Bond Graph Model Of A Water Heat Exchanger

This paper presents a Bond Graph (BG) modelling approach to add and exploit on existing Modelica models some information on the energy structure of the systems. The developed models in the ThermosysPro library (Modelica-based) are already validated against the experimental data in previous works. A plate heat exchanger (PHE), which is equipment for nuclear power plants, is considered as a case study in this paper. Simulation results of the BG model for the counterflow PHE are compared with simulation results of the tested Modelica model. Comparisons show good agreement between both model results. INTRODUCTION Nowadays, the major problems of the numerical computation of mathematical models for complex processes are solved by using different commercial and open source software packages. The representation of the models in these languages is often based on model equations. The bond graph representation allows a physical structural analysis which is based on the system energy structure. This facilitates the exchange of models and simulation specifications. Bond graph is a graphical representation methodology for modelling multidisciplinary physical systems (Jardin et al. 2009). Heat exchange is an important unit operation that contributes to efficiency and safety of many processes (nuclear power plants, steam generators, automotive, heat pumps, etc.). A plate heat exchanger is a type of heat exchanger that uses metal plates to transfer heat between two fluids. The plate heat exchanger was invented by Dr Richard Seligman in 1923 and revolutionised methods of indirect heating and cooling of fluids (Crepaco 1987). Plate heat exchangers are widely used in many other applications (food, oil, chemical and paper industries, HVAC, heat recovery, refrigeration, etc.) because of their small size and weight, their cleaning as well as their superior thermal performance compared to other types of heat exchangers (Guo et al. 2012). The plate heat exchanger model is one of over 200 0D/1D models of components belonging to the ThermosysPro library. This open source library, developed by EDF R&D, is used to model energy systems and different types of power plants (nuclear, conventional, solar, etc.) (El Hefni 2014; El Hefni and Bouskela 2006; El Hefni et al. 2011, 2012; Deneux et al. 2013). The Modelica model is developed in Dymola. Modelica representation leads to static analyses which are based on model equations, while BG representation permits a physical structural analysis which is based on the system’s energy structure. The bond graph representation in this paper is built using the graphical editor MS1. MS1, an acronym of Modelling System One, is an interactive environment for modelling, simulation and analysis of non-linear dynamic systems (Jardin et al. 2008). In the literature, bond graph modelling of heat exchangers is widespread (Shoureshi and Kevin 1983; Hubbard and Brewer 1981; Delgado and Thoma 1999). Due to difficulties in handling entropy and heat transfer rate, many efforts have been made to develop pseudobond graph representations of thermo-fluid transport and heat exchange (Karnopp and Azerbaijani 1981; Karnopp 1978, 1979; Ould Bouamama 2003). All these references mentioned above have different assumptions. For instance, in (Shoureshi and Kevin 1983) a temperature-entropy bond graph technique has been proposed based on three lump models to predict the reversal of flow. In this model, the authors have considered that the fluid domain is operated independently from the thermal domain. In (Karnopp 1978), pseudo bond graph strategies have been proposed with using the temperature and heat flow as effort and flow. This paper uses pseudo bond graph method for heat/mass transfer modelling. Furthermore, multi-port C and multi-port R elements have been used. This method is based on finite volume approach considering the thermal and fluid bonds. First, fundamental theory of thermofluid is given. Then, the plate heat exchanger models are explained: the Modelica model and the BG model. In the section after that, simulation results are discussed. The last section contains conclusion and future research paths. THERMOFLUID SYSTEM Thermofluid or thermal fluid sciences involve the study of the thermodynamics, fluid mechanics, heat and mass transfer in complex engineering systems. In the open system case, the energy and mass equations for a thermodynamic system are formulated as (see nomenclature page 7) dEs dt = Q̇in +Ẇin + Ėi− Ėe (1) where (dEs/dt) is the rate of increase in energy within the system, Q̇in is the rate at which heat enters the system, Ẇin is the rate at which work enters the system, Ėi is the rate at which energy is brought in by the mass entering the system, and Ėe is the rate at which energy is removed by the mass leaving the system. dms dt = ṁi− ṁe (2) Proceedings 30th European Conference on Modelling and Simulation ©ECMS Thorsten Claus, Frank Herrmann, Michael Manitz, Oliver Rose (Editors) ISBN: 978-0-9932440-2-5 / ISBN: 978-0-9932440-3-2 (CD) where (dms/dt) represents the rate of increase in mass within the system, and mi and me represent the respective rates at which mass entering and leaving the system. In many thermal application, the reduced heat equation is used Q̇ = dQ dt = mCp dT dt = KA(∆T ), (3) where Q̇ is the heat-flow-rate (named just heat rate), Cp is the specific heat capacity, m is the mass flow rate, the global heat transfer coefficient K (associated to a bounding area A and the average temperature jump ∆T between the system and the surroundings). More details about the above equations can be seen in reference (Martìnez 1992). i i+ 1 ∆Pi ∆Pi+1 ṁi, hi ṁi+1, hi+1 Volume I-1 Volume I Volume I+1 hI−1, PI−1 hI, PI hI+1, PI+1 Figure 1: Staggered finite volume scheme The cooling water heat exchanger used in this study is an equipment for nuclear power plants. Two main approach for the dynamic modelling of the heat exchanger are the moving boundaries (MB) and the discretized models, known as finite-volume models (FVM) (Bendapudi et al. 2004; Desideri et al. 2015). The moving boundary method is useful for developing feedback controllers, in this approach the heat exchanger is divided into zones based on the fluid phase in each region and the location of the boundary between regions vary in time according to the current conditions. In finite-volume models the 1D flow is subdivided into several equal control volumes as shown in Figure 1. The modelling technique used in this paper is based on finite volumes approach. A pictorial representation of the discretized counterflow heat exchanger is shown in Figure 2. PLATE HEAT EXCHANGER MODELS The plate heat exchanger is the component that transforms heat (thermal energy) from one fluid to another. Plate heat exchangers have a high heat transfer rate compared to other types of heat exchangers due to their large surface area. Modelling of Water/Water Heat Exchangers in Modelica The dynamic water/water heat exchanger component used belongs to the ThermoSysPro library. The core model of the heat exchanger was written in Modelica and simulated with the Dymola simulation environment. Figure 3 shows the schematic of the heat exchanger model in Dymola. This model has two parts: the upper part for hot water and the other part for cold water, Hot water flow direction Cold water flow direction Hot Hot Hot Hot Hot