- Email: [email protected]
Thermosyphon circulation in solar collectors
Solar Energy Vol. 24, pp. 191-198 Pergamon Press Ltd., 1980. Printed in Great Britain
THERMOSYPHON CIRCULATION IN SOLAR COLLECTORS G. L. MORRISON
School of Mechanical and Industrial Engineering, University of New South Wales, Kensington, 2033, Australia and D. B. J. RANATUNGA Solar Energy Division, National Engineering Research and Development Centre, Colombo, Sri Lanka (Received 5 March 1979; revision accepted 2 October 1979) Abstract--Theoretical predictions of flow rate in thermosyphon solar collectors are compared with experimental measurements obtained using a laser doppler anemometer. Modifications to the usual method of analysis are proposed to improve the accuracy of the predictions, and the results are compared with flow rate predictions and measurements in other investigations.
l. INTRODUCTION
Solar collectors utilizing thermosyphon flow to transport energy from the collector to the store are one of the simplest and most widely used solar collection devices. There has been extensive work on the analysis of the performance of such systems [1-7] and many experimental tests have been reported on the overall thermodynamic performance. Although these studies cover a period of more than 30 yr there have only been two reports of investigations in which the actual thermosyphon velocity was measured. The obvious reason for the lack of detailed investigation of thermosyphon velocity is the problem of measuring a relatively slow flow without introducing additional friction which would affect the hydrodynamic operation of the system. As the thermosyphon driving head is usually in the range of 1-30 mm of water it is not possible to use an insertion or restriction flow meter, nor a device which has a non-linear resistance, as this would distort the system characteristics. As thermosyphon flow is also important in such devices as the Trombe-Michel wall [8] and other passive collectors and storage devices, the following study was initiated to analyse and measure the characteristics of thermosyphon flow in typical solar configurations.
temperature height data for the system shown in Fig. 1. By analysing the radiation absorption properties of the collector the change of bulk temperature along the riser tube (points 2 to 3 in Fig. 1) can be evaluated in terms of the flow rate. The density of the fluid at either end of the collector is then computed in terms of the bulk temperature as follows: p = A T 2 + B T + C.
(1)
The density variation along the collector is usually assumed to be linear; however, the case of non-linear bulk temperature rise has been investigated by Zirrin et al. [9]. The thermosyphon head (area of the height vs density diagram) is equated to the friction head as follows: h Ts -
#( ) ~
T2
flU 2 KU 2 (2ATm + B) = 2gdgd + - 2 g -
(2)
where Tm is the average bulk mean temperature in the collector and g(h) = 2(h3 - hi) - (h2 - hi)
(h 3 h6 --
h5) 2
hs
(3)
By combining eqn (2) with an energy balance for the collector the thermosyphon flow and bulk temperature rise through the collector can be evaluated in terms of the solar radiation and ambient conditions. As part of this analysis the following assumptions 2. ANALYSISOF THERMOSYPHON FLOW are made: (a) The friction head is evaluated for fully The first published analysis of a thermosyphon. developed laminar flow conditions. (b) The thermosolar water heater circuit was by Close I-1]. There syphon head in the riser is computed from the bulk havebeen many other publications on the analysis of mean temperature at the inlet and outlet to the collecthese systems but they are all based on the original tor. formulation [1]. The validity of the first assumption will depend on The essential feature of this analysis is the compu- the particular situation being analysed, however in tation of the thermosyphon driving head from the collector tubes the flow will nearly always be in the S.E.
24/2--F
191
192
G.L. MORRISONand D. B. J. RANATUNGA
/I
TQnk
3
"~ Cottector -2
Temperature
Fig. 1. Temperature distribution in a thermosyphon collector system.
developing flow regime. Also in most systems the supply and return pipes are l~ept as short as possible, thus friction is likely to be influenced by developing flow in all pipe segments. The effect of increased friction due to developing flow is well documented [10]. However, the friction in the collector tubes is complicated by the heat transfer from the wall which may cause a significant difference between the velocity gradients in the driving section of a thermosyphon circuit and in unheated developing flow. An important aspect of thermosyphon flow is that in the riser tubes the density and thus thermosyphon head depends on the actual temperature distribution over the cross-section rather than the bulk temperature. In most circuits the flow out of the collector tubes is well mixed in the header and thus the density of the fluid in the connecting tubes can be computed from the bulk temperature, but in the collector tubes the fluid density should be computed by integrating r
i
the actual temperature distribution over the crosssection and length of the riser. 3. T H E R M O S Y P H O N
FLOW
The first reported measurement of flow rate in a thermosyphon solar collector was made by Ong [2] who timed the passage of an injected dye trace. Ong compared the variation of actual and predicted flow over a typical day and found that the theoretical analysis underestimated the flow during most of the day. Shitzer e t a l . [ l l ] also measured thermosyphon flow using a thermal dissipation tracing method which introduced an hydraulic resistance of less than 1 mm of water at a Reynolds number of 1100. The mass flow measurements in [11] were found to be approximately 30 per cent higher than the theoretical predictions during the period of steady flow near
i
i O
~
i
11
10
2
~
8
z
\
lb
MEASUREMENTS
I'1
h
AM
t
~ PM
Time
Fig. 2. Thermosyphon flow rate.
