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The storage of low grade thermal energy using phase change materials
THE STORAGE OF LOW GRADE THERMAL ENERGY USING PHASE CHANGE MATERIALS
K. K. PILLAI and B. J. BRINKWORTH
Solar Energy Unit, Department of Mechanical Engineering and Energy Studies, University College, Newport Road, Cardiff (Wales)
S UMMA R Y
The use of phase change materials in energy storage systems is considered. The properties of such materials and the types of phase change they undergo are enumerated. Selection criteria are discussed and a list of some useful materials given. The feasibility of system designs is considered, and the generalised, basic requirements of storage systems are presented.
NOMENCLATURE
A h l Q S t T 0 x,y
= = = = = = = = =
Heat transfer area H e a t transfer coetficient Length o f storage system H e a t flux Storage capacity Time Temperature T e m p e r a t u r e excess C a r t e s i a n co-ordinates
Subscripts a b c, d p s 1 2
refers to when flux i n p u t begins refers to when flux i n p u t ends refer to times defined by Fig. 5 = Period = Store = P r i m a r y fluid = Secondary fluid 205 Applied Energy (2) (1976)--© Applied Science Publishers Ltd, England, 1976 Printed in Great Britain
206
K. K. PILLAI, B. J. B R I N K W O R T H
INTRODUCTION
The steadily increasing cost of fuel has now brought about a growing interest in the utilisation of low grade thermal energy. Many sources of such energy (solar radiation, exhaust gases, cooling water, etc.) are becoming increasingly attractive for heat recovery processes. The recovered energy can, however, only be put to a limited number of applications. Space and water heating systems can be operated directly, while thermodynamic cycles must be tailored to suit particular applications. The temperature levels involved mean that cycle efficiencies are inevitably low, and since the required duty is often out of phase with the availability of the recovered energy, it is necessary that cheap and efficient methods of energy storage and transport be devised. Thermal energy can readily be stored either as: (a) the sensible heat required to raise the temperature of some high heat capacity material, or (b) the transitional energy required to produce a reversible change in the physical or chemical state of some material. 1- 3 In the first category, water or boulders are often used as storage media. While such systems are both simple and cheap, they are often very bulky or excessively heavy. The unique property of phase change materials (PCM's), however, is their ability to absorb or liberate large quantities of heat at a constant temperature. Only a very small proportion of the energy stored need be in the form of a temperature gain. Thus, by selecting a PCM having a suitable transition temperature, system designs can be made more cost-effective.
SELECTION OF PHASE C H A N G E MATERIALS
There are various physical and chemical transformations that a material may undergo, accompanied either by the absorption or the liberation of heat. These transformations will all be referred to as 'phase changes', although they may not all involve physical changes of state. They are (i) Solid-gas phase change. (ii) Liquid-gas phase change. (iii) Solid-solid transition. (iv) Solid-liquid phase change. (v) Crystalline solid-liquid solution transformation. Of these, the solid-gas and liquid-gas transformations exhibit the largest heats of transition. They are, however, accompanied by very large volume changes, and the complexity Of the designs required to accommodate, them appears impractical. Solid-solid transformations have the lowest storage capability, but could be useful in specialised applications requiring a particular transition temperature. Solid-liquid melting processes involve only very small volume changes and exhibit a
S T O R A G E OF E N E R G Y U S I N G PHASE C H A N G E MATERIALS
207
useful range of heats of fusion. The crystalline solid-liquid solution transformation is almost exclusively a property of hydrated salts, which absorb heat as they dissolve in their water of crystallisation. Thermodynamically, this process is very similar to the melting process, and the heats of transition are of the same order as the heats of fusioh. These last two processes are therefore the most promising. Whilst there is no PCM having all the various desirable properties to an ideal degree, these can be enumerated separately: 2 (i) Transition process: The process must be completely reversible and only temperature dependent. (ii) Transition temperature: Essentially an externally imposed condition that the PCM must satisfy. (iii) Heat of transition: Must be high; whether on a weight or on avolume basis will depend upon the system design. (iv) Thermal conductivity: Must be high in both phases to assist in the addition and removal of heat. (v) Specific heat: Must be high, especially in the higher temperature phase, so that storage temperatures--and hence losses--can be kept low. (vi) Density: Must be high in both phases to keep the total bulk--and hence containment costs--low. (vii) Reliability: The phase change process must be amenable to repeated cycling. Although the above criteria may often be satisfactorily met by a PCM, its utility may be obviated by the existence of some undesirable characteristic. Some of the more commonly encountered hazards are given below: (i) Material instability: Some materials may be inflammable or may decompose or explode on heating. (ii) Volume changes: Although generally small for solid-liquid transitions, they may be sufficiently high so as to make designs impractical. (iii) Corrosion: Any vessels or containers used must be compatible with the PCM's corrosive characteristics. (iv) Toxicity: Toxic substances may only be used in sealed, and consequently expensive, systems. (v) Cost and availability: Otherwise promising materials are often prohibitively expensive.
