heat loses from parabolic trough solar collectors.pdf

8/9/2019 Heat Loses from parabolic trough solar collectors.pdf

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Heat losses from parabolic trough solar collectors

A. Mohamad1,*,

, J. Orfi2 and H. Alansary2

1Department of Mechanical Engineering, Schulich School of Engineering, CEERE, Calgary, AB, T2N1N4, Canada2Department of Mechanical Engineering, KSU, Riyadh, KSA

SUMMARY

Parabolic trough solar collector usually consists of a parabolic solar energy concentrator, which reects solar energy into anabsorber. The absorber is a tube, painted with solar radiation absorbing material, located at the focal length of the concentrator,usually covered with a totally or partially vacuumed glass tube to minimize the heat losses. Typically, the concentration ratioranges from 30 to 80, depending on the radius of the parabolic solar energy concentrator. The working uid can reach atemperature up to 400C, depending on the concentration ratio, solar intensity, working uid ow rate and other parameters.Hence, such collectors are an ideal device for power generation and/or water desalination applications. However, as the lengthof the collector increases and/or the uidow rate decreases, the rate of heat losses increases. The length of the collector may

reach a point that heat gain becomes equal to the heat losses; therefore, additional length will be passive. The current workintroduces an analysis for the mentioned collector for single and double glass tubes. The main objectives of this work are tounderstand the thermal performance of the collector and identify the heat losses from the collector. The working uid, tubeand glass temperatures variation along the collector is calculated, and variations of the heat losses along the heated tube areestimated. It should be mentioned that the working uid may experience a phase change as itows through the tube. Hence,the heat transfer correlation for each phase is different and depends on the void fraction and ow characteristics. However,as arst approximation, the effect of phase change is neglected. Copyright 2013 John Wiley & Sons, Ltd.

KEY WORDS

solar energy; trough collector; heat losses; thermal system analysis

Correspondence

*A. Mohamad, Department of Mechanical Engineering, Schulich School of Engineering, CEERE, Calgary, AB, T2N1N4, Canada.E-mail: [email protected]

Received 27 June 2012; Revised 5 November 2012; Accepted 4 December 2012

1. INTRODUCTION

In general, solar collectors can be classied into three

categories, Point collector (high temperature, order of

1000C or more), line collector (intermediate temperature,

order of 300C or more) and plane collector (low tempera-

ture, order of 100C or less). Point collectors usually consist

of a parabolic mirror, which concentrates the solar radiation

into a small area (point), or it consists of many mirrors

directing the solar energy into a small region. Those mirrors

are usually monitored electronically. This type of collectorneeds a sophisticated solar tracking mechanism and usually

applied in power generation, metal melting, hydrogen

production, etc. The second type of the collector is the line

collector, which usually consists of a parabolic cylinder that

directs solar radiation into a tube (line), located at the focal

length of the collector. The tube is coated with solar absorb-

ing material and covered with a glass tube. The gap between

the glass tube and tube is fully or partially evacuated from air

to reduce the heat losses. Also, for better performance, the

absorber is covered with selective materials and the glass

tube coated with anti-reective material. This type of

collector can reach 300C or more depending on the concen-

tration ratio, ow rate and solar intensity. The tracking

mechanism for this type of collectors is simpler than the

tracking mechanism for the point collectors. It has been

applied to power generation in many locations around

the world [15]. State of art reviews of the trough solar

collector applications for power generation with history

are given by Price et al. [6]; Fernandez-Garcia et al. [7]

and Garcia et al. [8]. Using natural convection heat tube

integrated with solar trough collector experimentallyinvestigated by Zhang et al. [9]. They claimed that their

system achieved a thermal efciency of about 38%.