"
Thermosyphon circulation in solar collectors solar noon. Shitzer et al. attribute the difference to dynamic effects and uncertainty in assessing the values of the parameters used in the collector efficiency calculation. They also observed that the flow rate fluctuated considerably even when other factors we,re constant, and suggested that this may be due to hydrodynamic instability in the collector-storage tank system. As part of the study reported in this paper, a preliminary investigation of the flow rate in an operating collector system was carried out [12] using a laser doppler anemometer system outlined in Section 4 of this paper. The variation of thermosyphon flow during a clear day is compared with a theoretical prediction in Fig. 2. During the midday period when the external conditions and solar radiation were steady the predicted flow was found to be approximately 10 per cent less than the measured value. However, in the early morning and late afternoon the theoretical results were higher than the measured values. The reason for the change of sign is thought to be due to the; omission of a factor to allow for reflection off the cover of the collector during the beginning and end of the: day. However, in the middle of the day when the beam direction of the sun was approximately normal to the collector, the theoretical analysis was found to underestimate the measured flow. In all the above investigations there were a number of uncertainties in the calculation of thermosyphon flow and the heat absorption of the collector. As there is very little data on the flow structure and even a possibility of flow instabilities [-11, 13] in the thermosyphon circuits, the following investigations were carried out in an electrically heated circuit to avoid the uncertainties associated with the heat absorption so that the accuracy of the thermosyphon analysis could be investigated.
were carefully monitored to ensure that the thermosyphon head did not vary during the measurements due to density variations in the tank between the inlet and outlet points. The flow rate was measured with a laser doppler anemometer to avoid introducing any restriction into the circuit. As the driving head in the circuit considered here was never greater than 15 mm of water, even the flow meter used by Shitzer et al. [11] w o u l d have interfered with the flow. The important feature of the laser doppler anemometer is that there is no flow disturbance and the instrument response is independent of all fluid properties provided the light can pass through the fluid. The light beams crossed the flow in a short section of perspex pipe which was machined out to the same internal diameter as the connecting pipes and joined by keyed flanges to accurately align with the supply. The arrangement of the laser anemometer optics and signal processing system is outlined in Fig. 4. As the laser system gives a point measurement of velocity it was necessary to integrate across the pipe to obtain the overall mass flow rate. The anemometer was used to check that the velocity profile at the measuring station followed the theoretical parabolic laminar distribution. The flow rate was subsequently determined by positioning the laser to measure the centre line velocity and using the known laminar flow profile to relate mass flow rate to centre line velocity. The accuracy of the flow measurements was checked by blocking the return pipe to the tank and bleeding flow from the top header. The flow rate measured by collecting the flow from the header was within 2 per cent of the value obtained from the combination of the laser measurement and the laminar profile.
4. APPARATUS An outline of the flow circuit used for the tests is shown in Fig. 3. A single riser 0.011 m dia. and 1.1 m long was connected between two headers and a storage tank by 0.022 m dia. piping. This model was not designed to simulate the flow conditions in an actual collector but to provide a simple flow circuit in which a test of thermosyphon flow calculations could be made. The heat input was provided by an electric heating cable wrapped around the full length of the riser, with 20 mm of insulation around the heater assembly. Temperatures were measured using calib r a t e d copper-constantan thermocouples inserted through the pipe wall and into the flow. The temperature in the tank between the inlet and outlet pipes was kept uniform by stirring the contents approximately 30 rain before each test, and the temperature distribution was checked by traversing a thermocouple down the tank. The tank depth above the return pipe connection was sufficient to ensure that hot return water was always above the upper connection. These factors
193
W.--.37
T PipeNo.5
'i
Upperhe~er 'L3t,
h2
~"" Pipe
No.I
1.1 Electncal~ht~riserhaCt __~ 1
1.42- monitodr~ staten Fig. 3. Dimensions of electrically heated test circuit (metres).
194
G.L. MORRISONand D. B. J. RANATUNGA
t Perspex pipe.,...,~~ Photocliode
I 'o- I ~arn sOtitler ~
.....
I
Fig, 4. Laser anemometer. 5. RESULTS The flow rate and temperature were measured for three values of vertical separation between the tank and riser as described in Table I and Fig. 3. The length of all other pipes were the same as shown in Fig. 3 and pipes 1 and 5 and the riser were vertical. The results of the measurements of mass flow rate and temperature change across the riser are shown as a function of heat input in Figs. 5 and 6. A comparison between the measured flow and the flow predicted by solving eqns (2) and (3) is shown in Fig. 7, The substantial deviation between the measured and predicted flow rates indicates that the analysis of thermosyphon flow outlined in Section 2 is inadequate. 6. DETAILED ANALYSIS
this analysis are given in Table 2 as the ratio (M) of pressure drop in developing flow compared to the pressure drop in an equal length of fully developed flow at the same Reynolds number. The data in Table 2 is described by the following function: 0.038 M = 1.0 + (l/d Rd)0'96" (4) For a typical riser 1.5 m long and 0.01 m dia. at a Reynolds number of 1000 the ratio of frction in undeveloped to developed flow is 1.23:1, thus the friction is underestimated by 19 per cent and at a Reynolds number of 2000 the error is 32 per cent. Thus a correction for developing flow should be incorporated in friction calculations by increasing the friction factor in eqn (2) by the amount given by eqn (4).
The results obtained above suggest a number of 6.3 Minor losses improvements that could be made to the analysis of In most published work the effect of minor head thermosyphon flow rate. losses at bends and exits has been included; however, 6.1 Friction Due to the long development length in laminar flow the friction analysis should take into account the increased resistance in the developing section. The flow development length in a 0.025 m dia~ pipe is 1.45 m at a R~ of 1000 and 2.9 m at a RN of 2000. As these lengths are greater than the length of most risers, it is likely that the increased friction in developing flow will have a significant effect on thermosyphon flow. 6.2 Correctionsfor developingflow Detailed analysis of developing flow in straight tubes was made by Langhaar [10]. The results of Table 1
Experiment A B C
Connecting pipe lengths (m) Pipe 1 1.15 L36 1.78
Pipe 5 0.49 0.70 1.14
Vertical heights (m) h1 0.25 0.27 0.27
h2 1.35 1.37 1.35
°o
3o0 transport (~atts)
Fig. 5. Measurements of temperature change in the riser: O, A, D, experiments A, B, C.
