Direct measurement and analysis of thermosiphon flow

Solar Energy Vol. 35. No. 2, pp. 167-173, 1985

0038-092X/85 $3.00 + .00 ~ 1985 Pergamon Press Ltd.

Printed in the U.S.A.

DIRECT MEASUREMENT AND ANALYSIS OF THERMOSIPHON FLOW~ A. I. KUDISH. P. SANTAMAURA-~and P. BEAUFORT§ Solar Energy Laboratory, Department of Chemical Engineering, Ben-Gurion University of The Negev, Beer-Sheva, Israel

(Received 31 May 1984; accepted 11 January 1985) Abstract--The thermosiphon flow rate has been measured directly by adapting a simple and wellknown laboratory technique, a constant level device, to a solar collector operating in the thermosiphon mode. The measurements were performed as a function of thermosiphon head and inlet temperature. The thermosiphon flow rate data were correlated both with the temperature change across the solar collector (A T) and the global insolation rate. The minimum A T threshold value, necessary to initiate thermosiphon flow in the morning was determined as a function of thermosiphon head and the corresponding thermosiphon pressure heads were observed to be invariable. The thermosiphon flow data were utilized to construct a standard efficiency test curve, thus showing that this technique can be applied for testing collectors in the thermosiphon mode. The instantaneous collector efficiency was also determined as a function of time of day.

1. INTRODUCTION

them. We have isolated the solar collector and have developed a relatively simple technique for direct measurement of thermosiphon flow.

Thermosiphon solar D H W systems are the most widely used of all man-made solar energy thermal convension devices, the reason being that they are cost competitive with the alternative conventional energy D H W systems available in many regions of the world. There are today in excess of 600,000 such units operating in Israel[l], which are capable of supplying, in most cases, about 70% of a consumer's annual D H W requirement. The performance of thermosiphon systems has been investigated extensively, both experimentally and analytically, by numerous researchers[2-12]. A comprehensive review on this subject has been published recently[13]. In particular, the flow rate of the heat exchange fluid, almost exclusively water, has intrigued many investigators. Due to its nature, viz., a very low pressure head, thermosiphon flow is amenable only with difficulty to measurement by the standard laboratory flow rate measuring devices. It can be measured accurately only by those techniques that do not add any flow resistance to the system. Thermosiphon flow has been measured previously by indirect techniques such as dye injection[4], thermal dissipation tracing[7], laser Doppler anemometer[8, 9] and rate of change of storage tank temperatures[12]. In all the previously reported studies, thermosiphon flow was investigated on a complete D H W system comprised of solar collector(s), storage tank and the auxiliary plumbing connections between

2. DESCRIPTION OF EXPERIMENTAL SYSTEM

+ Presented, in part, ASES Annual Meeting, Minneapolis, MN June (1983). Current address: 181 Dunvegan Rd.. Toronto, Ontario, Canada. § Current address: Gen. Dibbetslaan 83, 5623 JM Eindhoven, The Netherlands.

The experimental technique used in this study differed from those used previously in that the thermosiphon flow rate was measured directly. This was possible since we isolated the solar collector by eliminating the storage tank. Thermosiphon flow was simulated by means of a constant level device attached to the inlet pipe of the solar collector (Fig. 1). The constant level device consisted of an outer cylinder (height 30 cm, diameter 14 cm) open on top to the atmosphere and closed at the bottom. The bottom plate had two holes drilled for (1) a ~ in. fitting flush with its outer surface for connecting it to the collector inlet pipe, and (2) an adjustable fitting for insertion of the internal drain pipe (2 in.). Soldered onto the cylinder surface 20 cm above the bottom plate was a a in. inlet tube for mains (makeup) water. The latter was maintained in all cases - 5 cm below the water surface in the cylinder so that the kinetic energy or the make-up water would be dissipated radially. The water level in the constant level device was set equal to that in the outlet pipe from the collector (i.e. h3) by fine adjustment of the height of the internal drain pipe. The flow rate of the mains water entering the constant level device was adjusted to exceed (by - 5 0 % ) the maximum measured thermosiphon flow rate, thereby ensuring a constant water level on the inlet side of the system. Thus, the hydrostatic pressure across the solar collector was maintained equal to zero and any flow measured was caused by the thermosiphon pressure head only. The solar collector in this study operated in a single-pass mode, which is typical of

