Enhancement of the Hydrodynamic Characteristics in Shell-and-Tube Heat Exchangers by Using W-Baffle Vortex Generators

Improving the hydrodynamic characteristics of STHECs (Shell-and-Tube Heat Exchanger Channels) by using BVGs (Baffle-type Vortex Generators) is among the common passive methods due to their proved efficiency. In this computational investigation, the same method is used to enhance the hydrodynamic behavior of STHECs, by inserting W-shaped Baffle-type Vortex Generators. The numerical model represented by the computational FVM (Finite Volume Method) is used to simulate and analyzed the considered physical model. The fluid used is air, its thermal physical properties are constant, turbulent, incompressible, and its temperature is 300 K at the inlet section of the STHEC. The flow velocity ( Uin ) and atmospheric pressure ( Patm ) are considered as boundary conditions at the entrance (x = 0) and exit (x = L) of the channel, respectively. The results showed that the friction coefficients were related to the pressure, velocity, and Reynolds number values. High values of Re yielded an acceleration of the fluid, resulting thus in increased pressure on the solid walls and augmented friction values.


Introduction
Several hydrothermal configurations have been proposed and studied by many authors to single out an optimized structure for improving the energy performance of various thermal devices such as the solar heaters and Heat Exchangers. Using numerical and experimental methods, Ary et al. [1] studied the hydrothermal characteristics of inclined and perforated type baffles in a rectangular section channel. They used the SST k-ω model to model the turbulent fluid field. Using inclined solid and perforated type baffles, Dutta and Hossain [2] experimentally investigated the local characteristics of heat transfer as well as the profiles of skin friction coefficients inside a channel of rectangular form. In this experiment, two baffles with similar overall size were reported to increase the heat transfer. The first baffle is placed on the hot upper wall while the station, orientation, as well as the form of the second baffle, is changed to determine the optimum geometry for improved thermal transport. Using fully/half perforated type baffles, Karwa and Maheshwari [3] experimentally reported the results of thermal transfer and skin friction aspects in a duct with a rectangular section. Using various configurations of transverse and perforated type ribs, Nuntadusit et al. [4] determined the hydrothermal behavior of air inside a horizontal section channel. The impact of the angle of perforation/hole inclination, as well as the station of the hole on the rib, were studied and analyzed experimentally. Using a rectangular type baffle, Gajusingh et al. [5] experimentally conducted a study to examine the flow configuration inside a channel of square section. Using a three-dimensional numerical model, Promvonge et al. [6] simulated the laminar heat transfer behavior in a square channel with inclined baffles of different flow blockage ratios. Using perforated and semiattached type ribs, Liu and Wang [7] numerically determined the local thermal transport and fluid field characteristics inside a rectangular type channel. Five various configurations of ribs, as well as two stations, were investigated. Using new continuous rectangular type baffles, Menasria et al. [8] numerically presented the turbulent heat transfer structure for a channel in its rectangular section. The commercial Fluent was used to simulate the turbulent convective transfer of heat, while the RNG k-ε type model was used to model the turbulent flow. Using different arrangements of fins, Mokhtari et al. [9] reported a three-dimensional simulation to investigate the laminar convective transfer of heat inside a horizontal type channel. Using an inclined baffle type obstacle, Nasiruddin and Siddiqui [10] numerically analyzed the improvement of transfer of heat inside a HE (Heat Exchanger) tube. The used numerical model simulated the impact of the obstacle size as well as its orientation on the hydrothermal enhancement. In this study, three various obstacle arrangements were reported, i.e., vertical, upstream inclined, and downstream inclined. Using inclined and detached type ribs of various values of angle of flow attack, Yongsiri et al. [11] numerically determined the turbulent convective thermal transport inside a channel. A vertical obstacle was also presented for comparison. Ko and Anand [12] experimentally reported a study to determine the average values of thermal transfer coefficients inside a rectangular type channel with a wall placed porous type obstacles. Li et al. [13] conducted a numerical analysis to investigate the characteristics of flow and heat transfer for a rectangular type channel with staggered and porous type blocks. The velocity field structure as a function of Da (Darcy number), Re (Reynolds number), and porous block structural parameters was analyzed. Guerroudj and Kahalerras [14] numerically used the triangular, trapezoidal, and rectangular-type porous-structure blocks to increase the overall performance of a 2D channel with parallel plates. Targui and Kahalerras [15] numerically simulated the performance of a double pipe type HE with porous type baffles. Using impermeable and porous type baffles, Santos and de Lemos [16] showed the numerical results of a laminar type flow in a horizontal section channel. Kiwan and Al-Nimr [17] used the porous type fins as a novel method to enhance the transfer of heat from a given surface. The solid conventional fins were also presented for comparison. Using inclined horseshoes baffles, Promvonge et al. [18] determined the coefficients of heat transfer and friction, as well as the factor of thermal improvement for an experimental tubular HE. Using solid and porous type materials, Ramani et al. [19] theoretically and experimentally studied the thermal and pressure drop characteristics of a double pass SAC (Solar Air Collector). Using the SST method, Deng et al. [20] experimentally investigated the thermal enhancement in a flat-plate type SAC. Saedodin et al. [21] numerically and experimentally used the PMF (Porous-Metal-Foam) to augment the energetic performance of a flat-plate type SC. Using an experimental validation, Hernández and Quiñonez [22] estimated the natural convection heat transfer in SAHCs (Solar-Air-Heating-Collectors). Using circular and V-shaped obstacles placed on the absorber, Rajaseenivasan et al. [23] reported an experimental and theoretical analysis of the capacity of a SPSAH (Single-Pass-Solar-Air-Heater). Using numerically triangular wavy type baffles, Eiamsaard and Promvonge [24] enhanced the laminar heat transfer characteristics of a rectangular form channel. Using a CFD software, Jiang et al. [25] showed a simulation on the HEs (Heat Exchangers) with helical type baffles. To investigate the thermal transport and pressure loss behaviors, Tan et al. [26] experimentally used non-Newtonian type nanofluids in the shell-side of a helical type baffle with low-finned-tubes. Wang et al. [27] experimentally evaluated and compared the performance of HEs with COTH (Circumferential-Overlap-Trisection-Helical) type baffles and oil-water type fluids. Using a numerical technique, Galushchak et al. [28] simulated the thermal behavior of a tube with PHT (Punched-Helical-Tape) baffles. Other flow and heat transfer structures can be found in Ghachem et al. [29], Al-Rashed et al. [30,31], Ghalambaz and Zhang [32], Ghalambaz et al. [33][34][35] [68], and Selimefendigil [69][70][71][72].
The aim of the study was mainly focused on improving the hydrodynamic characteristics of Shell-and-Tube Heat Exchanger Channels through the technique of planting obstacles on their inner walls. The method is very well known, as mentioned in many previous studies. The various main points that were included in this study are: • Control of fluid flow by presenting the streamlines • Define fast-flow zones by giving axial velocity fields • Identify low-pressure regions and their relationship to recycling zones • The relationship of axial velocity to pressure and its effect on the coefficients of friction • Relation of Reynolds' values to flow characteristics.