Thermosyphon circulation in solar collectors i
i
i
i
Table 2
t
1 d. RN
AP developing flow (M) AP fully developed flow
0.0137 0.0179 0.0237 0.0341 0.0449 0.062 0.076 0.1 0.3 0.5
3.24 2.78 2.39 2.01 1.78 1.57 1.47 1.36 1.12 1.07
;8
6
2
I
,~
~o
38o
H~T
TRANSPO~ff
~8o
~o
(watts)
Fig. 6. Measurement of thermosyphon mass flow rate: O, A, D, experiments A, B, C. the loss factors that have been used were all based on data for turbulent flow. In laminar flow the kinetic energy correction factor is 100 per cent, thus exit head loss coefficients are double the values used in turbulent flow. This can be shown by integrating across a laminar flow profile to obtain the exact kinetic energy of the flow as follows. dQ =
dr = 2"
g
2g
Q.
(5)
Similarly for a sudden enlargement such as the entry of a pipe into a header the head loss coefficient for fully developed laminar flow is
V2(Ai?
8 A1
KL=E~\A22/ -3A22 + 2 I
I
I
I
]
I
.
195
(6) I
1,4
For an area increase of 4:1 which is typical for headers in a collector, the loss coefficient is KL = 1.38, while the corresponding value for turbulent flow is K r = 0.56. The losses associated with enlargements and exits are usually insignificant in turbulent flow, however for laminar thermosyphon flow the losses associated with these factors may contribute a significant component of the flow resistance. When the friction corrections outlined above are included in the evaluation of thermosyphon flow in Section 2, the error in the estimation of flow rate is reduced at high RN where there is a significant component of developing flow but the deviation is unchanged at low Reynolds numbers (Fig. 8). 6.4 Thermosyphonhead The usual procedure for calculating thermosyphon head is to relate the density at various points in the circuit to the bulk mean temperatures using a secondorder function [eqn (1)]. The density calculated in terms of bulk mean temperature in the supply pipes is valid but in the riser it is necessary to take account of the temperature distribution across the flow. Thus although the energy transfer is governed by the change of bulk mean ternperature along the riser, the thermosyphon h e a d J
i
i
i
1.2
~r
mv
1.C
~o
~o
~o
,o'~ ,~o
RN
Fig. 7. Comparison of predicted mass flow rate (rhr) based on eqn. (11) and measured mass flow rate (riaM):O, A, [], experiments A, B, C.
RN
Fig. 8, Comparison of predicted mass flow rate (fiVr) based on eqn. (11) and developing friction correction and measured mass flow rate (rhM):O, A, El, experiments A, B, C.
196
G.L. MORRISONand D. B. J. RANATUNGA
depends on the spatial average temperature and not the bulk mean temperature. An example of the magnitude of the difference in density calculated from the bulk mean and average temperatures in the riser can be found for fully developed laminar conditions as follows. The temperature profile in fully developed constant heat flux conditions is
r = T,~
2U dTm 0t dl
r2 +
(7) 16ro2
Density
and the average density over the cross-section is given by 1
r"
Jo 2nr p(r) dr
(8)
where p(r) is evaluated from eqns (1) and (7). The resqlt of the integration of eqn (8) is
[6
Pl = A rZ,. +
+B
GT,, + ~
Tm+~G
1
G2
+C.
(9)
The average density obtained directly from the bulk mean temperature and eqn (1) is
Pz = A T ~ + 8T,,, + C.
(10)
At the inlet to the riser eqn (10) is the correct function since the inlet temperature is uniform over the cross-section, but at outlet (if fully developed conditions have been achieved) eqn (9) is the appropriate function. If the temperature along the inlet pipes is constant the values of riser thermosyphon head calculated from eqns (9) and (10) are as follows: (a) Thermosyphon head based on eqn (10)
HrA = 0.5 oH(p2 in
-
-
Fig. 9. Variation of density in thermosyphon circuit.
across the flow as a result of the change from a nonuniform velocity profile out of the riser to a uniform velocity in the header after mixing. Although the change of density is small it has a significant effect of the nett thermosyphon head. The amount by which eqn (11) underestimates the thermosyphon head in the total circuit for experiment B varies from 10 per cent for a Reynolds number of 100 to 40 per cent for RN = 1000. These corrections decrease the difference between the predicted and measured flow shown in Fig. 8 at low RN but increase the difference at high RN. However at high RN the profile at the riser outlet will not be fully developed and the thermosyphon head will be less than the value given by eqn (12). A better estimate of the thermosyphon head at high RN can be obtained by assuming that the density variation along the riser is the same as the initial section of a much longer riser with the same bulk mean temperature gradient. The density at any point can be estimated by considering a linear density gradient between the inlet and the density obtained by integrating the fully developed temperature profile [eqn
P2 out)/P
= 0.5 gH[A(TZ,.. - T m 2 o) + B(Tm, -- Tmo)]/P. (11) (b) Thermosyphon head based on a linear density transition between an inlet section at uniform temperature and at an outlet section with a fully developed temperature profile [eqn (9)].
-20
HTs = 0.5gH(P2i, - Plo,t)/P = 0 . 5 g H [ A t T 2, - T~ o) + BtTm, - 7",,o) - A ( 6 G T " " + a 6 " 2 G 2 ] - 3 Bi/ G]/#'121
I~ -10
(12)
The variation of density around the circuit implied by the above analysis is shown in Fig. 9. This figure shows that as the fluid is mixed in the upper header, the average fluid density increases even though the bulk mean temperature does not change. The change of spatial mean density when the fluid is mixed in the header is caused by the transfer of thermal energy
A
B
t
t
C
,t
1.0 HT/H
2.0
Fig. 10. Error in estimation of thermosyphon head, as a function of height of storage tank inlet (HT) above the riser, and the vertical height of riser H.
