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Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement

622

efficiency slightly decreases from the central point to the

lateral positions.

An accurate analysis of Fig. 3 shows that the “C” optics

creates images characterised by very uniform distribution

of the light and high collection efficiency. Furthermore the

diameter of the “C” image maintain its value almost in all

five locations.

While the diameter of the image focused by the “T” optics

slightly enlarges increasing the distance d.

The “T” optics reaches a good uniformity, within the image

diameter of 2 mm, for d = 3.6, 3.1 and 2.6 mm; but

reducing d the situation worsens.

In conclusion, the advantages of “C” optics are: high

concentration efficiency, elevated image uniformity and

very good stability with respect to defocusing. In this case

the PV cell is placed in the focal position. The drawbacks

of “C” optics are large thickness and long distance of the

focal point.

The advantages of “T” optics are: very high concentration

efficiency, good image uniformity and quite good stability.

For “T” optics the drawbacks are difficulty in

manufacturing the aspherical mirrors and slight instability

of PV cell location.

4. REFERENCES

(1) R. A. Sherif et. Al, "The Path to 1 GW of Concentrator

Photovoltaics Using Multijunction Solar Cells", 31st

IEEE PVSC, pp. 17-22 (2005).

(2) K. Araki et al, "Development of a Robust and High

Efficiency Concentrator Receiver", WCPEC-3, pp.

630-633 (2003).

(3) K. Araki et al, "Sunshine environment and spectrum

analysis for concentrator PV systems in Japan", Sol. En.

Mater. Sol. Cells 75, pp. 715-721 (2003).

(4) K. Araki et al, "A 28 % Efficient, 400x and 200 Wp

Concentrator Module", 19th European PVSEC, pp.

2495-2498 (2004).

(5) K. Araki et al, "Comparison of Efficiency Measurement

for a HCPV Module with 3J-Cells in 3 Sites", 31st

IEEE PVSC, pp. 846-849 (2005).

(6) P. J. Verlinden et al, "Performance and Reliability of

Multi-Junction III-V Dense Array Modules for

Concentrator Dish and Central Receiver Applications",

IEEE 4th World Conference on Photovoltaic Energy

Conversion, Hawaii - USA (2006).

(7) J. L. Alvarez et al, "Optical Performance Measurements

of very High Concentration Systems", 20 European

PVSC, pp. 2357-2359 (2005).

(8) Sarno et al, "The PhoCUS Project", Proc. of the PV in

Europe Conference, Rome - Italy (2002).

(9) W. Bett et al "FLATCON/TM and FLASHCON/TM:

Concepts for high concentration PV", 19th European

PVSEC, pp. 2488-2491 (2004).

(10) Ciamberlini, F. Francini, G. Longobardi, M. Piattelli, P.

Sansoni, "Solar system for the exploitation of the whole

collected energy", Optics and Laser in Engineering

39/2, pp. 233-246 (2003).

(11) Fontani,

F. Francini, D. Jafrancesco, G. Longobardi, P.

Sansoni, "Optical design and development of fibre

coupled compact solar collectors", Lighting Research

& Technology 39, 1, pp.17-30 (2007).

(12) F. Francini, D. Fontani, D. Jafrancesco, L. Mercatelli,

P. Sansoni, Designing solar collectors and optical

fibers for daylighting. "A novel system exploits solar

energy by collecting and channeling sunlight to

illuminate interior spaces" - Illumination & Displays -

Science and Technology: SPIE Newsroom DOI:

10.1117/2.1200612.0487 (2006).

(13) Fontani,

F. Francini, P. Sansoni, "Optical

characterisation of solar collectors", Optics and Laser

in Engineering 45, pp. 351-359 (2007).

(14) J. M. Gordon and D. Feuermann, "Optical per-

formance at the thermodynamic limit with tailored

imaging design" Appl. Opt. 44, 12, pp. 2327-2331

(2005).