W-shaped baffled channel under study
The channel model studied is shown in Fig. 1. It is a horizontal channel, according to the axial axis, that has a rectangular section, with two obstacles (or vortex generators) of the shape "W". All channel elements, i.e., walls and W-baffles, as well as their dimensions, are shown in Fig. 1. Air is used as a working fluid. This study is complementary to the study mentioned in the referenced paper [73]. Assuming that the airflow is steady, turbulent, Newtonian, incompressible, and then the flow equations can be written as [74]: (1) • Momentum equation (Eq. (2)): The standard k-ε model [75] was used for modeling the turbulence, for a range of Reynolds number varying from 12,000 to 32,000. The model relationships for the turbulent-kinetic-energy (k) and its rate (ε) of dissipation are as follows: and ∂ ∂ ( The hydraulic boundary conditions are defined as: • At the intake, (x = 0, −H/2 ≤ y ≤ H/2): • At the outlet, x = L: • At the solid walls, y = H/2 and y = −H/2: • Reynolds number, Re • The hydraulic diameter of the channel, D h • Skin friction coefficient, Cf • Friction factor, f

Numerical methods
The simulation adopts the computational method of finite volumes [76] to give the numerical solution, using the Commercial CFD ANSYS Fluent 12.0 [77]. To discretize the computational domain, a structured mesh In the first part of this research work, which contains the "heat transfer aspect", previously published (see [73]), we compared our dimensionless axial velocity ( u/U in ) curves with the numerical ones from Demartini et al. [74], to validate the present numerical model used, see Fig. 3.
In the second part of our research work, which includes the "hydrodynamic features", a comparison of the predicted pressure coefficients against the experimental data of Demartini et al. [74] was made. The comparison was carried out under the same flow and geometry conditions, used by Demartini et al. [74]. After proving the validity of our numerical model, we used this validated numerical model for the present new channel with W-shaped baffles for simulation.

