1. Introduction
Global energy demand is increasing together with the growing world population, and this energy is mostly provided by nonrenewable energy sources [
1], which also contribute to climate change and global warming [
2]. Using renewable energy resources can aid in reducing harmful gases; however, the implementation of new renewable energy programs is a slow process that is still not preferred by many countries [
3]. Therefore, debate continues on the best strategies to increase the efficiency of the existing power plants and reduce their fossil fuel consumption. One of the promising methods that can be applied to existing systems that use components with high heat exchange capabilities [
4] is improving the thermal performance of the heat exchangers.
Heat exchanger design may undergo significant modification based on the heat exchanger type and function. Therefore, various types of heat exchangers, such as plate-fin [
5], fin tube [
6], microchannel [
7], double pipe [
8], and shell and tube [
9], have been developed so far by altering shapes, sizes, and materials and inserting different types of flow mixers into heat exchange locations. Among the studies focused on the thermal performance enhancement of heat exchangers, the majority of them include passive methods because they require no additional power and are easy to implement [
10,
11]. Active methods, on the other hand, require external power to generate magnetic fields [
12], electric fields [
13], acoustic effects [
14], mechanical movements [
15], and pulsations or vibrations, which is a significant disadvantage when compared to passive methods [
16]. Nevertheless, some studies [
17,
18] included both methods to increase heat transfer. To date, various shapes of vortex generators have been proposed [
19]. The fundamental purpose of adopting vortex generators in heat exchangers is that they form secondary flow by breaking the thermal boundary layer along the surface of the heat exchanger to carry heat better to the central locations of the flow. This reduces the time of heat transfer intended to be diffused through the fluid. In exchange for that, they cause pressure drop due to enhanced drag.
Joardar and Jacobi [
20] conducted experimental research with winglet-type vortex generator arrays considering Reynolds numbers in the range of 220 to 970, and reported that the heat transfer coefficient was enhanced by up to 68.8% while pressure drop increased by 87.5%. They concluded that the thermal performance of fin-tube heat exchangers can be enhanced with vortex generator arrays. In another study conducted by Samadifar et al. [
21], the performance of a fin-plate heat exchanger having a triangular cross-section was investigated numerically using six different vortex generators. They found that thermal performance is at its highest with rectangular-type vortex generators (RVGs) compared to others. In addition to that, 45° vortex generators demonstrated the highest heat transfer rate. Abdollahi and Shams [
22] studied the effects of shape and the attack angle of winglet vortex generators in terms of heat transfer increment in a rectangular channel by combining three different methods. They used an artificial neural network (ANN), a multi-objective genetic algorithm, and computational fluid dynamics. They reported that with respect to shape comparison, RVGs show the highest heat transfer performance owing to the larger area that confronts the fluid flow. Therefore, the pressure drop with RVGs was also the highest. Gentry and Jacobi [
23,
24] performed similar experiments in 1997 [
23] and 2002 [
24] to demonstrate heat transfer enhancement using delta wing vortex generators (DWVGs) on a flat plate with the flow at a low Reynolds number. The results showed that the increment in heat transfer was 50–60% higher than that without vortex generators. In another similar study, Zhao et al. [
25] found that a delta winglet–vortex generator pair in a common-flown-down arrangement put in the middle and rear of the tip surface decreased the boundary layer thickness while creating vortices between the turbulators and increasing the heat transfer by 7.4%. A detailed examination of a delta winglet vortex generator used in a solar air heater by Sawhney [
26] showed that the highest possible thermal performance enhancement was 223% with the parameters set as the longitudinal pitch of three- and five-wave winglets in an experimental setup with a flow with Reynolds number of 4000. However, the friction factor dramatically increased 10.3-fold compared to the heater without a delta wing. Three-dimensional computational fluid dynamics analysis of heat exchanger performance with louvered fins was carried out by attaching delta winglet vortex generators [
27]. They have reported that with the same power supply for the fan, the heat exchanger shows higher thermal performance with the delta winglet. However, a greater pressure penalty was noted due to the increased friction and barricade against flow caused by delta winglets integrated into the louvered fins. They also emphasized that some heat transfer augmentation mechanisms, such as fluid mixing, boundary layer thinning, and flow separation delay from the surface, were better when delta winglets were used.
As explained above, designing a delta winglet vortex generator to enhance the heat transfer performance of heat exchangers is quite a complex task, including several variables to optimize. At this stage, machine learning may be crucial in determining the combination of variables with the desired properties. Machine learning is a technique for discovering hidden patterns in large and complex datasets, making it simpler to comprehend the data and draw conclusions from the available dataset [
28,
29,
30].
As a result, there is an increasing trend in the use of machine learning methods to detect the effects of the design elements of such systems. For instance, Liao et al. [
31] assembled two machine learning methods, i.e., multilayer perceptron and Bayesian optimization, to obtain the optimum design of a near-field thermal radiative modulator considering the rotation angle, layer thickness, and the gap distance of the multilayer materials of modulators. In another study, Ren et al. [
32] included different machine learning tools, such as reinforcement learning using proximal policy approximation (PPO) and non-Oberbeck–Boussinesq approximation (NOB). They proposed a smart active flow control system to increase the heat transfer of fluid in laminar flow conditions. Heat transfer enhancement of 76.7% was reported through extensive training. Wang and Vafai [
33] used support vector regression (SVR) algorithms as a machine learning method and combined them with thermal simulation analysis to efficiently predict hotspot temperature variations in multilayer 3D chips.
