Experimental Investigation of the Thermoﬂuid Characteristics of Shell-and-Plate Heat Exchangers

: An experimental study regarding the thermoﬂuid characteristics of a shell-and-plate heat exchanger with di ﬀ erent chevron angles (45 ◦ / 45 ◦ , 45 ◦ / 65 ◦ , and 65 ◦ / 65 ◦ ) with a plate diameter of 440 mm was carried out. Water was used as the working ﬂuid on both sides and the corresponding temperatures ranged from 30–70 ◦ C. The ﬂow rate on the plate or shell side ranged from 10–60 m 3 / h. The e ﬀ ects of chevron angles on the heat transfer and ﬂuid ﬂow characteristics of shell-and-plate heat exchangers were studied in detail. With regard to the heat transfer performance on the plate side, a higher chevron angle (65 ◦ / 65 ◦ ) resulted in a signiﬁcantly better performance than a low chevron angle (45 ◦ / 45 ◦ ). The e ﬀ ect of the chevron angle became even more pronounced at high Reynolds numbers. Unlike the plate side, an increase in the chevron angle had a negative e ﬀ ect on the heat transfer performance of the shell side. Additionally, this opposite e ﬀ ect was more prominent at low Reynolds numbers due to the comparatively large contribution of the manifold. The friction factor increased appreciably with the increase in the chevron angle. However, when changing the chevron angle from 45 ◦ / 45 ◦ to 65 ◦ / 65 ◦ , the increase in the friction factor was about 3–4 times on the plate side while it was about 2 times on the shell side. This can be attributed to the presence of the distribution / collection manifold on the shell side. Empirical correlations for the Nusselt number and friction factor were developed for di ﬀ erent combinations of chevron angles with mean deviations of less than 1%.


Introduction
Shell-and-tube heat exchangers are the most common heat exchangers and are widely used in several industries as well as having process and petrochemical applications. Although shell-and-tube heat exchangers (STHE) are versatile and reliable and they can withstand high pressure and temperature, they have some disadvantages. For example, the thermal efficiency is relatively low (40-60%) in comparison with plate heat exchangers (>90%). Additionally, periodic alterations in the shell flow stream as a result of the baffle plates can cause a large drop in pressure. Also, if a flow recirculation zone exists in the shell side, this can appreciably weaken the shell-side performance. Furthermore, there are several leakage and bypass issues on the shell side. Another disadvantage of this type of heat exchanger is the vibration induced by the fluid flow due to fluid instability, vortex shedding, multi-phase buffeting, etc. [1]. Many of the aforementioned problems (e.g., flow re-circulation, high pressure drop, leakages and bypasses, low thermal efficiency, and vibration) can be addressed through the use of a plate heat exchanger (PHE), which offers high heat transfer performance, less volume, lower weight, and is easy to clean (for the gasket type). However, they can withstand lower pressure and temperature and leakages may still occur in gasket type PHEs.
that mass flux has a significant effect on the evaporation HTC in both types of evaporators, while the influence of saturation temperature is negligible. An increase in vapor quality reduces the evaporation HTC in a PHE, while its influence in a SPHE is also insignificant. The two-phase ∆P is highly affected by the saturation temperature and mass flux in both types of evaporators. Correlations for Nu and f were also developed. Song et al. [16] performed an experimental study on the evaporation heat transfer performance of a SPHE in high-temperature R-245fa heat pumps. Results showed improved evaporation HTC and increased two-phase ∆P with the increase in mass flux and vapor quality. Moreover, the heat transfer characteristics of a SPHE with an upward flow direction outperform the downward flow direction. The correlations developed for Nu and two-phase f were also presented. A detailed investigation of the fluid flow characteristics of an SPHE with corrugated sinusoidal pattern was carried out experimentally by Wang et al. [17] and the corresponding flow patterns in the upward and downward flow were proposed.
Despite the outstanding features of SPHE, studies on the thermofluid performance of this type of heat exchangers are still very rare. Also, most of the research is associated with two-phase flow including evaporation or condensation. Although the most effective geometrical parameter for the thermofluid characteristics of SPHEs is the chevron angle, very few studies have examined this parameter in detail. Although numerical simulations can be used for the design and optimization of heat exchangers and can easily show detailed flow behavior, they also need validation from experimental data. Also, numerical errors due to discretization of governing equations, simplifying assumptions, geometry simplification, turbulence modeling, etc., may occur. To ensure the suitability of simulations, test data is first required before further optimizations and simulations can be carried out. The objective of this study was to experimentally investigate the heat transfer and flow friction performance of this type of heat exchanger with different combinations of chevron angles on both the shell and plate side. The effects of different parameters such as the chevron angle of the shell side and plate side on the heat transfer and flow friction characteristics of SPHE are studied in detail. Empirical correlations for the heat transfer and flow friction characteristics of shell-and-plate heat exchangers were developed based on different chevron angles, which have not been reported in prior studies.

