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Engineering Optimization
ISSN: 0305-215X (Print) 1029-0273 (Online) Journal homepage: http://www.tandfonline.com/loi/geno20
Multiphysics design optimization model for
structural walls incorporating phase-change
materials
A. Stockwell, N. Neithalath & S.D. Rajan
To cite this article: A. Stockwell, N. Neithalath & S.D. Rajan (2015) Multiphysics design optimization model for structural walls incorporating phase-change materials, Engineering Optimization, 47:3, 308-327, DOI: 10.1080/0305215X.2014.887706
To link to this article: https://doi.org/10.1080/0305215X.2014.887706
Published online: 20 Mar 2014.
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Vol. 47, No. 3, 308–327, http://dx.doi.org/10.1080/0305215X.2014.887706
Multiphysics design optimization model for structural walls
incorporating phase-change materials
A. Stockwell, N. Neithalath and S.D. Rajan∗
School of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, Arizona, USA
(Received 27 May 2013; accepted 17 December 2013)
The development of energy-efficient building envelopes has been an ongoing effort in many countries owing to the pressing need to achieve energy independence. In this study numerical optimization techniques and finite element analysis provide the means to find a compromise point between adding phase-change materials (PCMs) to a concrete wall, the energy savings and the wall’s structural capacity. The primary objective is to minimize the overall lifetime cost of a wall by understanding the implications of PCM layer thickness, material properties and position in the wall on the overall energy consumption. While it is difficult to manually configure a typical wall for the lowest total cost, the developed computational framework provides an automated tool for searching for the best design. The results show that successful designs can be obtained where material and energy costs can be minimized through a judicious combination of existing building materials with thermal energy storage materials.
Keywords: numerical optimization; phase-change material; finite element analysis; cost minimization
1. Introduction
The development of energy-efficient building envelopes has been an ongoing effort in many countries owing to the pressing need to achieve energy independence. The fact that building operations consume about one- third of the world’s energy (Building Energy Data Book 2013), and the understanding that the building envelope is the major determinant of the heating and cooling costs, have led to a number of studies dealing with new materials and systems for envelope construction and retrofitting. More than 80% of the energy use over a building’s life typically occurs during its operational phase, and hence the development of durable, reliable and energy-efficient envelope technologies is paramount in ensuring building energy efficiency.
As the materials used in building and construction continue to increase in strength and become more advanced, there is less of a need to build thick and massive structures. This is a huge progression in the building industry towards reducing the overall building footprint: the smaller the footprint, the less material used, and the lower the impact on the natural resources and energy needed for building construction. There is one major downside, as a result of this, especially in concrete buildings. Concrete provides an energy-efficient barrier between the interior and exterior of a building, which allows a slight regulation of the interior temperatures. However, as ∗Corresponding author. Email:[email protected]
the thickness of the concrete walls decreases, this temperature regulation also decreases and the use of air conditioning is increased, which can greatly increase the energy cost during the operation of a building. This energy consumption can be regulated by looking at the use of thermal energy storage (TES) materials (Demirbas 2006;Mehling and Cabeza 2008). TES can be accomplished through sensible or latent heat storage (Sharma et al. 2009; Baetens et al. 2010). Currently, there is a lot of discussion about the use of phase-change materials (PCMs), which are a type of TES material that use latent heat to store energy, and how the integration of these into building systems could greatly reduce energy consumption. PCMs have a specific phase-change range; when temperatures exceed this range energy can be stored, and when temperatures drop below this range the energy is released back into the surrounding environment. Thus, PCMs can provide very high energy storage density per unit volume as opposed to pure storage media (such as concrete). As a result, incorporating PCMs can either shift the building heating and cooling loads to off-peak periods or minimize the use of a heating, ventilation and air-conditioning (HVAC) system by storing and releasing the energy back into a room when temperatures fall (Khudhair and Farid 2004;Cabeza et al. 2007).