Thermosyphon circulation in solar collectors (9)] situated a distance L along the riser; where L is the thermal development length for the flow and is given by L = 0.05Rs Pr. d
(13)
When the above assumptions are applied the expression for the nett thermosyphon head in the riser becomes
Hrc
=
(0.5gH/~)~ -A
(6
A(T 2, 36.2
-
T m2L ) + B { T . ,
)
31/
GT.,. + ~ 1 G2 - B f ~ G
-
TmL)
fi (14)
197
of this factor increases the deviation between measured and predicted results at high RN. Without further information on the flow structure find temperature profiles in the riser it is not possible to improve the thermosyphon head analysis presented in this report. However, the nature of the results suggests that at low RN the thermosyphon head produced by the heat transfer from the walls may not be sufficient to entrain the flow in the centre of the riser. Thus a peak may develop in the velocity profile near the wall with a dip or recirculation in the centre of the riser. The result of this would be a deviation of the velocity and temperature profiles in the riser from the forced convection conditions assumed in the analysis. It is proposed to investigate this aspect of natural convection in the next stage of this study.
where TmLis obtained by extrapolating the bulk mean temperature gradient in the riser to the thermal development length L. 8. CONCLUSIONS The difference between the total system thermosyThe measurements have shown that the generally phon head calculated from eqns (1 I) and (14) is shown in Fig. 10 as a function of the height of the storage accepted method of calculating flow rate in thermotank inlet above the top of the riser• The results of syphon circuits underestimates the flow rate for Reynolds numbers less than 300 and overestimates this analysis have very little dependence on RN thus the problem of the incorrect sign of the thermosyphon • the flow for high Reynolds numbers. By incorporating the effect of friction in developing head correction still remains for high RN results. flow i'egions the accuracy of the analysis can be improved, but for low RN flows the analysis still under7. DISCUSSION estimates the flow rate by a significant amount. It is postulated that the flow may be influenced by nonComparison of the measured and predicted thermouniformit{es in the riser and that the deviation of the syphon flow rates shown in Fig. 7 indicates that the velocity and temperature profiles from the forced conconventional thermosyphon analysis1-1-3,9, 11, 12] underestimates the flow rate at low RN and overesti- vection conditions may cause the observed errors in mates it at high R~. The magnitude of the error will the analysis. depend on the arrangement of the total thermo• syphon circuit and the heat input to the system. The data on actual operating thermosyphon sysNOMENCLATURE tems 1-3,12] is in basic agreement with the predictions A, B, C constants relating density to temperature shown in Fig. 7. The circuit used in reports [3, 12] is d diameter of piping similar to case C in this investigation although the use G = 22Ur2(dTddl)/96ct of multiple risers will change the Reynolds number in # acceleration due to gravity H height of riser the supply and return pipes. The errors reported by HrA thermosyphon head based on bulk mean temOng and Shitzer [-3, 11] were approximately - 30 per perature cent for a RN of 220, and Ho [12] reported an error of Hr~ thermosyphon head based on spatial mean tem- 1 0 per cent at a R~ of 450. Although these experiperature ments are not directly equivalent to case C the results h vertical height K head loss coefficient indicate errors of the same sign and .similar magniKL head loss coefficient in laminar flow tude to the data presented in Fig. 7. Kr head loss coefficient in turbulent flow The major factor omitted from past investigations L thermal development length is a consideration of the additional friction due to ! length of flow circuit M ratio Of friction in developing flow and fully developing flow. When developing flow effects are developed flow included there is a significant reduction in the differRs Reynolds number based on diameter of riser ence between the observed and predicted flow rates at r radius high RN but at low RN the theoretical analysis still T temperature T,, bulk mean temperature underestimates the flow rate. /7 mean velocity Detailed analysis of the thermosyphon head in Section 6.4 indicates that actual force is higher than the Greek symbols value calculated by the usual analysis. Although the ct thermal diffusivity thermosyphon head corrections improve the accuracy p(r) density at radius "r" average density over cross section of pipe. of the theoretical calculation at low R~, consideration
198
G.L. MORRISON and D. B. J. RANATUNGA REFERENCES
1. D. J. Close, The performance of solar water heaters with natural circulation. J. Solar Energy 6, 33-40 (1962). 2. K. S. Ong, A finite-difference method to evaluate the thermal performance of a solar water heater. J. Solar Energy 16, 137-147 (1974). 3. K. S. Ong, An improved computer program for the thermal performance of a solar water heater. J. Solar Energy 18, 181-191 (1976). 4. H. C. Hottel and B. B. Woertz, The performance of fiat-plate solar heat collectors. Trans. ASME 64, 91-104 (1942). 5. C. L. Gupta and H. P. Garg, System design in solar water heaters with natural circulation. J. Solar Energy 12, 163-182 (1968). 6. A. Whillier and G. Saluja, The thermal performance of solar water heaters. J. Solar Energy 9, 21-26 (1965). 7. D. Chinnery, Solar water heating in South Africa. CSIRO Rept 248 (1967).
8. P. Ohanessian and W. W. S. Charters, Thermal simulation of a passive solar house using a Trombe-Michel wall structure. J. Solar Energy 20, 275-281 (1978). 9. Y. Zvirin, A. Shitzer and G. Grossman, The natural circulation solar heater-models with linear and nonlinear temperature distributions. Int. J. Heat & Mass Transfer 20, 997-999 (1977), 10. H. L. Langhaar, Steady flow in the transition length of a straight tube, ASME J. Applied Mechanics 9, 55-58 (1942). 11. A. Shitzer, D. Kalmanoviz, Y. Zvirin and G. Grossman, Experiments with a Flat Solar Water Heating System in Thermosyphonic Flow. Teehnion, Israel, Mech. Eng. Rept TME 328 (1978). 12. Mau-Sun Ho, Thermosyphon flow in flat plate solar collectors. M. Eng. Sc. Thesis, University of N.S.W. (1977). 13. J. B. Keller, Periodic oscillations in a model of thermal convection. J.F.M. 26, 599--606 (1966).
