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Optimising PCM thermal storage systems for maximum energy storage effectiveness
Available online at www.sciencedirect.com
Solar Energy 86 (2012) 2263–2272 www.elsevier.com/locate/solener
Optimising PCM thermal storage systems for maximum energy storage effectiveness N.A.M. Amin a,b,⇑, M. Belusko a, F. Bruno a, M. Liu a a
Barbara Hardy Institute, School of Advanced Manufacturing and Mechanical Engineering, University of South Australia, Mawson Lakes, South Australia 5095, Australia b School of Mechatronic Engineering, Universiti Malaysia Perlis, Main Campus Ulu Pauh, 02600 Arau, Perlis, Malaysia Received 30 December 2011; received in revised form 20 March 2012; accepted 24 April 2012 Available online 19 May 2012 Communicated by: Associate Editor Halime Paksoy
Abstract A new performance parameter for PCM thermal storage systems, the energy storage effectiveness, is defined. This parameter can be used to optimise the design of any PCM thermal storage system to maximise the use of the thermal storage media. The paper presents results of a parametric study using an experimentally validated numerical model for PCM encapsulated in plates. The results are used to calculate the energy storage effectiveness which is ultimately used to optimise the useful energy that can be stored in the PCM thermal storage system. The energy storage effectiveness is also used to compare the useable storage capacity of the PCM relative to a sensible energy storage system. Ó 2012 Elsevier Ltd. All rights reserved. Keywords: Phase change material; Energy storage effectiveness; Thermal energy storage
1. Introduction Phase change materials (PCMs), with high latent heat of transition, are potentially effective thermal energy storage materials suitable for use in heating and cooling applications (Guobing et al., 2011; Kousksou et al., 2011; Zalewski et al., 2011). The use of PCMs represents a particular effective solution for off peak thermal storage for refrigeration applications (Wang et al., 2002; Liu et al., 2012; Amin et al., 2009a, 2012a). Considerable research has been conducted on applying PCMs to thermal energy storage on the basis of the potential to significantly increase the volumetric thermal energy storage density (Mehling and ⇑ Corresponding author at: School of Mechatronic Engineering, Universiti Malaysia Perlis, Main Campus Ulu Pauh, 02600 Arau, Perlis, Malaysia. Tel.: +61 8 8302 3230; fax: +61 8 8302 3380. E-mail address: [email protected] (N.A.M. Amin).
0038-092X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2012.04.020
Cabeza, 2008). A critical requirement of enhancing the energy reductions within low energy solar heating or cooling systems is to maximise the level of thermal storage for a given volume, which is the prime objective of a current IEA Task under the Solar Heating and Cooling Program, Task 4224; Compact thermal energy storage: Material development and system integration (http://www.ieashc.org, 2009). Thermal storage is defined by a charging and discharging process in any thermal system. The application of thermal energy storage results in an exergy loss due to the additional process of discharging (Bejan, 2006). Limited research has been presented determining the usefulness of a PCM system and no generic method exists for comparing one storage system against another. This paper presents a new parameter, the energy storage effectiveness, capable of determining the useful volumetric energy density of PCM thermal storage based on minimising the exergy losses in the thermal store. This parameter can be used to
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Nomenclature a a Cp Dh Er et ed ec e ed ec HL f l m_ gp gps PL DP
energy storage density coefficient (–) modified energy storage density coefficient (–) specific heat (J/kg K) hydraulic diameter (m) comparative energy storage ration (–) local heat exchange effectiveness (–) melting or discharging effectiveness (–) freezing or charging effectiveness (–) modified phase change effectiveness (–) modified melting or discharging effectiveness (–) modified freezing or charging effectiveness (–) latent heat of fusion (J/kg) friction factor (–) length of gap or PCM slab (m) mass flow rate of HTF between slabs (kg/h) pumping efficiency (–) power station efficiency (–) primary energy of the pumping losses (J) pressure drop (kg/m2)
optimise a PCM store for any thermal system and enable a direct comparison with sensible energy storage. Referring to the thermal energy storage model by Cabeza et al. (2006), the work completed within the International Energy Agency Solar Heating and Cooling Program (Schultz et al., 2007), it was concluded that the energy savings relative to the sensible energy storage capacity of water, for domestic hot water storage, for the same volume was negligible. The use of the PCM, sodium acetate trihydrate, could only achieve a reduction in storage volume for a temperature lift of 20 °C. No benefit was identified for temperature lifts of 50 °C, typical in a hot water system. Therefore, in this case, sensible energy storage proved more energy dense than the PCM option. In other research, Helm et al. (2009) investigated the use of a PCMin-tank system as a heat rejection system in an absorption chiller, again based on a low temperature range. The study clearly demonstrated that the useable energy storage density was significantly higher than a sensible energy storage system. This highlights that PCMs are more effective in systems with a relatively low temperature difference between the heat source and sink. A major factor which affects the volumetric energy storage density of PCM systems is the amount of volume occupied by the PCM within the thermal storage system. Be´de´carrats et al. (1996) indicate that the PCM occupies 50% of the volume of the tank for sphere type PCM storage system whereas for the plate type the value can achieve 95% (Mehling and Cabeza, 2008). For PCM in plates, the potential for a high proportion of PCM to total storage
density of the HTF (kg/m3) qhtf qpcm density of the PCM (kg/m3) Qact actual stored energy (J) Qmax maximum theoretical stored energy (J) Tin inlet temperature (°C) Tout outlet temperature (°C) Tout_model outlet temperature from TRNSYS model (°C) Tout_exp outlet temperature from experiment (°C) Tpcm temperature of PCM (°C) DT temperature different (°C) t time (s) t thickness of PCM slab (m) l dynamic viscosity of the HTF (mPa s) m mean velocity of the HTF (m/s) Vfull volume of the full tank (m3) _V volumetric flow rate (m3/s) w width of gap (m) c compactness factor (–)
volume, or the compactness factor, exists when fluid gaps are small (Belusko and Bruno, 2008; Amin et al., 2009b). Of equal importance which affects the useable energy storage density of a PCM storage system is the effectiveness of the heat transfer which can be exchanged between the heat transfer fluid and the PCM. In most sensible energy stores such as a tank of water, the heat transfer fluid directly stores the thermal energy, therefore exergy losses only occur due to additional pumping and heat losses to the surroundings. In a PCM system the heat that is transferred is a function of the thermal resistance between the heat transfer fluid and PCM at the phase change front (Ismail et al., 1999; Tay et al., 2012a). If the thermal resistance is relatively high, then the heat transfer rate over the time of operation is relatively low, reducing the effective energy that is stored within the PCM. Considerable research has been conducted on minimising the thermal resistance in PCM systems. Cabeza et al. (2002) investigated the use of conductors, which showed a doubling of heat transfer. Five commercial heat exchangers functioning as latent heat thermal energy storage systems were investigated (Medrano et al., 2009). From the experimental work, the design which delivered the highest heat transfer incorporated a double pipe arrangement for the heat transfer fluid embedded in a PCM graphite matrix. The PCM graphite matrix has a very high thermal conductivity relative to conventional PCMs minimising the resistance to heat transfer (Cabeza et al., 2002; Medrano et al., 2009). Metal foams embedded in PCMs have also been investigated and found to increase the overall heat
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transfer rate by 3–10 times (Zhao et al., 2010). These systems involve the PCM being directly contained within the thermal store, as opposed to encapsulated in containers. PCM slurries have similar characteristics of sensible energy stores, with the added advantage of phase change within the microencapsulated PCM. However, being a mixture of PCM/heat transfer fluid the overall energy densities are 27.6% of the original PCMs (Wang et al., 2008). The impact of design parameters of a PCM-in-plate system has been investigated using experimentally validated numerical models (Halawa et al., 2010; Liu et al., 2011a,b). The models are capable of determining the heat transfer between the PCM and heat transfer fluid for any design and inlet conditions. A parametric study of an air based system has investigated the impact on the heat transfer of various design parameters identifying how the heat transfer can be increased (Halawa and Saman, 2011). However, this information does not assist with the design or optimisation of a PCM system based on the usable amount of thermal storage media, as well as enabling a comparison to sensible energy storage systems. In a PCM system any thermal resistance between the heat transfer fluid and the PCM represents an exergy loss. Therefore, reliance on storing in the sensible component of a PCM, reduces the relevance of using the latent component. It can therefore be argued that sensible energy storage in a PCM system should be ignored, relative to a sensible energy store using the heat transfer fluid itself. In contrast, if the PCM system is effective at transferring the latent energy to the heat transfer fluid, it will be effective at transferring any sensibly stored energy. A number of researchers have identified that the heat exchange effectiveness is a useful measure to characterise the heat transfer in a PCM system. Ismail et al. (1999) specify a local effectiveness which varies with time and Belusko and Bruno (2008) define it with respect to the proportion of phase change. Tay and other researchers have experimentally determined the average effectiveness over the phase change process for coil in tank PCM storage systems (Tay et al., 2012a,b,c; Castell et al., 2011). Amin et al.
