-dimensional numerical simulation of turbulent fluid flow and heat transfer has been focused in using CFD COMSOL Multiphysics 5.1 software. For
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different flow velocities represented by eight value of the Reynolds number which is shifted up from 3000 to 10 000 in the hydraulic diametre. The shell side heat transfer coefficient and friction factor are analyzed for a segmental baffles with three spacing values 106.6, 80 and 64 mm expressing by the number of baffles used: 6, 8, 10 baffles) and three baffles orientation relatively with the first baffle orientation in the inlet side which are 180 , 90 and 45 . The effect of thies other baffles orientation 60 , 120 , 150 are tested by fixing the baffle spacing parameter in 64 mm (10 baffles) with the same range of Reynolds number. The non-isothermal flow predefined Multiphysics coupling model configured with the Reynolds-Average Navier-Stokes (RANS) models which include the standard k-ε turbulence model is used in this study. The selected model provided accurate results as checked in experimental literature [38,39].
pitch arrangement (Fig. 1) and 640 mm of length with segmental baffles had a 38% of baffle cut value, is the design studied in this paper. The effect of two parameters has been investigated, Three values of baffles spacing (106.6, 80 and 64.0 mm) expressing by the baffles numbers (6, 8, 10 baffles) are considered, respectively. In order to create a better mixing of fluid flow, six baffle orientation angles are tested, which are: 45 , 60 , 90 120 , 150 and 180 , the case of 10 baffles with three-orientation angle of 180 , 90 and 45 is shown in (Fig. 2). As the tube side is simple to modulate, we assuming the external boundary of the tubes side as a solid cylinders to impose a constant temperature of 353.15 K on it, to avoid studying the flow and the heat transfer between the hot fluid and the tubes side walls. Table 1 summarize all the details of the necessary geometrical parameters and all the properties of the fluid which working with. 2.1. Boundary condition
2. Model descriptions Shell and tube heat exchanger contains 9 tubes having a square
All boundary conditions are set regarding the model needs. The tubes are assumed as a solid and a temperature of 353.15 K is imposed on their external surface, the baffles walls supposed like internal walls. A thin layer boundary condition is practically used to account the heat flux in thin shell structures, which had a 5 mm of thickness and it's supposed made in aluminum. Wall function condition is applied for all the walls of the shell, the tubes and the baffles [40]. The inlet side velocity of the fluid is determined according to Reynolds numbers range used which varied from 3000 to 10 000 with a step of 1000. In addition, a normal flow condition with atmospheric pressure is assumed in the outlet side. Other detailed boundary conditions and design parameters are summarized in Table 1. 2.2. Mesh selection and solver settings
Fig. 1. Tubes arrangement.
The geometry of the system investigated (Fig. 2), was created and meshed by using the computer code COMSOL Multiphysics,
Fig. 2. STHX arrangement with 10 baffles, (a) a ¼ 180 , (b) a ¼ 90 , (c) a ¼ 45 .
M. Mellal et al. / International Journal of Thermal Sciences 121 (2017) 138e149
version 5.1. As it is well suited for complex-shaped geometries, the tetrahedral element which operates under the free tetrahedral element is used to mesh the computational domain; this algorithm provides unstructured mesh with a varying element size, allowing us to perform more dense mesh around the tubes and the baffles (Fig. 3). For the STHE without baffles, mesh tests were achieved by realizing the following series of grids: 887 560, 1 049 924, 1 166 493, 1 212 797 and 1 285 357 mesh elements. The stability of results is
Table 1 Boundary conditions and geometrical parameters. Designation
Value/Unit
Baffle cut ðBc Þ Heat exchanger length ðLÞ fluid working with Inlet & outlet shell nozzle diameter Number of Baffles ðNB Þ Number of tubes ðNt Þ Longitudinal pitch ðPt Þ Shell inside diameter ðDS Þ Tube outside diameter ðDT Þ External boundary tube temperature Inlet water temperature
38% 640 mm water 30 mm 6, 8, 10 9 30 mm 135 mm 20 mm 353.15 K 293.15 K
141
obtained from 1 166 493 elements, where the variation of the Nusselt number and friction factor did not exceed 2% and 1.75% respectively with the increases of the grid density. Hence, the final grid number accepted and used for the next computations is 1212797 elements. The similar approach was achieved for the other geometry configurations, where the adopted grids element varied from 1 444 793 to 1 619 958 elements. COMSOL Multiphysics 5.1 which is based on the finite elements method, is the computer code used to analyze the fluid flow and heat transfer phenomena for the present study. Segregated solvers are used to solve the governing equations. The Generalized Minimal Residual (GMRES) iterative method solver is used to calculate the parameters with estimated factor error and tolerance of 20 and 0.001, respectively. The geometric Multi-grid solver is used with Parallel Sparse Direct Linear Solver (PARDISO) as a pre-conditioner.
2.3. Mathematical formulation The flow equations used in this study are written according to the conditions of the simulated case. For stationary models with an incompressible flow characterized by a low Mach number less than 0.3, the resulting governing equations are: Continuity equation
Fig. 3. Meshed geometry with tetrahedral type.
Fig. 4. Results validation: (a) Nusselt number, (b) friction factor.
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V:ðruÞ ¼ 0 Momentum equation
(1)
ðV:uÞru ¼ Vp þ V:m Vu þ ðVuÞT Energy equation
Fig. 5. Nusselt number versus Reynolds number.
(2)
M. Mellal et al. / International Journal of Thermal Sciences 121 (2017) 138e149
Fig. 6. Friction factor versus Reynolds number.
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Fig. 7. Streamlines temperature (K) distribution for different baffles orientation angles, at 10 baffle number (a) a ¼ 180 , (b) a ¼ 90 , (c) a ¼ 45 .
