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Scenarios for the future of renewable energy through 2050 are reviewed to explore how much renewable energy is considered possible or desirable and to inform policymaking. Existing policy targets for2010 and 2020 are also reviewed for comparison. Common indicators are shares of primary energy, electricity, heat, and transport fuels from renewable. Global, Europe-wide, and country-specific scenarios show 10% to 50% shares of primary energy from renewable by2050. By 2020, many targets and scenarios show 20% to 35% share of electricity from renewable, increasing to the range 50% to 80%by 2050 under the highest scenarios. Carbon-constrained scenarios for stabilization of emissions or atmospheric concentration depict trade-offs between renewable, nuclear power, and carbon capture and storage (CCS) from coal, most with high energy efficiency. Scenario outcomes differ depending on degree of future policy action, fuel prices, carbon prices, technology cost reductions, and aggregate energy demand, with resource constraints mainly for biomass and bio fuels.
Renewable energy has grown rapidly in recent years. Overall, renewable produced 16.5% of world primary energy in 2005. The share of world electricity from renewable was 19%,mostly from large hydropower (hydro) and the rest from other sources such as wind, biomass, solar, geothermal, and small hydro. In addition, biomass and solar energy contribute to hot water and heating, and bio fuels provide transportation fuels. Although large hydro is growing at modest rates of 1% to 2%annually, most other renewable technologies have been growing at rates of 15% to 60%annually since the late 1990s. It is this group of technologies that is projected to grow the fastest in the coming decades, making renewable a highly significant and potentially majority share of world energy.
Attention has become more focused on the future of renewable for a variety of environmental, economic, social, and security reasons. There is a growing body of literature describing that future, including policy targets, socioeconomic and technology scenarios, carbon-constrained scenarios, and future social visions. Policy targets for future shares of renewable energy are described for regions, specific countries, states or provinces, and cities. Shares of renewable energy are also described in scenarios that show future energy consumption on the basis of analytical models or projections. Some scenarios project forward using assumed growth rates or future technology shares on the basis of policy, technology, economic, or resource factors. Other scenarios project backward from specified future conditions or constraints, such as limits to global carbon emissions, stabilization of atmospheric CO2 concentration, minimum or maximum energy consumption percapita, and sustainable land use. Scenarios can explore technologies, costs, policies, investments, emissions, time frames, social appropriateness, and shares relative to fossil fuel sand nuclear energy.
NATIONAL SCENARIOS OF RENEWABLE ENERGY SOURCES
Current installed base of Renewable energy is 16,492.42 MW which is 10.12% of total installed base with the southern state of Tamil Nadu contributing nearly a third of it (5008.26 MW) largely through wind power. India is world's 6th largest energy consumer, accounting for 3.4% of global energy consumption. The economy of India, measured in USD exchange-rate terms, is the twelfth largest in the world, with a GDP (Gross Domestic Product) of around $1 trillion (2008). GDP growth rate of 9.0% for the fiscal year 2007-2008 which makes it the second fastest big emerging economy, after China, in the world. There is a very high demand for energy, which is currently satisfied mainly by coal, foreign oil and petroleum, which area part from being a non-renewable.
In solar energy sector, some large projects have been proposed, and a 35,000 kmÂ² area of the Thar Desert has been set aside for solar power projects, sufficient to generate 700 to 2,100 gigawatts. India is endowed with rich solar energy resource. The average intensity of solar radiation received on India is 200 MW/km square (megawatt per kilometer square). With a geographical area of 3.287 million km square, this amounts to 657.4 million MW. However, 87.5% of the land is used for agriculture, forests, fallow lands, etc., 6.7% for housing, industry, etc., and 5.8% is either barren, snow bound, or generally inhabitable. Thus, only 12.5% of the land area amounting to 0.413 million km square can, in theory, be used for solar energy installations.
The development of wind power in India began in the 1990s, and has significantly increased in the last few years. Although a relative newcomer to the wind industry compared with Denmark or the US, India has the fifth largest installed wind power capacity in the world. The worldwide installed capacity of wind power reached 157,899 MW by the end of 2009 . USA (35,159 MW), Germany (25,777 MW), Spain (19,149MW) and China (25,104 MW) are ahead of India in fifth position (Fig. 11). The short gestation periods for installing wind turbines, and the increasing reliability and performance of wind energy machines has made wind power a favored choice for capacity addition in India.
Suzlon, India's largest wind power company has risen to ranking 5th worldwide, with 7.7%of the global market share in just over a decade. Suzlon holds some 52 percent of market share in India. Suzlon's success has made India the developing country leader in advanced wind turbine technology(fig 1.1)
Fig 1.1 India in top 10 countries: Installed wind power capacity
India is endowed with economically exploitable and viable hydro potential assessed to be about 84,000 M Watt 60% load factor (1,48,701 MW installed capacity). In addition, 6780 MW in terms of installed capacity from Small, Mini, and Micro Hydel schemes have been assessed. Also, 56 sites for pumped storage schemes with an aggregate installed capacity of 94,000 MW have been identified . However, only 19.9% of the potential has been harnessed so far. Hydroelectricity is the term referring to electricity generated by hydropower; the production of electrical power through the use of the gravitational force of falling or flowing water. It is the most widely used form of renewable energy. India is blessed with immense amount of hydro-electric potential and ranks 5th in terms of exploitable hydro-potential on global scenario. India was one of the pioneering countries in establishing hydro-electric power plants. The power plant at Darjeeling and Shimsha (Shivanasamudra) was established in 1898 and 1902 respectively and is one of the first in Asia. The installed capacity as of 2008 was approximately 36,877. The public sector has a predominant share of 97% in this sector. In addition, 56 number of pumped storage projects have also been identified with probable installed capacity of 94,000 MW. In addition to this, hydro-potential from small, mini & micro schemes has been estimated as 6 782 MW from 1 512 sites.
India has reasonably good potential for geothermal; the potential geothermal provinces can produce 10,600MW of power. Rocks covered on the surface of India ranging in age from more than 4500 million years to the present day and distributed in different geographical units. The rocks comprise of Archean, Proterozoic, the marine and continental Palaeozoic, Mesozoic, Territory, Quaternary etc., More than 300 hot spring locations have been identified by Geological survey of India (Thussu, 2000).But yet geothermal power projects has not been exploited at all, owing to a variety of reasons, the chief being the availability of plentiful coal at cheap costs.