Recent studies on PCMs incorporated into building materials show that the latent heat storage capacity of the material allows better temperature regulation of a room and lowers the energy requirement in maintaining indoor thermal comfort (Diaconu and Cruceru 2010;Sadineni et al. 2011;Hembade et al. 2012). Studies have reported the influence of type, chemistry, dosage and method of incorporation of PCMs on the cement hydration and the resulting material properties (Khudhair and Farid 2004;Bentz and Turpin 2007;Manari and Neithalath 2012). While PCM incorporation in concrete is a potentially beneficial technology (Schossig et al. 2005), placing a large amount of PCM in a concrete wall or roof slab could cost more than the consequent energy savings it would provide. As a result, there must be a balance between how much PCM is added to a concrete wall or slab (either as an integral part of the material, or as separate strata1) when considering the lifetime cost of the wall that includes both the initial material cost and the energy cost for the analysis period. If larger amounts of PCM are required in a structural member, it will decrease the overall structural capacity of the member, which also should be factored in to any structural and/or economic analysis. The need to find a compromise point between adding PCM into a concrete wall, the energy savings and the structural capacity that comes with it calls for the use of optimization techniques. This article illustrates the use of an optimization framework coupled with a finite element (FE) analysis scheme for heat transfer to find this optimal point between material costs and energy costs to create the most cost-effective wall design for a specific environment. The objective of this study is to minimize the overall lifetime cost of a wall by understanding the implications of PCM layer thickness, material prop-erties and position in the wall on the overall energy consumption under different thermal loading conditions.
2. Model development
The overall study looks at the development of a wall model that contains both concrete and PCM layers that can be optimized to create the most efficient and cost-effective model. The details of the model are discussed in this section.
2.1. Temperature conditions
This study was performed for the weather conditions of Phoenix, Arizona, USA, which has a subtropical desert climate. The average outdoor temperature profile of Phoenix consists of three
different temperature conditions over a typical year: summer temperature days, winter temperature days and spring/fall (autumn) temperature days. Data from 14 June 2011 are taken as a typical summer day with a temperature range of 37− 51◦C, typical winter day data are taken from 1 January 2011 with a range of 3− 14◦C and the spring/fall day data are from 4th March 2011 with a temperature range of 16− 34◦C. It should be noted that the record low temperature for Phoenix is−9◦C (7 January 1913) and the record high temperature is 50◦C (26 June 1990). Instead of applying solar radiation as a flux on the outside face of the wall, an equivalent temperature (Teq) is calculated. The radiation effect during sunshine hours is calculated as (Kuznik, Virgone, and Noel 2008)
Teq= Te+ αS
he
(1)
where Teis the ambient temperature without the radiation effects (in ◦C), α is the absorption coefficient (unitless), S is the solar insolation (defined as rate of delivery of solar radiation per unit area with units of kWh/m2per day), taken as 309.2 Ws/m2(Khudhair and Farid 2004;Lee
et al. 2009), heis the convective heat transfer coefficient, assumed to be 20 W/m2◦C, and α is the solar absorption coefficient, taken as 0.65. The effective ambient temperature profiles that include the equivalent radiation effects are shown in Figure1. It is assumed that the indoor air temperature is controlled by an HVAC system. In the model, the indoor air temperature is referred to as inside face air temperature (IFAT). The IFAT values are taken to reflect perceived human comfort conditions for different times of the year and different times of the day, i.e. summer and spring/fall days: 20◦C during the day and 25◦C during the night; winter days: 20◦C during the day and 16◦C during the night. These values are selected in consultation with the energy audit personnel working for the local utility company and are based on the facts that Phoenix has a drier climate (lower humidity) than most places, permitting a higher indoor target temperature with the same comfort level; and that during warm and hot days, evenings are hot and the night-time cooling takes place gradually.
2.2. Material properties
Two categories of materials are used in a typical design: conventional Portland cement concrete made using normal weight aggregates, and PCM. The relevant thermal properties of the materials considered in this study are listed in Table1.
Two different types of PCM are investigated: those with a phase-change temperature range that would work on hot days and those for cold days ,in order to handle the range of temperatures in a climate like that in Phoenix. All materials can store thermal energy as sensible energy, but PCMs can also store latent energy. The amount of latent energy that can be stored in a PCM is much larger than its sensible energy storage capacity, as seen in Table2. There is very minimal volume change during this phase transition, and hence their performance is not significantly influenced in either the bulk or encapsulated forms.
The amount of energy stored is calculated for each material, both when the material temperature is in its phase-change range (latent energy) and when it is not (sensible energy). Using a layer thickness of 0.005 m with an area of 1 m2 and with 1◦C of temperature change, the material energy storage capacities are computed and listed in Table2 for the materials considered in this study.
Five hot-climate and two cold-climate PCMs are used as candidate materials. While there are tens of commercially available materials, only those that had material properties as well as cost figures were selected.
(a) (b)
(c)
Figure 1. Ambient air temperature with radiation and target inside temperature (Phoenix, AZ, USA): (a) on 14 June 2011; (b) on 1 January 2011; and (c) on 4 March 2012. Note that the temperature axis scales are not the same in the three graphs.
Table 1. Material properties.
Density Conductivity Specific heat Latent heat Solidus temp. Liquidus temp.
