A Dynamic Model Of A Vapor Compression Liquid Chiller

Dynamic models of vapor compression systems are important tools for HVAC engineers in the development and evaluation feedback control and fault detection and diagnostic (FDD) algorithms. Significant literature exists on dynamic models of vapor compression systems. Much of it is restricted to air-to-air systems and few papers deal with liquid chillers. Most of existing liquid chiller models reviewed were found to use lumped capacitances for the heat exchangers, and black-box models for the compressor. Also, little or no information has been presented on execution speeds. The current work was undertaken to meet the requirement of a dynamic model of a vapor compression centrifugal chiller based on first-principles that runs at speeds close to real-time. A dynamic centrifugal water chiller model is developed and validated using experimental data. The shell-and-tube heat exchangers are modeled using a finite-volume formulation. The centrifugal compressor is developed from a combination of a simple physical model and a quasi-steady state model. Inlet guide vane capacity control is incorporated. A first principles thermostatic expansion valve is used. The model is validated using data from a 90ton centrifugal chiller test stand, operating with R134a. Model performance during start-up and a typical load change transient is presented. The model was implemented in C++, and allows for flexibility in application to other systems of similar configuration. Also, the model is modular, allowing component models to be replaced. Modelspeed to real-time ratios in the range 1.0-1.2 are achieved on a Pentium 4 1.8GHz/512MB computer. NOMENCLATURE Symbols A heat transfer area . m mass-flow rate . V volumetric flow rate a0...a4 Constants M Mass v specific volume c0...c4 regression coefficients Nu Nusselt number W specific polytropic work Cp specific heat P Pressure, power y valve lift C Constants Pr Prandtl number α heat transfer coefficient D tube diameter . Q heat transfer rate γ control factor f friction factor Re Reynolds number η polytropic efficiency g Accn. due to gravity T temperature (C) μ dynamic viscosity h specific enthalpy u specific internal energy ρ density k thermal conductivity, spring compliance V node volume (m ) . " r Q refrigerant heat flux Subscripts 1 Evap exit 2 Comp exit 3 Cond exit 4 Evap inlet b Bulb c Cond e Evap i i node t Tube we Evap water cc Comp cooling em Electro-mech in Inlet, inner v Vapor, valve wc Cond water INTRODUCTION Dynamic models are crucial tools for the controls engineer in developing efficient control algorithms. Dynamic performance modeling of vapor compression systems has been of interest for well over 20 years, beginning with Dhar and Soedel [1979]. In preparation for this model development exercise, an extensive literature survey was carried out and is reported in a separate document (Bendapudi and Braun [2002]). Papers related to liquid chiller models include Sami et al [1987], Svensson [1999], Wang and Wang [2000], Browne and Bansal [2000] and Grace and Tassou [2000]. None of these models is comprehensive in that they either do not consider centrifugal compressors or they use simplified heat exchanger models that cannot adequately model large and small scale transients. Sami’s model used a hermetically sealed reciprocating compressor, while Browne’s dealt with screw compressors. Svensson’s work presented only transients triggered by feedback control. Wang’s model, which does characterize a centrifugal liquid chiller model, utilizes very simple heat exchanger models. Grace and Tassou modeled a reciprocating compressor with a shell-and-tube evaporator that operated with refrigerant flowing inside the tubes. The heat exchangers were modeled as done by MacArthur and Grald [1987]. Browne and Bansal [1998], in their compilation work on issues related to modeling of vapor compression liquid chillers, highlight the need for a liquid chiller model that incorporates detailed heat exchangers. To summarize, it was found that no publicly available system models existed that could predict the complete dynamic performance of vapor compression centrifugal liquid chillers despite such systems being among the more popular configurations in the field. These observations provided the motivation for defining the modeling objectives as follows: Develop a transient model of a vapor compression centrifugal liquid chiller system that: • is based on first principles wherever available information permits • can capture start-up transients, as well as transients caused by feedback control • can execute close to real-time, if not faster and • can be used to study (in the future) the impact of common faults that occur in such systems TEST STAND DESCRIPTION The test stand used for the validation of the model is a 90-ton water chiller charged with R134a. The refrigeration system itself consists of a centrifugal compressor with variable inlet guide-vanes for capacity control. The heat exchangers are of shell and tube construction, with two-water passes and one refrigerant pass. The expansion valve is a cascaded device consisting of a main valve driven by a pilot valve. The compressor is powered by an electric motor. The motor and transmission are cooled by the refrigerant through a bleed line tapped off of the liquid line, as shown in Fig. 1. This refrigerant returns to the evaporator inlet. The load on the chiller system is controlled by an arrangement of heat exchangers that simulate the building load, as shown in the Fig. 2. For clarity, the pumps and valves that control the water flow rates are not shown. The load on the system can be varied by altering the temperatures of the water entering the evaporator and condenser, i.e., varying the operating conditions of these peripheral heat exchangers. An exhaustive description of the test stand and instrumentation is provided in Comstock [1999]. Fig. 1 Refrigerant flow paths Fig. 2 Water flow paths Condenser