Abstract
In this analysis, the baffling method is used to increase the efficiency of channel heat exchangers (CHEs). The present CFD (computational fluid dynamics)based work aims to analyze the constant property, steady, turbulent, Newtonian, and incompressible fluid flow (air), in the presence of transversesection, arcshaped vortex generators (VGs) with two various geometrical models, i.e., arc towards the inlet section (called arcupstream) and arc towards the outlet section (called arcdownstream), attached to the hot lower wall, in an inline situation, through a horizontal duct. For the investigated range of Reynolds number (from 12,000 to 32,000), the order of the thermal exchange and pressure loss went from 1.599–3.309 to 3.667–21.103 times, respectively, over the values obtained with the unbaffled exchanger. The arcdownstream configuration proved its superiority in terms of thermal exchange rate by about 14% than the other shape of baffle. Due to ability to produce strong flows, the arcdownstream baffle has given the highest outlet bulk temperature.
1 Introduction
The enhancement of the efficiency of heat exchangers (HEs) by the deflector insertion technique in the fluid flow domain has many engineering and industrial applications. By using numerical simulations, Pirouz et al. [1] used the Lattice Boltzmann Method (LBM) to explore the thermal behavior in a channel heat exchanger (CHE) equipped by upper and lower wallinserted baffles. The influence of several geometrical variables of helical baffles on the overall performances of HEs was explored by Du et al. [2]. Based on the concepts of permeability and porosity, You et al. [3] introduced a numerical approach for shellandtube heat exchangers (STHXs). They used the distribution of turbulence kinetic energy, dissipation rate of energy, and heat source to estimate the effect of tubes on fluid. Eiamsaard and Promvonge [4] explored the efficiency of a CHE having grooves on the lower wall. Also, Afrianto et al. [5] predicted the hydrothermal characteristics of liquid natural gas (LNG) in a HE. Additionally, for several Reynolds numbers (from 4,475 to 43,725), Ozceyhan et al. [6] explored the influence of the presence of rings near the wall and their clearance on the overall performances of a CHE. Furthermore, the improvements in heat transfer rates that are yielded by the baffling technique in a pipe heat exchanger (PHE) have been reported by Nasiruddin and Siddiqui [7]. Moreover, via the CFD software FLUENT, Zhang et al. [8] provided details on a PHE with overlapped helical baffles. Also, under laminar flow conditions and with the help of CFD software, Sripattanapipat and Promvonge [9] analyzed the hydrothermal characteristics through a 2D CHE. They used baffles with diamond shape and inserted in a staggered arrangement. Additionally, Santos and de Lemos [10] were interested in a channel having baffles constructed from porous and impermeable materials. Via numerical analysis and for a tube heat exchanger (THE), Xiao et al. [11] used different values of Prandtl number and helical tilt angles for helical baffles. Mohsenzadeh et al. [12] analyzed the forced convective thermal transfer through a horizontal CHE. They explored the influence of baffle clearance and Reynolds number. Under turbulent flow conditions, Valencia and Cid [13] used the CFD method to study the hydrothermal details in a CHE provided with square bars in the streamwise direction of flow. In another study, Promvonge et al. [14] determined the hydrothermal fields in a 3D CHEinclined Vshaped discrete thin VGs (vortex generators).
By experiments, Zhang et al. [15] explored the hydrothermal fields of STHEs equipped by helical baffles. Also, Wang et al. [16] were interested in the flow through a channel provided with pin fins. Additionally, Dutta and Hossain [17] were interested in a CHE having perforated baffles under various inclination angles. In another study, Ali et al. [18] studied the thermal transfer phenomenon from the outer surface of horizontal cylinders. Furthermore, Wang et al. [19] characterized the hydrothermal fields through a channel having periodic ribs on one wall. Moreover, Rivir et al. [20] achieved measurements of the flow details in a CHE equipped with transverse ribs on the sidewalls. They explored the effect of three geometrical cases: single rib, staggered multiple ribs, and inline multiple ribs.
