Solar Energy Collectors and Storage

Solar Energy and Thermal Applications

• Major challenges involve effective solar energy collection and storage.
• Solar collectors are designed for solar energy collection.
• Non-concentrating and concentrating collectors are the two primary categories.

Non-Concentrating Collectors

• These collectors do not focus solar energy
• Flat Plate Collectors (FPC) and Evacuated Tube Collectors (ETC) are major types
• Both FPC and ETC use a black surface to absorb solar radiation.
• Both operate in the temperature range of approximately 40°C to 100°C
• Special insulation and glass covers minimize heat loss and trap solar radiation.
• ETCs use a vacuum to avoid convection losses, unlike FPCs.

Concentrating Collectors

• Concentrating collectors use concentrators and receivers to focus solar radiation.
• Point concentration and line concentration are the two types.

Thermal Storage

• Crucial for storing solar energy for use during off-sunshine hours
• Thermal, electrical, mechanical, and chemical are the types of storage available
• Sensible and latent heat storage are the two types of thermal storage

Sensible Heat Storage

• Typically utilizes rock solid material such as pebbles
• Liquid materials can also be used
• Used for solar air heaters and solar water collectors
• Can be used for a wide range of temperatures

Latent Heat Storage

• Uses phase change materials (PCM)
• Important to consider the phase change temperature of the material
• An insulated tank where hot water from collectors releases heat and becomes cold water before returning to the collectors exemplifies this
• Another fluid moves heat to the load

Thermal Storage Example

• Solid material is filled in an insulated tank with screen meshes, and hot air from a solar air heater loses heat, then returns to the collector.

Other Storage Methods

• Batteries for electrical storage
• Mechanical storage utilizes compressed air
• Chemical storage uses endothermic and exothermic reactions.

Applications of Solar Energy

• Solar energy has a broad range of applications.
• Applications include: water and space heating, distillation, drying, cooking, space cooling, refrigeration, and power generation

Water Heating Applications

• Flat Plate Collector (FPC) is used with a water tank; cold water goes to FPC, gets heated, and returns to the tank.
• Hot water is taken out for use, and cold water is sent in to compensate
• Can operate in natural circulation mode through thermosyphon effect or in forced circulation using a pump
• Forced circulation systems have a control system to check the temperature of the water coming out of the FPC and the hot water in the tank

Space Heating Applications

• Active (using fans and blowers) and passive by natural circulation (e.g., Trombe wall)
• In an active system, hot water comes from the flat plate collector and goes to storage
• Then it is taken using a pump to the FPC, and sent to a heat exchanger where cold air is converted to hot air.

Distillation

• Solar still incorporates an insulated arrangement filled with saline water.
• Solar radiation heats the water, produce clean water from condensate, and deposit salt in the dome.

Drying

• Solar drying uses a collector arrangement where solar radiation comes in and heats the product on perforated trays, removing the moisture
• Air circulation is also provisioned

Cooking

• Box-type solar cookers with a glass cover absorb solar radiation, heating the food kept in a shallow container

Refrigeration

• Vapor absorption system is a famous application for solar energy
• System includes a generator attached to FPC to produce refrigerant vapors
• Different collectors can be used depending on the refrigerant and temperature needed.

Power Generation

• Solar energy utilized for power generation
• Electricity is generated using a turbine, which requires vapor produced by a vapor generator.
• Collector arrays can directly provide the heat, but using PTC (parabolic trough collector) may be wiser for higher temperature requirements.

