Chap2 STS Till 19OCT12

7/29/2019 Chap2 STS Till 19OCT12

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Department of Mechanical EngineeringHITEC University Taxila

1

Remember

Available and Absorbed Solar Radiation

Irradiance (Symbol G, Unit: W/m2): Rate of radiant energy falling on a surface

per unit area of the surface

Irradiation (Symbol H or I, Unit: J/m2): Incident energy per unit area on a

surface obtained by integrating irradiance over a specified time interval

o Specifically, for solar irradiance this is called insolation

o Symbol H for insolation for a day andI for insolation for an hour


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Extraterrestrial Radiation on a Horizontal Surface

Several types of radiation calculations are most conveniently done using

normalized radiation levels, i.e, the ratio of radiation level to the theoretically

possible radiation that would be available if there were no atmosphere

At any point in time, the solar radiation incident on a horizontal plane outside ofthe atmosphere is

30

31

Gsc is the solar constant and n is the day of the year, coszis from Eq. (17)



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It is often necessary for calculation ofdaily solar radiation to have the integrateddaily extraterrestrial radiation on a horizontal surface, Ho.

It is obtained by integrating Eq. (31) over the period from sunrise to sunset. IfGo

is in watts per square meter, Ho in joules per square meter is

32

sis the sunset hour angle, in degrees Eq. (6)



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To calculate the extraterrestrial radiation on a horizontal surface for an hour

period. Integrating Eq. (31) for a period between hour angles 1and 2which

define an hour (where 2is the larger),


The limits 1 and 2may define a time other than an hour

33



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Mean radiation Ho is plotted as a function of latitude for the northern andsouthern hemispheres

The curves are for

dates that give the

mean radiation for the

month and thus show

Ho



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Determine the extraterrestrial normal radiation and the extraterrestrial radiation on

a horizontal surface on March 10 at 2:00 pm solar time for 35N latitude. Determine

also the total solar radiation on the extraterrestrial horizontal surface for the day.

Example

What is the solar radiation on a horizontal surface in the absence of the

atmosphere at latitude 43 N on April 15 between the hours of 10 and 11?

Example



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Terrestrial Irradiation

knowledge of long-term monthly, daily or hourly average insolation data for the

locality under consideration is required

oTo design a solar thermal system

oTo judge its long-term performance

Monthly Average Clearness Index

= =

Bar over the symbols signifies a long-term average

oHo can be calculated from Eq. (32) for a particular day of the year in the given month for

which the daily total extraterrestrial insolation is estimated to be the same as the

monthly mean value

oTables or Figures: values ofHo for each month as a function of latitude, together with

the recommended dates of each month that would give the mean daily values ofHo

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Monthly Av. Daily Extraterrestrial Insolationon Horizontal Surface (Mj/m2)


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= Daily Clearness Index


35

Hourly Clearness Index

= 36

H, H, I are from measurements of total solar

radiation on a horizontal surface Pyranometers_


Beam and Diffuse Components of Hourly Radiation

There are Methods for estimation of the fractions of total horizontal radiation

that are diffuse and beam

Approach is to correlate Id/I, fraction of the hourly radiation on a horizontal plane

which is diffuse, with KT


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Beam and Diffuse Components of Hourly Radiation---Contd---

Example: Plot of Diffuse Fraction VS kT forCape Canaveral

To obtain Id/I vs kT correlations,

data is divided into ranges of

values ofkT

Data in each range are averaged

to obtain a point on the plot

Set of these points is the basis

of correlation


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Beam and Diffuse Components of Hourly Radiation---Contd---

Orgill and Hollands Correlation

= .

.

... For kT< 0

For 0.35 0.80

Erbst Correlation

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38


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Beam and Diffuse Components of Daily Radiation

Like hourly radiation, Studies of

available daily radiation data have

shown that the average fraction which

is diffused, Hd/H, is a function ofKT

= . . + . . + .. For k

T

< 0.715

For kT 0.715

Fors 81.4o

=

. . . + .. For kT < 0.722

For kT 0.722

Fors > 81.4o

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Erbst Correlation:


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Beam and Diffuse Components of Monthly Radiation

Erbst et al. developed monthly average

diffuse fraction correlations from the

daily diffuse correlations

Winter curve lies below the other

indicating lower moisture and dust in

the winter sky resulting lower

Diffuse Fractions

= .. + . . Fors 81.4o and 0.3 KT 0.8

40

= .. + .

