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Performance studies of a solar energy storing heat exchanger
Solar Energy Vol. 41. No. 6. pp. 503-512. 1988
0038-092X/88 $3.00 + ,00 Copyright ~ 1988 Pergamon Press plc
Printed in the U.S.A.
PERFORMANCE STUDIES OF A SOLAR ENERGY STORING HEAT EXCHANGER DAVID L. BUSHNELL* Physics Department, Northern Illinois University, DeKalb. IL 60115, U.S.A. Abstract--The design, construction, and performance of a solar energy storing heat exchanger is presented as a step toward a solar cooking concept. The solid-solid transition of pentaerythritol is the principal mechanism for energy storage. The methods for describing the system performance are explained and applied to a test system containing a controllable replacement for the solar input power. This first stage of the project will be followed by another in which the heat exchanger is connected to a concentrating array of CPC cylindrical troughs. Although a size appropriate to commercial cooking may prove easier to design from the point of view of economics in the United States, the system discussed herein is sized for domestic use and addresses the question of what solar collector area and PCM mass are needed in order to provide adequate energy for several family-size meals with sufficient storage to cook at night and one or two days later. The performance is described from efficiency measurements and the determination of a figure of merit.
1. INTRODUCTION
tubes. Ultimately, this unit is to be located in a thermally efficient oven. Although we have constructed such an oven, it is being tested separately and used for a test bed to measure high-temperature insulation conductivities. The simulation test system used for the performance measurements is shown in Fig. 3. Since the storage performance of the heat exchanger is a critical element in determining the feasibility of developing a useful solar oven, we have concentrated on developing a measuring method that can be used on a variety of heat exchanger designs. For clarity, we have picked the simulation arrangement shown in Fig. 3. This allows simplicity and control of the input power. We leave for another study the measurement of extraction rates for this heat exchanger and alternative designs. Based on these results, we are preparing to test run the system with the solar collector and oven as depicted in Fig. 1. In designing this system, preliminary studies of the literature[2-12] on phase change storage materials were conducted, the results of which are presented in Table 1. In selecting a heat transfer fluid, water was ruled out to avoid the problems of a high-pressure system. The solar group at Argonne National Laboratory[ 13] had some experience selecting oil for high-temperature solar applications and told us about the therminol from Monsanto. One of the therminol oils could function with rather low viscosity and high temperature allowing its use in this application in place of water. The higher-temperature application, and the lower conductivity of the oil compared to water, made it necessary to modify the shelf model CPC solar collector obtained from Energy Design Corporation. The plumbing of the flow line uses half-inch diameter copper tubing and brass compression fittings to install the pump. Selection of a pump proved to be a difficult task because there are very few pumps
This article presents the results of a study of the performance of an energy storing heat exchanger designed for use with a high temperature solar collector and a system to provide heat for a cooking oven. It has been suggested by Robert H. Socolow in Physics Today[l] . . . . ~that more efficient cooking technology could permit enormous energy resources to be freed for redeployment in other tasks." Solar energy could make an important contribution but its limitations, due to cloudiness and nighttime demand, need to be removed if widespread application in the world is to be achieved. The storing heat exchanger described in this article is a prototype to test the concept of energy storage for application to solar cooking and it employs a phase change material (PCM) called pentaerythritol. It is a heavy (molecular weight 136.15 g) alcohol with a solid-solid phase transition at 183°C (362°F) and a solid-liquid phase transition at 259°C (498°F). The former transition provides about 10 times more energy absorption than the latter and allows for transition cycles having only solid storage material. 2. THE SYSTEM In order to be able to do effective oven cooking, it is necessary to obtain temperatures between about 150°C (300*F) and 260°C (500°F) that require concentration of the solar insolation. The complete system is described in Fig. 1. It consists of a compound parabolic concentrating trough array, a closed loop pumping line containing oil (therminol 60 from Monsanto), and an energy storing heat exchanger. The heat exchanger, shown in Fig. 2, has a rectangular geometry and contains phase change material and fin *ISES member. 503
504
DAVID L . BUSHNELL
Colleclor Manifold
Top view of C P C
I
o
Evacuated IF_. ~ Double Glass Receiver I Tube I~
/// iii
Wall
outside
i
Manifold .,_l
L~
L__~_
Y// /// //~
t / // M
side r~_~
Fig. 3. Oil distribution and insulation.
Fig. 1. Solar energy storage system. manufactured having low enough pumping speeds (~4 liters/min) and high temperature capability (to about 300°C (572°F)). The pump that we use for the work originally failed at 227°C (440°F), but, following some adjustments, that same gear pump is now operating at temperatures over 250°C (482°F) for 12-h periods of time repeatedly with no difficulty. 3. S O L A R E N E R G Y S T O R I N G
HEAT EXCHANGER
3.1 Design criteria In order to determine the feasibility of the energy storing solar oven concept, it is essential to design a heat exchanger of high efficiency that is integrated with a storage material whose specific storing capacity (energy per unit mass) is very large. This heat exchanger should meet the following criteria: (1) rapid heat transfer from input to storage, (2) effective defense against heat loss from storage, (3) high efficiency, (4) easy extraction of heat from storage, and (5) a modest size both of mass and volume. We have designed, constructed, and tested a prototype energy-storing heat exchanger. From examination of the results of the test measurements presented below, you will be able to see that answers to some sizing questions and clues for alternative de-
/ ~
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Heat Exchanger
Reflector,,,. I ~'~
///
~, o') ~ (j.,
Heater Tank
Steel vessel
.~'-"- - - :,J___L
f--I
Fin tube
[' ~ 10.8 cm
Fig. 2. Heat exchanger and fin tube.
signs having promise of improved performance are obtained. From the tests, we have obtained information about rates of heat transfer, amount of energy stored, time of energy input, and the time during which energy is held in storage. A figure of merit is defined to characterize the success of the design in satisfying the first three of the above design criteria. 3.2 Sizing In our location with latitude 41.5 °, it xs possible to have solar insolation intensity on a vertical aperture in winter as high as 800 W/m-" and a 4-h average of 400 W/m-'. Our collector aperture is 24 ft" or about 2 m ~', so it would be feasible under the best of conditions to collect at an 800-W rate for 4 h. If we could maintain a collector efficiency of 50%, we could feed the heat transfer oil at a 400-W rate on the average over the 4 h. It should be noted that a 2-m 2 collector implies a system sizing for domestic rather than commercial use. The mass of pentaerythritol needed to take the corresponding energy is given by m = Ptc/L,, where P is the power in watts entering the oil stream, tc is the time of collection, and Ls, is the latent heat for the solid-solid phase change transition from solid I to solid II. Since L,, = 72 cal/g, the mass is about 20 kg. The containment for this mass was sized to hold the heat transfer surfaces that are in the form of standard home heating fin tubes. Figure 2 shows the steel containment box and the fin tubes located inside. The amount of mass ultimately recommended for this level of power input should be larger than the above estimate by enough to prevent the temperature of the solid II structure from going far into the high temperature sensible heat range, thus avoiding the melting point. 3.3 Construction Since the heat transfer oil could be expected to go to temperatures over 260°C (500°F) on occasion, it was necessary to braze the copper to the exit holes in the end walls of the steel containment box. The steel thickness chosen (0.8 mm) was not quite enough to eliminate wall buckling caused by seam welding and wall bulging caused by the mass loaded into the
Solar energy heat exchanger
505
Table 1. Some prospective phase change materials for thermal storage
Material PCM Pentaerythritol Adipic Acid 2,2-Bis (hydroxymethyl) proprionic acid Hydroquinone 0.5 NaOH/0.5 KOH K-Salt (0.5 NaNO 0.35 KNO~, 0.15 NaNO_,) Draw salt (0.5 NaNO3, 0.5 KNO~)
Reference 2, 3 2
Mole weight (g) 136.15
3 4. 5
Transition temperatures °C (°F)
AHss
..XHsL
Tss
TsL
(cal/g)
(cal/g)
1.107 a 1.075 ~
184 (363)
258 (496) 152 (306)
72.5
8.80 59.6
1.72 1.328
153 (307)
195 (383) 172 (342)
68.6
6.5 58.8
Density p (g/ml)
170 (338)
6 1.89
7 7
Thermkeep
2, 8, 9
Anthracene LiNO3 Solder
2, 5 10. 11 12
pAHss (cal/g) 80.3
118
p..XHsL (cal/g) 9.74 64.1 11.0
64
199 (390)
1.87
2.060 a 1.85 68.94
234 (453) 293 (559)
1.283 2.38
227 234 293 218 252 183
(-W,O) (453) (559) (424) (486) (361)
98 38.5 87.8 11
49.4 207
aOur measurement. box. Both of these effects were too small to cause any significant difficulty. The fin tubes are connected in series and the manifold for distribution is on the outside rather than the inside of the box for ease of construction. The latter decision was made at the expense of performance since one could expect that heat losses would occur from the manifold. Indeed, we have found that the test results indicate about a 70% efficiency so that the insulation around the manifolds held the manifold loss to about 30% (line losses are included in the heater efficiency discussed later). Loading the box with the solid pentaerythritol powder required melting it in batches of about 5 kg amounts to pour it into the box to allow a complete distribution among the fins and tubes. After placing 20.8 kg into the box, it appeared to be full. Later, during our test measurements, we found there were cavities so we remelted and added more mass to completely fill the box and cover the fins. The final mass of pentaerythritol became 27.3 kg and the steel containment vessel and fin tubes had a mass of 7.4 kg for a total of 34.7 kg. The steel containment box is connected to the oil supply tank (5.7 liters) by two 1.27 cm (0.5 in.) diameter copper tubes of length 43 cm (17 in.) running horizontally. The return line enters the supply tank near its top and the source line enters about 20 cm (8 in.) lower near its bottom where the 800-W hotplate heater coil is located. The circulating pump is located in the lower line. The system has no pressure since the return line spills into the surface of the oil in the supply tank (see Fig. 3). Most of our data were obtained using a high-temperature, high-density, semirigid insulating fiber tightly formed around the heater tank and the two supply lines to a nominal thickness of 5 to 10 cm. The heat
exchanger containment box had an insulation thickness of 10.2 cm (4 in.) surrounding all sides and completely enclosing the manifolds. This insulation has a conductivity of 0.059 W / m K (0.41 Btu i n / h r if:°F) at 204°C (400°F) and is usable to 704°C (1300°F). It goes under the name Fibrex 1300 block and has a listed density of t77 k g / m 3 (11 lb/ft~). We also used a high-temperature, high-density, fiberglass insulation called Insul-Quick for some of the experiments. Its upper limit temperature is 427°C (800°F) and its conductivity about 0.058 W / m K . 3.4 Phase change material The various possible materials available for energy storage at temperatures near 200°C (392°F) are listed in Table 1. The choice of a material must be based on the transition temperature, the latent heat of transition, the density, and other considerations such as toxicity, corrosiveness, and hydrogenation. One additional feature has to do with the type of phase change. We chose pentaerythritol (CsHl,,O4) primarily because it has a large solid-solid transition energy but also because we would not have to design for liquid containment or for hazardous material. It has little or no toxicity[3]. This allowed us to leave the containment unsealed using either a loose lid or no lid at all. There are two low-cost grades of pentaeD'thritol. One is called a tech grade ( - 8 8 % pure) and the other, which we are using, is called a pure grade ( ~ 9 8 % pure and $1.60/kg). The 27.3-kg of material cost $44. Our experiments both by design and on several occasions by accident liquified small portions of the pentaerythritol with no apparent ill effects on its thermal characteristics. We have full cycled a small sample ( ~ 2 0 0 g)
506
D A V I D L . BUSHNELL
completely 10 times with no ill effects thermally. By full cycle we mean a temperature increase through the solid-solid phase change, the melting phase change, and the boiling phase change, followed by a decrease to the initial temperature. Our large mass experiments described below cycled the material 13 times through the solid-solid transition. Several of these experiments led to complete melting and partial evaporation of the material. No thermal degradation has been detected. Cycling experiments having over 700 cycles done by the Solar Energy Research Institute[7] revealed no significant physical changes. In the case of the 98% pure material, the remaining 2% is a dimer of pentaerythritol. There is, therefore, no expectation of degradation of physical properties resulting from repeated charge-discharge cycles.