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(2012b) have experimentally determined the average effectiveness for PCM encapsulated in spheres. Using this average effectiveness concept, this paper combines this factor with the compactness factor, to develop the energy storage effectiveness for a PCM system. This paper reports on a complete parametric and optimisation study conducted on a PCM system encapsulated in plates using a liquid heat transfer fluid. This study aimed to validate the energy storage effectiveness as the defining performance measure of a PCM system, and demonstrate that through optimisation of this parameter, the selected design will achieve the least exergy losses when applied to any thermal system. Furthermore, the study demonstrates how it can be used to determine the amount of PCM required and compare a PCM storage system against a sensible storage system of equivalent volume. The study is conducted in the context of off peak refrigeration storage. 2. Characterisation of PCM system The PCM storage system consists of several flat PCM slabs (Fig. 1). The slabs are arranged in layers with a passage in between for the heat transfer fluid. Heat transfer to the surroundings is ignored. When operating as an off peak storage system, a heat sink is developed in the PCM during the solidification or charging of the PCM and heat is absorbed during melting or discharging process. During the phase change process, heat is exchanged between the heat transfer fluid and the phase change interface within the PCM, at the phase change temperature. This heat transfer is a function of the thermal resistance in the heat transfer fluid and in the PCM proportion which has already changed phase. Therefore the outlet fluid temperature is determined by the thermal resistance in the system and limited by the phase change temperature. Maximum heat transfer is achieved when the outlet temperature is equal to the phase change temperature. In order to achieve energy efficient storage, the inlet temperature of the heat transfer fluid during charging or freezing of the PCM should be as high as possible to maximise
adiabatic wall
l
PCM
tw
y
HTF
wt
x z
Fig. 1. Schematic diagram of the PCM model.
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the coefficient of performance of the refrigeration system. The maximum possible temperature is determined by the required rate of heat removal from the PCM during the charge period, which is determined by the thermal resistance to heat transfer. To maximise the charge fluid temperature, the outlet fluid temperature should be equal to the PCM phase change temperature, while providing adequate heat transfer. The thermal resistance also affects the discharge temperatures which are achieved from a PCM storage system. Discharge temperatures are specified by the cooling requirements of the load. Ideally, the discharge temperature should equal to the phase change temperature of the PCM. However, due to thermal resistance, the discharge temperature will be above this temperature, and therefore a lower temperature PCM is required. As a result, charging this PCM is more energy intensive. Consequently, energy efficient storage is dependent on minimising the thermal resistance to heat transfer in the PCM storage system, effectively minimising the temperature difference between the heat sink and heat source. This approach minimises any sensible storage in the PCM which is defined by the change in temperature of the material, and as a result, sensible energy storage is ignored. The outlet temperature from the PCM system determines the heat transferred between the heat transfer fluid and the PCM and consequently, thermal performance can be expressed in terms of a heat exchange effectiveness. This effectiveness directly relates to the thermal resistance in the PCM storage system as explained by Belusko and Bruno (2008) and Tay et al. (2012b). If the heat transfer rate does not vary with time, the effectiveness of a PCM storage system is defined by ec;d ¼ Qact =Qmax ¼ ðT in T out Þ=ðT in T pcm Þ
ð1Þ
Over the period of phase change, the actual energy stored and released is defined by this effectiveness, which directly affects the useful energy that is stored. Consequently the actual useful energy which is stored is the product of the effectiveness of charging and discharging. The compactness factor for PCM in plates is shown by Eq. (2), and directly affects the volumetric energy density of a storage system. c ¼ t=ðw þ tÞ
ð2Þ
Therefore the expected energy storage density of a PCM storage system can be defined by the energy storage effectiveness, a ¼ ec ed c
To consider pumping losses within the PCM storage system a modified effectiveness value was determined using ec ;d ¼ ec;d ðP L =Qmax Þ Total losses of the system are then calculated using P L ¼ DP V_ =ðgp gps Þ
ð5Þ
Pump efficiency, gp and power station efficiency, gp.s were fixed at 50% and 35%, respectively. As the heat transfer fluid moves between the parallel plates of the PCM store, the pressure drop can be evaluated DP ¼ f l q v2 =ð2 Dh Þ
ð6Þ
The entrance and exit losses are ignored as these exist in any sensible storage system. Therefore, the modified energy storage effectiveness of the system, a can be written as: a ¼ ec ed c
ð7Þ
The energy storage effectiveness can be used to directly determine the amount of PCM needed in a PCM storage system as well as compare to the volumetric energy storage density of sensible storage systems which store energy directly within the heat transfer fluid. In a refrigeration application, any storage system must be capable of meeting the peak cooling demand over a number of hours. For a given mass flow rate and the required thermal load, the temperature drop of the heat transfer fluid within the thermal store can be determined. This temperature drop determines the stored energy needed in a sensible energy store. The PCM storage system stores latent energy in the PCM as well as a small amount of sensible energy in the heat transfer fluid that remain in the gaps of the PCM system. Therefore in order to determine the amount of PCM needed and compare the system to a sensible energy store, the sensible energy stored in the heat transfer fluid within the PCM storage tank need to be considered. Therefore the useful stored energy within a PCM thermal store can be expressed as: Q ¼ a H L qpcm V full þ qhtf Cp DT ð1 cÞ V full
ð8Þ
For a design period of time the required stored energy can also be expressed as: _ Q ¼ mCp DT t
ð9Þ
Therefore for a given mass flow rate, the PCM tank volume and corresponding volume of PCM can be determined from V pcm ¼
ð3Þ
This effectiveness directly identifies how much of the volume is used to store useful energy. A value of unity indicates that the useful stored energy is defined by the entire volume of the storage facility multiplied by the volumetric energy storage density of the PCM, representing the most ideal PCM storage system.
ð4Þ
c m_ Cp DT t þ qhtf Cp DT ð1 cÞ a H L qpcm
ð10Þ
Based on Eq. (8), the comparative energy storage ratio (Er), which is the ratio of the useful energy stored in a PCM system relative to a sensible energy storage tank filled with the heat transfer fluid, is defined by: Er ¼
a H L qpcm þ ð1 cÞ qhtf Cp DT
ð11Þ
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The comparative energy storage ratio is based on no losses to the surroundings, ignores the pumping losses related to flow through the sensible storage tank and assumes perfect mixing in the sensible energy storage tank. In any PCM thermal storage system, the discharged amount of PCM is restricted by the requirement that heat can only flow from a high temperature to a lower temperature, as defined within the 2nd Law of Thermodynamics. Therefore any given design is only valid if the effectiveness is above a critical value defined by the heat source temperature, in the case of refrigeration. The minimum effectiveness is based on the required temperature difference to achieve the design load for a specific flow rate. Therefore, for a given design the determined discharge effectiveness is required to be greater than this minimum effectiveness (Eq. (12)): emin ¼ DT =ðT source T pcm Þ
ð12Þ
Tsource is the temperature of the heat source. For any design the performance of the thermal storage system for any application can be defined by the energy storage effectiveness. A direct comparison can be made with a sensible storage system using the heat transfer fluid through the comparative energy storage ratio, and the minimum effectiveness ensures that all the available stored energy can be used for the design specifications provided. 3. PCM plate numerical model In this study, to determine the charging and discharging effectiveness, an experimentally validated numerical model of PCM plates (Liu et al., 2011a) has been used. This model uses the finite-difference calculation method. The difficulty of solving the heat transfer problem during the phase change process is due to the nonlinear movement of the solid–liquid interface, namely moving boundary problems or Stefan problem (Lacroix, 2002; Ettouney et al., 2005). Models based on temperature formulations are particularly suitable for solving the phase change problem at a fixed temperature. It has been successfully used to investigate the influence of various parameters (such as Rayleigh, Stefan and Prandtl numbers, and aspect ratios of the containers). The ice bank of parallel plates has been investigated, and a one-dimensional temperature-based model was studied (Ismail et al., 1999). The model applied the finite difference method. The agreement between the predicted results and the experimental results was good. The model used in this study was developed based on temperature formulations. Both solid–liquid and mixed phases are considered. Research for air based systems has shown that the heat transfer is 1-D due to the high length to thickness ratio of the plate (Halawa et al., 2010). This research included an experimental validation of the model. Being 1-D, the model ignores the thermal conductivity of the PCM. The model also ignores any natural convection in the PCM, which has been shown to be small due to the thin slab thicknesses (Halawa and Saman, 2011). This
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factor is particularly irrelevant if the temperature difference between the fluid and the phase change temperature is small. Supercooling is also ignored in the model. The model has been validated against experimental results with plates of a PCM with a freezing point of 27 °C in a liquid based system (Liu et al., 2011a). The experiments involved 19 plates of dimensions 0.26 m long 1.70 m wide 0.025 m thick, separated by a 6 mm gap. Charging was achieved using a refrigeration system to chill the heat transfer fluid. Discharging involved pumping the heat transfer fluid into a cold room through an indoor air/liquid heat exchanger. The heat transfer fluid used was a glycol based liquid, with properties shown in Table 1. Reasonable agreement was achieved between the predicted and experimental results, for discharging, as shown in Fig. 2. Phase change can be observed by the sudden changes in temperature gradient as presented by Mehling and Cabeza (2008) and Tay et al. (2012a). Fig. 3 shows the instantaneous heat exchange effectivenesses from Fig. 2. The results show that the sensible energy stored in the PCM causes the heat exchange effectiveness to be high (and can be above unity) at the beginning of the melting process. The sensible energy stored in the PCM raises the initial temperature above the melting point, resulting in the outlet temperature being above the melting delivering an over unit effectiveness as defined by Eq. (1). The heat exchange effectiveness then gradually reduces over the phase change process. This decrease can be attributed to a gradual increase in the inlet temperature due to the heat load from the cold room being greater than the cooling delivered by the thermal storage system. Therefore, in these experiments, the thermal storage system was under-designed. The average effectiveness over the phase change process is 0.58 at a flow rate of 0.32 l/s and 0.6 at a flow rate of 0.22 l/s. As defined by heat exchanger theory, a reduced mass flow rate results in an increase in the effectiveness. Based on a compactness factor of 0.466, the storage effectivenesses translate to 0.157 and 0.167 respectively when charge and discharge effectivenesses are assumed to be the same and the pressure losses effect is ignored. These values are considerably low and highlight how in all likelihood, this application of this design of the PCM cannot be justified. Using this model it is possible to conduct an extensive parametric study of the storage effectiveness, and determine the optimum design which minimises the exergy losses of any thermal system using PCM. For a given inlet tem-
Table 1 Properties of heat transfer fluid working temperature. Temperature (°C)
Dynamic viscosity (mPa s)
Thermal conductivity (W/m K)
Specific heat (kJ/ kg K)
Density (kg/m3)
30 20 10
9.222 6.495 4.916
0.459 0.469 0.479
2.820 2.843 2.866
1343 1337 1332
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Fig. 2. Mathematical model compared with the experimental test results for (a) 0.32 l/s and (b) 0.22 l/s mass flow rates.
