Model-based dimensionless neural networks for fin-and-tube condenser performance evaluation

Highlights

• We developed dimensionless neural networks for fin-and-tube condensers.

• Dimensionless Pi-groups were derived from model-based dimensional analysis method.

• Three-layer perceptron neural network was served as the performance model.

• Neural networks well predicted the condenser performance with different refrigerants.

Abstract

The paper presents a dimensionless neural network modeling method for the fin-and-tube refrigerant-to-air condensers which are widely used in air-cooled refrigeration and heat pump systems. The model-based dimensional analysis method is applied to develop the dimensionless Pi-groups for the condenser performance. The three-layer perceptron neural network is served as the performance model using the dimensionless Pi-groups as its inputs and outputs. Compared with a well-validated tube-by-tube first-principle model, the standard deviations of trained dimensionless neural networks are 0.66%, 4.83% and 0.11% for the heating capacity, the refrigerant pressure drop and the air pressure drop, respectively. The accuracy is also consistent with the previously developed dimensional neural networks. Furthermore, independent model validation using different refrigerants shows that the dimensionless models have good potential in predicting the condenser performance if the Pi-groups were in the range of training data.

Introduction

Fin-and-tube heat exchangers are widely applied as the refrigerant-to-air condensers in refrigeration and heat pump systems. How to predict the condenser performance has drawn a lot of attention since it's put in use. As the fin-and-tube condenser involves complex heat transfer processes and a large number of geometric variables, very complex model and method are required to design this type of condensers (Domanski and Yashar, 2007, Jiang et al., 2006, Liu et al., 2004). However, owing to the fairly low robustness and time-consuming simulations, this type of condenser design models are not recommended for direct use in the complex system modeling, such as the multi-split air-conditioning systems.

Researchers have developed many simple semi-empirical or empirical models for fast and robust simulations of heat exchanger performance in different systems, particularly complex systems. Among these models, neural network (NN) theory is a fast developing branch because of its good generality and accuracy in modeling multi-input multi-output nonlinear objects. For different purposes, NNs were used for prediction of heat transfer coefficients (Jambunathan et al., 1996, Sablani et al., 2005, Wang et al., 2006, Zdaniuk et al., 2007), prediction of heat exchanger performance (Akbari et al., 2012, Díaz et al., 1999, Hayati et al., 2009, Islamoglu, 2003, Jiang et al., 2012, Pacheco-Vega et al., 2001a, Pacheco-Vega et al., 2001b, Peng and Ling, 2009, Tan et al., 2009, Wu et al., 2008, Xie et al., 2007, Zhao et al., 2010, Zhao and Zhang, 2010), optimization of heat exchangers (Peng and Ling, 2008, Zdaniuk et al., 2011) and control of heat exchangers (Díaz et al., 2001, Gang and Wang, 2013, Vasičkaninová et al., 2011). For more information, there are two review papers. Yang (2008) reviewed NN applications in thermal science and engineering. Recently Mohanraj et al. (2012) gave an overview of NN applications in refrigeration, air-conditioning and heat pump systems.

From the NN applications in heat exchanger performance evaluation published to-date, we can find the following main issues to be solved. Firstly, most NN models of heat exchangers performance were dimensional, which limits the generality of NNs. Secondly, most researchers were only concerned about the heat transfer rate of heat exchanger and missed other important performance parameters such as pressure drops. Lastly, the over-fitting risk was raised by training a relatively large NN with limited testing data.

This paper thus proposes a dimensionless NN model of fin-and-tube condenser performance. We look forward to generality improvement from dimensional to dimensionless model. In addition to the heating capacity, both air side and refrigerant side pressure drops are taken into account so that the NN model can be well fit to the system modeling. A well-validated tube-by-tube first-principle condenser model is employed as the training and testing data generator so that we can have sufficient data to cover the envelope of dimensionless PI-groups and minimize the over-fitting risk.