Thermal Energy Storage for Building: Thermodynamic and Heat Transfer Analysis for Integration of PCMs in Building Walls Yasin Ozcan Mechanical Engineering Department University of Texas at San Antonio [email protected] Amir Karimi Mechanical Engineering Department University of Texas at San Antonio [email protected]

Abstract Saving energy has become very crucial in today’s world. Fossil fuels are commonly used for more electric power generation. Their availability is continually decreasing, in addition they contribute to the environmental global warming. Therefore, we should find ways to increase the efficiency of systems using electrical power. Electricity is commonly used directly for heating or cooling building spaces. The use of thermal energy storage is one way to make the current energy systems sustainable, efficient, economic, and environmental friendly. Thermal energy could be stored in different ways. Basic storage methods are sensible heat, latent heat storage and thermochemical or combination of these. Thermal energy storage with phase change materials are achieved by using the solid-liquid phase change. PCMs can be used for both space heating and cooling applications. In building applications, the PCM is associated with structuring components. It is possible to improve thermal comfort and energy performance of buildings with integration of PCM in building walls. This paper investigates the feasibility of PCMs for cooling application in San Antonio and similar environmental locations. This study examines the possibility of integration of PCMs in building walls in San Antonio in order to reduce to the amount of energy consumed in cooling applications. It will describe the advantages and limitations of integrating PCMs in building walls. The results of a one-dimensional transient heat transfer model will be presented in the paper.

Introduction Energy has become a very crucial element of today’s world. Since electricity generated from fossil sources, which decreases sharply day by day, counts for the main bulk of today’s energy production, we should find a way to increase energy efficiency. The most effective way of increasing energy efficiency is to bring energy consumption under control. To do so, we have four main areas where energy efficiency can be boosted: residential, industrial, transportation and agriculture. In many countries, the energy required for space heating and cooling has the highest share of (40%) of the all total energy consumed in a residential building [1]. The consumption of energy in buildings is influenced by the heating and cooling system used. Thermal energy storage is helpful in making the current energy systems sustainable, efficient, economic, and environmental-friendly. Energy can be stored in different forms. Energy storage systems can be uniform of thermal, mechanical, chemical, biological and magnetic systems. Thermal energy could be stored in different ways. The basic thermal storage methods are sensible heat, latent heat, thermochemical and combination of these. Proceedings of the 2015 ASEE Gulf-Southwest Annual Conference Organized by The University of Texas at San Antonio Copyright © 2015, American Society for Engineering Education

The characteristic of latent heat represents the amount of energy absorbed or released by a substance during its change in physical state, which occurs without a change in temperature. Latent heat is one of the most efficient ways of storing thermal energy [2]. Latent heat storage systems can be described as fusion associated with the melting and freezing of a material. Latent heat storage materials are also considered as phase change materials (PCMs) [3]. Energy storage systems will play a vital role in making an energy policy. PCMs have been very important for many years and are widely studied in many areas of engineering. Integration of PCM in building walls is very useful and ideal solution for building energy management. Because PCM stores and releases thermal energy during the process of melting and freezing. There are many options to use PCM for energy saving. PCMs can be used for both space heating and cooling applications [4]. PCM is associated with HVAC systems where the heat or cold stored in PCM by using special technical equipment. This type is called active thermal storage. Another way to use PCM for heating and cooling applications, the PCM can be integrated into building walls. During the day outdoor temperature rises or falls beyond the phase change temperature and the heat or cold automatically are stored and released by the building walls without using special technical equipment. Systems that are based on this technique are called passive systems. In building applications, the PCM can be encapsulated in construction materials such as gypsum wallboard, concrete, in the ceiling or in the floor to increase their thermal storage capacity [4-5].

