Development of a Zonal Model. to Analyze a Thermal Storage Tank with an Electric Heater

Transcription

1 Development o a Zonal Model to Analyze a hermal Storage ank with an Electric Heater Seung Hyo Baek, 1 Hyun Min Nam, 1 Myoung Souk Yeo, 2 and Kwang Woo Kim. 2 1 Department o Architecture and Architectural Engineering, Graduate School o Seoul National University, Seoul, Korea 2 Department o Architecture and Architectural Engineering, College o Engineering, Seoul National University, Seoul, Korea ABSRAC A thermal storage tank with an electric heater is a common type o storage or solar domestic hot water system, and is operated to supply remainder energy, which is not provided by the solar collector. In order to evaluate the energy perormance o solar domestic hot water systems, it is necessary to analyze water low and the heat transer o water contained in the storage tank. In general, it is possible to analyze water low and the heat transer o the storage by using CFD. However, using CFD is a very complex and time-consuming process. In this paper, we propose a zonal model or thermal storage with an electric heater. Computer simulation by using a zonal model is conducted, and we ind that the developed analysis model is appropriate to predict luid motion and the water temperature o the thermal storage tank, based on simulation results. INRODUCION In Korea, solar energy systems have mainly been applied in buildings or the purpose o supplying hot water. Most solar domestic hot water (SDHW systems are meant to urnish 20% to 80% o the annual hot water demand; the remainder should be provided by auxiliary heaters, such as electric heater and boilers. In the case o an immersed electric heater installed in a thermal storage tank, thermal stratiication in the storage tank will be destroyed, due to the operation o the auxiliary heater. he perormance o a SDHW is aected by the temperature distribution in the storage tank. hereore, accurate modelling o a SDHW system requires an accounting or the thermal stratiication in the storage tank. Dynamic energy simulation programs, such as RNSYS and EnergyPlus, are in general use or evaluating the thermal perormance o SDHW systems. hese tools adopt a one-dimensional model to predict water low and the temperature distribution in a storage tank. he one-dimensional model is simple and eicient in terms o calculation. hereore this model is particularly suitable or implementation into an overall energy simulation program. However, this model is not appropriate or predicting luid motion in a storage tank, because water circulation caused by the operation o a heater cannot be evaluated. CFD models can accurately predict luid motion and water temperature. However, the accuracy o the CFD calculation results strongly depends on the assumptions, such as boundary conditions and simpliication. hereore, the users should have good theoretical knowledge. Furthermore, CFD

2 models require large computational resources and computing time. Consequently, they are not applicable to evaluate the long-term thermal perormance o SDHW systems. In order to predict luid motion and water temperature o a thermal storage tank with an electric heater, this paper proposes a simpliied zonal model. his research is carried out in three main steps. Firstly, existing analysis methods, such as the CFD method and simpliied models, are reviewed. Secondly, a simpliied zonal model is proposed, that includes a heat balance model and mass balance model. Lastly, a luid analysis program is developed, and the proposed analysis model is validated through simulation. ANALYSIS OF HE EXISING ANALYSIS MEHODS CFD methods CFD (Computational Fluid Dynamics methods have been widely used to predict luid motion and water temperature inside a thermal storage tank. he governing equations or luid are written as ollows: Mass conservation: ( u u u 0 (1 Du P 2 g Momentum conservation: v u (2 Dt 0 0 Energy conservation: u 2 (3 t where, is the density (kg/m 3, u is the velocity vector (m/s, t is the time (seconds, is the water temperature (, P is the pressure (N/m 2, and g is the gravitational acceleration (m/s 2. In general, CFD analysis is preerred, because it is more accurate than other analysis methods. However, it requires many input data, and using CFD is a very complex and time-consuming process. CFD is also suitable or the prediction o luid motion, but not prediction o the energy perormance o a solar domestic hot water system. Simpliied luid motion and water temperature prediction method One-dimensional stratiied model his model is valid only in the case that the temperature gradient in the radial direction is small, and that stratiication in the tank is well ormed. It is assumed that the water low is one-directional, and the water in the tank is divided into multiple nodes o equal volume. Dierential equations governing the energy balances on the nodes are solved simultaneously, using the numerical method. Inversion mixing occurs when the node below is warmer than the node above. his buoyancy orce causes the nodes to mix. Since inversion mixing occurs very rapidly, the low rate caused by inversion mixing is assumed to be the maximum value that will provide a stable solution, given the node mass and the time step. Several one-dimensional methods are suggested in previous research, and are implemented in namic energy simulation tools, such as EnergyPlus and RNSYS. Plume entrainment model

