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

602

“Correlations for Laminar Mixed convection

Flows on vertical, Inclined, and Horizontal Flat

Plates”, ASME J. Heat Transfer, 108, 1986, p.

835-840.

(12) Frank P. Incropera and David P. Dewitt,

“Fundamentals of Heat and ZMass transfer” 5

edition, 2002, John Wiley & Sons, New York.

(13) M. Fishenden and O. A. Saunders, “An

Introduction to Heat Transfer”, 1950, Oxford Univ.

Press, London.

(14) M. Yazdanian and J. H. Klems, “Mesurement of

the exterior convective film coefficient for

windows in low- rise buildings”, ASHARE

Transactions, vol. 100, 1994, p. 1087- 1096.

APPENDIX 1

M. Yazdanian and J. H. Klems (1994) had suggested a

correlation involving both forced convection and natural

convection for exterior convective heat transfer coefficient

for vertical windows exposed to wind in low-rise buildings

as given by

ext

= { [ 0.84(T

-T

ext

)

1/3

]

+ ( 2.38V

0.89

)

}

1/2

(12)

where,

ext

is exterior convective heat transfer coefficient (W/m

K),

is surface temperature (

C), T

ext

is ambient temperature

(

C) and V is wind speed in m/s.

By using the experimental data of present study, the

convective heat transfer coefficient has been calculated

from equation (12). These values of convective heat

transfer coefficient have been compared with the

experimental values of convective heat transfer

coefficient obtained in present study. The comparison is

shown in Fig. 4. It is noted that there is difference

between values of convective heat transfer coefficient

obtained in present study (for horizontal surface) and

obtained from Yazdanian and Klems correlation (equation

12) for vertical surface.

V = 0 to 0.4 m/s

20 22 24 26 28 30 32 34

(T -T ) K

Convective heat transfer

coefficient(W/m

Present Study

Yazdanian and

Klems

Fig. 4: Comparison of Present Study with other different

study.

CPC-TROUGH—COMPOUND PARABOLIC COLLECTOR FOR COST EFFICIENT

LOW TEMPERATURE APPLICATIONS

Muhammad Nadeem Baig

M.S. Thermal Power Engineering,

Project Engineer, Alternative Energy Development Board (AEDB)

344-B, PM Secretariat, Islamabad, Pakistan

deemibaig@yahoo.com

Asad Khan Durrani

National University of Sciences & Technology

Islamabad, Pakistan

Durani_a_k@hotmail.com

Ammar Tariq

National University of Sciences & Technology

Islamabad, Pakistan

Jungle_boy_of_2000@yahoo.com

ABSTRACT

The high-performance CPC-Trough Collector has been

developed for the utility scale generation of low

temperature solar steam and hot water for low temperature

process heat applications including solar air conditioning.

With an optical concentration of 7.5:1, operating

temperatures over 130

C may be reached. This novel

design has included a FEM validation and is compatible

with the standard reflectors and evacuated tubes in the

market. The peak efficiencies of 35% with unshielded and

more than 45% with evacuated tube receivers were

obtained. This CPC collector requires intermittent tracking

i.e tilt adjustment is only once in a week for more than 8

hours collection in summer and 6-7 hours in winter

seasons.

1. INTRODUCTION

The Alternative Energy Development Board (AEDB),

Pakistan currently leads the research and development (R&

D) efforts on cost efficient compound parabolic collectors

(CPCs), a simple technology for the wide use of renewable

energy, accessible to the technologically less developed

countries that are sunny and often has limited raw material

resources and skilled labor. These CPCs are non-imaging,

that function seasonally or annually with minimum or

intermittent tracking requirements.

The paper presents theory, practical experience, and

economy of CPC: First a simple structure design is

described. Then results from designing and operating the

test module in Pakistan are presented. Eventually technical

issues and basic economic data for future commercial

CPC,s for low temperature applications in Pakistan.