Other interesting studies are available in the literature for various fluid flow situations and different numerical solutions, for example, see Kazem et al. [21], Rashidi et al. [22], Kumar et al. [23,24,25], Ghanbari et al. [26], Goufo et al. [27], Shafiq et al. [28], Ilhan et al. [29], Basha et al. [30], Baskonus [31], Guedda and Hammouch [32], Ahmad et al. [33,34,35,36], and Menni et al. [37,38,39,40,41,42]. Most of the studies carried out focused on the HE in order to improve its performance. Enhancing heat transfer is the goal of most researches in both numerical and experimental studies. So, the topic is very interesting, which led us to search a technique to increase the effectiveness of the exchanger. This work is a numerical analysis of a constant property, steady, turbulent, Newtonian, and incompressible fluid flow (air) inside a rectangular duct heat exchanger. Two types of transverse, solidtype, and arcshaped obstacles are attached on the lower hot wall in inline arrays, namely, an arc towards the inlet section (called arcupstream) and an arc towards the outlet section (called arcdownstream). Both obstacle forms give a different structure to the flow, which enhances heat transfer in different amounts. The study compares the best performance which identifies the effective model.
2 Physical model under analysis
A numerical simulation was reported on the turbulent flow and forcedconvection of an incompressible Newtonian fluid (air) with constant thermal physical properties and flowing inside a channel (Figure 1). Two transverse, solid, inline obstacles having various geometrical configurations, i.e., arc towards the inlet section of the channel, called arcupstream (Figure 1a), and arc towards the exit section of the channel, called arcdownstream (Figure 1b), were fitted into the duct and attached on the bottom wall to lengthen the trajectory of the fluid and increase the heat exchange surface.
Figure 1
Two new models of VGs are suggested in the present study, namely, arcupstream and arcdownstream baffles. The values of height (H) and length (L) of the channel are 0.146 and 0.554 m, respectively. The first arcshaped baffle is attached on the lower wall at L _{in} = 0.218 m from the entrance section of the channel, while the 2nd arcshaped obstacle is inserted at c = 0.142 m from the first obstacle. The baffles height (a), thickness (b), and attack (θ) are 0.08 m, 0.01 m, and 45°, respectively. Air is used as a working fluid and Reynolds numbers are changed from 12,000 to 32,000.
3 Modelling and simulation
For the steady state with neglected radiation thermal exchange mode, the equations of mass, momentum, and energy are expressed as [7]
where,
where, μ _{ t } is the fluid turbulent viscosity (kg m^{−1} s^{−1}); and C _{ μ }, C _{1ε }, C _{2ε }, σ _{ k }, and σ _{ ε } are the model constants. The present thermal and hydrodynamic limit conditions are expressed as [45]:
At x = 0
At y = ±H/2
At x = L
where, ϕ stands for the dependent variables u, v, k, T, and ε. The calculations are achieved with the finite volume technique [46], SIMPLE algorithm [46], and the Quick scheme [47]. The Nu_{0} and f _{0} values of the unbaffled channel were verified [38] by comparing them with the correlations of Dittus–Boelter [48] and Petukhov [49], respectively. The comparison demonstrated that there is a quantitative agreement between the CFD data and the experimental relationships results [48,49].
4 Results and discussion
4.1 Streamfunction field
Figure 2 illustrates the streamlines for the different arcbaffle configurations, i.e., arcupstream and arcdownstream. For the two studied geometrical models, the flow is uniform until reaching the 1st arcbaffle. Then, recirculating flows are formed at the baffled region, referenced here as ‘zone A.’ The size of these vortices is significant in the case of arcupstream type baffles. The sharp edge of the baffle presents a point of detachment, the so referenced here as ‘zone B.’ The flow is then detached from the arcbaffle, resulting thus in a depression behind baffles. Furthermore, recirculation areas (zones ‘C’ and ‘D’) are formed behind baffles, where the widest recirculation zone is observed with the arcdownstream baffle. It is surrounded by isosurfaces that take elliptical shapes.