167

168

A. I. KUDISH et al. CONSTANTLEVEL

B

i TOUT

h2 h3

TIN

- - F

~

h~ t

Fig. I. Schematic diagram of experimental simulated thermosiphon system.

most Israeli thermosiphon D H W systems. A somewhat different application of such a single-pass thermosiphon system has been reported recently[14]. The direct measurement of the thermosiphon flow rate was accomplished by simply collecting the solar heated water effluent from the solar collector in a graduated cylinder during a prescribed time interval (usually 1 min.). The inlet and outlet water temperatures to and from the solar collector were monitored continuously by means of type T (copper-constantan) thermocouples inserted into 4-mm copper tubing probes and connected to a multipoint recorder (Chino) (see Fig. 1). The inlet and outlet legs (viz. auxiliary plumbing) of the solar collector were insulated with glass wool molded shells, which were wrapped with aluminum laminate. The latter prevented external heat gain via solar radiation. The global insolation was measured at the tilt angle of the solar collector (i.e. 30°) by means of an Eppley pyranometer, Model PSP, connected to a calibrated recorder (Cole-Parmer). The latter provided us with instantaneous insolation values necessary for calculating instantaneous solar collector efficiencies. The solar collector used in this study was a standard Israeli commercial type. It consists of eight ~in.-O.D, copper tube risers connected to two l~-in.O.D. copper tube leaders. The solar absorption surface being of a honeycomb structure, viz. aluminum fins spaced at 4-ram intervals perpendicular to the riser tubes. Its overall dimensions are 220 x 95 x 10 cm (aperture area = 1.89 m 2) and it is intended to operate in conjunction with a 120-1 storage tank. The thermosiphon head was altered by raising (lowering) both the constant level device and the outlet pipe by the same amount (i.e. the overall length of the auxiliary plumbing, vertical pipes, was changed). This enabled us to study the effect of the height of the thermosiphon head (h3 - h~) on the

flow rate. The rate of thermosiphon flow was measured periodically throughout the day during the sunshine hours. The threshold AT (i.e. Tout - Ti,) values necessary for the initiation of thermosiphon flow in the morning, corresponding to the different thermosiphon heads studied, were also determined. This was achieved by continuously monitoring the inlet and outlet temperature to and from the solar collector. The threshold A T value corresponds to the instant when thermosiphon flow is initiated and is evidenced graphically when the inlet temperature drops to the main's water temperature and the outlet temperature rises rapidly (cf Fig. 2). The meas-

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v

L~

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ii

8 I

f

- - i !

6

20

I

40

I

60

I

80

TEMPERATURE (°C) Fig. 2. Experimental plot of temperature vs time for Sept. 17, 1982 (h3 - h~ = 1.98 m). Arrow indicates the rapid temperature change corresponding to initiation of thermosiphon flow.