Experimental Setup and Procedure
The schematic of the experimental setup is illustrated in Figure 1. The working fluid is water for both the hot and cold sides. For the hot side, water is heated in a PHE by hot water that comes from the boiler and is subsequently pumped into the SPHE. PHE is used for the accurate control of the hot side water. Water for the cold side is cooled by a cooling tower and pumped to the SPHE in the test section. The SPHE is insulated in order to prevent heat loss as shown in Figure 2b. A sample of the plates inside the SPHE is presented in Figure 2c. The cross section of the plates has a wavy configuration (Figure 2d). The geometrical parameters of the SPHE are tabulated in Table 1. The plates are circular and consist of two different chevron angles. Hot water enters the shell side from the top nozzle with an inlet temperature of 70 • C and is distributed in the shell side plates, while cold water enters the plate side from the bottom nozzle with an inlet temperature of 30 • C and is distributed in the plate side plates (Figure 2a). The hot and cold streams flow counter-currently. Resistance temperature detectors (RTD) were used to obtain highly accurate temperature measurements at the inlets and outlets and these RTDs were pre-calibrated with 0.1 • C precision. The pressure drops were measured by Yokogawa differential pressure transducers with ±0.35% accuracy. The remote type with model numbers of AXF050G, AXFA14G, AXF100G, and AXFA14G were used for the shell side, while models AXF150G and AXF250G of the integral type were used for the plate side. The inlet and outlet pressure were measured using WIKA A-10 pressure transducers with ±0.5% accuracy. Yokogawa flowmeters were also applied to measure the flow rates on both the hot (model EJA118E with an accuracy of ±0.2%) and cold (model EJA110A with accuracy of ±0.065%) side. and comparatively large to ensure the dominant resistance on the plate side. Then a follow-up Wilson plot method was employed to derive the relationship on plate side. Analogously, the relationship of the shell-side can be obtained by fixing a very large flow rate at the plate side, followed by using the Wilson plot technique to obtain the heat transfer relation of the shell-side. Further details of the Wilson plot technique are given below.     1.196 Experiments were carried out for three different cases: chevron angles of 45 • , chevron angles of 65 • , and a combination of chevron angles of 45 • and 65 • ( Table 2). For each case, the volumetric flow rate of shell side changed, while the volumetric flow rate of the plate side was maintained as constant and comparatively large to ensure the dominant resistance on the plate side. Then a follow-up Wilson plot method was employed to derive the relationship on plate side. Analogously, the relationship of the shell-side can be obtained by fixing a very large flow rate at the plate side, followed by using the Wilson plot technique to obtain the heat transfer relation of the shell-side. Further details of the Wilson plot technique are given below.

Data Reduction
The Reynolds number (Re) is the ratio of the inertial force to the viscous force and can be obtained as follows: where Dh is the hydraulic diameter, which is calculated from the following formula [16]: The heat transfer rate ( ) is calculated from the following correlation:

Data Reduction
The Reynolds number (Re) is the ratio of the inertial force to the viscous force and can be obtained as follows: where D h is the hydraulic diameter, which is calculated from the following formula [16]: The heat transfer rate ( . Q) is calculated from the following correlation: where ∆T is the temperature difference between the inlet and outlet and ∆T lm is the logarithmic mean temperature difference, which can be obtained from the following correlation: UA can be also determined as follows: The Nusselt number (Nu) can be obtained by using the Wilson plot [18,19] based on the following correlation: where C 2 can be considered constant as 1/3 [16] and Pr is the Prandtl number, which can be obtained from the following formula: The flow rate is varied on a specific side (e.g., plate side) while the thermal resistance of the other side is kept comparatively small and constant. By combining Equations (3) to (7) and using linear fitting data with R 2 > 0.999, C 0 and C 1 can be calculated by trial and error (since there are two unknown parameters in one equation [3]) and consequently, the Nusselt number for the shell and plate sides can be specified.
In order to determine the friction factor (f ), the frictional pressure drop was specified. The measured total pressure drop (∆P) in the SPHE consists of frictional (∆P f ), elevation (∆P g ), acceleration (∆P a ), and port (∆P port ) pressure drops [15]. By specifying the frictional pressure drop (∆P f ) from the measured total pressure drop, the friction factor (f ) can be determined from the following correlation: Note that the velocity is obtained at the centerline of the plate or shell side. In order to obtain the friction factor for the plate side or shell side, l is substituted by l p or l s in the above correlation, respectively, with the relative frictional pressure drop. V is the mean channel flow velocity, which is obtained in the maximum cross-sectional area of the plate [14].