(15) D. Lynden-Bell, "Exact optics: a unification of optical

telescope design", Mon. Not. R. Astron. Soc. 334, pp.

787-796 (2002).

(16) R. V. Willstrop and D. Lynden-Bell, "Exact optics-II.

Exploitation of design on-axis and off-axis", Mon. Not.

R. Astron. Soc. 342, pp. 33-49 (2003).

REVIEW ON THE DEVELOPMENT OF FLAT-PLATE SOLAR COLLECTOR

AND ITS BUILDING-INTEGRATED DESIGNING

Xu Xinjian

Jiangsu Sunrain Solar Energy Co.,Ltd.

Lianyungang, Jiangsu Province, 222200, China

Yang Lei, Zhang Xiaosong, Peng Donggen

School of Energy & Environment, Southeast University

Nanjing, 210096, China

rachpe@seu.edu.cn

ABSTRACT

Flat-plate solar collector is a promising solar collector

with advantages of higher cost performance and feasible

building-integrated construction. Applications and

technologies of flat-plate solar collector were reviewed

in this paper. Meanwhile, the present technology

obstacles in this field were analyzed, and related

advanced technologies and their developing directions

were discussed and prospected, which focused on the

absorber coating, cover with high transmittance and

construction designing.

1. INTRODUCTION

Solar utilization is an old but rising subject. With the

shortage of fossil energy source and environment pollution

in the world, solar energy has become increasingly

favorable. As a most common solar application, solar water

heater have been widely researched and manufactured in

many countries. Solar collector was a significant part of

solar water heater, which greatly influences solar water

heater’s overall performance. Currently, used solar

collectors include flat-plate collector, glass evacuated tubes

collector, heat pipe type collector, and etc. For the simpler,

feasible building -integrated configuration, and lower cost,

flat-plate collector have become more attractive and

obtained a great developing prospect. This paper reviewed

the development of flat-plate solar collector. Performance

of this type collector was analyzed. Also, the building

integrated utilizations are introduced.

2. DEVELOPMENT OF FLAT-PLATE SOLAR WATER

HEATER

2.1 Developing Status in China

The solar water heater industry in China was developed

from 1980s. With fast development in decades, China has

already become a leading production and marketing

country. Annual sales and total storage quantity are both

NO.1 in the world. Table 1 shows the market shares of

glass evacuated tubes collector water heater, flat-plate

water heater and integral collector storage solar water

heater.

It is seen that the market share of flat-plate solar water

heater in China have been decreasing in recent years. The

main reasons are: (1) flat-plate solar collectors produced

in China have achieved a performance as good as other

country. As the heat loss coefficient is higher than that of

evacuated tube collector, the heat gain is lower in winter.

(2) The metal price is rising at present, and flat-plate

collectors are not large-scaled produced in China, making

cost of high quality flat-plate water heater expensive. (3)

Cost of all-glass evacuated tube water heater drops

sharply. Directly insert type water heater with advantages

of anti-freezing and simply constructed is therefore

widely used. Especially, 70% of total promote solar water

heater in China are sold in town and country where

people’s purchasing power is limited. Therefore, flat-plate

Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement

624

collector has no competitiveness with evacuated tube

water heater [1].

TABLE 1: MARKET SHARES OF COLLECTORS IN

CHINA

TIME

GLASS

EVACUATE

D TUBE (%)

FLAT

-PLATE

(%)

INTEGRAL

COLLECTOR

STORAGE (%)

1999 55 33 12

2000 77.5 16.4 6.1

2003 87.5 11.3 1.2

2004 87.8 11.1 1.1

2005 87 12 1.0

The development of solar water heater have experienced

from unselective coat like normal black lacquer, to

selective coat like vulcanized lead, metal oxide, and from

black nickel and black chrome to aluminum anodic coat,

etc. With the advancement of coat technique, coat

performance improved greatly. Currently, selective coat

like aluminum bar with anodic color or copper bar with

black chrome is mostly used on the absorb surface of

flat-plate collector. With the appearance of evacuated tube

heat collector, interim magnetron sputtering

aluminum-nitrogen-aluminum selective absorb coat

technology was developed. But this kind of coat has week

weather endurance, and thus is not appropriate for flat-plate

heat collector. As to weather endurable vacuum coating,

some manufacturers have attempted to produce stainless

steel nitride and stainless steel carbide and demonstrated

for flat-plate heat collector in small scale [2].