Application of a trough solar collector for water disinfec-

tion is given by Malato et al. [10]. Also, it is an ideal

device for water desalinations, where the salted water

can be ashed after passing through the collector. The

evaporated water can be condensed and used as fresh

water after certain processes. Flat plate type of solar

collectors usually consists of a at plate to absorb solar

radiation with a glass cover. In general, the at plate

INTERNATIONAL JOURNAL OF ENERGY RESEARCH

Int. J. Energy Res.2014; 38:2028

Published online 11 February 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.3010

Copyright 2013 John Wiley & Sons, Ltd.20


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collector does not need the solar tracing mechanism. This

type of collector usually operates at temperature of order of

100C. However, for vacuumed glass tubes and if the solar

intensity is high, the temperature may reach about 150C.

The more attractive feature of this type of collector is that it

does not need the solar tracking mechanism. The main

application of this type of collector is for domestic water

and space heating. Different types of solar collectors and

their applications were reviewed by Kalogirou [11].

In this paper, the second type of the collector (line) is

considered. However, the model developed can be applied

even for at plate with vacuumed tubed collector, by

setting the concentration ratio to order of unity. Hence,

the model developed in this research is targeted by both

types of collectors.

Espana and Rodriguez [12] developed a mathematical

model for simulating the performance of a trough collector.

They assumed that the absorber is a bare tube exposed to

ambient conditions. In other words, the absorbing tube is

not covered with glass tube.

Grald and Kuehn [13] studied the thermal performanceof a cylindrical trough solar collector with innovative

porous absorber receiver. They solved uid dynamic and

energy equations using nite difference method. The

system is designed to reduce the heat losses as much as

possible by allowing cold water pass through the outer

layer of the absorber, and hotuid extracted from the core

of the absorber. The estimated thermal efciency of the

system is about 60% for a low temperature difference

between the uid outlet temperature and ambient tempera-

ture. However, the efciency of the system drops to about

30% for high temperature differences.

Kalogirou et al. [3] published an analysis for hot water

ow through a trough solar collector with water ashing

system. The results of analysis indicated that about 49%

of the solar energy can be used for steam generation.

Odeh et al. [14] presented an analysis for water ow

inside the absorber tube as an application for direct steam

generation. The analysis considered phase change of the

liquid water to steam. The convective heat transfer coef-

cient is assumed to be a function of steam quality and

Shahs equation was used [15,16]. The model predictions

were evaluated against Sandia Laboratory tests of LS2

collector [1]. Odeh and Morrison [17] examined the

performance of solar trough collector integrated with water

storage system to compensate the intermittency of the solar

energy. Performance of a combo system (photovoltaic and

thermal) was reported by Coventry [18] by using a troughcollector covered with photovoltaic materials with a concen-

tration ratio of 37. It is found that the thermal efciency of

the system can reach 58%, and electric efciency is around

11%. Yan et al. [19,20] simulated the thermal performance

of a solar trough system used for steam generation for a

power-plant or to heat the feed water.

All the mentioned works did not illustrate the variation

of the local heat losses from the collector, which is the

subject of this work. It is essential to understand the

variation of heat losses along the absorber tube to estimate

the length of the collector for a better performance. It is

expected that the heat losses increase as the collector

length increases because the temperature difference

between the collector and ambient increases. At a certain

location along the collector, the balance between heat

losses and collected energy may reach the equilibrium

conditions. Hence, beyond that location, extra length of

collector may be useless, or it has insignicant effect on

the operation of the collector. For example, the length

one of the trough solar collectors used for power genera-

tion in Spain is more than 100 m [21] and can reach about

785 m [22]. The current work analyzes heat transfer from a

trough solar collector with single and double glass covers.

The gaps between glass covers and between the glass cover

and absorber are assumed to be evacuated from air. The main

objective of the work to identify the losses associated with

the trough solar collector, especially for high-temperature

application. As a fact, the rate of heat losses increases as

the temperature difference between a system and ambient

increases. Hence, using a double glass cover may be

benecial to a certain temperature difference. Burkholderand Kutscher [23] showed that heat losses per unit

collector length can reach about 250 W/m for collector

temperature of 400C.