M. Mellal et al. / International Journal of Thermal Sciences 121 (2017) 138e149
rcp uðVTÞ ¼ V:ðKVTÞ þ Q
(3)
The keε standard model of turbulence that is based on the energy dissipation ε (Eq. (4)) and the turbulent kinetic energy k (Eq. (5)) is used in this study.
rðu:VÞε ¼ V:
rðu:VÞk ¼ V:
mþ
mþ
(4)
Pk ¼ mT Vu : Vu þ ðVuÞ
(5)
T
i
(6)
The turbulent viscosity is modeled as:
mt ¼ rCm
De ¼
4 Pt2 025pd2o
k2 ε
(7)
Nu ¼ 0:36Re0:55 Pr0:33
mt mw
0:14
h ¼ Qm_ =ðDTLM:A0 Þ
(15)
The heat transfer rate of fluid in the shell side is:
_ out Tin Þ Qm_ ¼ Cp mðT
Cε1 ¼ 1:44; Cε2 ¼ 1:92; Cm ¼ 0:09; sk ¼ 1; se ¼ 1:3
DTLM is the log mean temperature difference and defined as:
The friction factor (f) is calculated by using the computed pressure drop (DP) across the length of the channel (L) as
DTLM ¼
(8)
(14)
By using the log mean temperature difference DTLM method [43], the shell-side convective heat transfer coefficient can be calculated through Eq. (15), which can be used to determine the area-average Nusselt number using Eq. (10).
The empirical constants for the standard keε model are assigned the following values:
2 DP f ¼ rU 2 L=D
(12)
(13)
pdo
mT Vk þ Pk rε sk
K 0:55 0:33 mt 0:14 Re Pr De mw
where De , the equivalent diameter, is calculated by:
mT ε ε2 Vε þ Cε1 Pk Cε1 r ; ε ¼ ep k sε k
where the production term is:
h
h ¼ 0:36
145
DTmax DTmin lnðDTmax =DTmin Þ
(16)
(17)
DTmax ¼ Tw Tin
(18)
DTmin ¼ Tw Tout
(19)
A0 ¼ Nt :pdo L
(20)
h
For the heat transfer rate inside the channel, the local Nusselt number is given by:
NuðxÞ ¼
hx Dx KF
(9)
And the area-average Nusselt number can be obtained by
Nu ¼
1 A
Z NuðxÞ vA
(10)
The thermal enhancement factor h is defined by
h ¼ ðNu=Nu0 Þ=ðf =f0 Þ1=3
where m_ is the mass flow rate, Tin and Tout are the inlet and outlet fluid temperature, respectively. A0 is the heat transfer area. However the friction factor is calculated by using the pressure drop computed between the inlet and outlet shell side due to fluid friction with the tubes using Eq. (9) and compared with that obtained by the Colebrook's equation Eq. (21) [43,44] and Petukhov's correlation [45,46] Eq. (22). The Colebrook's equation [44,45] is defined as:
(11)
Nu0 &f0 are respectively the Nusselt number and the friction factor of the base case (STHE without baffles).
3. Results and discussions 3.1. Validation of results In order to validate the numerical model of the present investigation, tests of the Nusselt number and friction factor results are performed for the STHE case without baffles. These results are compared with methods and correlations available in literature. Nusselt number values are validated by using the log mean temperature difference DTLM and the Kern's method [1]. By using the correlation (Eq. (14)), Kern's method is assumed to simplify the complicated calculus of the heat transfer in the shell side [41,42].
Fig. 8. Nusselt number versus Reynolds number at 10 baffle number for different baffles orientation angles, (a) a ¼ 150 , (b) a ¼ 120 , (c) a ¼ 60 .Fig. 9. Thermal Performance Factor verses Reynolds number.
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f ¼ ð0:782 ln Re 1:51Þ2
(21)
The Petukhov's correlation [46,47] is defined as:
f ¼ ð1:82 ln Re 1:64Þ2
(22)
shell and tube heat exchanger without baffle is the case used to validate our numerical model with the existing literature, Fig. 4-a, illustrate the variation of the Nusselt number vs. Reynolds number obtained by our numerical simulation, the Kern's correlation and DTLM method. Fig. 4-b present the variation of the friction factor vs. Reynolds number obtained by the present numerical study and by
the use of Petukhov's and Colebrook's correlations. Regarding the Nusselt number illustrated in Fig. 4-a, the results deviation noted between the present study and Kern method are varied between ±7:07% and ±20:76% like a minimum and maximum value respectively with an average of ±14:29%. For DTLM method the min and the max value noted are respectively ±5:26% and ±13:97% with an average of ±9:29%. Wherever for the friction factor which is illustrated in Fig. 4-b, the deviation of our results have a minimum value of ±5:56% and ±8:03%, and have a maximum value of ±21:79% and ±23:22% by using the Petukhov's and Colebrook's correlations respectively, the average friction factor deviation value noted are ±15:64% and ±17:46% for the both correlation
Fig. 9. Streamlines temperature (K) distribution at 10 baffle number for different baffles orientation angles, (a) a ¼ 150 , (b) a ¼ 120 , (c) a ¼ 60 .
M. Mellal et al. / International Journal of Thermal Sciences 121 (2017) 138e149
with the same citation order. Generally, the graphs shown in Fig. 4 indicate that the RNG k-ε turbulence model proposed for this study and the numerical calculation method is accurate. 3.2. Heat transfer In this section, effects of the baffle spacing arrangement and baffles orientation on the Nusselt number are presented. To perform tests, six geometrical configurations are realized: three cases of baffle spacing (106.6, 80 and 64 mm) corresponding respectively to the number of baffles: 6, 8 and 10 and three cases of baffle orientation angles (45 , 90 and 180 ). The distribution of the Nusselt number versus Reynolds number is shown in Fig. 5. In a comparison between the baffle orientation angle 180 and the base line cases (Fig. 5a), the max difference reached in Nusselt numbers are 286.19%, 223.66% and 165.80% with the baffles numbers: 10, 8 and 6, respectively. However, for the baffle orientation angle 90 , a rise of 244.85%, 244.85% and 146.26% is observed for 10, 8 and 6 baffles, respectively (Fig. 5b). As remarked in Fig. 5c, the differences in Nusselt numbers for the baffle orientation angle of 45 are 172.75%, 135.73% and 104.01% for the three baffle numbers: 10, 8 and 6, respectively. As a rule, the use of the baffles in the shell side is not just against bending of the tubes or as an support to reduce the vibration, but also they serve a function of directing the flow and favors a thorough mixing of the fluid after its interaction with the hot surface of tubes bundles, this leads to an enhancement in the thermal shell side performance. However, the use of smaller escapement between two successive baffles helps to intense the turbulence and fluctuations of velocity near the walls; the heat transfer coefficient is augmented consequently. Therefore, as shown in Fig. 5(aec), the variation in Nusselt number is very sensitive to the baffles spacing parameters. However, the effects of the baffle orientation angle can be shown clearly in Fig. 5(def), where the variation of Nusselt number versus Reynolds number for the three baffles spacing cases (106.6, 80 and 64 mm) are presented. The comparison between the performance of these three angles (45 , 90 and 180 ) shows that the highest Nusselt number is obtained with the angle 180 . However, we observed a further reduction in Nusselt number with the baffle orientation angle of 45 , this reduction due to the great space between the baffles (45 ), where the fluid flows easily through the shell causing a decrease in the turbulence intensity and as a consequence leads to a decrease in the heat transfer. This flow mode can be clearly observed in the streamline presented in the contours of Fig. 7. As discussed above, the baffles orientation angle plays an important role to improve the thermal performance of a shell and tube heat exchanger, which encouraged us to test others orientation angles. Therefore, baffle orientation angles of (150 , 120 and 60 ) for 64 mm baffles spacing (10 Baffles) are investigated. Fig. 8 illustrates the variation of Nusselt number versus Reynolds number for all the baffles orientation angles proposed under the 10 baffles arrangement case. As shown in this figure, the Nusselt number increases in the rise of the baffle orientation angle. Where, the augmentation of the baffle orientation angle creates more fluid mixing (Fig. 9) and intense the turbulence in the tubular heat exchanger which and augments the heat transfer coefficients.
