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An experimental investigation of inclined open thermosyphons
Solar Energy Vol. 47, No. 4, pp. 313-326, 1991
0038--O92X/91 $3.00 + .00 Copyright © 1991 Pergamon Press plc
Printed in the U.S.A.
AN EXPERIMENTAL INVESTIGATION OF INCLINED OPEN T H E R M O S Y P H O N S M. BEHNIA and G. L. MORRISON School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney. Australia Abstract--This paper describes an investigation of free convective flow and thermal structures in an open ended inclined cylindrical thermosyphon with application to an evacuated tubular solar collector. The flow structure was visualised using dye and rheoscopic tracer particles and temperature measurements were made by a traversing thermocouple rake. During steady-state uniform heating a significant stagnant region was observed near the closed end of the tube, the length of which decreased with increasing wall temperature. For the case of differential heating, with the top half of the tube cross section at a higher temperature than the bottom half, there was no stagnant region. When the top half was at a lower temperature than the bottom half, there was a significant region of multicellular motion in the closed end of the tube. An inactive stagnant or multicellular region in an evacuated tube solar collector and other open thermosyphons would decrease the effectivenessof the heat transfer through the open end of the tube. l. INTRODUCTION
Natural convection of fluids in the presence of gravitational or Coriolis forces can be implemented as an effective means for cooling (or heating) applications. A particular application of this process is the transfer of heat from the hot wails of a tube to a cold reservoir. This is referred to as thermosyphon circulation. In the first scientifically documented application of such devices, Holzwarth[1] suggested a system for cooling of gas turbine blades. Ernest Schmidt[2] also proposed to use a thermosyphon for cooling turbine blades, and a turbine incorporating his idea was designed and built in Germany during World War II. The thermosyphon problem, with many engineering applications, has been the focus of numerous experimental and analytical studies. Such applications include, but are not limited to, cooling of turbine blades, electrical machine rotors, transformers, nuclear reactors, cryogenic equipment, internal combustion engines, water tube boilers, and solar collector tubes. A comprehensive review of the applications and pertinent research is given by Japikse [ 3 ]. Thermosyphon systems in the form of a tube, open to a reservoir at the top and closed at the lower end, are referred to as open thermosyphons. The study reported in this paper describes an experimental investigation of heat transfer by natural convection in an inclined heated tube sealed at its lower end and connected to a large constant temperature reservoir at the upper end. The direct application of interest is that of evacuated tubular solar collectors.
2. PREVIOUS WORK
The first reported study of open thermosyphons was an analytical study by Eckert and Jackson[4] using the assumptions that the flow was basically a boundary layer phenomenon and that it would be turbulent in most practical applications. They attempted to find
the maximum tube aspect ratio that could be used without the boundary layer becoming thick enough to block the circulation in the tube. The first experiments on an open thermosyphon were reported by Foyle[2] who observed that eddy motion developed as the fluid passed between the tube and the reservoir. He also noted that the heat transfer was independent of the tube length beyond a certain critical value, though it increased quickly with increasing diameter. Lighthill[5 ] presented the first detailed analytical study ofthermosyphons for laminar and turbulent flow. Leslie[6] extended Lighthill's analysis to include the effect of small angles of inclination to the vertical. Detailed experimental studies of the problem have been carded out by Foster[7 ] and Martini8]. The analytical study performed by Lighthill has served as the foundation for most thermosyphon analysis and it identifies the basic flow regimes in an open thermosyphon. Lighthill's analysis yielded three laminar regimes and three turbulent regimes. For large tube aspect ratios (i.e., radius/length) or large Rayleigh numbers, Lighthill showed that a boundary layer flow will apply since the boundary layer will occupy only a small portion of the tube. For smaller aspect ratios the boundary layers reach the centreline of the tube and the incoming and outgoing streams interfere and restrict the circulation, thus giving rise to a second regime. For high aspect ratios the interaction of wall effects produces a constant flow profile and a similarity solution is thus possible, giving a third flow regime. Leslie [ 6 ] published the first analytical treatment of an inclined thermosyphon. He used a laminar perturbation technique restricted to small inclination angles. His analysis showed that tilting increased the heat transfer for both the impeded similarity solution and for the boundary layer flow solution. This analysis does not reproduce the unstable effects that were shown by Martin to decrease the heat transfer for small inclinations; however, qualitative agreement was observed with Martin's measurements for larger angles. 313
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M. BEHNIAand G. L. MORRISON
For vertical thermosyphons Lighthill [ 5 ] predicted that if the product of Rayleigh number times the aspect ratio is less than 350, a stagnant region forms at the closed end of the tube. For an inclined tube the nature of the flow is governed by this parameter multiplied by the cosine of the tube inclination to the vertical. Martin [ 9 ] presented the first experimental study of inclined open thermosyphon behaviour for both laminar and turbulent conditions. For a Prandtl number in the range of 20-700, it was observed that the Nusselt number initially decreased with increasing inclination up to six degrees from the vertical. For larger angles, the Nusselt number increased and reached the value for a vertical tube at an inclination of 45 °. The initial drop in heat transfer was attributed to a disorderly flow pattern and the consequent mixing of the hot and cold fluid streams. For larger angles the secondary pressure gradients normal to the tube axis, yielded a more stable flow structure in which the hot stream is displaced toward the top edge. 3. PRESENT STUDY The particular application that prompted this study is the problem of heat extraction in Dewar type evacuated tubular solar collectors. Several types of absorber tubes have been designed, the most common design consists of two concentric glass tubes closed at one end with the inner tube (the solar absorber) being coated by a selective surface. These evacuated tubular solar collectors consist of a number of 30-50 m m diameter, 1.5-2.5 m long glass tubes manifolded at one end. The absorbed energy can be removed by natural convection of water in and out of the open end of tubes to the large diameter header tube. Details of the evacuated tubular solar collectors and manifolding are given by Window and Harding [ 10 ], Window [ 11 ], and Zhiqiang et al.[121. In the present study, an experimental apparatus was designed and built to study the flow structure and temperature field in an open ended inclined thermosyphon differentially heated and connected to a large tank. Numerical modelling of the flow is currently underway and will be reported later. The experimental study complements the work of Zhiqiang et al.[12] who measured temperature gradients along the outer wall of an electrically heated tube but did not investigate the flow structure in the tube. This study also applies to other applications such as flow in turbine blades, nuclear reactors and transformer cooling. In these flows, fluid adjacent to the heated tube wall rises (due to buoyancy) to the upper side of the inclined tube and discharges from the open end, while cool fluid is drawn into the bottom side of the open end of the tube. Inclination of the tube sets up a pressure gradient normal to the tube axis, which assists the circulation of fluid from the bottom to top side of the tube. Inclination of the tube might be expet:ted to improve the heat transfer relative to vertical tubes.