2. TECHNICAL FEATURES

2.1 Functional Principle

Schematic shows the working of a CPC test module with

electro-polished anodized high purity aluminum or glass

mirror reflectors along with the semicircular absorber at

focal line. A heat transfer fluid is circulated in the absorber

which is heated to the temperature of nearly 160

C for

steam generation applications and subsequently water is

circulated for hot water applications.

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

604

Fig. 1: Functional Principle of CPC Test Module Collector

Structure.

The CPC-Trough collector model is made up of 3.6476m

long collector unit. It comprises of 3 parabolic aluminum

sheets or mirror panels on each side. These reflecting

panels are supported on a V-shaped mild steel structure of a

hollow square cross-section pipe fixed at six points on its

backside. This permits the aluminum foil/mirrors to bend

within the range of its flexibility without effect on the focal

point. The accuracy of the parabolas is achieved by

machining six light weight parabolic ribs from 25mm thick

polypropylene sheets using CNC cutting machine. These

parabolic ribs are bolted to the V-shaped steel structure.

The axial horizontal hollow members provide additional

strength and bracing. The accuracy of the parabolic ribs and

the method of assembly reduced the time and cost of

fabrication and minimized the degree of technical skill

required by workshop staff, while providing sufficient

structural strength.

Fig. 2: Computer Model of the CPC frame Design.

Detailed FEM of the CPC and its interaction at high

expected wind loads at different positions of the collector

were analyzed. These investigations on structural behavior

(under various wind loads for range of pitching angles of

the collector) for various designs, ease of manufacturing

and assembly, and complex computation were performed to

obtain the best possible solution of the CPC structure, cost

and simplicity.

Based on these study and observations, light weight

v-shaped structure with fewer deformations has been

selected for the CPC. This simple structure has been made

by welding three pieces at two joints on a jig platform for

better accuracy, reduced time and less dependency on

skilled labor. The absorber is simply bolted with the

rectangular slots machined at the base of the Polypropylene

parabolic ribs and covered with a rectangular sheet channel

fixed at the base of the polypropylene parabolic ribs. The

space between the absorber and the rectangular channel is

filled up with glass wool so as to minimize the heat loss

from the absorber.

Fig. 3: CPC Trough Test Module Consisting out of (a) 6

simple steel V-frames screwed to parabolic ribs;

(b) 6 polypropylene Parabolic Ribs; (c) 6

Aluminium Reflectors; (d) 2 steel bracing member

bolted with parabolic ribs.

Greek symbols

α absorptivity of the absorber surface

τ Transmissivity of the cover

Effective reflectivity of the concentrator surface

Instantaneous efficiency

Aluminum Reflector

Steel Frame

Absorber

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

605

TABLE 1: Specifications of CPC-Trough Test Module

CPC-Trough Test Module

Characteristic Parameters

Absorber Type Rectangular with circular

tubes at the base

Aperture Width 0.3538 m

Collector Length 3.6576 m

No of Aluminum foil or

Mirror Facets

CPC surface reflectivity 0.94

Number of Absorber tubes 2

Diameter of each tube 0.0127 m

Weight of Steel Structure 5-6 Kg per Sq. meter

Aperture Area 1.2940 m

Height to Aperture width ratio 4.2120

Acceptance Angle 15.3245°

Dimension of each Facet 1.2192 X 0.9144 m

Percentage Truncation 44.36%

Transmissivity of cover 0.90

3. PERFORMANCE ANALYSIS OF CPC

3.1 Total Flux Absorbed by the Absorber

The working fluid enters the tubes at a mass flow rate m

and inlet fluid temperature T

and

exits at a temperature of

. The mass flow rate of the fluid can be adjusted with a

by pass pipeline with a valve for easy control of the

flowrate of fluid.