FORM AND CHARACTERISTICS OF RENEWABLE ENERGY SOURCES
Solar energy - Solar energy is the most readily available and free source of energy since prehistoric times. It is estimated that solar energy equivalent to over15,000 times the world's annual commercial energy consumption reaches the earth every year. India receives solar energy in the region of 5 to 7 kWh/m2 for 300 to 330 days in a year. This energy is sufficient to set up 20 MW solar power plant per square kilometer land area. Solar energy can be utilized through two different routes, as solar thermal route and solar electric (solar photovoltaic) routes. Solar thermal route uses the sun's heat to produce hot water or air, cook food, drying materials etc. Solar photovoltaic uses sun's heat to produce electricity for lighting home and building, running motors, pumps, electric appliances, and lighting.
Wind energy - Wind energy is basically harnessing of wind power to produce electricity. The kinetic energy of the wind is converted to electrical energy. When solar radiation enters the earth's atmosphere, different regions of the atmosphere are heated to different degrees because of earth curvature. This heating is higher at the equator and lowest at the poles. Since air tends to flow from warmer to cooler regions, this causes what we call winds, and it is these airflows that are harnessed in windmills and wind turbines to produce power.
Wind power is not a new development as this power, in the form of traditional windmills-for grinding corn, pumping water, sailing ships - have been used for centuries. Now wind power is harnessed to generate electricity in a larger scale with better technology.
Bio energy - Biomass is a renewable energy resource derived from the carbonaceous waste of various human and natural activities. It is derived from numerous sources, including the by-products from the wood industry, agricultural crops, raw material from the forest, household wastes etc. Biomass does not add carbon dioxide to the atmosphere as it absorbs the same amount of carbon in growing as it releases when consumed as a fuel. Its advantage is that it can be used to generate electricity with the same equipment that is now being used for burning fossil fuels. Biomass is an important source of energy and the most important fuel worldwide after coal, oil and natural gas. Bio-energy, in the form of biogas, which is derived from biomass, is expected to become one of the key energy resources for global sustainable development. Biomass offers higher energy efficiency through form of Biogas than by direct burning.
Hydro energy - The potential energy of falling water, captured and converted to mechanical energy by waterwheels, powered the start of the industrial revolution. Wherever sufficient head, or change in elevation, could be found, rivers and streams were dammed and mills were built. Water under pressure flows through a turbine causing it to spin. The Turbine is connected to a generator, which produces electricity.
In order to produce enough electricity, a hydroelectric system requires a location with the following features:
In India the potential of small hydro power is estimated about 10,000 MW. A total of 183.45 MW small Hydro projects have been installed in India by the end of March 1999. Small Hydro Power projects of 3 MW capacities have been also installed individually and 148 MW project is under construction.
Solar irradiation, or insolation is the "rate of delivery of direct solar radiation per unit of horizontal surface", measured in W/m2
The earth revolves around the sun with its axis tilted at an angle of 23.5 degrees. It is this tilt that gives rise to the seasons. The strength of sun is dependent upon the angle at which it strikes the earth's surface, and so, as this angle changes during the year, so the solar insolation changes. Thus, in northern countries, in the depths of winter, where the sun is low in the sky to the south, the radiation strikes the earth's surface obliquely and solar energy is low.
The two phenomena described above provide an explanation for the variations of solar irradiation with season and latitude.
Fig 1.2 The angle of the earth to the sun changes throughout the year
The total solar irradiation received in a day can vary from 0.5 kWh /m2 / day in the UK winter to 5 kWh /m2 in the UK summer and can be as high as 7 kWh /m2/ day in desert regions of the world, such as regions of Nigeria and the Sahara in Algeria. Many tropical regions do not have large seasonal variations and receive an average 6 kWh/m2/day throughout the year.
The diagram below shows the approximate percentages of direct and diffuse solar insolation that reaches the surface of the earth. As the direct insolation forms a larger proportion of the total received, it follows that varying factors such as the weather, i.e. cloud cover, and the time of day will greatly affect the amount of solar insolation reaching the surface of the earth. It is interesting to note that whilst both direct and diffuse radiation is useful, diffuse radiation cannot be concentrated.
Fig 1.3Dispersion of solar irradiance through the atmosphere
Solar energy reaches the earth's surface as short wave radiation, absorbed by the earth and objects on the earth that heat up and re-radiated as long-wave radiation. Obtaining useful power from solar energy is based on the principle of capturing the short wave radiation and preventing it from radiating away into the atmosphere. For storage of this trapped heat, a liquid or solid with a high thermal mass is used. In a water heating system this will be the fluid that runs through the collector, whereas in a building the walls will act as the thermal mass. Pools or lakes are sometimes used for seasonal storage of heat.
Glass will allow short wave radiation to pass through it but prevents long wave radiation heat escaping.
If this energy is being used to heat water with a collector panel, then the tilt and orientation of the panel is critical to the level of energy captured and hence the temperature of the water. The collector surface should be orientated towards the sun as much as is possible. Most solar water-heating collectors are fixed permanently to roofs of buildings and cannot be adjusted. More sophisticated systems for power generation use tracking devices to follow the sun through the sky during the day.
1.6 SOLAR RADIATION MEASURING INSTRUMENTS (RADIOMETERS)
A radiometer absorbs solar radiation at its sensor, transforms it into heat and measures the resulting amount of heat to ascertain the level of solar radiation. Methods of measuring heat include taking out heat flux as a temperature change (using a water flow pyrheliometer, a silver-disk pyrheliometer or a bimetallic pyranograph) or as a thermoelectromotive force (using a thermoelectric pyrheliometer or a thermoelectric pyranometer). In current operation, types using a thermopile are generally used.
The radiometers used for ordinary observation are pyrheliometers and pyranometers that measure direct solar radiation and global solar radiation, respectively, and these instruments are described in this section.
A pyrheliometer is used to measure direct solar radiation from the sun and its marginal periphery. To measure direct solar radiation correctly, its receiving surface must be arranged to be normal to the solar direction. For this reason, the instrument is usually mounted on a sun-tracking device called an equatorial mount.
The structure of an Angstrom electrical compensation pyrheliometer is shown in Figure 1.6(a) This is a reliable instrument used to observe direct solar radiation, and has long been accepted as a working standard. However, its manual operation requires experience.
