Elsevier

Energy

Volume 262, Part A, 1 January 2023, 125099
Energy

Insights into modelling and evaluation of thermodynamic and transport properties of refrigerants using machine-learning methods

https://doi.org/10.1016/j.energy.2022.125099Get rights and content

Abstract

The thermophysical properties of refrigerating systems should be accurately understood for designing low-temperature refrigeration cycles of economic acceptance. The present work has tried to simplify this complicated procedure by proposing reliable and new correlative methods for determining thermodynamic and transport properties of four refrigerating substance classes, namely halocarbon, inorganic, hydrocarbon, and cryogenic fluids. New machine learning methods e.g., particle swarm optimisation adaptive neuro-fuzzy inference system (PSO-ANFIS), genetic programming (GP), and hybrid adaptive neuro-fuzzy inference system (Hybrid ANFIS) algorithms were utilised. The development of a new, simple and comprehensive correlation was for the first time introduced to estimate saturated vapour enthalpy, entropy, velocity of sound, and viscosity of refrigerants without having in-depth knowledge of complicated parameters. The accuracy and validity of the proposed models were assessed using a variety of statistical and graphical demonstrations. The findings were compared, and it was found that Hybrid ANFIS models are more accurate because Absolute Average Relative Errors (%AARD) for enthalpy, entropy, the velocity of sound, and viscosity were estimated as 0.5558, 1.3105, 0.5215, and 1.5727 in respective order. In addition, the proposed models' results were compared to the results of recently previously published models, and it confirms the reliability of our results. The innovation of this research is the design of reliable correlative methods having elevated precisions for thermodynamic and transport specifications of refrigerating substances.

Introduction

Refrigerants are operational substances in a cycle to obtain the chilling impact in the evaporator [1]. After discovering the halogen-derived hydrocarbons by Midgley [2], they were utilised as outstanding refrigerating substances with optimal properties thermodynamically [3]. To develop cycles, it is necessary to be accurately knowledgeable of thermophysical specifications of refrigerating substances [4].

It is essential to have modern measurement technological tools, and it is highly costly to determine thermodynamic properties. It is necessary to know thermodynamic properties to apply the energy balance equation to a refrigerant vapour since they are connected to functions of temperature and pressure and the quality of these properties [5]. Equations of thermodynamic properties for refrigerating substances include solving multiplex differential equations [6].

The operational fluid transport specifications strongly influence the heat transfer and pressure fall properties in refrigerating systems. To determine the fluid flow behaviour, convection characteristics, two-phase heat transfer, and pressure fall in heat exchangers, it is necessary to accurately know viscosity, thermal conductivity, and Prandtl number [7].

Fluid-specific four correlations represent the uppermost precision for refrigerant transfer properties [8]. Besides these fluid-specific correlations, previous studies have mostly focused on modelling transfer properties of refrigerating substances by the Extended Corresponding States (ECS) [9].

Since it is impossible to find experimentally measured transfer properties in the interesting situations in previous studies, there is great attention to estimating them by dependable techniques [10].

The knowledge of the operational fluid's transport properties, e.g., thermal conductivity and viscosity, is essential in the examined state. There is currently little database for transport properties. There are often very high errors in meeting engineering design requirements despite multiple correlation equations for viscosity and thermal conductivity. These result from the difficulty in measuring transport properties precisely and the absence of an acceptable theory of transport properties of actual dense gases and liquids.

Halogenated hydrocarbons are widely used in refrigerating devices since they are supplied richly and have outstanding physicochemical specifications. In particular, multiple halogenated hydrocarbon alternatives, e.g., CH2FCF3 (R134a), CHF2CF3 (R125), CH3CHF2 (R152a), CH2F2 (R32), and CHCl2CF3 (R123) are utilised as refrigerating substances following the prohibition of manufacturing and using chlorofluorocarbons, e.g., CCl2F2 (R12), CHClF2 (R22), and CCl3F (R11). Little data are available on the transport properties of these new refrigerating substances [11].

The investigation aims to offer an approach for estimating the viscosity of various refrigerating substances. Many attuned factors have to be determined to model within satisfactory uncertainty of pressure-volume–temperature (PVT) and vapour–liquid-equilibrium (VLE) data by commonly used thermodynamic models [12]. It is boring to adjust these factors, and obtaining the finest series of factors (problem of local minima) is not ever evident [13].

The thermodynamic properties of many materials and their mixtures can be estimated satisfactorily through various semi-empirical [14] and machine learning models [15]. Some types of mathematical modelling are typically used to determine the specifications of refrigerants. McLinden et al. [9] used an equation of state with proper formulation that could reproduce experiential mental property data within the experiential uncertainty of data and produced the entire interesting thermodynamic properties via integration and differentiation. The presence of many equations of state models having the aforementioned capabilities, such formulas represent the drawback of their lower calculation rate. The majority of the thermodynamic properties formulas are implied and need further repetitions. These requirements are not addressed by conventional approaches based on equations of state due to inevitable repetitions in calculations. However, estimations of interest for thermophysical specifications of refrigerating substances should be of high rapidity, accuracy, and stability in simulating refrigerating systems. Plain and effective mathematical models should be available for calculating and simulating refrigerating systems in an engineered manner to determine refrigerant properties thermodynamically [16].

