A dynamic mathematical model of a direct expansion (DX) water-cooled air-conditioning plant Deng Shiming* Department of Building Services Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Received 8 July 1999; accepted 23 August 1999 Abstract A dynamic mathematical model for a direct expansion water-cooled air-conditioning plant typical to many actual installations in buildings has been developed. The system components modelled are a compressor, a thermostatic expansion valve, a water cooled condenser and a direct expansion evaporator which is also the cooling and dehumidifying coil in the air side. The evaporator (cooling coil) model consists of a novel set of equations which can distinguish between two-phase superheated and refrigerant region in the refrigerant side, and between dry and wet cooling of an air handling process in the air side. The model has been validated using the experimental data collected from the plant, and was separately reported. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Air-conditioning; Mathematical model; Dynamic; Control; Direct-expansion 1. Introduction A good mathematical model can help people to understand system characteristics and enhance the de- sign of real plants and their control systems. Modelling of refrigeration and air-conditioning systems has been the subject of many studies over the last few decades [1±12]. A review on the philosophy and challenges in devel- oping simulation models of vapour-compression re- frigeration was presented by Browne and Bansal [13]. The review indicated that most work on modelling vapour-compression refrigeration systems focused on steady-state modelling and on small systems such as domestic refrigerators and heat pumps. Although most of the work focused on steady-state modelling, a few dynamic mathematical models for re- frigeration systems and heat pumps have been devel- oped [10±12]. However, most of these dynamic models developed are not for air-conditioning application. Recently, a dynamic mathematical model for a split unit domestic air-conditioner, which is air cooled, was developed [14]. This paper reports the derivation of a dynamic mathematical model of a direct expansion (DX) water- cooled air-conditioning plant typical to many actual installations in buildings. In this paper, a description of the plant is given ®rst, followed by a detailed pres- entation of the model development. A brief of the model validation process is also included in this paper. 2. Description of the DX air-conditioning plant The experimental air-conditioning plant that was the model is shown in Fig. 1. It is a simple DX air cooling and dehumidifying system. The major components in the refrigeration circuit are a condensing unit, which is composed of a semi-hermetic reciprocating compressor and a low ®n shell and tube water cooled condenser, a thermostatic expansion valve (TEV), and a direct expansion evaporator with copper tubes and alu- Building and Environment 35 (2000) 603±613 0360-1323/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S0360-1323(99)00049-9 www.elsevier.com/locate/buildenv * Tel.: +852-2766-5847; fax: +852-2774-6146. E-mail address: besmd@polyu.edu.hk (Deng Shiming).