4. H E A T E X C H A N G E P E R F O R M A N C E MEASUREMENTS
The theoretical analysis of this system suggests that with steady-state temperatures around the flow loop and under the assumption of no line losses, the performance would be independent of pumping speed and the system efficiency would be strongly dependent on the performance of the heat exchanger. Figure 4 shows a system schematic diagram to help depict these ideas. In that figure, G~ !s the global insolation (irradiance in W/m") and Q~ is the heat rate leaving the collector receiving surface and entering the heat transfer fluid. Then we have
(~ = "q,.AG~
(1)
where "qc is the collector efficiency and A the collector aperture area. If the line losses are zero as depicted, then Qc = Q~x where Qe, is the heat rate entering the heat exchanger. Also,
(~ex =rhoCo(Oi - 0o)
(2)
where tho is the mass flow rate of heat transfer oil, Co is the specific heat of the oil, and 0~ and 0,, are the input and output oil temperatures at the heat exchanger. In our test measurement, we replace the solar collector with an electric submersion heater located in the bottom of a 5.7-liter (1.5 gal) cylindrical supply
=
/
, ,Heat JExchan(er '
O .... :0
To
. I Collector
m
L._)
....
~
<
,
Fig. 4. System schematic.
&
tank (see Fig. 5). The heater power simulates the solar input power given by AG r We define our test system efficiency ('q,y) by the relation "q,y = (2¢,,/P,.
= rhoCo(O,
-
Oo)/P~.
(3)
where P~. is the power input provided by the electric heater. Energy storage first occurs as sensible heat raising the PCM temperature to the transition temperature. The transition occurs at about constant temperature followed by another sensible heat storage. A typical example of this heat storage process is shown in Fig. 6. A system efficiency can be defined for the sensible heat ranges as follows:
"q,y = MC(T)(AT/At)rPg I
(4)
where C(T) is the average specific heat of the storage material at temperature T, M is its mass, and (AT/ At)r is the slope of the heating curve (T versus t) at temperature T. Similarly, for the efficiency during the transition we define
~sy
=
,~'IL/Pi,
(5)
where M is the mass transition rate from solid I to solid II and L is the latent heat. Our only way of obtaining ML is from the heat extraction rate described by eqn (2). Measurement based on eqn (3) will be called the flow method and that based on eqn (4) the slope method. A performance test is designed so that T~, To, 0, and 8o are measured by thermocouples and recorded frequently during both heating and cooling. The output of thermocouples located inside the storage medium are also recorded while the system is heated up to the melting point, at which time the power is shut off both to the heater and to the circulating pump. As a practical matter, we define a "temperature range of interest" for the phase transition from solid I to solid II. Therefore, we measure the time to raise the storage medium from 171°C (340°F) to 193°C (380°F) and label it as heat charging time or input time, t~,. This contains two small sensible heat contributions to storage and one latent heat contribution. We also measure the time of cooling from 193°C (3800F) to 1710C (340°F), and label it the time heat is held in storage or storage time, tst. Two slope methods are used to measure the system efficiency, "q,y, using eqn (4). One method employs the average AT/At at 171°(2 (340°1) and at 193°(= (380°F) obtained from the sensors placed in the pentaerythyitol. The other method employs the slope of the average of 0o and 0~. In Fig. 6 we see a typical response of a thermocouple in the PCM. The 0o and 0~ curves are very similar in shape to the PCM response since these points are thermally well coupled to the PCM mass. For these methods we compute an average specific heat ((C)) for the total storage mass at both 171°C (340°F) and 193°C (380°F) from the
Solar energy heat exchanger
507
StoringHeatExctlanger f
,! PentaerythritolPCM Insulatingenvelope Fig. 5. Heat exchanger test system. equatio n
(C)=~i m,Ci/~m,
(6)
Using three terms where subscripts b, p, and o stand for box, pentaerythritoi and oil, respectively, we have
(C) =
mb(C)t, + mpCp + moCo
(7)
m b + mp + mo
Here the m o is that portion of the heat transfer oil mass that is always located inside the fin tubes, and (C)b is the average specific heat of the steel box and the fin tubes that are made of copper tubes and aluminum fins. When power input is high ( - 8 7 0 W), the first method fails at 193°C (380°F) because the number of sensors (usually six) sampling the A T / A t for the mass in the box is too small to obtain a good average. The high power causes steep spatial gradients at many points and also localized spots of liquid. As a result, the distribution of slopes (AT/At) is widened and a
Power 250 I-
Off
larger sampling is required to get a good average A T / At. If some of the cooler spots are not sampled, the average can be statistically weighted to very high slopes leading to impossibly high efficiency results. The AO/At of the heat transfer oil is a reliable measure of the average slope for the whole mass and so method 2 is used exclusively when adequate sensor sampling is impractical. The slope method cannot be used to determine the efficiency during the phase change transition. The flow method can be used at all temperatures, and its results can be compared with those from the slope method both at temperatures above and below the transition temperature. In order to obtain a more accurate flow calorimeter measure of the system efficiency during the latent heat process, " % ,L), we placed three thermocoupies at both the flow line input and output of the heat exchanger and ran the pump speed as low as feasible to obtain a maximum temperature difference, 0r - 0o. Figure 7 shows two examples of complete heating-cooling curves for both a poorly insulated case and a well-insulated case. The system efficiency ('qsy) can be defined in terms of a heat exchanger efficiency (rl,~) times a heat source efficiency ('qh). The heat exchanger factor includes the effect of the delivery lines. We define it as the ratio of the heat storing rate to the heat rate supplied by the source to the distribution lines. It reduces to -q<, = ( o i -
l
171°C
2°° fLg?-*c-.--/Z--~-
/
//,:
"
//mlnn++
\
79S*'c ---, . ~
i
i
100 I /
curve
!
,.,
-'-I
I/ 2
4
6
8 10 12 Time (hours)
14
Fig. 6. Typical PCM heating curve.
16
7",)
(8)
The "qh factor is the heater source efficiency for the test system, whereas it is the solar collector efficiency in the real solar case. In the test system it is given by Xlh = t h o C o ~ Z / P i n
'
~1
Oo)/(To -
(9)
where AT = To - Ti Then the system efficiency as defined above agrees with eqn (3). The typical response of the system during heating as seen in Figs. 6 and 7 shows a slope (dT/dt) that decreases as the system approaches the temperature for the latent transition from solid I to solid II. This slope decrease is primarily due to the increase of the pentaerythrital specific heat with temperature, so that the product C(AT/At) remains rather constant. How-
508
DAVIDL. BUSHNELL
I.
~ ] Cooling l• Heating
Good Insulation
42°1:
.
.
.
