*1.2. Machine Learning Algorithms for Two-Phase Flow Heat Transfer*

Machine learning is a rapidly growing field that allows data-driven optimization, and it has been recently extended to flow identification and design of cooling devices at different scales, considering the most significant design parameters as inputs and flow regimes or thermal resistance as outputs, depending on the application. The use of these algorithms is predominant in regression problems for heat transfer coefficients and pressure drop, although the classification of flow patterns can still be found in the available literature.

Several challenges related to two-phase flow heat transfer have been addressed via the use of machine learning techniques. The prediction of flow patterns using support vector machines (SVMs) was proposed by Guillén-Rondon et al. [35]. Here, the authors trained an SVM with a large two-phase flow pattern dataset and achieved on average 95% prediction accuracy when testing the algorithm on different groups and combinations of flow patterns. Another interesting contribution is within flow boiling and condensation

heat transfer. The prediction of heat transfer coefficients for both phase changes is a challenging task, and the use of machine learning has proven to be beneficial for facilitating these estimations. An example is the work by Zhu et al. [36] which proposed the use artificial neural networks (ANNs) to predict flow boiling and condensation heat transfer coefficients for micro-channel systems with serrated fins. The authors were able to identify the most relevant geometrical and operational parameters to minimize the prediction error and evaluate the influence of specific operational parameters such as mass and heat flux into the prediction accuracy of the ANN. The results were promising, showing that the relative deviation from experimental data was on average 11.4% and 6.10% for flow boiling and condensation, respectively. The use of ANN is also useful in image recognition and analysis. A recent study published by Suh et al. [37] established an automated framework for determining boiling curves from high-quality bubble images using convolutional neural networks (CNNs). The image analysis performed by the neural network was able to capture relevant physical features used for its training and learning of the underlying statistics between bubble dynamics and corresponding boiling curves. The prediction error was reported to be 6% on average.

In terms of the identification of flow patterns in PHP systems, few attempts were found. Most efforts focused on common heat pipes and two-phase systems. Hernandez et al. [38] developed a decision-tree-based classifier to identify flow regimes and select appropriate predictive models for several two-phase flow systems. Zhang et al. [39] proposed two different machine learning classification algorithms for two-phase nuclear systems. The first one was designed for real-time flow regime identification based on SVMs, and the second classifier was designed for transient flow regime classification using CNNs. Both classifiers performed with high accuracy, allowing for a fast response when dealing with complex two-phase systems. Note that the above-mentioned contributions are related to two-phase flow systems, where no pulsating phenomenon occurs, and the transition from one flow regime to another may be less rapid than when the flowrate and its direction are not controlled (as it is the case with PHP systems).

In the context of PHP devices, most research attempts have dedicated their efforts to the prediction of key design parameters, such as thermal resistance and pressure drop. Jokar et al. [40] presented a novel approach for simulation and optimization of PHPs, based on a multilayer perceptron (MLP) neural network. According to the authors, PHPs, as a complex system, can be successfully simulated by means of artificial neural networks. Jalilian et al. [41] extended the study to the optimization of a flat plate PHP for application in a solar collector. The trained network was validated with experimental data and used to evaluate the objective function to maximize the thermal efficiency of the system. A comprehensive discussion of the thermal performance prediction of PHPs based on an artificial neural network (ANN) and regression/correlation analysis (RCA) was proposed by Patel and Metha [42]. The authors investigated the influence of nine major input variables, considering more than 1600 experimental points from the literature. Wang et al. [43] proposed a similar predicting model based on ANN for the optimization of the effects of different working fluids, extending the current state-of-the-art approaches. Table 1 summarizes the main input parameters and machine learning approaches adopted in the abovementioned work. Note that the implementation of these machine learning algorithms is rather recent, indicating that there are still further studies to perform, although promising results have been obtained.


**Table 1.** Relevant studies on machine learning applied to PHPs.

On the basis of the findings shown in Table 1, there is still a need for understanding the complex phenomenon of flow regime transition in PHP systems, and for the classification of the flow pattern when the device is in operation. The capability of identifying the flow regime for a set of operating conditions allows for a more accurate prediction of design parameters and for useful insights regarding the behavior of the system during operation. Within this context, the use of machine learning is beneficial, as it leverages the abundance of significant sets of data. The advantages of machine learning techniques, namely, the direct use of data, the variety of methods for specific purposes, and their equation-free nature, provide unique characteristics that can improve the optimization of experiment design, speed in experimental analysis, and scaling to different scenarios.

This work proposes, for the first time, the use of machine learning classifiers to identify flow patterns and flow pattern transition in a single-loop PHP system with two different working fluids and in varying gravity conditions using data from the European Space Agency Parabolic Flight Campaigns [11,25]. Since the single-loop PHP allows the visualization of flow patterns, this makes the present analysis unique in understanding if ML can be successfully trained to recognize PHP flow patterns. The selection of the most suitable classifier is carried out by comparing the accuracies of such classifiers when predicting the flow regime on unseen data (or testing sets). The selected classifier is used for devising flow pattern maps for both working fluids, to identify the location of the flow regime transition zone. It is expected that this capability provides a more systematic approach when identifying flow regimes, reducing observation uncertainty (when used).