Name (kg/m3) (W/m◦C) (J/kg◦C) (J/kg) (◦C) (◦C) Normal concrete 2400 1.45 750 − − − PCMA 800 0.20 2,400 169,000 27 31 PCMB 860 0.22 2,100 185,000 23 27 PCMC 850 0.22 1,830 189,000 27 31 PCMD 860 0.22 2,550 200,000 27 31 PCME 300 0.25 2,500 110,000 22 25 PCMF 860 0.22 2,410 185,000 10 14 PCMG 860 0.22 2,000 180,000 6 10
Table 2. Material energy storage capacities (for specified dimensions and conditions).
Solidus temp. Liquidus temp. Latent energy capacity Sensible energy capacity
Material (◦C) (◦C) (J/◦Cm2) (J/◦Cm2) Concrete − − − 9,000 PCMA 27 31 169,000 9,600 PCMB 23 27 198,875 9,030 PCMC 27 31 200,813 7,778 PCMD 27 31 215,000 10,965 PCME 22 25 55,000 3,750 PCMF 10 14 198,875 10,363 PCMG 6 10 193,500 8,600
2.3. Wall geometry and layout
Two wall models are considered. The first model is a three-layer wall (3LW) model where the inside and the outside layers are normal concrete (NC) and the middle layer is composed of PCM, as shown in Figure2(a). The second model is a five-layer wall (5LW) model, as shown in Figure2(b). For both models, the overall wall thickness is taken as 0.20 m (8 in.), which corresponds to typical precast concrete wall thickness for industrial and high-rise buildings.
3. Finite element modelling
The wall is modelled for multi-physics analysis using the FE method. Both the thermal per-formance and structural perper-formance are evaluated with each wall configuration. An in-house developed FE program (WallDesign) is used for thermal analysis. The commercially available program ABAQUS version 6.10 is used for stress analysis. Methods for examining the spatial and temporal convergence of computational fluid dynamics simulations are presented byRoache (1998), and the convergence analysis technique is employed here for studying the convergence behaviour of all the FE models.
3.1. Finite element model for thermal analysis
A one-dimensional heat flow through the wall is assumed. However, a two-dimensional FE model is used as shown in Figure2(c,d) so that the same model potentially can be used in later studies to include flow through non-uniform walls such as those containing openings. It should be noted that the presence of a nonlinear material (PCM) in the model necessitates a nonlinear, transient analysis. The wall height is taken as 1 m. Mixed boundary conditions are imposed on the outside and the inside faces. The ambient temperatures used as inputs to the model are obtained from Figure1. The exterior convective heat transfer coefficient, he, is taken as 20 W/m2◦C and the interior convective heat transfer coefficient, hint, is taken as 5 W/m2◦C (Khudhair and Farid
2004;Lee et al. 2009). Details of the analysis assumptions, FE model, convergence analysis to obtain the most computationally and efficient mesh and time steps are discussed in an earlier publication (Hembade, Neithalath, and Rajan 2012).
To study the thermal efficiency of a wall design, the following metrics were studied.
(1) Energy flow through the inside face (EFTIF): This energy flow can take place from the outside of the wall to the inside or from the inside to the outside. The total amount of energy flow is summed over the second 24 hour period and represents the comparative amount of energy that an HVAC system would be using in a day to keep the interior at the ambient indoor
concrete
PCM Outside face Inside face
20 cm
HVAC-controlled
enclosure
concrete
PCM
Outside face Inside face
20 cm HVAC-controlled enclosure (b) (c) (a) (d)
Figure 2. (a) Three-layer wall (3LW); (b) five-layer wall (5LW); (c) 3LW finite element (FE); and (d) 5LW FE models. PCM= phase-change material; HVAC = heating, ventilation and air-conditioning.
temperature. The more efficient the wall system, the smaller the EFTIF will be and the less energy an HVAC system will use. EFTIF is calculated by using the heat flux values, τx(rate of heat energy transfer through a unit area), from the FE model to compute the energy flow through all the elements on the inside face as
EFTIF= tf ti 1 0 τxdydt (2)
(2) Phase-change material efficiency (PCME): The energy stored in or released from the PCM is due to both the sensible and latent heat storage capacities of the PCM and they are computed as
Qs=
Tf
Ti
QL= m HPCM (4) where Qsis the sensible heat storage capacity, QLis the latent heat storage capacity, m is the mass of the PCM or concrete, Cpis the specific heat capacity, and HPCMis the latent heat capacity of the PCM.