Fig. 3. Effectiveness results from Fig. 2.
perature, mass flow rate and physical dimensions of the PCM system, the outlet temperature can be determined from the model as shown in Fig. 4. The figure shows a constant outlet temperature and this is attributable to having a constant inlet temperature. In all cases studied the outlet temperature was constant. The focus of this study is the effectiveness related to latent energy storage. In order to
Temperature, T ( C)
-25.4 -25.8 T in T out T pcm
-26.2 -26.6 -27.0
0
20
40
60
80
100
Time (s)
Fig. 4. Temperature parameters from the PCM system during discharging.
minimise the sensible component, which is modelled in the numerical model used, the temperature difference between the inlet temperature and the phase change temperature was fixed at 1 °C. The sensible energy was found to be negligible being 2.53% of the latent energy. Heat transfer was assumed to be complete when the temperature change of the heat transfer fluid was less than 0.01 °C. The heat exchange effectiveness of the process was based on the average outlet temperature, and found using Eq. (1). Since thermal conductivity and natural convection are ignored, the thermal resistance in the PCM is the same for both discharging and charging and therefore the thermal resistance in the system is defined by the geometry and the mass flow rate only. Therefore the effectiveness for charging is equal to the effectiveness of discharging, and from this point on will be referred to as the phase change effectiveness. 4. Thermal storage optimisation A parametric study of the energy storage effectiveness was conducted, investigating the impact of the PCM slab thickness, gap width between slabs and the mass flow rate. A PCM with a melting point of 27 °C is used for this analysis because it is suitable for refrigeration applications (Liu et al., 2011a) along with a low temperature heat transfer fluid with properties provided in Table 1. The amount of PCM used in this study is fixed at 1 m3. Therefore, when the slab thickness is varied, the number of slabs is changed so that the total PCM volume is constant. The properties of the PCM and the range of parameters investigated during the simulation are specified in Table 2. The default values for the PCM storage system consist of a 0.01 m gap, a mass flow rate of 100 kg/h and 45 slabs with a thickness of 23 mm. This configuration achieves a
N.A.M. Amin et al. / Solar Energy 86 (2012) 2263–2272 1
Table 2 Preset and changing parameters through simulations. Parameter
Quantity
0.99
Changing parameter No of slabs Thickness of slabs Gap between slabs Mass flow rate
1.42 106 1.11 107 1200 3650 2.2 0.55 1305 1363 26.7 144,000 1 1
m2/s m2/s J/kg K J/kg K W/m K W/m K kg/m3 kg/m3 °C J/kg m m
5–105 Default is 45 0.2–0.01 Default is 0.023 0.005–0.75 Default is 0.01 50–7500 Default is 100
– – m m m m kg/h kg/h
discharging and charging effectiveness of 0.986. The compactness factor is 0.69 and the true energy density equates to 0.675. 4.1. Gap width effects The first simulation investigated the effect of the gap between PCM slabs, on the storage effectiveness (Fig. 5). The gap is increased from 0.005 m to 0.75 m through repeated simulations. The rapid reduction in the energy storage effectiveness was due to the decrease in the compactness ratio which is caused by an increasing gap. Fig. 6 shows the variation in the phase change effectiveness and shows that pumping losses are negligible even though the temperature difference between inlet and outlet is less than 1 °C. Fig. 6 shows that the phase change effectiveness remains relatively constant near unity, which can be explained by 1
0.97
0.05, 0.969
0.96 0.075, 0.951 0.1, 0.945
0.95
0.75, 0.945
0.5, 0.944
0.25, 0.942
0.94 0.93
0
0.2
0.4
0.6
0.8
Fig. 6. Phase change effectiveness, e and modified phase change effectiveness, e for various gap width, w with fixed t at 0.01 m and HTF mass flow rate of 100 kg/h respectively.
the fact that the total heat transfer area remains fixed. The sudden drop and the gradual rise can be explained by changes in the convection heat transfer coefficient due to the change in the hydraulic diameter and the fluid velocity. 4.2. Mass flow rate effects Figs. 7 and 8 show the impact of mass flow rate of the fluid. The compactness ratio is constant, and therefore, all the variation in the energy storage effectiveness results from the change in phase change effectiveness. Fig. 7 shows how an increasing flow rate decreases the effectiveness, and as per the effectiveness–NTU approach to heat exchange analysis, this result is expected. The impact of pressure losses is still small but not negligible representing a reduction in the storage effectiveness of 15.24% at the maximum flow rate of 7500 kg/h. 4.3. Slab thickness effects The impact of the PCM slab thickness is shown in Figs. 9 and 10. The number of slabs was increased from 5 to 105, as the thickness decreased from 0.2 m to 0.01 m, to maintain a constant volume of PCM. The gap between slabs was fixed at a default value of 0.01 m. The simulation is 0.8
0.8
50, 0.683 50, 0.682 75, 0.679 75, 0.678 750, 0.568 0.6 750, 0.562 1000, 0.54 1000, 0.533 100, 0.675 100, 0.675 250, 0.649 0.4 250, 0.647 500, 0.604 2500, 0.414 500, 0.607 2500, 0.398
0.005, 0.799 0.0075, 0.732 0.01, 0.675
0.6
0.025, 0.456
0.4
0.05, 0.294 0.075, 0.212 0.1, 0.167
0.2
0.2
0.25, 0.07
0
0.005, 0.986 0.0075, 0.986 0.01, 0.986 0.025, 0.978
Unit 0.98
Preset parameter Solid thermal diffusivity Liquid thermal diffusivity Solid specific heat Liquid specific heat Solid thermal conductivity Liquid thermal conductivity Solid density Liquid density PCM phase change temperature Latent heat of fusion Length of slabs Width of slabs
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0
0.2
0.5, 0.034
0.4
0.6
5000, 0.267 5000, 0.243
0.75, 0.023
0.8
Fig. 5. True energy density, a and modified true energy density, a for various gap width, w with fixed t at 0.01 m and HTF mass flow rate of 100 kg/h respectively.
0
0
2000
4000
6000
7500, 0.21 7500, 0.178
8000
Fig. 7. True energy density, a and modified true energy density, a for various HTF mass flow rates with fixed t and w of 0.01 m respectively.
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50, 0.991 50, 0.991 75, 0.988 75, 0.988 100, 0.986 100, 0.986 250, 0.962 250, 0.964 500, 0.931 500, 0.928 750, 0.895 750, 0.891 1000, 0.873 1000, 0.868 2500, 0.778 2500, 0.764
0.9 0.8 0.7 0.6
5000, 0.612 5000, 0.583
0.5 0.4
0
1000
2000
3000
4000
5000
7500, 0.539 7500, 0.496
6000
7000
8000
Fig. 8. Phase change effectiveness, e and modified phase change effectiveness, e for various HTF mass flow rates with fixed t and w of 0.01 m respectively.
run repeatedly with the mass flow rate at 50, 100, 500, and 1000 kg/h. Fig. 10 shows the modified phase change effectiveness decreasing at larger slab thickness which is due to the decreasing heat exchanger area as the number of slabs decreased. This decrease becomes more dramatic at higher flow rates. Fig. 9 shows an optimum slab thickness. Given that the gap is fixed at 0.01 m, this optimum can be attributable to an increasing compactness ratio in combination with a decreasing effectiveness with increasing slab thickness. This optimal thickness increases with a decreasing
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.05
0.1
0.15
0.2
Fig. 9. True energy density, a and modified true energy density, a versus slab thickness, t for various HTF mass flow rates with fixed w of 0.01 m.
flow rate. At the lowest flow rate, the energy storage effectiveness reaches a constant maximum and this is due to the effectiveness also being relatively constant. This near constant effectiveness occurs, as with a decrease in area there is also an increase in the overall heat transfer coefficient between the wall and the heat transfer fluid as the mass flow rate is fixed. From Fig. 9 the optimum slab thickness was 0.023 m (with 45 slabs) for a flow rate of 1000 kg/h giving an optimised true energy density of 0.533, respectively. It also shows how pumping losses remain small.
