Machine learning approach for predicting refrigerant two-phase pressure drop inside Brazed Plate Heat Exchangers (BPHE)
Introduction
The experimental and theoretical investigations on two-phase flow inside Brazed Plate Heat Exchangers (BPHE) available in the open literature are mainly focused on the measurements and the prediction of convective heat transfer coefficients, whereas only a relatively limited number of works refer to pressure drops. On the contrary, the availability of extensive experimental pressure drop databases and accurate pressure drop computational procedures is fundamental for the design of BPHE. This is even more true for refrigeration and air-conditioning application that involves the use of new low-GWP refrigerants which thermodynamic and thermophysical properties, in some cases, are not yet well established. In fact, the design of any heat transfer equipment must take into account two different concurrent issues: the increase of the heat transfer coefficients, which involves a reduction of size and direct costs of the heat exchanger for a set thermal effectiveness, and the reduction of pressure drops, which increases the global efficiency of the system reducing also pumping indirect costs. The final optimum solution derives from the balance between these two contrasting aspects.
Amalfi et al. [1,2] reviewed pressure drop correlations for refrigerant boiling in BPHE, while Tao and Infante Ferreira [3] surveyed pressure drop correlations for refrigerant condensation in BPHE. Both found that the existing computational procedures for two-phase flow pressure drop in BPHE exhibit poor performances, therefore they proposed new correlations based on huge databases and a dimensional analysis coupled with a multi-variable regression approach.
The Amalfi et al. [1,2] correlation is based on 4 non-dimentional variables:
The Amalfi et al. [1,2] equation shows a MAPE of 21.5% with 90.9% of the predicted data within ± 50% against their boiling database consisting of 1513 pressure gradient data-points.
The Tao and Infante Ferreira [3] equation consists of 3 non-dimentional variables and a dimensional parameter:where the inclination angle of the corrugation β must be expressed in radian.
The Tao and Infante Ferreira [3] correlation exhibits a MAPE of 31.2% with 87.5% of the predicted data within ± 50% against their condensation database consisting of 1590 pressure gradient data-points.
In the authors' opinion, it is difficult to obtain a substantially better predicting performance by using an analytical approach due to the intrinsic complexity of two-phase flow inside BPHE, which requires deep analysis of physical mechanisms, wide-ranging databases, and innovative non-linear regression techniques such as, for example, the Machine Learning techniques.
The aim of this paper is to present a wide database on refrigerant two-phase diabatic (boiling and condensation) flow pressure gradient inside BPHE and to develop a high performing machine learning model for predicting refrigerant two-phase pressure gradient inside BPHE.
Section snippets
Two-phase flow database
The authors of the present paper carried out in the past an extensive measurement campaign on refrigerant boiling [4], [5], [6], [7], [8], [9], [10] and condensation [11], [12], [13], [14], [15], [16], [17], [18] inside a commercial BPHE. Several traditional HFC refrigerants (R134a, R410A, R236fa, R404A), HydroCarbon (HC) refrigerants (R600a, R290, R1270), low-GWP HFC refrigerants (R152a, R32), HydroFluoroOlefin (HFO) refrigerants (R1234yf, R1234ze(E), R1234ze(Z)) and a HydroChloroFluoroOlefin
GBM model
This paragraph presents a Gradient Boosting Machines (GBM) model for predicting refrigerant two-phase diabatic (boiling and condensation) flow frictional pressure gradient inside BPHE based on the huge database illustrated in the previous paragraph. The variables used as input for the GBM model were corrugation enlargement ratio Φ, reduced inclination angle β/βmax, liquid Prandtl number PrL, specific kinetic energy number , reduced pressure P/Pcr, and type of two-phase heat transfer process
Conclusion
This paper presents and analyses a database on refrigerant two-phase diabatic (boiling and condensation) flow inside BPHE consisting of 2549 data-points relative to 16 plate geometries and 16 refrigerants, including 4 natural refrigerants and 6 low-GWP refrigerants. A Gradient Boosting Machines (GBM) model for predicting refrigerant two-phase diabatic flow inside BPHE is presented. The model accounts for the effect of plate geometry, operating conditions and refrigerant properties. The model is
Declaration of Competing Interest
The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.
Acknowledgement
The research project was carried out within the International Network "Low GWP Refrigerants" which involves the Khyshu University, the Saga University, the Sangyo University, the Iwaki Meisei University, The Catholic University of America, the University of Padova, the US National Institute of Standard and Technology (NIST), the Construction Technology Institute of the National Research Council of Italy (CNR-ITC), and the Italian National Metrology Institute (INRIM) while the first author
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