147
the inlet and outlet sections. Through Fig. 6a, variations of the friction factor versus Reynolds number for the baffle orientation angle (180 ) are shown. The differences between the friction factor obtained from the baseline case and those obtained from the three baffle numbers: 10, 8 and 6 are: 0.047, 0.030 and 0.017, respectively. With the same order of baffle numbers, the differences are: 0.030, 0.018, and 0.016 (respectively) for the baffle orientation angle 90 (Fig. 6b), and are 0.011, 0.0085 and 0.0065 (respectively) for the baffle orientation angle 45 . Results of the friction factor versus Reynolds number are illustrated in Fig. 6(def) for different baffle orientation angles (45 , 90 and 180 ), while the number of baffles is kept constant. As shown in these figures, the difference in friction factor is very high for the case 180 due to the zigzag flow mode assured by this angle which creates more friction than the angle 90 . However, the angle 45 offers a large space between baffles, allowing thus easy fluid flows with less friction through the shell. This flow mode is clearly observed in Fig. 11. The decrease of the baffles spacing yields an increase in the friction factor. Beyond that, under the same baffle number and the same flow rate, the baffle orientation is found to be an important parameter to control the pressure drop. A very high friction is created by the angle 180 ; however a less friction is acquired by the angle 45 . Habitually, the augmentation of heat transfer coefficient associates a penalty of pressure drop. However, as shown in Fig. 10 which illustrates the variation of the friction factor versus Reynolds numbers, at 10 baffles case under different baffle orientation angle (45 , 60 , 90 , 120 , 150 and 180 ), It's appears clearly that the increases in baffle orientation angle augment the friction factor due to the generation of vortex and the change of the flow direction inside the tubes heat exchangers. 3.4. Thermal performance factor Variations of the Thermal Performance Factor (TPF) versus Reynolds number are depicted in Fig. 12 for all cases studied. It is clearly observed that the performance factors are all superior than 2.0, where the case of 10 baffles inclined by 180 assured the highest thermal performance factor with a maximum value of 3.55 for Re ¼ 3000. This case is selected to be as the best one from all configurations studied in this paper. 4. Conclusion The thermal and dynamic characteristics in the shell side of a
3.3. Pressure drop By the following, the dynamic behavior in the shell side of STHE is explored by examining the effects of the baffle spacing and baffles orientation on the friction factor and pressure drop between
Fig. 10. Friction factor versus Reynolds number at 10 baffle number for different baffles orientation angles, (a) a ¼ 150 , (b) a ¼ 120 , (c) a ¼ 60 .
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Fig. 11. Streamlines velocity (m/s) distribution for different baffles orientation angles, at 10 baffle number.
shell and tube heat exchanger fitted with segmental baffles and different arrangements were numerically analyzed. Three geometrical configurations with different baffles spacing are realized, which are: 106.6, 80, and 64 mm. These values correspond
respectively to the baffle numbers: 6, 8 and 10 baffles. Effects of the baffle orientation angles (45 , 60 , 90 , 120 , 150 and 180 ) are also studied. The investigations are conducted with Reynolds number ranging from 3000 to 10 000, at a baffle cut value of 38%. The
M. Mellal et al. / International Journal of Thermal Sciences 121 (2017) 138e149
[14]
[15]
[16] [17] [18] [19] [20]
[21] Fig. 12. Thermal Performance Factor verses Reynolds number. [22]
conclusions are summarized as follows: A change in baffle spacing leads to a change in the heat exchanger performance, where a decrease in the baffles spacing results an increase in the Nusselt number and the friction factor. The baffle orientation is also an important parameter to design an efficient shell and tube heat exchanger. The highest heat transfer coefficient is obtained with the case 180 , where the fluid particles are forced to change their direction with a maximum angle of 180 , creating thus a zigzag flow mode with a short bypass. This flow mode has the advantage to increase the turbulence intensity which will promote the heat transfer, will increase the pressure drop and therefore will increase the friction factor. The case of 10 baffles inclined by 180 assured the highest thermal performance factor with a maximum value of 3.55 at Re ¼ 3000. This configuration is found to be the best one through our investigations and it is recommended to enhance the thermal performances of shell and-tube heat exchangers.