300,,
~~
I• ,,
6
[
10
Heating ~-
tst=l 6.5~,,,, 14
300 t ..... 4
"
p
, . . . . . . . . . 18 22 26
-=
~Poor Insulation
t,,~ _~,.1
,150
> Cooling
....... 340 i1~._~
/
.
oU.. 340 I~,._..I -"
/
I=
ts,=10 h
%
200 ~[175
, ....... ~ ~ T ~ T r ~ f I J 4150 8 12 16 20 24 Time (hours) Fig. 7. Heating-cooling curves.
ever, we know that some points in the exchanger convert earlier than others, so there is no precise time definition for the onset of the transition. Some regions of mass will be entering a constant temperature condition while others are still undergoing sensible heat storage and a temperature vs. time slope. As the converted mass fraction shifts, the average slope will decrease toward zero. After the completion of the transition, sensible heat storage continues to raise the temperature and simultaneously the specific heat of the PCM varies going through a local minimum before a rapid rise[3]. All these higher-temperature specific heats are greater than before, and so the after phase transition slope is less than the before phase transition slope (see Fig. 6). The heat rate during transition is obtained from (~L = rhoCo(Oi - 0") where 0" is the heat exchanger outflow temperature corrected for the radial oil temperature gradient resulting from streamline flow. The data obtained from a heating test designed to more clearly define the four temperatures (To, T~, 0~, 0o), revealed that 0~ - 0o was somewhat larger than To - T~. More important, when the oil slope method (eqn (4)) was used, we obtained a system efficiency of 0.65, whereas the flow colorimetry method (eqn (3)) gave "rl,y = 1.4. This could only mean that 0~ 0o was much too large. The explanation is that 0o is severely depressed due to the pentaerythritol absorbing heat from the outer layers of flowing oil and very little from the inner regions. Thus, the outer temperature, as measured by a sensor in contact with the outer surface of the tube, is much cooler than the inner temperature and therefore less than the crosssectional average temperature. The measurement of temperature distribution along the return flow line revealed the size of the effect just described. In Fig. 8 we see that as the oil flows around a 90 ° turn into a constriction and a smaller pipe where some turbulence may be formed, the oil temperature rises at point b as hot inner portions of the oil stream mix with the cooler outer portions. As the oil continues its flow and leaves the region of heavy insu-
lation near the heat exchanger and enters the return pipe region of lesser insulation, it cools. The rise in temperature toward Ti is due to a small direct heating from the heater along the copper tube wall in the opposite direction of the oil flow. This type of data allows us to correct 0o upward to 0o-the value at point b. If provision is made in the fin tube design to induce turbulence, we should see some improvement in efficiency and ease of defining and measuring 0o. 5. RESULTSAND CONCLUSIONS The measurements of the performance of our prototype design are summarized in Tables 2 and 3. We have reported system efficiencies measured at three appropriate temperatures for each complete run. The low temperature, designated "1o" in Tables 2 and 3, is far enough below the latent transition temperature 183°C (362°F) so that all pentaerithrytol mass is undergoing sensible heat absorption. The high temperature, designated "hi" in Tables 2 and 3, is similarly located above the transition temperature. The third temperature is the transition temperature, designated L for latent, and 0i - 0o is taken in the middle of the time interval to minimize the possibility that there is any mass undergoing sensible heat absorption. This allows us to use both the slope and flow methods for the two sensible cases while only using the flow method in the transition case. Our results suggest that the system concept is feasible for domestic application. In support of this notion, we note that the prototype system under good solar conditions could be thermally loaded by increasing the temperatures across the temperature range of interest (from 171°C (340°F) to 193°C (380°F)) in less than 2 h (see the ti, column in Table 3) with a system efficiency of about 50%. The contributing efficiency from the heater (solar collector simulator) in the latent range fluctuated somewhat from run to run averaging 0.65, whereas the heat exchanger had a rather steady average efficiency in the latent range of
509
Solar energy heat exchanger
484
0; ~
T,
Pump
250
480 476
245
47; T(°C)
T(OF) 46{ 240
400 , , , , . 456
-
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'
~
~
Set=2.0 i b ~
LL~452
/
~.,.q
/F
N -
10 I_.-,
20 Centimeters
•
I
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i
J
235 k,
30 40 ~/~//7//7/7"//--~//-~/~ y / ~ / ~ / / ~ nsu at on ~////~
stee,Heat::~::er;il ~l "It
Fig. 8. Oil return line temperature distribution.
0 . 6 9 . It is easy to i m p r o v e the heat e x c h a n g e r efficiency s o m e w h a t with better design. H o w e v e r , it may be difficult to m a i n t a i n a solar collector e f f i c i e n c y o f greater than 6 0 % . T h e e x p e c t e d heater e f f i c i e n c y red u c t i o n with i n c r e a s e d t e m p e r a t u r e s h o w s up clearly in the w e l l - m e a s u r e d runs (such as run 17) and this
e x p e c t a t i o n is c o n s i s t e n t with all runs within their ranges o f error. This high t e m p e r a t u r e trend is larger for s o m e runs due to a failure to m i n i m i z e the small heat losses f r o m lost oil v a p o r and small p u m p leaks. O v e r h e a t i n g the s y s t e m a b o v e 193°C (380°F) to a r o u n d 210°C (410°F) requires additional hours o f
Table 2. System efficiency results System efficiency (-%) Lo range Input power Run (watts) 1' 2' 3' 5 6 7 11 b 12 b 13~ 14 15c 16d 17"
870 870 870 870 870 955 870 870 870 870 590 870 835
th(L)(g/s) 50 50 50 47 47 47 16 16 50 69 77 15 14
Maximum To C°(F°) 215 226 232 265 256 270 206 250 255 258 258 250 249
(420) (440) (450) (509) (493) (518) (403) (483) (492) (496) (496) (482) (481)
Slope (eqn (4)) 0.28 0.44 0.38 0.49 0.51 0.51 0.53 0.55 0.52 0.47 0.50 0.50 0.53
Flow (eqn (3))
Latent range Flow (eqn (3))
Hi range Slope (eqn (4))
Flow (eqn (3))
0.18 0.35 ± 0.03 ± 0.04
(0.49) f (0.51) f
.4- 0 . 0 4
± 0.04 ± 0.04 -- 0.03 +-- 0.03 - 0.03 --- 0.03 - 0.02
(0.51) f
0.39 ± 0.06 0.43 -- 0.06 0.47 -- 0.06
0.34 0.37 - 0.05
0.54 -- 0.02 0.53 -- 0.07 0.48 ± 0.08
0.46 ± 0.02 0.47 ± 0.07 0.45 ± 0.08
0.41 ± 0.04
0.52 ± 0.03 0.54 ± 0.02
0.43 ± 0.02 0.47 - 0.02
0.42 --- 0.05 0.38 --. 0.02
0.39 ± 0.03
"Runs not fully instrumented. Inferior insulation and low peak temperature. ~Run terminated prior to completion of the solid-solid transition following return line temperature gradient measurement. CLow power input and high pumping speed leads to AT's being too small to measure accurately so that calculation of the system efficiency by the flow method (eqn (3), ~sy = (ritoCoao/Pi.)) is too uncertain. *I'his run was the most accurately measured to this point but has mass reduced roughly 20% due to overheating in run 15 and earlier runs. Top fin tube completely exposed. *Mass lost in earlier runs restored for this run. Also, oil-soaked heater insulation was replaced as well as heat exchanger insulation. More sensor redundancy and slower pumping speed give most precise data. fValues from slope method used in flow calculation to find a A0 to be used in the ~iatent" flow calculation. These runs had only one sensor for each temperature and no data on return line temperature distribution.
870 b 87@ 870 ' 870 870 955 870 870 870 870 590 870 835
Run
I 2 3 5 6 7 II 12 13 14 15a 16" 17'
50 50 50 47 47 47 16 16 50 69 77 15 14
ih(L) (g/s)
215 (420) 2 2 6 (440) 232 (450) 265 (509) 256 (493) 270(518) 206 (403) 250 (483) 255 (492) 258 (496) 258 (496) 250 (482) 249 (481)
Maximum 7",, C°(F ")
0 . 5 7 "- 0 . 0 5 0.68 ± 0.05
0.63 ± 0.04 0.71 --- 0 . 0 4
0.72 ± 0.04 0 . 6 7 +- 0 . 0 4
0 . 8 4 -+ 0 . 1 6 0 . 7 8 --+ 0 . 1 4
High range
0.74 ± 0.20
0 . 6 5 -+ 0 . 1 2 0.73 + 0.15 0.73 ± 0 . 1 4
Latent r a n g e
0.69 ± 1,).1,)4 0.68 ± 0.1,)4 0.69 + O. 16 0.65 ± O. 16 0.65 ± 0.25 0.71 ± 0 . 2 5
0 . 6 6 --- 0 . 1 2 0 . 8 5 - O. 16 0.75 ± 0.14
Low range
E x c h a n g e r e f f i c i e n c y "~,.~ (eqn (8))
0.71 -+ 0 . 0 5 0 . 8 0 -+ 0 . 0 6
0.78 -+ 0.06 0.77 ± 0.1,)9 0.73 ± 0.12
1,).74 ± (I.08 (I.61) ± 0 . 0 8 0.62 - 0.07
L o w range
0.68 -+ 0 . 0 4 0 . 6 6 -+ 0 . 0 4
1,,I.68± 0.04 0.73 -+ 0.09 0 . 6 8 ± 0.11
0.59 ± 0.07 1,1.58 + 0 . 0 7 0.65 ± 0.07
Latent range
0 . 6 5 --- 0 . 0 4 0 . 5 7 ± 0.03
1,).61 -'- 0 . 1 0
1).59 --. 0.07 0.61 ± 0 . 0 6
H i g h range
H e a t e r e f f i c i e n c y ",]h (eqn (9))
4.2 2.5 3.3 1.3 1.3 1.0 1.4 1.6 1.3 1.4 2.8 1.2 1.7
t,,
13 1I 11 20
10 16 17 18 17 16
t,,
Charging and holding times"
24
20 20
27 24 24
12 18
t,,,
"t,,,, is the e n e r g y h o l d i n g t i m e m e a s u r e d from the t i m e that the input p o w e r is turned off until the t e m p e r a t u r e d r o p s to 171 ° C. t,, and &, are e n e r g y input and storage t i m e s , r e s p e c t i v e l y , as m e a s u r e d b e t w e e n t e m p e r a t u r e 171 ° C (340 ° F) and 193 ° C (380 ° F). "External heater in run n u m b e r I and significant p u m p leak. "Significant p u m p leak d u r i n g these runs. d25% o f the P C M m a s s w a s lost d u r i n g this run, also the AT's w e r e ttx) s m a l l to m e a s u r e a c c u r a t e l y so n e i t h e r ~ , = AO/AT nor ",q,, = t}JCAT/P,, were calculable. ' T h i s run was m a d e with 2 5 % o f the P C M m a s s lost and one fin tube c o m p l e t e l y e x p o s e d . fThe lost mass w a s restored and new i n s u l a t i o n installed. S m a l l h i g h t e m p e r a t u r e p u m p leak l o w e r e d 1],,.