The expression for the total effective flux entering the

aperture plane is:

ατρ

rIS

⎥

⎦

⎤

⎢

⎣

⎡

(1)

3.2 Useful Heat Gain Rate

()

⎥

⎦

⎤

⎢

⎣

⎡

−−=

afi

SWLFQ (2)

Where,

1exp

FbUL

bU L mC

⎡⎤

⎛⎞

=−−

⎢⎥

⎜⎟

⎢⎥

⎝⎠

⎣⎦

(3)

and

FUNDhπ

⎛⎞

= +

⎜⎟

⎝⎠

(4)

3.3 Exit Fluid Temperature and Collector Efficiency

T += (5)

and

WLrIrI

ddbb

)( +

=η

(6)

Fig. 4: CPC under construction with parabolic ribs, frames

and bracing members.

3.4 Performance over a Day

Using input data for solar radiation, ambient temperature

and wind speed, the performance of the collector test

module is studied for several whole days in summer and

winter seasons. Data was obtained with water as the

working fluid both in the closed loop configuration under a

variety of weather conditions; this module required only

four tilt adjustments in a year, at intervals of four months,

in order to ensure a minimum of 7 hours of collection per

day.

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

606

Temp. Vs Efficiency

Temp.

Efficiency

Fig. 5: Efficiency as a function of absorber temperature.

Plot shows the variation of efficiency with increase in inlet

temperature. It will be noted that the general pattern of

efficiency variation over a day is the same for all days of

the year. On any day, the value of efficiency decreases; this

is due to the fact that efficiency is strongly influenced by

the heat loss at elevated temperatures.

The temperature attained by the CPC is more than 120°C in

summer season and below 100°C in winter, thus best suited

for the low temperature applications like Solar air

conditioning, hot water for tanning, Solar heaters etc.

3.5 Cost Reduction

Following cost reduction potential have been exploited:

Cost reduction by simplification of the design:

Less different profiles, parts, better transportation;

assembly concept; cost reduction by weight reduction of

the structure; frame work structure, Finite Element method

for structural design calculations, wind analysis for proper

wind load case.

Cost reduction by the optical performance of the collector:

Rigid support structure, frame work, manufacturing and

assembly accuracy.

4. NOMENCLATURE

Beam radiation on horizontal Surface

Diffused Radiation

Tilt factor for beam radiation

tilt factor for diffused radiation

C Geometric concentration ratio

Useful heat gain rate

D Absorber tube diameter

W Aperture Width

Heat removal factor

Overall heat loss coefficient

N No. of tubes

heat transfer coefficient

m Mass flow rate of working fluid

Specific heat capacity at constant pressure

b Absorber width

L Collector Length

Temp. Temperature

Fluid Temp. at inlet

Fluid Temp. at outlet

Ambient temp.

S Absorbed Flux

5. ACKNOWLEDGMENTS

We would like to thank the AEDB and SYNERCON for the

grant for the manufacturing of CPC and technical support.

All of us are also wish to thank AutoDesk, The National

University of Sciences and Technology (NUST), MSC

Softwares for their help in structural analysis.

6. REFERENCES

(1) Duffie J.A. and W.A.Bechman (1991). Solar

engineering of thermal processes, John Wiley & Sons,

New York, USA, pp. 588-619.

(2) Sukhatme, S. P. (1996). Solar Energy, Second edition,

TaTa McGraw-Hill, New Delhi, India, pp. 234-248.

(3) Yunus A. Cengel (1998). Heat Transfer, Second Edition,

McGraw-Hill, USA, pp. 416-427.

(4) Saeed Moaveni, Finite Element Analysis, Second

Edition, Prantice Hall, USA, pp 109-129, 182-206.

(5) Frank P. Incropera, David P. Dewitt (2006). Fifth

Edition, Fundamental of Heat & Mass Transfer, John

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

607

Wiley & Sons, New York, USA, pp. 487-496.

(6) J.N.Reddy (1993). Second Edition, Finite Element

Method, McGraw-Hill, pp. 167-177.