[23]
[24]
[25] [26]
[27]
[28] [29] [30]
[31] [32]
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exchangers, Part I: experimental verification. Heat Transf Eng 1996;17: 93e101. Wang Q, Chen Q, Chen G, Zeng M. Numerical investigation on combined multiple shell pass shell and tube heat exchanger with continuous helical baffles. Int J Heat Mass Transf 2009;52:1214e22. Xiao X, Zhang L, Li X, Jiang B, Yang X, Xia Y. Numerical investigation of helical baffles heat exchanger with different Prandtl number fluids. Int J Heat Mass Transf 2013;63:434e44. Lei YG, He YL, Chu P, Li R. Design and optimization of heat exchangers with helical baffles. Chem Eng Sci 2008;63:4386e95. Bell KJ. Heat exchanger design for the process industries. ASME J Heat Transf 2004;126:877e85. Wang Q, Chen G, Chen Q, Zeng M. Review of improvements on shell-and-tube heat exchangers with helical baffles. Heat Transf Eng 2010;31:836e53. Bhatt D, Javhar PM. Shell and tube heat exchanger performance Analysis. Int J Sci Res (IJSR) 2014;3(9):2319e7064. Raj RT, Ganne S. Shell side numerical analysis of a shell and tube heat exchanger considering the effect of baffle inclination angle on a fluid flow. Therm Sci Therm Sci 2012;16(4):1165e74. Gay B, Jenkins JD, Mackley NV. Shell side hat transfer in double segmentally baffled cylindrical shell and tube heat exchanger. Int J Heat mass Transf 1982;9:39e47. Bergelin OP, Brown GA, Colbum AB. Heat transfer and fluid friction during flow across banks of tubes, Part V a study of a cylindrical baffled exchanger without leakage. Soc Mech Engrs 1954;76:841e50. Gay B, Jenkins JD, Mackley NV. Shell side hat transfer in double segmentally baffled cylindrical shell and tube heat exchanger, the influence of geometrical factors. I the non-leakage case. Lett Heat Mass Transf 1977;4:41e52. Roetzel W, Lee D. Experimental investigation of leakage in shell and tube heat exchanger with segmental baffles. Int J Heat Mass Transf 1993;36(15): 3765e71. Tinker T. Shell side characteristics of shell and tube heat exchangers, parts I, II and III, General Discussion on Heat Transfer. Soc Mech Engrs 1951:89e116. Tinker T. Shell side characteristics of shell and tube heat exchangers, a simplified rating system for commercial heat exchangers. Trans ASME 1958;80:36e52. Emerson WH. Shell side pressure drop and heat transfer with turbulent flow in segmentally baffled shell and tube heat exchanger. Int J Heat Mass Transf 1963;6(8):649e68. Short BE. A review of heat transfer coefficients and friction factor for tubular heat exchangers. Soc Mech Engrs 1942;64(8):779e85. Short BE. Heat transfer and pressure drop in heat exchanger. university of Texas; 1943. p. 4324. Short BE. The effect of baffle height and clearance on heat transfer and pressure drop in heat exchanger. New York: American Society of Mechanical Engineers; 1947. p. 47e105. Ozden E, Tari I. Shell side CFD analysis of a small shell and tube heat exchanger. Energy Convers Manag 2010;51:1004e14. Zhang Z, Yanzhong L. CFD simulation on inlet configuration of plate fin heat exchangers. Cryogenics 2003;43:673e8. Kumar V, Saini S, Sharma M. Pressure drop and heat transfer study in tube intubate helical heat exchanger. Chem Eng Sci 2006;61:4403e16. Rennie TJ, Raghavan VGS. Numerical studies of a double pipe helical heat exchanger. Appl Therm Eng 2006;26:1266e73. Prithiviraj M, Andrews MJ. Three dimensional numerical simulations of shell and tube heat exchangers, Part 1: foundation and fluid mechanics. Numer Heat Transf Part A 1998;33:799e816. Prithiviraj M, Andrews MJ. Three dimensional numerical simulations of shell and tube heat exchangers. Part II: heat transfer. Numer Heat Transf 1998;33: 817e28. You Y, Chen Y, Xie M, Luo X, Jiao L, Huang S. Numerical simulation and performance improvement for a small size shell and tube heat exchanger with trefoil-hole baffles. Appl Therm Eng 2015;89:220e8. Kakac S, Shah RK. Handbook of single phase convective heat transfer. New York: John Wiley & Sons; 1987. Comsol multiphyisics, CFD, heat transfer module. April 2015., Version 5.1. . Craft TJ, Gerasimov A, Iacovides H, Launder BE. Progress in the generalisation of wall function treatments. Int J Heat Fluid Flow 2002;23:148e60. Sinnot R. Chemical engineering design. Coulson Richardson’s Chem Eng 2005;6. Kraus AD, Aziz A, Welty J. Extended surface heat transfer. New York: John Wiley & Sons; 2001. Thulukkanam K. Heat exchanger design handbook. second ed. New York: CRC Press Taylor & Francis Group; 2013. White FM. Heat transfer. reading, MA: Addison Wesley; 1984. Colebrook CF. Turbulent flow in pipes with particular reference to the transition region between the smooth and rough pipe laws. J Inst Civ Eng 1939;11(4):133e56. Petukhov BS. Heat transfer and friction in turbulent pipe flow with variable physical properties. Adv Heat Transf 1970;6:503e64. Kakac S, Liu H, Pramuanjaroenkij A. Heat exchangers selection, rating and thermal design. third ed. New York: CRC press Taylor & Francis Group; 2012.
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Hydro-thermal shell-side performance evaluation of a shell and tube heat exchanger under different baffle arrangement and orientation Mustapha Mellal a, *, Redouane Benzeguir a, Djamel Sahel a, Houari Ameur b a Laboratoire des Carburants Gazeux et Environnement, Facult e de G enie M ecanique, Universit e des Sciences et de la Technologie d’Oran, USTO-MB, BP1505, El-M’Naouer, Oran 31000, Algeria b ^ma), BP 66, 45000 Naa ^ma, Algeria Institut des Sciences et Technologies, Centre Universitaire Salhi Ahmed (Ctr Univ Naa
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 February 2017 Received in revised form 10 April 2017 Accepted 15 July 2017
In the present study, a three-dimensional numerical simulation of turbulent fluid flow and heat transfer in the shell side of a shell and tube heat exchanger (STHE) has been investigated. Two primordial parameters are tested: baffles spacing of 106.6, 80 and 64 mm and six baffles orientation angles of 45 , 60 , 90 , 120 , 150 and 180 . The investigations are performed with the CFD COMSOL Multiphysics 5.1 software using the finite elements method, for Reynolds number ranging from 3000 to 10 000. Some numerical results are validated with available experimental data and an adequate agreement is found. The numerical results show the important role of the studied parameters in the shell side thermal performance enhancement, where the case of baffle orientation angle of 180 , at 64 mm of baffle spacing is the best design that assures mixing flow, giving thus a highest value of thermal performance factor of 3.55 compared with STHE without baffles. © 2017 Published by Elsevier Masson SAS.