2. ANALYSIS

Schematic diagram of trough solar collector is shown in

Figure 1. Solar radiation is mainly absorbed at the outer

surface of the absorber tube as a heat. Part of the absorbed

heat transfers to the working uid by conduction through

tube wall and convection from the inner surface of the tube

to the uid. Other parts of the heat transfers as a loss byradiation to the inner surface of the glass through the

vacuum and then by conduction from the inner surface of

the glass to the outer surface of the glass. The heat

dissipated to ambient from the outer surface of the glass

Figure 1. Schematic diagram of the collector.

Heat losses from trough collectors A. Mohamad, J. Orand H. Alansary

21Int. J. Energy Res. 2014;38:2028 2013 John Wiley & Sons, Ltd.DOI: 10.1002/er


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by two mechanisms, convection to the surrounding air and

by radiation to the surrounding surfaces (buildings and

sky). Figure 2 shows the thermal resistance diagram for

the heat transfer process, for single glass cover (a) and double

glass covers (b). Extra resistance is needed to be added to

model double glass covers, after R4in the diagram.

By assuming that the surrounding surface temperature

is equal to the ambient air temperature, the model equation

for a single glass cover can be expressed as:

I a tD Tto Tfb

R1 R2

Tto Ts

R3 R4 R15 R

16

1

(1a)

And for double glass covers:

I a tD Tto Tfb

R1 R2

Tto Ts

R3 R4 R3dR4d R15 R

16

1 (1b)

Energy balance for the working uid can be formulated as,

_mcdTfb

dx

Tto Tfb

R1 R2(2)

The left-hand side of the equation (1) represents the

total solar energy absorbed by the outer surface of the tube

per unit length. The rst term on the right-hand side of the

equation represents the rate of heat transfer to the uid

inside the tube, useful energy. The second term on the

right-hand side of the equation (1) represented the heat

losses to the ambient. The left-hand side of the equation

(2) represents useful rate of heat transferred to rise theuid temperature as it passes through the tube.

The above equations are coupled and nonlinear

because the rate of heat transfer from the tube to glass

takes places by radiation. Also, the rate of heat to the

surrounding surfaces and sky takes place by radiation.

However, the above equation can be combined into one

equation by replacing the right-hand side of equation (2)

into the rst equations, yields

_mcdTfb

dx I a tD

Tto Ts

R3 R4 R15 R

16

1

(3)

Equation (3) contains two unknowns, Tfb and Tto;

hence, there is need to solve equation (3) coupled with

equation (1).

The explicit forms for the thermal resistances are as follow:

R1 1

2prtih(4-a)

R2 1

2pktln

rto

rti(4-b)

R3 1

2psrto

1

et

1 eg

eg

rto

rgi

T2t T2g

Tt Tg h i1

(4-c)

R4 1

2pkgln

rgo

rgi(4-d)

R3d 12psrgo

1et

1 egeg

rgorgid

T2g T2gd

Tg Tgd h i1

(4-e)

R4d1

2pkgln

rgod

rgid(4-f)

R5 1

2prgodha(4-g)

And

R6 1

E s2 prgod Tgod Ts

T2god T2s

(4-h)

It is fair to assume that R2, R4and R4dare negligible com-

pared with other thermal resistances. Then, inner surface

temperature of the tube (Tti) is equal to the outer surface of

the tube (Tto). Also, the outer surface temperature of the glass

tube (Tgo) is equal to the inner surface temperature of the glass

cover (Tgi). Hence, equations (1) and (2) simplify to,

(a)

(b)

Figure 2. Thermal resistances diagram (a) single glass cover, (b) double glass covers.

Heat losses from trough collectorsA. Mohamad, J. Or and H. Alansary

22 Int. J. Energy Res.2014;38:2028 2013 John Wiley & Sons, Ltd.DOI: 10.1002/er


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I a tD Tto Tfb

R1

Tto Ts

R3 R15 R

16

1

(5)

and

_mcdTfb

dx

Tbo Tfb

R1(6)

respectively. Yet, the above equations are not easy to solve

analytically because nonlinearity introduced by radiative heat

transfer (see R3 and R6). Hence, equations (5) and (6) are

needed to be solved iteratively, using nite difference method.