THERMOSYPHON CIRCULATION IN SOLAR COLLECTORS G. L. MORRISON
School of Mechanical and Industrial Engineering, University of New South Wales, Kensington, 2033, Australia and D. B. J. RANATUNGA Solar Energy Division, National Engineering Research and Development Centre, Colombo, Sri Lanka (Received 5 March 1979; revision accepted 2 October 1979) Abstract--Theoretical predictions of flow rate in thermosyphon solar collectors are compared with experimental measurements obtained using a laser doppler anemometer. Modifications to the usual method of analysis are proposed to improve the accuracy of the predictions, and the results are compared with flow rate predictions and measurements in other investigations.
l. INTRODUCTION
Solar collectors utilizing thermosyphon flow to transport energy from the collector to the store are one of the simplest and most widely used solar collection devices. There has been extensive work on the analysis of the performance of such systems [1-7] and many experimental tests have been reported on the overall thermodynamic performance. Although these studies cover a period of more than 30 yr there have only been two reports of investigations in which the actual thermosyphon velocity was measured. The obvious reason for the lack of detailed investigation of thermosyphon velocity is the problem of measuring a relatively slow flow without introducing additional friction which would affect the hydrodynamic operation of the system. As the thermosyphon driving head is usually in the range of 1-30 mm of water it is not possible to use an insertion or restriction flow meter, nor a device which has a non-linear resistance, as this would distort the system characteristics. As thermosyphon flow is also important in such devices as the Trombe-Michel wall [8] and other passive collectors and storage devices, the following study was initiated to analyse and measure the characteristics of thermosyphon flow in typical solar configurations.
temperature height data for the system shown in Fig. 1. By analysing the radiation absorption properties of the collector the change of bulk temperature along the riser tube (points 2 to 3 in Fig. 1) can be evaluated in terms of the flow rate. The density of the fluid at either end of the collector is then computed in terms of the bulk temperature as follows: p = A T 2 + B T + C.
(1)
The density variation along the collector is usually assumed to be linear; however, the case of non-linear bulk temperature rise has been investigated by Zirrin et al. [9]. The thermosyphon head (area of the height vs density diagram) is equated to the friction head as follows: h Ts -
#( ) ~
T2
flU 2 KU 2 (2ATm + B) = 2gdgd + - 2 g -
(2)
where Tm is the average bulk mean temperature in the collector and g(h) = 2(h3 - hi) - (h2 - hi)
(h 3 h6 --
h5) 2
hs
(3)
By combining eqn (2) with an energy balance for the collector the thermosyphon flow and bulk temperature rise through the collector can be evaluated in terms of the solar radiation and ambient conditions. As part of this analysis the following assumptions 2. ANALYSISOF THERMOSYPHON FLOW are made: (a) The friction head is evaluated for fully The first published analysis of a thermosyphon. developed laminar flow conditions. (b) The thermosolar water heater circuit was by Close I-1]. There syphon head in the riser is computed from the bulk havebeen many other publications on the analysis of mean temperature at the inlet and outlet to the collecthese systems but they are all based on the original tor. formulation [1]. The validity of the first assumption will depend on The essential feature of this analysis is the compu- the particular situation being analysed, however in tation of the thermosyphon driving head from the collector tubes the flow will nearly always be in the S.E.
24/2--F
191
192
G.L. MORRISONand D. B. J. RANATUNGA
/I
TQnk
3
"~ Cottector -2
Temperature
Fig. 1. Temperature distribution in a thermosyphon collector system.
developing flow regime. Also in most systems the supply and return pipes are l~ept as short as possible, thus friction is likely to be influenced by developing flow in all pipe segments. The effect of increased friction due to developing flow is well documented [10]. However, the friction in the collector tubes is complicated by the heat transfer from the wall which may cause a significant difference between the velocity gradients in the driving section of a thermosyphon circuit and in unheated developing flow. An important aspect of thermosyphon flow is that in the riser tubes the density and thus thermosyphon head depends on the actual temperature distribution over the cross-section rather than the bulk temperature. In most circuits the flow out of the collector tubes is well mixed in the header and thus the density of the fluid in the connecting tubes can be computed from the bulk temperature, but in the collector tubes the fluid density should be computed by integrating r
i
the actual temperature distribution over the crosssection and length of the riser. 3. T H E R M O S Y P H O N
FLOW
The first reported measurement of flow rate in a thermosyphon solar collector was made by Ong [2] who timed the passage of an injected dye trace. Ong compared the variation of actual and predicted flow over a typical day and found that the theoretical analysis underestimated the flow during most of the day. Shitzer e t a l . [ l l ] also measured thermosyphon flow using a thermal dissipation tracing method which introduced an hydraulic resistance of less than 1 mm of water at a Reynolds number of 1100. The mass flow measurements in [11] were found to be approximately 30 per cent higher than the theoretical predictions during the period of steady flow near
i
i O
~
i
11
10
2
~
8
z
\
lb
MEASUREMENTS
I'1
h
AM
t
~ PM
Time
Fig. 2. Thermosyphon flow rate.
