Available online at www.sciencedirect.com

ScienceDirect Energy Procedia 78 (2015) 1690 – 1695

6th International Building Physics Conference, IBPC 2015

Modelling of an active PCM thermal energy storage for control applications Vasken Dermardiros*, Yuxiang Chen, Andreas K. Athienitis Concordia University, 1455 de Maissoneuve Blvd. W., Montréal, Québec H3G 1M8, Canada

Abstract This paper presents the results of an experimental and numerical study focusing on the control-oriented modelling of an actively charged/discharged phase-change material (PCM) thermal energy storage (TES) system. The PCM-TES system consists of five layers of commercial macro-encapsulated PCM panels with an air cavity in its center. Air can flow through the cavity to charge/discharge the PCM panels. The PCM-TES was tested in an environmental chamber and its dynamic response was carefully monitored. A detailed fifth order thermal network finite difference model for the system is developed and verified against experimental results. The detailed model is then simplified to a 2nd order model for control purposes. A five-parameter equation is developed to model the storage of heat in the PCM. An average and maximum temperature difference of 0.8°C and 2.0°C, respectively, is achieved between the experiment data and that simulated by the detailed model. The second order model has an average and maximum temperature difference of 0.2°C and 0.9°C, respectively, compared to the detailed model. It is thus adequate for real time model predictive control of the system. © 2015 2015The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license © Published by Elsevier Ltd. This Peer-review under responsibility of the CENTRO CONGRESSI INTERNAZIONALE SRL. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the CENTRO CONGRESSI INTERNAZIONALE SRL Keywords: phase-change material; thermal energy storage; building-integrated thermal energy storage; modelling; reduced order

1. Introduction In order to reduce the peak energy demand of a building, enhance thermal comfort by reducing short-term temperature fluctuation, aid in demand-side management, the use of a thermal energy storage (TES) system is paramount [1]–[3]; buildings constructed with light-weight materials (e.g.: wood) lack significant thermal storage

* Corresponding author +1 514 848-2424 x7080 E-mail address: [email protected]

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the CENTRO CONGRESSI INTERNAZIONALE SRL doi:10.1016/j.egypro.2015.11.261

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Nomenclature T it i j Cp k h ρ Δx A

Temperature of node i at time t, °C Subscript, current node Subscript, neighbouring node Specific heat, J·kg-1·K-1 Conductivity, W·m-1·K-1 Convective coefficient, W·m-2·K-1 Density, kg·m-3 Layer thickness, m Area, m2

Specific heat function Δh Enthalpy of fusion, J·kg-1 Approximate phase change temperature, °C Tc ω Phase change temperature range, K

Δt R C Q̇ ṁ ΔTln DSC PCM TES

Timestep, s Thermal resistance, K·W-1 Thermal capacitance, J·K-1 Heat flux, W Mass flow, kg·s-1 Logarithmic temperature difference, K Differential scanning calorimetry Phase-change material Thermal energy storage

skew Skewness of curve Cp,average Averaged Cp of solid & liquid phases, J·kg-1·K-1 erf(…) Error function

capacity. One way to increase the effective storage mass of a building, without adding a substantial structural load, is through the use of phase-change materials (PCM). [4]–[7] The field of phase-change materials applied to buildings has seen significant activity in the past 30 years [8], but even after so much dedicated research, there still remains many challenges to overcome. Kenisarin and Mahkamov [9] cast doubt on the reliability of the thermo-physical property data produced and distributed by the manufacturers and that it must be verified by an independent institution. PCM characterisation is based on “quick” methods on very small samples such as differential scanning calorimetry (DSC) which could result in important discrepancies [9], [10], and full scale experimental methods would be preferred [11]. In this study, characterization data from Kuznik et al. [12] is used. Chemical stability remains an issue with repeated cycling and PCMs remain too costly [9], [13]. Modelling the thermal behaviour of PCMs is different than modelling sensible storage systems due to the strong non-linearity in enthalpy and conductivity when undergoing a phase transition. The heat capacity method of modelling is intuitive, easy to program and suitable for gradual phase change; however, it can be computationally inefficient. It consists of gradually varying the specific heat of the material as a function of temperature. The method accounts for both sensible and latent heat. [14] In previous numerical studies on active PCM-TES systems utilizing PCM panels, the developed models were based on numerous 1-dimensional (1-D) control volumes which were connected to one another through the circulation air node – this is sometimes referred as a quasi-2D model. [7], [15], [16] This approach is valid since the panels are quite thin. Although some models can evaluate a 3-dimensional heat transfer process, it was concluded that it did not offer additional accuracy compared to the previously validated 2-dimensional model [14]. The objective of this study is to develop a simplified control-oriented model of an actively charged and discharged PCM-TES system. The model captures the dynamic behaviour and will be used in an anticipatory model-based control strategy. Advanced controls are necessary to ensure the material undergoes a phase change and its latent capacity is fully utilized. In this paper, a shape-stabilized 60% microencapsulated paraffin within a copolymer (ethylene polymer) was used as the PCM. [12] Paraffin is one of the most common organic PCMs, is thermally stable and demonstrates very little sub-cooling. [7], [13] 2. Experimental study The objective of the experiment is to study the active charging/discharging behaviour of the PCM-TES. An isolated system with a single airflow channel was used (Fig. 1); other prospective configurations will be studied in the future including room-integrated systems. Here, 5 layers of shape-stabilized PCM panels were used with a 30 mm air channel between the 3rd and 4th layers. The front and back of the PCM wall was insulated. This configuration could be used in a stand-alone system in a partition wall or in the ceiling space possibly connected to the ducting. The experiment

