To determine the position of the Sun in the sky at a certain moment of the year

and in a certain place, it is necessary to define a few characteristic angles. These

angles are [1]:

• the solar height or altitude a — the angle formed by the direction of the solar rays and their projection on a horizontal plane;

• the zenithal angle — the angle formed by the solar rays and the zenith direction; this angle and a are complementary;

• the solar azimuth a, which indicates the variance of the solar rays’ projection on the horizon’s plane as regards the south; by convention, eastward orientations are negative while westward orientations are positive;

• the hour angle h, which indicates the angular distance between the Sun and its midday projection along its apparent trajectory on the celestial vault; the time angle is also equal to the angle that the Earth has to rotate to bring the Sun back above the local meridian;

• the latitude L — the angle formed by the straight line that connects the place taken into consideration and the Earth’s core and its projection on the equator’s

plane; this angle is positive in the northern hemisphere but negative in the south­ern hemisphere;

• the solar declination d — the angle formed between the solar ray and the equa­tor’s plane measured on the solar midday plane, that is, the meridian plane pass­ing by the Sun; the solar declination is positive when the Sun is above the equa­torial plane and negative when it is under the equatorial plane (Fig. 4).

The solar height a and the solar azimuth a define the instant position of the Sun [1]:

sen a = sen L sen d + cos L cos d cos h (5)

sen a = cos d sen h/cos a (6)

Solar declination d is calculated using Cooper’s equation :

d = 23.45 sen[360(284 + n)/365] (7)

where n stands for the nth day of the year. Declination depends only on the date; therefore, it is the same for all places on the planet.

The hour angle for dawn ha or sunset ht can be calculated using eqn (5), avoiding sen a, as [1]:

Many factors affect the positioning of the solar system’s intercepting surfaces. Among them, the most important is the study of the place and users’ requirements; actually, it is important to examine carefully the consumptions trend during the year. Another factor that has a strong impact on the positioning of the intercepting surfaces is the shading phenomenon at the installation site. To determine accu­rately the shades which can appear on a certain surface, we can use the solar tra­jectories diagram or the Sun’s position diagram (par. 10), which provides precise information on the Sun’s position in the celestial vault during the day and the year at a certain place.

It is clear that the best orientation for an intercepting surface is the one that is orthogonal to the solar rays. The fixed intercepting surfaces (i. e. the ones that do not have automatic Sun chasing devices) meet that orthogonality condition once a day. Hose surfaces are normally installed southward to maximize the energy received during the day. However, this is not a strict norm, especially where the roof is not north-south oriented. Panels which are eastward or south-eastward ori­ented favour the morning running while the westward or south-westward oriented panels favour the afternoon running.

Choosing the best inclination is not easy and immediate; generally, it is chosen such that it is equal to the latitude L decreased by about 10° to maximize the energy collected during the year (e. g. in Rome since the latitude is 42°, the best inclination will be 30°).

If users require the system to work especially in winter months, this value will not be satisfactory. During winter, the apparent trajectory of the Sun in the celestial vault is on average low so that the average inclination of solar radiation reaches the minimum yearly values. A panel inclination higher than the mentioned 30° (e. g. 60° for a hotel located in a skiing resort) will be necessary to favour the intercept­ing surfaces’ exposure to direct radiation.

On the contrary, in summer (e. g. for an open air swimming pool) users can maximize the service with an inclination of about 10°.

The last factor which contributes to the correct positioning of surfaces is the economic result of the investment: the right dimensions and the correct realization of the system minimize the need for the active surface and therefore the number of collectors to be bought and the overall cost of the operation. Eventually, it is necessary to point out that small positioning variations compared to the best panel positioning can lead to negligible loss of energy received [2, 5].