2.2 Developing Status worldwide

Installation areas in Europe has exceeded 11 million square

meters by 2001, in which Germany takes 50% and Greece

18%. The average occupancy quantity for each person is

290 square centimeters. It is noted that flat-plate heat

collector plays an absolutely leading role [3].

Many researchers carried out a lot of investigations on

flat-plate heat collector with building-integrated designing.

In order to acquire perfect combination between collector

and architecture, the collector’s absorb plate was proposed

to be colored and performance of such a colored flat-plate

collector with and without glass cover were tested [4]. In

addition, concept of “solar architecture”, using solar energy

both actively and passively to produce hot water, space

heating, refrigerating, and generating electricity by PV

modules was put forward [5].

3. PERFORMANCE OF FLAT-PLATE COLLECTOR

3.1 Higher Cost Performance

Fig. 1 shows the efficiencies of four solar heat collectors. It

is clear that flat-plate heat collector’s efficiency is only a

little lower than evacuated tube heat collector but higher

than the other two, only 0.1 lower in the range of medium

and low temperature (<ć. Meanwhile, relative lower

price and mature manufacturing technology make it

achieves a preferable cost performance [6].

Fig. 1: Efficiencies of four types solar heat collectors.

3.2 Well-Suited for Building-Integrated Installation

Nowadays, collector designing and installation in harmony

with building appearance has become a significant

challenge. Collector could be integrated into the buildings

and may acts as one part of construction, such as walls and

roofs. Meanwhile, it should have a life cycle the same as or

longer than buildings. Compared to other collector,

flat-plate heat collector has superiorities as follows:

(1) Water or working fluid flows through the metal tube

instead of the glass tube. So there is no danger of cold burst

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

625

or hot burst and conseqently have a longer life cycle.

(2) Metal jointing between the absorber and tubes for

preventing water leak avoids using of rubber which is aging

with time in other collectors. Therefore, the long-term

reliability was improved.

(3) It can operate on forced circulation by pump. Flat-plate

collector with flexible frame may also have the function of

traditional roof surface, like heat preservation, heat

insulation, blanching and keeping off wind or rain. Thus it

can be easily integrated with building in aesthetics at the

same time reduce building construction cost.

(4) Flat-plate heat collector applying two loops circulation

with anti-freezing fluid could achieve all-year-around

operation in high latitude areas [7].

3.3 Technical Difficulties of Flat-Plate Collector

First, there is problem of scaling in the plate tube,

especially in hard water quality areas

[8]

. The main

components of furring are CaCO

ǃCaSO

ǃMgCO

Mg(OH)

, and etc. When the plate tube scaled, the local

heat transfer performance decreased and even jam the tube.

Second, there is technical difficulty of using solar water

heater in tall buildings because of the overlong conduit and

limited installation areas. Third, heat loss of flat-plate solar

collector including radiation loss and convection loss is

higher than evacuated tube collector. And the efficiency

decreases sharply with the increase of water temperature. It

was indicated in Fig. 1.

4. DEVELOPING DIRECTION OF FLAT-PLATE SOLAR

COLLECTOR

4.1 Weather Endurable Selective Absorbing Materials and

Film Design

As a weather endurable selective absorb material, cermet

film is researched mostly [2]. It is categorized into

asymmetry particle film, and has favorable heat resistance

stability. Its Humidity resistance lies on metal particle and

medium matrix. AlǃMgO and SiO

are perfect medium

matrixes whose refractive ratio in visible area are all less

than 2.0. Furthermore, some metal nitride and carbide like

AlNǃTiNǃTiC can be used as medium matrix as well. For

selective absorbing composite film, its optical performance

is significantly influenced by metal particle’s volume

fraction and film’s optical thickness. In order to improve

coat’s corrosion resistance, film layer adopts double deck

intervene absorbing configuration. By adding a piece of

compact AIN medium layer onto film’s exterior face,

reflecting is reduced and absorbing layer is protected.