Fig 1.6Angstrom electrical compensation pyrheliometer
A: Aperture B: Battery C: Sensor surface D: Cylinder
P: Switch R: Variable resistor S: Shutter
T: Thermocouple G: Galvanometer m A: Ammeter
This pyrheliometer has a rectangular aperture, two manganin -strip sensors (20.0 mm Ã-2.0 mm Ã-0.02 mm) and several diaphragms to let only direct sunlight reach the sensor. The diaphragms are the same as those in the silver-disk pyrheliometer in Figure 1.7 and in the thermoelectric pyrheliometer in Figure 1.8. The sensor surface is painted optical black and has uniform absorption characteristics for short-wave radiation. A copper-constantan thermocouple is attached to the rear of each sensor strip, and the thermocouple is connected to a galvanometer. The sensor strips also work as electric resistors and generate heat when a current flows across them (see the principle drawing in Figure 1.6 (b)).When solar irradiance is measured with this type of pyrheliometer, the small shutter on the front face of the cylinder shields one sensor strip from sunlight, allowing it to reach only the other sensor. A temperature difference is therefore produced between the two sensor strips because one absorbs solar radiation and the other does not, and a thermoelectromotive force proportional to this difference induces current flow through the galvanometer. Then, a current is supplied to the cooler sensor strip (the one shaded from solar radiation) until the pointer in the galvanometer indicates zero, at which point the temperature raised by solar radiation is compensated by Joule heat. A value for direct solar irradiance is obtained by converting the compensated current at this time. If S is the intensity of direct solar irradiance and i is the current, then
S = Ki2,
Where K is a constant intrinsic to the instrument and is determined from the size and electric resistance of the sensor strips and the absorption coefficient of their surfaces. The value of K is usually determined through comparison with an upper-class standard pyrheliometer.
The structure of a silver-disk pyrheliometer is shown in Figure 1.7. This instrument was developed as a portable version of a water flow pyrheliometer, which was the former primary standard.
Fig 1.7Silver-disk pyrheliometer
The sensing element is a silver disk measuring 28 mm in diameter with a thickness of 7 mm that is painted black on its radiation-receiving side. It has a hole from the periphery toward the center to allow insertion of the bulb of a high-precision mercury-in-glass thermometer. To maintain good thermal contact between the disk and the bulb, the hole is filled with a small amount of mercury. It is enclosed outside by a heat-insulating wooden container. The stem of the thermometer is bent in a right angle outside the wooden container and supported in a metallic protective tube. A cylinder with diaphragms inside is fitted in the wooden container to let direct solar radiation fall onto the silver disk. There is a metallic-plates hutter at the top end of the cylinder to block or allow the passage of solar radiation to the disk.
During the measurement phase, the disk is heated by solar radiation and its temperature rises. The intensity of this radiation is ascertained by measuring the temperature change of the disk between the measurement phase and the shading phase with the mercury-in-glass thermometer.
The structure of a thermoelectric pyrheliometer is shown in Figure 1.8. This instrument uses thermopile at its sensor, and continuously delivers a thermoelectromotive force in proportion to the direct solar irradiance. While Angstrom electrical compensation pyrheliometers and silver-disk pyrheliometer shave a structure that allows the outer air to come into direct contact with the sensor portion, this type has transparent optical glass in the aperture to make it suitable for use in all weather conditions. It is mounted on a sun-tracking device to enable outdoor installation for automatic operation by JMA. There are several types of thermoelectric pyrheliometer, but their structures are similar. Figure 1.8 shows the structure of the one used by JMA. Copper-plated constantan wire is used as the thermopile in the sensor portion, which is attached to the bottom of the cylinder at right angles to the cylinder axis. The cylinder is fitted with diaphragms to direct sunlight to the sensor portion. It is made of a metallic block with high heat capacity and good thermal conductivity, and is enclosed in a polished intermediate cylinder and a silver-plated outer brass cylinder with high reflectivity to prevent rapid ambient temperature changes or outer wind from disturbing the heat flux in the radiation-sensing element. The cylinder is kept dry using a desiccant to prevent condensation on the inside of the aperture window.
Fig 1.8Thermoelectric pyrheliometer
In this pyrheliometer, a temperature difference is produced between the sensor surface (called the hot junction) and the reference temperature point, i.e., the metallic block of the inner cylinder (called the cold junction). As the temperature difference is proportional to the intensity of the radiation absorbed, the level of solar radiation can be derived by measuring the thermoelectromotive force from the thermopile. Since this type of pyrheliometer is a relative instrument, calibration should be performed to determine the instrumental factor through comparison with a standard instrument. As the thermo electromotive force output depends on the unit's temperature, the temperature inside the cylinder should be monitored to enable correction.
A pyranometer is used to measure global solar radiation falling on a horizontal surface. Its sensor has a horizontal radiation-sensing surface that absorbs solar radiation energy from the whole sky (i.e. a solid angle of 2Ï€ sr) and transforms this energy into heat. Global solar radiation can be ascertained by measuring this heat energy. Most pyranometers in general use are now the thermopile type, although bimetallic pyranometers are occasionally found.
Thermoelectric pyranometers are shown in Figure 1.9. The instrument's radiation-sensing element has basically the same structure as that of a thermoelectric pyrheliometer. Another similarity is that the temperature difference derived between the radiation-sensing element (the hot junction) and the reflecting surface (the cold junction) that serves as a temperature reference point is expressed by a thermopile as anthermoelectromotive force. In the case of a pyranometer, methods of ascertaining the temperature difference are as follows:
Several pairs of thermocouples are connected in series to make a thermopile that detects the temperature difference between the black and white radiation-sensing surfaces (Figures 1.9 (a)and (c)).
The temperature difference between two black radiation-sensing surfaces with differing areas is detected by a thermopile.
The temperature difference between a radiation-sensing surface painted solid black and a metallic block with high heat capacity is detected by a thermopile (Figure 1.9 (b)).
Fig 1.9Thermoelectric pyranometer
A bimetallic pyranograph is shown in Figure 1.10. The radiation-sensing element (in the upper right of the figure) consists of two pairs of bimetals, one painted black and the other painted white, placed in opposite directions (face up and face down) and attached to a common metal plate at one end. At the other end, the white bimetallic strips are fixed to the frame of the pyranograph, and the black ones are connected to the recorder section via a transmission shaft. The deflection of the free edge of the black strips is transmitted to the recording pen through a magnifying system. When the air temperature changes, the black and white strips attached to the common plate at one end both bend by the same amount but in opposite directions. As a result, only the temperature difference attributed to solar radiation is transmitted to the recording pen.