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A solar greenhouse, which is set against a building or is made out of a building, consists of a closed glazed space located on the south side of a house which is separated from it by a thermal accumulator wall (Fig. 74). The greenhouse can be used as both a direct gain non-warmed space and an indirect system since the rooms next to it receive heat through the intermediate wall which works as a storage. It is also possible that the rooms receive heat from the air in the greenhouse through a natural or forced ventilation system. Solar greenhouse planning can follow different criteria: if it is considered as a cheap extension of the house where people live for the greatest part of the year, it will be necessary to employ a big storage mass placed both on the walls and also on the floor and some movable insulation panels for the night. Instead, if the greenhouse is seen as a solar wall system, with an air space which is a few metres wide rather than a few centimetres, it should be planned to ensure that the greatest quantity of intercepted energy will be taken from the air space to heat up the adjacent rooms. In this case, a forced air change using the greenhouse to pre-heat the incoming air could be also planned (Fig. 75).

Solar greenhouses can be realized in a wide range of geometrical configura­tions. It can be considered as a simple addition to a wall, as a semi-jutting out element or as an element which is set in a building (with three of its sides sur­rounded by living spaces). Moreover, the solar greenhouse can be considered as a structure which covers the entire width of the house and is a single storey or two storeys. Even a greenhouse which is isolated from the building structure can supply thermal energy to the building through a system of ventilators and grooves.

Eventually, a correct solar greenhouse plann has to restrict the inner overheating phenomenon during the summer to its minimum. The simplest technique is one which allows ventilation directly from outside by opening the glazed windows, but the use of screenings or glazed surfaces fitted with sun block control is also possible [1, 3, 4].

The solar energy which reaches Earth’s surface is much smaller than that which reaches a surface situated outside the atmosphere. This happens because of the phenomenon of diffusion and absorption of solar radiation by components of the atmosphere. The collision with molecules of air, steam and atmospheric dust results in scattered reflection because of which a part of the radiation is sent back to outer space. Absorption, instead, is principally due to ozone (O3), steam (H2O) and carbon dioxide (CO2). O3 absorbs mainly in the ultraviolet region while H2O absorbs in the infrared region.

Figure 7 shows the spectral distribution of solar radiation when the Sun is at the zenith.

The part of the solar radiation which reaches the Earth’s surface following the direction of the solar rays without being absorbed and reflected is called directed radiation (on soil), while the part that reaches the Earth’s surface from all direc­tions (because of the scattering) is called scattered radiation. Global radiation on soil refers to the sum of directed and scattered radiation.

Diffuse radiation can be picked up almost entirely by flat panels since glass is actually transparent to all solar radiation which arrives with an angle of incidence i (i. e. the angle between a solar ray and a normal surface) smaller than the maxi­mum value of reflection (70-80°). On the other hand, concentrators, assuming that they work in conformity with the rules of geometrical optics, have to be oriented towards directed radiation; they do not pick up diffuse radiation.

If we do not consider horizontal surfaces, which are inclined in any manner, besides directed and diffuse radiation, it is necessary to take into consideration a third kind of radiation: the reflected solar radiation, the radiation reflected from the soil or from the objects near the given surface; its intensity is influenced by the albedo of those objects. Albedo is the fraction of solar radiation that is received

and suddenly reflected by a surface. Every kind of soil and vegetation has its own value of albedo [1-3].

Albedo can also be defined as a transmission coefficient of the atmosphere, which depends on the wavelength and the route of the solar rays in the atmosphere, besides depending on atmospheric composition, which varies with local weather conditions. In the case of clear sky days, the transmission coefficient of directed radiation, given by the ratio between directed radiation on the soil and extraterrestrial radiation on the orthogonal surface, can be calculated using the following equation:

ть = 0.5{exp[ -0.65m(z, a)] + exp[ -0.95m(z, a)]} (9)

We can assume:

m(z, a) = m(0,a)p(z )/p (0) (10)

where p(z) and p(0) are the atmospheric pressures at level z and sea level, respectively.

The adimensional parameter m(z, a) is the air mass for an altitude z above the sea level. This parameter is defined as the ratio between the effective route length of solar rays and their shortest route length, with the Sun at the zenith; a is the angle formed by solar rays with a horizontal plane (see Fig. 8).

The air mass m(0,a) for the sea level can be calculated using the approximated equation:

m(0,a) = 1/sen a = cosec a (11)

which gives an error percentage of 1% per a > 15°, or it can be calculated with the exact formula, taking into consideration the Earth’s and the atmosphere’s bending:

m(0,a) = [1229 + (614sen a)2]05 -614sena (12)

The angle a determines the Sun’s position in space at any time; the relative air mass m has a certain value; therefore, we calculate tb.