These expressions are evaluated for each time step (60 minutes) and their absolute values are summed over the time duration to compute the total energy value. The PCME value is calculated based on the energy stored in the PCM at any given time as
PCME= Energy stored in PCM
Energy storage capacity of PCM× 100 (5)
Since the cost of the PCM is a function of the amount of PCM used in the wall (thickness of the PCM layer), PCM characteristics should be chosen that result in the maximum possible efficiency.
3.2. Finite element model for structural performance
To ensure that placing one or more PCM layers within the wall does not degrade the structural performance, an FE analysis is carried out (Frankl 2008;Hassan and Rizkalla 2010). It is assumed that the wall is not a load-bearing wall and is only subjected to wind loads calculated for Phoenix. The wind speed is taken as 115 mph (using the ASCE 7-2010 Design Manual, which can be used as per City of Tempe design codes to create a load of 0.942 Pa acting on the outside face of the wall (Rajan 2001). Thermal stress analysis was conducted and showed that the wind-induced stresses were much higher than thermal stresses. Hence, only wind-induced stress analysis was carried out during the design optimization studies. The concrete material is assumed to have a compressive strength of 28 MPa with a Poisson’s ratio of 0.15. The overall dimensions of the model (flat panel) used in the FE analysis are taken as 3 m× 3 m × 0.20 m. First order, four-node tetrahedral elements are used in carrying out stress analysis.
Assuming that the PCM has no structural strength, the layers that are PCM are modelled as void space. However, on the four edges of a typical panel, the inside and outside concrete layers are assumed to be connected to each other over a distance of 0.05 m, much like a picture frame. The wind load is applied as a normal pressure to the outside face of the wall. Three different boundary conditions were studied: pin supports at the four corners, two opposite edges fixed and all four edges fixed.A mesh convergence study was carried out to find the optimal mesh configuration using both computational effort and accuracy (predicting principal stresses and maximum displacement) as metrics. The element sizes varied from 0.1 m to 0.0125 m using tetrahedral elements. Based on the results of the convergence study, a typical element size of 0.0125 m was used. For the three-layer wall, the number of FEs is 91,586 and the number of nodes is 22,825. For the five-three-layer wall, the number of FEs is 132,276 and the number of nodes is 33,097.
4. Design optimization
The main goal of the optimization process was to create the most cost-effective wall by using a combination of PCM and concrete, (1) to minimize the total cost over a 10-year period—the one-time, initial material cost and the annual energy cost, and (2) to meet structural performance and constructability requirements. Cost calculations are based on a hypothetical room with dimensions
l× w × h (l = w = h = 3 m) with heat exchange taking place from five sides that contain the
materials describing a typical wall configuration. No openings are assumed in any of the walls. It is assumed that concrete and PCM thermal performance do not degrade over time and that
they require little or no maintenance. It has been shown that PCMs are generally capable of undergoing a large number of thermal cycles without appreciable performance degradation (PCM
Products 2013). However, more studies are warranted in this respect. Therefore, the lifetime cost is calculated as the energy cost over the 10-year period plus the initial material costs only (BASF 2013). Different annual cost escalations are considered for the energy component of the total cost based on different inflation rates (1% and 5%) over the 10-year period.
4.1. Design problem formulation
The cost values are based on the following information.
(1) The cost of normal weight concrete (Reed Construction Data 2009) is $113.85/m3.
(2) The cost of the PCM varies based on the way it is manufactured (Roth et al. 2002)(whether it is available in bulk form, or is encapsulated2) and the publicly available cost values are shown in Table3(a). It is clear that the (initial) cost of PCM is extremely high compared to the cost of concrete.
(3) The cost of energy was found from the Residential Pricing Chart of Arizona Public Service (APS) and is shown in Table3(b) (APS 2012). There is a 20% increase in the summer energy cost and a 10% increase in the spring/fall energy cost compared to the lowest cost that is available during the winter season.
The overall optimization problem can be stated as follows (units are kg, m, s, W and $).
Find x= {b1, . . . , bn, m1, . . . , mn} (6) to minimize ¯C = (2lh + 2wh + lw) ⎛ ⎝ ⎡ ⎣cc c j=1 bj+ cpcm c+p j=c+1 bj ⎤ ⎦ + t ce 3 l=1(EFTIF)l 3.6× 106 ⎞ ⎠ (7)
Table 3. (a) Material cost.
Material Estimated cost ($/m3) Normalized cost ($/m3)
Concrete 113.85 1.0 PCMA 5463.66 47.99 PCMB 3792.34 33.31 PCMC 3747.94 32.92 PCMD 3792.34 33.31 PCME 2645.87 23.24 PCMF 3792.34 33.31 PCMG 3792.34 33.31
(b) Energy costs in Phoenix, Arizona.