Direct measurement and analysis of thermosiphon flow

ca

FLOW

200 180

RATE VS DELTA

T

._J

LId <~

140 120

The results for the correlation between the thermosiphon flow rate and A T are shown in Fig. 3 for (h3 - h2) = 0.7 m and in Fig. 4 for ( h 3 - h 2 ) = 0 m. The former is also representative of the data f o r ( h 3 - h 2 ) = 0.35 and 1 m in that two distinct flow rate ranges, a high and low, were observed. They corresponded to the time of day the measurements were performed. The high range was measured during the time period 10:00-14:00 (solar time) and the flow rate was observed to be fairly constant. During this time period the range of/x T values measured was quite narrow (see Fig. 3) and the global insolation rate was also relatively constant. The low flow rate range corresponded to those measurements performed either prior to 10:00 or after 14:00. During these time periods both the range of A T values measured and the global insolation rate were changing (increasing for < 10:00 and decreasing for >14:00). The data in this range are therefore scattered. The average thermosiphon flow rates in the high range are reported in Table 1 for ( h 3 - h 2 ) = 0 . 3 5 , 0 . 7 0 a n d 1 m . The results for ( h 3 - h 2 ) = 0 m are distinct from the others in that there appears to be a linear correlation between the thermosiphon flow rate and AT. The measurements in this case were all performed during the time period 10:00-14:00. (The reason for this will be discussed in section 4). The measurements in the case of ( h 3 - h2 = 0 m were also performed as a function of the collector inlet temperature range. The linear correlation between thermosiphon flow rate and A T for five different Ti, ranges are listed in Table 2. The relatively poorer correlation factor for the lowest reported T~, range may be explained by the fact that the corresponding measurements were performed in the winter ( N o v . Dec. 1982), whereas the other four sets were measured in the summer (July-Aug. 1983). The former being less amenable to outdoor measurements (i.e.

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•

oe

•

•

•

60 [g

40

•

LL

20 o

•

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i 45

55

i 55

TOuT-TIN ( DEG £ ) Fig. 3. T h e r m o s i p h o n f l o w r a t e vs A T f o r (h3 - h2) = 0.7 m. • 10:00-14:00; • <10:00 and >14:00.

urements were performed for four values of ( h 3 hi), viz. 1.98, 1.68, 1.33, and 0.98 m. The experimental system was adapted, by the addition of heating tape and powerstat, for measurement of the collector efficiency curve while operating in the thermosiphon mode. In general, collector efficiency tests are performed in the forced circulation mode. The heating tape was wrapped around the inlet pipe (vertical section) and then insulated. The instantaneous efficiency was calculated from the inlet and outlet temperatures, instantaneous insolation and measured flow rates. The inlet temperature was varied by means of the powerstat to which the heating tape was connected. 3. R E S U L T S

The measured thermosiphon flow rate data were analyzed by attempting to correlate them to the temperature increase across the collector (i.e. A T = Tout - Tin) and to the instantaneous global insolation rate, in the different thermosiphon heads studied.

FLOW

169

RATE

VS

DELTA

T

H=OM

I00 9080-

Z 70-

..J v

LU H<~ 135

60-

ill

•

5040El

•

•

:.'5020~-

0 _J ii

I0

0

I 65

55

TOU T - TIN F i g . 4. T h e r m o s i p h o n

I 75 (DEG

I

85

.C)

f l o w r a t e vs A T f o r

(h~ -

h2) = 0 m .

170

A. I. KUDISH et al.

Table 1. A v e r a g e t h e r m o s i p h o n flow rate v s during the time period 10:00-14:00 (h3

-

(h3

-

days are not as clear and wind gusts are much more frequent).

h2)

A v e r a g e t h e r m o s i p h o n flow rate

h2)

(m) 0.35 0.70 1.

B. F l o w rate and global insolation The correlation between the thermosiphon flow r a t e a n d t h e g l o b a l i n s o l a t i o n w a s o b s e r v e d to b e l i n e a r in all c a s e s s t u d i e d . T h e r e s u l t s f o r (h3 - h2) = 0 . 7 m a r e s h o w n in Fig. 5. T h e l i n e a r c o r r e l a t i o n s f o r all c a s e s a r e r e p o r t e d in T a b l e 3.

(ml/min.m 2) 85.0 _+ 15.5 157.1 _+ 16.6 177.3 +_ 20.6

C. Collector efficiency and time o f day T h e i n s t a n t a n e o u s c o l l e c t o r e f f i c i e n c y w a s calculated as a function of time of day by simply applying

Table 2. Linear correlation b e t w e e n t h e r m o s i p h o n flow rate and A T for ( h 3 - hD = 0 m T~n range (°C) 18-26 29-35 35-39 40-44 48-53 ay -