Results and discussion 4.1 Streamlines and axial velocity contours
To display the hydraulic characteristics included in this study, the flow fields are shown in terms of streamlines and axial velocity contours, as reported in Figs. 4 and 5, respectively.
The effect of each of the WBs, i.e., W-shaped baffles, and the number of Reynolds, from 12,000 to 32,000, are also   shown. The angle of flow attack, from the WBs, was fixed at 45°, during the simulation. The flow field, in the presence of WBs, can be visualized by using these fluid contours.
The flow field of air clearly shows a decrease in axial velocity values, near the surfaces of the WBs, especially in areas near the rear sides. This is due to the concentration of a large ring of recycling cells in the region.
On the other hand, there is an increase of the axial velocity in the areas located near the top edges of the WBs, which extend to the channels wall surfaces. This increase is due to the presence of WBs, as a first cofactor. While, the second factor is the results of the presence of recycling cells on the right side of the WBs. These two factors cause a sudden change in the flow direction.
Moreover, maximum axial velocity values are present in the last section of the channel, and precisely, in the vicinity of its upper wall, to the right of the lower WB. This behavior from the flow field is due to the presence of the WBs.
The analysis of the flow field also showed that the axial values of velocity are affected by the change in Reynolds number, as there is a direct correlation between them.

Axial velocity profiles
The axial velocity profiles are also presented in the study, for a good detail in analyzing the results.  While, the negative velocities, found in the upper part of the channel, are evidence of the extension of the rotating ring found behind the first WB, to the region.
In the third section of the channel, precisely at 0.029 m before the exit section (x = L), i.e., 0.145 m to the right of the bottom WB, i.e., in the position x = 0.525 m, the speed values are maximal as they are 3.314 times the speed of the inlet. This is due to the reduced flow area that is resulted by the presence of WBs, as well as the presence of powerful cells for recycling on their rear sides, Fig. 6 (d).

Axial velocity as a function of Reynolds number
It is obvious that the axial velocity is proportional to variations of the Reynolds number values in the various previously examined regions, as reported in Fig. 7 (a)  The fluid flows from the left to right, according to a direct path, with positive axial velocities. Also, the presence of the WBs creates reverse flows, the axial velocity of which is negative. Both speeds improve as Reynolds' number improves.

Skin friction coefficient
In addition to the axial profiles, there are also normalized skin friction coefficient profiles ( Cf / f 0 ), as shown in Fig. 8

Skin friction coefficient as a function of Re number
Effects of Reynolds number on the friction can also be studied as shown in Fig. 9 (a) and (b), for both the upper and lower walls, respectively. Reynolds' values are within the specified range, between 12,000 and 32,000.
As we saw earlier in terms of changing velocity values and their relationship to Reynolds values, it is evident that the value of the friction coefficient is affected when the Reynolds number changes. This can be explained by the fact that the increase in the value of Reynolds number increases the flow disturbance, which increases the dynamic pressure values across the narrow passages, i.e., the gaps, and consequently increases the flow velocity and improves the size of the recycling cells, which induce to raise the values of the coefficients of friction, especially across the gaps.

Friction factor as a function of Reynolds number
The factor of friction is also discussed in this study by using the Eq. (16). Fig. 10 gives different values for this parameter due to the different Re number values used. By comparing all the states presented in Fig. 10, we conclude the factor of friction is an increasing function of the Re variable. This confirms the data in the previous Fig. 9.

Conclusion
In addition to the given heat transfer characteristics [73], we list some of the hydrodynamic features obtained through this study: • The air flows from the left to right, according to a direct path, with positive axial velocities. Also, the presence of the WBs creates reverse flows, the axial velocity of which is negative. The following studies are suggested to complement this research work: • Using the perforated model for WBs in order to reduce the friction loss in the channel, • Using the inclined model for WBs in order to decrease the pressure drop in the channel.