5. Optimal design From the parametric study it is possible to determine an optimal design of a thermal storage system with PCM. Fig. 11 presents the maximum true energy density achieved for the optimal slab thickness, at each of the flow rates presented in Fig. 9 for a fixed gap of 0.01 m. The range of this optimum true energy density is 0.53–0.83, and is presented in Table 3 with the corresponding mass flow rate. Interestingly these values indicate that PCM in slabs have the capacity to deliver high energy density storage values. Above 1000 kg/h, the true energy density is presented for a fixed slab thickness of 0.01 m from Fig. 7. From these values, the Er can be determined based on the heat transfer fluid used in this study. One metre cubed of the PCM specified in Table 2, charging over 12 h, equates to a constant load of 4.5 kW. This value is based on a storage facility with unity effectiveness for discharging and charging, and therefore 1 m3 of PCM represents the ideal capacity to meet this load. Table 3 presents the PCM volume based on Eq. (10). The data clearly identifies how with decreasing true energy density values, the amount of PCM needed dramatically increases, and can be significantly higher than the ideal volume. Table 3 shows the temperature differences required by the heat transfer fluid to meet this load at each flow rate. At low flow rates, the sensible energy storage system achieves a higher volumetric energy density, however as flow rates increase the PCM storage system is more energy 0.9
1
50, 0.835
0.9
100, 0.797
0.8
0.8 0.7
0.7
500, 0.634 0.6
0.6 0.5
1000, 0.533
0.5
0.4 0.3
0
0.05
0.1
0.15
0.2
Fig. 10. Modified phase change effectiveness, e versus slab thickness, t (m) for various HTF mass flow rates with fixed w of 0.01 m.
0.4
0
200
400
600
800
1000
Fig. 11. Optimum modified true energy density, a for various HTF mass flow rates with fixed w of 0.01 m.
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Table 3 Energy stored within a PCM and sensible energy storage system, for a gap of 0.01 m.a m_
Slab thickness (m)
DT needed to achieve 4.5 kW
a
c
Required PCM volume (m3)
Required tank volume (m3)
Er
eðd Þ
emin
50 100 500 1000 2500 5000 7500
0.067 0.067 0.029 0.023 0.01 0.01 0.01
116 58 12 5.8 2.3 1.2 0.77
0.835 0.797 0.634 0.533 0.411 0.364 0.178
0.87 0.87 0.75 0.67 0.5 0.5 0.5
0.8 0.9 1.1 1.2 1.2 1.3 2.7
1.15 1.15 1.34 1.49 2 2 2
0.5 0.9 3.2 5.2 10 17 13
0.991 0.986 0.928 0.868 0.764 0.583 0.496
12.9 6.4 1.3 0.64 0.25 0.13 0.09
a
For flow rates up to 1000 kg/h the results are based on the optimum slab thickness.
dense, despite a decreasing energy storage effectiveness. These high Er can be attributed to a relatively high energy storage effectiveness, from the optimisation study. At the maximum flow rate Er reduces, reflecting a very small storage effectiveness. Table 3 also presents the minimum phase change effectiveness required for discharging as per Eq. (12). The source temperature was defined as 18 °C as the cold space temperature and the PCM temperature is taken from Table 2. No consideration is given as to the effectiveness of any heat exchange between the heat transfer fluid and the cold space. The table shows that apart from the first three mass flow rates, the discharging effectiveness ðed Þ is above the minimum phase change effectiveness, which are also not feasible solutions, being above unity. For the following mass flow rates the discharging effectiveness is above the minimum phase change effectiveness indicating these designs will deliver temperatures to the cold space below the cold space temperature. Table 3 identifies the most optimum design, defined by a mass flow rate of 1000 kg/h, for the case considered. This design has the maximum energy storage effectiveness, while meeting the minimum effectiveness criteria, reflecting the design which achieves the lowest exergy loss. This result is confirmed by the volume of PCM required being only 18% higher than the ideal value of 1 m3, being significantly lower than the amount of PCM needed at higher flow rates. 6. Conclusions Using an experimentally validated numerical model of a PCM in plate system, a parametric study has identified that with increasing gap thickness between the plates and mass flow rate the storage density coefficient decreases. The study identified that for a given gap, an optimum plate thickness exists for each mass flow rate which maximises the storage density coefficient. Using this coefficient the useful energy storage within a PCM system can be directly compared to a sensible storage system. It was determined that the useful energy stored relative to a sensible storage system increases significantly at low temperature differences between the fluid and the phase change temperature, and only reduces at high flow rates when the effectiveness is relatively lower. At low temperature differences the required mass flow rates are high impacting on the effectiveness, however due to the
design of the PCM arrangement, heat exchange effectivenesses are still sufficiently high that adequate cooling can still be achieved. The energy storage effectiveness parameter was also determined to be an important design parameter to ensure that the PCM system is able to meet temperature specifications during discharging. Pumping losses were found to be small, and can be neglected. Overall, PCM systems which deliver a high energy storage density, require a design which can achieve reasonable effectivenesses at high mass flow rates. PCM encapsulated in plates achieve this outcome. Acknowledgements The authors are very grateful to the Barbara Hardy Institute at the University of South Australia for enabling this project. The Ministry of Higher Education, Malaysia, is also thanked for financing the project through the Universiti Malaysia Perlis. References Amin, N.A.M., Bruno, F., Belusko, M., 2009a. Maximizing the energy storage performance of phase change thermal storage systems. In: Proceeding of the IASTED International Conference on Solar Energy – 2009, Phuket, Thailand (647), pp. 55–60. Amin, N.A.M., Bruno, F., Belusko, M., 2009b. Optimisation of a phase change thermal storage system. World Academy of Science, Engineering and Technology 56, 765–769. Amin, N.A.M., Bruno, F., Belusko, M., 2012a. Investigation of conducting pins in sphere filled with phase change material for enhancing heat transfer in thermal energy storage. Advanced Materials Research 472– 475, 1693–1697. Amin, N.A.M., Bruno, F., Belusko, M., 2012b. Effectiveness–NTU correlation for low temperature PCM encapsulated in spheres. Applied Energy 93, 549–555. Be´de´carrats, J.P., Strub, F., Falcon, B., Dumas, J.P., 1996. Phase-change thermal energy storage using spherical capsules: performance of a test plant. International Journal of Refrigeration 19 (3), 187–196. Bejan, A., 2006. Advanced Engineering Thermodynamics, third ed. John Wiley & Sons, Hoboken. Belusko, M., Bruno, F., 2008. 140 – Design methodology of PCM thermal storage systems with parallel plates. In: Proceeding of the EUROSUN 2008, 1st International Congress on Heating, Cooling, and Buildings, Lisbon, Portugal, pp. 1–8. Cabeza, L.F., Mehling, H., Hiebler, S., Ziegler, F., 2002. Heat transfer enhancement in water when used as PCM in thermal energy storage. Applied Thermal Engineering 22, 1141–1151.
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Cabeza, L.F., Iba´n˜ez, M., Sole´, C., Roca, J., Nogue´s, M., 2006. Experimentation with a water tank including a PCM module. Solar Energy Materials and Solar Cells 90, 1273–1282. Castell, A., Belusko, M., Bruno, F., Cabeza, L.F., 2011. Maximisation of heat transfer in a coil in tank PCM cold storage system. Applied Energy 88 (11), 4120–4127. Ettouney, H., El-Dessouky, H., Al-Ali, A., 2005. Heat transfer during phase change of paraffin wax stored in spherical shells. Journal of Solar Energy Engineering 127 (3), 357–366. Guobing, Z., Yang, Y., Xu, H., 2011. Energy performance of a hybrid space-cooling system in an office building using SSPCM thermal storage and night ventilation. Solar Energy 85, 477–485. Halawa, E., Saman, W., 2011. Thermal performance analysis of a phase change thermal storage unit for space heating. Renewable Energy 36, 259–264. Halawa, E., Saman, W., Bruno, F., 2010. A phase change processor method for solving a one-dimensional phase change problem with convection boundary. Renewable Energy 35, 1688–1695. Helm, M., Keil, C., Hiebler, S., Mehling, H., Schweigler, C., 2009. Solar heating and cooling system with absorption chiller and low temperature latent heat storage: energetic performance and operational experience. International Journal of Refrigeration 32, 596–606. http://www.iea-shc.org (accessed 10.05.09). Ismail, K.A.R., Quispe, O.C., Henrı´quez, J.R., 1999. A numerical and experimental study on a parallel plate ice bank. Applied Thermal Engineering 19 (2), 163–193. Kousksou, T., Bruel, P., Cherreau, G., Leoussoff, V., El Rhafiki, T., 2011. PCM storage for solar DHW: from an unfulfilled promise to a real benefit. Solar Energy 85, 2033–2040. Lacroix, M., 2002. Modeling of Latent Heat Storage Systems, Thermal Energy Storage, Systems and Applications. John Wiley & Sons, Chichester, England. Liu, M., Saman, W., Bruno, F., 2011a. Validation of a mathematical model for encapsulated phase change material flat slabs for cooling applications. Applied Thermal Engineering 31 (14–15), 2340–2347. Liu, M., Bruno, F., Saman, W., 2011b. Thermal performance analysis of a flat plate phase change thermal storage unit with liquid-based heat transfer fluid for cooling applications. Solar Energy 85 (11), 3017– 3027.