Time of year Energy cost, year 1 (2012) ($/kWh) Number of days/year
Summer 0.112 120
Winter 0.0939 90
Spring/fall 0.1033 155
Note: The phase-change material (PCM) costs shown here are based on information provided by the manufacturers. In the long run it is expected that the cost reduction will take place when these PCMs are manufactured in bulk (as will be the case when large-scale use is possible), or with the development of cheaper PCMs with comparable properties, when the market demand rises to warrant such R&D efforts.
subject to 0.20≤ c j=1 bj+ c+p j=c+1 bj≤ 0.21 (8) 0.02≤ bj≤ 0.10, j = 1, . . . , c (9) 0.005≤ bj≤ 0.10, j = c + 1, . . . , c + p (10) mj⊂ [m p 1, m p 2, . . . , m p 8], j = 1, . . . , c + p (11)
σmaxt ≤ 1.7 MPa, σmaxc ≤ 27.6 MPa (12)
where ¯C is material plus energy cost over a 10-year period; bjis the thickness of the jth layer of the wall (concrete or PCM); c and p are the number of concrete and PCM layers, respectively;
cc, cpcm and ceare the unit costs for concrete, PCM and energy, respectively; mjis material for the jth layer of the wall; n is the number of layers used in the wall; and t is a time multiplication factor.
Equation (6) shows the potential design variables, which are the thickness of each layer and the material used in each layer. However, as shown later, the material selection is restricted to certain layers only. The objective function (Equation7) is computed as the sum of material cost and the 10-year energy cost. Equation (8) restricts the overall thickness of the wall to be between 0.20 m and 0.21 m. Equations (9) and (10) show the range of permissible thicknesses for concrete and PCM layers, respectively, in the wall. Equation (11) shows that the material in each layer must be one of the eight materials listed in Table3(a). Finally, Equation (12) restricts the maximum principal tensile stress and compressive stress to the specified values. As stated earlier, the FE analysis for each wall was performed for a total of 48 hours and the results of the energy flow for only the second 24 hours were considered in the objective function.
4.2. Design optimization computational framework
Population-based design optimization techniques are used since the design problem formulation involves the simultaneous use of discrete and continuous design variables. Genetic algorithm (GA) (Chen and Rajan 1998;Rajan 2001),and differential evolution (DE) (Argod et al. 2008;
Price and Storn 2013) methods were used as the optimizers. It should be noted that the flow during design optimization for DE is very similar to GA. In DE, a new population is created by combining randomly selected individuals from the current population using weighted functions. Superior individuals are retained and form members of the new population. Through a few trial runs, it was determined that each design optimization model required 20 iterations (generations) and a population size of 30 (for a total of 600 function evaluations involving one FE analysis per function evaluation) to yield acceptable results.
The custom software development was done using C++ and the entire design optimization process took place with no user intervention once the program was launched.
5. Numerical results
Both the 3LW and 5LW designs were optimized to determine the optimal wall configurations for each model based on the problem formulation discussed earlier. A two-stage optimization is carried out to better understand the use of different PCMs and the results of changing the layer thickness.
5.1. Stage 1 optimization
The primary goal was to select the appropriate material for the PCM layer. All seven PCM materials were considered as candidate materials for layer 3 in the 3LW model, and layers 2 and 4 in the 5LW model. The results from this stage of the optimization are shown in Table4, where the material-optimized models are compared against the concrete-only design (NC wall model). Two cost models are considered for computing the energy cost: a 1% annual cost escalation (labelled energy cost 1%) and a 5% annual cost escalation (labelled energy cost 5%). Arizona’s annual residential electricity price over the past two decades shows an initial peak of about $0.097/kWh (1992–1993), decreasing to about $0.084/kWh (2002) and thereafter, showing a rapid annual increase to a price of about $0.107/kWh (2009) (Evans and James 2011). The concrete and PCM thickness were chosen based on previous studies, where it was determined that the PCM is most energy efficient when placed as thicker layers (Hembade, Neithalath, and Rajan 2012).
The results show that (1) a hot day PCM (PCMD) is the best PCM choice in the 3LW model, and (2) placing the cold day PCM (PCMF) closer to the exterior face of the wall and the hot day PCM (PCMD) closer to the interior face of the wall was the most efficient design for the 5LW model. The figures in parentheses in the last two columns represent the cost increase (+) or cost decrease (−) with respect to the NC wall model. With these models, the NC wall model is the most cost-efficient model when 1% annual cost escalation is considered, and the 3LW model is the most cost-efficient model when 5% annual cost escalation is considered. The initial PCM material cost is a huge component of the entire 10-year cost and an optimized design could result from a lower use of PCM material. This scenario could be changed if the use of PCM becomes more accepted and manufacturers devise materials and methods to drive down the material cost. The framework developed and presented here could easily incorporate such changes and provide the optimized design for the end user.