3.1 Experimental apparatus The experimental apparatus shown in Fig. 1 was designed to simulate the geometry of an evacuated tubular solar collector. The thermosyphon tube was made of a glass cylinder 1300 m m long and 21.3 mm in internal diameter with a 0.5 m m wall thickness. A concentric annular heat exchanger (jacket) 1200 m m long and 60 m m in diameter was placed around the tube for heating. The heat exchanger was made of perspex for visualising the flow in the central tube. This heating jacket was partitioned in such a way that the top and bottom halves of the tube cross section could be independently heated. The partition consisted of a 2 m m thick splitter plate located in the annular space between the inner glass tube and the concentric perspex heat exchanger outer wall. If the tube was moved to a horizontal position the splitter plate would also be horizontal. The tube was heated by circulating water from two constant temperature baths through the two halves of the heating jacket at a flow rate of about 15 L/rain. The flow rate was sufficiently high to ensure isothermal conditions on the outside of the glass tube. The thermosyphon tube was connected by a 100 m m long unheated section of tube to an isothermal reservoir of 500 × 500 m m cross section. A 300 m m depth of water was maintained above the thermosyphon tube to ensure a uniform reservoir temperature at the level of the thermosyphon entry during the experiment. The thermosyphon tube was sealed at its lower end and the open top end was connected to the large constant temperature reservoir. The distance from the connection point to the bottom of the reservoir was 300 ram. Three connection points were provided on the side of the reservoir so that the tube could be inclined at angles of 30", 45", and 60* (to the vertical). The fluid temperature inside the tube was measured by a specially designed traversing thermocouple rake (Fig. 2). Five very fine copper constantan thermocoupies were fed through the 2 m m shaft o f a 2 m m stainless steel T-bar rake. One of the thermocouples was mounted on the centre of the head of the rake which spanned the thermosyphon tube diameter. The other four thermocouples were mounted 5 and 10 m m on either side of the centreline of the tube. The rake could be moved axially along the tube by feeding it through a sealed gland in the bottom end of the thermosyphon tube. The T-bar was moved very slowly by hand to the desired location and the temperatures were recorded aRer equilibrium conditions were achieved. The thermocouples were calibrated prior to installation in the tube. A calibrated thermocouple was also used to measure the tank water temperature. The thermocouple was located in the tank at the level of the entrance to the thermosyphon tube. A traversing thermocouple was also used in the reservoir to check for uniform conditions over the depth of the thermocouple tube entry. A multichannel data logger was used for recording the thermocouple outputs at prescribed time intervals. For flow visualisation, a three outlet 2 m m stainless
An experimental investigation of inclined open thermosyphons
/
T
Constant
temperature
315
rese r voi r
I
Glass tube
6 0 0 mm
T 300mm
500 mm
W a t e r from temperature Water
constant bath 1 _
from
constant temperature bath 2
Fig. I. General arrangement of the experimental apparatus.
steel T-bar, similar to the thermocouple rake, was designed for thymol blue dye or rheoscopic tracer solution injection into the thermosyphon tube. This tube could either be inserted from the open top of the thermosyphon or from the closed end in place of the thermocouple T-bar tube. The dye or rheoscopic tracer solution was fed into the tube from a temperature regulated reservoir. The tracer particles were illuminated by a sheet of light produced by a cylindrical lens. 3.2
Experimentalprocedure
For all experiments, the reservoir was filled with water to a depth of 600 ram. The reservoir was filled with water at the laboratory temperature, thoroughly mixed to eliminate thermal stratification and then covered with insulation and allowed to settle for two hours to ensure that no currents existed in the tank. During this time the two constant temperature baths
were regulated to the desired temperatures. The heating was then started by passing the water from the constant temperature baths through the two halves of the heat exchanger for a period of about one hour to ensure steady state conditions. The temperature in the reservoir at the entrance to the thermosyphon tube remained constant during each test. This was achieved by using a large reservoir ( 500 X 500 mm cross section ) and a 300 m m depth of water above the thermosyphon tube entry. During a test the hot layer of water that developed at the top of the reservoir did not penetrate to the level of the thermosyphon entry. Once steady state was reached, temperature measurement a n d / o r dye injection was initiated. The flow was visualised by either a diluted solution of thymol blue dye or a rheoscopic tracer solution. During the flow visualisation experiments, the flow pattern was recorded by hand-drawn sketches and still photogra-
316
M. BEHNIAand G. L. MORRISON
Thermocouples
Glass tube Perspex
tube~_
Heating fluid ~D. from bath1 --"---r
End cover
Heating fluid from bath 2
Thermocoupte rake
Fig. 2. Sectional view of the thermocouple rake inside the thermosyphon tube.
phy. The temperature distribution along the tube was recorded by slowly traversing the thermocouple rake. 4. RESULTS The first stage of the project reported in this paper is concerned with the overall flow and thermal structures as well as the stability of the flow, this information is needed to gain a better understanding of the problem in order to develop a numerical method for the prediction of flow structure and heat transfer. To this end, two series of experiments were performed. In the first series, the heating fluid temperature in both halves of the jacket was the same--this is referred to as uniform heating. In the second series, the heating fluid temperature in the two halves of the jacket were different (i.e., differential heating). It is noted that the tube heating technique used here corresponds to nearly uniform (along the tube) thermosyphon wall temperatures.
4.1 Uniform heating results The experiments were performed for tube inclinations of 30, 45, and 60 °. For each inclination a series of experiments were carried out for temperature differences between the water jacket and the reservoir from AT = 2 K up to the point where temperature unsteadiness was detected in the tube. For these angles of inclination the flow structure consisted of two re-
gions: ( 1) an active region where there is circulation of fluid between the tank and tube and (2) a stagnant region near the closed end of the tube in which there is very little circulation. For AT = 4 K, the flow patterns for angles of 0 = 30 ° and 60 ° are shown in Figs. 3 and 4. The stagnant region was identified by dye injection and was found to be very stable, occupying a fixed length of the tube for the duration of the experiments (up to 8 hours). The stability of the stagnant region was investigated by physically disturbing the interface between the stagnant and recirculating regions using the thermocouple rake; it was found to be stable. Further, the stagnant region was also disturbed thermally by increasing the heating jacket fluid temperature until the flow became turbulent and the stagnant region broke up. The temperature was then reduced to the initial value and reestablishment of the stagnant region was observed. Flow structure in the circulating region of the thermosyphon was studied by injecting dye in the flow region between the tube inlet and the top of the stagnant region. Flow visualisation at the tube mouth indicated that cold flow from the reservoir entered through the bottom two-thirds of the cross section and the hot flow left through the top one-third of the orifice cross-sectional area. As the cold flow in the bottom of the tube was heated, it moved up and around the curved walls until it entered the reverse hot stream at the top of the tube. The plan view of the patterns of stream lines
An experimental investigation of inclined open thermosyphons
317
\X \
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~0
";;
PLAIN VIEW
SIDE VIEW Fig. 3. Flow pattern inside thermosyphon tube for 30° inclination (uniform heating).
(observed. by dye tracing) appeared in the form of a crescent ( Figs. 3 and 4). The dye tracing indicated that the outgoing flow was faster in the case of steeper angles. For this heating condition ( A T = Tj,cket- T , ~ o i r = 4 K), the first streak line from the cold stream peeled off and joined the outgoing flow at a distance of 20 diameters (D) from the orifice for 60 ° inclination and at 30D from the orifice for 30 °. Before the interchange with the warm outgoing stream begins, the incoming stream travels a greater distance down the tube for tube inclination of 30 ° than for 60 °. The length of the stagnant region was about 5D and 16D for 30 ° and 60 ° inclination, respectively. The length of each cres-
cent formed when a stream line turned up the tube wall and entered the hot return stream was 4D for 30 ° and 2D for 60 ° inclination (Figs. 3 and 4). Lighthill [ 5 ] suggested that the modified parameter (for inclined tubes) that predicts the existence of a stagnant region is defined as: r =Rar.cosO/L where Ra is the Rayleigh number based on the tube radius (r) and the temperature difference between the wall and the tube axis; L is the tube length. According to Lighthill if the value o f t is less than 350, the stagnant
318
M. BEHNIAand G. L. MORRISON
76"o
~,,J'~>,~ST'.,,
PLAN VIEW
"r4"G/04/ SIDE VIEW Fig. 4. Flow pattern inside thermosyphon tube for 60 ° inclination (uniform heating).
region forms. For the tube geometry used in this study, the critical value of T corresponds to a temperature difference of less than 2.8, 3.4, and 4.8 K for inclinations of 30, 45, and 60 ° , respectively. These values of Lighthilrs modified criteria were found to underestimate the conditions at which a stagnant region developed in the experiments reported here. This may be due to Lighthill's assumption of a very large Prandtl number that resulted in inertia terms being neglected in the governing equations. The observed ratio of stagnant region length to total tube length ( L J L ) as a function of the parameter ~for different inclinations is #oven in Fig. 5. It is noted that the Rayleigh number was based on the tube radius and the temperature difference between the heating jacket fluid and the reservoir ( A T ) . In Lighthill's correlation the temperature difference is between the tube wall and the incoming fluid. Due to the temperature drop across the glass tube the temperature difference used to correlate the experimental data shown in Fig. 5 will be approximately 20% larger than the temperature difference between the inside wall surface and the incoming fluid (estimated from the conductivity ofthe glass tube and the free convection film resistance on the inside surface of the tube. For a #oven heating condition (i.e., A T ) , the length of the stagnant region (L,) is the smallest at 0 = 45 °, and largest at 30 °. The smaller the value of Ls the greater is the length of tube actively transferring energy to the open top. Therefore, from this point of view, of the three angles tested, the 45 ° inclination yields better energy extraction.