PHASE C H A N G E MATERIALS
A list of some PCM's, suitable for energy storage at temperatures between 0 ° and 100°C, is given in the Appendix. The list is not exhaustive but includes most materials actively being considered as storage media. The PCM's fall into three convenient categories, the generalised properties Iof which are given below.
208
K. K. PILLAI, B. J. BRINKWORTH
Paraffins 4 - 6, 7
Paraffins have the general formula C.HEn + 2, and all of the series having more than 15 carbon atoms per molecule are waxy solids at room temperature. Paraffins having an even number of carbon atoms are generally preferred, being cheap, more abundant and more stable. Melting points increase with increasing molecular weight, as do the heats of fusion. Paraffins, however, have very low thermal conductivities, and, within a very small physical space, can exist in all three phases. Temperature gradients are inevitable, and metallic fillers have to be used to increase the 'effective' conductivity. Aluminium honeycomb has been used successfully as a filler. 7 The properties of solid paraffins are summarised below: (a) Are moderately inflammable. 5 (b) Are non-toxic and non-corrosive. 5 (c) Are chemically stable below 500°C. 5 (d) Exhibit reliable melting and freezing. 4 (e) Have low volume change at melting ( < 5 per cent). 5 (f) Have high heats of fusion. 4 (g) Have low thermal conductivities. 5' 7 (h) Are cheap. 6 (i) Have high wetting ability, v Non-paraffin organic solids 4 - 6
This is the largest category and generalisation of properties is difficult. Some features, however, are common to most organic solids: (a) Low thermal conductivity. 5 (b) Inflammability. s' 6 (c) Varying levels of toxicity. 5 (d) Low flash points. 6 (e) Instability at high temperatures. 5 (f) High heats of fusion. 4' ~ Organic solids, like the paraffins, would require the use of metallic fillers to improve their thermal conductivity and diffusivity. H y d r a t e d salts 3 - 6
Crystalline salt hydrates have the general chemical formula X(Y)n. mH20. On heating up to the transition temperature, one of the following reactions will occur: X(Y)n. m H 2 0 ~ X(Y) n . k H 2 0 + (m - k ) H 2 0 X(Y)n. m H 2 0 ~ X(Y)~ + m H 2 0 Thus, at the transition point, the crystalline hydrate releases some water to produce either a lower hydrate or the anhydrous salt. Most hydrated salts undergo an incongruent transition, the water released not being sufficient to dissolve all the solid phase present. Thus, at the transition point, two solid phases may be present, along with a saturated solution of the lower hydrate. In such cases the lower hydrate (or the
STORAGE OF ENERGY U S I N G PHASE C H A N G E MATERIALS
209
anhydrous salt), being usually of higher density, settles to the bottom of the container, preventing complete recrystallisation upon cooling. Furthermore, many hydrates exhibit marked supercooling which has to be eliminated. Complete recrystallisation of an incongruently melting salt can be promoted, either by: (a) mechanical means (stirring, vibration, etc.) or by (b) the use of thickening agents 8 which prevent the settling of the lower hydrate. Similarly, supercooling can be avoided by promoting nucleation, either by: (a) mechanical means (cracks or pits in the container preventing the dehydration of small quantities of the original material, and these pockets then acting as nucleation sites), or by (b) the addition of small quantities of a nucleating agent. 9 The properties of salt hydrates can be summarised as follows: (a) Have high heats of transition. 6- 8 (b) Have small volume changes. 5 (c) Exhibit incongruent melting; nitrates are exceptions but these can explode on heating. 5 (d) Have relatively high thermal conductivities. 5' 6 (e) Exhibit" considerable supercooling. 3' 9 (f) Are moderately corrosive. 5 (g) Are mildly toxic. 5' 6 (h) Are relatively cheap. 3
P E R F O R M A N C E O F PCM'S AS STORAGE MEDIA
The use ofa PCM is only justified when it offers significant advantages over a storage system employing sensible heat storage. The storage capability of some PCM's, compared with that of water and rocks, is illustrated in Fig. 1. A cost comparison can only be carried out when the storage temperature levels, and insulation and containment costs have been determined. It is clear, however, that heat transfer requirements can be better met, and that losses can be reduced, with the constant temperature condition imposed by the PCM. The design of storage systems using PCM's is controlled by the input and output requirements to be met. Some of the envisaged systems are shown in Fig. 2. Clearly, the PCM acts, not merely as a storage medium, but also as a heat exchange medium between two substances. Thus, any system design must, in addition to providing the required storage capability, be capable of coping with the prevailing energy input and output conditions. The storage requirement can be stated simply as:
S>_fi"[Q,,(t)-Qou,(t)]dt
where: S = Storage capability. Q~, = Heat flux into system. Oout= Heat extraction rate.