The numeric instruments, including neural networks, have been developed to represent and accurately estimate the properties of refrigerants within the experiential uncertainties, suggesting potential techniques for completing this function [13].

Intelligent and soft computing approaches have been extensively applied to estimate various refrigerant properties. Arcaklıoğlu et al. [17] have examined the performance of a vapour compression heat pump with differing ratios of R12 and R22 refrigerant admixtures by artificial neural networks (ANNs). In a study by Su et al. [18], Group Contribution Methods (GCMs), which are used to evaluate the properties of working fluids for the estimation of cycle performance, were reviewed. The properties include thermodynamic, environmental, transport, economic and physicochemical properties. Kasaeian et al. [19] reviewed the theoretical and experimental studies carried out with environmentally friendly refrigerant groups such as hydrofluorocarbons, hydrocarbons, R744 (carbon dioxide) nanorefrigerants and hydrofluoric olefin. In comparison with various classes of hydrofluorocarbon, hydrofluoric olefins have a remarkably lower Global Warming Potential (GWP) [20].

An ANN-based alternate method was introduced by Sozen et al. [21] to measure specific volume, enthalpy, and entropy values of an alternate refrigerating substance (R508b) for both saturated liquid–vapour and superheated vapour regions [22]. Sozen et al. [21] offered a procedure based on ANNs to estimate thermodynamic specifications of a novel ozone-compatible refrigerating substance R404a. Correct interval values were obtained with the experiential formulations determined by ANNs. ANNs were applied by Sozen et al. [6] in determining the thermodynamic properties of an eco-friendly alternate refrigerating substance (R407c) for both saturated liquid–vapour and superheated vapour regions.

Moghadassi et al. [23] examined the capability of multilayer perceptron ANNs based on a back-propagation algorithm to determine dimethyl ether densities and vapour pressures. They compared the findings and observed that experiential data agreed well with network forecasts. Şencan et al. [24] used a data mining process for refrigerants, namely R134A, R404A, R407C, and R410A, to estimate enthalpy, entropy, and specific volume. They reported that this procedure was successful in being applied in determining enthalpy, entropy, and specific volume values for all temperatures and pressures of refrigerating substances. Specifications including heat conduction viscosity, saturated liquid density, thermal conductivity, and specific volume of pure and mixed refrigerating substances were determined using ANNs [25]. R413A, R417A, R422A, R422D, and R423A are the alternate refrigerating substances employed here. The ANN approach was used to formulate the thermophysical properties of the refrigerating substances. The thermophysical specifications of R417A were also determined using an ANFIS model by Şencan et al. [26]. ANFIS was used to determine the thermophysical specifications, including heat conduction coefficient, dynamic viscosity, kinematic viscosity, thermal diffusivity, density, and specific heat capacity [27].

The aim of the present study was to develop a new and very rapid correlation with high accuracy for thermodynamic specifications such as enthalpy, entropy, and the velocity of sound and transport properties such as viscosity of refrigerating substances in the saturated vapour region of our study with the utmost importance. Indeed, the proposed designed correlation is useable by other studies with no former knowledge regarding intricate intelligent algorithms. In the present article, an alternate methodology based on Artificial intelligence (AI), namely PSO-ANFIS, GP, and Hybrid ANFIS, is also proposed to specify thermodynamically and transfer properties.

Section snippets

Reviewing thermodynamic and transport properties

In this section, the thermodynamic and transport properties of refrigerants such as density, enthalpy, entropy, the velocity of sound, viscosity, and thermal conductivity have been reviewed.

Theory of models

In this study, four models were proposed to estimate the thermodynamic properties as enthalpy, entropy, and the velocity of sound and viscosity as transport property of refrigerants. GP and MNR techniques provide a simple procedure for evaluating target data using mathematical equations. In addition, PSO-ANFIS and Hybrid-ANFIS as AI methods are used to estimate thermodynamic and transport properties. More details about the implemented models can be found in supplementary data.

Data collection

This is common in literature that some variables such as T, P and critical properties like critical temperature, critical pressure and critical volume have been used as inputs for modelling and estimating of thermodynamic properties of refrigerant [28,37,38,41,65,66]. In this study, in addition to the mentioned properties, other variables such as critical density (ρc), critical enthalpy (hc), and critical entropy (Sc) have been used as inputs for obtaining better models with the lowest AARD%

Results and discussion

The Hybrid-ANFIS, PSO-ANFIS, GP, and MNR models were developed in this work to estimate enthalpy, entropy, the velocity of sound, and viscosity of refrigerants. More details about the result of these methods are described as follows.