Directed radiation is then given by:

I = 11

bn 10 b (13)

Hottel’s model is the second way to calculate the radiation on soil during clear sky days. This model estimates direct radiation on clear sky days for a standard atmosphere with 23 km visibility and four kinds of climate.

The transmission coefficient of normal direct radiation (7bn//0) is calculated using these relations/equations, which are valid for altitudes lower than 2.5 km:

tb = a0 + a^xp( — k/ sena) a0 = r0[0.4237 — 0.00821(6 — Z )2] a1 = r1[0.5055 + 0.00595(6.5 — Z )2] k = rk [0.2711 + 0.01858(2.5 — Z )2]

where Z is the observer altitude expressed in km and r0, r1 and rk are adimensional corrective coefficients.

To achieve global radiation on soil it is also necessary to determine diffuse radi­ation. Liu and Jordan developed an empirical relation between the coefficient of direct radiation tb and that of diffuse radiation td during clear sky days:

td =0.2710 — 0.2939tb (15)

td is the ratio between diffuse radiation on soil over a horizontal plane and extra­terrestrial radiation over a horizontal plane (I0 sen a) [1, 3].

1 Introduction

There are two principal ways of solar energy exploitation:

• heat production (for use in the domestic, civil and production fields; in this case, we talk about thermal solar energy);

• electricity production by the direct conversion of energy (photovoltaic solar energy).

Thermal solar technologies are divided into low, medium and high temperature

ones.

The low temperature technology includes systems which, thanks to appropriate devices (solar collectors, see par. 2.2.2.1), are able to heat fluids at temperatures less than 100°C. These systems are generally installed to produce sanitary hot water (for domestic use, collective users, sport centres, etc.), to produce domestic heating and, in general, other room heating, to heat water in swimming pools, to produce heat at a low temperature for industrial utilization (usually to warm the water used to swill machines or to preserve different kinds of fluids at a certain temperature inside tanks, etc.).

The medium temperature technology includes systems, which allow reaching temperatures of more than 100°C and less than 250°C. Currently, medium — temperature solar thermal power systems are not widespread; among their applica­tions, the most common application is the one represented by simple devices which use solar radiation to cook food (the so-called solar ovens, see par. 2.3).

The high temperature technology includes systems which, thanks to appropriate devices that are able to concentrate solar radiation to a thermal receiver (in this case we talk about concentrating solar power (CSP) technology, see par. 2.4), allow heating a fluid at temperatures more than 250°C.

Concentrated solar technology has its application in electricity production (in this case, we talk about ‘solar thermodynamics’ where the heat at a high tempera­ture is exploited in thermodynamic cycles for electricity production) and in the

fulfilment of chemical processes at high temperatures, such as production of hydrogen. [2, 12-15].

The third and last approach to passive heating is the isolated gain system. In this system, the solar collector and the storage are thermally insulated from the rooms that are to be heated up. The system can run apart from the building which draws energy only when heat is required. Where systems are completely passive, the energy transfer from the collector to the room or to the storage and from the storage to the room happens only by natural processes and not by forced processes such as convection and radiation. The most common technique is the one to create natural circulation systems composed of a flat plane collector and a thermal accumulator tank. The thermal vector fluid is normally air. An air radiator system (Fig. 76) uses a glazed collector located in the most suitable position to get the greatest quantity of the Sun’s radiation, but it must be distant and below the thermal storage tank.

The absorbed heat warms up the air which, because of the density gradient, moves up and enters the storage (made of either a compact conglomerate mass or an incoherent bed of stone) thereby heating it up. The stored heat is then distrib­uted over the air in the room by convection. The thermal storage mass can be put below the floor of the building, below the windows or inside pre-fabricated plug­ging elements. The space orientation of the building is less important for the sys­tem’s efficiency compared with the other kinds of solar gain [1, 3, 4].