In open thermosyphon tubes, a partitioning plate is sometimes placed at the opening to separate the cold incoming and hot outgoing streams[ 10]. In order to determine the effect of the tube entry geometry on the flow, the horizontal centreline of the inlet orifice (21.3 m m dia.) was covered by a 5 mm wide tape. It was observed that the length of the stagnant region decreased by 75% compared to the unrestricted entry. This effect is attributed to better separation of the incoming and outgoing streams. Further, when the tape was replaced by a 5 mm diameter cylindrical rod, the
0"8
Ls/Lo. 4
o.21_ 2
"--4=_230 ° 6
10
1/,
18
22
28
Ratcose/1oo Fig. 5. Observed nondimensional length of stagnant region versus inclination for uniform heating. (Arrow indicates Lightill's large Prandtl number criteria.)
An experimental investigation of inclined open thermosyphons
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1.0
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319
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I
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J
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(c)
I
0"8
1-0
(d)
Fig. 6. Dimensionless fluid temperature along a thermosyphon tube inclined at 30* (uniform heating).
same effect was observed. When the obstructions were placed vertically across the opening, the length of the stagnant region increased by 50% and 30% for the tape and cylindrical rod, respectively. Thus the boundary conditions at the open end of the thermosyphon have a significant effect on the flow structure near the closed end of the tube. Modelling this open end boundary condition is the most difl~cult aspect of numerical simulation of this type of flow.
The fluid temperatures measured inside the tube were nondimensionalised with respect to the temperature difference between the jacket and the reservoir ( A T ) , i.e., t = (Tx-
T~r~oir)lAT
where t is the dimensionless temperature and Tx is the fluid temperature at location x measured from the
320
M. BEHNIAand G. L. MORRISON
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0-8
1"0
(c)
0 0
I 0"2
"~ I 0.4
I 0"6
I 0"8
1"0
X/L (d)
Fig. 7. Dimensionless fluid temperature along a thermosyphon tube inclined at 45 ° (uniform heating).
closed end of the tube. The distance x was nondimensionalised with respect to the total thermosyphon tube length L. The thermocouple rake was positioned such that temperature profiles were measured on a vertical plane passing through the axis of the tube. For an inclination of 30 ° , the dimensionless temperature profiles for different heating conditions are shown in Fig. 6. The open end of the thermosyphon is located at x / L
= 1. The temperature profiles To and 7"4 are the dimensionless temperatures near the top and bottom walls of the tube, respectively. 7"2 is the dimensionless temperature along the axis of the tube. T~ and 7"3 are dimensionless temperatures halfway between To, 7"2 and Tz, 7"4 positions, respectively. The interface between the recirculating and stagnant regions can be identified from where the temperature profiles merge
An experimental investigation of inclined open thermosyphons
1.0
1"0
0"~
321
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TI
0.I-
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02
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I
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1.0
(d)
Fig. 8. Dimensionless fluid temperature along a thermosyphon tube inclined at 60 ° (uniform heating).
together. At this point, there is a very sharp temperature gradient in the stagnant region. As expected from the flow visualisation results, the temperature measurements also indicate that the stagnant region length decreases with an increase in the temperature difference between the reservoir and the jacket (AT). Similar behaviour was observed from temperature measurements at other tube inclinations (see Figs. 7 and 8). Again, in support of the flow visualisation results, for
a given heating condition, the temperature measurements indicate a shorter stagnant region at 45 ° (compared to 30 ° and 60 ° inclinations), for 45 ° a AT > 4 K destroys the stagnant region. It can be seen that for a low AT, temperature profile T, crosses T~ toward the end of the recirculation zone. This is due to very weak recirculation near the stagnant region resulting in heat transfer by conduction becoming more significant than convection in this region.
M. BEHNIA and G: L. MORRISON
322
% O
Fig. 9. Flow pattern inside a thermosyphon tube for the differential heating and tube inclination of 60*.
Further, it is also observed t h a t the t e m p e r a t u r e near the u p p e r wall o f the t u b e decreases towards the tube e n t r a n c e (see To profiles). T h i s is d u e to m i x i n g between h o t fluid m o v i n g along the u p p e r wall o f the tube with cold inlet fluid convected up the curved walls. F o r all t u b e inclinations a n d heating conditions, t h e t e m p e r a t u r e o f the cold fluid stream o n the b o t t o m o f t h e t u b e increased all the way d o w n to the s t a g n a n t end. T h i s c a n be seen from 7"4 profiles in Figs. 6-8.
4.2
Table 1. Length of the multicellular region for different tube inclinations and heating conditions* Length of stagnant or multiceUular region (mm) Tube inclination
30*
45 °
60 °
t
80*
350t
ATtop = 4 K -
O
-
-
100
ATbot = 4 K - - O ATt~ = 5 K
250
300
550
ATto, = 4 K - - O- A T~,,~ = 6 K
300
340
660
ATto, = 4 K - - 0 - AT~ = 8 K
400
500
720
450
560
800
-
ATtoo = 4 K -
O
8K
O
J'
Fig. 10. Temperature difference (with respect to the reservoir) measured on a vertical plane passing through the centre of the tube, inclination = 30*.
Differential heating results
This series o f e x p e r i m e n t s were p e r f o r m e d with the fluid in the 2 halves o f the heating j a c k e t at different temperatures. T h e heating c o n d i t i o n is identified by
-
O~
-
0
-
-
&Tb~ = 10 K
* Tube diameter = 21.3 ram, tube length = 1200 mm. t Indicates stagnant ~ , i o n .
the t e m p e r a t u r e difference between the heating fluid a n d the reservoir ( A T ) . W i t h the t o p h a l f A T l e s s t h a n t h a t o f the b o t t o m half, the flow structure was different from t h a t o f u n i f o r m heating. In this case, the bulk flow from the t a n k p e n e t r a t e d in the tube in a similar fashion to u n i f o r m heating. However, instead o f the s t a g n a n t region at the e n d o f the tube, there was a multicellular region w h i c h was visualized by injecting rheoscopic tracer particles. F o r a heating c o n d i t i o n o f the b o t t o m a n d t o p halves A T equal to 8 a n d 4 K, respectively, the flow p a t t e r n at a n inclination o f 60 ° is given in Fig. 9. F o r this particular experiment, the length o f the multicellular region was 30 tube diameters. Flow visualisation e x p e r i m e n t s were carried o u t at different heating c o n d i t i o n s a n d tube inclinations to q u a n t i f y the length o f the multiceilular region. T h e results are t a b u l a t e d in Table I. For c o m p a r i s o n purposes, the u n i f o r m heating results (i.e., the length o f the s t a g n a n t region) are also included. Increased bott o m half heating results in increased multicellular region length at the e n d o f the tube. W h e n the b o t t o m half o f the tube is at a higher t e m p e r a t u r e t h a n the t o p half, the cooler d e n s e r fluid layers are situated above the w a r m e r ones a n d as a consequence, a muiticellular flow is established in this region. It is n o t e d t h a t unlike the u n i f o r m heating results, the length o f this region increases m o n o t o n i c a l l y with the tube inclination. T e m p e r a t u r e profiles m e a s u r e d o n a vertical plane
An experimental investigation of inclined open thermosyphons
7.0,
:%
~'c
8K~ Fig. 11. Temperature difference(with respect to the reservoir) measured on a vertical plane passing through the centre of the tube, inclination = 45 °.