"
Thermosyphon circulation in solar collectors solar noon. Shitzer et al. attribute the difference to dynamic effects and uncertainty in assessing the values of the parameters used in the collector efficiency calculation. They also observed that the flow rate fluctuated considerably even when other factors we,re constant, and suggested that this may be due to hydrodynamic instability in the collector-storage tank system. As part of the study reported in this paper, a preliminary investigation of the flow rate in an operating collector system was carried out [12] using a laser doppler anemometer system outlined in Section 4 of this paper. The variation of thermosyphon flow during a clear day is compared with a theoretical prediction in Fig. 2. During the midday period when the external conditions and solar radiation were steady the predicted flow was found to be approximately 10 per cent less than the measured value. However, in the early morning and late afternoon the theoretical results were higher than the measured values. The reason for the change of sign is thought to be due to the; omission of a factor to allow for reflection off the cover of the collector during the beginning and end of the: day. However, in the middle of the day when the beam direction of the sun was approximately normal to the collector, the theoretical analysis was found to underestimate the measured flow. In all the above investigations there were a number of uncertainties in the calculation of thermosyphon flow and the heat absorption of the collector. As there is very little data on the flow structure and even a possibility of flow instabilities [-11, 13] in the thermosyphon circuits, the following investigations were carried out in an electrically heated circuit to avoid the uncertainties associated with the heat absorption so that the accuracy of the thermosyphon analysis could be investigated.
were carefully monitored to ensure that the thermosyphon head did not vary during the measurements due to density variations in the tank between the inlet and outlet points. The flow rate was measured with a laser doppler anemometer to avoid introducing any restriction into the circuit. As the driving head in the circuit considered here was never greater than 15 mm of water, even the flow meter used by Shitzer et al. [11] w o u l d have interfered with the flow. The important feature of the laser doppler anemometer is that there is no flow disturbance and the instrument response is independent of all fluid properties provided the light can pass through the fluid. The light beams crossed the flow in a short section of perspex pipe which was machined out to the same internal diameter as the connecting pipes and joined by keyed flanges to accurately align with the supply. The arrangement of the laser anemometer optics and signal processing system is outlined in Fig. 4. As the laser system gives a point measurement of velocity it was necessary to integrate across the pipe to obtain the overall mass flow rate. The anemometer was used to check that the velocity profile at the measuring station followed the theoretical parabolic laminar distribution. The flow rate was subsequently determined by positioning the laser to measure the centre line velocity and using the known laminar flow profile to relate mass flow rate to centre line velocity. The accuracy of the flow measurements was checked by blocking the return pipe to the tank and bleeding flow from the top header. The flow rate measured by collecting the flow from the header was within 2 per cent of the value obtained from the combination of the laser measurement and the laminar profile.
4. APPARATUS An outline of the flow circuit used for the tests is shown in Fig. 3. A single riser 0.011 m dia. and 1.1 m long was connected between two headers and a storage tank by 0.022 m dia. piping. This model was not designed to simulate the flow conditions in an actual collector but to provide a simple flow circuit in which a test of thermosyphon flow calculations could be made. The heat input was provided by an electric heating cable wrapped around the full length of the riser, with 20 mm of insulation around the heater assembly. Temperatures were measured using calib r a t e d copper-constantan thermocouples inserted through the pipe wall and into the flow. The temperature in the tank between the inlet and outlet pipes was kept uniform by stirring the contents approximately 30 rain before each test, and the temperature distribution was checked by traversing a thermocouple down the tank. The tank depth above the return pipe connection was sufficient to ensure that hot return water was always above the upper connection. These factors
193
W.--.37
T PipeNo.5
'i
Upperhe~er 'L3t,
h2
~"" Pipe
No.I
1.1 Electncal~ht~riserhaCt __~ 1
1.42- monitodr~ staten Fig. 3. Dimensions of electrically heated test circuit (metres).
194
G.L. MORRISONand D. B. J. RANATUNGA
t Perspex pipe.,...,~~ Photocliode
I 'o- I ~arn sOtitler ~
.....
I
Fig, 4. Laser anemometer. 5. RESULTS The flow rate and temperature were measured for three values of vertical separation between the tank and riser as described in Table I and Fig. 3. The length of all other pipes were the same as shown in Fig. 3 and pipes 1 and 5 and the riser were vertical. The results of the measurements of mass flow rate and temperature change across the riser are shown as a function of heat input in Figs. 5 and 6. A comparison between the measured flow and the flow predicted by solving eqns (2) and (3) is shown in Fig. 7, The substantial deviation between the measured and predicted flow rates indicates that the analysis of thermosyphon flow outlined in Section 2 is inadequate. 6. DETAILED ANALYSIS
this analysis are given in Table 2 as the ratio (M) of pressure drop in developing flow compared to the pressure drop in an equal length of fully developed flow at the same Reynolds number. The data in Table 2 is described by the following function: 0.038 M = 1.0 + (l/d Rd)0'96" (4) For a typical riser 1.5 m long and 0.01 m dia. at a Reynolds number of 1000 the ratio of frction in undeveloped to developed flow is 1.23:1, thus the friction is underestimated by 19 per cent and at a Reynolds number of 2000 the error is 32 per cent. Thus a correction for developing flow should be incorporated in friction calculations by increasing the friction factor in eqn (2) by the amount given by eqn (4).
The results obtained above suggest a number of 6.3 Minor losses improvements that could be made to the analysis of In most published work the effect of minor head thermosyphon flow rate. losses at bends and exits has been included; however, 6.1 Friction Due to the long development length in laminar flow the friction analysis should take into account the increased resistance in the developing section. The flow development length in a 0.025 m dia~ pipe is 1.45 m at a R~ of 1000 and 2.9 m at a RN of 2000. As these lengths are greater than the length of most risers, it is likely that the increased friction in developing flow will have a significant effect on thermosyphon flow. 6.2 Correctionsfor developingflow Detailed analysis of developing flow in straight tubes was made by Langhaar [10]. The results of Table 1
Experiment A B C
Connecting pipe lengths (m) Pipe 1 1.15 L36 1.78
Pipe 5 0.49 0.70 1.14
Vertical heights (m) h1 0.25 0.27 0.27
h2 1.35 1.37 1.35
°o
3o0 transport (~atts)
Fig. 5. Measurements of temperature change in the riser: O, A, D, experiments A, B, C.
