Reflecting Parabolic Solar Collectors

8/12/2019 Reflecting Parabolic Solar Collectors

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SOCRATES PROGRAMME

A EUROPEAN SUMMER SCHOOL

AN INTENSIVE COURSE ON

ICT Tools on PV - Systems Engineering: Teaching & Learning

3 1 !"ly# $%%

Technological E'"cational Instit"te o( Patra

)esign# Sim"lation an' Per(ormance o( *e(lecting Para+olic Solar

Collector

GEORGE BARAKOS

Department of Mechanical Engineering

Technological Educational Institute of PatraGR!""# GREE$E

%ara&os'teipat(gr

Intro'"ction:

In this lecture a stud) of mini para%olic collectors s)stems is presented( The mini

Para%olic $ollector S)stems *P($(S(+ are designed as to %e integrated on the roofs of a

residential %uildings or in a larger scale on the roofs of %igger %uildings, *offices,

store houses, green farm houses+( The common approach to locate collector-s arra)s

on roofs is to slope them at appro.imatel) the optimum solar collector angle(

Then a detailed parametric anal)sis of the constructed para%olic trough/concentrating

collectors *P(T($(+ %) using a simulation method de0eloped is made( The simulation

procedure re0eals the indi0idual contri%utions of %oth direct and diffuse components

of the solar radiation to the flu. reaching the c)lindrical a%sor%er of the P(T($(

In addition, one ma) stud) the effects of 0arious optical and thermal parameters of

the collector-s performance(

Collectors ,eometric Elements:

In this section an anal)sis of the geometrical characteristics of the mini para%olic solar

collectors is made(

The data of the mini para%olic s)stem *fig(1+ used for our stud) are pro0ided( 2et us

suppose that the length, l1$.%mm#is %ig enough to a0oid end effects, as the image

from the end of the trough is formed %e)ond the end of the recei0er 314(

The length or aperture sy$ , and the height hof the para%ola are gi0en as data input

according to the designer(

5rom the e6uation of the para%ola one ma) o%tain the focus length ((

/0y(

$

=

1
mailto:[email protected]:[email protected]


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2et the c)lindrical a%sor%er tu%e ha0e diameter '7ere some definitions a%out linear

concentrating s)stems or para%olic trough concentrating s)stems ma) %e gi0en 3, ",

#4(

Fig.1:Characteristics of the parabola

2ert"reis the opening through 8hich the solar radiation enters( 22$ys

Concentrator or otical system is the part of the collector that directs

radiation onto the recei0er(

2rea concentration ratio C or geometric concentration ratioCis the ratio

of the area of aperture to the area of the recei0er(

4l"5 concentration ratiois defined as the ratio of the a0erage energ) flu. on

the recei0er to that on the aperture(

2ccetance angle $67is the angular range o0er 8hich all or almost all ra)s

are accepted 8ithout mo0ing all or part of the collector( The half acceptance

angle for the para%olic trough collector is gi0en at the position y%) the

formulae9

=$y

($

y1($

'sin

*1+

This means that a ra) hits the a%sor%er if the angle of incidence is y (


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y Is the angle at 8hich the ra)s reach the recei0er tu%e tangentiall)(

y 9 Increases 8ith )(

5or Syy the a%o0e formulae gi0es , the largest angle for 8hich allincident ra)s are accepted( This acceptance, half : angle of the para%olic trough, can

%e 8ritten in terms of rim angle * and concentration ratio C

C

sinsin * = *+*im angle 8*( This angle is related to aperture and focal length (%)

($

y

(0

y$

$tan ss* = or

1y(1& y(tan $s s* *"+

The linear concentrating s)stems to %e used in this stud) 8ill %e fi.ed, integrated

on the roof, oriented to 9on Trac;


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Fig.2a, b:Head and base parabola.

Fig. 2c, d:CNC machine where our base and head parabola constructed

Those para%olas *%ase and head+ are constructed from common aluminum foil of

mm thic&ness(

The %ase para%ola using cutting tool 8ith radius *must ha0e9

Aperture 9 bb= 2ys + 2Sf/ sin 2!/sin *#+

7eight 9 hb= h + Sf " ! *@+

5ocal distance 9 fb = #bb/2$2/ 4hb *!+

The head para%ola must ha0e9

Aperture 9 bh= 2ys + 2Sf/ sin *;+

7eight 9 hh= h + ! *+

5ocal distance 9 fh = #bh/2$2/ 4hh *+

#


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The sinus =is due to the fact that the tangent to the para%ola on the upper e.treme A

of the aperture, see fig( comes from9

($

y

(0

y$

'y

'/tan

s

22 =

=

= *1?+

The e6uation of the para%ola in a >?# y# /+ s)stem is9

y2= 4 f % *11+

The aluminum reflecting para%ola foil for e0er) channel of the P($(S( 8ill ha0e a

mean length e6ual to9

m

$

m

$

mm

m

$

m$

m

$

mm +

h1&+h0ln

h

+h1&+

$

1L

*11+

8here,

(m

(sm

S$

1hh

sin

Sy$+

*1+

5or the o0erall dimensions of the para%olic trough collector see figure "a and "%(

@

Fig.&a: The parabolic trough collector of

single aperture 100mm.