An inclined surface situated on the terrestrial plane is characterized by two geo­metrical quantities: inclination b, the inclination of the surface compared to the horizontal, and surface’s azimuth aw, the angle that the projection on the normal to the surface’s horizontal plane has to rotate to superimpose itself on the southern direction. If that rotation is counter clockwise, angle aw is considered to be posi­tive. The angle between the solar rays and the normal to the surface is called the angle of incidence i.

The direct radiation intercepted by a surface is:

Gb = Ibn cos i

The general expression for cos i:

cos i = cos(a — aw )cos a sen b + sen a cos b (17)

or, as a function of the fundamentals angles L, d and h:

cos i = send (sen L cos b — cos L sen b cos aw)

+ cos d cos h(cosL cos b + sen L sen bcos aw)

+ cos d sen b senawsenh (18)

This expression indicates three cases of particular interest:

• For a horizontal surface (b = 0°), we have:

cos i = sen d sen L + cos d cos L cos h = sen a (19)

• For a vertical surface facing south (aw = 0°, b = 90°), we have:

cos i = — sen d cos L + cos d sen L cos h (20)

The introduction of the surface’s azimuth aw results in a remarkable complication when compared with the case where aw = 0°. In that case, using geometrical demon­stration, it can be easily shown that radiation on an inclined surface of angle b at latitude L is equal to the radiation on latitude (L — b), these being surfaces parallels. Therefore, for an inclined surface facing south, we have:

cos i = sen(L — b)sen d + cos(L — b)cos h cos d (21)

Often, it is useful to know when the Sun rises and sets as regards an oriented surface: the surface ‘sees’ the Sun when the angle of incidence is lower than 90° and the solar altitude is more than 0° at the same time. The Sun rises and sets on
the surface connected with the minimum hour angle ha’ (and ht’), between the absolute value which is calculated by ignoring sen a (hour angle of dawn and sun­set on the horizon), and the absolute value is obtained by ignoring cos i (i. e. con­sidering i = 90°).

As a rule, in the northern hemisphere for southward oriented surfaces, when it is winter and days are short, it is sufficient to ignore sen a; however, during sum­mer, when the angle of incidence is more than 90° and the Sun has already risen and before it sets, it is enough to ignore cos i. The general rule, valid only if the surface actually sees the Sun, is given by the following equations:

min ha(a = 0°), ha(i = 90°)

= min ht (a = 0°), ht(i = 90°)|

In the simple case of inclined surfaces facing south, we have: cos i = cos 90° = 0

= sen(L — b)sen d + cos (L — b)cos d cos h

I ha (i = 90°) = I ht (i = 90°) =arcos [ — tg (L — b) tg d] (25)

|ha (a = 0°) = |ht(a = 0°) = arcos [ — tg L tg d] (26)

For northward oriented surfaces, there could be both two dawns and two sunsets (in spring and in summer, in the northern hemisphere) and no dawns and no sun­sets, that is, absence of direct lightening (in autumn and winter).

When the surface is not oriented southward, it is not possible to get simple closed — form expressions for the hour angles on the surface at dawn and sunset.

Assuming that 4o is the instantaneous direct radiation on a horizontal plane, linked to normal direct radiation by the relation:

hn=ho/sena (27)

and applying the (16), we get:

G = /bocos i/sen a = I bo R (28)

where

Rb = cos i/sen a (29)

Rb is the inclination factor for direct radiation; remembering that for a horizontal surface it is sufficient to put b = 0°, expression (28) states that the direct radiation Gb on a surface that is inclined and oriented in any direction is equal to the product of direct radiation Ibo on a horizontal plane and the inclination factor [1, 3].

For a southward oriented surface, we have:

Based on thermodynamic considerations, the use of electrical energy to produce hot water is not recommended, since a prized kind of energy is used and also because the global efficiency of the water heating process is lower than the produc­tion of many other direct water heating processes. In fact, heat is a kind of energy which we inevitably find in every real process as consequence of the irreversibility of this process. So it does not make sense to degrade completely a noble form of energy to obtain heat, without getting the mechanical work which can be obtained from that energy.