5.2. Stage 2 optimization
With the knowledge gained from Stage 1 optimization, a second stage optimization was carried out using only the concrete and PCM layer thicknesses as the design variables. As found from Stage 1 optimization, the material selection for this stage was PCMD as the PCM in the 3LW model and a combination of PCMF and PCMD in the 5LW model.
Table 4. Baseline design comparison.
NC wall Material-optimized Material-optimized
model 3LW model 5LW model
Layer 1 Material Concrete Concrete Concrete
Thickness (m) 0.04 0.075 0.05
Layer 2 Material Concrete PCMF
Thickness (m) 0.04 0.025
Layer 3 Material Concrete PCMD Concrete
Thickness (m) 0.04 0.05 0.05
Layer 4 Material Concrete PCMD
Thickness (m) 0.04 0.025
Layer 5 Material Concrete Concrete Concrete
Thickness (m) 0.04 0.075 0.05
Total wall thickness (m) 0.20 0.20 0.20
Material cost ($) $1,024.65 $9,352.77 (+813%) $9,300.38 (+808%)
Energy cost 1% cost escalation ($) $13,966.21 $6,792.35 (−52%) $7,165.07 (−49%) Energy cost 5% cost escalation ($) $16,790.48 $8,165.91 (−52%) $8,613.99 (−49%) Total cost 1% cost escalation ($) $14,990.86 $16,145.12 (+7.7%) $16,465.45 (+10%) Total cost 5% cost escalation ($) $17,815.13 $17,518.68 (−1.6%) $17,914.37 (+0.5%)
5.2.1. Results for the three-layer and five-layer models
The results from this optimization problem are summarized in Table5. The stress plots are shown in Figure3. Stress concentration can be seen at the corners where the wall is supported. However, the stress values reported in Table5are at locations slightly away from the corners.
In the 3LW model, the optimization process increased the concrete content in the wall (from 0.15 m to 0.198 m) and decreased the PCM content (from 0.05 m to 0.008 m). The total cost decreased nominally from $16,145.12 to $15,036.67 (1% cost escalation) and from $17,815.13 to $17,594.61 (5% cost escalation).
In the 5LW model, the optimization process increased the concrete content in the wall (from 0.15 m to 0.171 m) and decreased the PCM content (from 0.05 m to 0.035 m). The total cost decreased noticeably from $16,465.45 to $15,203.37 (1% energy cost escalation) and from $17,914.37 to $16,892.92 (5% energy cost escalation).
With these models, the NC wall model is the most cost-efficient model when 1% annual cost escalation is considered, and the 5LW model is the most cost-efficient model when 5% annual cost escalation is considered.
Figure3shows the change in temperature on the inside face of the wall for the different wall configurations, along with the ambient temperature conditions for the three different temperature cycles. The wall with no PCM has an inside wall temperature very closely correlated to the outside ambient temperature, but the material-optimized and the thickness-optimized wall designs result in inside wall temperatures closer to the indoor ambient temperature. It appears that the material-optimized wall design regulates the inside wall temperature better owing to the much larger amount of PCM used, almost 80% more than in the thickness-optimized design. However, use of a smaller amount of PCM still regulates the inside wall temperature better than not using any PCM, but at a much lower material cost. As a result of better temperature regulation on the inside face of the wall, the indoor ambient temperature will stay much closer to the comfortable range with much less work needed from the HVAC system. The results from the Stage 1 optimization are ideal for this temperature regulation because of the thicker layer of PCM.
Table 5. Three-layer wall (3LW) and five-layer wall (5LW) optimized designs.
