Model-based dimensionless neural networks for fin-and-tube condenser performance evaluationRéseaux neuronaux adimensionnels basés sur des modèles pour l'évaluation de la performance d'un condenseur à tubes à ailettes
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.
Section snippets
Dimensional analysis of fin-and-tube condenser
For a given fin-and-tube condenser with certain working fluid, we can clearly identify the operating parameters as the inputs and outputs of the condenser performance model (Zhao and Zhang, 2010). However, this type of dimensional model would be very limited in use. Any changes on the working fluid or the condenser configuration will lead to unpredictable results.
A general approach to better generality is to develop dimensionless Pi-groups for this problem using the dimensional analysis method (
Condenser performance data bank
Sufficient data are very important for NN training and testing to mitigate the over-fitting risk. Meanwhile, in order to fairly compare the present dimensionless NNs and the previous dimensional ones (Zhao and Zhang, 2010), the same condenser (as shown in Fig. 1) and the performance data bank generated by the same well-validated tube-by-tube first-principle model is used in this study. In the data bank, the primary working fluid is R410A and there are 2074 sets of data for R410A in NNs training
Neural network
Nowadays neural networks are widely applied in nonlinear function approximation. Among hundreds of types of NNs, the multi-layer perceptron (MLP) network is the most popular neural network in engineering application, and a three-layer perceptron network is capable of approximating any function with a finite number of discontinuities. Therefore, three-layer perceptron network was used in the previous work (Zhao and Zhang, 2010) and is still used in the present work for apple-to-apple comparison.
Conclusions
In the present work, we developed dimensionless NNs for the fin-an-tube condenser performance evaluation using the model-based dimensional analysis method. We took into account the fluid properties in the dimensionless Pi-groups and used the Pi-groups as the inputs and outputs of NNs. The dimensionless NNs have equivalent accuracy as the dimensional ones. Compared with a well-validated tube-by-tube first-principle model, the standard deviations of trained dimensionless neural networks are
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant No. 51206123), the Innovation Program of Shanghai Municipal Education Commission (Grant No. 11ZZ30), and the China Postdoctoral Science Foundation (Grant No. 2013M541539).
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