Liu, M., Saman, W., Bruno, F., 2012. Development of a novel refrigeration system for refrigerated trucks incorporating phase change material. Applied Energy 92, 336–342. Medrano, M., Yilmaz, M.O., Nogue´s, M., Martorell, I., Roca, J., Cabeza, L.F., 2009. Experimental evaluation of commercial heat exchangers for use as PCM thermal storage systems. Applied Energy 86, 2047– 2055. Mehling, H., Cabeza, L.F., 2008. Heat and Cold Storage with PCM: An up to Date Introduction into Basics and Applications. SpringersVerlag, Berlin, Heidelberg. Schultz, J.M., Sole´, C., Cabeza, L.F., Bony, J., Heinz, A., 2007. In: Wolfgang Streitcher (ed.), Laboratory Prototypes of PCM Storage Units. A Report of IEA Solar Heating and Cooling Programme – Task 32. Advance Storage Concepts for Solar and Low Energy Buildings. Tay, N.H.S., Belusko, M., Bruno, F., 2012a. Experimental investigation of tubes in a phase change thermal energy storage system. Applied Energy 90, 288–297. Tay, N.H.S., Belusko, M., Bruno, F., 2012b. An effectiveness–NTU technique for characterising tube-in-tank phase change thermal energy storage systems. Applied Energy 91, 309–319. Tay, N.H.S., Bruno, F., Belusko, M., 2012c. Experimental validation of a CFD model for tubes in a phase change thermal energy storage system. International Journal of Heat and Mass Transfer 55, 574–585. Wang, F., Maidment, G., Missenden, J., Tozer, R., 2002. A review of research concerning the use of PCMS in air conditioning and refrigeration engineering. Advances Building Technology 2, 1273– 1280. Wang, X., Niu, J., Li, Y., Zhang, Y., Wang, X., Chen, B., Zeng, R., Song, Q., 2008. Heat transfer of microencapsulated PCM slurry flow in a circular tube. AIChE Journal 54, 1110–1120. Zalewski, L., Joulin, A., Lassue, S., Dutil, Y., Rousse, D., 2011. Experimental study of small-scale solar wall integrating phase change material. Solar Energy 86 (1), 208–219. Zhao, C.Y., Lu, W., Tian, Y., 2010. Heat transfer enhancement for thermal energy storage using metal foams embedded within phase change materials (PCMs). Solar Energy 84, 1402–1412.
Solar Energy 86 (2012) 2263–2272 www.elsevier.com/locate/solener
Optimising PCM thermal storage systems for maximum energy storage effectiveness N.A.M. Amin a,b,⇑, M. Belusko a, F. Bruno a, M. Liu a a
Barbara Hardy Institute, School of Advanced Manufacturing and Mechanical Engineering, University of South Australia, Mawson Lakes, South Australia 5095, Australia b School of Mechatronic Engineering, Universiti Malaysia Perlis, Main Campus Ulu Pauh, 02600 Arau, Perlis, Malaysia Received 30 December 2011; received in revised form 20 March 2012; accepted 24 April 2012 Available online 19 May 2012 Communicated by: Associate Editor Halime Paksoy
Abstract A new performance parameter for PCM thermal storage systems, the energy storage effectiveness, is defined. This parameter can be used to optimise the design of any PCM thermal storage system to maximise the use of the thermal storage media. The paper presents results of a parametric study using an experimentally validated numerical model for PCM encapsulated in plates. The results are used to calculate the energy storage effectiveness which is ultimately used to optimise the useful energy that can be stored in the PCM thermal storage system. The energy storage effectiveness is also used to compare the useable storage capacity of the PCM relative to a sensible energy storage system. Ó 2012 Elsevier Ltd. All rights reserved. Keywords: Phase change material; Energy storage effectiveness; Thermal energy storage
1. Introduction Phase change materials (PCMs), with high latent heat of transition, are potentially effective thermal energy storage materials suitable for use in heating and cooling applications (Guobing et al., 2011; Kousksou et al., 2011; Zalewski et al., 2011). The use of PCMs represents a particular effective solution for off peak thermal storage for refrigeration applications (Wang et al., 2002; Liu et al., 2012; Amin et al., 2009a, 2012a). Considerable research has been conducted on applying PCMs to thermal energy storage on the basis of the potential to significantly increase the volumetric thermal energy storage density (Mehling and ⇑ Corresponding author at: School of Mechatronic Engineering, Universiti Malaysia Perlis, Main Campus Ulu Pauh, 02600 Arau, Perlis, Malaysia. Tel.: +61 8 8302 3230; fax: +61 8 8302 3380. E-mail address: [email protected] (N.A.M. Amin).
0038-092X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2012.04.020
Cabeza, 2008). A critical requirement of enhancing the energy reductions within low energy solar heating or cooling systems is to maximise the level of thermal storage for a given volume, which is the prime objective of a current IEA Task under the Solar Heating and Cooling Program, Task 4224; Compact thermal energy storage: Material development and system integration (http://www.ieashc.org, 2009). Thermal storage is defined by a charging and discharging process in any thermal system. The application of thermal energy storage results in an exergy loss due to the additional process of discharging (Bejan, 2006). Limited research has been presented determining the usefulness of a PCM system and no generic method exists for comparing one storage system against another. This paper presents a new parameter, the energy storage effectiveness, capable of determining the useful volumetric energy density of PCM thermal storage based on minimising the exergy losses in the thermal store. This parameter can be used to
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Nomenclature a a Cp Dh Er et ed ec e ed ec HL f l m_ gp gps PL DP
energy storage density coefficient (–) modified energy storage density coefficient (–) specific heat (J/kg K) hydraulic diameter (m) comparative energy storage ration (–) local heat exchange effectiveness (–) melting or discharging effectiveness (–) freezing or charging effectiveness (–) modified phase change effectiveness (–) modified melting or discharging effectiveness (–) modified freezing or charging effectiveness (–) latent heat of fusion (J/kg) friction factor (–) length of gap or PCM slab (m) mass flow rate of HTF between slabs (kg/h) pumping efficiency (–) power station efficiency (–) primary energy of the pumping losses (J) pressure drop (kg/m2)
optimise a PCM store for any thermal system and enable a direct comparison with sensible energy storage. Referring to the thermal energy storage model by Cabeza et al. (2006), the work completed within the International Energy Agency Solar Heating and Cooling Program (Schultz et al., 2007), it was concluded that the energy savings relative to the sensible energy storage capacity of water, for domestic hot water storage, for the same volume was negligible. The use of the PCM, sodium acetate trihydrate, could only achieve a reduction in storage volume for a temperature lift of 20 °C. No benefit was identified for temperature lifts of 50 °C, typical in a hot water system. Therefore, in this case, sensible energy storage proved more energy dense than the PCM option. In other research, Helm et al. (2009) investigated the use of a PCMin-tank system as a heat rejection system in an absorption chiller, again based on a low temperature range. The study clearly demonstrated that the useable energy storage density was significantly higher than a sensible energy storage system. This highlights that PCMs are more effective in systems with a relatively low temperature difference between the heat source and sink. A major factor which affects the volumetric energy storage density of PCM systems is the amount of volume occupied by the PCM within the thermal storage system. Be´de´carrats et al. (1996) indicate that the PCM occupies 50% of the volume of the tank for sphere type PCM storage system whereas for the plate type the value can achieve 95% (Mehling and Cabeza, 2008). For PCM in plates, the potential for a high proportion of PCM to total storage
density of the HTF (kg/m3) qhtf qpcm density of the PCM (kg/m3) Qact actual stored energy (J) Qmax maximum theoretical stored energy (J) Tin inlet temperature (°C) Tout outlet temperature (°C) Tout_model outlet temperature from TRNSYS model (°C) Tout_exp outlet temperature from experiment (°C) Tpcm temperature of PCM (°C) DT temperature different (°C) t time (s) t thickness of PCM slab (m) l dynamic viscosity of the HTF (mPa s) m mean velocity of the HTF (m/s) Vfull volume of the full tank (m3) _V volumetric flow rate (m3/s) w width of gap (m) c compactness factor (–)
volume, or the compactness factor, exists when fluid gaps are small (Belusko and Bruno, 2008; Amin et al., 2009b). Of equal importance which affects the useable energy storage density of a PCM storage system is the effectiveness of the heat transfer which can be exchanged between the heat transfer fluid and the PCM. In most sensible energy stores such as a tank of water, the heat transfer fluid directly stores the thermal energy, therefore exergy losses only occur due to additional pumping and heat losses to the surroundings. In a PCM system the heat that is transferred is a function of the thermal resistance between the heat transfer fluid and PCM at the phase change front (Ismail et al., 1999; Tay et al., 2012a). If the thermal resistance is relatively high, then the heat transfer rate over the time of operation is relatively low, reducing the effective energy that is stored within the PCM. Considerable research has been conducted on minimising the thermal resistance in PCM systems. Cabeza et al. (2002) investigated the use of conductors, which showed a doubling of heat transfer. Five commercial heat exchangers functioning as latent heat thermal energy storage systems were investigated (Medrano et al., 2009). From the experimental work, the design which delivered the highest heat transfer incorporated a double pipe arrangement for the heat transfer fluid embedded in a PCM graphite matrix. The PCM graphite matrix has a very high thermal conductivity relative to conventional PCMs minimising the resistance to heat transfer (Cabeza et al., 2002; Medrano et al., 2009). Metal foams embedded in PCMs have also been investigated and found to increase the overall heat