However, to close the solution, there is a need for another

equation to nd glass temperature (Tg), which is,

Tbo Tg

R3

Tbo Ts

R3 R15 R

16

1

(7)

3. CALCULATING HEAT TRANSFER

COEFFICIENT

The rate of heat transfer for turbulent forced ow in a tube

is given by Dittus-Boelter correlation as [24],

Nu 0:023Re0:8Pr1=3 (8)

Where Nu=h dp/kf, Re=(4 m)/(md p).

Convective heat transfer coefcient from the outer

surface of the glass tube to ambient air is calculated from

the following correlation,

ho 0:0191 0:006608Vwind (9)

Where Vwindis wind velocity in m/s, and hois in W/m2

.K.For double glass cover, the resistance R3 can be

replaced by two resistances (R3 and R3d), hence, R3 in

equations (5) and (7) replaced by,

R3 1

2psrto

1

et

1 eg1

eg1

rto

rg1

T2t T2g1

Tt Tg1 h i1

1

2psrg1

1

eg1

1 eg2

eg2

rg1

rg2

T2g1 T2g2

Tg1 Tg2 h i1

(10)

Where subscript g1 and g2 stand forrst and second glass

covers, respectively. Also, for double glass cover, t in

equation (1) should be replaced by t2.

4. RESULTS AND DISCUSSION

The results are presented for the aperture diameter of 1 and

3 m. The range ofow rate investigated is from 0.005 to

0.05 kg/s. All the simulations were done for a constant

solar intensity of 500W/m2

. Table I summarizes other

parameters used in the simulations.

Figure 3a shows the uid, absorber and glass cover

temperatures variation along the collector for the ow rate of

0.005 kg/s. For such a low ow rate, it is possible for the uid

to reach temperature of about 230C for the collector with

Table I. Typical values for properties used in the simulation,

unless otherwise stated.

Property Value

Glass tube emissivity 0.9

Glass tube transmissivity 0.94

Absorber tube absorptivity 0.94

Absorber tube diameter (m) 0.05

Glass tube diameter (m) 0.10

Absorber length (m) 20

Ambient temperature (C) 30

Inlet uid temperature (C) 30

Typical solar intensity (W/m2) 500

Aperture length (m) 3.0

L (m)

T(C)

0 5 10 15 20

50

100

150

200

250

Fluid

Tube

Glass

Flow rate =0.005 kg/s, I =500 W/m^2, D=1.0 m

x (m)

Heat(W)

%

efficiency

0 5 10 15 200

2000

4000

6000

8000

10000

0

20

40

60

80

100

Heat Losses (W)

Heat Input (W)

Efficiency

Flow rate =0.005 kg/s, I=500 W/m^2, D=1.0 m

a

Figure 3. (a) Fluid, absorber and glass cover temperature varia-

tion along the collector. (b) Heat input, heat losses and ef ciency

of the collector as a function of collector length.




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aperture of 1 m and 20 m long. However, the heat losses

increase as the length of the collector increases (Figure 3b).

For a collector of 10 m long, the thermal efciency of the

collector is about 60%. As the length of collector increase,

the heat losses increase because the temperature difference

between the absorber and ambient increase (Figure 3), and

efciency decreases to 40% for a collector length of 20 m.

The outlet temperature of the uid from the collector

decreases as the ow rate increase to 0.01kg/s (Figure 4a).

The outlet uid temperature for the specied collector

reaches about 170C for the ow rate of 0.01 kg/s compared

with 230C for the ow rate of 0.005. However, the losses

decrease as the ow rate increase. Figure 4b illustrates the

heat losses and efciency of the collector as a function of

collector length for the ow rate of 0.01kg/s. The thermal

efciency of the collector of length 20 m is about 60%

compared with 40% for ow rate of 0.005 kg/s. Further

increasing the ow rate to 0.05 kg/s decreases the uid outlet

temperature and increases the efciency of the collector, as

shown in Figure 5a and 5b, respectively. For such a high

ow rate, the outlet uid temperature is only about 70

C.