(1)
210
K. K. PILLAI, B. J. BRINKWORTH
320
/ /
J
/ //
¢
/
/
/
/
j-
f
J 80
/
/
/ 10
2O
~ * ~ ~0~
30
60
Fig. 1. Comparison of storage capacities of various materials. Ordinate: storage capacity (kJ/kg). Abscissa: temperature excess over 20 °C (0 deg K).
t = Time. tp = Time period being considered. Equation (1) implies the obvious pre-condition that:
If, to satisfy heat requirements, the geometry of the system would have to be such that its storage capacity is insufficient to satisfy eqn. (1), the system is simply not feasible. If, on the other hand, the required system geometry provides an excessive storage capability, the cost-effectiveness will be impaired. Thus, storage capacities must be kept as close as possible to some minimum value, whilst the heat transfer
STORAGE OF ENERGY USING PHASE CHANGE MATERIALS
211
processes must be simultaneously maximised. Design optimisation studies, comparing the behaviour of different PCM's in varying system geometries, are now in hand. The evaluation process is particular to the job in hand and can only be generalised to a limited extent. Consider the schematic system illustrated in Fig. 3. For simplicity the temperature, Ts, within the PCM is assumed to be a function only o f x and t. Energy
_
_
_
~..,
o~
I
Q(t)
PCM----------~ ~ " ~
f I: Fig. 2.
::
I
(b)
:i
(c)
: :1
Heat storage systems. (a) Finned annulus containing PCM. (b) Finned cylinder containing PCM. (c) Tube banks surrounded by PCM.
is obtained from the primary fluid at some temperature T 1(x, t), and the secondary fluid is required to be at a temperature T2(x, t). At any plane, x, the temperature histories of the PCM and the two fluids will be as shown in Fig. 4. Clearly, the flow of primary fluid must be controlled so as to prevent any heat transfer to it from the store. Energy input to the PCM will thus be limited to those times when T1 > Ts. Assuming, for example, that heat transfer from each fluid is subject to a constant heat transfer coefficient, the heat flux-time curves can be plotted for each x-plane as
212
K. K. PILLAI, B. J. BRINKWORTH
shown in Fig. 5. The basic criterion for system feasibility can now be stated as:
I' (dA11tb(x)
- h da2 fl p02dt ) d x > 0
hl-~x 01dr+ do \ j,o(x) 2 dx where: h = H e a t transfer coefficient. A(x) = H e a t transfer area. ! = Length o f storage system (Fig. 3).
(3)
-
O = T - L. t,(x) = Time in 0 - tp, where 01 = 0, and ?,O~/~?t> O. tb(X) = Time in 0 - tp, where 01 = 0, and c)O~/~t < O.
Primary fluid
j
,
/.
//
."
/ ' ~
//
j"
./'1
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/"
~/
j/ "
I I
.-
.
I
.
....... . /"
/
.-
~"
. . .....
. /
//
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i
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//
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~/
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.
s ~ i d fluid Secondary Fig. 3.
/"
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.-,.
/"
/"
T2
/
/.
,."
/-
.
/
.
. ."
.. .,"
/" "
.-" "
Schematic PCM storage system.
Satisfaction of eqn. (3) implies that the envisaged geometry (specified by A l(x), A2(x) a n d / ) meets the heat transfer requirements, and that the required output can be met by storing the surplus input. The m i n i m u m storage can also be obtained from Fig. 5. Clearly, two criteria are available, as follows. (1) Based on the output requirement, the m i n i m u m storage must be capable of meeting the output for those times when the input is less than the output:
213
STORAGE OF ENERGY USING PHASE CHANGE MATERIALS
S ~ -
02 dt d x
h 2 J o d x \ J 0 02 dt + d
--IhlftodAl(\~o01dt+~:O,dt)dx 3
(4)
(2) Based on the available input which is surplus to requirements:
j dA,(j,~f'~(O~ +02)dt)dx
S > hI _ o ~ - \
(5)
r~
T.
Fig. 4. Temperature histories in PCM storage system. Ordinate: temperature. Abscissa: time.