NC wall model Thickness-optimized 3LW Thickness-optimized 5LW
Layer 1 Material Concrete Concrete Concrete
Thickness (m) 0.04 0.099 0.085
Layer 2 Material Concrete PCMF
Thickness (m) 0.04 0.01
Layer 3 Material Concrete PCMD Concrete
Thickness (m) 0.04 0.008 0.045
Layer 4 Material Concrete PCMD
Thickness (m) 0.04 0.025
Layer 5 Material Concrete Concrete Concrete
Thickness (m) 0.04 0.099 0.041
Total wall thickness (m) 0.20 0.206 0.206
Max. tensile stress (kPa) 120 216
Max. compressive stress (kPa) 406 524
Material cost ($) $1,024.65 $2,387.43 (+133%) $6,848.39 (+568%)
Energy cost 1% cost escalation ($)
$13,966.21 $12,649.24 (−9.4%) $8,354.98 (−40.5%) Energy cost 5% cost
escalation ($)
$16,790.48 $15,207.18 (−9.4%) $10,044.53 (−40.5%) Total cost 1% cost escalation
($)
$14,990.86 $15,036.67 (+0.31%) $15,203.37 (+1.4%) Total cost 5% cost escalation
($)
(a) (b)
(c)
Figure 3. Three-layer wall (3LW) model: temperature variation as a function of time on the inside face of the wall: (a) summer day; (b) winter day; (c) spring/fall day. NC= normal concrete.
Figure4shows the energy flow through the inner face of the wall. These energy flow graphs show the same trend as seen in the temperature profiles. A wall with no PCM is much less energy efficient than a wall with PCM for all the temperature conditions. The results for the summer temperature show the largest difference in energy flow between the material-optimized and thickness-optimized designs, but this is again due to the 84% reduction in PCM thickness. Since the PCM selected for the 3LW was PCMD, a hot day PCM, it is obvious that the thick-ness of this PCM layer will affect the wall temperature performance during the summer day the most.
In Figure5, the temperature on the inside face of the 5LW model is displayed for the three temperature profiles. The results show that the thickness-optimized wall design and material-optimized wall design behave similarly in regulating the temperature. The winter day has the
(a) (b)
(c)
Figure 4. Three-layer wall (3LW) model: energy flow through inner face with respect to time: (a) summer day; (b) winter day; (c) spring/fall day. NC= normal concrete.
largest difference between the two walls with PCM and this is a result of the 40% decrease in the thickness of layer 2, which is PCMF, the cold day PCM. With the decrease in the thickness of this layer, the wall does not have as large a latent heat storage capacity during the winter day, so the energy regulation is minimal.
The energy flow through the inner face of the five layer model is shown in Figure6. The same type of correlation is seen in these graphs. The thickness-optimized design appears to have higher energy flow than the material-optimized design, as seen in the 3LW as well. This is also seen in Table5, as the cost of energy of the thickness-optimized design is greater than the cost of energy for the material-optimized design of the 5LW, but it is again the difference in the material costs of the thickness-optimized designs that lower the overall lifetime cost significantly when compared to just the material-optimized design.
Figure7(a) shows the temperature profile across the wall for the summer day only. Figure7(b) shows the temperature for the material-optimized wall design for the 3LW model. Figure7(c)
(a)60 50 40 30 30 36 32 28 24 20 16 20 10 0 20 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 (b) (c)
Figure 5. Five-layer wall (5LW) model: temperature variation as a function of time on the inside face of the wall: (a) summer day; (b) winter day; (c) spring/fall day. NC= normal concrete.
represents the temperature profile in the final, thickness-optimized design for the 3LW model. The temperature profiles for the material-optimized design of the 5LW model are shown in Figure7(d), and Figure7(e) shows the temperature profiles for the final, thickness-optimized design for the 5LW model.
The results of the 5LW model showed a clear benefit for use over the 3LW model, and the efficiency of the PCM layers in each model shows these benefits. Figure 8 shows the PCM efficiency of all the models for the summer day, winter day and spring day. The graphs show that the 5LW model is using both layers of PCM much more effectively throughout the year, and thus adds to the overall cost reduction during the entire year and not just for one season. In vastly varying climatic conditions seen through a typical year, it is difficult to achieve 100% PCM efficiency on all three typical types of day evaluated in this study. However, the optimizer is able to find a compromise solution that has the minimum total cost.
(a) (b)
(c)
Figure 6. Five-layer wall (5LW) model: energy flow through inner face with respect to radiation: (a) summer day; (b) winter day; (c) spring/fall day. NC= normal concrete.
The major findings are summarized below. Summer day:
• The PCM layer in the thickness-optimized 3LW (layer 3) has the highest efficiency owing to the small volume of PCM in this layer that is saturated during the entire day.
• Layer 4 in the thickness-optimized 5LW, which is the hot day PCM, has the second highest efficiency. Its volume is slightly less than that of the material-optimized 3LW and 5LW, and hence is used more effectively.