Thermosyphon circulation in solar collectors i
i
i
i
Table 2
t
1 d. RN
AP developing flow (M) AP fully developed flow
0.0137 0.0179 0.0237 0.0341 0.0449 0.062 0.076 0.1 0.3 0.5
3.24 2.78 2.39 2.01 1.78 1.57 1.47 1.36 1.12 1.07
;8
6
2
I
,~
~o
38o
H~T
TRANSPO~ff
~8o
~o
(watts)
Fig. 6. Measurement of thermosyphon mass flow rate: O, A, D, experiments A, B, C. the loss factors that have been used were all based on data for turbulent flow. In laminar flow the kinetic energy correction factor is 100 per cent, thus exit head loss coefficients are double the values used in turbulent flow. This can be shown by integrating across a laminar flow profile to obtain the exact kinetic energy of the flow as follows. dQ =
dr = 2"
g
2g
Q.
(5)
Similarly for a sudden enlargement such as the entry of a pipe into a header the head loss coefficient for fully developed laminar flow is
V2(Ai?
8 A1
KL=E~\A22/ -3A22 + 2 I
I
I
I
]
I
.
195
(6) I
1,4
For an area increase of 4:1 which is typical for headers in a collector, the loss coefficient is KL = 1.38, while the corresponding value for turbulent flow is K r = 0.56. The losses associated with enlargements and exits are usually insignificant in turbulent flow, however for laminar thermosyphon flow the losses associated with these factors may contribute a significant component of the flow resistance. When the friction corrections outlined above are included in the evaluation of thermosyphon flow in Section 2, the error in the estimation of flow rate is reduced at high RN where there is a significant component of developing flow but the deviation is unchanged at low Reynolds numbers (Fig. 8). 6.4 Thermosyphonhead The usual procedure for calculating thermosyphon head is to relate the density at various points in the circuit to the bulk mean temperatures using a secondorder function [eqn (1)]. The density calculated in terms of bulk mean temperature in the supply pipes is valid but in the riser it is necessary to take account of the temperature distribution across the flow. Thus although the energy transfer is governed by the change of bulk mean ternperature along the riser, the thermosyphon h e a d J
i
i
i
1.2
~r
mv
1.C
~o
~o
~o
,o'~ ,~o
RN
Fig. 7. Comparison of predicted mass flow rate (rhr) based on eqn. (11) and measured mass flow rate (riaM):O, A, [], experiments A, B, C.
RN
Fig. 8, Comparison of predicted mass flow rate (fiVr) based on eqn. (11) and developing friction correction and measured mass flow rate (rhM):O, A, El, experiments A, B, C.
196
G.L. MORRISONand D. B. J. RANATUNGA
depends on the spatial average temperature and not the bulk mean temperature. An example of the magnitude of the difference in density calculated from the bulk mean and average temperatures in the riser can be found for fully developed laminar conditions as follows. The temperature profile in fully developed constant heat flux conditions is
r = T,~
2U dTm 0t dl
r2 +
(7) 16ro2
Density
and the average density over the cross-section is given by 1
r"
Jo 2nr p(r) dr
(8)
where p(r) is evaluated from eqns (1) and (7). The resqlt of the integration of eqn (8) is
[6
Pl = A rZ,. +
+B
GT,, + ~
Tm+~G
1
G2
+C.
(9)
The average density obtained directly from the bulk mean temperature and eqn (1) is
Pz = A T ~ + 8T,,, + C.
(10)
At the inlet to the riser eqn (10) is the correct function since the inlet temperature is uniform over the cross-section, but at outlet (if fully developed conditions have been achieved) eqn (9) is the appropriate function. If the temperature along the inlet pipes is constant the values of riser thermosyphon head calculated from eqns (9) and (10) are as follows: (a) Thermosyphon head based on eqn (10)
HrA = 0.5 oH(p2 in
-
-
Fig. 9. Variation of density in thermosyphon circuit.
across the flow as a result of the change from a nonuniform velocity profile out of the riser to a uniform velocity in the header after mixing. Although the change of density is small it has a significant effect of the nett thermosyphon head. The amount by which eqn (11) underestimates the thermosyphon head in the total circuit for experiment B varies from 10 per cent for a Reynolds number of 100 to 40 per cent for RN = 1000. These corrections decrease the difference between the predicted and measured flow shown in Fig. 8 at low RN but increase the difference at high RN. However at high RN the profile at the riser outlet will not be fully developed and the thermosyphon head will be less than the value given by eqn (12). A better estimate of the thermosyphon head at high RN can be obtained by assuming that the density variation along the riser is the same as the initial section of a much longer riser with the same bulk mean temperature gradient. The density at any point can be estimated by considering a linear density gradient between the inlet and the density obtained by integrating the fully developed temperature profile [eqn
P2 out)/P
= 0.5 gH[A(TZ,.. - T m 2 o) + B(Tm, -- Tmo)]/P. (11) (b) Thermosyphon head based on a linear density transition between an inlet section at uniform temperature and at an outlet section with a fully developed temperature profile [eqn (9)].
-20
HTs = 0.5gH(P2i, - Plo,t)/P = 0 . 5 g H [ A t T 2, - T~ o) + BtTm, - 7",,o) - A ( 6 G T " " + a 6 " 2 G 2 ] - 3 Bi/ G]/#'121
I~ -10
(12)
The variation of density around the circuit implied by the above analysis is shown in Fig. 9. This figure shows that as the fluid is mixed in the upper header, the average fluid density increases even though the bulk mean temperature does not change. The change of spatial mean density when the fluid is mixed in the header is caused by the transfer of thermal energy
A
B
t
t
C
,t
1.0 HT/H
2.0
Fig. 10. Error in estimation of thermosyphon head, as a function of height of storage tank inlet (HT) above the riser, and the vertical height of riser H.