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Fig. 1. Schematic of the experiment showing the thermocouple positions. (a) Front view; (b) Cross-section view.

was conducted in the Concordia University Solar Simulator and Environmental Chamber (SSEC) research facility (Montreal, Canada). Type T thermocouples were placed at 9 locations on each layer interface to determine the temperature distribution. The right side of the wall was split into 6 nodes along the height. The left wall had only thermocouples in the center of the PCM panels. The assumption here was that the behaviour of the left and right panels should be similar due to symmetry and so the thermocouples on the left wall were used to verify the assumption. On the bottom section of the right wall, extra thermocouples were placed around the edges of the panels to check if there were any edge effects. On the air stream side, cool or warm air supplied by the environmental chamber enters the inlet plenum of the PCM-TES and exits through the outlet plenum where it is directed towards a calibrated orifice flow meter. Two differential thermocouples – or thermopiles – were installed to accurately measure the temperature difference between the inlet and outlet. Initially, the PCM TES was charged by supplying air at 28°C at 400 kg/h (93 l/s, 200 CFM, 1.3 m/s average and 2.0 m/s midpoint, measured) until steady state was attained. Next, the heater was turned off and cold air from the chamber at 13°C was supplied, again, until steady state was attained. 13°C (55°F) is the typical supply air temperature of HVAC systems in North America. This process was rerun 3 times to verify repeatability. The flow rate was chosen since it would provide a good convection heat transfer rate with minimal pressure losses. The temperatures were read every 15 seconds and the average was recorded minutely. 3. Numerical formulation and validation The model (Fig. 2.a) is designed to be able to compare with temperature values from the experiment. It consists of 5 nodes with capacitance (Layers 1, 2… 5) with intermediate massless nodes (Nodes A, B… H). The thermocouples are fixed on the PCM surface (Nodes A, B… J) along the horizontal plane; implanting thermocouples into the center of the PCM was not practical. Node D has an equivalent heat source connected where the energy comes from the inlet air. The convective heat transfer coefficient on the two sides of the cavity was estimated to be 18 W·m-2·K-1 using Martinelli’s correlation [17]. The boundaries – the front and back of the PCM wall – were well insulated and the environmental heat loss is assumed to be minimal. So, all the heat gained or lost by the air stream is lost or gained by the PCM-TES. Along the height, the PCM-TES could be split into control volumes and connected at the air nodes. The PCM panels are quite thin compared to the total height – a ratio of around 150 to 1. The vertical heat transfer between control volumes is relatively small compared to the heat transfer in the transversal direction and so the thermal network could be 1-dimensional in a given control volume. For this study, one control volume was used. For a more detailed analysis, additional control volumes can be considered where the air outlet of one would become the air inlet of the next. The simulation timestep was set to 1 minute to assure numerical stability. Heat conduction through the medium is governed by Fourier’s Law. However, since the specific heat and conductivity of the material vary with temperature, a closed form solution can seldom be obtained and a finite

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Fig. 2. (a) Thermal network of the detailed model, the boundary conditions are assumed adiabatic; (b) for the simplified model, the front three layers are combined as well as the back two.

difference approach is necessary (Eq. 1). For nodes with negligible heat capacity, the capacitance value can be set to zero. t 1 § T jt 1  Ti t 1 · t Ti ¸ ¨ ¦j ¨ Rt 1 ¸  C (T )i 't  Q i ij ¹ ©

Tit C (T ) 't t i

(1)

The heat transferred to and from the storage medium must come from the circulating fluid for the well-insulated case. The heat balance equation (Eq. 2) can be written and then solved for the outlet air temperature (Eq. 3):

'Q

h

t Tair _ outlet

convection

 ˜ C p ˜ (Toutlet  Tinlet )]air ˜ APCM _ surface ˜ 'Tln  [m

§  hconv ˜ APCM t ¨ Tair _ inlet ˜ exp ¨ © m air ˜ C p ,air

0

ª · §h ˜A t ¸  Tsurface ˜ «1  exp ¨ conv PCM ¸ ¨ m ˜ C «¬ ¹ © air p ,air

(2)

·º ¸» ¸ ¹»¼

(3)

The enthalpy and the specific heat of a PCM varies greatly with temperature. In building simulation software such as EnergyPlus or TRNSYS, the user must input an enthalpy or specific heat lookup table. A lookup table is computationally inefficient. Another approach would be to represent the curve with a mathematical function. Athienitis [4] had approximated the specific heat curve by a triangle. Egolf and Manz [18] have used two exponential curves connected at the peak phase change temperature to represent the enthalpy curve. Their approach requires 6 parameters and is much simpler and quicker to use than a full lookup table. The limitation of Egolf and Manz’ approach is that, taking the derivative of a curve with a kink, there is a discontinuity in the specific heat correlation at the peak phase change temperature. A continuous curve based on a skewed normal distribution requiring 5 parameters is proposed (Eq. 4). The curve could be more detailed by the addition of parameters, but the former yields reasonable results and would be applicable for PCMs with limited sub-cooling, such as organic materials [13].

