Investigation on the heat transfer and pressure loss of flow boiling in smooth and microfin tubes using machine learning methods

Abstract

The estimation of heat transfer coefficients (HTC) and pressure drop (Delta P) in flow boiling processes is essential for the effective design and operation of refrigeration systems. In this study, the artificial neural network (ANN), locally weighted regression (LWR), and gradient boosted machine (GBM) methods are employed to predict the boiling heat transfer coefficient (HTC) and pressure drop (Delta P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta P$$\end{document}) in flow boiling of R134a. The study focuses on horizontally positioned both straight and microfin tubes. The ANN, LWR, and GBM methodologies are utilized to ascertain the parameters of boiling HTC and Delta P as outputs. These parameters are determined by considering the mass flux, saturation pressure, heat flux, vapor quality, Reynolds number, Lockhart-Martinelli parameter, Froud number, Weber number, and Bond number as inputs. The training dataset is partitioned into 5 sections for the purpose of hyperparameter tweaking for each model. Out of these sections, 4 parts, consisting of approximately 111 samples, are utilized for training, while 1 part, including around 27 samples, is allocated for validation. The optimal hyperparameters are determined by calculating the average R2 score over the 5 validation sets. Using raw measurements, HTC and Delta P are successfully modeled using a relatively much smaller dataset of 174 measurements, with 82.4% R2 score and 0.7% weighted average relative deviation for HTC, and 88.9% R2 score and 4.1% weighted average relative deviation for Delta P across multiple tube types, achieved by LWR algorithm. Model performances are validated with an extrapolation test and found to be consistent with traditional train-validation-test sampling scheme with 75.9% R2 score and -6.2% weighted average relative deviation for HTC, and 89.3% R2 score and -3.9% weighted average relative deviation for Delta P, showing the consistency of the hypotheses created by a hybrid of parametric and nonparametric model families even outside the observed measurement range for multiple tube types. Local weighted regression models are the most performant, especially for limited data availability. However, calculated measurements increase error rates, suggesting that HTC and Delta P models work best with raw measurements.