323
For the bottom and top half AT of 4 and 8 K, respectively, the temperature profiles are shown in Fig. 14. In this case, for all inclinations, the fluid near the top half is consistently warmer than the fluid near the bottom half. It is noted that the incoming bulk flow is heated all the way to the end of the tube (see T2, T3, and 7"4). The outgoing flow is heated part way up the tube and then cooled by the incoming flow before it leaves the open end (see To and T~ ). It is interesting to note that the outgoing To at the mouth of the thermosyphon is nearly the same for both 30 ° and 45 ° inclinations. For an inclination of 45 ° the temperature profiles indicate a similar trend to those of Zhiqiang et al.[ 12 ]. It should be noted that their measurements were based on a constant wall heat flux condition; however, our results correspond to a nearly uniform wall temperalure.
5. CONCLUSIONS passing through the centre of the tube at different locations for the top and bottom half AT of 4 and 8. K, respectively, are given in Figs. 10 to 12. It is noted that in these figures the temperature difference with respect to the reservoir is plotted. In the multicellular zone near the closed end, the temperature adjacent to the top half tube wall is somewhat lower than the bottom. However, in the bulk flow region, the temperature near the top half is highei" although the bottom half heating is more intense. This is due to the fact that as the fluid is heated near the bottom it rises to the top of the tube and is then convected away toward the open end. The results presented in Figs. 10-12 are repiotted in Fig. 13 as the temperature measured by each individual thermocouple along the tube. For the case of differential heating, the dimensionless temperature, t is defined in the same way as for uniform heating experiments but the larger AT is used. The temperature profiles along the tube indicate that near the closed end 7"4 is slightly higher than To for all inclination angles (Fig. 13 ). However, toward the open end To is markedly higher than T4. The crossing of these two profiles corresponds to the interface between the multicellular and the bulk flow regions. Further, as the fluid enters the tube, it is heated along the tube by the heating jacket bottom wall (see 7"2, T3, and 7"4profiles in Fig. 13). The outgoing fluid near the top wall is continuously cooled (see To and Tj profiles). The gradient of T2, T3, and 7"4 profiles is sharper than that of To and T~. Experiments were also performed with the top half jacket temperature difference higher than the lower half. Flow field observations indicated that the bulk flow entering from the reservoir penetrated to the end of the thermosyphon tube and no stagnant or multicellular regions existed. In this case, increased top half heating resulted in a stronger bulk flow between the tank and the tube compared to that of uniform heating.
Free convection flow and temperature fields in an open-ended inclined cylindrical thermosyphon with application to evacuated tube solar collectors have been experimentally studied in the laboratory. Different tube inclinations and heating conditions were considered. For uniform heating of a single-ended thermosyphon tube, a significant stable stagnant region exists near the closed end of the tube, the length of which decreases with increasing heating fluid temperature. The stagnant region length varies nonmonotonicaily with the angle of inclination and shows a m i n i m u m at 45 °. The tube entry geometry was found to be important. For the differential heating with the top half of the tube cross section at a lower temperature than the bottom half, there was a significant region of cellular motion near the closed end of the tube. For the top half heating more intensely than the bottom half, there was
z~ '
18K,
Fig. 12. Temperature difference (with respect to the reservoir) measured on a vertical plane passing through the centre of the tube, inclination = 60 °.
324
M. BEHNIAand G. L. MORRISON
0"8
0"8
0:30 °
8 =45 °
0-6
0'6 t
O'Z.
To
ro
t
]'1
0- 4
&T=4 K
0.2
-
0.2
T1 &T=4 N
AT=8 K
o 0
~
0"2
0"4
'3
0"6 X/L
0"8
1"0
0
0-2
0-4
0"6
0'8
1.0
X/L
(a)
(b)
0"81 0=60*
t
ro Fig. 13. Dimensionless fluid temperature along the tube for differential heating.
AT=4K
rel 0
..... i 0"2
,
0.4
0"6
~T, 0"8
1.0
X/L
(c)
a strong bulk flow that penetrated the entire length of the tube. As evacuated tubular solar absorbers in concentrating collectors experience higher bottom heating
than top heating, the multicellular circulation observed in these experiments may influence the thermosyphon energy extraction efficiency.
An experimental investigation of inclined open thermosyphons
0.~ -
0=30
o
O'=45 o
0.8 ~
325
To
0"6
To 0.6
t
t
0"4
0-4
0.2
0"2~
KL
0
I
I
0"6
0"8
T4 0
0
0"2
0"4
1'0
0
I
I
I
I
I
0"2
0"4
0-6
0"8
1"0
~
X/L
(b)
(a)
0=60 °
0'8 -
0.6
-
To
~
t
T~
0
"
0 0
4
I 0.2
~
Fig. 14. Variation of dimensionless fluid temperature along the tube for differential heating.
t
I
I
I
0.4
0-6
0'8
1"0
X/L
REFERENCES
1. H. Holzwa~h, Die Entwicklungder Holzwa~h-GasTurbine, Holzwa~h-Ga~urbinen G.M.B.H., MuehlheimRuhn(1938).
2. R. T. Foyle, General discussion on heat transfer, Proc. Inst. Mech. Eng. ASME London, Conf. Proc., p. 382 (1951). 3. D. Japikse, Advances in thermosyphon technology, Adv. Heat Trans., 9, 1-111, (1972).
326
M. BEHNIA and G. L. MORRISON
•4. E. R. G. Eckert and T. W. Jackson, Analysis of turbulent free-convection boundary layer on a fiat plate, Nat. Adv. Comm. Aeronaut. NACA TC 2207 (1950). 5. M. J. Lighthill, Theoretical considerations on free convection in tubes, Quarterly Journal of Applied Mathematics, 6(4), 398--439 (1953). 6. F. M. Leslie, Free convection in the tilted open thermosyphon, J. Fluid Mech., 7, 115-127 (1959). 7. C. V. Foster, Heat transfer by free convection to fluids contained in vertical tubes, Ph.D Thesis, University of Delaware, Newark, Delaware ( 1953 ). 8. B.W. Martin, Free convection in an open thermosyphon, Proc. Roy. Soc., A230, 502 (1955).
9. B.W. Martin, Free convection heat transfer in the inclined open thermosyphon, Proc. Inst. Mech. Engg., 173, 761 (1959). 10. B. Window and G. L. Harding, Buoyancy effect and manifolding of single ended absorber tubes, Solar Ener~', 31, 152 (1983). I 1. B. Window, Heat extraction from single ended glass absorber tubes, Solar Energy, 31, 159 (1983). 12. Y. Zhiqiang, G. L. Harding, and B. Window, Water in glass manifolds for heat extraction from evacuated solar collector tubes, Solar Energy. 32, 223 (1984).
0038--O92X/91 $3.00 + .00 Copyright © 1991 Pergamon Press plc
Printed in the U.S.A.