Currently, developed countries, especially Europe, produce

selective absorb material with two main features. One is the

utilization of vacuum film plating. The other is continuous

plating by convolute manner even in humid film plating. For

example, BATEC in Denmark uses continuous plating on

copper belt. Optical and weather performance of the black

chrome absorbing coat produced in this way are both perfect.

4.2 High Transmittance Materials for Collector Cover

In order to reduce heat loss, cover material needs to

permeate the visible light but not the infrared part of

sunlight. At present, mainly used cover material in China

include toughened glass, also applied mostly, acrylic

methyl-esters and glass steel. In other countries, low iron

rate glass is widely used in high quality collector. This type

of glass cover has high transmittance of above 90%.

Recently, with the development of film technology, minus

reflecting coat has been used on the cover. Double face

minus reflecting glass made by Sunarc, Denmark can

reduce the reflectance from 8% to 3%. Consequently, the

transmittance is up to 96% and thus thermal efficiency of

collector can be increased by 4%.

4.3 Heat Pipe Type Flat-Plate Collector

H.M.S.Hussein proposed a new flat-plate heat collector, as

shown in Fig. 2 [9]. It integrates the technologies of

flat-plate collector and heat pipe collector. Solar energy

absorbed by plate absorber is transferred to cross-flow heat

exchanger by heat pipe, and then heating water.

4.4 Building-Integrated Flat-Plate Collector

As mentioned above, building-integrated flat-plate solar

collector is the developing trend. It should be combined

with both modern and traditional buildings. Fig. 3 shows an

example of flat-plate solar water heater hormonally

integrated into Chinese traditional building.

Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement

626

Fig. 2: Non-core heat pipe flat-plate solar collector.

Fig. 3: Flat-plate water heater in Chinese traditional

building.

5. CONCLUSIONS

Solar water heater is a feasible and economical thermal

utilization of solar energy. Performance superiority and

developing obstacles of flat-plate solar water heater were

presented. Advanced technologies for performance

improvement were proposed, which is focused on the

absorber coating, cover with high transmittance and

construction designing. In addition, building integrated

designing of flat-plate solar collector is a significant

developing direction of solar water heater.

6. REFERENCES

(1) Z.C Huo, Z.T. Luo, “Developing situation of flat-plate

solar water heater in domestic and abroad”, Solar

Energy, No.6, 2006, p. 6–8.

(2) G. M. Xie, “Progress of absorb and permeate material

in flat-plate solar water heater”, Solar Energy

, No.3,

2004, p. 34–36.

(3) Athanassios, Argiriou, Sevastianos Mirasgedis, “The

solar thermal market in Greece-review and

perspectives” Renewable and Sustainable Energy

Reviews, No.7, 2003, p. 397–418.

(4) Y. Tripanagnostopoulos, M. Souliotis , TH. Nousia,

“Solar collectors with colored absorbers”, Solar Energy

Vol. 68, No.4, 2000, p. 343–356.

(5) A.G. Hestnes, “Building integration of solar energy

systems”, Solar Energy

, Vol. 67, 1999, p. 181–187.

(6) Brian Norton, “Anatomy of a solar collector:

Developments in Materials, Components and

Efficiency Improvements in Solar Thermal Collector

Systems”, Refocus

, Vol. 7, No. 3, 2006, p. 32-35.

(7) Qi Xin, “Introduction of building-integrated all copper

solar collecting system engineering”, Solar Energy

Paper, No.5, 2003, p. 42-43.

(8) W.B. Chen, “Manage of plate core scaling in flat-plate

solar water heater”, Country Energy Source

, Vol. 83,

No.1, 1999, p. 13.