Keywords: Shell and tube heat exchanger CFD Turbulence Friction factor Baffle spacing
1. Introduction Over the time, it was proved that the shell-and-tube is the most widely used heat exchanger type in many engineering processes, such as food industry, oil and petrochemical industries, electric power generation, etc. The multi-purpose services and application possibilities provided by the STHXs make this device an essential component which plays a fundamental role in these industrial processes. For this context, the looking for their performance enhancement been an essential point and important factor in all the strategies followed to conserve and rationalize the energy consumption [1,2]. In this field, and because the shortage of the fundamental information concerning the flow patterns and associated heat transfer rates most of the research that has been done, has been focused on the heat exchanger shell side to improve their performance by testing several parameters to design a heat exchanger such as: shape, the metal used, the fluid used, etc. Baffles locations inside STHEs are an important technique to improve the thermal performance, they intense the turbulence of the fluid flow in the shell side across the tubes to ensure a high heat transfer coefficients and also to provide a mechanical resistance for
* Corresponding author. E-mail address: [email protected] (M. Mellal). http://dx.doi.org/10.1016/j.ijthermalsci.2017.07.011 1290-0729/© 2017 Published by Elsevier Masson SAS.
the tube bundle. Diverse baffles shapes are exploited to enhance the shell side thermal performance of the shell and tube heat exchangers. Mica et al. [3] by their experimental investigations of fluid flow and heat transfer in a shell-and-tube heat exchanger with one pass of warm water on the shell side and two passes of cold water in tube bundle, proved that the STHE's heat exchange performance is strongly depending on the shell side geometry parameters such as baffles number, baffle size, distance between baffles, the first and the last baffle position to inlet and outlet shell side, size of the constructive clearances. Baffles shape is also an important parameter where the most widely used type is the conventional segmental baffle which is a circle with a cut area called baffle cut, this baffle cause a change in the flow direction and augment the fluctuation velocity on the shell-side fluid across the tube bundle, this phenomenon enhance the thermal performance by improving the turbulence or local mixing on the shell-side, but unluckily increases also the shell side pressure loss which requires a huge pumping power and as a consequence, augments the energy consumption [4]. Nowadays, the use of the computational fluid dynamics (CFD) package becomes some indispensable and useful tools to study the hydro-thermal fluid behavior phenomena, by solving numerically the problems which represented by the governing equations. The CFD code can also gave us the opportunity to create a virtual
M. Mellal et al. / International Journal of Thermal Sciences 121 (2017) 138e149
Nomenclature A Bc Cp DS do Dh De f h GK Kf k L NB Nt Nu P
Total heat transfer surface area [m2] Baffle cut [%] Specific heat [J/(kg K)] Shell inside diameter [m] Tube outside diameter [m] Hydraulic diameter [m] diameter equivalent [m] Friction factor Heat transfer coefficient [W/(m2 K)] Turbulent kinetic energy production [kg/m s3] Thermal conductivity [W/(m K)] Turbulent kinetic energy [m2/s2] Heat exchanger length [m] Number of baffle Number of tube Nusselt number Pressure [Pa]
prototype for the system investigated and test many parameters in a short time and with low cost. However, the misuse of these codes can lead to a wrong data and incorrect comprehension. In this field, it is worth mentioning that in the numerical simulation when we use the computational methods to study leakage and bypass flow characteristics and thermal performances of any heat exchangers type. It should be emphasized that if any heat transfer or friction factor correlation from the literature is used, the geometrical characteristics must be evaluated in the same manner as in the original source of the correlations [5]. In order to analyze the flow and heat transfer behaviors, a numerical investigation of fluid-solid coupled heat transfer with variable physical propriety in the LBEhelium heat exchanger is performed by Chen et al. [6]. They found that the performance of heat transfer can be appreciably enhanced by augmenting the mass flow rate of helium in the shell side. Helical baffles or helix-changer is another efficient arrangement in the shell side. The helical shape of baffles enhances the flow circulation and minimizes the principle weakness in design of the usual segmental baffles whereas the flow patterns produced by this shape are also much close to plug flow condition, which causes a diminution in shell-side pressure loss and enhances the heat transfer execution in heat exchangers [7e14]. Xiao et al. [15] simulated numerically the fluid flow and heat transfer characteristics for helical baffles heat exchanger with different Prandtl number (Pr) fluids and different helical tilt angle (b). By comparing heat exchangers with the same required heat transfer capacity, they found that the heat exchanger contained water as the shell side fluid achieves the best heat transfer coefficients when b is at 40 . However, for a shell side fluid with a higher Prandtl number, the small angle design is the optimal selection. Also, they concluded that the pressure drop provided by helical baffle is feeble compared with segmental baffles. Lei et al. [16] studied experimentally and numerically the characteristics of hydrodynamics and heat transfer of a heat exchanger with single-helical baffles by the comparison of the thermal performance of those three different heat exchangers designs: single-segment baffles, single-helical baffles and twolayer helical baffles. Their results show that the heat exchangers with helical baffles ensures a higher heat transfer rate with the same pressure drop than that with segmental baffles, and the configuration of the two-layer helical baffles has better
Pt Pr U T
139
Tube pitch [m] Prandtl number Velocity [m/s] Temperature [K]
Greek letters Baffles orientation angle (degree) Dynamic viscosity [kg/(m s)] Density [kg/m3] Thermal Performance Factor
a m rh
Subscript e f in out o t w 0
Equivalent Fluid Inlet Outlet Outer Tube Wall Base case (STHE without baffles)
Abbreviations STHE Shell and Tube Heat Exchanger
performance than that with single-helical baffles. The high heat transfer achieved in a shell and tube heat exchanger by using segmental baffles, still make this kind of heat exchanger the most widely used in the industry. However, the disadvantage of this type is the great pressure loss coming through zigzag flow manner in the shell-side [17e20]. Gay et al. [21] studied the heat transfer shell-side performance in double-segmental baffled cylindrical shell and tube heat exchangers, by using a plane through a diameter parallel to the baffle cut; this design creates a symmetrical geometry in order to allow the fluid flow distributes itself equally between the two halves of the bundle. They concluded that a double-segmental baffled exchanger cannot be viewed as two single segmental baffled exchangers back-toback, but the effects of this configuration are likely to be greater than those for single-segmental baffled units [22,23]. Roetzel et al. [24] investigated experimentally the thermal performance in a shell and tube heat exchanger with segmental baffles by changing five variables: stream flow direction, shell side flow rate, tube side flow rate, clearance between baffles and shell, and distance between baffles [25,26]. Emerson et al. [27] proposed empirical correlations for the shell side pressure drop and heat transfer of a segmental baffled shell and tube heat exchanger, by considering methods to estimate the magnitude of the non-effective fluid streams in the shell, so that the effective flow through the tube bundle may be determined [28e30]. Ozden et al. [31], by using a CFD package, studied the performance of a single shell and single tube pass heat exchanger with different number of segmental baffles and different turbulent flows for two baffle cut values. Their results indicate that the shell side flow and the temperature distribution are very sensitive to modeling choices such as mesh, order of discretization and turbulence modeling [32e36]. You et al. [37] proved the sensitivity of the shell side thermo-hydraulic performance about the baffle spacing parameters, by computing the shell side turbulent heat transfer enhancement in a small shell and tube heat exchanger using trefoil-hole baffles. In this paper, and in order to enchane the STHE performances, the effect of two parameters are considered: baffles orientation angles and baffles spacing on the hydro-thermal shell side performance of a shell and tube heat exchanger. A three-dimensional numerical simulation of turbulent fluid flow and heat transfer has been focused in using CFD COMSOL Multiphysics 5.1 software. For
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different flow velocities represented by eight value of the Reynolds number which is shifted up from 3000 to 10 000 in the hydraulic diametre. The shell side heat transfer coefficient and friction factor are analyzed for a segmental baffles with three spacing values 106.6, 80 and 64 mm expressing by the number of baffles used: 6, 8, 10 baffles) and three baffles orientation relatively with the first baffle orientation in the inlet side which are 180 , 90 and 45 . The effect of thies other baffles orientation 60 , 120 , 150 are tested by fixing the baffle spacing parameter in 64 mm (10 baffles) with the same range of Reynolds number. The non-isothermal flow predefined Multiphysics coupling model configured with the Reynolds-Average Navier-Stokes (RANS) models which include the standard k-ε turbulence model is used in this study. The selected model provided accurate results as checked in experimental literature [38,39].