AN EXPERIMENTAL INVESTIGATION OF INCLINED OPEN T H E R M O S Y P H O N S M. BEHNIA and G. L. MORRISON School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney. Australia Abstract--This paper describes an investigation of free convective flow and thermal structures in an open ended inclined cylindrical thermosyphon with application to an evacuated tubular solar collector. The flow structure was visualised using dye and rheoscopic tracer particles and temperature measurements were made by a traversing thermocouple rake. During steady-state uniform heating a significant stagnant region was observed near the closed end of the tube, the length of which decreased with increasing wall temperature. For the case of differential heating, with the top half of the tube cross section at a higher temperature than the bottom half, there was no stagnant region. When the top half was at a lower temperature than the bottom half, there was a significant region of multicellular motion in the closed end of the tube. An inactive stagnant or multicellular region in an evacuated tube solar collector and other open thermosyphons would decrease the effectivenessof the heat transfer through the open end of the tube. l. INTRODUCTION
Natural convection of fluids in the presence of gravitational or Coriolis forces can be implemented as an effective means for cooling (or heating) applications. A particular application of this process is the transfer of heat from the hot wails of a tube to a cold reservoir. This is referred to as thermosyphon circulation. In the first scientifically documented application of such devices, Holzwarth[1] suggested a system for cooling of gas turbine blades. Ernest Schmidt[2] also proposed to use a thermosyphon for cooling turbine blades, and a turbine incorporating his idea was designed and built in Germany during World War II. The thermosyphon problem, with many engineering applications, has been the focus of numerous experimental and analytical studies. Such applications include, but are not limited to, cooling of turbine blades, electrical machine rotors, transformers, nuclear reactors, cryogenic equipment, internal combustion engines, water tube boilers, and solar collector tubes. A comprehensive review of the applications and pertinent research is given by Japikse [ 3 ]. Thermosyphon systems in the form of a tube, open to a reservoir at the top and closed at the lower end, are referred to as open thermosyphons. The study reported in this paper describes an experimental investigation of heat transfer by natural convection in an inclined heated tube sealed at its lower end and connected to a large constant temperature reservoir at the upper end. The direct application of interest is that of evacuated tubular solar collectors.
2. PREVIOUS WORK
The first reported study of open thermosyphons was an analytical study by Eckert and Jackson[4] using the assumptions that the flow was basically a boundary layer phenomenon and that it would be turbulent in most practical applications. They attempted to find
the maximum tube aspect ratio that could be used without the boundary layer becoming thick enough to block the circulation in the tube. The first experiments on an open thermosyphon were reported by Foyle[2] who observed that eddy motion developed as the fluid passed between the tube and the reservoir. He also noted that the heat transfer was independent of the tube length beyond a certain critical value, though it increased quickly with increasing diameter. Lighthill[5 ] presented the first detailed analytical study ofthermosyphons for laminar and turbulent flow. Leslie[6] extended Lighthill's analysis to include the effect of small angles of inclination to the vertical. Detailed experimental studies of the problem have been carded out by Foster[7 ] and Martini8]. The analytical study performed by Lighthill has served as the foundation for most thermosyphon analysis and it identifies the basic flow regimes in an open thermosyphon. Lighthill's analysis yielded three laminar regimes and three turbulent regimes. For large tube aspect ratios (i.e., radius/length) or large Rayleigh numbers, Lighthill showed that a boundary layer flow will apply since the boundary layer will occupy only a small portion of the tube. For smaller aspect ratios the boundary layers reach the centreline of the tube and the incoming and outgoing streams interfere and restrict the circulation, thus giving rise to a second regime. For high aspect ratios the interaction of wall effects produces a constant flow profile and a similarity solution is thus possible, giving a third flow regime. Leslie [ 6 ] published the first analytical treatment of an inclined thermosyphon. He used a laminar perturbation technique restricted to small inclination angles. His analysis showed that tilting increased the heat transfer for both the impeded similarity solution and for the boundary layer flow solution. This analysis does not reproduce the unstable effects that were shown by Martin to decrease the heat transfer for small inclinations; however, qualitative agreement was observed with Martin's measurements for larger angles. 313
314
M. BEHNIAand G. L. MORRISON
For vertical thermosyphons Lighthill [ 5 ] predicted that if the product of Rayleigh number times the aspect ratio is less than 350, a stagnant region forms at the closed end of the tube. For an inclined tube the nature of the flow is governed by this parameter multiplied by the cosine of the tube inclination to the vertical. Martin [ 9 ] presented the first experimental study of inclined open thermosyphon behaviour for both laminar and turbulent conditions. For a Prandtl number in the range of 20-700, it was observed that the Nusselt number initially decreased with increasing inclination up to six degrees from the vertical. For larger angles, the Nusselt number increased and reached the value for a vertical tube at an inclination of 45 °. The initial drop in heat transfer was attributed to a disorderly flow pattern and the consequent mixing of the hot and cold fluid streams. For larger angles the secondary pressure gradients normal to the tube axis, yielded a more stable flow structure in which the hot stream is displaced toward the top edge. 3. PRESENT STUDY The particular application that prompted this study is the problem of heat extraction in Dewar type evacuated tubular solar collectors. Several types of absorber tubes have been designed, the most common design consists of two concentric glass tubes closed at one end with the inner tube (the solar absorber) being coated by a selective surface. These evacuated tubular solar collectors consist of a number of 30-50 m m diameter, 1.5-2.5 m long glass tubes manifolded at one end. The absorbed energy can be removed by natural convection of water in and out of the open end of tubes to the large diameter header tube. Details of the evacuated tubular solar collectors and manifolding are given by Window and Harding [ 10 ], Window [ 11 ], and Zhiqiang et al.[121. In the present study, an experimental apparatus was designed and built to study the flow structure and temperature field in an open ended inclined thermosyphon differentially heated and connected to a large tank. Numerical modelling of the flow is currently underway and will be reported later. The experimental study complements the work of Zhiqiang et al.[12] who measured temperature gradients along the outer wall of an electrically heated tube but did not investigate the flow structure in the tube. This study also applies to other applications such as flow in turbine blades, nuclear reactors and transformer cooling. In these flows, fluid adjacent to the heated tube wall rises (due to buoyancy) to the upper side of the inclined tube and discharges from the open end, while cool fluid is drawn into the bottom side of the open end of the tube. Inclination of the tube sets up a pressure gradient normal to the tube axis, which assists the circulation of fluid from the bottom to top side of the tube. Inclination of the tube might be expet:ted to improve the heat transfer relative to vertical tubes.
3.1 Experimental apparatus The experimental apparatus shown in Fig. 1 was designed to simulate the geometry of an evacuated tubular solar collector. The thermosyphon tube was made of a glass cylinder 1300 m m long and 21.3 mm in internal diameter with a 0.5 m m wall thickness. A concentric annular heat exchanger (jacket) 1200 m m long and 60 m m in diameter was placed around the tube for heating. The heat exchanger was made of perspex for visualising the flow in the central tube. This heating jacket was partitioned in such a way that the top and bottom halves of the tube cross section could be independently heated. The partition consisted of a 2 m m thick splitter plate located in the annular space between the inner glass tube and the concentric perspex heat exchanger outer wall. If the tube was moved to a horizontal position the splitter plate would also be horizontal. The tube was heated by circulating water from two constant temperature baths through the two halves of the heating jacket at a flow rate of about 15 L/rain. The flow rate was sufficiently high to ensure isothermal conditions on the outside of the glass tube. The thermosyphon tube was connected by a 100 m m long unheated section of tube to an isothermal reservoir of 500 × 500 m m cross section. A 300 m m depth of water was maintained above the thermosyphon tube to ensure a uniform reservoir temperature at the level of the thermosyphon entry during the experiment. The thermosyphon tube was sealed at its lower end and the open top end was connected to the large constant temperature reservoir. The distance from the connection point to the bottom of the reservoir was 300 ram. Three connection points were provided on the side of the reservoir so that the tube could be inclined at angles of 30", 45", and 60* (to the vertical). The fluid temperature inside the tube was measured by a specially designed traversing thermocouple rake (Fig. 2). Five very fine copper constantan thermocoupies were fed through the 2 m m shaft o f a 2 m m stainless steel T-bar rake. One of the thermocouples was mounted on the centre of the head of the rake which spanned the thermosyphon tube diameter. The other four thermocouples were mounted 5 and 10 m m on either side of the centreline of the tube. The rake could be moved axially along the tube by feeding it through a sealed gland in the bottom end of the thermosyphon tube. The T-bar was moved very slowly by hand to the desired location and the temperatures were recorded aRer equilibrium conditions were achieved. The thermocouples were calibrated prior to installation in the tube. A calibrated thermocouple was also used to measure the tank water temperature. The thermocouple was located in the tank at the level of the entrance to the thermosyphon tube. A traversing thermocouple was also used in the reservoir to check for uniform conditions over the depth of the thermocouple tube entry. A multichannel data logger was used for recording the thermocouple outputs at prescribed time intervals. For flow visualisation, a three outlet 2 m m stainless
An experimental investigation of inclined open thermosyphons
/
T
Constant
temperature
315
rese r voi r
I
Glass tube
6 0 0 mm
T 300mm
500 mm
W a t e r from temperature Water
constant bath 1 _
from
constant temperature bath 2
Fig. I. General arrangement of the experimental apparatus.