In the ideal situation these two conditions (eqns. (4) and (5)) will coincide, giving: \
dx-
01 dt + 2 dx
0 2 dt
dx = 0
(6)
Clearly, this condition represents the situation where the surplus input is only just sufficient to provide the required output. Where this condition is not met, the larger of the two requirements, given by eqns. (4) and (5), must be adopted.
214
K. K. PILLAI, B. J. BRINKWORTH
i/:;i(!i!/
i
I
i
i¸
td I
Fig. 5. Flux-time curve at any x-plane. Ordinate: heat flux. Abscissa: time. Complications are introduced in practice by the fact that the PCM temperature, Ts, is not constant along any plane x (Fig. 3). A phase change boundary will exist at some point along this plane, and T~will be a function of both spatial dimensions and time. Heat transfer to and from the PCM will now be controlled, not by a single temperature, T~, but by the two temperatures, T~I and T~2,as shown in Fig. 6. If now: 01 = T 1 - T~l and 02 = /'2 - T~2 eqns. (3) to (5) will still hold. However, storage will now take place in three distinct modes: (1) sensible heat storage in the solid phase; (2) transitional energy storage and (3) sensible heat storage in the liquid phase. Consequently, a knowledge of the temperature distribution within the PCM is essential to the design process. For most geometries the phase change process itself allows of no analytical solutions, and
~
: :--
I liquicl~
r~
i
/
---
~
.~; W~;I- ~-._~ -~ .. T-:
-
x,t,'
1
~
~'
~
;.
LX
Fig. 6. Temperatureswithin the PCM storage system.
Y
215
S T O R A G E OF E N E R G Y U S I N G P H A S E C H A N G E M A T E R I A L S
numerical solutions, corresponding to a specific set of boundary conditions, must be used. However, the fact that these boundary conditions are, themselves, the heat transfer requirements to be met, necessitates that the design process be iterative. This process can be started by assuming the phase change material temperature to be constant at the transition temperature, and the fluid temperatures to be linear in x. The system geometry can thus be specified, and then modified in the light of the phase change material's melting behaviour, so that, eventually, both heat transfer and storage requirements are satisfied.
CONCLUSION
Phase change materials offer a convenient means of storing low grade thermalenergy within compact systems. A wide range of PCM's is available but selection is entirely dependent upon the particular situation being considered. The thermo-physical data of PCM's is now being collected, and a data bank, suitable for the selection of materials having desired combinations of properties, is being set up. While the storage process using PCM's is simple in principle, the difficulties attached to predicting their melting, behaviour have limited the production of working designs. Design optimisation studies, considering the storage and heat transfer capabilities of PCM systems, are now in hand.
A P P E N D I X 1: EXAMPLES OF PHASE C H A N G E MATERIALS FOR ENERGY STORAGE
Material name and/or chemical jbrmula
Transition temperature
Heat of transition
Type of transition
Reference
(kJ/kg)
(~c) Hexadecane C16H34 Octadecane C18H38 Eicosane
C2oH42 Polyethyleneglycol Acetic acid Stearic acid Acetamide Methyl Fumarate di-amino penta-crythritol
17
237
(iv)
4
28
243
(iv)
4, 5
37 75 62 69 81 99 68
247 146 187 199 241 242 184
(iv) (iv) (iv) (iv) (iv) (iv) (iii)
5 5 5 5 4, 5 5 4, 5
216 tri-methylolethane N a z H P O 4. 1 2 H 2 0 Na2SO4.10H20 Na2S203.5H20 Ba(OH) 2 . 8H20 LiNO3.3H20
K. K. PILLAI, B. J. BRINKWORTH 81 36 32 48 78 30
192 280 251 210 301 296
(iii) (v) (v) (v) (v) (v)
5 3 3, 4 3, 5 4, 5 3, 4, 5
REFERENCES 1. M. GOLDSTEIN,Some physiqal chemical aspects of heat storage, UN Conference on New Sources of Energy, April, 1961. 2. M. TELKES,Solar heat storage, ASME Paper 64-WA/SOL-9, 1964. 3. M. TELKES,Solar energy storage, ASHRAE Jnl (September, 1974) pp. 38~-4. 4. D.V. HALEet al., Phase change materials handbook. NASA Report, NASA-CR-61363, September, 1971. 5. R. H. PERRY and C. H. CHILTOrq (Eds), Chemical engineer's handbook (Sth edn), McGrawHill-Kogakusha Ltd, 1973. 6. F.O. ROSSINIet al., Selected values of chemical thermodynamic properties, US National Bureau of Standards, Circular 500, July, 1961. 7. E.W. BENTILLAand A. P. SCHLOSINGER,Research and development study on thermal control by use of fusible materials, Northrop Space Laboratories Report, NSL-65-16, 1965. 8. M. TELKES,Heat Storage Unit, US Patent 2677367, May, 19§4. 9. M. TELKES,Nucleation of supersaturated inorganic salt solutions, Ind. Eng. Chem., 44(6) (1952) p. 1308.