(7) J.P.Holman (1997). Eighth Edition, Heat Transfer,

McGraw-Hill, pp. 254-263

(8) Winston Series CPC, Technical Manual for solar

collection, Solargenix Energy Inc,.pp.1-16

(9) Msc Patran (Structural), 2005 r2 software.

(10) Autodesk Mechanical Desktop 2006 Software

INCIDENCE ANGLE MODIFIERS: A GENERAL APPROACH FOR ENERGY

CALCULATIONS

Maria João Carvalho, Pedro Horta, João Farinha Mendes

INETI – Instituto Nacional de Engenharia Tecnologiae

Inovação, IP

Estrada do Paço do Lumiar, 22

1649-038 Lisboa, Portugal

mjoao.carvalho@ineti.pt

Manuel Collares Pereira, Wildor Maldonado Carbajal

AO SOL , Energias Renováveis, S.A .

P. Industrial do Porto Alto, Sesmaria Limpa,

2135-402 Samora Correia, Portugal

mpicp@aosol.pt

ABSTRACT

The calculation of the energy (power) delivered by a given

solar collector, requires special care in the consideration of

the way it handles the incoming solar radiation.

Some collectors, e.g. flat plate types, are easy to

characterize from an optical point of view, given their

rotational symmetry with respect to the incident angle on

the entrance aperture. This in contrast with collectors

possessing a 2D (or cylindrical) symmetry, such as

collectors using evacuated tubes or CPC collectors,

requiring the incident radiation to be decomposed and

treated in two orthogonal planes.

Analyses of incidence angle modifier (IAM) along these

lines were done in the past for parabolic through, evacuated

tube (ETC) or compound parabolic concentrator (CPC)

collectors [1-6].

The present paper addresses a general approach to IAM

calculation, treating in a general, equivalent and systematic

way all collector types.

This approach will allow the proper handling of the solar

radiation available to each collector type, subdivided in its

different components, folding that with the optical effects

present in the solar collector and enabling more accurate

comparisons between different collector types, in terms of

long term performance calculation.

1. INTRODUCTION

The amount of solar radiation reaching the absorber surface

is affected by a number of optical effects related with

collector geometry and materials properties.

In instantaneous power calculations (and thus delivered

energy), these effects are accounted for by considering the

optical efficiency, η

(θ), measured at normal incidence, and

an incidence angle modifier, Κ(θ), which relates the optical

efficiency for any given incidence angle, to that at normal

incidence.

The rotational symmetry (or 1D) of flat plate collectors

renders the use of the IAM, Κ(θ), easy and direct from the

incidence angle value. Yet, the cylindrical (or 2D)

symmetry of tubular or line focus collectors, requires an

incidence angle (θ) decomposition onto two orthogonal

planes - longitudinal (θ

), referred to the collector axis;

transversal (θ

), referred to the collector section - in view of

a composed IAM calculation, Κ(θ

, θ

In general, IAM measurements are included in collector

efficiency test procedures[3], which determine, in the

present, the measurement of: one IAM value at a 50º

incidence angle , Κ(50), for 1D collectors; three IAM

values in the transversal plane, at 20º, 40º and 60º

transversal incidence angles (Κ(0,20), Κ(0,40), Κ(0,60)),

and one IAM measurement in the longitudinal plane, at 50º

longitudinal incidence angle, Κ(50,0), for 2D collectors.

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

609

(a) (b)

Fig. 1: IAM referential for (a) 1D and (b) 2D collector

types.

Therefore, the calculation of IAM values at different

incidence angles requires the use of adequate

approximation functions based on the available measured

values.

In the present paper, a general approach to beam radiation

IAM is presented in chapter 3, chapter 4 addresses the

calculation of IAM affecting diffuse and reflected radiation

and the composed IAM calculation is addressed in 5. A set

of conclusions is presented in chapter 6.

For the sake of completeness, the foregoing analysis is

based in the most complex case of 2D collector optics,

namely a truncated CPC collector (θ

= 56.8º, θ

= 78º),

considering that 1D optics embody the generalization of 2D

longitudinal plane analysis.