Correlation factor

y = mx + b a y y y y y

= = = = =

2.0x 3.6x 4.3x 4.6x 5.8x

- 86 - 150 - 152 - 142 - 152

"q = thCvA T/G,

0.81 0.90 0.95 0.91 0.93

t h e r m o s i p h o n flow rate (ml/min.m2); x -

AT

(°C)

w h e r e ~q is t h e i n s t a n t a n e o u s e f f i c i e n c y ; & , t h e t h e r m o s i p h o n f l o w r a t e ( m l / m i n . m 2 ) ; Cp, t h e h e a t c a pacity of water (KJ/kg.°C); and G, the instantaneous global insolation rate (KJ/min.m2). The results for (h3 - h2) = 0.35 a r e r e p o r t e d in Fig. 6 a n d t y p i f y

Table 3. Linear correlation between t h e r m o s i p h o n flow rate and global insolation rate (h3 - h2) (m)

Tin Range (°C)

1

--

0.70 0.35 0 0 0 0 0

--18-26 29-35 35-39 40-44 48-53

y = mx + b a y y y y y y y y

= = = = = = = =

4.2x 4.1x 2.6x 2.4x 3.2x 3.2x 3.2x 4.6x

-

Correlation factor

66.5 74.9 58.1 73.4 73.7 68.8 73.6 140.3

0.88 0.97 0.94 0.81 0.98 0.96 0.92 0.88

a y - t h e r m o s i p h o n flow rate (ml/min.m2); x - global insolation rate ( K J / m i n . m 2)

FLOW

RATE

H=O7M

VS INSOLATION

20O 180

.U

160 140 Ld I--

120

rY

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0 / LL

60

%

4O 2O 0

20

(1)

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40

50

60

70

INSOLATION ( K J / M I N * M * ~2) Fig. 5. T h e r m o s i p h o n flow rate vs global insolation rate for

(h3

-

h2)

=

0.7 m.

Direct measurement and analysis of thermosiphon flow EFFICIENCY

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•

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TIME

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H =0 5 5 M

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TIME Fig.

6.

(HR)

Instantaneous collector efficiency vs time for

those for all cases. The instantaneous collector efficiency increases with increasing thermosiphon head [viz. ( h 3 -- hj)]. This is expected; since rh increases more rapidly, then A T decreases with increasing thermosiphon head. Also the early morning (<10:00) efficiency values are greater than the late afternoon (>14:00) values and that the latter decrease quite rapidly. It is of interest to note that the maximum instantaneous efficiency (i.e. the range) decreases with increasing values of Tm (see Table 4). This is caused by the increased temperature gradient (Tin - Tamb) and consequent faster rate of heat loss.

D. Thermosiphon threshold A T values The minimum magnitude of A T (threshold value) required to initiate thermosiphon flow in the morning was measured, as described in section 2, as a function of the thermosiphon head. The average values are reported in Table 5. These results will be further analyzed in section 4. E. Standard efficiency test The data from the measurement of thermosiphon flow rate as a function of Tin were utilized to construct a standard efficiency curve for the case of (h3 - h2) = 0 m. It is important to note that these measurements were performed over a period of about 5 weeks and not under the stringent restrictions (viz. climatic conditions) required for such testing. It is our purpose to show that this experimental technique can be used for standard effiTable 4. Maximum instantaneous efficiency range as a function of inlet temperature range (°C)

"q.... Range

29-35 35-39 40-44 48-53

0.46-0.54 0.44-0.52 0.44-0.50 0.41-0.49

-

h2)

=

0.35

m.

ciency testing of solar collectors in the thermosiphon mode (in which they are intended to operate) as opposed to the widely used forced circulation mode of testing. The results are presented graphically in Fig. 7 and the linear regression curve for these data is "q = FR('ra)e - FRUL

( T i n - Tamb) G

where FR('ra)e = 0.79, FRUL = 22.4 the correlation factor = 0.95.