K. K. PILLAI and B. J. BRINKWORTH
Solar Energy Unit, Department of Mechanical Engineering and Energy Studies, University College, Newport Road, Cardiff (Wales)
S UMMA R Y
The use of phase change materials in energy storage systems is considered. The properties of such materials and the types of phase change they undergo are enumerated. Selection criteria are discussed and a list of some useful materials given. The feasibility of system designs is considered, and the generalised, basic requirements of storage systems are presented.
NOMENCLATURE
A h l Q S t T 0 x,y
= = = = = = = = =
Heat transfer area H e a t transfer coetficient Length o f storage system H e a t flux Storage capacity Time Temperature T e m p e r a t u r e excess C a r t e s i a n co-ordinates
Subscripts a b c, d p s 1 2
refers to when flux i n p u t begins refers to when flux i n p u t ends refer to times defined by Fig. 5 = Period = Store = P r i m a r y fluid = Secondary fluid 205 Applied Energy (2) (1976)--© Applied Science Publishers Ltd, England, 1976 Printed in Great Britain
206
K. K. PILLAI, B. J. B R I N K W O R T H
INTRODUCTION
The steadily increasing cost of fuel has now brought about a growing interest in the utilisation of low grade thermal energy. Many sources of such energy (solar radiation, exhaust gases, cooling water, etc.) are becoming increasingly attractive for heat recovery processes. The recovered energy can, however, only be put to a limited number of applications. Space and water heating systems can be operated directly, while thermodynamic cycles must be tailored to suit particular applications. The temperature levels involved mean that cycle efficiencies are inevitably low, and since the required duty is often out of phase with the availability of the recovered energy, it is necessary that cheap and efficient methods of energy storage and transport be devised. Thermal energy can readily be stored either as: (a) the sensible heat required to raise the temperature of some high heat capacity material, or (b) the transitional energy required to produce a reversible change in the physical or chemical state of some material. 1- 3 In the first category, water or boulders are often used as storage media. While such systems are both simple and cheap, they are often very bulky or excessively heavy. The unique property of phase change materials (PCM's), however, is their ability to absorb or liberate large quantities of heat at a constant temperature. Only a very small proportion of the energy stored need be in the form of a temperature gain. Thus, by selecting a PCM having a suitable transition temperature, system designs can be made more cost-effective.
SELECTION OF PHASE C H A N G E MATERIALS
There are various physical and chemical transformations that a material may undergo, accompanied either by the absorption or the liberation of heat. These transformations will all be referred to as 'phase changes', although they may not all involve physical changes of state. They are (i) Solid-gas phase change. (ii) Liquid-gas phase change. (iii) Solid-solid transition. (iv) Solid-liquid phase change. (v) Crystalline solid-liquid solution transformation. Of these, the solid-gas and liquid-gas transformations exhibit the largest heats of transition. They are, however, accompanied by very large volume changes, and the complexity Of the designs required to accommodate, them appears impractical. Solid-solid transformations have the lowest storage capability, but could be useful in specialised applications requiring a particular transition temperature. Solid-liquid melting processes involve only very small volume changes and exhibit a
S T O R A G E OF E N E R G Y U S I N G PHASE C H A N G E MATERIALS
207
useful range of heats of fusion. The crystalline solid-liquid solution transformation is almost exclusively a property of hydrated salts, which absorb heat as they dissolve in their water of crystallisation. Thermodynamically, this process is very similar to the melting process, and the heats of transition are of the same order as the heats of fusioh. These last two processes are therefore the most promising. Whilst there is no PCM having all the various desirable properties to an ideal degree, these can be enumerated separately: 2 (i) Transition process: The process must be completely reversible and only temperature dependent. (ii) Transition temperature: Essentially an externally imposed condition that the PCM must satisfy. (iii) Heat of transition: Must be high; whether on a weight or on avolume basis will depend upon the system design. (iv) Thermal conductivity: Must be high in both phases to assist in the addition and removal of heat. (v) Specific heat: Must be high, especially in the higher temperature phase, so that storage temperatures--and hence losses--can be kept low. (vi) Density: Must be high in both phases to keep the total bulk--and hence containment costs--low. (vii) Reliability: The phase change process must be amenable to repeated cycling. Although the above criteria may often be satisfactorily met by a PCM, its utility may be obviated by the existence of some undesirable characteristic. Some of the more commonly encountered hazards are given below: (i) Material instability: Some materials may be inflammable or may decompose or explode on heating. (ii) Volume changes: Although generally small for solid-liquid transitions, they may be sufficiently high so as to make designs impractical. (iii) Corrosion: Any vessels or containers used must be compatible with the PCM's corrosive characteristics. (iv) Toxicity: Toxic substances may only be used in sealed, and consequently expensive, systems. (v) Cost and availability: Otherwise promising materials are often prohibitively expensive.