(9) H.M.S. Hussein, “Theoretical and experimental

investigation of wickless heat pipes flat-plate solar

collector with cross flow heat exchanger”, Energy

Conversion and Management, Vol. 48, No.4, 2007, p.

1266-1272.

STUDY OF THE THERMAL PERFORMANCE AND AIR-FLOW FEATURES

OF A SOLAR AIR HEATER WITH EVACUATED TUBES

E. Papanicolaou, V. Belessiotis,

Solar & other Energy Systems Laboratory

“Democritos” National Center for Scientific Research

Aghia Paraskevi, Attiki, GREECE 15310

sollab@ipta.demokritos.gr

X.Li, Ζ. Wang

Solar Energy Laboratory

Institute of Electrical Engineering,

Chinese Academy of Sciences

P.O. Box 2703

Beijing 100080, China

ABSTRACT

In the present paper, aspects related to the energy

performance of a solar air heater comprising an array of

dual-glass evacuated tubes using air as the working fluid,

are investigated. Design parameters affecting the

performance of the heater are the air flow-rate, the diameter

and length ratios (insert tube/inner glass tube), the latter

defining the discharge location, the flow configuration

(series or parallel connection of tubes) etc.. Numerical

simulations of flow and heat transfer within a single tube

are performed for a selected configuration, giving insight

into details of the flow and temperature fields, which are

valuable in the pursuit of the optimal design of the

geometric and physical parameters. Besides, efficiency

curves for the air heater are obtained from experimental

measurements at both cooperating laboratories.

1. INTRODUCTION

The evacuated-tube technology for solar collectors has

been steadily increasing for over two decades now, as this

can significantly limit the heat losses which flat-plate

collectors are subject to at high operating temperatures. The

evacuated-tube collectors do, however, suffer from several

comparative disadvantages, such as high cost and difficulty

in transferring the heat from the absorbing surface to the

working fluid, due to their large length [1]. The majority of

solar thermal collectors to the present day use water as the

working fluid, the more so evacuated-tube collectors. In the

latter case, problems associated with water are evaporation

under stagnation conditions and leakage, whereas there are

applications where the immediate availability of hot air

rather than water is desirable.

Therefore, in the course of a bilateral R & D cooperation

program between Greece and China, of which the present

study constitutes a summary of the main activities, it was

found useful to investigate the use of air as the working

fluid in suitably constructed solar collectors with evacuated

tubes (air heaters). The collaborating laboratories, briefly

referred to from now as SESL/NCSR “D” from Greece and

SEL-CAS from China, have carried out theoretical and

experimental investigation aiming at assessing the energy

output of such a heater which is presented in Figure 1,

along with its main geometric dimensions. In this particular

design there are 12 dual-wall glass tubes which contain the

vacuum, all connected in parallel and with the cylindrical

absorbing surface formed on the outer wall of the inner

tube. The tubes are mounted on a suitably constructed and

insulated metal frame equipped with a header for the air

supply and return. The ambient air supply is achieved

through a horizontal cylindrical tube parallel to the main

axis of the header, from where air is distributed by means

of insert metal tubes, which discharge the air in the inner

glass tubes here at a depth roughly equal to ¾ of their

length. After discharge towards the closed end of the tubes,

air reverses its direction and heats up as it flows towards

the upper (open) end of the glass tubes into the return

Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement

628

section of the header. From there, it may be directed to the

desired application, which may be space heating,

air-conditioning, drying of agricultural products etc.

evacuated tube

(lenght=1126mm, Ö20mm

)

Ö47mm L=1500mm

insert tube

air inlet

air outlet

insulation

(a)

(b)

Fig. 1: (a) Schematic and structural details of the air heater

and (b) test unit at the outdoor testing facilities of

SESL/ NCSR “D”.