4. A N A L Y S I S

W/m2'°C

(2) and

OF THE RESULTS

A. Thermosiphon flow rates The experimental system, on which the thermosiphon flow measurements were performed, differed from those studied previously [2-12], the present one being an open system. We have adapted the analytical approach first used by Close[2] to the conditions prevalent in our system, viz. no storage tank, and it is significantly simplified. The thermosiphon head equation (cf eqn (11) in [2]) reduces to hr = ½(Sin - -

Sout)(h3

-

hi),

(3)

where S is the specific gravity. Utilizing the parabolic relationship between specific gravity and temperature[2], rather then the linear one assumed in Table 5. Threshold AT and thermosiphon pressure head values as a function of the thermosiphon head (m)

(h3 - h2) (m)

1.98 1.68 1.33 0.98

1 0.70 0.35 0

(h3 - hi) Tin R a n g e

(h~

AT

pghT

(°C)

(kg/s 2"m)

12.7 + 0.6 63.2 15.5 _+ 0.6 59.2 19.1 +_ 0.3 59.6 33.3 _+ 3.5 59.3 pghr = 60.3 -+ 1.9

172

A.I. KUDISHet al.

Io[07!

0.50

"~"

,

025-

0

I O[

I 012

I 015

I 04

1

05

(Tin -Tomb)/G [°C/(KJ/ml.m,n)] Fig. 7. Standard efficiency test curve for eqn (3), we arrive at hr = Ti, - Tout (2AT - B)(h3 - hl), 2

(4)

where A = - 1.25 × 10 -6, B = 5.83 x 10 -5 and = (Tin + Tom)/2. (The temperature units for eqn (4) are °F as per the parabolic equation fit for the specific gravity in [2]). The thermosiphon flow through the collector was analyzed by means of applying Bernoulli's equation between A and B, on Fig. 1, i.e. PA + gZAPA + - ~ DA v~

= PB Jr- gZBPB "~- T

_ v~

OB -~ E l~'i T

Pi,

(5)

where P is the pressure; Z, height above reference; p, density; V, linear velocity; and F, friction factor. In our system Pa = PB, ZA = ZB, and VA = 0 (i.e. in the constant level device). Thus eqn (5) reduces to

v~

v~

(h3

-

h2)

=

0 m.

factor (i.e. the sum of the individual section friction factors adjusted by the continuity equation, p~ VIA~ = p2V2A2). The fluid temperature does not vary in transit between the Tou, probe position and the pipe outlet (B) due to both the insulation and its relatively short residence time. Thus, the value of 9B corresponds to that at T = Tou t and the value of V8 is the volumetric flow rate measured divided by the outlet pipe cross-sectional area. We have utilized the continuity equation to calculate the linear flow rate within the various sections of the experimental system. The temperature (density) was assumed constant within the inlet and outlet legs of the solar collector. The temperature within the riser was assumed to increase linearly and the density as per the parabolic relationship in [2]. The friction factor, skin and fittings, was determined for each section of the system. The values for the thermosiphon pressure head and overall system friction factor were inserted into eqn (7) which was then solved for VB. The agreement between the calculated and experimental values was about 10%, which is quite satisfactory considering the lack of precision in determining friction factors for any particular system.

(7)

B. Thermosiphon threshold values A priori, it is reasonable to assume that the magnitude of the thermosiphon pressure head required to initiate thermosiphon flow in the morning should be constant, since it must overcome what may be termed the system inertia.It Thus, the increase in the threshold A T values (cf Table 5) with decrease in the thermosiphon head was as expected, since

where B corresponds to the conditions at the collector outlet, and F~ is the overall system friction

If The change in the overall system skin friction factor with the change in the length is negligible relative to the overall system friction factor.

gZ(Pa - 9n) = --~ PB + ~ F,-~- p,.

(6)

The term in the left-hand side of eqn (6) is the thermosiphon pressure head which can be substituted for by use of eqn (4), viz.