N.A.M. Amin et al. / Solar Energy 86 (2012) 2263–2272
transfer rate by 3–10 times (Zhao et al., 2010). These systems involve the PCM being directly contained within the thermal store, as opposed to encapsulated in containers. PCM slurries have similar characteristics of sensible energy stores, with the added advantage of phase change within the microencapsulated PCM. However, being a mixture of PCM/heat transfer fluid the overall energy densities are 27.6% of the original PCMs (Wang et al., 2008). The impact of design parameters of a PCM-in-plate system has been investigated using experimentally validated numerical models (Halawa et al., 2010; Liu et al., 2011a,b). The models are capable of determining the heat transfer between the PCM and heat transfer fluid for any design and inlet conditions. A parametric study of an air based system has investigated the impact on the heat transfer of various design parameters identifying how the heat transfer can be increased (Halawa and Saman, 2011). However, this information does not assist with the design or optimisation of a PCM system based on the usable amount of thermal storage media, as well as enabling a comparison to sensible energy storage systems. In a PCM system any thermal resistance between the heat transfer fluid and the PCM represents an exergy loss. Therefore, reliance on storing in the sensible component of a PCM, reduces the relevance of using the latent component. It can therefore be argued that sensible energy storage in a PCM system should be ignored, relative to a sensible energy store using the heat transfer fluid itself. In contrast, if the PCM system is effective at transferring the latent energy to the heat transfer fluid, it will be effective at transferring any sensibly stored energy. A number of researchers have identified that the heat exchange effectiveness is a useful measure to characterise the heat transfer in a PCM system. Ismail et al. (1999) specify a local effectiveness which varies with time and Belusko and Bruno (2008) define it with respect to the proportion of phase change. Tay and other researchers have experimentally determined the average effectiveness over the phase change process for coil in tank PCM storage systems (Tay et al., 2012a,b,c; Castell et al., 2011). Amin et al.
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(2012b) have experimentally determined the average effectiveness for PCM encapsulated in spheres. Using this average effectiveness concept, this paper combines this factor with the compactness factor, to develop the energy storage effectiveness for a PCM system. This paper reports on a complete parametric and optimisation study conducted on a PCM system encapsulated in plates using a liquid heat transfer fluid. This study aimed to validate the energy storage effectiveness as the defining performance measure of a PCM system, and demonstrate that through optimisation of this parameter, the selected design will achieve the least exergy losses when applied to any thermal system. Furthermore, the study demonstrates how it can be used to determine the amount of PCM required and compare a PCM storage system against a sensible storage system of equivalent volume. The study is conducted in the context of off peak refrigeration storage. 2. Characterisation of PCM system The PCM storage system consists of several flat PCM slabs (Fig. 1). The slabs are arranged in layers with a passage in between for the heat transfer fluid. Heat transfer to the surroundings is ignored. When operating as an off peak storage system, a heat sink is developed in the PCM during the solidification or charging of the PCM and heat is absorbed during melting or discharging process. During the phase change process, heat is exchanged between the heat transfer fluid and the phase change interface within the PCM, at the phase change temperature. This heat transfer is a function of the thermal resistance in the heat transfer fluid and in the PCM proportion which has already changed phase. Therefore the outlet fluid temperature is determined by the thermal resistance in the system and limited by the phase change temperature. Maximum heat transfer is achieved when the outlet temperature is equal to the phase change temperature. In order to achieve energy efficient storage, the inlet temperature of the heat transfer fluid during charging or freezing of the PCM should be as high as possible to maximise
adiabatic wall
l
PCM
tw
y
HTF
wt
x z
Fig. 1. Schematic diagram of the PCM model.
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the coefficient of performance of the refrigeration system. The maximum possible temperature is determined by the required rate of heat removal from the PCM during the charge period, which is determined by the thermal resistance to heat transfer. To maximise the charge fluid temperature, the outlet fluid temperature should be equal to the PCM phase change temperature, while providing adequate heat transfer. The thermal resistance also affects the discharge temperatures which are achieved from a PCM storage system. Discharge temperatures are specified by the cooling requirements of the load. Ideally, the discharge temperature should equal to the phase change temperature of the PCM. However, due to thermal resistance, the discharge temperature will be above this temperature, and therefore a lower temperature PCM is required. As a result, charging this PCM is more energy intensive. Consequently, energy efficient storage is dependent on minimising the thermal resistance to heat transfer in the PCM storage system, effectively minimising the temperature difference between the heat sink and heat source. This approach minimises any sensible storage in the PCM which is defined by the change in temperature of the material, and as a result, sensible energy storage is ignored. The outlet temperature from the PCM system determines the heat transferred between the heat transfer fluid and the PCM and consequently, thermal performance can be expressed in terms of a heat exchange effectiveness. This effectiveness directly relates to the thermal resistance in the PCM storage system as explained by Belusko and Bruno (2008) and Tay et al. (2012b). If the heat transfer rate does not vary with time, the effectiveness of a PCM storage system is defined by ec;d ¼ Qact =Qmax ¼ ðT in T out Þ=ðT in T pcm Þ
ð1Þ
Over the period of phase change, the actual energy stored and released is defined by this effectiveness, which directly affects the useful energy that is stored. Consequently the actual useful energy which is stored is the product of the effectiveness of charging and discharging. The compactness factor for PCM in plates is shown by Eq. (2), and directly affects the volumetric energy density of a storage system. c ¼ t=ðw þ tÞ
ð2Þ
Therefore the expected energy storage density of a PCM storage system can be defined by the energy storage effectiveness, a ¼ ec ed c
To consider pumping losses within the PCM storage system a modified effectiveness value was determined using ec ;d ¼ ec;d ðP L =Qmax Þ Total losses of the system are then calculated using P L ¼ DP V_ =ðgp gps Þ
ð5Þ
Pump efficiency, gp and power station efficiency, gp.s were fixed at 50% and 35%, respectively. As the heat transfer fluid moves between the parallel plates of the PCM store, the pressure drop can be evaluated DP ¼ f l q v2 =ð2 Dh Þ
ð6Þ
The entrance and exit losses are ignored as these exist in any sensible storage system. Therefore, the modified energy storage effectiveness of the system, a can be written as: a ¼ ec ed c
ð7Þ
The energy storage effectiveness can be used to directly determine the amount of PCM needed in a PCM storage system as well as compare to the volumetric energy storage density of sensible storage systems which store energy directly within the heat transfer fluid. In a refrigeration application, any storage system must be capable of meeting the peak cooling demand over a number of hours. For a given mass flow rate and the required thermal load, the temperature drop of the heat transfer fluid within the thermal store can be determined. This temperature drop determines the stored energy needed in a sensible energy store. The PCM storage system stores latent energy in the PCM as well as a small amount of sensible energy in the heat transfer fluid that remain in the gaps of the PCM system. Therefore in order to determine the amount of PCM needed and compare the system to a sensible energy store, the sensible energy stored in the heat transfer fluid within the PCM storage tank need to be considered. Therefore the useful stored energy within a PCM thermal store can be expressed as: Q ¼ a H L qpcm V full þ qhtf Cp DT ð1 cÞ V full
ð8Þ
For a design period of time the required stored energy can also be expressed as: _ Q ¼ mCp DT t
ð9Þ
Therefore for a given mass flow rate, the PCM tank volume and corresponding volume of PCM can be determined from V pcm ¼
ð3Þ
This effectiveness directly identifies how much of the volume is used to store useful energy. A value of unity indicates that the useful stored energy is defined by the entire volume of the storage facility multiplied by the volumetric energy storage density of the PCM, representing the most ideal PCM storage system.