2. IAM AFFECTING BEAM RADIATION

The calculation of the IAM affecting beam radiation

depends on an instantaneous incidence angle value, to be

used directly (1D collectors case), or to be decomposed

onto longitudinal and transversal planes (2D collectors

case).

As mentioned in [7], the optical effects that might be

reflected in the IAM function are manifold and depend not

only on collector materials properties, but also (and

strongly) on collector geometry. Examples of such effects

are: angular variation of transmissivity-absorptivity

properties; radiation spilling or end-mirror reflection effects;

acceptance function; angular variation of the average

number of reflections.

2.1 Longitudinal IAM

The major optical effects which might be present in the

longitudinal direction are those related with the angular

variation of transmissivity-absorptivity properties and with

radiation spilling or end-mirror reflection effects.

A known approximation to the flat-plate IAM (which suits

the effects present in the longitudinal IAM, for 2D

geometries), was presented in the past by Souka [8]. As

mentioned in [7], McIntire [2] and Tesfamichael [9] further

showed that the variation of each of the optical effects

present along the longitudinal presents a similar behavior,

so that the longitudinal IAM may well be fitted by an

expression of the type:

()

01 1

cos

Kθ, +b

⎡⎤

⎛⎞

⎢⎥

≈ −

⎜⎟

⎢⎥

⎝⎠

⎣⎦

(1)

The (+) sign in Eq.(1) means that only positive or zero IAM

values are to be considered.

As shown in [7], the coefficients b

and c in Eq.(1) may be

calculated, after Eq.(1), by knowledge of IAM values for

two different longitudinal incidence angles (different from

0º or 90º, in light of the approximation used), according to

the following expressions:

()

log

⎛⎞

−

⎜⎟

−

⎝⎠

(2)

()

cos

=− (3)

() ()

101 0

K, K ,

θθ−−

(4)

One of the known longitudinal IAM values is that provided

in efficiency test results, Κ(50,0). If no other measured

longitudinal IAM values are available, a 0.05 value for

Κ(85,0), estimated after Souka IAM approximation, might

be used.

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

610

2.2 Transversal IAM

As shown in (7), a good approximation for the transversal

IAM follows a simple linear connection between measured

transversal IAM values, considering also the theoretical

values at 0º (1) and 90º (0) transversal incidence angles.

Yet, in cases where the transversal IAM is likely to present

abrupt variations, such as in the case of CPC collectors at

truncation or acceptance angles, e.g., additional transversal

IAM values (around such angles) might be recommended.

2.3 Composed IAM

An approximation to the composed IAM, based on its

longitudinal and transversal components, was proposed by

McIntire (2) for 2D collectors. After this approximation, the

overall IAM is calculated according to the following

expression:

() ( ) ( ) ( )

00,Kθ Kθ,θ Kθ, K θ≡≈ (5)

The graphics in Figure 2 (a) and (b) show the composed

IAM for the reference CPC collector, calculated after a 3D

ray-trace (30 x 126 rays) and after Eq.(5) approximation

based in common efficiency test measured IAM values.

(a) (b)

Fig. 2: Composed IAM for the reference CPC collector,

calculated after (a) a 3D ray-trace (30 x 126 rays)

and (b) approximation based in available measured

IAM values.

3. IAM FOR DIFFUSE AND REFLECTED RADIATION

Given the distributed nature of both diffuse and ground

reflected radiation, the IAM affecting these radiation

components is not calculated for an instantaneous incidence

angle, but for the hemispherical section, centered in the

collector aperture plane, from which the radiation

component may reach the collector absorber, contributing

for the overall power available to the collector.

An obvious hemispherical cut-off effect is that arising from

the aperture angle, in concentrating collectors, which

renders negligible the diffuse and reflected radiation

contributions at higher concentration factors.