pitch arrangement (Fig. 1) and 640 mm of length with segmental baffles had a 38% of baffle cut value, is the design studied in this paper. The effect of two parameters has been investigated, Three values of baffles spacing (106.6, 80 and 64.0 mm) expressing by the baffles numbers (6, 8, 10 baffles) are considered, respectively. In order to create a better mixing of fluid flow, six baffle orientation angles are tested, which are: 45 , 60 , 90 120 , 150 and 180 , the case of 10 baffles with three-orientation angle of 180 , 90 and 45 is shown in (Fig. 2). As the tube side is simple to modulate, we assuming the external boundary of the tubes side as a solid cylinders to impose a constant temperature of 353.15 K on it, to avoid studying the flow and the heat transfer between the hot fluid and the tubes side walls. Table 1 summarize all the details of the necessary geometrical parameters and all the properties of the fluid which working with. 2.1. Boundary condition
2. Model descriptions Shell and tube heat exchanger contains 9 tubes having a square
All boundary conditions are set regarding the model needs. The tubes are assumed as a solid and a temperature of 353.15 K is imposed on their external surface, the baffles walls supposed like internal walls. A thin layer boundary condition is practically used to account the heat flux in thin shell structures, which had a 5 mm of thickness and it's supposed made in aluminum. Wall function condition is applied for all the walls of the shell, the tubes and the baffles [40]. The inlet side velocity of the fluid is determined according to Reynolds numbers range used which varied from 3000 to 10 000 with a step of 1000. In addition, a normal flow condition with atmospheric pressure is assumed in the outlet side. Other detailed boundary conditions and design parameters are summarized in Table 1. 2.2. Mesh selection and solver settings
Fig. 1. Tubes arrangement.
The geometry of the system investigated (Fig. 2), was created and meshed by using the computer code COMSOL Multiphysics,
Fig. 2. STHX arrangement with 10 baffles, (a) a ¼ 180 , (b) a ¼ 90 , (c) a ¼ 45 .
M. Mellal et al. / International Journal of Thermal Sciences 121 (2017) 138e149
version 5.1. As it is well suited for complex-shaped geometries, the tetrahedral element which operates under the free tetrahedral element is used to mesh the computational domain; this algorithm provides unstructured mesh with a varying element size, allowing us to perform more dense mesh around the tubes and the baffles (Fig. 3). For the STHE without baffles, mesh tests were achieved by realizing the following series of grids: 887 560, 1 049 924, 1 166 493, 1 212 797 and 1 285 357 mesh elements. The stability of results is
Table 1 Boundary conditions and geometrical parameters. Designation
Value/Unit
Baffle cut ðBc Þ Heat exchanger length ðLÞ fluid working with Inlet & outlet shell nozzle diameter Number of Baffles ðNB Þ Number of tubes ðNt Þ Longitudinal pitch ðPt Þ Shell inside diameter ðDS Þ Tube outside diameter ðDT Þ External boundary tube temperature Inlet water temperature
38% 640 mm water 30 mm 6, 8, 10 9 30 mm 135 mm 20 mm 353.15 K 293.15 K
141
obtained from 1 166 493 elements, where the variation of the Nusselt number and friction factor did not exceed 2% and 1.75% respectively with the increases of the grid density. Hence, the final grid number accepted and used for the next computations is 1212797 elements. The similar approach was achieved for the other geometry configurations, where the adopted grids element varied from 1 444 793 to 1 619 958 elements. COMSOL Multiphysics 5.1 which is based on the finite elements method, is the computer code used to analyze the fluid flow and heat transfer phenomena for the present study. Segregated solvers are used to solve the governing equations. The Generalized Minimal Residual (GMRES) iterative method solver is used to calculate the parameters with estimated factor error and tolerance of 20 and 0.001, respectively. The geometric Multi-grid solver is used with Parallel Sparse Direct Linear Solver (PARDISO) as a pre-conditioner.
2.3. Mathematical formulation The flow equations used in this study are written according to the conditions of the simulated case. For stationary models with an incompressible flow characterized by a low Mach number less than 0.3, the resulting governing equations are: Continuity equation
Fig. 3. Meshed geometry with tetrahedral type.
Fig. 4. Results validation: (a) Nusselt number, (b) friction factor.
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V:ðruÞ ¼ 0 Momentum equation
(1)
ðV:uÞru ¼ Vp þ V:m Vu þ ðVuÞT Energy equation
Fig. 5. Nusselt number versus Reynolds number.