2. NUMERICAL SIMULATION OF FLOW AND

TEMPERATURE FIELDS

Due to the peculiarities of the particular collector and the

fact that little information is available for this type in the

literature, it was decided to develop a mathematical and

numerical model in order to simulate the flow and heat

transfer problem within a single tube. The development of

the model is presented below.

2.1 Model Formulation

A representative computational domain for the simulation

was defined based on the geometric and functional data of

the tube (Fig. 2(a)) as shown in Fig. 2(b). The heating of air

is achieved through the outer surface of the inner glass tube,

which is the absorbing surface. The heat flux incident on

this surface exhibits, in general, spatial variations along the

perimeter of the tube as well as temporal variations during

the day. Nevertheless, as an initial approximation an

averaged, constant value may be considered as

representative of the entire surface of the tube, giving thus

rise to an axisymmetric model for flow and heat transfer in

the glass tube. In addition, since the geometric details in

that region are not important for the present simulation

purposes, the closed end of the tube may be taken as flat

and also any heat exchange between the incoming air,

flowing inside the insert tube and the return air in the

annulus between insert and glass tubes is neglected.

The problem that arises thus may be characterized for its

major part (here, for instance, the

3/4 of the length of the

tube) as a convective heat transfer problem in a cylindrical

annulus with constant heat flux on its outer surface. In the

remaining part of the tube (roughly the bottom 1/4), there is

flow in a cylindrical cavity defined between discharge

location and closed end. The particular configuration with

the given boundary conditions has some unique features

such that no data are readily available in the literature (e.g.

[2]) that would allow the characterization of the flow and

estimation of the heat transfer needed to predict the energy

output of the collector. Therefore, this information has to be

obtained from the numerical simulation results of the

procedure described below.

2.2 General Description

In the present problem, a system of equations in terms of

the dimensionless stream function Ψ and vorticity Ω is

written for the flow field and the dimensionless temperature

θ, where the buoyancy forces due to temperature

differences are also accounted for through the Boussinesq

approximation. The non-dimensionalization is done using

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

629

the radius of the annulus : r

= r

– r

for the space

coordinates, the mean discharge velocity u

for the

velocities and the ratio r

for time. The dimensionless

temperature has been defined as : θ = (Τ – Τ

) / ΔΤ , using

the constant heat flux q″ of the heated surface and a

characteristic temperature difference : ΔΤ = q″ r

/ k. Within

the glass wall, only the energy equation is solved (U

= U

= 0) and is coupled with the corresponding equation for air,

using suitable conditions at the interface. In the solid, the

ratio of thermal diffusivity of the solid ‘s’ (glass) over the

corresponding property of the fluid ‘f’ (air) is involved, i.e.,

= α

/ α

. Thus, the Reynolds and Grashof number for the

problem are respectively defined as : Re = u

/ ν and Gr =

/νβ

rTg Δ , while the parameter Gr/Re

arises as the

coefficient of the buoyancy term in the vorticity equation.

2.3 Boundary Conditions – Model Parameters

As may be seen in Fig. 2(b), discharge at the bottom end of

the insert tube with a parbolic velocity profile is considered

(fully-developed flow), with a mean dimensionless velocity

= 1.0. On the solid surfaces no-slip conditions are

imposed, whereas at the upper end of the annulus outflow

conditions for all variables are sepcified (∂( ) / ∂Ζ = 0). The

constant heat flux is applied on the outer surface of the

inner glass tube, where the boundary condition in

dimensionless form may be written as : ∂θ / ∂r = 1 / λ

with λ

= k

/ k

the ratio of thermal conductivities (glass

wall/air). For borosilicate glass, the value λ

= 34.603 is

obtained, along with λ

= 0.018.