Thermosyphon circulation in solar collectors (9)] situated a distance L along the riser; where L is the thermal development length for the flow and is given by L = 0.05Rs Pr. d
(13)
When the above assumptions are applied the expression for the nett thermosyphon head in the riser becomes
Hrc
=
(0.5gH/~)~ -A
(6
A(T 2, 36.2
-
T m2L ) + B { T . ,
)
31/
GT.,. + ~ 1 G2 - B f ~ G
-
TmL)
fi (14)
197
of this factor increases the deviation between measured and predicted results at high RN. Without further information on the flow structure find temperature profiles in the riser it is not possible to improve the thermosyphon head analysis presented in this report. However, the nature of the results suggests that at low RN the thermosyphon head produced by the heat transfer from the walls may not be sufficient to entrain the flow in the centre of the riser. Thus a peak may develop in the velocity profile near the wall with a dip or recirculation in the centre of the riser. The result of this would be a deviation of the velocity and temperature profiles in the riser from the forced convection conditions assumed in the analysis. It is proposed to investigate this aspect of natural convection in the next stage of this study.
where TmLis obtained by extrapolating the bulk mean temperature gradient in the riser to the thermal development length L. 8. CONCLUSIONS The difference between the total system thermosyThe measurements have shown that the generally phon head calculated from eqns (1 I) and (14) is shown in Fig. 10 as a function of the height of the storage accepted method of calculating flow rate in thermotank inlet above the top of the riser• The results of syphon circuits underestimates the flow rate for Reynolds numbers less than 300 and overestimates this analysis have very little dependence on RN thus the problem of the incorrect sign of the thermosyphon • the flow for high Reynolds numbers. By incorporating the effect of friction in developing head correction still remains for high RN results. flow i'egions the accuracy of the analysis can be improved, but for low RN flows the analysis still under7. DISCUSSION estimates the flow rate by a significant amount. It is postulated that the flow may be influenced by nonComparison of the measured and predicted thermouniformit{es in the riser and that the deviation of the syphon flow rates shown in Fig. 7 indicates that the velocity and temperature profiles from the forced conconventional thermosyphon analysis1-1-3,9, 11, 12] underestimates the flow rate at low RN and overesti- vection conditions may cause the observed errors in mates it at high R~. The magnitude of the error will the analysis. depend on the arrangement of the total thermo• syphon circuit and the heat input to the system. The data on actual operating thermosyphon sysNOMENCLATURE tems 1-3,12] is in basic agreement with the predictions A, B, C constants relating density to temperature shown in Fig. 7. The circuit used in reports [3, 12] is d diameter of piping similar to case C in this investigation although the use G = 22Ur2(dTddl)/96ct of multiple risers will change the Reynolds number in # acceleration due to gravity H height of riser the supply and return pipes. The errors reported by HrA thermosyphon head based on bulk mean temOng and Shitzer [-3, 11] were approximately - 30 per perature cent for a RN of 220, and Ho [12] reported an error of Hr~ thermosyphon head based on spatial mean tem- 1 0 per cent at a R~ of 450. Although these experiperature ments are not directly equivalent to case C the results h vertical height K head loss coefficient indicate errors of the same sign and .similar magniKL head loss coefficient in laminar flow tude to the data presented in Fig. 7. Kr head loss coefficient in turbulent flow The major factor omitted from past investigations L thermal development length is a consideration of the additional friction due to ! length of flow circuit M ratio Of friction in developing flow and fully developing flow. When developing flow effects are developed flow included there is a significant reduction in the differRs Reynolds number based on diameter of riser ence between the observed and predicted flow rates at r radius high RN but at low RN the theoretical analysis still T temperature T,, bulk mean temperature underestimates the flow rate. /7 mean velocity Detailed analysis of the thermosyphon head in Section 6.4 indicates that actual force is higher than the Greek symbols value calculated by the usual analysis. Although the ct thermal diffusivity thermosyphon head corrections improve the accuracy p(r) density at radius "r" average density over cross section of pipe. of the theoretical calculation at low R~, consideration
198
G.L. MORRISON and D. B. J. RANATUNGA REFERENCES
1. D. J. Close, The performance of solar water heaters with natural circulation. J. Solar Energy 6, 33-40 (1962). 2. K. S. Ong, A finite-difference method to evaluate the thermal performance of a solar water heater. J. Solar Energy 16, 137-147 (1974). 3. K. S. Ong, An improved computer program for the thermal performance of a solar water heater. J. Solar Energy 18, 181-191 (1976). 4. H. C. Hottel and B. B. Woertz, The performance of fiat-plate solar heat collectors. Trans. ASME 64, 91-104 (1942). 5. C. L. Gupta and H. P. Garg, System design in solar water heaters with natural circulation. J. Solar Energy 12, 163-182 (1968). 6. A. Whillier and G. Saluja, The thermal performance of solar water heaters. J. Solar Energy 9, 21-26 (1965). 7. D. Chinnery, Solar water heating in South Africa. CSIRO Rept 248 (1967).
8. P. Ohanessian and W. W. S. Charters, Thermal simulation of a passive solar house using a Trombe-Michel wall structure. J. Solar Energy 20, 275-281 (1978). 9. Y. Zvirin, A. Shitzer and G. Grossman, The natural circulation solar heater-models with linear and nonlinear temperature distributions. Int. J. Heat & Mass Transfer 20, 997-999 (1977), 10. H. L. Langhaar, Steady flow in the transition length of a straight tube, ASME J. Applied Mechanics 9, 55-58 (1942). 11. A. Shitzer, D. Kalmanoviz, Y. Zvirin and G. Grossman, Experiments with a Flat Solar Water Heating System in Thermosyphonic Flow. Teehnion, Israel, Mech. Eng. Rept TME 328 (1978). 12. Mau-Sun Ho, Thermosyphon flow in flat plate solar collectors. M. Eng. Sc. Thesis, University of N.S.W. (1977). 13. J. B. Keller, Periodic oscillations in a model of thermal convection. J.F.M. 26, 599--606 (1966).