Input power (watts)
T a b l e 3. Heat e x c h a n g e r test results
-r
z
t"
5
~7 ). <:
O
Solar energy heat exchanger
511
PCM = 36.32 kg Pump Setting 2.0 (r~ (L) = 14 gm/s at 183 °C) P~. = 835w
I O0
80
E(D
~'-"'1'-~.-
60 03 O-
.--O- "/.
~.. ~
-rl,x
"" rib
40 rlsy~t.~ = rl,,rlh 20 I
I
I
I
125
150
175
200
PCM Temperature (°C) Fig. 9. Efficiencies vs. average PCM temperatures.
collection but not totaling more than 5 h. This increases the total storage time (to,) as measured from the time when energy collection is terminated by as much as 8 h for a total of as much as 27 h. (See the last column of Table 3.) If 50% more mass is used with reduced surface to volume ratio in the heat exchanger exterior containment surfaces and a modest improvement in insulation, a 40-h storage holding time seems attainable with only small additional expense. The latter because the t~, is only about 2 h - - o n l y half of the design sizing time--so no new collector area is needed to charge the extra mass. We can note from Table 3 that a tst/ t~, ratio of at least 10:1 is achievable with this design so if ti, is 4 h, then with adequate mass to prevent melting, 50 h of storage (tst) could be expected. The next design will employ smaller fin tubes but use twice as many tubes. The manifolds on either end will be taken to the interior, contiguous with the PCM material. Even with reduced diameter tubes, we are considering installing turbulizers in the fin tubes for better heat transfer from the center portions of the oil stream in a fin tube. Our measuring methods require larger temperature differences for good precision, and so we must either pump slowly or increase the power input or both. Also, thermocouple redundancy is important for getting good statistics on the four oil temperatures needed to measure the heat exchanger contribution to the system efficiency. Run numbers 16 and 17 listed in Tables 2 and 3 contained four thermocouples for 0o and 0i, and three for To and T,. The low pumping speed for those runs produced temperature differences of about 18°(] (32"1=) for To - T,-, and 140C (25"F) for 0~ - 0o. Whereas at the moderate speed these differences were only about 6°C (11°F) and 40C (8°F), respectively (runs 5, 6, 7, and 13). The highest pumping speed with lowest power (590 W), yielded about 3°C (5°1=) and 2°C (4°F), respectively. Our pump cannot be run slower and
maintain stability, so we will increase the power input in the future tests. Pump calibrations revealed that as the temperature increased and the oil viscosity diminished, the volume flow rate decreased. An 11% reduction in the angular velocity of the pump was observed as the temperature increased from room temperature to 267°C (480°F). Note that the amount of power specifically required to overcome flow resistance in the test system and also in the expanded plumbing of the real solar system is significantly less than 1 W ( - 0 . 1 - 0 . 0 0 1 W in our temperature range). It is feasible to employ an electric motor-pump combination as small as a few watts to handle this system, provided the high viscosity start up problem is resolved. A high-torque, low-speed motor performance is needed when the system's line temperature falls to below about 65°C (150°F). In any event, the average of 400 W for 4 delivered to end use cooking is three orders of magnitude larger than the needed end use electrical energy for pumping. This seems to be a small energy *cost" in order to get the free solar energy for the task. An oven designed and constructed to hold this heat exchanger (but without the existing modification of external manifolds) has been given a preliminary cooking test. The performance suffered compared to the data shown in Table 3 because the external manifold pipes took up too much space in the oven rear corners so that only 1 in. of insulation could be used to defend against the losses to ambient. A 2-kg chicken was cooked in 1.8 h (meat temperature raised from 22°C-85°C) reducing the storage time from 14 h to 11.8 h. The spatial temperature dependance led to a 40°C (72°17) temperature reduction from the storage mass in the rear wall of the oven to the central position occupied by the chicken. A future experimental study will examine the question as to how best to
512
DAVID L. BUSHNELL
extract the heat for cooking and to measure cooking effectiveness. W e have conceived and are constructing a new heat exchanger that addresses the need to be able to extract heat rapidly in order to be able to cook effectively and features a larger surface-to-volume ratio, a greater internal density of fin tubes, and a modular concept. A modular design allows the assembly of an enveloping array of energy storing modules, which creates more uniform heat distribution and convective heat transfer.
Acknowledgments--There are three student contributors whose work has been important to the progress of this research: Ilkhcehi Nureddin, Molaei Hossein, and Mohammad Riahi. REFERENCES
1. Robert H. Socolow, Reflections on the 1974 APS Energy Study. Phys. Today 39 (1), 60-68 (1986). 2. F. Baylin and M. Merino, A survey of sensible and latent heat thermal energy storage projects. Solar Energy Research Institute, SERI/RR-355-456, pp. 231, 263, 285, 293, Golden Colorado, May (1981). 3. D. K. Benson, J. D. Webb, R. W. Burrows, J. D. O. McFadden, C. Christensen, Materials research for passive solar systems: solid state phase-change materials. Solar Energy Research Institute, SERI/TR-255-/1828, Golden Colorado, March (1985).
4. CRC Handbook of Chemistry. and Phy'sics, 50th ed., p. B156 (1969-70), ed. Robert C. Weast, Chemical Rubber Co., Cleveland, Ohio. 5. J. W. Mullin, Crystallisation, Second Edition. CRC Press, Boca Raton, FL (1979). 6. T. T. Bramlette, R. M. Green, J. J. Barrel, D. K. Ottesen, C. T. Schaffer, and T. D. Bmmleve, Survey of high temperature thermal energy storage. Sandia Laboratories Energy Report, SAND75-8063, Albuquerque, NM, March (1976). 7. R. J. Copeland, M. E. Karpuk, and J. L. Ullman, A preliminary screening of thermal storage concepts for water, steam, and organic fluid solar thermal receiver systems. Solar Energy Research Institute, SERI/TR631-647, pp. 10-11, Golden, Colorado. April (1980). 8. B. M. Cohen, R. E. Rice, and P. E. Rowney, Comstock & Wescott Inc., DOE/NASA/0615-79/I, NASA CR-159465. Prepared for National Aeronautics and Space Administration, Lewis Research Center for U.S. Dept. of Energy, Washington, D.C., December (1978). 9. Barry M. Cohen, Comstock and Wescott Inc., 765 Concord Ave., Cambridge, MA 02138. private communication (1984). 10. CRC Handbook of Chemistry and Phy'sics, 50th ed., p. B124 (1969-70), ed. Robert C. Weast. Chemical Rubber Co., Cleveland, Ohio. 11. O. J. Kleppa, Heats of fusion of the monovolent nitrates by high temperature reaction calorimetry. J. Chem. Eng. Data. 8 (3) 331-332 (1963). 12. CRC Handbook of Material Science, Vol. II (1983), ed. Charles T. Lynch. CRC Press, Boca Raton, FL (1983). 13. John Alien, Argonne National Laboratory., Argonne, IL private communication (1983).
APPENDIX
Defining a figure of merit We define a system figure of merit (FOM) for use to compare the performance of different storing heat exchangers by the relation FOM,y = ('q)G
(A1)
where (rl) is the average system efficiency over the temperature range of interest and t,, is the time that heat is held in storage. If we wish to include a factor that represents extraction performance so that we have a figure of merit including the oven cooking process, we then define t., FOMo = (B) _z
(A2)
t,
where FOMo is the oven figure of merit and t, the cooking or extraction time standardized to some specific extraction event such as cooking a 2-kg chicken.
Since we can show that ('q) is inversely proportional to t,. we modify the above equations (AI and A2) to FOM,y = t,,/t,. (A3) and FOMo = G/t~,t,
(A4)
A value for FOM,~ can be obtained for the present heat exchanger by using data from run 17 listed in Table 3 to find trite, to be 11.8. With improved design and insulation, it is within reason to be able to increase (rl) from 0.52 (see Table 2 Run 17) to 0.55 with a corresponding reduction in t~. and increase of t,, to 30 h leading to a tdt~ ratio of about 18. Preliminary efforts to determine t, indicate that extracting heat to cook a 2-kg chicken reduced the storage holding time by 16%, maintained about the same t, of 1.8 h, and required 1.8 h to raise the chicken temperature from a room temperature of 220C (72"F) to a cooked temperature of 77°C (170"17). The new t d t m ratio becomes 9.9 and the FOMo = 5.5 h -z.