Thermoelectric pyranometers and bimetallic pyranographs are both hermetically sealed in a glass dome to protect the sensor portion from wind and rain and prevent the sensor surface temperature from being disturbed by wind. A desiccant is placed in the dome to prevent condensation from forming on the inner surface. The glass allows the passage of solar radiation in wavelengths from about 0.3 to 3.0 Âµm - arrange that covers most of the sun's radiation energy. Some models are equipped with a fan to prevent dust or frost, which greatly affect the amount of light received, from collecting on the dome's outer surface. It is necessary to check and clean the glass surface at regular intervals to ensure that the dome wall constantly allows the passage of solar radiation.
Fig 1.10 bimetallic pyranometer
1.7 SOURCES OF ERROR
Radiometer measurement errors are attributed to sensitivity, response characteristics and other factors common to ordinary meteorological instruments. In addition to these influences, the following sources of measurement errors are also peculiar to radiometers:
Wavelength Characteristics (for pyrheliometers and pyranometers) : The absorption coefficient of the radiation sensor surface and the transmission coefficient of the glass cover or glass dome of a radiometer should be constant for all wavelengths of solar radiation. In reality, however, these coefficients vary with wavelength. Since this wavelength characteristic differs slightly from radiometer to radiometer, observation errors occur when the energy distribution of solar radiation against wavelength varies with the sun's elevation or atmospheric conditions.
Temperature Characteristics (for pyrheliometers and pyranometers) : As the
thermoelectromotive force of a thermopile is nonlinear and the heat conductivity inside a radiometer depends on temperature, the sensitivity of these instruments varies and an error occurs when the ambient temperature and the temperature of the radiometer change.
Characteristics against Elevation and Azimuth (for pyranometers): The output of the ideal pyranometer decreases with lower sun elevation angles in proportion to cosz (z: zenith angle). In reality, however, output varies with the sun's elevation or azimuth due to the uneven absorption coefficient and with the shape of the radiation sensor surface. The characteristic may also deviate and errors may occur because of the uneven thickness, curvature or material of the glass cover. Usually, sensitivity rapidly decreases at an elevation angle of around 20 degrees or lower.
Field of View (for pyrheliometers) : The field of view of a pyrheliometer is somewhat larger than the viewing angle of the sun. If the field of view differs, the extent of influence from diffuse sky radiation near the sun also differs. Pyrheliometers with different fields of view may make different observations depending on the turbidity of the atmosphere. (WMO recommends a total opening angle of five degrees.)
1.8 SOLAR THERMAL COLLECTOR
Solar energy collectors are special kind of heat exchangers that transform solar radiation energy to internal energy of the transport medium. The major component of any solar system is the solar collector. This is a device which absorbs the incoming solar radiation, converts it into heat, and transfers this heat to a fluid (usually air, water, or oil) flowing through the collector. The solar energy thus collected is carried from the circulating fluid either directly to the hot water or space conditioning equipment or to a thermal energy storage tank from which can be drawn for use at night and/or cloudy days. There are basically two types of solar collectors: non-concentrating or stationary and concentrating. A non-concentrating collector has the same area for intercepting and for absorbing solar radiation, whereas a sun-tracking concentrating solar collector usually has concave reflecting surfaces to intercept and focus the sun's beam radiation to a smaller receiving area, thereby increasing the radiation flux. A large number of solar collectors are available in the market. A comprehensive list is shown in Table 1. In this section a review of the various types of collectors currently available will be presented. This includes FPC, ETC, and concentrating collectors.
1.8.1 Stationary collectors
Solar energy collectors are basically distinguished by their motion, i.e. stationary, single axis tracking and two axes tracking, and the operating temperature. Initially, the stationary solar collectors are examined. These collectors are permanently fixed in position and do not track the sun. Three types of collectors fall in this category:
1. Flat plate collectors (FPC);
2. Stationary compound parabolic collectors (CPC);
3. Evacuated tube collectors (ETC).
18.104.22.168 Flat plate collectors (FPC) - A typical flat-plate solar collector is shown in Fig. 1.11.
When solar radiation passes through a transparent cover and impinges on the blackened absorber surface of high absorptivity, a large portion of this energy is absorbed by the plate and then transferred to the transport medium in the fluid tubes to be carried away for storage or use. The underside of the absorber plate and the side of casing are well insulated to reduce conduction losses. The liquid tubes can be welded to the absorbing plate, or they can be an integral part of the plate. The liquid tubes are connected at both ends by large diameter header tubes. The transparent cover is used to reduce convection losses from the absorber plate through the restraint of the stagnant air layer between the absorber plate and the glass. It also reduces radiation losses from the collector as the glass is transparent to the short wave radiation received by the sun but it is nearly opaque to long-wave thermal radiation emitted by the absorber plate (greenhouse effect). FPC is usually permanently fixed in position and requires no tracking of the sun. The collectors should be oriented directly towards the equator, facing south in the northern hemisphere and north in the southern. The optimum tilt angle of the collector is equal to the latitude of the location with angle variations of 10-158 more or less depending on the application.
Fig 1.11 Pictorial view of a flat-plate collector
A FPC generally consists of the following components as shown in Fig.1.12:
Fig 1.12 Exploded view of a flat-plate collector
Glazing - One or more sheets of glass or other diathermanous (radiation-transmitting) material.
Tubes, fins, or passages - To conduct or direct the heat transfer fluid from the inlet to the outlet.
Absorber plates - Flat, corrugated, or grooved plates, to which the tubes, fins, or passages are attached. The plate may be integral with the tubes.
Headers or manifolds - To admit and discharge the fluid.
Insulation - To minimize the heat loss from the back and sides of the collector.
Container or casing - To surround the aforementioned components and keep them free from dust, moisture, etc.
FPC has been built in a wide variety of designs and from many different materials. They have been used to heat fluids such as water, water plus antifreeze additive, or air. Their major purpose is to collect as much solar energy as possible at the lower possible total cost. The collector should also have a long effective life, despite the adverse effects of the sun's ultraviolet radiation, corrosion and clogging because of acidity, alkalinity or hardness of the heat transfer fluid, freezing of water, or deposition of dust or moisture on the glazing, and breakage of the glazing because of thermal expansion, hail, vandalism or other causes. These causes can be minimized by the use of tempered glass.
More details are given about the glazing and absorber plate materials.