ð4Þ
c m_ Cp DT t þ qhtf Cp DT ð1 cÞ a H L qpcm
ð10Þ
Based on Eq. (8), the comparative energy storage ratio (Er), which is the ratio of the useful energy stored in a PCM system relative to a sensible energy storage tank filled with the heat transfer fluid, is defined by: Er ¼
a H L qpcm þ ð1 cÞ qhtf Cp DT
ð11Þ
N.A.M. Amin et al. / Solar Energy 86 (2012) 2263–2272
The comparative energy storage ratio is based on no losses to the surroundings, ignores the pumping losses related to flow through the sensible storage tank and assumes perfect mixing in the sensible energy storage tank. In any PCM thermal storage system, the discharged amount of PCM is restricted by the requirement that heat can only flow from a high temperature to a lower temperature, as defined within the 2nd Law of Thermodynamics. Therefore any given design is only valid if the effectiveness is above a critical value defined by the heat source temperature, in the case of refrigeration. The minimum effectiveness is based on the required temperature difference to achieve the design load for a specific flow rate. Therefore, for a given design the determined discharge effectiveness is required to be greater than this minimum effectiveness (Eq. (12)): emin ¼ DT =ðT source T pcm Þ
ð12Þ
Tsource is the temperature of the heat source. For any design the performance of the thermal storage system for any application can be defined by the energy storage effectiveness. A direct comparison can be made with a sensible storage system using the heat transfer fluid through the comparative energy storage ratio, and the minimum effectiveness ensures that all the available stored energy can be used for the design specifications provided. 3. PCM plate numerical model In this study, to determine the charging and discharging effectiveness, an experimentally validated numerical model of PCM plates (Liu et al., 2011a) has been used. This model uses the finite-difference calculation method. The difficulty of solving the heat transfer problem during the phase change process is due to the nonlinear movement of the solid–liquid interface, namely moving boundary problems or Stefan problem (Lacroix, 2002; Ettouney et al., 2005). Models based on temperature formulations are particularly suitable for solving the phase change problem at a fixed temperature. It has been successfully used to investigate the influence of various parameters (such as Rayleigh, Stefan and Prandtl numbers, and aspect ratios of the containers). The ice bank of parallel plates has been investigated, and a one-dimensional temperature-based model was studied (Ismail et al., 1999). The model applied the finite difference method. The agreement between the predicted results and the experimental results was good. The model used in this study was developed based on temperature formulations. Both solid–liquid and mixed phases are considered. Research for air based systems has shown that the heat transfer is 1-D due to the high length to thickness ratio of the plate (Halawa et al., 2010). This research included an experimental validation of the model. Being 1-D, the model ignores the thermal conductivity of the PCM. The model also ignores any natural convection in the PCM, which has been shown to be small due to the thin slab thicknesses (Halawa and Saman, 2011). This
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factor is particularly irrelevant if the temperature difference between the fluid and the phase change temperature is small. Supercooling is also ignored in the model. The model has been validated against experimental results with plates of a PCM with a freezing point of 27 °C in a liquid based system (Liu et al., 2011a). The experiments involved 19 plates of dimensions 0.26 m long 1.70 m wide 0.025 m thick, separated by a 6 mm gap. Charging was achieved using a refrigeration system to chill the heat transfer fluid. Discharging involved pumping the heat transfer fluid into a cold room through an indoor air/liquid heat exchanger. The heat transfer fluid used was a glycol based liquid, with properties shown in Table 1. Reasonable agreement was achieved between the predicted and experimental results, for discharging, as shown in Fig. 2. Phase change can be observed by the sudden changes in temperature gradient as presented by Mehling and Cabeza (2008) and Tay et al. (2012a). Fig. 3 shows the instantaneous heat exchange effectivenesses from Fig. 2. The results show that the sensible energy stored in the PCM causes the heat exchange effectiveness to be high (and can be above unity) at the beginning of the melting process. The sensible energy stored in the PCM raises the initial temperature above the melting point, resulting in the outlet temperature being above the melting delivering an over unit effectiveness as defined by Eq. (1). The heat exchange effectiveness then gradually reduces over the phase change process. This decrease can be attributed to a gradual increase in the inlet temperature due to the heat load from the cold room being greater than the cooling delivered by the thermal storage system. Therefore, in these experiments, the thermal storage system was under-designed. The average effectiveness over the phase change process is 0.58 at a flow rate of 0.32 l/s and 0.6 at a flow rate of 0.22 l/s. As defined by heat exchanger theory, a reduced mass flow rate results in an increase in the effectiveness. Based on a compactness factor of 0.466, the storage effectivenesses translate to 0.157 and 0.167 respectively when charge and discharge effectivenesses are assumed to be the same and the pressure losses effect is ignored. These values are considerably low and highlight how in all likelihood, this application of this design of the PCM cannot be justified. Using this model it is possible to conduct an extensive parametric study of the storage effectiveness, and determine the optimum design which minimises the exergy losses of any thermal system using PCM. For a given inlet tem-
Table 1 Properties of heat transfer fluid working temperature. Temperature (°C)
Dynamic viscosity (mPa s)
Thermal conductivity (W/m K)
Specific heat (kJ/ kg K)
Density (kg/m3)
30 20 10
9.222 6.495 4.916
0.459 0.469 0.479
2.820 2.843 2.866
1343 1337 1332
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Fig. 2. Mathematical model compared with the experimental test results for (a) 0.32 l/s and (b) 0.22 l/s mass flow rates.
Fig. 3. Effectiveness results from Fig. 2.
perature, mass flow rate and physical dimensions of the PCM system, the outlet temperature can be determined from the model as shown in Fig. 4. The figure shows a constant outlet temperature and this is attributable to having a constant inlet temperature. In all cases studied the outlet temperature was constant. The focus of this study is the effectiveness related to latent energy storage. In order to
Temperature, T ( C)
-25.4 -25.8 T in T out T pcm
-26.2 -26.6 -27.0
0
20
40
60
80
100
Time (s)
Fig. 4. Temperature parameters from the PCM system during discharging.
minimise the sensible component, which is modelled in the numerical model used, the temperature difference between the inlet temperature and the phase change temperature was fixed at 1 °C. The sensible energy was found to be negligible being 2.53% of the latent energy. Heat transfer was assumed to be complete when the temperature change of the heat transfer fluid was less than 0.01 °C. The heat exchange effectiveness of the process was based on the average outlet temperature, and found using Eq. (1). Since thermal conductivity and natural convection are ignored, the thermal resistance in the PCM is the same for both discharging and charging and therefore the thermal resistance in the system is defined by the geometry and the mass flow rate only. Therefore the effectiveness for charging is equal to the effectiveness of discharging, and from this point on will be referred to as the phase change effectiveness. 4. Thermal storage optimisation A parametric study of the energy storage effectiveness was conducted, investigating the impact of the PCM slab thickness, gap width between slabs and the mass flow rate. A PCM with a melting point of 27 °C is used for this analysis because it is suitable for refrigeration applications (Liu et al., 2011a) along with a low temperature heat transfer fluid with properties provided in Table 1. The amount of PCM used in this study is fixed at 1 m3. Therefore, when the slab thickness is varied, the number of slabs is changed so that the total PCM volume is constant. The properties of the PCM and the range of parameters investigated during the simulation are specified in Table 2. The default values for the PCM storage system consist of a 0.01 m gap, a mass flow rate of 100 kg/h and 45 slabs with a thickness of 23 mm. This configuration achieves a
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Table 2 Preset and changing parameters through simulations. Parameter
Quantity
0.99
Changing parameter No of slabs Thickness of slabs Gap between slabs Mass flow rate
1.42 106 1.11 107 1200 3650 2.2 0.55 1305 1363 26.7 144,000 1 1
m2/s m2/s J/kg K J/kg K W/m K W/m K kg/m3 kg/m3 °C J/kg m m
5–105 Default is 45 0.2–0.01 Default is 0.023 0.005–0.75 Default is 0.01 50–7500 Default is 100
– – m m m m kg/h kg/h
discharging and charging effectiveness of 0.986. The compactness factor is 0.69 and the true energy density equates to 0.675. 4.1. Gap width effects The first simulation investigated the effect of the gap between PCM slabs, on the storage effectiveness (Fig. 5). The gap is increased from 0.005 m to 0.75 m through repeated simulations. The rapid reduction in the energy storage effectiveness was due to the decrease in the compactness ratio which is caused by an increasing gap. Fig. 6 shows the variation in the phase change effectiveness and shows that pumping losses are negligible even though the temperature difference between inlet and outlet is less than 1 °C. Fig. 6 shows that the phase change effectiveness remains relatively constant near unity, which can be explained by 1
0.97
0.05, 0.969
0.96 0.075, 0.951 0.1, 0.945
0.95
0.75, 0.945
0.5, 0.944
0.25, 0.942
0.94 0.93
0
0.2
0.4
0.6
0.8
Fig. 6. Phase change effectiveness, e and modified phase change effectiveness, e for various gap width, w with fixed t at 0.01 m and HTF mass flow rate of 100 kg/h respectively.