PCM for cooling in buildings In order to reduce energy consumption in cooling applications, temperature fluctuations need to be smoothed out. PCM integrated walls can store large amount of energy while maintaining the indoor temperature within small temperature changes. For cooling applications, PCM can absorb heat during the day and then release it again at night when outdoor temperature rises or falls beyond the phase change temperature. Today some PCMs are commercially used for storing heat and cold into walls and its components to increase the thermal mass and thereby reducing temperature swings inside the building[6]. According to the researchers, PCMs that have a phase change temperature that is between 20°C and 30°C should be used in building applications [7-8].

Figure 1. Operating principle of heat storage Free cooling applications were investigated many times. Free cooling applications serve the purpose of storing outdoors` cold during the night and releasing it indoors during the day. This concept is Proceedings of the 2015 ASEE Gulf-Southwest Annual Conference Organized by The University of Texas at San Antonio Copyright © 2015, American Society for Engineering Education

feasible in climates where the temperature difference between the day and the night in summer is over 15°C [9]. Experimental methods are powerful methods to study the PCM applications in buildings such as PCM microencapsulated into concrete walls or concrete floors, PCM as insulating layer, impregnating gypsum wallboard and other architectural materials [10–14]. The study of the heat transfer of PCM wallboard using analytical method has been conducted by Neeper in 1989. He found that the thermal storage provided by PCM wallboard would be sufficient to enable a large solar heating fraction with direct gain [15]. A simplified theoretical model was established to optimize an interior PCM in lightweight building components by Xin Wang. For optimal phase change temperature, analytical equations are presented in his research [16]. In most of the researches, many numerical methods are seen in literature for modeling PCM. Saleh Nasser and Zhai reviewed the different modeling methods like enthalpy method, the heat capacity method, the temperature transforming model, and the heat source method. In their studies PCM simulation models are compared and information is given about the advantages, disadvantages and limitations of these methods [17]. Another researcher reviewed the theories and simulations for the heat transfer analysis and application of phase change materials. The advantages of using the enthalpy method in simulation model for the energy equations in dealing with the phase change transition temperature in the given range was presented [18]. Shilei used numerical modeling to analyze PCM enhanced building envelope. They analyzed thermal energy savings for the PCM systems and also researched internal temperature developments for the PCM in wall and roof. They validated numerical result with the experiment data [19].

Heat Transfer in the Wall Model The schematic of the heat transfer through the wall, in the conditions that the room temperature is fixed at 24oC and the external outdoor has sinusoidal varying temperature, is shown in Figure 2. In this schematic it is seen that the PCM is integrated to the interior wall surface. The PCM absorbs energy at daytime and releases it in the evening.

Figure 2. Diagram of the layers of the external wall Table 1 shows the average high and low air temperatures in San Antonio from January to December from 1981 to 2010. Based on the data given in Table 1. It was determined that San Antonio needs more cooling than heating. Using PCMs for cooling applications is more practical.

Proceedings of the 2015 ASEE Gulf-Southwest Annual Conference Organized by The University of Texas at San Antonio Copyright © 2015, American Society for Engineering Education

Table 1. Average high and low temperatures in San Antonio from 1981 - 2010 Month High °C Low °C Heating or cooling necessary? January 17 5 Heating February 19 7 Heating March 23 11 Heating April 27 14 Heating and Cooling May 31 19 Cooling June 33 23 Cooling July 35 24 Cooling August 36 24 Cooling September 32 21 Cooling October 28 16 Cooling and Heating November 22 10 Heating December 18 6 Heating To arrive at an analytical solution for heat transfer, it is necessary to apply thermal and geometrical restrictions. It is assumed that no change in volume occurs due to the solid-liquid phase change, during which, convection heat transfer is not considered. Building wall components and their thermophysical properties appear in Table 2. Table 2. Physical properties Material Concrete PCM XPS Plasterboard