steel T-bar, similar to the thermocouple rake, was designed for thymol blue dye or rheoscopic tracer solution injection into the thermosyphon tube. This tube could either be inserted from the open top of the thermosyphon or from the closed end in place of the thermocouple T-bar tube. The dye or rheoscopic tracer solution was fed into the tube from a temperature regulated reservoir. The tracer particles were illuminated by a sheet of light produced by a cylindrical lens. 3.2
Experimentalprocedure
For all experiments, the reservoir was filled with water to a depth of 600 ram. The reservoir was filled with water at the laboratory temperature, thoroughly mixed to eliminate thermal stratification and then covered with insulation and allowed to settle for two hours to ensure that no currents existed in the tank. During this time the two constant temperature baths
were regulated to the desired temperatures. The heating was then started by passing the water from the constant temperature baths through the two halves of the heat exchanger for a period of about one hour to ensure steady state conditions. The temperature in the reservoir at the entrance to the thermosyphon tube remained constant during each test. This was achieved by using a large reservoir ( 500 X 500 mm cross section ) and a 300 m m depth of water above the thermosyphon tube entry. During a test the hot layer of water that developed at the top of the reservoir did not penetrate to the level of the thermosyphon entry. Once steady state was reached, temperature measurement a n d / o r dye injection was initiated. The flow was visualised by either a diluted solution of thymol blue dye or a rheoscopic tracer solution. During the flow visualisation experiments, the flow pattern was recorded by hand-drawn sketches and still photogra-
316
M. BEHNIAand G. L. MORRISON
Thermocouples
Glass tube Perspex
tube~_
Heating fluid ~D. from bath1 --"---r
End cover
Heating fluid from bath 2
Thermocoupte rake
Fig. 2. Sectional view of the thermocouple rake inside the thermosyphon tube.
phy. The temperature distribution along the tube was recorded by slowly traversing the thermocouple rake. 4. RESULTS The first stage of the project reported in this paper is concerned with the overall flow and thermal structures as well as the stability of the flow, this information is needed to gain a better understanding of the problem in order to develop a numerical method for the prediction of flow structure and heat transfer. To this end, two series of experiments were performed. In the first series, the heating fluid temperature in both halves of the jacket was the same--this is referred to as uniform heating. In the second series, the heating fluid temperature in the two halves of the jacket were different (i.e., differential heating). It is noted that the tube heating technique used here corresponds to nearly uniform (along the tube) thermosyphon wall temperatures.
4.1 Uniform heating results The experiments were performed for tube inclinations of 30, 45, and 60 °. For each inclination a series of experiments were carried out for temperature differences between the water jacket and the reservoir from AT = 2 K up to the point where temperature unsteadiness was detected in the tube. For these angles of inclination the flow structure consisted of two re-
gions: ( 1) an active region where there is circulation of fluid between the tank and tube and (2) a stagnant region near the closed end of the tube in which there is very little circulation. For AT = 4 K, the flow patterns for angles of 0 = 30 ° and 60 ° are shown in Figs. 3 and 4. The stagnant region was identified by dye injection and was found to be very stable, occupying a fixed length of the tube for the duration of the experiments (up to 8 hours). The stability of the stagnant region was investigated by physically disturbing the interface between the stagnant and recirculating regions using the thermocouple rake; it was found to be stable. Further, the stagnant region was also disturbed thermally by increasing the heating jacket fluid temperature until the flow became turbulent and the stagnant region broke up. The temperature was then reduced to the initial value and reestablishment of the stagnant region was observed. Flow structure in the circulating region of the thermosyphon was studied by injecting dye in the flow region between the tube inlet and the top of the stagnant region. Flow visualisation at the tube mouth indicated that cold flow from the reservoir entered through the bottom two-thirds of the cross section and the hot flow left through the top one-third of the orifice cross-sectional area. As the cold flow in the bottom of the tube was heated, it moved up and around the curved walls until it entered the reverse hot stream at the top of the tube. The plan view of the patterns of stream lines
An experimental investigation of inclined open thermosyphons
317
\X \
%
~0
";;
PLAIN VIEW
SIDE VIEW Fig. 3. Flow pattern inside thermosyphon tube for 30° inclination (uniform heating).
(observed. by dye tracing) appeared in the form of a crescent ( Figs. 3 and 4). The dye tracing indicated that the outgoing flow was faster in the case of steeper angles. For this heating condition ( A T = Tj,cket- T , ~ o i r = 4 K), the first streak line from the cold stream peeled off and joined the outgoing flow at a distance of 20 diameters (D) from the orifice for 60 ° inclination and at 30D from the orifice for 30 °. Before the interchange with the warm outgoing stream begins, the incoming stream travels a greater distance down the tube for tube inclination of 30 ° than for 60 °. The length of the stagnant region was about 5D and 16D for 30 ° and 60 ° inclination, respectively. The length of each cres-
cent formed when a stream line turned up the tube wall and entered the hot return stream was 4D for 30 ° and 2D for 60 ° inclination (Figs. 3 and 4). Lighthill [ 5 ] suggested that the modified parameter (for inclined tubes) that predicts the existence of a stagnant region is defined as: r =Rar.cosO/L where Ra is the Rayleigh number based on the tube radius (r) and the temperature difference between the wall and the tube axis; L is the tube length. According to Lighthill if the value o f t is less than 350, the stagnant
318
M. BEHNIAand G. L. MORRISON
76"o
~,,J'~>,~ST'.,,
PLAN VIEW
"r4"G/04/ SIDE VIEW Fig. 4. Flow pattern inside thermosyphon tube for 60 ° inclination (uniform heating).
region forms. For the tube geometry used in this study, the critical value of T corresponds to a temperature difference of less than 2.8, 3.4, and 4.8 K for inclinations of 30, 45, and 60 ° , respectively. These values of Lighthilrs modified criteria were found to underestimate the conditions at which a stagnant region developed in the experiments reported here. This may be due to Lighthill's assumption of a very large Prandtl number that resulted in inertia terms being neglected in the governing equations. The observed ratio of stagnant region length to total tube length ( L J L ) as a function of the parameter ~for different inclinations is #oven in Fig. 5. It is noted that the Rayleigh number was based on the tube radius and the temperature difference between the heating jacket fluid and the reservoir ( A T ) . In Lighthill's correlation the temperature difference is between the tube wall and the incoming fluid. Due to the temperature drop across the glass tube the temperature difference used to correlate the experimental data shown in Fig. 5 will be approximately 20% larger than the temperature difference between the inside wall surface and the incoming fluid (estimated from the conductivity ofthe glass tube and the free convection film resistance on the inside surface of the tube. For a #oven heating condition (i.e., A T ) , the length of the stagnant region (L,) is the smallest at 0 = 45 °, and largest at 30 °. The smaller the value of Ls the greater is the length of tube actively transferring energy to the open top. Therefore, from this point of view, of the three angles tested, the 45 ° inclination yields better energy extraction.