the fact that the total heat transfer area remains fixed. The sudden drop and the gradual rise can be explained by changes in the convection heat transfer coefficient due to the change in the hydraulic diameter and the fluid velocity. 4.2. Mass flow rate effects Figs. 7 and 8 show the impact of mass flow rate of the fluid. The compactness ratio is constant, and therefore, all the variation in the energy storage effectiveness results from the change in phase change effectiveness. Fig. 7 shows how an increasing flow rate decreases the effectiveness, and as per the effectiveness–NTU approach to heat exchange analysis, this result is expected. The impact of pressure losses is still small but not negligible representing a reduction in the storage effectiveness of 15.24% at the maximum flow rate of 7500 kg/h. 4.3. Slab thickness effects The impact of the PCM slab thickness is shown in Figs. 9 and 10. The number of slabs was increased from 5 to 105, as the thickness decreased from 0.2 m to 0.01 m, to maintain a constant volume of PCM. The gap between slabs was fixed at a default value of 0.01 m. The simulation is 0.8
0.8
50, 0.683 50, 0.682 75, 0.679 75, 0.678 750, 0.568 0.6 750, 0.562 1000, 0.54 1000, 0.533 100, 0.675 100, 0.675 250, 0.649 0.4 250, 0.647 500, 0.604 2500, 0.414 500, 0.607 2500, 0.398
0.005, 0.799 0.0075, 0.732 0.01, 0.675
0.6
0.025, 0.456
0.4
0.05, 0.294 0.075, 0.212 0.1, 0.167
0.2
0.2
0.25, 0.07
0
0.005, 0.986 0.0075, 0.986 0.01, 0.986 0.025, 0.978
Unit 0.98
Preset parameter Solid thermal diffusivity Liquid thermal diffusivity Solid specific heat Liquid specific heat Solid thermal conductivity Liquid thermal conductivity Solid density Liquid density PCM phase change temperature Latent heat of fusion Length of slabs Width of slabs
2269
0
0.2
0.5, 0.034
0.4
0.6
5000, 0.267 5000, 0.243
0.75, 0.023
0.8
Fig. 5. True energy density, a and modified true energy density, a for various gap width, w with fixed t at 0.01 m and HTF mass flow rate of 100 kg/h respectively.
0
0
2000
4000
6000
7500, 0.21 7500, 0.178
8000
Fig. 7. True energy density, a and modified true energy density, a for various HTF mass flow rates with fixed t and w of 0.01 m respectively.
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50, 0.991 50, 0.991 75, 0.988 75, 0.988 100, 0.986 100, 0.986 250, 0.962 250, 0.964 500, 0.931 500, 0.928 750, 0.895 750, 0.891 1000, 0.873 1000, 0.868 2500, 0.778 2500, 0.764
0.9 0.8 0.7 0.6
5000, 0.612 5000, 0.583
0.5 0.4
0
1000
2000
3000
4000
5000
7500, 0.539 7500, 0.496
6000
7000
8000
Fig. 8. Phase change effectiveness, e and modified phase change effectiveness, e for various HTF mass flow rates with fixed t and w of 0.01 m respectively.
run repeatedly with the mass flow rate at 50, 100, 500, and 1000 kg/h. Fig. 10 shows the modified phase change effectiveness decreasing at larger slab thickness which is due to the decreasing heat exchanger area as the number of slabs decreased. This decrease becomes more dramatic at higher flow rates. Fig. 9 shows an optimum slab thickness. Given that the gap is fixed at 0.01 m, this optimum can be attributable to an increasing compactness ratio in combination with a decreasing effectiveness with increasing slab thickness. This optimal thickness increases with a decreasing
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.05
0.1
0.15
0.2
Fig. 9. True energy density, a and modified true energy density, a versus slab thickness, t for various HTF mass flow rates with fixed w of 0.01 m.
flow rate. At the lowest flow rate, the energy storage effectiveness reaches a constant maximum and this is due to the effectiveness also being relatively constant. This near constant effectiveness occurs, as with a decrease in area there is also an increase in the overall heat transfer coefficient between the wall and the heat transfer fluid as the mass flow rate is fixed. From Fig. 9 the optimum slab thickness was 0.023 m (with 45 slabs) for a flow rate of 1000 kg/h giving an optimised true energy density of 0.533, respectively. It also shows how pumping losses remain small.
5. Optimal design From the parametric study it is possible to determine an optimal design of a thermal storage system with PCM. Fig. 11 presents the maximum true energy density achieved for the optimal slab thickness, at each of the flow rates presented in Fig. 9 for a fixed gap of 0.01 m. The range of this optimum true energy density is 0.53–0.83, and is presented in Table 3 with the corresponding mass flow rate. Interestingly these values indicate that PCM in slabs have the capacity to deliver high energy density storage values. Above 1000 kg/h, the true energy density is presented for a fixed slab thickness of 0.01 m from Fig. 7. From these values, the Er can be determined based on the heat transfer fluid used in this study. One metre cubed of the PCM specified in Table 2, charging over 12 h, equates to a constant load of 4.5 kW. This value is based on a storage facility with unity effectiveness for discharging and charging, and therefore 1 m3 of PCM represents the ideal capacity to meet this load. Table 3 presents the PCM volume based on Eq. (10). The data clearly identifies how with decreasing true energy density values, the amount of PCM needed dramatically increases, and can be significantly higher than the ideal volume. Table 3 shows the temperature differences required by the heat transfer fluid to meet this load at each flow rate. At low flow rates, the sensible energy storage system achieves a higher volumetric energy density, however as flow rates increase the PCM storage system is more energy 0.9
1
50, 0.835
0.9
100, 0.797
0.8
0.8 0.7
0.7
500, 0.634 0.6
0.6 0.5
1000, 0.533
0.5
0.4 0.3
0
0.05
0.1
0.15
0.2
Fig. 10. Modified phase change effectiveness, e versus slab thickness, t (m) for various HTF mass flow rates with fixed w of 0.01 m.
0.4
0
200
400
600
800
1000
Fig. 11. Optimum modified true energy density, a for various HTF mass flow rates with fixed w of 0.01 m.
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Table 3 Energy stored within a PCM and sensible energy storage system, for a gap of 0.01 m.a m_
Slab thickness (m)
DT needed to achieve 4.5 kW
a
c
Required PCM volume (m3)
Required tank volume (m3)
Er
eðd Þ
emin
50 100 500 1000 2500 5000 7500
0.067 0.067 0.029 0.023 0.01 0.01 0.01
116 58 12 5.8 2.3 1.2 0.77
0.835 0.797 0.634 0.533 0.411 0.364 0.178
0.87 0.87 0.75 0.67 0.5 0.5 0.5
0.8 0.9 1.1 1.2 1.2 1.3 2.7
1.15 1.15 1.34 1.49 2 2 2
0.5 0.9 3.2 5.2 10 17 13
0.991 0.986 0.928 0.868 0.764 0.583 0.496
12.9 6.4 1.3 0.64 0.25 0.13 0.09
a
For flow rates up to 1000 kg/h the results are based on the optimum slab thickness.
dense, despite a decreasing energy storage effectiveness. These high Er can be attributed to a relatively high energy storage effectiveness, from the optimisation study. At the maximum flow rate Er reduces, reflecting a very small storage effectiveness. Table 3 also presents the minimum phase change effectiveness required for discharging as per Eq. (12). The source temperature was defined as 18 °C as the cold space temperature and the PCM temperature is taken from Table 2. No consideration is given as to the effectiveness of any heat exchange between the heat transfer fluid and the cold space. The table shows that apart from the first three mass flow rates, the discharging effectiveness ðed Þ is above the minimum phase change effectiveness, which are also not feasible solutions, being above unity. For the following mass flow rates the discharging effectiveness is above the minimum phase change effectiveness indicating these designs will deliver temperatures to the cold space below the cold space temperature. Table 3 identifies the most optimum design, defined by a mass flow rate of 1000 kg/h, for the case considered. This design has the maximum energy storage effectiveness, while meeting the minimum effectiveness criteria, reflecting the design which achieves the lowest exergy loss. This result is confirmed by the volume of PCM required being only 18% higher than the ideal value of 1 m3, being significantly lower than the amount of PCM needed at higher flow rates. 6. Conclusions Using an experimentally validated numerical model of a PCM in plate system, a parametric study has identified that with increasing gap thickness between the plates and mass flow rate the storage density coefficient decreases. The study identified that for a given gap, an optimum plate thickness exists for each mass flow rate which maximises the storage density coefficient. Using this coefficient the useful energy storage within a PCM system can be directly compared to a sensible storage system. It was determined that the useful energy stored relative to a sensible storage system increases significantly at low temperature differences between the fluid and the phase change temperature, and only reduces at high flow rates when the effectiveness is relatively lower. At low temperature differences the required mass flow rates are high impacting on the effectiveness, however due to the
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