Solar Radiation Parameters

• Solar angles, sunrise/sunset, day length, sun path diagrams, and solar radiation on horizontal and tilted surfaces will be covered
• Calculation of solar radiation parameters will be reviewed

Solar Angles

• Nine angles are important for analyzing solar radiation parameters: latitude, declination angle, hour angle, solar altitude angle, zenith angle, surface azimuth angle, solar azimuth angle, slope, and angle of incidence

Horizontal and Tilted Planes

• Horizontal plane is the base reference, the tilted plane is adjusted for maximum solar absorption
• Tilt angle (beta) describes the angle of the tilt
• Zenith is normal to the horizontal plane, while a similar normal is defined for the tilted surface
• Sun rays are considered as the line of sight

Latitude Angle

• Angle made by the radial line joining a location to the center of the earth
• Measured positive for the northern hemisphere, ranging from -90° to +90°
• 0° at the equator and 90° at the poles
• Longitude is also defined for the location, measured from the prime meridian and useful in calculating solar time

Declination Angle

• Angle made by the line joining the centers of the earth and sun with its projection on the equatorial plane
• Varies from +23.45° on June 21 (summer solstice) to -23.45° on December 21 (winter solstice).
• Zero on the equinox days (March 21 and September 22)
• Formula: δ = 23.45° * sin(360/365 * (284 + N)), where N is the nth day of the year

Hour Angle

• Angular measure of time equivalent to 15° per hour
• Varies from +180° to -180°, positive in the morning and negative in the afternoon
• Solar noon (12:00) is 0°, 6:00 in the morning is +90°
• Formula: Hour Angle = (Solar Time - 12) * 15 in degrees

Surface Azimuth Angle

• Angle made on the horizontal surface between the line due south and the projection of the normal to the surface on the horizontal plane
• Varies from -180° to +180°
• Due south is 0°, due north is 180°
• Positive if the normal is east of south, negative if west of south.

Angle of Incidence

• Angle between the sun's ray (line of sight) and the normal to the surface
• Theta denotes the angle of incidence
• Zenith angle is the angle of incidence when the surface is horizontal
• Given by formula: cos θ = sin(φ)sin(δ) + cos(φ)cos(δ)cos(ω) for horizontal surfaces (simplified from a more general equation)

General Equation

• Theta is defined as function of latitude φ, declination δ, tilt angle β, surface azimuth angle γ, and hour angle ω

Vertical Surfaces

• For vertical surfaces, tilt angle beta is 90 degrees

Horizontal Surfaces

• For horizontal surfaces, tilt angle beta is 0

Angle of Incidence for South-Facing Surfaces

• Azimuth angle (γ) is 0° for surfaces facing south.
• With azimuth angle (γ) at 0°, the sine term in the equation becomes 0, simplifying the calculation.
• For south-facing surfaces (γ = 0), the equation includes terms with sine φ sine δ cos β and cos δ, since cos(γ) becomes 1.
• The equation includes cos ω sine β and cos φ cos δ cos ω cos β for south-facing surfaces.
• The term - sine δ cos γ sine β simplifies to - sine δ sine β since cos(γ) = 1 when facing south.
• For a vertical surface, beta (β) is 90°.
• When β = 90° and γ = 0, further simplification occurs, potentially eliminating more terms.
• Equation simplifies to sine φ cos delta cos omega - cos phi sine delta for due south facing vertical surfaces

Slope Angle (β)

• Slope angle (β) is the angle made by a plane surface with the horizontal, ranging from 0 to 180 degrees.
• Slope towards south is positive, ranging from 0 to 180 degrees.
• Slope towards north is indicated with negative sign.

Solar Altitude Angle (α)

• Solar altitude angle (α) is the vertical angle between the sun's rays' projection on the horizontal plane and the sun's ray direction.
• Maximum at solar noon.
• It is related to the solar zenith angle (θz): α + θz = 90 degrees.
• Can be calculated as 90 - θz, varying between 0 and 90 degrees.

Solar Zenith Angle (θz)

• It is the vertical angle between the sun’s rays and a line perpendicular to the horizontal plane.
• The angle between the beam from sun and vertical.
• Complementary angle of solar altitude angle.
• For a horizontal surface with no tilt (β = 0°) pointing due south (γ = 0°), the zenith angle can be calculated.
• The zenith angle is sine φ sine δ cos φ cos δ cos ω.

