Eleventh International IBPSA Conference Glasgow, Scotland July 27-30, 2009 NUMERICAL METHOD FOR CALCULATING LATENT HEAT STORAGE IN CONSTRUCTIONS CONTAINING PHASE CHANGE MATERIAL Jørgen Rose1, Andreas Lahme2, Niels Uhre Christensen3, Per Heiselberg4, Magne Hansen5, and Karl Grau1 1Danish Building Research Institute, Aalborg University, 2970 Hørsholm, Denmark. 2ALware, Technologiepark Braunschweig, D-38106 Braunschweig, Germany. 3Engineering College of Aarhus, 8000 Aarhus, Denmark. 4Aalborg University, Department 6, 9000 Aalborg, Denmark. 5Danish Technological Institute, 2630 Taastrup, Denmark. thermal model; this model includes both phase ABSTRACT change enthalpy and a temperature dependant In Denmark, cooling of office buildings during thermal conductivity. summer contributes significantly to electrical A different approach was taken by (Ibáñez et al., consumption. The use of phase change material 2005). This paper described a method for simulating (PCM) can help to reduce overtemperatures during PCMs in building applications using TRNSYS. The summer and even out temperature fluctuations over method was different from other approaches, as it did the day, hereby reducing both heating and cooling not aim at a correct simulation of processes within demands in buildings. materials. Instead, these processes were simplified in This paper describes a numerical method for an equivalent heat transfer coefficient that had to be calculating the latent storage performance of building determined for each material specifically. components containing PCM in order to evaluate the impact on heating and cooling demands. The MATHEMATICAL MODEL developed method was implemented in the whole- The general calculation routines used in BSim have building hygrothermal simulation software package been validated internationally on several occasions BSim (Wittchen et al., 2008). The paper also for instance (Lomas et al., 1994). The basic describes comparisons between laboratory measure- principles of BSim are explained below. ments on a specific building component containing In BSim a building is split into a number of thermal PCM and results obtained with the developed zones divided from each other, the outdoors or any simulation model. Finally, the paper presents some fictional zones by different types of constructions. simple calculations and a detailed case study. The heat balance for each zone couples to the heat INTRODUCTION transport through all adjacent constructions. In a numerical model like the one used in BSim, the PCM used in rooms will increase the thermal mass dynamic behaviour of a building is described in a significantly and thereby help reduce overheating. In discreet form. This means that a continuous process order for the building industry to start using these is described by changes from time-step to time-step, materials, it is necessary to document their abilities each time-step being of finite length. During a time- and investigate the potential energy saving step the model is in a quasi-steady-state, i.e. tempe- capabilities of the materials. A research project was ratures are constant. By using a sufficient amount of initiated with a primary objective of determining the time-steps, this is a reasonable approximation. potential of using PCM in Danish buildings. In order to achieve this, a simulation model was developed Heat transfer in constructions and incorporated into the whole-building hygro- In the same manner building materials are divided thermal simulation software package BSim. into control volumes, each represented by a node. In Several whole-building simulation programs exist each control volume the temperature is calculated as and a few of these can handle constructions a function of the heat fluxes to and from the volume containing PCM. (Stetiu and Feustel, 1998) used along with the heat capacity of the material. Even RADCOOL (Stetiu et al., 1995) in combination with though the control volume has a certain size, the DOE-2 to evaluate a PCM wallboard in an office thermal conditions are taken as uniform throughout building under California climate conditions. (Heim the volume. This is a reasonable approximation as and Clarke, 2003) introduced a first step for long as control volume sizes are small enough. implementing a PCM-module for ESP-r using the Heat transport within constructions is considered programs special materials facility, and this method transient, i.e. taking into account the heat capacity of was later expanded (Heim, 2005). The latter each layer. An example of the nodal partition is concludes that the numerical models required further shown in figure 1. refinement and experimental validation. (Pedersen, 2007) describes how a PCM-module is introduced in EnergyPlus using an implicit