PHASE C H A N G E MATERIALS
A list of some PCM's, suitable for energy storage at temperatures between 0 ° and 100°C, is given in the Appendix. The list is not exhaustive but includes most materials actively being considered as storage media. The PCM's fall into three convenient categories, the generalised properties Iof which are given below.
208
K. K. PILLAI, B. J. BRINKWORTH
Paraffins 4 - 6, 7
Paraffins have the general formula C.HEn + 2, and all of the series having more than 15 carbon atoms per molecule are waxy solids at room temperature. Paraffins having an even number of carbon atoms are generally preferred, being cheap, more abundant and more stable. Melting points increase with increasing molecular weight, as do the heats of fusion. Paraffins, however, have very low thermal conductivities, and, within a very small physical space, can exist in all three phases. Temperature gradients are inevitable, and metallic fillers have to be used to increase the 'effective' conductivity. Aluminium honeycomb has been used successfully as a filler. 7 The properties of solid paraffins are summarised below: (a) Are moderately inflammable. 5 (b) Are non-toxic and non-corrosive. 5 (c) Are chemically stable below 500°C. 5 (d) Exhibit reliable melting and freezing. 4 (e) Have low volume change at melting ( < 5 per cent). 5 (f) Have high heats of fusion. 4 (g) Have low thermal conductivities. 5' 7 (h) Are cheap. 6 (i) Have high wetting ability, v Non-paraffin organic solids 4 - 6
This is the largest category and generalisation of properties is difficult. Some features, however, are common to most organic solids: (a) Low thermal conductivity. 5 (b) Inflammability. s' 6 (c) Varying levels of toxicity. 5 (d) Low flash points. 6 (e) Instability at high temperatures. 5 (f) High heats of fusion. 4' ~ Organic solids, like the paraffins, would require the use of metallic fillers to improve their thermal conductivity and diffusivity. H y d r a t e d salts 3 - 6
Crystalline salt hydrates have the general chemical formula X(Y)n. mH20. On heating up to the transition temperature, one of the following reactions will occur: X(Y)n. m H 2 0 ~ X(Y) n . k H 2 0 + (m - k ) H 2 0 X(Y)n. m H 2 0 ~ X(Y)~ + m H 2 0 Thus, at the transition point, the crystalline hydrate releases some water to produce either a lower hydrate or the anhydrous salt. Most hydrated salts undergo an incongruent transition, the water released not being sufficient to dissolve all the solid phase present. Thus, at the transition point, two solid phases may be present, along with a saturated solution of the lower hydrate. In such cases the lower hydrate (or the
STORAGE OF ENERGY U S I N G PHASE C H A N G E MATERIALS
209
anhydrous salt), being usually of higher density, settles to the bottom of the container, preventing complete recrystallisation upon cooling. Furthermore, many hydrates exhibit marked supercooling which has to be eliminated. Complete recrystallisation of an incongruently melting salt can be promoted, either by: (a) mechanical means (stirring, vibration, etc.) or by (b) the use of thickening agents 8 which prevent the settling of the lower hydrate. Similarly, supercooling can be avoided by promoting nucleation, either by: (a) mechanical means (cracks or pits in the container preventing the dehydration of small quantities of the original material, and these pockets then acting as nucleation sites), or by (b) the addition of small quantities of a nucleating agent. 9 The properties of salt hydrates can be summarised as follows: (a) Have high heats of transition. 6- 8 (b) Have small volume changes. 5 (c) Exhibit incongruent melting; nitrates are exceptions but these can explode on heating. 5 (d) Have relatively high thermal conductivities. 5' 6 (e) Exhibit" considerable supercooling. 3' 9 (f) Are moderately corrosive. 5 (g) Are mildly toxic. 5' 6 (h) Are relatively cheap. 3
P E R F O R M A N C E O F PCM'S AS STORAGE MEDIA
The use ofa PCM is only justified when it offers significant advantages over a storage system employing sensible heat storage. The storage capability of some PCM's, compared with that of water and rocks, is illustrated in Fig. 1. A cost comparison can only be carried out when the storage temperature levels, and insulation and containment costs have been determined. It is clear, however, that heat transfer requirements can be better met, and that losses can be reduced, with the constant temperature condition imposed by the PCM. The design of storage systems using PCM's is controlled by the input and output requirements to be met. Some of the envisaged systems are shown in Fig. 2. Clearly, the PCM acts, not merely as a storage medium, but also as a heat exchange medium between two substances. Thus, any system design must, in addition to providing the required storage capability, be capable of coping with the prevailing energy input and output conditions. The storage requirement can be stated simply as:
S>_fi"[Q,,(t)-Qou,(t)]dt
where: S = Storage capability. Q~, = Heat flux into system. Oout= Heat extraction rate.