(2)
M. Mellal et al. / International Journal of Thermal Sciences 121 (2017) 138e149
Fig. 6. Friction factor versus Reynolds number.
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Fig. 7. Streamlines temperature (K) distribution for different baffles orientation angles, at 10 baffle number (a) a ¼ 180 , (b) a ¼ 90 , (c) a ¼ 45 .
M. Mellal et al. / International Journal of Thermal Sciences 121 (2017) 138e149
rcp uðVTÞ ¼ V:ðKVTÞ þ Q
(3)
The keε standard model of turbulence that is based on the energy dissipation ε (Eq. (4)) and the turbulent kinetic energy k (Eq. (5)) is used in this study.
rðu:VÞε ¼ V:
rðu:VÞk ¼ V:
mþ
mþ
(4)
Pk ¼ mT Vu : Vu þ ðVuÞ
(5)
T
i
(6)
The turbulent viscosity is modeled as:
mt ¼ rCm
De ¼
4 Pt2 025pd2o
k2 ε
(7)
Nu ¼ 0:36Re0:55 Pr0:33
mt mw
0:14
h ¼ Qm_ =ðDTLM:A0 Þ
(15)
The heat transfer rate of fluid in the shell side is:
_ out Tin Þ Qm_ ¼ Cp mðT
Cε1 ¼ 1:44; Cε2 ¼ 1:92; Cm ¼ 0:09; sk ¼ 1; se ¼ 1:3
DTLM is the log mean temperature difference and defined as:
The friction factor (f) is calculated by using the computed pressure drop (DP) across the length of the channel (L) as
DTLM ¼
(8)
(14)
By using the log mean temperature difference DTLM method [43], the shell-side convective heat transfer coefficient can be calculated through Eq. (15), which can be used to determine the area-average Nusselt number using Eq. (10).
The empirical constants for the standard keε model are assigned the following values:
2 DP f ¼ rU 2 L=D
(12)
(13)
pdo
mT Vk þ Pk rε sk
K 0:55 0:33 mt 0:14 Re Pr De mw
where De , the equivalent diameter, is calculated by:
mT ε ε2 Vε þ Cε1 Pk Cε1 r ; ε ¼ ep k sε k
where the production term is:
h
h ¼ 0:36
145
DTmax DTmin lnðDTmax =DTmin Þ
(16)
(17)
DTmax ¼ Tw Tin
(18)
DTmin ¼ Tw Tout
(19)
A0 ¼ Nt :pdo L
(20)
h
For the heat transfer rate inside the channel, the local Nusselt number is given by:
NuðxÞ ¼
hx Dx KF
(9)
And the area-average Nusselt number can be obtained by
Nu ¼
1 A
Z NuðxÞ vA
(10)
The thermal enhancement factor h is defined by
h ¼ ðNu=Nu0 Þ=ðf =f0 Þ1=3
where m_ is the mass flow rate, Tin and Tout are the inlet and outlet fluid temperature, respectively. A0 is the heat transfer area. However the friction factor is calculated by using the pressure drop computed between the inlet and outlet shell side due to fluid friction with the tubes using Eq. (9) and compared with that obtained by the Colebrook's equation Eq. (21) [43,44] and Petukhov's correlation [45,46] Eq. (22). The Colebrook's equation [44,45] is defined as:
(11)
Nu0 &f0 are respectively the Nusselt number and the friction factor of the base case (STHE without baffles).
3. Results and discussions 3.1. Validation of results In order to validate the numerical model of the present investigation, tests of the Nusselt number and friction factor results are performed for the STHE case without baffles. These results are compared with methods and correlations available in literature. Nusselt number values are validated by using the log mean temperature difference DTLM and the Kern's method [1]. By using the correlation (Eq. (14)), Kern's method is assumed to simplify the complicated calculus of the heat transfer in the shell side [41,42].
Fig. 8. Nusselt number versus Reynolds number at 10 baffle number for different baffles orientation angles, (a) a ¼ 150 , (b) a ¼ 120 , (c) a ¼ 60 .Fig. 9. Thermal Performance Factor verses Reynolds number.
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f ¼ ð0:782 ln Re 1:51Þ2
(21)
The Petukhov's correlation [46,47] is defined as:
f ¼ ð1:82 ln Re 1:64Þ2
(22)
shell and tube heat exchanger without baffle is the case used to validate our numerical model with the existing literature, Fig. 4-a, illustrate the variation of the Nusselt number vs. Reynolds number obtained by our numerical simulation, the Kern's correlation and DTLM method. Fig. 4-b present the variation of the friction factor vs. Reynolds number obtained by the present numerical study and by
the use of Petukhov's and Colebrook's correlations. Regarding the Nusselt number illustrated in Fig. 4-a, the results deviation noted between the present study and Kern method are varied between ±7:07% and ±20:76% like a minimum and maximum value respectively with an average of ±14:29%. For DTLM method the min and the max value noted are respectively ±5:26% and ±13:97% with an average of ±9:29%. Wherever for the friction factor which is illustrated in Fig. 4-b, the deviation of our results have a minimum value of ±5:56% and ±8:03%, and have a maximum value of ±21:79% and ±23:22% by using the Petukhov's and Colebrook's correlations respectively, the average friction factor deviation value noted are ±15:64% and ±17:46% for the both correlation
Fig. 9. Streamlines temperature (K) distribution at 10 baffle number for different baffles orientation angles, (a) a ¼ 150 , (b) a ¼ 120 , (c) a ¼ 60 .