In open thermosyphon tubes, a partitioning plate is sometimes placed at the opening to separate the cold incoming and hot outgoing streams[ 10]. In order to determine the effect of the tube entry geometry on the flow, the horizontal centreline of the inlet orifice (21.3 m m dia.) was covered by a 5 mm wide tape. It was observed that the length of the stagnant region decreased by 75% compared to the unrestricted entry. This effect is attributed to better separation of the incoming and outgoing streams. Further, when the tape was replaced by a 5 mm diameter cylindrical rod, the
0"8
Ls/Lo. 4
o.21_ 2
"--4=_230 ° 6
10
1/,
18
22
28
Ratcose/1oo Fig. 5. Observed nondimensional length of stagnant region versus inclination for uniform heating. (Arrow indicates Lightill's large Prandtl number criteria.)
An experimental investigation of inclined open thermosyphons
1.0
1.0
0"8--
:)'8
Y
0-6-
319
To
3-6
t 0-/.-
)-4
T2 0-2~-
).2 AT= 2K 1
0
0-2
AT=/. K I
I
0.6 0.4 XIL
0-8
1.0
0
0
I
I
1
I
0-2
0.4
0-6
0"8
1.0
×IL
(a)
(b)
1"0
1"0
0"8--
3"8
To 0"6
To )'6
t )./,
0"4
0'2 AT=6 K
)'2 1 0
m
0
0-2
0.4
0"6
0"8
1"0
X/L
= I
0
I
0"2
J
0./. 0"6 XIL
(c)
I
0"8
1-0
(d)
Fig. 6. Dimensionless fluid temperature along a thermosyphon tube inclined at 30* (uniform heating).
same effect was observed. When the obstructions were placed vertically across the opening, the length of the stagnant region increased by 50% and 30% for the tape and cylindrical rod, respectively. Thus the boundary conditions at the open end of the thermosyphon have a significant effect on the flow structure near the closed end of the tube. Modelling this open end boundary condition is the most difl~cult aspect of numerical simulation of this type of flow.
The fluid temperatures measured inside the tube were nondimensionalised with respect to the temperature difference between the jacket and the reservoir ( A T ) , i.e., t = (Tx-
T~r~oir)lAT
where t is the dimensionless temperature and Tx is the fluid temperature at location x measured from the
320
M. BEHNIAand G. L. MORRISON
1.o
1-0
0"8
0.8~
T°~T~T ~
0.6-
-6
T~
0-4 -
0"2
0-2
&Ti-
A T=/., K
0
0
0 0
0"2
0.4
0"6
0-8
t 0.2
1.0
T4\ I I 0.Z. 0"6 X/L
X/L
l 0"8
1"0
(b)
(a)
1"0 I
0 . 8 ~ 0"6
,°t
0"8
o,_
°i
0
AT=8K 0-2
0"4 0"6 X/L
0-8
1"0
(c)
0 0
I 0"2
"~ I 0.4
I 0"6
I 0"8
1"0
X/L (d)
Fig. 7. Dimensionless fluid temperature along a thermosyphon tube inclined at 45 ° (uniform heating).
closed end of the tube. The distance x was nondimensionalised with respect to the total thermosyphon tube length L. The thermocouple rake was positioned such that temperature profiles were measured on a vertical plane passing through the axis of the tube. For an inclination of 30 ° , the dimensionless temperature profiles for different heating conditions are shown in Fig. 6. The open end of the thermosyphon is located at x / L
= 1. The temperature profiles To and 7"4 are the dimensionless temperatures near the top and bottom walls of the tube, respectively. 7"2 is the dimensionless temperature along the axis of the tube. T~ and 7"3 are dimensionless temperatures halfway between To, 7"2 and Tz, 7"4 positions, respectively. The interface between the recirculating and stagnant regions can be identified from where the temperature profiles merge
An experimental investigation of inclined open thermosyphons
1.0
1"0
0"~
321
3.8
--
TI
0.I-
}6-
t )./., -
0.4-
0.2-
).2-
AT=/-, K
AT= 6 K
1
0 0
02
1
L
0.4 0-6 X/L
0"8
I
0
I
0
1-0
0"2
0-6
0-8
1.0
X/L
(a)
(b) 1"0
1.0 A 0-8
0-4
0"8
f
f 0-6
0"6-
TI
t
t
0"4
0-4-
T2
0.2
0-2I
0 0
0"2
I
I
0"/.. 0"6 X/L
I
0"8
-I
0 1"0
(c)
0
0.2
0'/.. 0.6 X/L
0.8
"4
1.0
(d)
Fig. 8. Dimensionless fluid temperature along a thermosyphon tube inclined at 60 ° (uniform heating).
together. At this point, there is a very sharp temperature gradient in the stagnant region. As expected from the flow visualisation results, the temperature measurements also indicate that the stagnant region length decreases with an increase in the temperature difference between the reservoir and the jacket (AT). Similar behaviour was observed from temperature measurements at other tube inclinations (see Figs. 7 and 8). Again, in support of the flow visualisation results, for
a given heating condition, the temperature measurements indicate a shorter stagnant region at 45 ° (compared to 30 ° and 60 ° inclinations), for 45 ° a AT > 4 K destroys the stagnant region. It can be seen that for a low AT, temperature profile T, crosses T~ toward the end of the recirculation zone. This is due to very weak recirculation near the stagnant region resulting in heat transfer by conduction becoming more significant than convection in this region.
M. BEHNIA and G: L. MORRISON
322
% O
Fig. 9. Flow pattern inside a thermosyphon tube for the differential heating and tube inclination of 60*.
Further, it is also observed t h a t the t e m p e r a t u r e near the u p p e r wall o f the t u b e decreases towards the tube e n t r a n c e (see To profiles). T h i s is d u e to m i x i n g between h o t fluid m o v i n g along the u p p e r wall o f the tube with cold inlet fluid convected up the curved walls. F o r all t u b e inclinations a n d heating conditions, t h e t e m p e r a t u r e o f the cold fluid stream o n the b o t t o m o f t h e t u b e increased all the way d o w n to the s t a g n a n t end. T h i s c a n be seen from 7"4 profiles in Figs. 6-8.
4.2
Table 1. Length of the multicellular region for different tube inclinations and heating conditions* Length of stagnant or multiceUular region (mm) Tube inclination
30*
45 °
60 °
t
80*
350t
ATtop = 4 K -
O
-
-
100
ATbot = 4 K - - O ATt~ = 5 K
250
300
550
ATto, = 4 K - - O- A T~,,~ = 6 K
300
340
660
ATto, = 4 K - - 0 - AT~ = 8 K
400
500
720
450
560
800
-
ATtoo = 4 K -
O
8K
O
J'
Fig. 10. Temperature difference (with respect to the reservoir) measured on a vertical plane passing through the centre of the tube, inclination = 30*.