(1)
210
K. K. PILLAI, B. J. BRINKWORTH
320
/ /
J
/ //
¢
/
/
/
/
j-
f
J 80
/
/
/ 10
2O
~ * ~ ~0~
30
60
Fig. 1. Comparison of storage capacities of various materials. Ordinate: storage capacity (kJ/kg). Abscissa: temperature excess over 20 °C (0 deg K).
t = Time. tp = Time period being considered. Equation (1) implies the obvious pre-condition that:
If, to satisfy heat requirements, the geometry of the system would have to be such that its storage capacity is insufficient to satisfy eqn. (1), the system is simply not feasible. If, on the other hand, the required system geometry provides an excessive storage capability, the cost-effectiveness will be impaired. Thus, storage capacities must be kept as close as possible to some minimum value, whilst the heat transfer
STORAGE OF ENERGY USING PHASE CHANGE MATERIALS
211
processes must be simultaneously maximised. Design optimisation studies, comparing the behaviour of different PCM's in varying system geometries, are now in hand. The evaluation process is particular to the job in hand and can only be generalised to a limited extent. Consider the schematic system illustrated in Fig. 3. For simplicity the temperature, Ts, within the PCM is assumed to be a function only o f x and t. Energy
_
_
_
~..,
o~
I
Q(t)
PCM----------~ ~ " ~
f I: Fig. 2.
::
I
(b)
:i
(c)
: :1
Heat storage systems. (a) Finned annulus containing PCM. (b) Finned cylinder containing PCM. (c) Tube banks surrounded by PCM.
is obtained from the primary fluid at some temperature T 1(x, t), and the secondary fluid is required to be at a temperature T2(x, t). At any plane, x, the temperature histories of the PCM and the two fluids will be as shown in Fig. 4. Clearly, the flow of primary fluid must be controlled so as to prevent any heat transfer to it from the store. Energy input to the PCM will thus be limited to those times when T1 > Ts. Assuming, for example, that heat transfer from each fluid is subject to a constant heat transfer coefficient, the heat flux-time curves can be plotted for each x-plane as
212
K. K. PILLAI, B. J. BRINKWORTH
shown in Fig. 5. The basic criterion for system feasibility can now be stated as:
I' (dA11tb(x)
- h da2 fl p02dt ) d x > 0
hl-~x 01dr+ do \ j,o(x) 2 dx where: h = H e a t transfer coefficient. A(x) = H e a t transfer area. ! = Length o f storage system (Fig. 3).
(3)
-
O = T - L. t,(x) = Time in 0 - tp, where 01 = 0, and ?,O~/~?t> O. tb(X) = Time in 0 - tp, where 01 = 0, and c)O~/~t < O.
Primary fluid
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s ~ i d fluid Secondary Fig. 3.
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.-,.
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Schematic PCM storage system.
Satisfaction of eqn. (3) implies that the envisaged geometry (specified by A l(x), A2(x) a n d / ) meets the heat transfer requirements, and that the required output can be met by storing the surplus input. The m i n i m u m storage can also be obtained from Fig. 5. Clearly, two criteria are available, as follows. (1) Based on the output requirement, the m i n i m u m storage must be capable of meeting the output for those times when the input is less than the output:
213
STORAGE OF ENERGY USING PHASE CHANGE MATERIALS
S ~ -
02 dt d x
h 2 J o d x \ J 0 02 dt + d
--IhlftodAl(\~o01dt+~:O,dt)dx 3
(4)
(2) Based on the available input which is surplus to requirements:
j dA,(j,~f'~(O~ +02)dt)dx
S > hI _ o ~ - \
(5)
r~
T.
Fig. 4. Temperature histories in PCM storage system. Ordinate: temperature. Abscissa: time.
In the ideal situation these two conditions (eqns. (4) and (5)) will coincide, giving: \
dx-
01 dt + 2 dx
0 2 dt
dx = 0
(6)
Clearly, this condition represents the situation where the surplus input is only just sufficient to provide the required output. Where this condition is not met, the larger of the two requirements, given by eqns. (4) and (5), must be adopted.