Glazing materials - Glass has been widely used to glaze solar collectors because it can transmit as much as 90% of the incoming shortwave solar irradiation while transmitting virtually none of the long wave radiation emitted outward by the absorber plate. Glass with low iron content has a relatively high transmittance for solar radiation (approximately 0.85-0.90 at normal incidence), but its transmittance is essentially zero for the long wave thermal radiation (5.0-50 mm) emitted by sun-heated surfaces.
Plastic films and sheets also possess high shortwave transmittance, but because most usable varieties also have transmission bands in the middle of the thermal radiation spectrum, they may have long wave transmittances as high as 0.40. Plastics are also generally limited in the temperatures they can sustain without deteriorating or undergoing dimensional changes. Only a few types of plastics can withstand the sun's ultraviolet radiation for long periods. However, they are not broken by hail of stones, and, in the form of thin films, they are completely flexible and have low mass. The commercially available grades of window and green-house glass have normal incidence transmittances of about 0.87 and 0.85, respectively. For direct radiation, the transmittance varies considerably with the angle of incidence.
Antireflective coatings and surface texture can also improve transmission significantly. The effect of dirt and dust on collector glazing may be quite small, and the cleansing effect of an occasional rainfall is usually adequate to maintain the transmittance within 2-4% of its maximum value.
The glazing should admit as much solar irradiation as possible and reduce the upward loss of heat as much as possible. Although glass is virtually opaque to the long wave radiation emitted by collector plates, absorption of that radiation causes an increase in the glass temperature and a loss of heat to the surrounding atmosphere by radiation and convection.
Various prototypes of transparently insulated FPC and CPC have been built and tested in the last decade. Low cost and high temperature resistant transparent insulating (TI) materials have been developed so that the commercialization of these collectors becomes feasible. A prototype FPC covered by TI was developed by Benz et al. It was experimentally proved that the efficiency of the collector was comparable with that of ETC. However, no commercial collectors of this type are available in the market.
Collector absorbing plates - The collector plate absorbs as much of the irradiation as possible through the glazing, while losing as little heat as possible upward to the atmosphere and downward through the back of the casing. The collector plates transfer the retained heat to the transport fluid. The absorptance of the collector surface for shortwave solar radiation depends on the nature and colour of the coating and on the incident angle. Usually black colour is used, however various colour coatings have mainly for aesthetic reasons.
By suitable electrolytic or chemical treatments, surfaces can be produced with high values of solar radiation absorptance (a) and low values of long wave emittance (Îµ). Essentially, typical selective surfaces consist of a thin upper layer, which is highly absorbent to shortwave solar radiation but relatively transparent to long wave thermal radiation, deposited on a surface that has a high reflectance and a low emittance for long wave radiation. Selective surfaces are particularly important when the collector surface temperature is much higher than the ambient air temperature.
An energy efficient solar collector should absorb incident solar radiation, convert it to thermal energy and deliver the thermal energy to a heat transfer medium with minimum losses at each step. It is possible to use several different design principles and physical mechanisms in order to create a selective solar absorbing surface. Solar absorbers are based on two layers with different optical properties, which are referred as tandem absorbers. A semiconducting or dielectric coating with high solar absorptance and high infrared transmittance on top of a non-selective highly reflecting material such as metal constitutes one type of tandem absorber. Another alternative is to coat a nonselective highly absorbing material with a heat mirror having a high solar transmittance and high infrared reflectance.
Today, commercial solar absorbers are made by electroplating, anodization, evaporation, sputtering and by applying solar selective paints. Much of the progress during recent years has been based on the implementation of vacuum techniques for the production of fin type absorbers used in low temperature applications. The chemical and electrochemical processes used for their commercialization were readily taken over from the metal finishing industry. The requirements of solar absorbers used in high temperature applications, however, namely extremely low thermal emittance and high temperature stability, were difficult to fulfill with conventional wet processes. Therefore, large scale sputter deposition was developed in the late 70s. The vacuum techniques are nowadays mature, characterized by low cost and have the advantage of being less environmentally polluting than the wet processes.
For fluid-heating collectors, passages must be integral with or firmly bonded to the absorber plate. A major problem is obtaining a good thermal bond between tubes and absorber plates without incurring excessive costs for labour or materials. Material most frequently used for collector plates are copper, aluminium, and stainless steel. UV-resistant plastic extrusions are used for low temperature applications. If the entire collector area is in contact with the heat transfer fluid, the thermal conductance of the material is not important. Fig. 1.13 shows a number of absorber plate designs for solar water and air heaters that have been used with varying degrees of success. Fig. 1.13A shows a bonded sheet design, in which the fluid passages are integral with the plate to ensure good thermal conduct between the metal and the fluid. Fig. 1.13B and C shows fluid heaters with tubes soldered, brazed, or otherwise fastened to upper or lower surfaces of sheets or strips of copper. Copper tubes are used most often because of their superior resistance to corrosion.
FPC are by far the most used type of collector. FPC are usually employed for low temperature applications up to 100 8C, although some new types of collectors employing vacuum insulation and/or TI can achieve slightly higher values. Due to the introduction of highly selective coatings actual standard FPC can reach stagnation temperatures of more than 2000C. With these collectors good efficiencies can be obtained up to temperatures of about 1000C.
The characteristics of a typical water FPC are shown in Table 2.
Lately some modern manufacturing techniques have been introduced by the industry like the use of ultrasonic welding machines, which improve both the speed and the quality of welds. This is used for the welding of fins on risers in order to improve heat conduction. The greatest advantage of this method is that the welding is performed at room temperature therefore deformation of the welded parts is avoided. These collectors with selective coating are called advance FPC and the characteristics of a typical type are also shown in Table 2.
Fig 1.13 various types of flat-plate solar collectors
22.214.171.124 Compound parabolic collectors-CPC are non-imaging concentrators. These have the capability of reflecting to the absorber all of the incident radiation within wide limits. The necessity of moving the concentrator to accommodate the changing solar orientation can be reduced by using a trough with two sections of a parabola facing each other, as shown in Fig. 1.14.Compound parabolic concentrators can accept incoming radiation over a relatively wide range of angles. By using multiple internal reflections, any radiation that is entering the aperture, within the collector acceptance angle, finds its way to the absorber surface located at the bottom of the collector. The absorber can take a variety of configurations. It can be cylindrical as shown in Fig. 1.14 or flat. In the CPC shown in Fig. 1.14 the lower portion of the reflector (AB and AC) is circular, while the upper portions (BD and CE) are parabolic. As the upper part of a CPC contribute little to the radiation reaching the absorber, they are usually truncated thus forming a shorter version of the CPC, which is also cheaper. CPCs are usually covered with glass to avoid dust and other materials from entering the collector and thus reducing the reflectivity of its walls.