0038-092X/88 $3.00 + ,00 Copyright ~ 1988 Pergamon Press plc
Printed in the U.S.A.
PERFORMANCE STUDIES OF A SOLAR ENERGY STORING HEAT EXCHANGER DAVID L. BUSHNELL* Physics Department, Northern Illinois University, DeKalb. IL 60115, U.S.A. Abstract--The design, construction, and performance of a solar energy storing heat exchanger is presented as a step toward a solar cooking concept. The solid-solid transition of pentaerythritol is the principal mechanism for energy storage. The methods for describing the system performance are explained and applied to a test system containing a controllable replacement for the solar input power. This first stage of the project will be followed by another in which the heat exchanger is connected to a concentrating array of CPC cylindrical troughs. Although a size appropriate to commercial cooking may prove easier to design from the point of view of economics in the United States, the system discussed herein is sized for domestic use and addresses the question of what solar collector area and PCM mass are needed in order to provide adequate energy for several family-size meals with sufficient storage to cook at night and one or two days later. The performance is described from efficiency measurements and the determination of a figure of merit.
1. INTRODUCTION
tubes. Ultimately, this unit is to be located in a thermally efficient oven. Although we have constructed such an oven, it is being tested separately and used for a test bed to measure high-temperature insulation conductivities. The simulation test system used for the performance measurements is shown in Fig. 3. Since the storage performance of the heat exchanger is a critical element in determining the feasibility of developing a useful solar oven, we have concentrated on developing a measuring method that can be used on a variety of heat exchanger designs. For clarity, we have picked the simulation arrangement shown in Fig. 3. This allows simplicity and control of the input power. We leave for another study the measurement of extraction rates for this heat exchanger and alternative designs. Based on these results, we are preparing to test run the system with the solar collector and oven as depicted in Fig. 1. In designing this system, preliminary studies of the literature[2-12] on phase change storage materials were conducted, the results of which are presented in Table 1. In selecting a heat transfer fluid, water was ruled out to avoid the problems of a high-pressure system. The solar group at Argonne National Laboratory[ 13] had some experience selecting oil for high-temperature solar applications and told us about the therminol from Monsanto. One of the therminol oils could function with rather low viscosity and high temperature allowing its use in this application in place of water. The higher-temperature application, and the lower conductivity of the oil compared to water, made it necessary to modify the shelf model CPC solar collector obtained from Energy Design Corporation. The plumbing of the flow line uses half-inch diameter copper tubing and brass compression fittings to install the pump. Selection of a pump proved to be a difficult task because there are very few pumps
This article presents the results of a study of the performance of an energy storing heat exchanger designed for use with a high temperature solar collector and a system to provide heat for a cooking oven. It has been suggested by Robert H. Socolow in Physics Today[l] . . . . ~that more efficient cooking technology could permit enormous energy resources to be freed for redeployment in other tasks." Solar energy could make an important contribution but its limitations, due to cloudiness and nighttime demand, need to be removed if widespread application in the world is to be achieved. The storing heat exchanger described in this article is a prototype to test the concept of energy storage for application to solar cooking and it employs a phase change material (PCM) called pentaerythritol. It is a heavy (molecular weight 136.15 g) alcohol with a solid-solid phase transition at 183°C (362°F) and a solid-liquid phase transition at 259°C (498°F). The former transition provides about 10 times more energy absorption than the latter and allows for transition cycles having only solid storage material. 2. THE SYSTEM In order to be able to do effective oven cooking, it is necessary to obtain temperatures between about 150°C (300*F) and 260°C (500°F) that require concentration of the solar insolation. The complete system is described in Fig. 1. It consists of a compound parabolic concentrating trough array, a closed loop pumping line containing oil (therminol 60 from Monsanto), and an energy storing heat exchanger. The heat exchanger, shown in Fig. 2, has a rectangular geometry and contains phase change material and fin *ISES member. 503
504
DAVID L . BUSHNELL
Colleclor Manifold
Top view of C P C
I
o
Evacuated IF_. ~ Double Glass Receiver I Tube I~
/// iii
Wall
outside
i
Manifold .,_l
L~
L__~_
Y// /// //~
t / // M
side r~_~
Fig. 3. Oil distribution and insulation.
Fig. 1. Solar energy storage system. manufactured having low enough pumping speeds (~4 liters/min) and high temperature capability (to about 300°C (572°F)). The pump that we use for the work originally failed at 227°C (440°F), but, following some adjustments, that same gear pump is now operating at temperatures over 250°C (482°F) for 12-h periods of time repeatedly with no difficulty. 3. S O L A R E N E R G Y S T O R I N G
HEAT EXCHANGER
3.1 Design criteria In order to determine the feasibility of the energy storing solar oven concept, it is essential to design a heat exchanger of high efficiency that is integrated with a storage material whose specific storing capacity (energy per unit mass) is very large. This heat exchanger should meet the following criteria: (1) rapid heat transfer from input to storage, (2) effective defense against heat loss from storage, (3) high efficiency, (4) easy extraction of heat from storage, and (5) a modest size both of mass and volume. We have designed, constructed, and tested a prototype energy-storing heat exchanger. From examination of the results of the test measurements presented below, you will be able to see that answers to some sizing questions and clues for alternative de-
/ ~
I~* ","," ~
Heat Exchanger
Reflector,,,. I ~'~
///
~, o') ~ (j.,
Heater Tank
Steel vessel
.~'-"- - - :,J___L
f--I
Fin tube
[' ~ 10.8 cm
Fig. 2. Heat exchanger and fin tube.
signs having promise of improved performance are obtained. From the tests, we have obtained information about rates of heat transfer, amount of energy stored, time of energy input, and the time during which energy is held in storage. A figure of merit is defined to characterize the success of the design in satisfying the first three of the above design criteria. 3.2 Sizing In our location with latitude 41.5 °, it xs possible to have solar insolation intensity on a vertical aperture in winter as high as 800 W/m-" and a 4-h average of 400 W/m-'. Our collector aperture is 24 ft" or about 2 m ~', so it would be feasible under the best of conditions to collect at an 800-W rate for 4 h. If we could maintain a collector efficiency of 50%, we could feed the heat transfer oil at a 400-W rate on the average over the 4 h. It should be noted that a 2-m 2 collector implies a system sizing for domestic rather than commercial use. The mass of pentaerythritol needed to take the corresponding energy is given by m = Ptc/L,, where P is the power in watts entering the oil stream, tc is the time of collection, and Ls, is the latent heat for the solid-solid phase change transition from solid I to solid II. Since L,, = 72 cal/g, the mass is about 20 kg. The containment for this mass was sized to hold the heat transfer surfaces that are in the form of standard home heating fin tubes. Figure 2 shows the steel containment box and the fin tubes located inside. The amount of mass ultimately recommended for this level of power input should be larger than the above estimate by enough to prevent the temperature of the solid II structure from going far into the high temperature sensible heat range, thus avoiding the melting point. 3.3 Construction Since the heat transfer oil could be expected to go to temperatures over 260°C (500°F) on occasion, it was necessary to braze the copper to the exit holes in the end walls of the steel containment box. The steel thickness chosen (0.8 mm) was not quite enough to eliminate wall buckling caused by seam welding and wall bulging caused by the mass loaded into the
Solar energy heat exchanger
505
Table 1. Some prospective phase change materials for thermal storage
Material PCM Pentaerythritol Adipic Acid 2,2-Bis (hydroxymethyl) proprionic acid Hydroquinone 0.5 NaOH/0.5 KOH K-Salt (0.5 NaNO 0.35 KNO~, 0.15 NaNO_,) Draw salt (0.5 NaNO3, 0.5 KNO~)
Reference 2, 3 2
Mole weight (g) 136.15
3 4. 5
Transition temperatures °C (°F)
AHss
..XHsL
Tss
TsL
(cal/g)
(cal/g)
1.107 a 1.075 ~
184 (363)
258 (496) 152 (306)
72.5
8.80 59.6
1.72 1.328
153 (307)
195 (383) 172 (342)
68.6
6.5 58.8
Density p (g/ml)
170 (338)
6 1.89
7 7
Thermkeep
2, 8, 9
Anthracene LiNO3 Solder
2, 5 10. 11 12
pAHss (cal/g) 80.3
118
p..XHsL (cal/g) 9.74 64.1 11.0
64
199 (390)
1.87
2.060 a 1.85 68.94
234 (453) 293 (559)
1.283 2.38
227 234 293 218 252 183
(-W,O) (453) (559) (424) (486) (361)
98 38.5 87.8 11
49.4 207
aOur measurement. box. Both of these effects were too small to cause any significant difficulty. The fin tubes are connected in series and the manifold for distribution is on the outside rather than the inside of the box for ease of construction. The latter decision was made at the expense of performance since one could expect that heat losses would occur from the manifold. Indeed, we have found that the test results indicate about a 70% efficiency so that the insulation around the manifolds held the manifold loss to about 30% (line losses are included in the heater efficiency discussed later). Loading the box with the solid pentaerythritol powder required melting it in batches of about 5 kg amounts to pour it into the box to allow a complete distribution among the fins and tubes. After placing 20.8 kg into the box, it appeared to be full. Later, during our test measurements, we found there were cavities so we remelted and added more mass to completely fill the box and cover the fins. The final mass of pentaerythritol became 27.3 kg and the steel containment vessel and fin tubes had a mass of 7.4 kg for a total of 34.7 kg. The steel containment box is connected to the oil supply tank (5.7 liters) by two 1.27 cm (0.5 in.) diameter copper tubes of length 43 cm (17 in.) running horizontally. The return line enters the supply tank near its top and the source line enters about 20 cm (8 in.) lower near its bottom where the 800-W hotplate heater coil is located. The circulating pump is located in the lower line. The system has no pressure since the return line spills into the surface of the oil in the supply tank (see Fig. 3). Most of our data were obtained using a high-temperature, high-density, semirigid insulating fiber tightly formed around the heater tank and the two supply lines to a nominal thickness of 5 to 10 cm. The heat
exchanger containment box had an insulation thickness of 10.2 cm (4 in.) surrounding all sides and completely enclosing the manifolds. This insulation has a conductivity of 0.059 W / m K (0.41 Btu i n / h r if:°F) at 204°C (400°F) and is usable to 704°C (1300°F). It goes under the name Fibrex 1300 block and has a listed density of t77 k g / m 3 (11 lb/ft~). We also used a high-temperature, high-density, fiberglass insulation called Insul-Quick for some of the experiments. Its upper limit temperature is 427°C (800°F) and its conductivity about 0.058 W / m K . 3.4 Phase change material The various possible materials available for energy storage at temperatures near 200°C (392°F) are listed in Table 1. The choice of a material must be based on the transition temperature, the latent heat of transition, the density, and other considerations such as toxicity, corrosiveness, and hydrogenation. One additional feature has to do with the type of phase change. We chose pentaerythritol (CsHl,,O4) primarily because it has a large solid-solid transition energy but also because we would not have to design for liquid containment or for hazardous material. It has little or no toxicity[3]. This allowed us to leave the containment unsealed using either a loose lid or no lid at all. There are two low-cost grades of pentaeD'thritol. One is called a tech grade ( - 8 8 % pure) and the other, which we are using, is called a pure grade ( ~ 9 8 % pure and $1.60/kg). The 27.3-kg of material cost $44. Our experiments both by design and on several occasions by accident liquified small portions of the pentaerythritol with no apparent ill effects on its thermal characteristics. We have full cycled a small sample ( ~ 2 0 0 g)
506
D A V I D L . BUSHNELL
completely 10 times with no ill effects thermally. By full cycle we mean a temperature increase through the solid-solid phase change, the melting phase change, and the boiling phase change, followed by a decrease to the initial temperature. Our large mass experiments described below cycled the material 13 times through the solid-solid transition. Several of these experiments led to complete melting and partial evaporation of the material. No thermal degradation has been detected. Cycling experiments having over 700 cycles done by the Solar Energy Research Institute[7] revealed no significant physical changes. In the case of the 98% pure material, the remaining 2% is a dimer of pentaerythritol. There is, therefore, no expectation of degradation of physical properties resulting from repeated charge-discharge cycles.