Differential heating results
This series o f e x p e r i m e n t s were p e r f o r m e d with the fluid in the 2 halves o f the heating j a c k e t at different temperatures. T h e heating c o n d i t i o n is identified by
-
O~
-
0
-
-
&Tb~ = 10 K
* Tube diameter = 21.3 ram, tube length = 1200 mm. t Indicates stagnant ~ , i o n .
the t e m p e r a t u r e difference between the heating fluid a n d the reservoir ( A T ) . W i t h the t o p h a l f A T l e s s t h a n t h a t o f the b o t t o m half, the flow structure was different from t h a t o f u n i f o r m heating. In this case, the bulk flow from the t a n k p e n e t r a t e d in the tube in a similar fashion to u n i f o r m heating. However, instead o f the s t a g n a n t region at the e n d o f the tube, there was a multicellular region w h i c h was visualized by injecting rheoscopic tracer particles. F o r a heating c o n d i t i o n o f the b o t t o m a n d t o p halves A T equal to 8 a n d 4 K, respectively, the flow p a t t e r n at a n inclination o f 60 ° is given in Fig. 9. F o r this particular experiment, the length o f the multicellular region was 30 tube diameters. Flow visualisation e x p e r i m e n t s were carried o u t at different heating c o n d i t i o n s a n d tube inclinations to q u a n t i f y the length o f the multiceilular region. T h e results are t a b u l a t e d in Table I. For c o m p a r i s o n purposes, the u n i f o r m heating results (i.e., the length o f the s t a g n a n t region) are also included. Increased bott o m half heating results in increased multicellular region length at the e n d o f the tube. W h e n the b o t t o m half o f the tube is at a higher t e m p e r a t u r e t h a n the t o p half, the cooler d e n s e r fluid layers are situated above the w a r m e r ones a n d as a consequence, a muiticellular flow is established in this region. It is n o t e d t h a t unlike the u n i f o r m heating results, the length o f this region increases m o n o t o n i c a l l y with the tube inclination. T e m p e r a t u r e profiles m e a s u r e d o n a vertical plane
An experimental investigation of inclined open thermosyphons
7.0,
:%
~'c
8K~ Fig. 11. Temperature difference(with respect to the reservoir) measured on a vertical plane passing through the centre of the tube, inclination = 45 °.
323
For the bottom and top half AT of 4 and 8 K, respectively, the temperature profiles are shown in Fig. 14. In this case, for all inclinations, the fluid near the top half is consistently warmer than the fluid near the bottom half. It is noted that the incoming bulk flow is heated all the way to the end of the tube (see T2, T3, and 7"4). The outgoing flow is heated part way up the tube and then cooled by the incoming flow before it leaves the open end (see To and T~ ). It is interesting to note that the outgoing To at the mouth of the thermosyphon is nearly the same for both 30 ° and 45 ° inclinations. For an inclination of 45 ° the temperature profiles indicate a similar trend to those of Zhiqiang et al.[ 12 ]. It should be noted that their measurements were based on a constant wall heat flux condition; however, our results correspond to a nearly uniform wall temperalure.
5. CONCLUSIONS passing through the centre of the tube at different locations for the top and bottom half AT of 4 and 8. K, respectively, are given in Figs. 10 to 12. It is noted that in these figures the temperature difference with respect to the reservoir is plotted. In the multicellular zone near the closed end, the temperature adjacent to the top half tube wall is somewhat lower than the bottom. However, in the bulk flow region, the temperature near the top half is highei" although the bottom half heating is more intense. This is due to the fact that as the fluid is heated near the bottom it rises to the top of the tube and is then convected away toward the open end. The results presented in Figs. 10-12 are repiotted in Fig. 13 as the temperature measured by each individual thermocouple along the tube. For the case of differential heating, the dimensionless temperature, t is defined in the same way as for uniform heating experiments but the larger AT is used. The temperature profiles along the tube indicate that near the closed end 7"4 is slightly higher than To for all inclination angles (Fig. 13 ). However, toward the open end To is markedly higher than T4. The crossing of these two profiles corresponds to the interface between the multicellular and the bulk flow regions. Further, as the fluid enters the tube, it is heated along the tube by the heating jacket bottom wall (see 7"2, T3, and 7"4profiles in Fig. 13). The outgoing fluid near the top wall is continuously cooled (see To and Tj profiles). The gradient of T2, T3, and 7"4 profiles is sharper than that of To and T~. Experiments were also performed with the top half jacket temperature difference higher than the lower half. Flow field observations indicated that the bulk flow entering from the reservoir penetrated to the end of the thermosyphon tube and no stagnant or multicellular regions existed. In this case, increased top half heating resulted in a stronger bulk flow between the tank and the tube compared to that of uniform heating.
Free convection flow and temperature fields in an open-ended inclined cylindrical thermosyphon with application to evacuated tube solar collectors have been experimentally studied in the laboratory. Different tube inclinations and heating conditions were considered. For uniform heating of a single-ended thermosyphon tube, a significant stable stagnant region exists near the closed end of the tube, the length of which decreases with increasing heating fluid temperature. The stagnant region length varies nonmonotonicaily with the angle of inclination and shows a m i n i m u m at 45 °. The tube entry geometry was found to be important. For the differential heating with the top half of the tube cross section at a lower temperature than the bottom half, there was a significant region of cellular motion near the closed end of the tube. For the top half heating more intensely than the bottom half, there was
z~ '
18K,
Fig. 12. Temperature difference (with respect to the reservoir) measured on a vertical plane passing through the centre of the tube, inclination = 60 °.
324
M. BEHNIAand G. L. MORRISON
0"8
0"8
0:30 °
8 =45 °
0-6
0'6 t
O'Z.
To
ro
t
]'1
0- 4
&T=4 K
0.2
-
0.2
T1 &T=4 N
AT=8 K
o 0
~
0"2
0"4
'3
0"6 X/L
0"8
1"0
0
0-2
0-4
0"6
0'8
1.0
X/L
(a)
(b)
0"81 0=60*
t
ro Fig. 13. Dimensionless fluid temperature along the tube for differential heating.
AT=4K
rel 0
..... i 0"2
,
0.4
0"6
~T, 0"8
1.0
X/L
(c)
a strong bulk flow that penetrated the entire length of the tube. As evacuated tubular solar absorbers in concentrating collectors experience higher bottom heating
than top heating, the multicellular circulation observed in these experiments may influence the thermosyphon energy extraction efficiency.
An experimental investigation of inclined open thermosyphons
0.~ -
0=30
o
O'=45 o
0.8 ~
325
To
0"6
To 0.6
t
t
0"4
0-4
0.2
0"2~
KL
0
I
I
0"6
0"8
T4 0
0
0"2
0"4
1'0
0
I
I
I
I
I
0"2
0"4
0-6
0"8
1"0
~
X/L
(b)
(a)
0=60 °
0'8 -
0.6
-
To
~
t
T~
0
"
0 0
4
I 0.2
~
Fig. 14. Variation of dimensionless fluid temperature along the tube for differential heating.
t
I
I
I
0.4
0-6
0'8
1"0
X/L
REFERENCES
1. H. Holzwa~h, Die Entwicklungder Holzwa~h-GasTurbine, Holzwa~h-Ga~urbinen G.M.B.H., MuehlheimRuhn(1938).
2. R. T. Foyle, General discussion on heat transfer, Proc. Inst. Mech. Eng. ASME London, Conf. Proc., p. 382 (1951). 3. D. Japikse, Advances in thermosyphon technology, Adv. Heat Trans., 9, 1-111, (1972).
326
M. BEHNIA and G. L. MORRISON
•4. E. R. G. Eckert and T. W. Jackson, Analysis of turbulent free-convection boundary layer on a fiat plate, Nat. Adv. Comm. Aeronaut. NACA TC 2207 (1950). 5. M. J. Lighthill, Theoretical considerations on free convection in tubes, Quarterly Journal of Applied Mathematics, 6(4), 398--439 (1953). 6. F. M. Leslie, Free convection in the tilted open thermosyphon, J. Fluid Mech., 7, 115-127 (1959). 7. C. V. Foster, Heat transfer by free convection to fluids contained in vertical tubes, Ph.D Thesis, University of Delaware, Newark, Delaware ( 1953 ). 8. B.W. Martin, Free convection in an open thermosyphon, Proc. Roy. Soc., A230, 502 (1955).
9. B.W. Martin, Free convection heat transfer in the inclined open thermosyphon, Proc. Inst. Mech. Engg., 173, 761 (1959). 10. B. Window and G. L. Harding, Buoyancy effect and manifolding of single ended absorber tubes, Solar Ener~', 31, 152 (1983). I 1. B. Window, Heat extraction from single ended glass absorber tubes, Solar Energy, 31, 159 (1983). 12. Y. Zhiqiang, G. L. Harding, and B. Window, Water in glass manifolds for heat extraction from evacuated solar collector tubes, Solar Energy. 32, 223 (1984).