M. Mellal et al. / International Journal of Thermal Sciences 121 (2017) 138e149
with the same citation order. Generally, the graphs shown in Fig. 4 indicate that the RNG k-ε turbulence model proposed for this study and the numerical calculation method is accurate. 3.2. Heat transfer In this section, effects of the baffle spacing arrangement and baffles orientation on the Nusselt number are presented. To perform tests, six geometrical configurations are realized: three cases of baffle spacing (106.6, 80 and 64 mm) corresponding respectively to the number of baffles: 6, 8 and 10 and three cases of baffle orientation angles (45 , 90 and 180 ). The distribution of the Nusselt number versus Reynolds number is shown in Fig. 5. In a comparison between the baffle orientation angle 180 and the base line cases (Fig. 5a), the max difference reached in Nusselt numbers are 286.19%, 223.66% and 165.80% with the baffles numbers: 10, 8 and 6, respectively. However, for the baffle orientation angle 90 , a rise of 244.85%, 244.85% and 146.26% is observed for 10, 8 and 6 baffles, respectively (Fig. 5b). As remarked in Fig. 5c, the differences in Nusselt numbers for the baffle orientation angle of 45 are 172.75%, 135.73% and 104.01% for the three baffle numbers: 10, 8 and 6, respectively. As a rule, the use of the baffles in the shell side is not just against bending of the tubes or as an support to reduce the vibration, but also they serve a function of directing the flow and favors a thorough mixing of the fluid after its interaction with the hot surface of tubes bundles, this leads to an enhancement in the thermal shell side performance. However, the use of smaller escapement between two successive baffles helps to intense the turbulence and fluctuations of velocity near the walls; the heat transfer coefficient is augmented consequently. Therefore, as shown in Fig. 5(aec), the variation in Nusselt number is very sensitive to the baffles spacing parameters. However, the effects of the baffle orientation angle can be shown clearly in Fig. 5(def), where the variation of Nusselt number versus Reynolds number for the three baffles spacing cases (106.6, 80 and 64 mm) are presented. The comparison between the performance of these three angles (45 , 90 and 180 ) shows that the highest Nusselt number is obtained with the angle 180 . However, we observed a further reduction in Nusselt number with the baffle orientation angle of 45 , this reduction due to the great space between the baffles (45 ), where the fluid flows easily through the shell causing a decrease in the turbulence intensity and as a consequence leads to a decrease in the heat transfer. This flow mode can be clearly observed in the streamline presented in the contours of Fig. 7. As discussed above, the baffles orientation angle plays an important role to improve the thermal performance of a shell and tube heat exchanger, which encouraged us to test others orientation angles. Therefore, baffle orientation angles of (150 , 120 and 60 ) for 64 mm baffles spacing (10 Baffles) are investigated. Fig. 8 illustrates the variation of Nusselt number versus Reynolds number for all the baffles orientation angles proposed under the 10 baffles arrangement case. As shown in this figure, the Nusselt number increases in the rise of the baffle orientation angle. Where, the augmentation of the baffle orientation angle creates more fluid mixing (Fig. 9) and intense the turbulence in the tubular heat exchanger which and augments the heat transfer coefficients.
147
the inlet and outlet sections. Through Fig. 6a, variations of the friction factor versus Reynolds number for the baffle orientation angle (180 ) are shown. The differences between the friction factor obtained from the baseline case and those obtained from the three baffle numbers: 10, 8 and 6 are: 0.047, 0.030 and 0.017, respectively. With the same order of baffle numbers, the differences are: 0.030, 0.018, and 0.016 (respectively) for the baffle orientation angle 90 (Fig. 6b), and are 0.011, 0.0085 and 0.0065 (respectively) for the baffle orientation angle 45 . Results of the friction factor versus Reynolds number are illustrated in Fig. 6(def) for different baffle orientation angles (45 , 90 and 180 ), while the number of baffles is kept constant. As shown in these figures, the difference in friction factor is very high for the case 180 due to the zigzag flow mode assured by this angle which creates more friction than the angle 90 . However, the angle 45 offers a large space between baffles, allowing thus easy fluid flows with less friction through the shell. This flow mode is clearly observed in Fig. 11. The decrease of the baffles spacing yields an increase in the friction factor. Beyond that, under the same baffle number and the same flow rate, the baffle orientation is found to be an important parameter to control the pressure drop. A very high friction is created by the angle 180 ; however a less friction is acquired by the angle 45 . Habitually, the augmentation of heat transfer coefficient associates a penalty of pressure drop. However, as shown in Fig. 10 which illustrates the variation of the friction factor versus Reynolds numbers, at 10 baffles case under different baffle orientation angle (45 , 60 , 90 , 120 , 150 and 180 ), It's appears clearly that the increases in baffle orientation angle augment the friction factor due to the generation of vortex and the change of the flow direction inside the tubes heat exchangers. 3.4. Thermal performance factor Variations of the Thermal Performance Factor (TPF) versus Reynolds number are depicted in Fig. 12 for all cases studied. It is clearly observed that the performance factors are all superior than 2.0, where the case of 10 baffles inclined by 180 assured the highest thermal performance factor with a maximum value of 3.55 for Re ¼ 3000. This case is selected to be as the best one from all configurations studied in this paper. 4. Conclusion The thermal and dynamic characteristics in the shell side of a
3.3. Pressure drop By the following, the dynamic behavior in the shell side of STHE is explored by examining the effects of the baffle spacing and baffles orientation on the friction factor and pressure drop between
Fig. 10. Friction factor versus Reynolds number at 10 baffle number for different baffles orientation angles, (a) a ¼ 150 , (b) a ¼ 120 , (c) a ¼ 60 .
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Fig. 11. Streamlines velocity (m/s) distribution for different baffles orientation angles, at 10 baffle number.
shell and tube heat exchanger fitted with segmental baffles and different arrangements were numerically analyzed. Three geometrical configurations with different baffles spacing are realized, which are: 106.6, 80, and 64 mm. These values correspond
respectively to the baffle numbers: 6, 8 and 10 baffles. Effects of the baffle orientation angles (45 , 60 , 90 , 120 , 150 and 180 ) are also studied. The investigations are conducted with Reynolds number ranging from 3000 to 10 000, at a baffle cut value of 38%. The
M. Mellal et al. / International Journal of Thermal Sciences 121 (2017) 138e149
[14]
[15]
[16] [17] [18] [19] [20]
[21] Fig. 12. Thermal Performance Factor verses Reynolds number. [22]
conclusions are summarized as follows: A change in baffle spacing leads to a change in the heat exchanger performance, where a decrease in the baffles spacing results an increase in the Nusselt number and the friction factor. The baffle orientation is also an important parameter to design an efficient shell and tube heat exchanger. The highest heat transfer coefficient is obtained with the case 180 , where the fluid particles are forced to change their direction with a maximum angle of 180 , creating thus a zigzag flow mode with a short bypass. This flow mode has the advantage to increase the turbulence intensity which will promote the heat transfer, will increase the pressure drop and therefore will increase the friction factor. The case of 10 baffles inclined by 180 assured the highest thermal performance factor with a maximum value of 3.55 at Re ¼ 3000. This configuration is found to be the best one through our investigations and it is recommended to enhance the thermal performances of shell and-tube heat exchangers.
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