4. H E A T E X C H A N G E P E R F O R M A N C E MEASUREMENTS
The theoretical analysis of this system suggests that with steady-state temperatures around the flow loop and under the assumption of no line losses, the performance would be independent of pumping speed and the system efficiency would be strongly dependent on the performance of the heat exchanger. Figure 4 shows a system schematic diagram to help depict these ideas. In that figure, G~ !s the global insolation (irradiance in W/m") and Q~ is the heat rate leaving the collector receiving surface and entering the heat transfer fluid. Then we have
(~ = "q,.AG~
(1)
where "qc is the collector efficiency and A the collector aperture area. If the line losses are zero as depicted, then Qc = Q~x where Qe, is the heat rate entering the heat exchanger. Also,
(~ex =rhoCo(Oi - 0o)
(2)
where tho is the mass flow rate of heat transfer oil, Co is the specific heat of the oil, and 0~ and 0,, are the input and output oil temperatures at the heat exchanger. In our test measurement, we replace the solar collector with an electric submersion heater located in the bottom of a 5.7-liter (1.5 gal) cylindrical supply
=
/
, ,Heat JExchan(er '
O .... :0
To
. I Collector
m
L._)
....
~
<
,
Fig. 4. System schematic.
&
tank (see Fig. 5). The heater power simulates the solar input power given by AG r We define our test system efficiency ('q,y) by the relation "q,y = (2¢,,/P,.
= rhoCo(O,
-
Oo)/P~.
(3)
where P~. is the power input provided by the electric heater. Energy storage first occurs as sensible heat raising the PCM temperature to the transition temperature. The transition occurs at about constant temperature followed by another sensible heat storage. A typical example of this heat storage process is shown in Fig. 6. A system efficiency can be defined for the sensible heat ranges as follows:
"q,y = MC(T)(AT/At)rPg I
(4)
where C(T) is the average specific heat of the storage material at temperature T, M is its mass, and (AT/ At)r is the slope of the heating curve (T versus t) at temperature T. Similarly, for the efficiency during the transition we define
~sy
=
,~'IL/Pi,
(5)
where M is the mass transition rate from solid I to solid II and L is the latent heat. Our only way of obtaining ML is from the heat extraction rate described by eqn (2). Measurement based on eqn (3) will be called the flow method and that based on eqn (4) the slope method. A performance test is designed so that T~, To, 0, and 8o are measured by thermocouples and recorded frequently during both heating and cooling. The output of thermocouples located inside the storage medium are also recorded while the system is heated up to the melting point, at which time the power is shut off both to the heater and to the circulating pump. As a practical matter, we define a "temperature range of interest" for the phase transition from solid I to solid II. Therefore, we measure the time to raise the storage medium from 171°C (340°F) to 193°C (380°F) and label it as heat charging time or input time, t~,. This contains two small sensible heat contributions to storage and one latent heat contribution. We also measure the time of cooling from 193°C (3800F) to 1710C (340°F), and label it the time heat is held in storage or storage time, tst. Two slope methods are used to measure the system efficiency, "q,y, using eqn (4). One method employs the average AT/At at 171°(2 (340°1) and at 193°(= (380°F) obtained from the sensors placed in the pentaerythyitol. The other method employs the slope of the average of 0o and 0~. In Fig. 6 we see a typical response of a thermocouple in the PCM. The 0o and 0~ curves are very similar in shape to the PCM response since these points are thermally well coupled to the PCM mass. For these methods we compute an average specific heat ((C)) for the total storage mass at both 171°C (340°F) and 193°C (380°F) from the
Solar energy heat exchanger
507
StoringHeatExctlanger f
,! PentaerythritolPCM Insulatingenvelope Fig. 5. Heat exchanger test system. equatio n
(C)=~i m,Ci/~m,
(6)
Using three terms where subscripts b, p, and o stand for box, pentaerythritoi and oil, respectively, we have
(C) =
mb(C)t, + mpCp + moCo
(7)
m b + mp + mo
Here the m o is that portion of the heat transfer oil mass that is always located inside the fin tubes, and (C)b is the average specific heat of the steel box and the fin tubes that are made of copper tubes and aluminum fins. When power input is high ( - 8 7 0 W), the first method fails at 193°C (380°F) because the number of sensors (usually six) sampling the A T / A t for the mass in the box is too small to obtain a good average. The high power causes steep spatial gradients at many points and also localized spots of liquid. As a result, the distribution of slopes (AT/At) is widened and a
Power 250 I-
Off
larger sampling is required to get a good average A T / At. If some of the cooler spots are not sampled, the average can be statistically weighted to very high slopes leading to impossibly high efficiency results. The AO/At of the heat transfer oil is a reliable measure of the average slope for the whole mass and so method 2 is used exclusively when adequate sensor sampling is impractical. The slope method cannot be used to determine the efficiency during the phase change transition. The flow method can be used at all temperatures, and its results can be compared with those from the slope method both at temperatures above and below the transition temperature. In order to obtain a more accurate flow calorimeter measure of the system efficiency during the latent heat process, " % ,L), we placed three thermocoupies at both the flow line input and output of the heat exchanger and ran the pump speed as low as feasible to obtain a maximum temperature difference, 0r - 0o. Figure 7 shows two examples of complete heating-cooling curves for both a poorly insulated case and a well-insulated case. The system efficiency ('qsy) can be defined in terms of a heat exchanger efficiency (rl,~) times a heat source efficiency ('qh). The heat exchanger factor includes the effect of the delivery lines. We define it as the ratio of the heat storing rate to the heat rate supplied by the source to the distribution lines. It reduces to -q<, = ( o i -
l
171°C
2°° fLg?-*c-.--/Z--~-
/
//,:
"
//mlnn++
\
79S*'c ---, . ~
i
i
100 I /
curve
!
,.,
-'-I
I/ 2
4
6
8 10 12 Time (hours)
14
Fig. 6. Typical PCM heating curve.
16
7",)
(8)
The "qh factor is the heater source efficiency for the test system, whereas it is the solar collector efficiency in the real solar case. In the test system it is given by Xlh = t h o C o ~ Z / P i n
'
~1
Oo)/(To -
(9)
where AT = To - Ti Then the system efficiency as defined above agrees with eqn (3). The typical response of the system during heating as seen in Figs. 6 and 7 shows a slope (dT/dt) that decreases as the system approaches the temperature for the latent transition from solid I to solid II. This slope decrease is primarily due to the increase of the pentaerythrital specific heat with temperature, so that the product C(AT/At) remains rather constant. How-
508
DAVIDL. BUSHNELL
I.
~ ] Cooling l• Heating
Good Insulation
42°1:
.
.
.