Fig.&b: The parabolic trough collector of single

aperture 160mm.


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)etermination o( Solar *a'iation Parameters concerning Para+olic Collectors:

The determination of the solar radiation intense *direct, diffuse and glo%al+, can %e

done e.perimentall), using p)ranometers, or theoreticall), using prediction methods(

Solar 0ectors9

In a specific instant time, fig( # sho8s the position of the sun in the O*.,),5# y@plane is the hori


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Fig.':Suns and collectors position on !"1#$1#%1& coordinate s$stem

The sun-s unit 0ector as it is gi0en %) *1"+ in the O *., ), i@n>n 111 *1@+The components of the solar unit 0ector in the coordinate s)stem *. 1,)1,@n> ss1s5s 1 sinsinesincosesincoscosecossincos@An>@n> ss1sys 1

*1!+

cossinsincoscos@;n>@n> s1s/s 1

;


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Chere 1i , 1A and 1k are the unit 0ectors of the a.is .1, )1,


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decrease is slightl) non/linear( The non/linearit) is due to the fact that the 0alue of the

o0erall loss coefficient increases slightl) as (iT increases(

An increase in the mass flo8 rate of the thermic fluid, has as a result an increase to

the heat transfer coefficient c(h and due to this the collector efficienc) factor 4 ,and the collector heat remo0al factor *4 and the efficienc) increases(

An increase in the concentration ratio C#%) decreasing the si


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The alge%raic e6uation of the c)lindrical a%sor%er section is9

$$

1

$

1 */y = *#+Chere *is the a%sor%er radius

The program ta&es under consideration the direct and the diffuse component of solar

radiation(

5inall), it summariC C1C1C1 on

the c)linder( At position $11 .. = 8e ha0e a circular section *fig(;+(

11


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Fig.): (eam directl$ impinging the absorber

Parameters sn and i' are not necessaril) located in the plane )1, or

11 ;sinAcos* if %y C1cos@n>@*n>cos 1/s1yssi' if %y C1>or

@sin>@n>@cos>@n>@*n>cos1/s1yssi'

if %y C1 '1 of theaperture is9

1'/

'1

1'y

11

1'5

1

n

//

n

yy

n

%5 == *"+The program chec&s initiall) if the random diffuse ra) presented %) the a%o0e

e6uation hits the a%sor%er directl)( Then it determines the point and angle of

incidence on the a%sor%er( If the diffuse solar e6uation line intersects the para%ola the

program chec&s the reflected diffuse ra)s that hit the a%sor%er(

The diffuse radiation directl) impinging the a%sor%er and the diffuse radiation

incident on the a%sor%er after reflection on the para%olas surface is in0estigated in the

follo8ing section(

)i(("se ra'iation 'irectly iminging the a+sor+er:

Sol0ing the s)stem of the c)linder e6uation *"+ and the diffuse irradiation e6uation

line *"+ 8e chec& if the solar line intersects the c)linders surface at a point

@/#y#5>C''' C1C1C1' on the c)linder( At position 'C11 55= 8e ha0e the circular

section of fig( 11

*"+

1


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Fig.11:*sotropic diffuse impinging the absorber directl$.

The 6uantities of the diffuse solar radiation unit 0ector @n> ' and the incident angle

i'' are not necessaril) located in the plane 11 y#/ (

8e ha0eC'1

C'1

y

/tan =

11 ;sinAcos* if %y C'1 >11 ;sinAcos* if %y C'1 <

sin@n>cos@n>@*n>cos11 /'y''i''

if %y C'1 >or

@sin>@n>@cos>@n>@*n>cos11 /'y''i''

if %y C'1 E''' E1E1E1' 8e

consider the para%ola of fig(1 in the position'E1

5 (

Fig.12:Schematic representation of the diffuse insolation.

The e6uation of the tangent tt to the para%ola at the point @/#y#5>E'1' E1'EE1' on

a plane 11 /#y at the a%scissa 'E15 is9

@yy>m//'N E11E11

Chere ($

y

(0

(0y

'y

'

'y

'/

tanm '

'

E1$$

1

E1

1 =

=

= Then, the e6uation of the tangent at point 'E is9

($/y($

y+my/

'E11

E1

11

The normal to the tangent at point 'E is9

($/y

y

($+y

m

1/

'

'

E11

E1

11

The unit 0ector of the normal to the para%ola at point 'E is9

?