Density Kg/m3 2,300 825 35 900

Thermal conductivity (w/mK) 1.28 0.2 0.037 0.14

Specific heat / Latent heat J/kg K 1,130 2,000 148,000 1,400 1,000

Thickness mm Without With PCM PCM 150 150 10 35 35 25 10

Theoretical analysis At the left x = 0 and at the right x = l of the object in Figure 2. Since there is a thermal interaction with the environment, the suitable boundary and initial condition should be set for a PCM wall. T k  ho (Te  Two ) (1) x x0 T k  hi (Twi  Ti ) (2) x xl T (0, t ) t 0  Te (3) Where Te is the environment temperature, Two is the external wall surface temperature, and ho and hi are the convective heat transfer coefficients on the external and the internal wall surfaces respectively which are used as ho=18w/m2 and hi=8w/m2. In steady state absence of phase transformation, equality is correct on the boundary. The difference in heat fluxes on both boundary sides will be spent for phase transitions. Heat transfer in the solid-liquid interface can be expressed by the transient conduction equations. The phase changing process is governed by the conservation of energy. Proceedings of the 2015 ASEE Gulf-Southwest Annual Conference Organized by The University of Texas at San Antonio Copyright © 2015, American Society for Engineering Education

Ein  E pcm  Eout  0

(4) For phase change process the interface temperatures are the same, other properties like the physical properties and temperature gradient are different for each phase. The following equation describes melting process of the materials [20]. ds (t ) T T L  ks  kl (5) dt x x Solid and liquid phases are referred by s and l respectively. During the solidification process, index l and s are interchanged and the latent heat of the PCM fusion L will be inversed in equation (5). In the solid-liquid interface, solid and liquid PCM temperatures are equal to each other. If the temperature distribution is known, the solid-liquid interface can be determined from the equation (5).The surface energy at the phase change interface is given by dT dT kl  ks (6) s  mL dx dx When the ratio of the sensible heat to the latent heat is small enough, it means the wall with PCM has a small Stephan number. Thus the sensible heat can be ignored for the quasi-steady state method to analyze the heat transfer. The quasi-steady state method can be applied for theoretical analysis when the PCM latent heat of fusion is higher than 50 kJ/kg [21]. If the sensible heat loss of liquid is neglected, storage energy is determined by Tm  T (t ) (7) q t    mL s  t  d wall 1   k kw ho Where m is the melting portion of the PCM mass. Defining the phase change mass and heat transfer coefficient U without PCM layer and melting speed is defined as ρ ds/dt, thus the following equation is derived.  Tm  T0 (t )  s 1 (8)   dt     ds k U   L  The phase change time can be found by solving equation (8). Therefore, the phase change time can be used to evaluate thermal performance of the PCM wall. As a driven result the longer period of transition time is beneficial for saving more energy and making indoor environment more comfortable [21].  s2 s  L t  (9) Tm  T0 (t )   2k U  The wall with PCM in solid state is heated at one surface by time dependent heat flux. Firstly, PCM gets heat and it reaches the melting temperature. During the melting process, PCM stores the heat energy to prevent wall surface temperature from increasing. The following expression can be used to determine the heat storage capacity of PCM. t

 h (T 0

o

o

 Two )dt  mL

(10)

When the PCM is totally melted, no more heat can be stored. After the phase change, heat passes through the wall and gets into the room.

Proceedings of the 2015 ASEE Gulf-Southwest Annual Conference Organized by The University of Texas at San Antonio Copyright © 2015, American Society for Engineering Education

Mathematical Model Ordinary building wall with the PCM has three states: solid, liquid and solid-liquid coexistence state [2]. T  2T  as 2 Solid state (11) t x T  2T  al 2 Liquid stated (12) t x ds (t ) T T s L  ks (13) x  s ( t )  kl x  s ( t ) Solid-liquid coexistent state dt x x Where α is the thermal diffusivity and k is the thermal conductivity, s(t) is the time function that identifies the position of the phase change boundary, L is the latent heat of fusion. Subscripts refer to the solid phase and liquid phase. In literature, these three equations together are known as moving boundary or Stefan problem. To calculate heat transfer through the wall, these three equations must be solved for the whole region. However this is not an easy task. Because liquid-solid interface is moving and its position is unknown. Therefore, determining the solid-liquid interface is very difficult or even impossible. In order to simplify the calculation, the enthalpy method or the heat source method could be applied for both of the phases which are based on the finite difference method. The enthalpy form as a function of temperature is given in the following expression [22]. H   .  k T  (14) t Where H is the total enthalpy which is the sum of the sensible heat (h) and latent heat (L) components. It can be expressed as follows; H  h  Lf (15) T

h   c p dT

(16)