C p (T )

'h ˜

§  (T  Tc ) 2 · ª 1 § skew ˜ (T  Tc ) ·º ¸¸ ˜ «1  erf ¨ ˜ exp ¨¨ ¸»  C p ,average 2 2S 2 ˜Z © ¹¼ © 2 ˜Z ¹ ¬

(4)

The PCM used in the experiment has been studied by Kuznik et al. [12], [19], [20]. Their DSC characterization curve along with the skewed-normal approximation (generated using Eq. 4) and the skewed-normal curve which best fits the experimental data is shown in Fig. 3. The best fit curve has a lower thermal capacity than the DSC curve. This is because the numerical model’s boundary conditions were assumed to be adiabatic and leak-related losses were also neglected, but it is not the real case. The results of Kuznik et al. had to be used since the current data provided by the manufacturer is limited for engineering purposes. With improved communication between engineers and material scientists, practical material characterization data can be generated to better aid in designing the PCM application for systems. Results show a good agreement between the experimental data and the model with the best-fit specific heat curve (Fig. 4.a & b). For the discharge curve, the experiment shows a slight sub-cooling effect at around (18 to 19) °C. The

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a.

b.

Fig. 3. (a) Melting curve showing Kuznik’s data [20] with the skew-normal approximation and best fit; (b) Freezing curve.

largest discrepancy occurs on the front layers. This is due that the boundary condition is not fully adiabatic as assumed. There is an average temperature difference of 0.8°C with a maximum of 2.0°C for the front-most layer. Energy stored and discharged quantities are given in Fig. 4.c. In order to reduce the simulation time, and to have a more general model with a variable number of layers around the air channel, the model is further simplified. A simple model is more appropriate for control purposes. The conductance of the PCM varies with temperature (± 12% from mean), however by taking the average value, there is a negligible difference in the resulting energy balance. Furthermore, the 5-capacitance model has been reduced to having two capacitances (Fig 2.b). The average nodal temperatures of the calibrated 5-capacitance model was used to verify the 2-capacitance model. The agreement was satisfactory with an average temperature difference of less than 0.2°C with a maximum of 0.9°C. With additional testing, the model will be further fine-tuned. 4. Future work Currently, the simplified model is being applied to a model-based control strategy. The thermal zone will have a parametric design to be able to study how a PCM-TES system would reduce the peak energy demand for various types of building construction and occupancy patterns. Experimentally, the control strategy will be implemented in a commercial controller and tested in the Environmental Chamber facility. Numerically, the different configurations will be studied including the room-integrated configuration and its impact on occupant comfort. Variations of PCM properties (e.g.: phase-change temperature, conductivity) will be studied to analyse their impact on performance and

Energy Stored (%)

Energy (kWh)

Charging Time (h)

Discharging Time (h)

c.

99 95 90 80 70 60 50

2.63 2.53 2.39 2.13 1.86 1.60 1.33

8.9 6.3 5.1 3.9 3.1 2.5 2.0

14.6 10.6 8.4 6.1 4.7 3.6 2.7

Fig. 4. Averaged temperature plots for charging (a) and discharging (b). The temperatures of the front 3 layers are averaged (black) and are the back 2 layers (gray). The experimental results are shown with long dashes; the 5-capacitance model in solid line; and, the 2-capacitance model in short dashes. For the experimental results, the temperatures between the layers are used. (c) Energy stored/discharged.

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to provide insight for future material research. Finally, continual experimentation will aid in characterizing and analyzing how the PCM behaves in partial charge and discharge modes. 5. Conclusion A PCM-TES system was tested in an environmental chamber and the monitored data was used for the development and validation of control-oriented thermal models. First, a 5-parameter specific heat equation was presented which offers a simplified way of inputting characterization data for low sub-cooling PCM and reduces computational time. Second, a fifth order 1-D thermal network finite difference model was developed that captures the main dynamic response of the PCM-TES system. Finally, the model was simplified to a 2-capacitance model with minimal loss of performance and would be adequate for real time model predictive control of the system. 6. Acknowledgements This study is part of an ongoing research at Concordia University funded under a Natural Sciences and Engineering Research Council (NSERC) & Hydro-Québec Industrial Research Chair held by Dr. Athienitis. We would like to acknowledge the help and input of Jiwu Rao and Diane Bastien, and the financial support received from the Concordia Graduate Scholarship in Natural Sciences and Engineering Research, the Faculty of Engineering and Computer Science Graduate Scholarship and the Concordia University 25 th Anniversary Fellowship Entrance Scholarship. 7. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]

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