Figure 2
4.2 Mean velocity field
Figure 3 reports the mean velocity fields for different configurations of arcbaffles, i.e., arcupstream and arcdownstream. The velocities are weak next to the left side of the first arcbaffle, region ‘A,’ for both models of arcobstacles studied. The velocity magnitudes are also low behind the second arcVG. The velocity is important at the edge of the first and the second arcshaped baffles, zone ‘E.’ In this same region, the fluid velocity for the second obstacle type (arcdownstream baffle) reaches up to 3.64 m/s, followed by that of the first type (arcupstream baffle), 3.28 m/s. In the regions between both the first and the second arcbaffles, zone ‘C,’ the airflow velocity is significant in the arcdownstream model than that of the other model.
Figure 3
4.3 Axial velocity field
Figure 4 illustrates the impact of the variation of the arcVG geometry on the axial velocity field. For both kinds of baffles, the streamlines are parallel in the unbaffled areas of the duct. However, the velocity magnitudes are almost negligible in the downstream areas of arcbaffles, zones ‘C’ and ‘D,’ which is caused by the presence of recirculating flows. An increase in the velocity is observed in the space between the tip of arcVG to the upper wall of the exchanger, referenced here as ‘zone E.’ This is due to the presence of the arcshaped VG and the abrupt modification in the flow direction.
Figure 4
The fluid flow is accelerated just after the first arcVG until reaching 274–346% of the inlet velocity, depending on the shape of VGs. It should be noted that the VG configuration has a significant influence in the zones ‘C,’ ‘D,’ and E,’ which is mainly caused by the modification in the streamlines. The arcupstream baffle increased the axial velocity by about 2.747 times over the inlet velocity U _{in} (Figure 4).
4.4 Transverse velocity field
The distribution of ytransverse velocity is plotted in Figure 5a and b for the arcupstream and arcdownstream baffles, respectively. Positive and negative velocity gradients are remarked at the tip of the 1st arcbaffle (zones ‘B’) and 2nd arcbaffle (zone ‘F’), respectively.
Figure 5
4.5 Dynamicpressure field
The dynamicpressure fields for both arcobstacle configurations are plotted in Figure 6. As illustrated in this figure, the values of the dynamicpressure coefficient are weak near the VGs due to the presence of vortices.
Figure 6
However, the dynamicpressure augments in the regions between the baffles tip and the upper wall of the exchanger, where the maximum values are located between the 1st and 2nd arcbaffles (zone ‘E’), which is resulted from the high airflow velocities. In addition, the highest amount of P _{d} depends on the shape of arcVG, where it is lower by about 18% for the arcupstream baffle than that for the other case.
4.6 Dimensionless axial velocity profiles
The curves of the dimensionless axial velocity (U/U _{in}) just after the two baffles are plotted in Figure 7. As observed, the reattachment length for the arcdownstream baffle is greater than that for the arcupstreambaffle, regardless of the value of Re.
Figure 7
4.7 Thermal fields
The thermal fields illustrated in Figure 8 show that the baffled region is the most heated. The temperature drops in the areas between the tip of arcobstacle and the surfaces of the duct, which is due to the high fluid velocity and interaction between the fluid particles in these regions.
Figure 8
A comparison of the outlet fluid temperature is provided in Figure 9, where the most considerable values of the temperature are reached with the arcdownstream baffle. Because of its ability to produce strong flows, the arcdownstreamshaped VG is more advantageous than the other model.
Figure 9
4.8 Heat transfer
The results of the ratio (Nu_{ x } /Nu_{0}) are summarized in Figure 10 for both arcshaped baffles. Both the arcdeflectors push the flow towards the upper part of the duct, which allows further absorption of the thermal energy from the heated surface. The lowest value of the Nu_{ x } /Nu_{0} is observed on the upstream side of the first arcbaffle, while the highest amount is remarked on the opposite side of the 2nd arcbaffle. This figure shows also that the Nu_{ x } /Nu_{0} is considerable in the downstream area of the 1st arcVG. This augmentation is yielded from the efficient mixing by vortices, which corresponds to high rates of the local thermal exchange. For both shapes of baffles, the values of (Nu_{ x } /Nu_{0}) are similar at the positions between (0 m) and (0.2 m). However, there is an important increase in the (Nu_{ x } /Nu_{0}) in the case of arcdownstream type baffle from the position (0.2 m) until the outlet of the duct.