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113 ;cosAsinn Chere($

yarctan '

E1

5or the reflection la89 ri (So, cosnsinnnncoscos

11 /'y''ri

The unit 0ector of the reflected ra) in the case of isotropic diffuse radiation is 3149

r'''' ncos$nnnn$nr

In this case, the reflected unit 0ector components are9

coscos$nr

sincos$nr

nr

r/s'/

rys'y

5s'5

11

11

11

The e6uation of the reflected solar radiation-s unit 0ector line from point 'E no8 is9

'/

E'11

'y

E'11

'5

E'11

111r

//

r

yy

r

55== *#1+

=o8, to determine the point 8here this line intersects the c)linder, 8e must sol0e the

s)stem of e6uations *"+ and *#1+( Ce ta&e into account onl) one reflectionN this is

true for the trough para%olic concentrator(

If the reflected line intersects the c)linder at point @/#y#5>C'''

C1C1C1 then 8e ha0e,

as in su%chapter @("(19

'

'

C1

C1

y

/tan = ,

11 ;sinicos* sinrcosr*rcos '/'y'ir' 11 , if %y 'C1

or

sinrcosr*rcos '/'y'ir' 11 , if %y 'C1 aert"retheoninci'entrateenergytotal

@'irectan''i(("se>a+sor+e'rateenergytotalo=

That is,

2*I*I

PPPP

''o++o

;

1i

'r'a+r+'

o == *#+

Or

T

''o

o'

T

++o

o+o

I

*I

I

*I *@?+

Notice: s far concerning the trough parabolic with a trac/ing s$stem with

reflectiit$ r and absorptiit$ -of the absorber for the direct beam radiation the

optical efficienc$ o3+ is appro"imatel$ aro+ we can chec/ this with theprogram results onl$ at noon

Instantaneo"s thermal collector e((iciency:

#


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The simulation code estimates the instantaneous thermal efficienc) using t8o

different paths( The first one is 0ia e6uation *1+(

Ta

"

I2

= Chere, ground reflected radiation is neglected and useful heat gain rate is9

(i(o" TTCm 3C4 *@1+m 9 5luid mass flo8 rate 3&gHsec4C9 Specific heat capacit) of the fluid 3H &gK4

(i(o T#T 9 5luid outlet and inlet temperatures respecti0el)

The second path for the estimation of the instantaneous thermal efficienc) can %e

descri%ed %) the e6uations *+

T

acL

oI

@TT>G #

T

a(iL

a

C

o*I

TTG

2

24

Long term er(ormance:

In order to ha0e the option to calculate the collectors- long / term performance 8e

constructed a fluid tan&(

The fluidflo8 rate mass m in the a%sor%er tu%e is e0er) time selected to ta&e @# literof fluid per hour and mof aperture surface

Fig. 14:Tan/ used on our e"periment

1%%%3&%%

2.0m tot

a= 3m"Hs4 *@+

Chere chsa nly$2 tot And chn is the num%er of para%olas channels(

The 0olume of the tan& *fig( 1#+ is e6ual to the 0olume of the fluid that comes thro8

the collector in an hour 8ith the a%o0e flo8 rate(

@


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3&%%mV 3m"4 *@"+

To e.ecute the soft8are, 8e supposed Tsi T(i Tc Tathen 8ith iteration after the

calculation of4*and GL8e ta&e(

Lc

"ac

acG2

I2TT

, i(

3

"

(o TCm

T

*@#+

And

(i

3

"

( TCm$

T

The program calculate the tan&-s useful energ) rate

@FTT>GIH2O4 asiLac*"s

Ce assume

4* %D 4*

5or a time period of an hour and for unit a%sor%er surface 8e ha0e9

@TT>@mc>2

3&%%(is(S

c

"s *@@+

And then

si

sc

"ss( T

@C.0>2

3&%%T = *@!+

*e(erences:

1( Duffie, ( A( and C( A Bec&man, Solar Energ) Thermal ProcessesF, ohn

Cile) and sons, =e8 or& *11+(

( Ra%l, A, Acti0e solar collectors and their applicationsF(O.ford ni0ersit)

Press, =e8 or&, *1@+

"( Kreith, 5 and ( 5( Kreider, principles of solar EngineeringF, Mc Gra8 : 7ill,

=e8 or& *1;

!


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#( Suhas P( Su&hatme, Solar Energ)F Tata Mc Gra8 : 7ill, =e8 Delhi *1!+

(R(

@( Sir 7( C( Masse) and 7( Kestelman, QAncillar) Mathematics-, Sir Isaac

Pitman Son, 2ondon *1!#+(

!( Grant R( 5o8les and G(2($assida) Anal)tical MechanicsF Saunders Golden

Sun%urst Series, Orlando *1"

;( D( E( Prapas, Optics of Para%olic :Trough Solar Energ) $ollectors

Possessing Small $oncentrating RatiosF, Solar Energ), 0", =o ! *1;+(

( S( =( Kaplanis The Monte $arlo MethodF , Thessaloni&i, *1;+, *in Gree&+

Documents

Reflecting Parabolic Solar Collectors