. 41

Fors 81.4o and 0.3 KT 0.8


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Estimation of Hourly Radiation from Daily Data


Forhour by hour(or othershort-time base) performance calculations, it may be

necessary to start with daily data and estimate hourly values from daily

numbers

In most cases hourly values are not available, long-term average daily radiation

data can be utilized to estimate hourly average radiation distribution usually

by Empirical Correlations

= 42

Liu and Jordon Correlation

rd = Ratio of hourly diffuse radiation to daily diffuse radiation


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Collares-Pereira Correlation

Estimation of Hourly Radiation from Daily Data


= +

=

.

+

.

= .+ .

43

rt = Ratio of hourly total radiation to dailytotal radiation


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Given the following empirical equation,

where Hd is the monthly average daily diffuse radiation on horizontal surface.

Estimate the average total radiation and the average diffuse radiation between

11:00 am and 12:00 pm solar time in the month of July on a horizontal surface

located at 35N latitude. The monthly average daily total radiation on a horizontal

surface, H, in J uly at the surface location is 23.14 MJ/m2-d.


Example


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Example


What is the fraction of the average January daily radiation that is received at

Melbourne, Australia, in the hour between 8:00 and 9:00?.

ExampleThe total radiation for Madison on August 23 was 31.4 MJ/m2. Estimate radiation

received between 1 and 2 PM.

ExampleThe average daily June total radiation on a horizontal plane in Madison is 22.1

MJ/m2. Estimate the average diffuse, the average beam and the average total

radiation for the hours 10 to 11 and 1 to 2.


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Radiation on Sloped Surfaces

How to estimate radiation on tilted surfaces based on the available total radiation on a

horizontal surface.!!!

We need the directions from which the beam and diffuse components reach the surface in

question

Distribution of diffuse radiation over the sky dome, is a function of cloudiness, and

atmospheric clarity,which are highly variable

Direction of beam radiation have been discussed in detail


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Diffuse radiation is considered to be consisted ofthree parts:



1. Isotropic distribution received uniformly

from the entire sky dome;

2. Circumsolar diffuse resulting from forward

scattering of solar radiation and concentratedin the part of the sky around the sun

3. Horizon Brightening concentrated near the

horizon and is most pronounced in clear skies

Many Sky models are devised, which are

mathematical representations of the diffuse

radiation


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The total incident solar radiation on a tilted surface such as solar collector

is then:

IT = IT,b + IT,d,iso + IT,d,cs + IT,d,hz + IT,refl 44IT,b =Beam Radiation

IT,d,iso

=Diffuse, Isotropic Radiation

IT,d,cs=Diffuse, Circumsolar Radiation

IT,d,cs=Diffuse, Horizon Radiation

IT,refl=Reflected Radiation

For a collector of Area Ac, total radiation in terms of beam, diffuse and

reflected radiation on the horizontal surface is:

AcIT = IbRbAc + Id,isoAsFs-c + Id,cs RbAc+ Id,hz AhzFhz-c+ IiiAiFi-c 45

T: Tilted


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AcIT = IbRbAc + Id,isoAsFs-c + Id,cs RbAc+ Id,hz AhzFhz-c+ IiiAiFi-c45

= =

IbRbAc Beam contribution

As = Sky Area (undefined)

Fs-c = View Factor from sky to collector

Id,isoAsFs-c Isotropic Diffuse Term

Id,cs RbAc Circumsolar Diffuse treated as comingfrom the same direction as the beam

Id,hz AhzFhz-c Diffuse from horizon from a band of undefined area AhzFhz-c = View Factor from horizon to collector

IiiAiFi-c reflected radiation streams from buildings, fields, etc.

Ii = Solar radiation incident on the ith surfacei = Diffuse reflectance of that surfaceFi-c = View Factor from ith surface to the tilted surface


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VIEW FACTOR



Radiation heat exchange between surfaces depends on the

orientation of the surfaces relative to each other, and thisdependence on orientation is accounted for by the ViewFactor

View Factor is a purely geometric quantity and is independentof the surface properties and temperature

View Factor F12 represents the fraction of radiation leaving

surface 1 that strikes surface 2 directly, and F21 represents the

fraction of the radiation leaving surface 2 that strikes surface 1

directly

A1 F12 = A2 F21 46

Reciprocity relation for view factors

Chap2 STS Till 19OCT12

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