3 I the incoming luid rom the heat source is cooler than the luid at the top o the tank, the hot luid in the tank will be entrained in the alling plume. hus, the incoming stream is heated up, and it will all down to the position in the tank where its density, and thereore temperature, matches that o the tank. he mathematical model o plume entrainment is based on energy and mass balance. he storage tank is modelled as having two separate sections: the plume region and the tank region. he energy balance equation o the stream region is written as: C p ( m SS C x p m x S (4 he energy equation o the tank region is written as: 2 ( m m AC C C ka UA ( 2 loss amb (5 t x x x where, m S is the mass low rate o the stream (kg/s, stream (, m is the mass low rate o the tank region (kg/s, and temperature o the tank region (. S is the temperature o the is the MAHEMAIC MODEL OF HERMAL SORAGE WIH AN ELECRIC HEAER Heat transer o a thermal storage tank node In this research we assumed that luid motion in the thermal storage is two-dimensional. It is considered that the temperature o the upper region o the heater is higher than that when a heater is not installed. he x-axis is divided into two parts. he storage tank heat transer model accounts or heater heat input, heat gain rom the heat exchanger, heat gain rom the heat source, conduction between adacent nodes, mixing between adacent nodes, thermal losses to the environment, and heat release to the load. he governing equations or luid are written as ollows: m k A m m c y p i 1, source d dt 1 i 1, source k A x k A m i 1, 1 m y use 1 1 use k A x m (6 m q i 1, i 1, 1 aux q i 1, HX 1 UA loss out where, m is the mass o a node (kg, C p is the speciic heat (J/kg, k is the thermal conductivity o the water (W/m K, A is the surace area o the node (m 2, is the distance between the centers o nodes (m, is the temperature o the water (, m S is the mass low rate rom node to adacent node, qaux is the heat transer rom the electric heater (J, q is the heat transer rom the heat exchanger HX

4 (J, UAloss is the heat loss coeicient o the storage (W/m2 K, out is the ambient temperature (, subscript i is the i th node on the x-axis, and subscript is the th node on the y-axis. he dierential equations governing the energy balances on the nodes are solved simultaneously, using the numerical method. Q HX Q aux Q source +1 i-1, i+1, Y Q loss Q use -1 X Conduction heat transer Convection heat transer Figure 1. Heat transer between the water node and adacent nodes Mass transer o the thermal storage tank node Mass low is introduced into the node, and then some water, equivalent to the amount o incoming water, should be extracted rom the node, to maintain mass balance. For each o the nodes, mass low between vertical adacent nodes, mass low between horizontal adacent nodes, mass low rom the source side, and mass low rom the load side will all contribute to its mass balance. he mass balance equation o each water node is written as below: m 0 in m out (7 where, m in is the introduced water low rom an adacent node (kg/s, and in the extracted water low to an adacent node (kg/s. o calculate the mass low rate, the momentum conservation and mass conservation o each node should be solved simultaneously, and grid discretization is required. We propose using a simpliied method to calculate the mass low rate o each node. I the temperature o the node below is higher than that o the node above, mass low rom the node below to the node above occurs. It is assumed that the density dierences between adacent nodes are mainly governed by variations in the driving low. o simpliy the calculation, the natural convection low was modelled by Boussinesq approximation, with the shape o a water node assumed to be rectangular. m is