finite difference - 400 - conditions are known, which is why equation (3) for the boundary control volume ("i"=1) becomes: 1ni-1 i i+1 T j+1 − T j ()ρc Δx 1 1 = p 1 1 Δt T − T j+1 T j+1 − T j+1 (4) q + air 1 + 2 1 x surfside1 R Δx Δx surfside1 1 2 + + R2 Figure 1 Control volumes and node structure 2λ1 2λ2 Initially all temperatures in the equation system is set The construction consists of several layers divided to a fixed temperature (standard is 20 °C), and from into control volumes. The enthalpy change for a these starting values the first day of the simulation control volume is calculated at each time-step by period is repeated several times until stability has summing the energy going in and out of the control been obtained, e.g. a steady circadian rhythm or a volume. From the specific heat capacity of the quasi-steady-state. control volume a temperature change can be Modelling phase change materials calculated. There are several issues to consider when modelling Assuming steady-state conditions, heat conduction PCM in a whole-building simulation program. The from control volume "i-1" to control volume "i" can main concern is the heat capacity's dependency on be calculated by Fourier's equation. This assumption temperature including the effect of the hysteresis. is often used in numerical calculations and will Previous investigations (Kuznik and Virgone, 2008) typically produce sensible results as long as the have shown that it is important to take into account discretization of the problem is not to coarse. the hysteresis to obtain the correct heat transfer. If the two materials have different heat conductions Another issue is the temperature dependency of the and the control volumes different thicknesses, the thermal conductivity. Here previous investigations equation can be generalised as shown in (1). (Hoffmann and Kornadt, 2006), (Heim and Clarke, T j+1 − T j+1 2003) and (Kuznik et al, 2008) have pointed out that q j+1 = − i i−1 (1) i Δx Δx the temperature dependency of the thermal í −1 i conductivity of the PCM is also relevant to include in + + Ri 2λi−1 2λi the model. The heat flux is positive along the x-axis, i.e. the The method used for performing PCM calculations in same positive direction as the indexing of the control BSim is best described through an example; The volumes. Micronal SmartBoard (30%, 23°C) is a building material containing PCM. The SmartBoard is a 15 The system of equations are solved through an mm thick gypsum board containing 30% (3 kg pr. implicit procedure as described shortly in the m2) of microencapsulated PCM (paraffin). The board following. has a specific heat capacity of 1.20 kJ/kgK, a thermal Through a time-step the implicit heat flux from conductivity of 0.18 W/mK (in solid state) and a equation (1) is taken as constant and the increase in latent heat capacity in the transition area of 330 enthalpy for control volume "i" is summed as kJ/m2. In figure 2 the enthalpy is shown as a function follows: of temperature. j+1 j hi − hi j+1 j+1 ρi Δxi = −()qi+1 − qi (2) Δt 80000 By expressing the specific enthalpy change as a 70000 temperature change multiplied by the specific heat 60000 capacity and by inserting the expressions for q from 50000 Melting 40000 (1), the following equation is obtained: Solidifying 30000 T j+1 − T j Enthalpy [J/kg] ρc Δx i i = 20000 ()p i i Δt 10000 T j+1 − T j+1 T j+1 − T j+1 (3) 0 i−1 i + i+1 i 0 5 10 15 20 25 30 35 Δx Δx Δx Δx Temperature [C] i−1 + i + R i + i+1 + R i i+1 Figure 2 Enthalpy as a function of temperature 2λi−1 2λi 2λi 2λi+1 This equation is constructed for all "i" and solved simultaneously. This is only possible if the boundary - 401 - In order to model the hysteresis we need to have information about the PCM state at the previous time-step in order to calculate the state of the present time-step, i.e. the state at any time is path-dependant. We have chosen to use a simplified method for taking into account the effect of the hysteresis. For a phase change material the heat capacity for control volume "i" in time-step "j" is based on the temperature of the control volume in time-step "j-1", i.e. the last known temperature of the control volume. Using this simplified approach we avoid adding unneccesary complexity to the simulation model. Figure 4 Experimental setup. 18 SmartBoards bolted However, it requires that time-steps are so small that together and surrounded by insulation. instability of the calculation is avoided. As mentioned earlier, before the actual simulation begins the temperature is 20°C throughout the model Test A and for any PCM in the model we define this initial In the first test steady-state conditions prevail when a state as being "on the melting curve". Hereafter, the 1000W lamp is lit on one side of the wall.