Chapter 3 – Vacuum tube solar collector
25
CHAPTER 3
VACUUM TUBE SOLAR COLLECTOR
3.1 Introduction
Chapter 3 contains the overall description of the vacuum tube sola
collectors. Most of explanation agrees with the basic theory of flat‐plate
collectors. Because of this, the main subject of the chapter is flat‐plate collectors
while the vacuum tube type is only discussed when differences appear.
The second paragraph introduces some overall aspects of solar collectors.
Then, Paragraph 3 describes the most relevant features of solar radiation, taking
into account the final users i.e. the solar collectors. Flat‐plate solar collectors are
described in Paragraph 4, where the equation for the useful energy gain has
been obtained. In Paragraph 5, vacuum tube solar collectors are introduced,
focusing on those aspects that differentiate this type from the flat‐plate
collectors. Paragraph 6 reports the matter of Incidence Angle Modifier and its
importance for vacuum tube solar collectors. The collector arrays, focussing on
the series connection and its influence on the useful energy gain, are explained
in Paragraph 7. Paragraph 8 describes the solar collector test. At last, some
practical considerations about the employ of the solar collectors and their real
behaviour compared to the developed theory are discussed in Paragraph 9.
Chapter 3 – Vacuum tube solar collector
26
3.2 Overview
A solar collector is a special kind of heat exchanger that transform solar
radiant energy into heat. A solar collector differs in several respects from more
conventional heat exchangers. The latter usually accomplish a fluid‐to‐fluid
exchange with high heat transfer rates and with radiation as an unimportant
factor. In the solar collector, energy transfer is from a distant source of radiant
energy to fluid.
Different types of solar collectors are available; flat‐plate models are the
most popular, while the evacuated glass tube type (with or without heat pipes)
are usually spread where the radiation heat losses assume large importance.
Flat‐plate collectors can be designed for applications requiring energy
delivery at moderate temperatures; they use both beam and diffuse solar
radiation, do not require tracking of the sun and are almost maintenance‐free.
The major applications of these units are in solar water heating, building
heating, air conditioning and industrial process heat.
3.3 Solar Radiation
The sun’s structure and characteristics determine the nature of the energy it
radiates into space. The radiation emitted by the sun and its spatial relationship
to the earth result in a nearly fixed intensity of solar radiation outside of the
earth’s atmosphere.
Chapter 3 – Vacuum tube solar collector
27
1366,1
[2] (3.3.1)
Where the solar constant G
sc
is the energy from the sun per unit time
received on a unit area of a surface perpendicular to the direction of propagation
of the radiation at mean sun‐earth distance outside the atmosphere.
In additional to total energy in the solar spectrum, it is useful to know the
spectral distribution of the extraterrestrial radiation. The solar spectral irradiance
ω (W m
‐2
μm
‐1
) as function of the wavelength λ (μm
‐1
) is shown in Figure 3.1 [4].
Figure 3.1 The spectral irradiance curve at mean earth-sun distance
The solar radiation received from the sun can be classified as:
• Beam radiation: it hasn’t been scattered by the atmosphere (often
referred to as solar direct radiation).
• Diffuse radiation: its direction has been changed by scattering in the
atmosphere.
Chapter 3 – Vacuum tube solar collector
28
The geometric relationship between the incoming beam solar radiation and a
plane of any orientation relative to the earth can be described in terms of angles,
as shown in Figure 3.2 [1].
Figure 3.2 Typical solar angles
Where:
Β: Slope, the angle between the plane of the surface in question and
the horizontal.
γ: Surface azimuth angle, the deviation of the projection on a
horizontal plane of the normal to the surface from the local
meridian (zero due south, east negative, west positive).
θ
z
: Zenith angle, the angle between the vertical and the line to the sun.
γ
s
: Solar azimuth angle, the angle between the local meridian and the
projection of beam radiation on the horizontal plane.
Chapter 3 – Vacuum tube solar collector
29
Solar radiation at normal incidence received at the surface of the earth is
subject to variation due to atmospheric scattering by air molecules, water and
dust, and atmospheric absorption by O
3
, H
2
O and CO
2
[3].
For an estimation of average incident solar radiation, measured radiation
data from the location object of study are the best source; it is also possible to
use data from locations of similar climate. The measured data are usually
reported as:
H (J m
‐2
): Irradiation for a day, it is the energy per unit of area on a surface,
found by integration of irradiance G.
I (J m
‐2
): Irradiation for an hour, also considered as an hourly energy rate.
Taking into account the loss effects, the flux of incident radiation is, at best,
approximately 1100 W m
‐2
in the wavelength range from 0.3 to 3 μm [1]. The
solar absorbed energy by a surface, eg. the collector absorber plate, can be
predicted using:
SI
b
R
b
τα b
I
d
τα d
1 cos β
2
ρ
g
I τα g
1‐ cos β
2
Where:
• S: the absorbed solar radiation per unit area
• I: the hourly irradiation (J m
‐2
)
• R
b
: the ratio of beam radiation on a tilted plane to that on the plane
of measurement
(3.3.2)
Chapter 3 – Vacuum tube solar collector
30
• τα: the product transmittance‐absorptance
• e ce of the ground ρ
g
: th reflectan
• , : the view factor from the collector to the sky and
from the collector to the ground respectively
b, d and g are the subscripts for beam, diffuse and ground respectively
3.4 Flat‐plate collectors
The important parts of a typical flat‐plate solar collector are shown in Figure
3.3.