Figure 10
Figure 11 presents the change of the average ratio (Nu/Nu_{0}), where a proportional increase is observed according to Re. The maximum Nu/Nu_{0} is reached with the arcdownstream case. Compared to the unbaffled exchanger and for Re = 12,000–32,000, the average Nu gains for the arcupstream and arcdownstream baffles are 159–284% and 187–331%, respectively. In addition, and at the highest Re, the arcdownstream baffle overcomes the other shape of baffles by about 14% in terms of thermal exchange rates (Nu/Nu_{0}) than that reached with the arcupstream (Figure 11).
Figure 11
4.9 Friction loss
The variation of the normalized skin friction coefficient (C _{f} /f _{0}) on the top wall of the duct is provided in Figure 12. From this figure, both shapes of the baffles give the same trends of C _{f} /f _{0}. Also, an increased C _{f} /f _{0} is observed in the region between the arcbaffles (0.228 m < x < 0.37 m). The arcupstream and arcdownstream baffles provided, respectively, an increase in C _{ f } by about 73 and 117 times over the unbaffled exchanger. Furthermore, the use of arcdownstream baffles gives higher thermal exchange than that of the other model by about 37%.
Figure 12
The changes of the friction factor ratio (f/f _{0}) vs Re are shown in Figure 13. A proportional increase is observed in the values of Re (f/f _{0}). In addition, and compared to the smooth duct, the arcupstream and arcdownstream baffles provided, respectively, an increase in (f/f _{0}) by about 3–16 and 4–21 times when Re has been changed from 12,000 to 32,000. This means that the arcdownstream baffle generates greater friction loss than the arcupstream baffle by around 23.266%, at the highest Re.
Figure 13
4.10 Effect of the arcshaped baffle
Finally, the results of the thermal performance factor (TEF) are summarized in Figure 14. As observed, the TEF tends to augment with the rise of Re for both shapes of VGs under inspection. At Re = 32,000, the optimum value of the TEF is about 1.138 and 1.212 for the arcupstream and arcdownstreamshaped baffles, respectively. Accordingly, the highest TEF is found with arcdownstream baffle, which is estimated to be higher than that of the arcupstream baffles by about 6%. The effect of arcdownstream baffles can also be highlighted based on literature data. In the presence of the following conditions: L = 0.554 m, L _{in} = 0.218 m, H = 0.146 m, D _{h} = 0.167 m, a = 0.08 m, b = 0.01 m, and Re = 32,000, their performance has been compared with many previously realized baffles [42]. The relative difference of results shows a remarkable improvement in the presence of an inline downstream arcbaffle pair by about 7.019, 3.958, 3.130, 3.580, 6.572, 10.815, 7.536, 1.715, 11.485, 10.971, and 8.221% over the upstreamarc, rectangular (simple), triangular, trapezoidal, corrugated, plus, S, V, W, T, and Γshaped onebaffle channel, respectively (Figure 15).
Figure 14
Figure 15
5 Conclusion
A numerical inspection has been conducted on the characteristics of the turbulent convection of air flowing in a baffled rectangular exchanger. Two shapes of arcbaffles were considered, namely, the arcupstream and arcdownstream shapes. These obstacles were inserted on bottom wall of the exchanger in inline arrays. The result analysis shows a reinforcement in fluid dynamics with a considerable enhancement in heat exchange in the case of the arcdownstream second obstacle due to the secretion of very strong cells on their back sides, which also caused a significant increase in skin friction coefficients, especially at high flow rates. This second configuration of the arcbaffle (arcdownstream) proved its superiority in terms of thermal exchange rate by about 14% than the other shape of baffle. At Re = 32,000, this optimal model of the arcbaffle showed an increase in the enhancement factor by about 7.019, 3.958, 3.130, 3.580, 6.572, 10.815, 7.536, 1.715, 11.485, 10.971, and 8.221% compared to the cases of one baffle, i.e., upstreamarc, rectangular (simple), triangular, trapezoidal, corrugated, plus, S, V, W, T, and Γ, respectively.

Funding: This work was supported by the National Natural Science Foundation of China (No. 71601072) and Key Scientific Research Project of Higher Education Institutions in Henan Province of China (No. 20B110006).
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