214
K. K. PILLAI, B. J. BRINKWORTH
i/:;i(!i!/
i
I
i
i¸
td I
Fig. 5. Flux-time curve at any x-plane. Ordinate: heat flux. Abscissa: time. Complications are introduced in practice by the fact that the PCM temperature, Ts, is not constant along any plane x (Fig. 3). A phase change boundary will exist at some point along this plane, and T~will be a function of both spatial dimensions and time. Heat transfer to and from the PCM will now be controlled, not by a single temperature, T~, but by the two temperatures, T~I and T~2,as shown in Fig. 6. If now: 01 = T 1 - T~l and 02 = /'2 - T~2 eqns. (3) to (5) will still hold. However, storage will now take place in three distinct modes: (1) sensible heat storage in the solid phase; (2) transitional energy storage and (3) sensible heat storage in the liquid phase. Consequently, a knowledge of the temperature distribution within the PCM is essential to the design process. For most geometries the phase change process itself allows of no analytical solutions, and
~
: :--
I liquicl~
r~
i
/
---
~
.~; W~;I- ~-._~ -~ .. T-:
-
x,t,'
1
~
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~
;.
LX
Fig. 6. Temperatureswithin the PCM storage system.
Y
215
S T O R A G E OF E N E R G Y U S I N G P H A S E C H A N G E M A T E R I A L S
numerical solutions, corresponding to a specific set of boundary conditions, must be used. However, the fact that these boundary conditions are, themselves, the heat transfer requirements to be met, necessitates that the design process be iterative. This process can be started by assuming the phase change material temperature to be constant at the transition temperature, and the fluid temperatures to be linear in x. The system geometry can thus be specified, and then modified in the light of the phase change material's melting behaviour, so that, eventually, both heat transfer and storage requirements are satisfied.
CONCLUSION
Phase change materials offer a convenient means of storing low grade thermalenergy within compact systems. A wide range of PCM's is available but selection is entirely dependent upon the particular situation being considered. The thermo-physical data of PCM's is now being collected, and a data bank, suitable for the selection of materials having desired combinations of properties, is being set up. While the storage process using PCM's is simple in principle, the difficulties attached to predicting their melting, behaviour have limited the production of working designs. Design optimisation studies, considering the storage and heat transfer capabilities of PCM systems, are now in hand.
A P P E N D I X 1: EXAMPLES OF PHASE C H A N G E MATERIALS FOR ENERGY STORAGE
Material name and/or chemical jbrmula
Transition temperature
Heat of transition
Type of transition
Reference
(kJ/kg)
(~c) Hexadecane C16H34 Octadecane C18H38 Eicosane
C2oH42 Polyethyleneglycol Acetic acid Stearic acid Acetamide Methyl Fumarate di-amino penta-crythritol
17
237
(iv)
4
28
243
(iv)
4, 5
37 75 62 69 81 99 68
247 146 187 199 241 242 184
(iv) (iv) (iv) (iv) (iv) (iv) (iii)
5 5 5 5 4, 5 5 4, 5
216 tri-methylolethane N a z H P O 4. 1 2 H 2 0 Na2SO4.10H20 Na2S203.5H20 Ba(OH) 2 . 8H20 LiNO3.3H20
K. K. PILLAI, B. J. BRINKWORTH 81 36 32 48 78 30
192 280 251 210 301 296
(iii) (v) (v) (v) (v) (v)
5 3 3, 4 3, 5 4, 5 3, 4, 5
REFERENCES 1. M. GOLDSTEIN,Some physiqal chemical aspects of heat storage, UN Conference on New Sources of Energy, April, 1961. 2. M. TELKES,Solar heat storage, ASME Paper 64-WA/SOL-9, 1964. 3. M. TELKES,Solar energy storage, ASHRAE Jnl (September, 1974) pp. 38~-4. 4. D.V. HALEet al., Phase change materials handbook. NASA Report, NASA-CR-61363, September, 1971. 5. R. H. PERRY and C. H. CHILTOrq (Eds), Chemical engineer's handbook (Sth edn), McGrawHill-Kogakusha Ltd, 1973. 6. F.O. ROSSINIet al., Selected values of chemical thermodynamic properties, US National Bureau of Standards, Circular 500, July, 1961. 7. E.W. BENTILLAand A. P. SCHLOSINGER,Research and development study on thermal control by use of fusible materials, Northrop Space Laboratories Report, NSL-65-16, 1965. 8. M. TELKES,Heat Storage Unit, US Patent 2677367, May, 19§4. 9. M. TELKES,Nucleation of supersaturated inorganic salt solutions, Ind. Eng. Chem., 44(6) (1952) p. 1308.