Page 144 - Design of Solar Thermal Power Plants

3.2 HELIOSTAT FIELD EFFICIENCY ANALYSIS 129

energy attenuation of the solar beam, and the nonuniform air refractive
index may result in the variation of amplitude and phase of the optical
wave. When the power of the optical wave is large enough and lasts for an
extremely short time, the nonlinearity effect may also influence the
characteristics of solar beams.
The integrated effects of absorption and scattering results in atten-
uation of the radiant intensity of transmitted light. Partial energy of
incident light is converted into other forms of energy through absorp-
tion (such as thermal), and partial energy deviates from its original
direction due to scattering (namely spatial reallocation of radiation
energy).
Monochromatic radiation with intensity is assumed to pass through a
thin atmospheric layer with thickness dl. Without considering nonline-
arity effects, optical intensity attenuation dI is proportional to I, namely

dI I I
0
¼ ¼ bdl (3.1)
I I
Atmospheric transmittance can be obtained through integral calculus
0 1
I Z L
T ¼ ¼ exp @ bdl A (3.2)
I 0 0
T ¼ expð bLÞ (3.3)
in which b is the atmospheric extinction coefficient, l/km, and L refers to
the transmission distance of solar radiation, km.
This is Lambert’s law for describing atmospheric attenuation, which
manifests the exponential law of decreased optical intensity with in-
creases in transmission distance.
As extinction coefficient b describes the influences of the two inde-
pendent physical processes of absorption and scattering on the radiant
intensity of transmitted light, b can be manifested as

b ¼ k m þ s m þ k a þ s a (3.4)
in which k m and s m are molecular absorption and scattering analysis
coefficients separately, and k a and s a are absorption and scattering
coefficients of aerosols in the atmosphere.
Research on atmospheric attenuation can be summarized as studies of
the four basic attenuation parameters mentioned above. When applying,
the commonly used unit for b is either L/km or dB/km, and the con-
version relationship is

bðdB=kmÞ¼ 4:343 bð1=kmÞ (3.5)