Figure 3.3 Cross section of a basic flat-plate solar collector
The selective surface is a “black” solar energy‐absorbing surface, which
absorbs and transfers energy to a fluid; the cover glazing is transparent to solar
radiation but it is mat to the IR radiation emitted by the inner part of the
collector; the back insulation reduces the conduction losses.
Chapter 3 – Vacuum tube solar collector
31
In steady state, the performance of a solar collector is described by means of
an energy balance, which suggests the distribution of incident solar energy into
useful energy gain, thermal losses and optical losses.
Where:
• Q
u
is the useful energy gain expressed in W
• S is the solar radiation absorbed per unit area, as defined by Equation 3.3.2
• A
c
is the collector area (m
2
)
• U
L
is the overall heat loss coefficient (W m
‐2
K
‐1
)
• T
pm
is the mean absorber plate temperature
• T
a
is the ambient temperature
The collector overall loss coefficient U
L
can be obtained as the sum of the
top, bottom and edge loss coefficient, if it is assumed that all losses occur to a
common sink temperature T
a
.
Where t, b and e are the subscripts for top, bottom and edge respectively [1].
The problem with Equation 3.4.1 is that the mean absorber plate
temperature T
pm
is difficult to calculate or measure as it depends on the collector
(3.4.1)
(3.4.2)
Chapter 3 – Vacuum tube solar collector
32
(3.4.3)
(3.4.4)
design, the incident solar radiation and the entering fluid conditions. Equation
3.4.1 can be reformulated in terms of the inlet fluid temperature and a
parameter called the heat removal factor F
R
, which can be evaluated analytically
or measured.
Where f, o and i are the subscripts for fluid, output and input respectively.
The quantity F
R
is equivalent to the effectiveness of a conventional heat
exchanger, which is defined as the ratio of the actual heat transfer to the
maximum possible heat transfer. The latter in a solar collector is the maximum
possible useful energy gain , which occurs when the whole collector is at the inlet
fluid temperature; heat losses to the surroundings are then at the minimum.
Using F
R
, Equation 3.4.1 can be rewritten as shown below.
With Equation 3.4.4 the useful energy gain is calculated as a function of the
inlet fluid temperature T
i
which is usually known or easy to measure. The effect
of F
R
is to reduce Q
u
from what it would have been had the whole collector
absorber plate been at the inlet fluid temperature to what actually occurs.
Chapter 3 – Vacuum tube solar collector
33
(3.4.5)
(3.4.6)
The absorbed solar radiation per unit area S could be obtained from a
function of the irradiance on tilted plane G
T
and the average transmittance‐
absorptance product (τα)
av
.
·
The transmittance‐absorptance product is weighted according to the
proportion of beam, diffuse and ground‐reflected radiation of the collector. At
last, the common form of the energy balance for solar collectors is:
3.5 Vacuum tube collectors
The preceding treatment has been developed for the basic collector design:
a sheet‐and‐tube solar water heater with parallel tubes on the back of the plate.
Different designs of solar collectors have been realized, but it is not necessary to
develop a completely new analysis for each situation [1].
Evacuated glass tube collectors are characterized by a long, narrow, flat
absorber mounted inside the vacuum tube. Convective and conduction heat
losses are almost eliminated evacuating the space between the absorber and the
Chapter 3 – Vacuum tube solar collector
34
cover. Three types of vacuum tube collectors are available as shown in Figure
3.4.
Type (a) is constructed with a single fin and tube with glass‐to‐metal seals at
both ends; bellows are used to accommodate the differential expansions of the
glass and the metal fin and tube.
In type (b), liquid flows “down and back”, with a U‐tube joining the two
conduits; the latter are in close proximity and a high thermal resistance between
the two conduits is necessary: if the resistance were zero, the two conduits
would be at the same temperature, and energy collection would be zero.
Figure 3.4 Evacuated tube collar collector types
Chapter 3 – Vacuum tube solar collector
35
Type (c) employs heat pipes to extract energy from evacuated collectors. The
portion of heat pipe in contact with the fin is the boiler portion. The condenser is
a short section in good thermal contact with the pipe through which the fluid to
be heated is pumped. The advantage of this design is that it has only one seal, at
one end of the tube, and the fin and heat pipe are free to expand inside the
evacuated space.
A heat pipe is a heat transfer mechanism that combines the principles of
both thermal conductivity and matter phase transition to efficiently manage the
transfer of heat between two chemical interfaces. At the hot interface within a
heat pipe, a pressurized fluid in contact with a thermally conductive solid surface
turns into a vapour by absorbing the latent heat of that surface, resulting in a
phase transition. The vapour naturally flows through the system and condenses
back into a liquid at the cold interface, releasing this latent heat. The fluid liquid
then returns to the hot interface through the gravity action where it evaporates
once more and repeats the cycle. In addition, the internal pressure of the heat
pipe can be set or adjusted to facilitate the phase change depending on the
demands of the working conditions of the thermally managed system [6]
Chapter 3 – Vacuum tube solar collector
36
Figure 3.5 The heat pipe principle applied to the evacuated tube solar collector
The main differences between flat‐plate collectors with flat covers and tube
collectors are about the absorbing surface and the angular dependence of solar
transmittance. The fin width must be less than the tube diameter, so the
absorbing surface will have project area less than that of the tube. The angular
dependence of solar transmittance will differ from cylindrical covers to flat
covers; a corrective factor will be introduced in Equation 3.4.6, as explained in
Paragraph 3.6.
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