Solar Azimuth Angle (γs)

• Solar azimuth angle (γs) is the solar angle in degrees along the horizon east or west of north.
• It is the horizontal angle measured from north to the horizontal projection of sun’s rays.
• Positive if projection of line of sight is east of south.
• Negative if projection of line of sight is west of south.
• It varies from 0 to 180 degrees.

Sunrise, Sunset, and Day Length

• At sunrise, Sun's rays are parallel to the horizontal surface; angle of incidence (θz) is 90°.
• The corresponding hour angle (ω) is calculated when cos(θz) = 0 (since θz = 90°).
• Simplified equation: 0 = sine δ sine φ - cos φ cos δ cos ω.
• Hour angle at sunrise/sunset: cos ωs = - tan φ tan δ.
• Angle between sunrise and sunset is given by cos inverse - tan phi and tan delta.
• Total day length calculation is 2 times omega that is nothing but 2 cos inverse of minus tan phi tan delta.
• 15 degrees of hour angle equals 1 hour duration.
• Duration of sunshine hours (td) = (2/15) cos-1(-tan φ tan δ).

Sun Path Diagram

• It represents the position of the sun with respect to any geographical location for a given time.
• Its applications are shadow determination, buildings' positions, solar panels installation.
• Sun rises exactly in the east and sets exactly in the west only on March 20th (Equinox days).
• Diagram divided into degrees (10-90) and meridian.
• Diagram hours ranges from 7 hours to 19 hours, 12 hours is noon.
• June 21st is the longest day of year that is summer time.
• December 21st is the shortest day in winter time
• Shadow determination is possible with H = Objects height, L = projection, e = elevation, tan e = H/L.

Solar Constant

• Radiant solar energy received in extraterrestrial region on a plane of unit area perpendicular to solar radiation at the mean sun-earth distance.
• Its value is 1367 W/m².
• Used to calculate the extraterrestrial radiation value.
• Earth’s motion is in elliptical orbit.
• Solar intensity/radiation/irradiance in the extraterrestrial region measured by NASA.
• Formula: I = Isc [1 + 0.033 cos(360n/365)] for nth day of year (Isc = solar constant).

Solar Time

• Reckoning of passage of time with reference to the position of Sun in the sky.
• Two types: apparent solar time (local apparent time) and mean solar time (clock time/standard time).
• Difference between them: Solar time - Standard time = ±4(LST - Lloc) + E
• LST (Standard Meridian for the Local Time Zone): 82.50° in the East for India.
• Lloc is the longitude of the location which you want to calculate solar time from.
• E is the Equation of Time, depends on the day of the year (n).

Solar Radiation on Horizontal Surface

• Correlations for hourly and daily diffusive/global radiation, sunshine hours.
• H refers to Daily diffusive or global radiation, I refers to hourly diffusive, and global radiation.
• Represents monthly average.
• "S bar" Monthly average of sunshine hours for a day.
• "S bar max" Maximum possible average for sunshine hours or day length.
• “H naught” refers to daily extraterrestrial radiation.

Solar Radiation on Inclined Surface

• Three types: beam, diffusive, reflected solar radiation.
• Rb (Tilt factor/Conversion factor) is the tilt factor for beam radiation ratio of beam radiation on an inclined surface to horizontal surface
• Rd (diffusive radiation Ratio of diffusive radiation incident on an inclined surface to horizontal surface) = (1 + cos β)/2.
• Rr (Reflected solar radiation): Conversion factor for reflected solar radiation = ρ (1 - cos β)/2.
• Reflection coefficient (ρ): 0.2 for ground/concrete/grass, 0.6 for snow.
• Zenith angle: angle of incidence on horizontal plane
• Theta I is the angles of incidence on the inclined surfaces

Total Solar Radiation Calculations

• This can be estimated using Liu and Jordan.
• IT = IbRb + IdRd + (Ib + Id)Rr, where IT is the total solar radiation.
• Ib = Beam radiation, Id = Diffuse radiation, Rb = Beam radiation tilt factor and Rd=Diffusive Radiation
• IT/Ig = (Ib/Ig)Rb + (Id/Ig)Rd + Rr can also show total solar radiation on surface.