300,,
~~
I• ,,
6
[
10
Heating ~-
tst=l 6.5~,,,, 14
300 t ..... 4
"
p
, . . . . . . . . . 18 22 26
-=
~Poor Insulation
t,,~ _~,.1
,150
> Cooling
....... 340 i1~._~
/
.
oU.. 340 I~,._..I -"
/
I=
ts,=10 h
%
200 ~[175
, ....... ~ ~ T ~ T r ~ f I J 4150 8 12 16 20 24 Time (hours) Fig. 7. Heating-cooling curves.
ever, we know that some points in the exchanger convert earlier than others, so there is no precise time definition for the onset of the transition. Some regions of mass will be entering a constant temperature condition while others are still undergoing sensible heat storage and a temperature vs. time slope. As the converted mass fraction shifts, the average slope will decrease toward zero. After the completion of the transition, sensible heat storage continues to raise the temperature and simultaneously the specific heat of the PCM varies going through a local minimum before a rapid rise[3]. All these higher-temperature specific heats are greater than before, and so the after phase transition slope is less than the before phase transition slope (see Fig. 6). The heat rate during transition is obtained from (~L = rhoCo(Oi - 0") where 0" is the heat exchanger outflow temperature corrected for the radial oil temperature gradient resulting from streamline flow. The data obtained from a heating test designed to more clearly define the four temperatures (To, T~, 0~, 0o), revealed that 0~ - 0o was somewhat larger than To - T~. More important, when the oil slope method (eqn (4)) was used, we obtained a system efficiency of 0.65, whereas the flow colorimetry method (eqn (3)) gave "rl,y = 1.4. This could only mean that 0~ 0o was much too large. The explanation is that 0o is severely depressed due to the pentaerythritol absorbing heat from the outer layers of flowing oil and very little from the inner regions. Thus, the outer temperature, as measured by a sensor in contact with the outer surface of the tube, is much cooler than the inner temperature and therefore less than the crosssectional average temperature. The measurement of temperature distribution along the return flow line revealed the size of the effect just described. In Fig. 8 we see that as the oil flows around a 90 ° turn into a constriction and a smaller pipe where some turbulence may be formed, the oil temperature rises at point b as hot inner portions of the oil stream mix with the cooler outer portions. As the oil continues its flow and leaves the region of heavy insu-
lation near the heat exchanger and enters the return pipe region of lesser insulation, it cools. The rise in temperature toward Ti is due to a small direct heating from the heater along the copper tube wall in the opposite direction of the oil flow. This type of data allows us to correct 0o upward to 0o-the value at point b. If provision is made in the fin tube design to induce turbulence, we should see some improvement in efficiency and ease of defining and measuring 0o. 5. RESULTSAND CONCLUSIONS The measurements of the performance of our prototype design are summarized in Tables 2 and 3. We have reported system efficiencies measured at three appropriate temperatures for each complete run. The low temperature, designated "1o" in Tables 2 and 3, is far enough below the latent transition temperature 183°C (362°F) so that all pentaerithrytol mass is undergoing sensible heat absorption. The high temperature, designated "hi" in Tables 2 and 3, is similarly located above the transition temperature. The third temperature is the transition temperature, designated L for latent, and 0i - 0o is taken in the middle of the time interval to minimize the possibility that there is any mass undergoing sensible heat absorption. This allows us to use both the slope and flow methods for the two sensible cases while only using the flow method in the transition case. Our results suggest that the system concept is feasible for domestic application. In support of this notion, we note that the prototype system under good solar conditions could be thermally loaded by increasing the temperatures across the temperature range of interest (from 171°C (340°F) to 193°C (380°F)) in less than 2 h (see the ti, column in Table 3) with a system efficiency of about 50%. The contributing efficiency from the heater (solar collector simulator) in the latent range fluctuated somewhat from run to run averaging 0.65, whereas the heat exchanger had a rather steady average efficiency in the latent range of
509
Solar energy heat exchanger
484
0; ~
T,
Pump
250
480 476
245
47; T(°C)
T(OF) 46{ 240
400 , , , , . 456
-
Insulation
'
~
~
Set=2.0 i b ~
LL~452
/
~.,.q
/F
N -
10 I_.-,
20 Centimeters
•
I
~L ~
i
J
235 k,
30 40 ~/~//7//7/7"//--~//-~/~ y / ~ / ~ / / ~ nsu at on ~////~
stee,Heat::~::er;il ~l "It
Fig. 8. Oil return line temperature distribution.
0 . 6 9 . It is easy to i m p r o v e the heat e x c h a n g e r efficiency s o m e w h a t with better design. H o w e v e r , it may be difficult to m a i n t a i n a solar collector e f f i c i e n c y o f greater than 6 0 % . T h e e x p e c t e d heater e f f i c i e n c y red u c t i o n with i n c r e a s e d t e m p e r a t u r e s h o w s up clearly in the w e l l - m e a s u r e d runs (such as run 17) and this
e x p e c t a t i o n is c o n s i s t e n t with all runs within their ranges o f error. This high t e m p e r a t u r e trend is larger for s o m e runs due to a failure to m i n i m i z e the small heat losses f r o m lost oil v a p o r and small p u m p leaks. O v e r h e a t i n g the s y s t e m a b o v e 193°C (380°F) to a r o u n d 210°C (410°F) requires additional hours o f
Table 2. System efficiency results System efficiency (-%) Lo range Input power Run (watts) 1' 2' 3' 5 6 7 11 b 12 b 13~ 14 15c 16d 17"
870 870 870 870 870 955 870 870 870 870 590 870 835
th(L)(g/s) 50 50 50 47 47 47 16 16 50 69 77 15 14
Maximum To C°(F°) 215 226 232 265 256 270 206 250 255 258 258 250 249
(420) (440) (450) (509) (493) (518) (403) (483) (492) (496) (496) (482) (481)
Slope (eqn (4)) 0.28 0.44 0.38 0.49 0.51 0.51 0.53 0.55 0.52 0.47 0.50 0.50 0.53
Flow (eqn (3))
Latent range Flow (eqn (3))
Hi range Slope (eqn (4))
Flow (eqn (3))
0.18 0.35 ± 0.03 ± 0.04
(0.49) f (0.51) f
.4- 0 . 0 4
± 0.04 ± 0.04 -- 0.03 +-- 0.03 - 0.03 --- 0.03 - 0.02
(0.51) f
0.39 ± 0.06 0.43 -- 0.06 0.47 -- 0.06
0.34 0.37 - 0.05
0.54 -- 0.02 0.53 -- 0.07 0.48 ± 0.08
0.46 ± 0.02 0.47 ± 0.07 0.45 ± 0.08
0.41 ± 0.04
0.52 ± 0.03 0.54 ± 0.02
0.43 ± 0.02 0.47 - 0.02
0.42 --- 0.05 0.38 --. 0.02
0.39 ± 0.03
"Runs not fully instrumented. Inferior insulation and low peak temperature. ~Run terminated prior to completion of the solid-solid transition following return line temperature gradient measurement. CLow power input and high pumping speed leads to AT's being too small to measure accurately so that calculation of the system efficiency by the flow method (eqn (3), ~sy = (ritoCoao/Pi.)) is too uncertain. *I'his run was the most accurately measured to this point but has mass reduced roughly 20% due to overheating in run 15 and earlier runs. Top fin tube completely exposed. *Mass lost in earlier runs restored for this run. Also, oil-soaked heater insulation was replaced as well as heat exchanger insulation. More sensor redundancy and slower pumping speed give most precise data. fValues from slope method used in flow calculation to find a A0 to be used in the ~iatent" flow calculation. These runs had only one sensor for each temperature and no data on return line temperature distribution.
870 b 87@ 870 ' 870 870 955 870 870 870 870 590 870 835
Run
I 2 3 5 6 7 II 12 13 14 15a 16" 17'
50 50 50 47 47 47 16 16 50 69 77 15 14
ih(L) (g/s)
215 (420) 2 2 6 (440) 232 (450) 265 (509) 256 (493) 270(518) 206 (403) 250 (483) 255 (492) 258 (496) 258 (496) 250 (482) 249 (481)
Maximum 7",, C°(F ")
0 . 5 7 "- 0 . 0 5 0.68 ± 0.05
0.63 ± 0.04 0.71 --- 0 . 0 4
0.72 ± 0.04 0 . 6 7 +- 0 . 0 4
0 . 8 4 -+ 0 . 1 6 0 . 7 8 --+ 0 . 1 4
High range
0.74 ± 0.20
0 . 6 5 -+ 0 . 1 2 0.73 + 0.15 0.73 ± 0 . 1 4
Latent r a n g e
0.69 ± 1,).1,)4 0.68 ± 0.1,)4 0.69 + O. 16 0.65 ± O. 16 0.65 ± 0.25 0.71 ± 0 . 2 5
0 . 6 6 --- 0 . 1 2 0 . 8 5 - O. 16 0.75 ± 0.14
Low range
E x c h a n g e r e f f i c i e n c y "~,.~ (eqn (8))
0.71 -+ 0 . 0 5 0 . 8 0 -+ 0 . 0 6
0.78 -+ 0.06 0.77 ± 0.1,)9 0.73 ± 0.12
1,).74 ± (I.08 (I.61) ± 0 . 0 8 0.62 - 0.07
L o w range
0.68 -+ 0 . 0 4 0 . 6 6 -+ 0 . 0 4
1,,I.68± 0.04 0.73 -+ 0.09 0 . 6 8 ± 0.11
0.59 ± 0.07 1,1.58 + 0 . 0 7 0.65 ± 0.07
Latent range
0 . 6 5 --- 0 . 0 4 0 . 5 7 ± 0.03
1,).61 -'- 0 . 1 0
1).59 --. 0.07 0.61 ± 0 . 0 6
H i g h range
H e a t e r e f f i c i e n c y ",]h (eqn (9))
4.2 2.5 3.3 1.3 1.3 1.0 1.4 1.6 1.3 1.4 2.8 1.2 1.7
t,,
13 1I 11 20
10 16 17 18 17 16
t,,
Charging and holding times"
24
20 20
27 24 24
12 18
t,,,
"t,,,, is the e n e r g y h o l d i n g t i m e m e a s u r e d from the t i m e that the input p o w e r is turned off until the t e m p e r a t u r e d r o p s to 171 ° C. t,, and &, are e n e r g y input and storage t i m e s , r e s p e c t i v e l y , as m e a s u r e d b e t w e e n t e m p e r a t u r e 171 ° C (340 ° F) and 193 ° C (380 ° F). "External heater in run n u m b e r I and significant p u m p leak. "Significant p u m p leak d u r i n g these runs. d25% o f the P C M m a s s w a s lost d u r i n g this run, also the AT's w e r e ttx) s m a l l to m e a s u r e a c c u r a t e l y so n e i t h e r ~ , = AO/AT nor ",q,, = t}JCAT/P,, were calculable. ' T h i s run was m a d e with 2 5 % o f the P C M m a s s lost and one fin tube c o m p l e t e l y e x p o s e d . fThe lost mass w a s restored and new i n s u l a t i o n installed. S m a l l h i g h t e m p e r a t u r e p u m p leak l o w e r e d 1],,.