Tm

Where f is the function of the liquid fraction. For the melting or solidification process, the PCM is initially liquid or solid, depends on its temperature of certain value above or below the phase transition temperature. For Tm is the temperature of the phase change and the liquid fraction can be defined as [23]; 0,  f   f (t ) 1 

Ti  Tm Ti  Tm

(17)

Tm  Ti

Substituting equation (15) and (16) into equation (14), gives; h k  2T f  L (18) 2 t  x t Equation (18) represents the mathematical model of conduction with phase change in the given conditions. When the temperature distribution is determined by solving equation (18), the location of phase change interface and amount of the heat transfer can be found. Proceedings of the 2015 ASEE Gulf-Southwest Annual Conference Organized by The University of Texas at San Antonio Copyright © 2015, American Society for Engineering Education

Thermal model based on explicit finite difference method when no phase change occurs Solving the heat equation numerically, the wall is divided into equal width slabs parallel to the two surfaces. ∆x is the thickness between two nodes. Each i nodes represent certain space. The time can be written as t=j.∆t where j is an integer at each time step.

Figure 3. Finite control volume [24] The heat transfer between the two adjoining nodes i and i-1 in the time interval ∆t,

T -T Q  - A.k i i -1 t xi - xi -1

(19)

The one-dimensional heat diffusion is given by T  2T i ci  ki 2 (20) t x Equation (20) can be rewritten by using the finite difference approximation, k  2T T  i (21) t i ci x 2 The value of derivative, at the i nodal point, is approximated as  2T Ti 1  2Ti  Ti 1  (22) x 2 x 2 In the time interval ∆t, derivative as time step j to j+1 is equal to T Ti , j 1  Ti , j  (23) t t Combining expressions (22) and (23), yields Ti , j 1  Ti , j k Ti 1, j  2Ti , j  Ti 1, j  i (24) t i ci x 2 The stability of the method, in the definition of time step and domain size, the following condition must be considered. k t 1 Foi  i  (25) i ci x 2 2 Where Fo is the dimensionless mesh Fourier number. For a single material inside node is, an explicit numerical solution form, given in the following equation [24].

Ti , j 1  Ti , j  Fo Ti 1, j  2Ti , j  Ti 1, j 

The following energy balance equations are accomplished on all the nodes for the system, Proceedings of the 2015 ASEE Gulf-Southwest Annual Conference Organized by The University of Texas at San Antonio Copyright © 2015, American Society for Engineering Education

(26)

Ein  Eout  Estored Ein  Eout  Estored

(27)

Ein ,net  Estored

It is possible to write the energy balance of the domain which is situated on the exterior or interior surface of the walls by considering the convection as well as the heat flux that the wall is subjected to. For the external and internal surfaces, temperatures of the nodes are formulated from the heat balance equation. Thermal energy balance for the first node, which is located on the exterior surface of the wall is given in the following expression [25].

x T c 2 t

x 0

 h0 (Te  Tw 0 )  k

T x

x x /2

(28)