Uncertainty Analysis
Uncertainty analysis was performed using the methods presented in [16,20]. The summary of the uncertainties of the measured parameters and the calculated parameters are tabulated in Table 3. Based on Table 3, the different uncertainties that exist in the measurements result in up to 10.2% and 10.19% error in the calculation of heat transfer coefficient and fiction factor, respectively. A sample of the procedure for the uncertainty calculation is included in the Appendix A.

Results and Discussions
As mentioned above, three cases with different combinations of chevron angles were investigated: 45 • /45 • , 45 • /65 • , and 65 • /65 • . The heat transfer and fluid flow characteristics of the SPHE in different cases are discussed in detail.

Heat Transfer Characteristics of SPHE
The Nusselt number was calculated by combining Equations (3) to (7). The Wilson plot for all cases mentioned in Table 2 is illustrated in Figure 3. From the linear fitting data (y = ax + b), constants C 0 and C 1 can be obtained so that a = C 0 −1 and x = Re (−C1) . The calculated C 0 and C 1 for all cases are tabulated in Table 4.

Results and Discussions
As mentioned above, three cases with different combinations of chevron angles were investigated: 45°/45°, 45°/65°, and 65°/65°. The heat transfer and fluid flow characteristics of the SPHE in different cases are discussed in detail.

Heat Transfer Characteristics of SPHE
The Nusselt number was calculated by combining Equations (3) to (7). The Wilson plot for all cases mentioned in Table 2 is illustrated in Figure 3. From the linear fitting data (y = ax + b), constants C0 and C1 can be obtained so that a = C0 −1 and x = Re (−C1) . The calculated C0 and C1 for all cases are tabulated in Table 4.    By obtaining the C 0 and C 1 through the Wilson plot technique, the Nusselt number and HTC can be calculated for all cases. Figure 4 shows the Nusselt number vs. the Reynolds number subject to different chevron angles on both the plate and shell sides. It can be seen that the Nusselt number increases with the rise in the Reynolds number for different chevron angles due to the higher heat transfer rate in higher flow rates. Furthermore, the Nu number increases remarkably with the chevron angle on the plate side as depicted in Figure 4a. Additionally, the increase becomes even more pronounced as the Reynolds number increases. For instance, at a Reynolds number of 3000, the Nu of the 65 • /65 • plate is about three times higher than that of the 45 • /45 • plate. This is illustrated in the schematic in Figure 5a,b. The increase in the chevron angle results in more turbulent mixing, which yields higher heat transfer performance like a typical plate heat exchanger [21], and also offers better flow distribution alongside the plate. Note that there is a basic difference between the round plate of the shell-and-plate heat exchanger and the convention rectangular plate in the plate heat exchanger. For a lower chevron angle combination like the 45 • /45 • plate shown in Figure 5a, the flow rate around the edge of the round plate is lower than in the center region due to its longer flow path. For a larger chevron angle such as the 65 • /65 • combination, the flow rate is effectively forced to circulate across the edge as depicted in Figure 5b, thereby resulting in a better flow distribution. In summary, on the plate side, higher turbulent mixing and better flow distribution contribute to a significant increase in the heat transfer performance of the 65 • /65 • plate. However, the effect of chevron angle on the heat transfer performance on the shell side does not follow the plate side. In fact, the increase in chevron angle slightly offsets the heat transfer performance when the chevron angle is increased from 45 • /45 • to 65 • /65 • as shown in Figure 4b. The deterioration is more prominent at a lower Reynolds number. Note that there is fundamental difference in the flow field between the plate side and the shell side. The flow on the shell side encounters the distribution/collection manifold, which causes the flow to spread, resulting in some secondary flow behind the distribution/collection manifold as schematically illustrated in Figure 5c,d. Apparently, the resultant secondary flow jeopardizes the heat transfer and increases the pressure drop. Although the increase in the chevron angle can create better mixing, it also increases the ineffective area behind the distribution/collection manifold, thus lowering the heat transfer performance significantly at the lower Reynolds numbers. Although better turbulent mixing at a higher Reynolds number can ease the negative effect of the chevron angle, the heat transfer performance of 45 • /45 • is still about 10 % higher than that of 65 • /65 • at a Reynolds number of 6000. distribution/collection manifold as schematically illustrated in Figure 5c,d. Apparently, the resultant secondary flow jeopardizes the heat transfer and increases the pressure drop. Although the increase in the chevron angle can create better mixing, it also increases the ineffective area behind the distribution/collection manifold, thus lowering the heat transfer performance significantly at the lower Reynolds numbers. Although better turbulent mixing at a higher Reynolds number can ease the negative effect of the chevron angle, the heat transfer performance of 45°/45° is still about 10 % higher than that of 65°/65° at a Reynolds number of 6000.