Such a low temperature is difcult to be utilized for power

generation or water desalination processes. The efciency

of power cycle is dictated by Carnot efciency,

Z 1 Tc

Th(11)

where Tc and Th are cold and hot absolute temperatures

bounding a system, respectively. Hence, as the absorber

temperature (Th) decreases, the efciency of power cycle

decreases. For instance, for temperature of 70C (343K)

and for ambient temperature of 20C (293 K), the maximum

ideal efciency of the cycle is about 14.6%. In fact, even

such a low efciency is not achievable in real cycle. In

practical cycle,only about half of Carnot efciency is usually

achievable, i.e. about 7.0%.

Results for aperture of 3 m are shown in Figure 6a and 6b

forow rate of 0.01 kg/s. The outlet temperature of theuid

can reach 370C. Nevertheless, the losses also are high,

where the efciency drops to about 45%. The maximum

cycle efciency working with uid temperature of 370

C

L (m)

T(C)

0 5 10 15 20

50

100

150

200

Fluid

Tube

Glass


x (m)

Heat(W)

%

efficiency

0 5 10 15 200

2000

4000

6000

8000

10000

0

20

40

60

80

100

Heat Losses (W)

Heat Input (W)

Efficiency


a




L (m)

T(C)

0 5 10 15 2020

40

60

80

Fluid

Tube

Glass


x (m)

H

eat(W)

%

efficiency

0 5 10 15 200

2000

4000

6000

8000

10000

0

20

40

60

80

100

Heat Losses (W)

Heat Input (W)

Efficiency


a







6/9

(643 K) and with ambient temperature of 20C (293) is about

54%. Practical cycle efciency may be about 30%.

In a summary, for high temperature application, the heat

losses increase drastically as the length of the collector

increases due to the fact that the temperature difference be-

tween the absorber and ambient increases. Therefore, it is

suggested that increasing the thermal resistance is neces-

sary at least for collector length greater than 10 m, as the

results of losses analysis suggest. It is expected that using

double glass covers with vacuumed gaps may decrease

the losses and increase overall efciency of the collector.It should be mentioned that with added extra glass layer,

the optical losses of the system also increase because the

glass absorbs and reects part of the incident solar radia-

tion. In simulating double glass cover, the left-hand side

of equations (1) and (5) is multiplied by t. In other words,

the t in the mentioned equations is replaced by t2

.

The results for a collector with double glass covers with

aperture of 1 m are presented for massow rate of 0.01 kg/s

(Figure 7a and 7b). It is possible to reach uid outlet temper-

ature of 190C, compared with 170C for single glass cover

collector, i.e. 20C gain in the temperature. However, the

gain in efciency is only a few percent. The efciency for

aperture of 3 m is about 50%, and outletuid temperature

is of about 400C compared with 45% and 370C for single

glass cover system (Figure 8a and 8b). Hence, there is some

gain by adding double glass layers compared with results of

single glass layer collector. Theresults suggested that it is not

economical or benecial to add double glass cover to the rst

part of the collector (at least to the rst 10 m). In the follow-

ing section, the results of analysis for partial covering the

collector with second glass cover will be presented.

The results show that using double glass covers for

solar collectors of length of 10 or less is not that econom-

ical. However, it may be benecial to use double glass cov-

ers for collector length larger than 10 m. Hence, it may be a

good idea to use single glass cover for the rst 10 m and

double glass cover for any length beyond that.

Figure 9a and 9b show typical results for a collector with

three meter of aperture. Therst half (rst 10m length) of the

L (m)

T(C)

0 5 10 15 20

50

100

150

200

250

300

350

400

Fluid

Tube

Glass


x (m)

Heat(W)

%efficiency

0 5 10 15 200

5000

10000

15000

20000

25000

30000

0

20

40

60

80

100

Heat Losses (W)

Heat Input (W)

Efficiency


a




L (m)

T(C)

0 5 10 15 20

50

100

150

200

250

Fluid

Tube

Glass


x (m)

Heat(W)

%efficiency

0 5 10 15 200

2000

4000

6000

8000

10000

0

20

40

60

80

100

Heat Losses (W)

Heat Input (W)

Efficiency


a

Figure 7. (a) Fluid, absorber and rst glass cover temperature

variation along the collector with double glass covers. (b) Heat

input, heat losses and efciency of the collector as a function

of collector length for a collector with double glazing covers.