From the heat balance equation, increase in the internal energy within the control volume is equal to the net heat conduction plus the heat convection across boundary. The final equations of the superficial temperature are as follows; External surface node temperature  h x h x  t  x 2 Ti , j 1  ai 2   2 0  2  Ti , j  2Ti 1, j  2 0 Te  (29) x  ai t ki ki   Internal surface node temperature  h x h x  t  x 2 Ti , j 1  ai 2   2 i  2  Ti , j  2Ti 1, j  2 i Tr  (30) x  ai t ki ki   Where a is the thermal diffusivity, hi and ho are the inside and the outside convection coefficients respectively, Te and Tr are the outside and inside temperatures respectively. The heat transfers between two boundaries along the thickness direction x, can be calculated using the thermal balance. When two phase occurs Finite differences method is used to solve for the heat transfer in the PCM integrated walls. When there is no phase change in the material, equation (14) is valid. If the phase change occurs, the left side of equation should be modified with the latent heat of fusion and the liquid fraction. The PCM absorbs or releases the latent heat energy from the surrounding system until the PCM totally changing its phase. The total latent energy stored in control volume is Qs  f . .h.x (31) There is a change in internal energy for every time step, when the temperature is constant during the entire phase change. For isothermal heat transfer analysis, we should consider four different cases: I. No phase change, II. Phase change, III. Phase change just started, IV. Phase change just ending. Case I. For fully solid or liquid phase, there is no phase change and the time variation of the liquid fraction is zero. Case II. When the phase change is beginning, it is easy to make some observations. During this process the temperature is the same to the value of the liquid fraction when it is between 0 and 1. 0  fi , j 1  1  0  fi , j  1 (32) In this case it is possible to state: Proceedings of the 2015 ASEE Gulf-Southwest Annual Conference Organized by The University of Texas at San Antonio Copyright © 2015, American Society for Engineering Education

h  0 , and Ti , j Ti , j 1  Tm t Case III. Phase change just started For the case of melting, 0  fi , j 1  1 and fi , j  0

(33) (34)

For a given time step Ti , j 1  Tm and Ti , j  Tm Case IV. Phase change just ended For the case of melting, 0  fi ,1  1 and f i , j 1  1

(35) (36)

For a given time step Ti , j 1  Tm and Ti , j  Tm (37) For the isothermal phase change Ti=Tm, sensible enthalpy remains constant and equation (18) can be written in explicit discretization form as follows, ki Ti 1, j  2Ti , j  Ti 1, j f L (38) 2 i x t The following expression is used to determine liquid fraction value. During the phase change for the liquid fraction, the expression can be written in explicit form as in the following [26].

fi , j 1  fi , j 

ki t Ti1, j  2Ti, j  Ti1, j  i Lx 2

(39)

Liquid fraction is changed from the temperature field and not from the sensible enthalpy field. When phase change just beginning, internal node temperature will be equal to the phase temperature Ti , j  Tm and liquid fraction will be as follows, c Tm  Ti , j k t fi , j 1  fi , j  i 2 Ti 1, j  2Ti , j  Ti 1, j  (40) i Lx L The inside node temperature distribution will be, L 1  fi , j k t Ti , j 1  Ti , j  i 2 Ti 1, j  2Ti , j  Ti 1, j  (41) i ci x c The internal surface nodes’ temperatures will be L 1  fi , j Ti , j 1  2 Fo Ti 1, j  BiTe  1  Fo  2 FoBi  Ti , j  (42) c Where Bi= hl/k is the Biot number. When phase change has just ended, the control volume is completely melted, the time variation of liquid fraction has become 1 and the nodes’ temperatures will start changing. The superficial temperature will be:











 











After phase change, PCM is fully liquid and internal nodes’ temperatures will be, Ti , j 1  Ti , j  Fo Ti 1, j  2Ti , j  Ti 1, j

(43)

Internal surface nodes’ temperatures will be, Ti , j 1  2 Fo Ti 1, j  BiTr  1  Fo  2 FoBi  Ti , j

(44)









As a result one-dimensional transient heat transfer model is developed. The PCM wall is analyzed and the interior surface temperatures are illustrated in Figure 4. Equations (42), (43) and (44) are used to predict thermal behavior of the PCM wall. Compared to the initial situation of the wall by integration of PCM in building walls, building thermal comfort and energy performance were Proceedings of the 2015 ASEE Gulf-Southwest Annual Conference Organized by The University of Texas at San Antonio Copyright © 2015, American Society for Engineering Education

improved. Integration of PCM is examined in order to reduce the amount of energy consumed in cooling applications.