v~

gpBh~ = T

v~

OB + (~, F;) T

OR,

Direct measurement and analysis of thermosiphon flow they should be inversely proportional if the thermosiphon pressure head is, indeed, invariable. This was verified by calculating the corresponding thermosiphon pressure heads, using the left-hand side of eqn (7), and the results are presented in Table 4, column 4. The standard deviation (-3.2%) is quite small considering the uncertainty involved in determining the threshold temperatures (cf. Fig. 2). The constant thermosiphon pressure head is evidence of the accuracy of our technique of insuring that the fluid levels (inlet and outlet) were equal (i.e. zero hydrostatic pressure head) prior to measuring the thermosiphon flow rate. C. Solar collector efficiency The increase in efficiency with increasing thermosiphon head is an important consideration when dealing with single-pass systems. In practice, while there is a minimum thermosiphon head necessary to prevent reverse thermosiphon flow during the night, the thermosiphon head is generally determined by where the system is positioned and its aesthetic and architectural interaction with its surroundings. The commencement of thermosiphonic flow is also a function of thermosiphon head, in that the greater (other parameters being constant) the earlier the onset of thermosiphon flow and consequent solar energy conversion. This is because the greater the thermosiphon head the lower the threshold A T value required to overcome system inertia. Thus, both system efficiency and total daily hours of operation are proportional to the thermosiphon head. This explains why the onset of flow in the case of (h3 - h2) = 0 was relatively late, i.e. after 10:00. 5. CONCLUSIONS 1. We have shown how a very simple and wellknown laboratory technique can be adapted to measure the rate of thermosiphon flow directly and thereby be used to perform standard efficiency tests on solar collectors operating in the thermosiphon mode. 2. The thermosiphon flow rate was found to stabilize during the mid-day hours as did the A T values across the solar collector. The exception to this observation was in the case of (h3 - h2) = 0, where the correlation between thermosiphon flow and A T was linear, independent of Ti, values. The latter may be a result of the greater sensitivity of the thermosiphon flow to A T since the thermosiphon pressure head is relatively low.

173

3. The correlation between thermosiphon flow and global insolation rate was observed to be linear for all cases studied. 4. The thermosiphon pressure head required to initiate flow in the morning was shown to be constant. 5. The friction factor analysis of the system verified the experimental technique.

Acknowledgement--The authors wish to express their gratitude to the International Association for the Exchange of Students for Technical Experience (IAESTE) for enabling two of us (P.S. and P.B.) to participate in this research project.

REFERENCES

1. Y. Nowarski, Israel Ministry of Energy and Infrastructure, Department of Energy Conservation, private communication. 1984. 2. D. J. Close, Performance of solar water heaters with natural circulation. Solar Energy 6, 33 (1962). 3. G. L. Gupta and H. P. Garg, System design in solar water heaters with natural circulation. Solar Energy 12, 163 (1968). 4. K. S. Ong, A finite-difference method ot evaluate the thermal performance of a solar water heater. Solar Energy 16, 137 (1974). 5. K. S. Ong, An improved computer program for the thermal performance of a solar water heater. Solar Energy 18, 183 (1976). 6. Y. Zvirin, A. Shitzer and H. Grossman, The natural circulation solar heater models with linear and nonlinear temperature distribution. Int. J. Heat Mass Transfer 20, 999 (1977). 7. A. Shitzer, D. Kalmanoviz, Y. Zvirin and G. Grossman, Experiments with a fiat plate solar water heating system in thermosiphone flow. Solar Energy 22, 27 (1979). 8. G. L. Morrison and D. B. J. Ranatunga, Transient response of thermosiphon solar collectors. Solar Energy 24, 55 (1980). 9. G. L. Morrison and D. B. J. Ranatunga, Thermosiphon circulation in solar collectors. Solar Energy 24, 191 (1980). 10. B. J. Huang, Similarity theory of solar water heater with natural circulation. Solar Energy 25, 105 (1984). 11. M. S. Sodha and G. N. Tiwari, Analysis of natural circulations solar water heating systems. Energy Conversion and Management 21, 288 ( 1981). 12. M. F. Young and J. B. Bergquam, Performance characteristics ofa thermosiphon solar domestic hot water system. ASME J. Solar Energy Engng. 103, 193 (1981). 13. B. Norton and S. D. Probert, Natural circulation solar-energy stimulated systems for heating water. Applied Energy 11, 167 (1982). 14. Y. F. Wang, Z. L. Liand and X. L. Sun. A "'oncethrough" solar water heating system. Solar Energy 29, 541 ~1982).