5 A two-dimensional model is also assumed; the vertical direction is assumed as the y-axis, and the radial direction is assumed as the x-axis. Since mass low is mainly caused by buoyancy orce, it is assumed that buoyant energy is transormed kinetic energy. he buoyancy orce is expressed as a unction o temperature: 1 2 v g 0 (8 2 where, is the thermal expansion coeicient, and 0 is the operating temperature (. As a general rule, we express the mass low rate that crosses a vertical and horizontal border between two current nodes by the ollowing expression: m Cd A v Cd A g ( (9 2 0 where, m is the mass low rate due to the buoyancy orce (kg/s, and Cd is the discharge coeicient. he discharge coeicient Cd is an empirical coeicient that includes viscous eects and the local contraction o streamlines when the low crosses an opening. his coeicient has to be determined experimentally, by the ratio between the actual mass low and the theoretical low. Analysis model evaluation An analysis model is developed using Microsot Visual Studio he analysis program consists o main two parts: data input and calculation. he thermal property o materials, system design data and weather data is treated in the data input part. he mass balance equations and heat balance equations are solved in the calculation part. he calculation procedure is as ollows: Start Input Mass balance calculation o storage hot water nodes Grid generation emperature calculation o storage hot water nodes ime Loop Initialize nodes Convergence true Hot water node temperature alse End Figure 2. Analysis process o the model

6 SIMULAION OF HE HERMAL SORAGE ANK ZONAL MODEL Simulation Conditions In order to validate the zonal model or a thermal storage tank, simulation is conducted or a cylindrical thermal storage with an electric heater. Fluid motion and the water temperature distribution are evaluated during heater operation, and without water low rom solar collectors and water low to buildings. able 1 summarizes the geometry o the thermal storage tank with the operational conditions. able 1. Input data or simulation Parameter Value Storage outside diameter 1.2m Storage height 2.4m Storage capacity 1,730liter Electric heater capacity 20kW Initial temperature o the water 25 (bottom ~ 1.2m 30 (1.2m ~ 1.8m 40 (1.8m ~ top Electric heater operation 1hour (continuously Flow rate rom source side 0lpm Flow rate to building 0lpm Results Water low rate(kg/s emperature( Location o an auxiliary heater [t = 0s] [t = 1,800s] [t = 3,600s] Figure 3. Simulation result: temperature distribution and water low rate at time=0s, time=1800s, and time=3600s Figure 3 presents the temperature distribution in the thermal storage tank and mass low rate rom node to adacent node, ater 30 minutes and 1 hour. Stratiication in the thermal tank has been maintained prior to the electric heater operation. I the heater starts operation, stratiication is destroyed, due to the rising o warm water. As can be seen rom the water low rate in the igures, the rising water low does not penetrate into the warm luid above, until they have reached the same temperature.

7 Ater 1 hour, the temperature o each water node is almost the same, due to mixing. Warm water is circulated in the upper region o the operation o an electric heater, thereore warm water does not reach the lower region o the electric heater. CONCLUSION A zonal model method or thermal storage with an electric heater is suggested, to predict luid motion and the water temperature o the tank. he zonal model method includes a 2-dimensional unstea state heat transer algorithm, and mass balance algorithm. In order to analyze water low due to buoyancy orce, a mass low analysis equation is suggested. he results rom computer simulation using the zonal model show the water low between water nodes and temperature distribution due to the warm water circulation, under the condition o the auxiliary heater operation. Based on the simulation results, the zonal model method can be incorporated as an energy simulation tool to evaluate the annual thermal perormance o SDHW systems. We intend to complete urther work to validate the developed analysis model through experiments. ACKNOWLEDGMENS his research was supported by the Basic Science Research Program through the National Research Foundation o Korea (NRF, and unded by the Ministry o Education, Science and echnology ( o the Korean Government. REFERECNES ASHRAE ASHRAE Handbook HVAC Applications, Atlanta. J. A. Duie and W. A. Beckman Solar Engineering o hermal Processes. John Wiley and Sons, New York E. M. Kleinbach. Perormance stu o one-dimensional models or stratiied thermal storage tanks. Master s thesis, University o Wisconsin-Madison, Madison, Wisconsin, United States, K. G.. Hollands, and M. F. Lightstone, A review o low-low stratiied- tank solar water heating systems. Solar Energy, 1989, V.43, No.2, pp N.M. Al-Naem, A.M. Al-Maraie, K.Y. Ezuddin, Analytical and experimental investigation o thermal stratiication in storage tanks, Int. J. Energy Res Mi-Soo Shin et al. Numerical and experimental stu on the design o a stratiied thermal storage system, Applied hermal Engineering, V. 24, pp