In recent years, researchers have shown growing interest in using machine learning techniques in hydraulic and thermal analyses. For instance, Seal et al. [
34] predicted the flow pattern images of a refrigerant, R-134a, condensation with more than 98% accuracy using convolutional neural network algorithms. They also proposed multilayer perceptron neural networks and principal component analysis for dataset visualization and decreased computational power. In another study, Farahani et al. [
35] investigated the thermal performance of a microchannel heat sink in terms of the porous medium, phase change material, and shape of the microchannel using the finite volume method and group method of a data handling algorithm (GMDH). The findings demonstrated that wavy microchannels could enhance thermal performance by roughly 10.6% and 5% compared with smooth and converging microchannels. Machine learning algorithms such as ANN, random forest, AdaBoost, and extreme gradient boosting (XGBoost) were also employed by Zhou et al. [
36] to predict flow condensation heat transfer coefficients in microchannels. They noted that XGBoost and ANN provided the highest accuracy of prediction among the algorithms utilized.
Other research carried out by Berber et al. [
37] related to the current study focused on heat convection in a rectangular channel with curved-winglet vortex generator inserts using machine learning. They investigated the impact of the proposed novel fin geometry and attack angle in the range of 30° to 90° with varying Reynolds numbers and plate temperatures on convection heat transfer with the help of ANN algorithms. Nusselt number deviations between experimental and machine learning results were less than 4% with a prediction accuracy parameter (R
2) of 0.9879. Longo et al. [
38] gathered extensive data on brazed plate heat exchangers (BPHE) with various geometries and diverse refrigerant types. Next, they used this database to estimate the two-phase refrigerant diabatic flow inside these heat exchangers by using a gradient boosting machine (GBM) model.
As reviewed above, the greater part of the literature on winglet-type vortex generators focused mostly on time-consuming experimental and numerical studies, and the number of studies based on machine learning is quite limited. Machine learning methods can be used to predict feature design variables more accurately and quickly using the available data, eliminating the need for time-consuming and extensive experimental and numerical studies for the thermo-hydraulic assessment of heat exchangers used with DWVGs. Therefore, machine learning methodologies may help to determine the correlations among individual or multiple combinations of design variables of DWVGs with thermal and hydraulic performance. For that purpose, Khan et al. [
39] collected experimental data on heat exchangers with delta winglet vortex generators from various publications, built a database of 300 data entries, and then employed ANN models to develop a correlation between the Reynolds numbers and the design variables of DWVGs. Accordingly, the optimum values of the variables that exhibit the highest thermal efficiency were determined.
In this study, the same database is analyzed further by explainable machine learning to reveal the individual or assembled effects of design features of DWVGs on the thermo-hydraulic performance of heat exchangers, as well as finding the pathways leading to high or low values of the performance variables. The primary goal of this research is to fill gaps in understanding the effects of design variables that are difficult to detect with the naked eye. The proposed outcomes of this study will lead to the rapid development of heat exchangers used mainly for energy conversion in terms of performance enhancement.
4. Conclusions
In this work, decision tree classification and the SHAP method were employed to analyze the thermo-hydraulic performance of heat exchangers based on the design features (Reynolds number, attack angle, length, wing-to-width ratio, and relative pitch ratio) of delta wing vortex generators. Three different target variables (Nusselt number, friction factor, and performance evaluation criterion) were chosen as target variables, and they were evaluated separately.
Decision trees were used to find the optimum ranges of design features to achieve the highest thermal and hydraulic performance. For instance, a high Nusselt number can be obtained when the Reynolds number is between 8160 and 9800 and the attack angle is greater than or equal to 47.5°. On the other hand, a high friction factor can be achieved if the attack angle is between 41° and 60° while keeping the Reynolds number lower than 8510 and the wing-to-width ratio greater than or equal to 0.4. Finally, to achieve a high-performance evaluation criterion, the length should be kept higher than 2250 mm, and the attack angle value should be set in the range of 47.5° to 60°.
The SHAP interpretable machine learning method was applied to discover the importance of design features and their positive and negative effects on the target variables. For the Nusselt number, the most significant design feature was the Reynolds number, followed by the attack angle and the relative pitch ratio. It was also found that higher Reynolds numbers and attack angles and medium relative pitch ratios positively affect the Nusselt number. It was revealed that a higher attack angle and relative pitch ratio may positively influence the friction factor. Finally, the length and the attack angle were found to be the most significant variables affecting the performance evaluation criterion.
As a final remark, the present study has extended our knowledge of the impact of the design features of DWVGs on the thermo-hydraulic performance of heat exchangers. Hence, the configurations provided here can be used for further related studies, which can potentially enhance energy efficiency and optimize performance.