Considering overall air flow rates from measurements in

the range 30-140 m

/ h, the corresponding range of values for

the Reynolds number is: Re

= 357-1669, i.e., a range

corresponding to the laminar-flow regime. A representative

value of the insolation over the measurement period is G =

800 W/m

. Since the heat flux varies in the azimuthal direction

[3] and in the present experimental setups no reflectors on the

back of the tubes have been used, values much smaller than G

are more representative for the heat flux, such as q″ = 400

W/m

which has been used as the base value. This gives

Gr=1875 for the Grashof number and Gr/Re

= 2.077 × 10

-3

therefore forced convection prevails, having as a consequence

that buoyancy and, therefore also, the angle of inclination of

the tubes do not play a significant role, particularly in the flow

along the annulus. The buoyancy terms was nevertheless

maintained in the model, since it was found out that natural

convection influences the behaviour at the bottom 1/4 of the

tube length (closed end region), therefore the problem has

been treated as mixed-convection problem, with a vertical

orientation of the tube.

(a) (b)

Fig. 2: (a) Geometric details of a single tube of the heater.

(b) Computational domain and boundary conditions

of the simulation model.

2.4 Model validation – Solution in the annulus only

For this purpose, results on simultaneous development of

velocity and temperature fields in cylindrical annuli have

been selected, for various radius ratios r

= r

/ r

and

thermal boundary conditions on the inner and outer wall, as

these were presented by Heaton et al. [4]. For these

calculations, a uniform velocity profile had to be specified,

with the inlet placed exactly at the discharge location but

with an upward flow direction. The part of the tube below

this location was in this case not considered. The solution

for a fully-developed velocity profile and making use of the

same dimensionless quantities as Heaton et al. is compared

with the present results in Fig. 3a, where it may be

observed that there is excellent agreement between the two

results. The temperature distribution of Heaton et al. is

given in terms of a mean temperature of the form: θ

= 4

x / (1+r

), where x = (x/D

)/(Re

Pr) is a dimensionless

axial coordinate distance, D

the hydraulic diameter of the

annulus (D

= 2 × r

) and Re

the accordingly defined

Reynolds number.

Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement

630

The comparison in terms of the mean temperature variation

along the length of the annulus with the analytical solution

of Heaton et al. [4] for a constant heat flux imposed exactly

on the inner wall (Fig. 3b) shows also a good agreement, a

fact that proves that the wall of the tube may be here

characterized as “thin” for the heat transfer, according to

the analysis of Shah και London [5]. The analytical solution

for heating on the outer wall and for r

= 0.5 is obtained by

interpolation between the solutions for r

= 0 (tube) and r

= 1 (parallel plates), in terms of the dimensionless

temperature difference between the outer, heated wall θ

οο

and the mean air temperature θ

mο

and the Nusselt number is

computed accordingly. The comparison to the results of the

present simulation are presented in Fig. 3c. It may be

observed that at large values of the normalized axial

coordinate the present solution approaches the analytical

solution for constant heat flux (solution «Η» [5]). For lower

values, the deviation is owing to the fact that here a

conjugate heat transfer problem has been considered with

conduction through the wall, and this conjugate effect is

more pronounced near the inlet to the annulus.

(r-r)/r

u/u

0 0.25 0.5 0.75 1

0.2

0.4

0.6

0.8

1.2

1.4

1.6

(a) (b)

θ - θ

10 10 10 10 10

(c)

Fig. 3: Numerical simulation results and comparisons with

analytical solution (points) for an annulus with r* =

0.5 [4]. (a) Radial profile of axial velocity at the

tube exit (b) mean air temperature along the annulus

and (c) temperature difference (wall – mean).

2.5 Results for the Full Tube Geometry

Four flow rates have been selected, 30, 40, 60 και 80 m

/ h,

with respective Reynolds numbers Re

= 357, 477, 715 και

953. Results for the flow field for Re

= 477 in the air

discharge region are shown in Fig. 4, in the form of

streamlines (a) and dimensionless temperature contours (b).

It may be observed that immediately after discharge, the air

flow is directed towards the glass-tube wall, building a

separation bubble on the surface of the insert tube, just

above the insert-tube exit. This bubble extends to roughly

4-5 times the radius of the annulus and the resulting flow

pattern is expected to affect significantly both the heat

transfer as well as the pressure drop within the tubes of

the collector. Despite the different form of the flow field

at the inlet to the annulus, at the exit, but already at a

lower distance along the annulus, the velocity has attained

the form of the fully-developed flow, exactly as depicted

in Fig. 3(a).