• No latent energy is stored in or released from layer 2 in the 5LW models. Winter day:
• While not at 100% efficiency, only layer 2 in both the 5LW models is utilized. The cold day PCM in the material-optimized 5LW (layer 2) has a higher efficiency than the thickness-optimized
(a) (b)
(d) (c)
(e)
Figure 7. Temperature distribution across the wall for the non-optimized, and material- and thickness-optimized designs for a summer day. NC= normal concrete.
100 80 60 40 20 0 100 80 60 40 20 0 0 5 10 15 20 25 100 80 60 40 20 0 0 5 10 15 20 25 (a) (b) (c)
Figure 8. Phase-change material (PCM) efficiency: (a) summer day; (b) spring/fall day; (c) winter day.
5LW owing to its location. In the thickness-optimized 5LW, layer 2 is closer to the inside wall than in the material-optimized 5LW.
• No latent energy is stored in or released from layer 2 in the 3LW models. Spring day:
• There is hardly any PCM used for its latent energy capacity because the temperatures never reach the phase-change range of either PCMD or PCMF.
• EFTIF is still less for the walls containing PCM and that is a result of the PCM providing a better thermal mass layer than the concrete alone.
5.3. Structural analysis results
The maximum tensile and compressive stresses on both the 3LW and 5LW are much lower than the allowable values. The maximum stresses are at the supports (see Table5). The 5LW model has a higher tensile stress than the 3LW model because a larger amount of the wall contains PCM: 17% of the 5LW is PCM, whereas only 4% of the 3LW is PCM. However, even with this increase in the PCM in the model, the stresses are still very small.
6. Concluding remarks
An optimal design methodology is developed for optimizing a concrete wall containing PCMs in different layers. The design goal is the minimization of material and energy cost for a specified lifespan (10 years) using specified annual energy cost escalation figures (1% and 5%) while preserving the structural performance. Different climatic conditions (spring/fall, summer and winter days) corresponding to Phoenix, Arizona, are considered in computing the energy cost. While it is difficult to manually configure a typical wall for the lowest total cost, the computational framework provides an automated tool to search for the best design that optimizes material and energy costs. The optimization process is carried out with realistic, publicly available cost figures. It should be noted that the focus of this research work is to develop and implement a general framework under which the wall optimization can be carried out with different input parameter values, i.e. cost figures, available material and local climatic conditions.
The major findings in this study are summarized below.
(1) The design optimization framework helps to determine the thickness and location of PCM and concrete in a wall for a given temperature profile. The use of PCM as a thermal layer in a wall is beneficial to regulate energy flow and energy costs in a building, but by finding the optimum material, location and thickness values, the most effective system to reduce the overall cost can be created.
(2) Current cost figures show that PCM costs 20 and 50 times as much as normal concrete. Even with this enormous cost difference, it is possible to reduce the overall cost by a judicious mix and placement of concrete and PCM layers.
(3) A five-layer wall model is more efficient than a three-layer wall. This is due to the ability to use two different PCMs for different temperature conditions experienced in a place such as Phoenix. The effects of ease (or lack thereof) of wall construction with multiple layers are not considered in the optimization scheme.
(4) In Phoenix, the proportion of the annual energy cost is the highest during the summer days. Using the 5% cost escalation for the NC model, 64%, 18% and 18% of the total energy costs are during the summer, spring/fall and winter days, respectively. Similarly, the corresponding figures for the 3LW optimized model are 64%, 18% and 18%, and for the 5LW optimized model are 58%, 21% and 21%.
(5) It is expected that an increase in demand for more energy-efficient buildings will lead to an increase in demand for economical PCM. Hence, it is expected that the development of high-efficiency, low-cost, sustainable PCM will take place with increased vigour (Kosny, Shukla, and Fallahi 2013).
Acknowledgements
The contents of this article reflect the views of the authors who are responsible for the facts and accuracy of the data presented herein, and do not necessarily reflect the views and policies of the funding agency, nor do the contents constitute a standard, specification or regulation.
Funding
The authors gratefully acknowledge the support from National Science Foundation [grant number CMMI 1130028] towards the conduct of this study.
Notes
1. This study considers the effects, in terms of both energy use and cost, of PCMs being added as separate strata (layers) in concrete. This is because more needs to be understood about the implications of direct addition of either bulk or microencapsulated PCMs in cementitious systems with respect to the development of concrete properties and the longevity of PCMs in such environments.
2. Microencapsulated PCMs are easy to incorporate in concrete elements even in situ, whereas bulk PCMs can be effectively introduced into the void space between the concrete layers only when they are in their liquid state, thereby requiring the local environment to be warmer than their phase-change temperature. While this could be easily accomplished in a precast concrete manufacturing facility, it poses some challenges in in situ construction.
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