7/9

collector is covered with one glass layer, and the second half

is covered with double glass layers. The difference between

results of Figure 8 and 9 are not that signicant. Therefore,

collector with partially covered with single glass is recom-

mended for high temperature applications.

For a given conditions, it is noticed that there is a

correlation between the mass ow rate and heat losses.

For instance, for I = 500 W/m2

and D = 1.0 m, different

mass ow rates multiplied by heat losses can be correlated

within 6% as shown in Figure 10.Furthermore, effects of absorber diameter on the rate of

heat losses and efciency of the collector are examined

(Figure 11). As the absorber diameter increases, the heat

losses increases, consequently, the collector efciency

decreases. This is due to the fact that as the surface area of

the absorber tube increases, heat losses increase, where heat

loss is function of surface area. Also, for a given mass ow

rate, the uid ow velocity decreases as the tube diameter

increases. Hence, the Reynolds number also decreases, which

decrease the convective heat transfer to the workinguid.

L (m)

T

(C)

0 5 10 15 20

50

100

150

200

250

300

350

400

450

Fluid

Tube

Glass


x (m)

Heat(W)

%efficiency

0 5 10 15 200

5000

10000

15000

20000

25000

30000

0

20

40

60

80

100

Heat Losses (W)

Heat Input (W)

Efficiency


a


variation along the collector with double glass covers. (b) Heat

input, heat losses and efciency of the collector as a function

of collector length for a collector with double glazing covers.

L (m)

T

(C)

0 5 10 15 20

50

100

150

200

250

300

350

400

450

Fluid

Tube

Glass


x (m)

Heat(W)

%efficiency

0 5 10 15 200

5000

10000

15000

20000

25000

30000

0

20

40

60

80

100

Heat Losses (W)

Heat Input (W)

Efficiency


a


variation along the collector for a collector partially covered with

single glass. (b) Heat input, heat losses and efciency of thecollector as a function of collector length for a collector partially

covered with single glass layer.

x (m)

Heat_loss*Flow(W.kg/s)

0 5 10 15 200

5

10

15

20

25

Flow=0.01

Flow0.05

Flow=0.005

Figure 10. Mass ow rate multiplied by heat losses from the

collector as a function of collector length for different massow

rates, I = 500W/m2, D= 1.0m.




8/9

5. CONCLUSIONS

The paper analyzes temperature variation along trough type

solar collector and associated heat losses. As the temperature

difference between the working uid and ambient increases,

the heat losses increase. Therefore, for high temperature

application, it is important to estimate the rate of heat losses.

It is found that using double glazing cover enhances the

thermal efciency of the collector operating at high temper-

ature. Also, it is found that using single glass cover for

collector of length 10 m or less is more economical than

adding double glazing layer. However, for a long collector

double glazing layers is recommend after certain length of

collector for better thermal performance. It is necessary to

estimate the heat losses from high temperature collector(large aperture diameter) because there is a possibility that

the temperature inside the absorber tube reaches the satura-

tion limit and adding extra length will not contribute to

collecting efciency of the collector. Also, it is clear that

increasing the diameter of absorbing tube enhances the rate

of heat transfer losses, consequently decreasing the thermal

efciency of the collector.

ACKNOWLEDGEMENT

The authors extend their appreciation to the Deanship of

Scientic Research at King Saud University for fundingthe work through the research group project No. RGP-VPP-091.

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x (m)

HeatL

osses(W)

%efficiency

0 5 10 15 200

500

1000

1500

2000

2500

3000

3500

4000

40

60

80

r=0.0125

r=0.025

r=0.05

r=0.05 r=0.025 r=0.0125

Figure 11. Heat losses and efciency of collector as function of

the collector length for different absorber diameter, I = 500W/

m2, mass ow rate= 0.05kg/s, D = 1.0m. r in m.




9/9

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