Results The calculations are done for the real conditions of a day time for San Antonio [27]. When the PCM phase change temperature and the latent heat capacity are properly selected, the PCM helps to diminish the amplitude of the instantaneous heat flux.

Figure 4. Internal wall surface temperatures

Figure 5. Heat flux comparison during the day in May

The numerical calculations are performed with Matlab and Excel programs by using the melting temperature of PCM [28]. PCM layer temperature of the node becomes equal to the melting temperature, phase change occurs. In this study, the PCM capacity is used as 148kj/kg. It was observed that the PCM was totally melted when the room temperature is lower than the outside temperature in May, refer to Figure 4 and 5. However, when the outside temperature is lower than room temperature, it was seen that the PCM didn’t release all of its stored energy completely. For a regular building wall, the inner wall surface temperature depends on the outer temperature and the heat transfer coefficient U. To evaluate the thermal performance of the regular wall, decrement factor and time lag are used. Conversely, to evaluate the thermal performance of a wall with PCM, the latent heat capacity of the PCM and the transitions period have to be considered. The results of a one-dimensional transient heat transfer model was presented for isothermal phase change. A finite difference model was developed which can be used to predict the thermal behavior of walls with PCMs. Based on the mathematical and numerical approximation, one-dimensional heat transfer was calculated to attempt to predict the thermal behavior of the Pcm. In this study, the room temperature in a building was investigated following the integration of PCM into its wall under the weather conditions of San Antonio. The integration of PCM decreased the internal surface wall temperature in May by up to 1oC without supplying any mechanical ventilation Proceedings of the 2015 ASEE Gulf-Southwest Annual Conference Organized by The University of Texas at San Antonio Copyright © 2015, American Society for Engineering Education

or cooling. The results show that the heat fluctuations of the PCM integrated wall is smaller than that of the regular wall. In additions, energy savings in PCM integrated walls can be improved by increasing latent heat capacity. If the PCM cannot melt and freeze completely, latent heat capacity would not change the saving. Moreover, the different phase change temperatures and capacities of the PCM can change the heat flux over time. PCMs can be extremely useful energy management solutions if outdoor temperatures cycle above and below the indoor temperature in a 24-hour period. Therefore, the PCM should be selected carefully according to the weather conditions. If the outside temperatures remain above the indoor set temperature during the day and the night, then the PCM is not a significant factor.

Comments San Antonio has hot weather conditions. During the summer period, night temperature will be too high for PCM solidification under the given parameters. This means during the daytime PCM cannot store energy. PCM can enhance thermal comfort and energy performance of buildings but only when outdoor temperature rises above and drops below the PCM phase change and room temperatures in a 24-hour period. Alternatively, PCM can be still considered for the possible solution to shift peak load. Nowadays most countries use dynamic electricity price, it means energy price is changing during the day depending on the demand. If city uses dynamic electricity price, we can store cooling energy in PCM wall during the night with low electricity price. On the peak time with high electricity rate, PCM starts melting, therefore it will be delaying the heat input into the room at the peak electrical demand. As a result the PCM can shift the peak electricity load in the summer. For this reason PCM will be considered useful. As a conclusion of this study it can be said that the application of PCM in building walls have the following advantages; The PCM decreases building energy consumption, increases indoor thermal stability by decreasing indoor temperature fluctuations. Also it delays the cooling loads.

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YASIN OZCAN Mr. Ozcan is a master’s student in the Mechanical Engineering Department at the University of Texas at San Antonio. This paper is part of his Special Project. His research interests are in the thermal sciences. AMIR KARIMI Dr. Karimi currently serves as a Professor of Mechanical Engineering at the University of Texas at San Antonio. His research interests include metastable thermodynamics, phase change heat transfer, and thermal system management. Dr. Karimi is a registered Professional Engineer in Texas.

Proceedings of the 2015 ASEE Gulf-Southwest Annual Conference Organized by The University of Texas at San Antonio Copyright © 2015, American Society for Engineering Education