These collectors are more useful as linear or trough-type concentrators. The acceptance angle is defined as the angles through which a source of light can be moved and still converge at the absorber. The orientation of a CPC collector is related to its acceptance angle (in Fig. 1.14). Also depending on the collector acceptance angle, the collector can be stationary or tracking. A CPC concentrator can be orientated with its long axis along either the north-south or the east-west direction and its aperture is tilted directly towards the equator at an angle equal to the local latitude. When orientated along the north-south direction the collector must track the sun by turning its axis so as to face the sun continuously. As the acceptance angle of the concentrator along its long axis is wide, seasonal tilt adjustment is not necessary. It can also be stationary but radiation will only be received the hours when the sun is within the collector acceptance angle. When the concentrator is orientated with its long axis along the east-west direction, with a little seasonal adjustment in tilt angle the collector is able to catch the sun's rays effectively through its wide acceptance angle along its long axis. The minimum acceptance angle in this case should be equal to the maximum incidence angle projected in a north-south vertical plane during the times when output is needed from the collector. For stationary CPC collectors mounted in this mode the minimum acceptance angle is equal to 478. This angle covers the declination of the sun from summer to winter solstices (2 * 23.58). In practice bigger angles are used to enable the collector to collect diffuse radiation at the expense of a lower concentration ratio. Smaller (less than 3) concentration ratio CPCs are of greatest practical interest.
Two basic types of CPC collectors have been designed, the symmetric and the asymmetric. These usually employ two main types of absorbers; fin type with pipe and tubular absorbers.
Fig 1.14 Schematic diagram of a compound parabolic collector
The characteristics of a typical CPC are shown in Table 3
126.96.36.199 Evacuated tube collectors - Conventional simple flat-plate solar collectors were developed for use in sunny and warm climates. Their benefits however are greatly reduced when conditions become unfavorable during cold, cloudy and windy days. Furthermore, weathering influences such as condensation and moisture will cause early deterioration of internal materials resulting in reduced performance and system failure. Evacuated heat pipe solar collectors (tubes) operate differently than the other collectors available on the market.
These solar collectors consist of a heat pipe inside a vacuum-sealed tube, as shown in Fig 1.15. ETC has demonstrated that the combination of a selective surface and an effective convection suppressor can result in good performance at high temperatures. The vacuum envelope reduces convection and conduction losses, so the collectors can operate at higher temperatures than FPC. Like FPC, they collect both direct and diffuse radiation. However, their efficiency is higher at low incidence angles. This effect tends to give ETC an advantage over FPC in day-long performance. ETC use liquid-vapour phase change materials to transfer heat at high efficiency. These collectors feature a heat pipe (a highly efficient thermal conductor) placed inside a vacuum-sealed tube. The pipe, which is a sealed copper pipe, is then attached to a black copper fin that fills the tube (absorber plate). Protruding from the top of each tube is a metal tip attached to the sealed pipe (condenser). The heat pipe contains a small amount of fluid (e.g. methanol) that undergoes an evaporating-condensing cycle. In this cycle, solar heat evaporates the liquid, and the vapour travels to the heat sink region where it condenses and releases its latent heat. The condensed fluid return back to the solar collector and the process is repeated. When these tubes are mounted, the metal tips up, into a heat exchanger (manifold) as shown in Fig 1.15. Water, or glycol, flows through the manifold and picks up the heat from the tubes.
The heated liquid circulates through another heat exchanger and gives off its heat to a process or to water that is stored in a solar storage tank. Because no evaporation or condensation above the
phase-change temperature is possible, the heat pipe offers inherent protection from freezing and overheating. This self limiting temperature control is a unique feature of the evacuated heat pipe collector. ETC basically consist of a heat pipe inside a vacuum sealed tube. A large number of variations of the absorber shape of ETC are on the market. Evacuated tubes with CPC-reflectors are also commercialized by several manufacturers. One manufacturer recently presented an all-glass ETC, which may be an important step to cost reduction and increase of lifetime. Another variation of this type of collector is what is called Dewar tubes. In this two concentric glass tubes are used and the space in between the tubes is evacuated (vacuum jacket). The advantage of this design is that it is made entirely of glass and it is not necessary to penetrate the glass envelope in order to extract heat from the tube thus leakage losses are not present and it is also less expensive than the single envelope system.
Fig 1.15 Schematic diagram of an evacuated tube collector
1.8.2 Sun tracking concentrating collectors
Energy delivery temperatures can be increased by decreasing the area from which the heat losses occur. Temperatures far above those attainable by FPC can be reached if a large amount of solar radiation is concentrated on a relatively small collection area. This is done by interposing an optical device between the source of radiation and the energy absorbing surface. Concentrating collectors exhibit certain advantages as compared with the conventional flat-plate type. The main ones are:
1. The working fluid can achieve higher temperatures in a concentrator system when compared to a flat-plate system of the same solar energy collecting surface. This means that a higher thermodynamic efficiency can be achieved.
2. It is possible with a concentrator system, to achieve a thermodynamic match between temperature level and task. The task may be to operate thermionic, thermodynamic, or other higher temperature devices.
3. The thermal efficiency is greater because of the small heat loss area relative to the receiver area.
4. Reflecting surfaces require less material and are structurally simpler than FPC. For a concentrating collector the cost per unit area of the solar collecting surface is therefore less than that of a FPC.
5. Owing to the relatively small area of receiver per unit of collected solar energy, selective surface treatment and vacuum insulation to reduce heat losses and improve the collector efficiency are economically viable.
Their disadvantages are:
1. Concentrator systems collect little diffuse radiation depending on the concentration ratio.
2. Some form of tracking system is required so as to enable the collector to follow the sun.
3. Solar reflecting surfaces may loose their reflectance with time and may require periodic cleaning and refurbishing.
Many designs have been considered for concentrating collectors. Concentrators can be reflectors or refractors, can be cylindrical or parabolic and can be continuous or segmented. Receivers can be convex, flat, cylindrical or concave and can be covered with glazing or uncovered. Concentration ratios, i.e. the ratio of aperture to absorber areas, can vary over several orders of magnitude, from as low as unity to high values of the order of 10 000. Increased ratios mean increased temperatures at which energy can be delivered but consequently these collectors have increased requirements for precision in optical quality and positioning of the optical system.