Input power (watts)
T a b l e 3. Heat e x c h a n g e r test results
-r
z
t"
5
~7 ). <:
O
Solar energy heat exchanger
511
PCM = 36.32 kg Pump Setting 2.0 (r~ (L) = 14 gm/s at 183 °C) P~. = 835w
I O0
80
E(D
~'-"'1'-~.-
60 03 O-
.--O- "/.
~.. ~
-rl,x
"" rib
40 rlsy~t.~ = rl,,rlh 20 I
I
I
I
125
150
175
200
PCM Temperature (°C) Fig. 9. Efficiencies vs. average PCM temperatures.
collection but not totaling more than 5 h. This increases the total storage time (to,) as measured from the time when energy collection is terminated by as much as 8 h for a total of as much as 27 h. (See the last column of Table 3.) If 50% more mass is used with reduced surface to volume ratio in the heat exchanger exterior containment surfaces and a modest improvement in insulation, a 40-h storage holding time seems attainable with only small additional expense. The latter because the t~, is only about 2 h - - o n l y half of the design sizing time--so no new collector area is needed to charge the extra mass. We can note from Table 3 that a tst/ t~, ratio of at least 10:1 is achievable with this design so if ti, is 4 h, then with adequate mass to prevent melting, 50 h of storage (tst) could be expected. The next design will employ smaller fin tubes but use twice as many tubes. The manifolds on either end will be taken to the interior, contiguous with the PCM material. Even with reduced diameter tubes, we are considering installing turbulizers in the fin tubes for better heat transfer from the center portions of the oil stream in a fin tube. Our measuring methods require larger temperature differences for good precision, and so we must either pump slowly or increase the power input or both. Also, thermocouple redundancy is important for getting good statistics on the four oil temperatures needed to measure the heat exchanger contribution to the system efficiency. Run numbers 16 and 17 listed in Tables 2 and 3 contained four thermocouples for 0o and 0i, and three for To and T,. The low pumping speed for those runs produced temperature differences of about 18°(] (32"1=) for To - T,-, and 140C (25"F) for 0~ - 0o. Whereas at the moderate speed these differences were only about 6°C (11°F) and 40C (8°F), respectively (runs 5, 6, 7, and 13). The highest pumping speed with lowest power (590 W), yielded about 3°C (5°1=) and 2°C (4°F), respectively. Our pump cannot be run slower and
maintain stability, so we will increase the power input in the future tests. Pump calibrations revealed that as the temperature increased and the oil viscosity diminished, the volume flow rate decreased. An 11% reduction in the angular velocity of the pump was observed as the temperature increased from room temperature to 267°C (480°F). Note that the amount of power specifically required to overcome flow resistance in the test system and also in the expanded plumbing of the real solar system is significantly less than 1 W ( - 0 . 1 - 0 . 0 0 1 W in our temperature range). It is feasible to employ an electric motor-pump combination as small as a few watts to handle this system, provided the high viscosity start up problem is resolved. A high-torque, low-speed motor performance is needed when the system's line temperature falls to below about 65°C (150°F). In any event, the average of 400 W for 4 delivered to end use cooking is three orders of magnitude larger than the needed end use electrical energy for pumping. This seems to be a small energy *cost" in order to get the free solar energy for the task. An oven designed and constructed to hold this heat exchanger (but without the existing modification of external manifolds) has been given a preliminary cooking test. The performance suffered compared to the data shown in Table 3 because the external manifold pipes took up too much space in the oven rear corners so that only 1 in. of insulation could be used to defend against the losses to ambient. A 2-kg chicken was cooked in 1.8 h (meat temperature raised from 22°C-85°C) reducing the storage time from 14 h to 11.8 h. The spatial temperature dependance led to a 40°C (72°17) temperature reduction from the storage mass in the rear wall of the oven to the central position occupied by the chicken. A future experimental study will examine the question as to how best to
512
DAVID L. BUSHNELL
extract the heat for cooking and to measure cooking effectiveness. W e have conceived and are constructing a new heat exchanger that addresses the need to be able to extract heat rapidly in order to be able to cook effectively and features a larger surface-to-volume ratio, a greater internal density of fin tubes, and a modular concept. A modular design allows the assembly of an enveloping array of energy storing modules, which creates more uniform heat distribution and convective heat transfer.
Acknowledgments--There are three student contributors whose work has been important to the progress of this research: Ilkhcehi Nureddin, Molaei Hossein, and Mohammad Riahi. REFERENCES
1. Robert H. Socolow, Reflections on the 1974 APS Energy Study. Phys. Today 39 (1), 60-68 (1986). 2. F. Baylin and M. Merino, A survey of sensible and latent heat thermal energy storage projects. Solar Energy Research Institute, SERI/RR-355-456, pp. 231, 263, 285, 293, Golden Colorado, May (1981). 3. D. K. Benson, J. D. Webb, R. W. Burrows, J. D. O. McFadden, C. Christensen, Materials research for passive solar systems: solid state phase-change materials. Solar Energy Research Institute, SERI/TR-255-/1828, Golden Colorado, March (1985).
4. CRC Handbook of Chemistry. and Phy'sics, 50th ed., p. B156 (1969-70), ed. Robert C. Weast, Chemical Rubber Co., Cleveland, Ohio. 5. J. W. Mullin, Crystallisation, Second Edition. CRC Press, Boca Raton, FL (1979). 6. T. T. Bramlette, R. M. Green, J. J. Barrel, D. K. Ottesen, C. T. Schaffer, and T. D. Bmmleve, Survey of high temperature thermal energy storage. Sandia Laboratories Energy Report, SAND75-8063, Albuquerque, NM, March (1976). 7. R. J. Copeland, M. E. Karpuk, and J. L. Ullman, A preliminary screening of thermal storage concepts for water, steam, and organic fluid solar thermal receiver systems. Solar Energy Research Institute, SERI/TR631-647, pp. 10-11, Golden, Colorado. April (1980). 8. B. M. Cohen, R. E. Rice, and P. E. Rowney, Comstock & Wescott Inc., DOE/NASA/0615-79/I, NASA CR-159465. Prepared for National Aeronautics and Space Administration, Lewis Research Center for U.S. Dept. of Energy, Washington, D.C., December (1978). 9. Barry M. Cohen, Comstock and Wescott Inc., 765 Concord Ave., Cambridge, MA 02138. private communication (1984). 10. CRC Handbook of Chemistry and Phy'sics, 50th ed., p. B124 (1969-70), ed. Robert C. Weast. Chemical Rubber Co., Cleveland, Ohio. 11. O. J. Kleppa, Heats of fusion of the monovolent nitrates by high temperature reaction calorimetry. J. Chem. Eng. Data. 8 (3) 331-332 (1963). 12. CRC Handbook of Material Science, Vol. II (1983), ed. Charles T. Lynch. CRC Press, Boca Raton, FL (1983). 13. John Alien, Argonne National Laboratory., Argonne, IL private communication (1983).
APPENDIX
Defining a figure of merit We define a system figure of merit (FOM) for use to compare the performance of different storing heat exchangers by the relation FOM,y = ('q)G
(A1)
where (rl) is the average system efficiency over the temperature range of interest and t,, is the time that heat is held in storage. If we wish to include a factor that represents extraction performance so that we have a figure of merit including the oven cooking process, we then define t., FOMo = (B) _z
(A2)
t,
where FOMo is the oven figure of merit and t, the cooking or extraction time standardized to some specific extraction event such as cooking a 2-kg chicken.
Since we can show that ('q) is inversely proportional to t,. we modify the above equations (AI and A2) to FOM,y = t,,/t,. (A3) and FOMo = G/t~,t,
(A4)
A value for FOM,~ can be obtained for the present heat exchanger by using data from run 17 listed in Table 3 to find trite, to be 11.8. With improved design and insulation, it is within reason to be able to increase (rl) from 0.52 (see Table 2 Run 17) to 0.55 with a corresponding reduction in t~. and increase of t,, to 30 h leading to a tdt~ ratio of about 18. Preliminary efforts to determine t, indicate that extracting heat to cook a 2-kg chicken reduced the storage holding time by 16%, maintained about the same t, of 1.8 h, and required 1.8 h to raise the chicken temperature from a room temperature of 220C (72"F) to a cooked temperature of 77°C (170"17). The new t d t m ratio becomes 9.9 and the FOMo = 5.5 h -z.