An alternative way to produce hot water involves the exploitation of solar energy, which represents a form of clean and inexhaustible energy, by low — temperature thermal solar technologies [16].

These technologies include systems using a solar collector to heat a fluid or the air. The aim of these low-temperature thermal solar systems is to intercept and transfer solar energy to produce hot water or heat buildings. By low temperature we mean the heating of fluids at a temperature of less than 100°C (it rarely reaches 120°C) [1, 2, 5, 13, 17].

The detailed description of low-temperature thermal solar systems can be found in par. 2.2.2.

Medium-temperature technology includes systems which are able to reach temper­atures between 100°C and 250°C. The most common application of the medium — temperature solar thermal system is represented by the solar oven (see Fig. 77): a parabolic reflector (composed of aluminium sheets mounted on a zinc-plated steel structure) concentrates the solar radiation towards a single point which works as a cooking-stove. At this point, a pot is placed which warms itself and cooks the food contained inside. Using a solar oven it is possible to reach the same temperature as a traditional cooking-stove (about 200°C).

A solar oven with a diameter of 1 m takes nearly 18 minutes to boil 1 L of water, while it takes only 9 minutes if the diameter is wider (1.4 m). The reflector can be oriented on the basis of the Sun’s position so that it is possible to cook from morn­ing to afternoon and even to exploit the shortest moment of radiation. In Italy, the use of solar ovens is not common; they represent a very small slice of the market and their use is restricted to the those who consider it a hobby. In countries where lack of energy resources is a daily problem (such as Africa), the solar ovens can have good applications [12, 13, 18, 41].

In spite of the various advantages offered by thermal solar systems, their great potential has not been exploited much in the industrial sector. Thermal solar sys­tems can partially meet the heat demand for low — and medium-temperature (up to 250°C) processes, which are typical of a few industrial sectors such as the chemi­cal, food and textile industry. The thermal solar collectors that are now available now in the market, which we analysed when we talked about low-temperature solar thermal systems (par. 2.2), can reach temperatures of 100°C. As regards applications which need higher temperature (up to 250°C), the experiences are limited and suitable collectors do not exist. In 2003, the International Energy Agency (IEA) started a research project called Task 33/IV which aims to find more promising industrial applications in the thermal solar field and also to calculate the overall potential of thermal solar applications for the production of medium-tem­perature process heat. One of the Task 33/IV activities is research, developed together with the industry, on new collectors which can produce processed heat between 100°C and 250°C (a temperature range that is consistent with several industrial processes) [42-44].

At present, the collector typologies which are more promising in the medium- temperature field are:

• high efficiency glazed flat plate collectors: these are flat collectors with double

antireflection glass;

• linear parabolic collectors, similar to the ones used in the high temperature field

but much smaller (these will be analysed in par. 4.4.1).

• static concentration solar collectors: these are flat plate collectors or more frequently evacuated tube collectors characterized by static mirrors (fixed) for the concentration of solar radiation.

Figure 78: Double-glazed flat plate collector with antireflection glass.

The instantaneous global power which weighs on an oriented surface is given by the sum of the direct component that is obtained from the eqn (28), the diffuse component, which comes from the celestial vault portion seen from the surface, and the part reflected by the soil and nearby objects towards the same surface.

If the sky’s behaviour is assimilated to that of an isotropic spring of diffuse radiation, it is possible to determine the diffuse component which reaches the surface as:

Gd=/do Rd (31)

where

Rd = cos2 (b/2) = (1+cos b)/2 (32)

where Ido is the diffuse radiation on the horizontal plane and Rd is the inclination factor of diffuse radiation.

We can express the radiation (direct and diffuse) reflected by the soil on a certain surface as:

(Ibo +Ido)Rr (33)

Rr, the inclination factor of reflected radiation, is equal to:

Rr = psen2 (b/2) = p(1 — cos b)/2 (34)

p is the soil’s reflection coefficient and it can assume values between 0.2 (grass, concrete) and 0.7 (snow). Therefore, the instantaneous solar power, which is received on a arbitrary oriented surface, in the case of isotropic sky, is equal to [1]:

G = Ibo Rb+Ido Rd+(Ibo+Ido)Rr (35)