Because of the apparent movement of the sun across the sky, conventional concentrating collectors must follow the sun's daily motion. There are two methods by which the sun's motion can be readily tracked. The first is the altazimuth method which requires the tracking device to turn in both altitude and azimuth, i.e. when performed properly, this method enables the concentrator to follow the sun exactly. Paraboloidal solar collectors generally use this system. The second one is the one-axis tracking in which the collector tracks the sun in only one direction either from east to west or from north to south. Parabolic trough collectors (PTC) generally use this system. These systems require continuous and accurate adjustment to compensate for the changes in the sun's orientation.
The collectors falling in this category are:
1. Parabolic trough collector;
2. Linear Fresnel reflector (LFR);
3. Parabolic dish;
4. Central receiver.
1.8.2 1 Parabolic trough collectors - In order to deliver high temperatures with good efficiency a high performance solar collector is required. Systems with light structures and low cost technology for process heat applications up to 4000C could be obtained with parabolic through collectors (PTCs). PTCs can effectively produce heat at temperatures between 50 and 4000C.
PTCs are made by bending a sheet of reflective material into a parabolic shape. A metal black tube, covered with a glass tube to reduce heat losses, is placed along the focal line of the receiver (Fig 1.16). When the parabola is pointed towards the sun, parallel rays incident on the reflector are reflected onto the receiver tube. It is sufficient to use a single axis tracking of the sun and thus long collector modules are produced. The collector can be orientated in an east-west direction, tracking the sun from north to south, or orientated in a north-south direction and tracking the sun from east to west. The advantages of the former tracking mode is that very little collector adjustment is required during the day and the full aperture always faces the sun at noon time but
the collector performance during the early and late hours of the day is greatly reduced due to large incidence angles (cosine loss). North-south orientated troughs have their highest cosine loss at noon and the lowest in the mornings and evenings when the sun is due east or due west.
Over the period of one year, a horizontal north-south trough field usually collects slightly more energy than a horizontal east-west one. However, the north-south field collects a lot of energy in summer and much less in winter. The east-west field collects more energy in the winter than a north-south field and less in summer, providing a more constant annual output. Therefore, the choice of orientation usually depends on the application and whether more energy is needed during summer or during winter.
The receiver of a parabolic trough is linear. Usually, a tube is placed along the focal line to form an external surface receiver (Fig 1.16). The size of the tube, and therefore the concentration ratio, is determined by the size of the reflected sun image and the manufacturing tolerances of the trough. The surface of the receiver is typically plated with selective coating that has a high absorptance for solar radiation, but a low emittance for thermal radiation loss.
A glass cover tube is usually placed around the receiver tube to reduce the convective heat loss from the receiver, thereby further reducing the heat loss coefficient. A disadvantage of the glass cover tube is that the reflected light from the concentrator must pass through the glass to reach the absorber, adding a transmittance loss of about 0.9, when the glass is clean. The glass envelope usually has an antireflective coating to improve transmissivity. One way to further reduce convective heat loss from the receiver tube and thereby increase the performance of the collector, particularly for high temperature applications, is to evacuate the space between the glass cover tube and the receiver.
Fig 1.16 Schematic diagram of an evacuated tube collector
188.8.131.52 Linear Fresnel reflector - LFR technology relies on an array of linear mirror strips which concentrate light on to a fixed receiver mounted on a linear tower. The LFR field can be imagined as a broken-up parabolic trough reflector (Fig 1.17), but unlike parabolic troughs, it does not have to be of parabolic shape, large absorbers can be constructed and the absorber does not have to move. A representation of an element of an LFR collector field is shown in Fig 1.18. The greatest advantage of this type of system is that it uses flat or elastically curved reflectors which are cheaper compared to parabolic glass reflectors. Additionally, these are mounted close to the ground, thus minimizing structural requirements. The first to apply this principle was the great solar pioneer Giorgio Francia who developed both linear and two-axis tracking Fresnel reflector systems at Genoa, Italy in the 60s. These systems showed that elevated temperatures could be reached using such systems but he moved on to two-axis tracking, possibly because advanced selective coatings and secondary optics were not available.
Fig 1.17 Fresnel type parabolic trough collector.
Fig 1.18 Schematic diagram of a downward facing receiver illuminated from an LFR field.
One difficulty with the LFR technology is that avoidance of shading and blocking between adjacent reflectors leads to increased spacing between reflectors. Blocking can be reduced by increasing the height of the absorber towers, but this increases cost.
The interleaving of mirrors between two receiving towers is shown in Fig 1.19. The arrangement minimizes beam blocking by adjacent reflectors and allows high reflector densities and low tower heights to be used. Close spacing of reflectors reduces land usage but this is in many cases not a serious issue as in deserts. The avoidance of large reflector spacing and tower heights is an important cost issue when the cost of ground preparation, array substructure cost, tower structure cost, steam line thermal losses and steam line cost are considered. If the technology is to be located in an area with limited land availability such as in urban areas or next to existing power plants, high array ground coverage can lead to maximum system output for a given ground area.
Fig 1.19 Schematic diagram showing interleaving of mirrors in a CLFR
with reduced shading between mirrors
184.108.40.206 Parabolic dish reflector (PDR) - A parabolic dish reflector, shown schematically in Fig 1.20, is a point-focus collector that tracks the sun in two axes, concentrating solar energy onto a receiver located at the focal point of the dish. The dish structure must track fully the sun to reflect the beam into the thermal receiver. For this purpose tracking mechanisms similar to the ones described in previous section are employed in double so as the collector is tracked in two axes.
Fig 1.20 Schematic Diagram of a parabolic dish collector
The receiver absorbs the radiant solar energy, converting it into thermal energy in a circulating fluid. The thermal energy can then either be converted into electricity using an engine-generator coupled directly to the receiver, or it can be transported through pipes to a central power-conversion system. Parabolic-dish systems can achieve temperatures in excess of 15000C. Because the receivers are distributed throughout a collector field, like parabolic troughs, parabolic dishes are often called distributed-receiver systems.