Flow Friction Characteristics of the SPHE
In order to perform a precise investigation of the flow friction characteristics of the SPHE, the pressure drop was measured in isothermal conditions, meaning that the inlet temperatures for both the cold and hot side were the same and there was no heat transfer between the plate and shell sides. The friction factor was plotted with various Reynolds numbers for all cases and these are shown in Figure 6. Based on the results, the friction factor decreases with an increase in the Reynolds number for all cases. The increase in the flow rate increases the frictional pressure drop. However, the increase in velocity is much higher than the increase in the frictional pressure drop and consequently, the

Flow Friction Characteristics of the SPHE
In order to perform a precise investigation of the flow friction characteristics of the SPHE, the pressure drop was measured in isothermal conditions, meaning that the inlet temperatures for both the cold and hot side were the same and there was no heat transfer between the plate and shell sides. The friction factor was plotted with various Reynolds numbers for all cases and these are shown in Figure 6. Based on the results, the friction factor decreases with an increase in the Reynolds number for all cases. The increase in the flow rate increases the frictional pressure drop. However, the increase in velocity is much higher than the increase in the frictional pressure drop and consequently, the friction factor declines slightly. In both cases, where the plate side flow rates are varied (Figure 6a) and the shell side flow rates are varied (Figure 6b), the increase in the chevron angle results in a considerable increase in the friction factor. Note that there is a difference in the increase rate of the friction factor between the plate side and shell side when the chevron angle is changed from 45 • /45 • to 65 • /65 • . On the plate side, there is a difference of about 3-4 times. However, there is a difference of about 2 times on the shell side. Again, this can be attributed to the presence of the distribution/collection manifold on the shell side. The main flow is forced to flow across the manifold, therefore lessening the effect of the pressure drop caused by the plate geometry (the chevron angle).

Development of Empirical Correlations
Up until now, there are no predictive correlations for the single-phase performance of the shelland-plate heat exchanger. Therefore, empirical correlations for the Nusselt number and friction factor for shell and plate sides were developed based on the present experimental data. The correlations are functions of the Reynolds number, the Prandtl number, and the chevron angle. Since each plate consists of two different chevron angles on each side (β1 and β2), the average chevron angle (α) in radian is used in the developed correlations, which is defined as follows: The Nusselt number for both the shell and plate sides can be obtained from the following correlation: where the parameters C0 and C1 are functions of the chevron angle and can be predicted from the following correlations for the shell and plate sides, respectively, which have been developed by data curve fitting and trial and error.
Shell side:

Development of Empirical Correlations
Up until now, there are no predictive correlations for the single-phase performance of the shell-and-plate heat exchanger. Therefore, empirical correlations for the Nusselt number and friction factor for shell and plate sides were developed based on the present experimental data. The correlations are functions of the Reynolds number, the Prandtl number, and the chevron angle. Since each plate consists of two different chevron angles on each side (β 1 and β 2 ), the average chevron angle (α) in radian is used in the developed correlations, which is defined as follows: The Nusselt number for both the shell and plate sides can be obtained from the following correlation: where the parameters C 0 and C 1 are functions of the chevron angle and can be predicted from the following correlations for the shell and plate sides, respectively, which have been developed by data curve fitting and trial and error. Shell side: Plate side: The comparison between the Nusselt numbers obtained from the experimental data and the developed correlations are illustrated in Figure 7. The correlations are able to predict all the experimental data within ±5%. The mean deviations for the predicted Nusselt numbers for the shell and plate sides are less than 0.5%.  The friction factor can be calculated from the following correlation for both shell and plate sides.
where the parameters f0 and f1 can be specified based on the following correlations as functions of the chevron angle. Shell side:  Figure 8 represents the comparison between the friction factors measured from the experimental data and those obtained from the developed correlations. It is quite clear that all the experimental data can be predicted by the developed correlations within ±5% with the mean deviations for the predicted friction factors for the shell and plate sides being less than 0.7%. The friction factor can be calculated from the following correlation for both shell and plate sides.
where the parameters f 0 and f 1 can be specified based on the following correlations as functions of the chevron angle.
Shell side: f 0 = 1.6671(tan α) 2 − 4.2324 tan α + 4.5853 (16) Plate side: f 0 = 1.3855(tan α) 2 − 0.865 tan α − 0.0167 (18) f 1 = − 0.0817(tan α) 2 − 0.1754 tan α + 0.1317 (19) Energies 2020, 13, 5304 12 of 15 Figure 8 represents the comparison between the friction factors measured from the experimental data and those obtained from the developed correlations. It is quite clear that all the experimental data can be predicted by the developed correlations within ±5% with the mean deviations for the predicted friction factors for the shell and plate sides being less than 0.7%.  It should be noted that the developed correlations were obtained in the range of 45° ≤ α ≤ 65°. More experiments are needed in the future in order to develop more generalized correlations.