However, the mean air temperature along the tube exhibits

some deviations compared to the form in Fig. 3(b). The

slope of the line may coincide with that for the analytical

solution in the annulus (Fig. 5(a), however now a parallel

shift upwards appears, owing to the preheating of air

between discharge from insert tube and inlet to the annulus

section, due to the high temperatures developing at the

closed end of the tube. In Fig. 5(b) radial temperature

distributions are presented (both in the air flow and within

the wall), at various dimensionless axial locations Z from

the inlet to the annulus section and above. At a distance of

Ζ=5.1, the effect of the bubble is still discernible, whereas

at longer distances (Ζ≥32) the fully-developed form

gradually establishes. In Figs. 5(a) and 5(b), the

aforementioned effect of preheating of air is also present, as

discrepancies are observed between the solution for the

annulus alone on one hand (dashed line) and the full

geometry on the other (solid line), both in terms of the axial

variation of the inner wall temperature (Fig. 5(a)) as well as

the corresponding variation of the local Nusselt number

(Fig. 5(c)), defined as Nu= h r

/ k, with h the local heat

transfer coefficient. Especially in the latter case, the

presence of the separation bubble is obvious, as the abrupt

fluctuations of the curve of Fig. 5(b) for coordinates Ζ ≤ 10

indicate.

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

631

0 1 2

-5

-2.5

2.5

7.5

0 1 2

-5

-2.5

2.5

7.5

(a) (b)

Fig. 4: (a) Flow and (b) temperature-field patterns at the air

discharge region for a flow rate of 40m

/ h. (21

contour lines for the stream function and

temperature, with value ranges -1.047 to 0.074

and 0 to 1.8 respectively).

2.6 Effect of Closed End and Boundary Conditions

Between the air-discharge location and the closed end of

the tube high temperatures develop, due to the inability of

the incoming air at ambient temperature to penetrate at a

significant depth below the discharge location (Fig. 4(a)),

having as a consequence the development of a recirculating

flow driven by natural convection. This region may be

characterized as a stagnation zone, a phenomenon which

has been also observed by other researchers in hot-water

thermosiphon systems with evacuated tubes [6]. This is

here

further enhanced by considering an adiabatic boundary

condition for temperature at the closed end. A more realistic

condition would have been obtained by taken heat losses

into account by means of a heat transfer coefficient. Thus,

the modeling effort is at present further developed by

considering alternative boundary conditions for the closed

end, so that the results of the experimental investigation, to

be presented below, are better approximated.

3. EXPERIMENTAL INVESTIGATION

3.1 SEL-CAS measurements – Array of collectors

0 25 50 75 100 125 150

0.2

0.4

0.6

0.8

1.2

1.4

(a) (b)

(c)

Fig. 5: (a) Mean air temperature θ

and comparison to the

theoretical value for a plain annulus (no upstream

section) and comparison in terms of the analytical

value for the wall temperature θ

at a flow rate of

40 m

/ h, (b) radial temperature profile development

at different locations along the annulus and (c) local

Nusselt number along the tube.

For the experimental measurements SEL-CAS has used an

array of 5 collectors of the form of Fig. 1, connected in

series as shown in Fig. 6. The measurements led to the

estimation of the efficiency of each collector of the array,

for flow rates equal to 30.6 m

/h και 42.6 m

/h and the

relevant results are graphically depicted in Fig. 6. The

abscissa is the normalized temperature T* = (t

- t

)/Ι, where

, t

are respectively the inlet temperature (different for

each collector) and the ambient temperature, whereas Ι is

the incident radiation (W/m

). The instantaneous efficiency

is given by a general expression of the form :

Труды Всемирного конгресса Международного общества солнечной энергии - 2007. Том 2

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