Parabolic dishes have several important advantages:
1. Because they are always pointing the sun, they are the most efficient of all collector systems;
2. They typically have concentration ratio in the range of 600-2000, and thus are highly efficient at thermal-energy absorption and power conversion systems;
3. They have modular collector and receiver units that can either function independently or as part of a larger system of dishes.
The main use of this type of concentrator is for parabolic dish engines. A parabolic dish-engine system is an electric generator that uses sunlight instead of crude oil or coal to produce electricity. The major parts of a system are the solar dish concentrator and the power conversion unit. Parabolic-dish systems that generate electricity from a central power converter collect the absorbed sunlight from individual receivers and deliver it via a heat-transfer fluid to the power-conversion systems. The need to circulate heat transfer fluid throughout the collector field raises design issues such as piping layout, pumping requirements, and thermal losses.
Systems that employ small generators at the focal point of each dish provide energy in the form of electricity rather than as heated fluid. The power conversion unit includes the thermal receiver and the heat engine. The thermal receiver absorbs the concentrated beam of solar energy, converts it to heat, and transfers the heat to the heat engine. A thermal receiver can be a bank of tubes with a cooling fluid circulating through it. The heat transfer medium usually employed as the working fluid for an engine is hydrogen or helium. Alternate thermal receivers are heat pipes wherein the boiling and condensing of an intermediate fluid is used to transfer the heat to the engine. The heat engine system takes the heat from the thermal receiver and uses it to produce electricity. The engine-generators have several components; a receiver to absorb the concentrated sunlight to heat the working fluid of the engine, which then converts the thermal energy into mechanical work; an alternator attached to the engine to convert the work into electricity, a waste-heat exhaust system to vent excess heat to the atmosphere, and a control system to match the engine's operation to the available solar energy. This distributed parabolic dish system lacks thermal storage capabilities, but can be hybridized to run on fossil fuel during periods without sunshine. The Stirling engine is the most common type of heat engine used in dish-engine systems. Other possible power conversion unit technologies that are evaluated for future applications are microturbines and concentrating photovoltaics.
220.127.116.11 Heliostat field collector
For extremely high inputs of radiant energy, a multiplicity of flat mirrors, or heliostats, using altazimuth mounts, can be used to reflect their incident direct solar radiation onto a common target as shown in Fig 1.21. This is called the heliostat field or central receiver collector. By using slightly concave mirror segments on the heliostats, large amounts of thermal energy can be directed into the cavity of a steam generator to produce steam at high temperature and pressure.
Fig 1.21 Schematic diagram of a Heliostat field collector
The concentrated heat energy absorbed by the receiver is transferred to a circulating fluid that can be stored and later used to produce power.
Central receivers have several advantages:
1. They collect solar energy optically and transfer it to a single receiver, thus minimizing thermal-energy transport requirements;
2. They typically achieve concentration ratios of 300-1500 and so are highly efficient both in collecting energy and in converting it to electricity;
3. They can conveniently store thermal energy;
4. They are quite large (generally more than 10 MW) and thus benefit from economies of scale.
Each heliostat at a central-receiver facility has from 50 to 150 m2 of reflective surface. The heliostats collect and concentrate sunlight onto the receiver, which absorbs the concentrated sunlight, transferring its energy to a heat transfer fluid. The heat-transport system, which consists primarily of pipes, pumps, and valves, directs the transfer fluid in a closed loop between the receiver, storage, and power-conversion systems. A thermal-storage system typically stores the collected energy as sensible heat for later delivery to the power-conversion system. The storage system also decouples the collection of solar energy from its conversion to electricity. The power-conversion system consists of a steam generator, turbine generator, and support equipment, which convert the thermal energy into electricity and supply it to the utility grid.
In this case incident sunrays are reflected by large tracking mirrored collectors, which concentrate the energy flux towards radiative/convective heat exchangers, where energy is transferred to a working thermal fluid. After energy collection by the solar system, the conversion of thermal energy to electricity has many similarities with the conventional fossil-fuelled thermal power plants.
The average solar flux impinging on the receiver has values between 200 and 1000 kW/m2. This high flux allows working at relatively high temperatures of more than 15000C and to integrate thermal energy in more efficient cycles. Central receiver systems can easily integrate in fossil-fuelled plants for hybrid operation in a wide variety of options and have the potential to operate more than half the hours of each year at nominal power using thermal energy storage.
Central receiver systems are considered to have a large potential for mid-term cost reduction of electricity compared to parabolic trough technology since they allow many intermediate steps between the integration in a conventional Rankine cycle up to the higher energy cycles using gas
turbines at temperatures above 10000C, and this subsequently leads to higher efficiencies and larger throughputs. Another alternative is to use Brayton cycle turbines, which require higher temperature than the ones employed in Rankine cycle. There are three general configurations for the collector and receiver systems. In the first, heliostats completely surround the receiver tower, and the receiver, which is cylindrical, has an exterior heat-transfer surface. In the second, the heliostats are located north of the receiver tower (in the northern hemisphere), and the receiver has an enclosed heat-transfer surface. In the third, the heliostats are located north of the receiver tower, and the receiver, which is a vertical plane, has a north-facing heat-transfer surface.
In the final analysis, however, it is the selection of the heat-transfer fluid, thermal-storage medium, and power conversion cycle that defines a central-receiver plant. The heat-transfer fluid may either be water/steam, liquid sodium, or molten nitrate salt (sodium nitrate/potassium nitrate), whereas the thermal-storage medium may be oil mixed with crushed rock, molten nitrate salt, or liquid sodium. All rely on steam-Rankine power-conversion systems, although a more advanced system has been proposed that would use air as the heat-transfer fluid, ceramic bricks for thermal storage, and either a steam-Rankine or open-cycle Brayton power conversion system.
1.9 SOLAR WATER HEATERS
The main part of a SWH is the solar collector array that absorbs solar radiation and converts it into heat. This heat is then absorbed by a heat transfer fluid (water, non-freezing liquid, or air) that passes through the collector. This heat can then be stored or used directly. Portions of the solar energy system are exposed to the weather conditions, so they must be protected from freezing and from overheating caused by high insolation levels during periods of low energy demand.
In solar water heating systems, potable water can either be heated directly in the collector (direct systems) or indirectly by a heat transfer fluid that is heated in the collector, passes through a heat exchanger to transfer its heat to the domestic or service water (indirect systems). The heat transfer fluid is transported either naturally (passive systems) or by forced circulation (active systems). Natural circulation occurs by natural convection (thermosyphoning), whereas for the