Conclusions
This study conducted experiments to investigate the thermofluid characteristics of a shell-andplate heat exchanger with different chevron angles (45°/45°, 45°/65°, and 65°/65°) and a plate diameter of 440 mm. Water was used as the working fluid on both sides and the corresponding temperatures ranged from 30-70 °C. The flow rates in the plate or shell side ranged from 10-60 m 3 /h. The heat transfer and frictional characteristics of the measurements are in terms of the Nusselt number and friction factor vs. Reynolds numbers. The heat transfer characteristics were obtained through the typical Wilson plot technique. Empirical correlations were developed for the Nusselt number and friction factor for both the shell and plate sides. Based on the above discussion, several major conclusions are drawn as follows: • For all cases, the Nusselt number increases with an increase in the Reynolds number, while the friction factor decreases with an increase in the Reynolds number.

•
For the heat transfer performance on the plate side, a higher chevron angle (65°/65°) significantly outperforms that of a low chevron angle (45°/45°). Additionally, the effect of the chevron angle becomes even more pronounced at high Reynolds numbers. This is because better flow distribution can be achieved.

•
Unlike the plate side, an increase in the chevron angle has a negative effect on the heat transfer performance. This is because of the presence of the distribution/collection manifold on the shell side, which results in appreciable secondary flow behind the manifold and lessens the influence of the plate geometry. This opposite effect is more prominent at low Reynolds numbers due to the comparatively large contribution of the manifold.

•
The friction factor is increased appreciably with an increase in the chevron angle. However, when changing the chevron angle from 45°/45° to 65°/65°, the increase in the friction factor is about 3-4 times on the plate side while it is about 2 times on the shell side. Again, this can be attributed to the presence of the distribution/collection manifold on the shell side.

•
The developed correlations for the Nusselt number and the friction factor as functions of the Reynolds number, Prandtl number, and chevron angle can predict all the experimental data accurately with mean deviations less than 1%. It should be noted that the developed correlations were obtained in the range of 45 • ≤ α ≤ 65 • . More experiments are needed in the future in order to develop more generalized correlations.

Conclusions
This study conducted experiments to investigate the thermofluid characteristics of a shell-and-plate heat exchanger with different chevron angles (45 • /45 • , 45 • /65 • , and 65 • /65 • ) and a plate diameter of 440 mm. Water was used as the working fluid on both sides and the corresponding temperatures ranged from 30-70 • C. The flow rates in the plate or shell side ranged from 10-60 m 3 /h. The heat transfer and frictional characteristics of the measurements are in terms of the Nusselt number and friction factor vs. Reynolds numbers. The heat transfer characteristics were obtained through the typical Wilson plot technique. Empirical correlations were developed for the Nusselt number and friction factor for both the shell and plate sides. Based on the above discussion, several major conclusions are drawn as follows: • For all cases, the Nusselt number increases with an increase in the Reynolds number, while the friction factor decreases with an increase in the Reynolds number.

•
For the heat transfer performance on the plate side, a higher chevron angle (65 • /65 • ) significantly outperforms that of a low chevron angle (45 • /45 • ). Additionally, the effect of the chevron angle becomes even more pronounced at high Reynolds numbers. This is because better flow distribution can be achieved.

•
Unlike the plate side, an increase in the chevron angle has a negative effect on the heat transfer performance. This is because of the presence of the distribution/collection manifold on the shell side, which results in appreciable secondary flow behind the manifold and lessens the influence of the plate geometry. This opposite effect is more prominent at low Reynolds numbers due to the comparatively large contribution of the manifold.

•
The friction factor is increased appreciably with an increase in the chevron angle. However, when changing the chevron angle from 45 • /45 • to 65 • /65 • , the increase in the friction factor is about 3-4 times on the plate side while it is about 2 times on the shell side. Again, this can be attributed to the presence of the distribution/collection manifold on the shell side.

•
The developed correlations for the Nusselt number and the friction factor as functions of the Reynolds number, Prandtl number, and chevron angle can predict all the experimental data accurately with mean deviations less than 1%.