In light of the hemispherical integration due in this case, the

so-called cosine effect must be accounted for, which implies a

weighting of the different incidences included in the

hemisphere. As mentioned in [7], a general expression for the

weighted average IAM, considering an isotropic distribution

of the distributed radiation component, is given in Eq.(6):

()

∫∫

lttl

dθθdθθ

dθθdθθθ,θK

sincos

(6)

The calculation of the IAM affecting diffuse (K

dif,d

) or

reflected (K

dif,r

) radiation follows from numerical integration

of Eq.(6) after integration limits as in Tables 1 and 2.

TABLE 1: INTEGRATION LIMITS FOR DIFFUSE

RADIATION

Longitudinal

integration

limits

Transversal

integration

limits

Collector type a b c d

1D −π/2+ β π/2 −π/2 π/2

<=π/2−

−π/2 π/2 −θ

>π/2−β −π/2 π/2 −π/2 + β θ

NS −π/2 + β π/2 −θ

3 SOLAR COLLECTOR TECHNOLOGIES AND SYSTEMS

611

TABLE 2: INTEGRATION LIMITS FOR REFLECTED

RADIATION

Longitudinal

integration

limits

Transversal

integration

limits

Collector type a b c d

1D −π/2 −π/2 +

−π/

π/2

<=π/2−

No reflected radiation reaches

absorber

>π/2−β −π/2 π/2 −θ

−π/2 + β

NS −π/2 −π/2 +

−θ

4. ENERGY CALCULATION

Energy calculations are based in hourly values of the useful

absorber irradiance, defined according to the following

expression:

() ()

cosG=I θKθ+K D+K R (7)

Yearly energy calculations were performed for four

different locations (Athens, 38º N; Davos, 46º N; Lisbon,

38º N; Stockholm, 59º N) after the reference ray-trace

based composed IAM and after transversal and longitudinal

IAM approximations based solely in available IAM

measured values (L1; T3) or in additional IAM values at

K(60,0) (L2) and K(0,55) (T4).

The final accumulated energy difference values (referred to

the reference ray-trace based IAM calculation) obtained

with the different composed IAM approximations are

presented, for each location, in Table 3.

TABLE 3: ENERGY CALCULATION RESULTS

DIFFERENCE

Approx. Athens Davos Lisbon Stockholm

L1-T3 -0.98% -0.85% -0.74% -0.80%

L1-T4 0.88% 0.92% 1.02% 1.27%

L2-T3 -1.76% -1.79% -1.72% -2.03%

L2-T4 0.04% -0.07% -0.02% -0.06%

5. CONCLUSIONS

The incidence angle modifier reflects the impact of optical

and positional characteristics of the solar collector in the

irradiance incident on the absorber surface and is essential

for calculation of instantaneous power (and thus energy).

In the present paper a general approach to the incidence

angle modifiers affecting beam, diffuse and reflected

radiation is presented, together with suitable

approximations based on available measured IAM values.

The results obtained for yearly energy calculation in four

different locations revealed energy estimation errors lower

than 1% for IAM approximations based in usually available

IAM measured values, and lower than 0.1% for IAM

approximations based in one additional measured IAM

value for both transversal and longitudinal directions.

The IAM calculation methodology herein presented is

applicable regardless of collector type, which encompasses

an advantage in view of its use in simulation tools.

6. NOMENCLATURE

D - diffuse radiation, [W/m

]

abs

- global irradiance incident on the absorber, [W/m

]

I - beam radiation, [W/m

]

- ground reflected radiation, [W/m

]

β - tilt angle, [º]

(θ) - collector optical efficiency

Κ(θ) - incidence angle modifier

dif,d

- diffuse radiation weighted average IAM

dif,r

- reflected radiation weighted average IAM

θ - incidence angle, [º]

- CPC acceptance angle, [º]

- CPC truncation angle, [º]

- longitudinal incidence angle, [º]

- transversal incidence angle, [º]

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

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