Conclusion

The temperature is lowered in a separate sub-system somewhat lower than its adjacent temperature in the refrigeration procedure. This investigation focused on refrigerating substances' thermodynamic and transport properties with the successful development of four different models, namely PSO-ANFIS, Hybrid ANFIS, GP, and MNR, for wide-ranging experiential data in previous studies. The temperature, pressure, and crucial specifications, namely temperature, pressure, density, volume, enthalpy, and

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This research has been supported by the EU project “Sustainable Process Integration Laboratory – SPIL”, project No. CZ.02.1.01/0.0/0.0/15_003/0000456 funded by EU “CZ Operational Programme Research, Development and Education”, Priority 1: Strengthening capacity for quality research.

References (71)

  • Y. Liu et al.

    Machine learning for predicting thermodynamic properties of pure fluids and their mixtures

    Energy

    (2019)
  • E. Arcaklıoğlu et al.

    Thermodynamic analyses of refrigerant mixtures using artificial neural networks

    Appl Energy

    (2004)
  • W. Su et al.

    Group contribution methods in thermodynamic cycles: physical properties estimation of pure working fluids

    Renew Sustain Energy Rev

    (2017)
  • A. Kasaeian et al.

    Applications of eco-friendly refrigerants and nanorefrigerants: a review

    Renew Sustain Energy Rev

    (2018)
  • S. Eyerer et al.

    Theoretical analysis and experimental investigation of material compatibility between refrigerants and polymers

    Energy

    (2018)
  • A. Sözen et al.

    Derivation of empirical equations for thermodynamic properties of a ozone safe refrigerant (R404a) using artificial neural network

    Expert Syst Appl

    (2010)
  • A. Sözen et al.

    Calculation for the thermodynamic properties of an alternative refrigerant (R508b) using artificial neural network

    Appl Therm Eng

    (2007)
  • A. Moghadassi et al.

    Estimation of thermophysical properties of dimethyl ether as a commercial refrigerant based on artificial neural networks

    Expert Syst Appl

    (2010)
  • M. Mohanraj et al.

    Applications of artificial neural networks for refrigeration, air-conditioning and heat pump systems—a review

    Renew Sustain Energy Rev

    (2012)
  • X. Liu et al.

    Investigation on the condensation process of HFO refrigerants by molecular dynamics simulation

    J Mol Liq

    (2019)
  • K. Srinivasan

    Saturated liquid densities of cryogenic liquids and refrigerants

    Int J Refrig

    (1989)
  • M.L. Huber et al.

    A predictive extended corresponding states model for pure and mixed refrigerants including an equation of state for R134a

    Int J Refrig

    (1994)
  • E.K. Goharshadi et al.

    Prediction of the volumetric and thermodynamic properties of some refrigerants using GMA equation of state

    Int J Refrig

    (2007)
  • M.A. Qyyum et al.

    Hydrofluoroolefin-based novel mixed refrigerant for energy efficient and ecological LNG production

    Energy

    (2018)
  • T. Bai et al.

    Thermodynamic assessment of a condenser outlet split ejector-based high temperature heat pump cycle using various low GWP refrigerants

    Energy

    (2019)
  • Y. Qin et al.

    Energy and exergy analysis of a Linde-Hampson refrigeration system using R170, R41 and R1132a as low-GWP refrigerant blend components to replace R23

    Energy

    (2021)
  • E.U. Küçüksille et al.

    Data mining techniques for thermophysical properties of refrigerants

    Energy Convers Manag

    (2009)
  • A. Mohebbi et al.

    A neural network for predicting saturated liquid density using genetic algorithm for pure and mixed refrigerants

    Int J Refrig

    (2008)
  • M. Alavianmehr et al.

    Modeling thermodynamic properties of refrigerants from new version of Tao-Mason equation of state

    Int J Refrig

    (2014)
  • M. Moosavi et al.

    Liquid density prediction of five different classes of refrigerant systems (HCFCs, HFCs, HFEs, PFAs and PFAAs) using the artificial neural network-group contribution method

    Int J Refrig

    (2014)
  • G. Brunner

    Properties of pure water

    Supercritical Fluid Science and Technology

    (2014)
  • E.U. Küçüksille et al.

    Prediction of thermodynamic properties of refrigerants using data mining

    Energy Convers Manag

    (2011)
  • A. Cleland

    Computer subroutines for rapid evaluation of refrigerant thermodynamic properties

    Int J Refrig

    (1986)
  • A. Cleland

    Polynomial curve-fits for refrigerant thermodynamic properties: extension to include R134a

    Int J Refrig

    (1994)
  • G. Soave

    Equilibrium constants from a modified Redlich-Kwong equation of state

    Chem Eng Sci

    (1972)
  • Cited by (4)

    View full text