Technical Description of Solar Thermal Collector Efficiency





What affects solar thermal collector efficiency?
  • A solar thermal collector is a complex heat exchanger which converts electromagnetic energy into heat energy.
  • Solar thermal collectors are not 100% efficient.
  • Losses come from several sources
    • Heat losses - solar radiation that is converted to heat, but lost before it can be used. Losses are due to three modes of heat transfer.
      • radiation heat transfer
      • convection heat transfer
      • conductive heat transfer
    • Optical losses - solar radiation incident upon the collector that is not converted to heat energy
  • Procedures have been developed to characterize the performance of flat plate, evacuated tube, and CPC evacuated tube solar thermal collectors. An explanation is as follows:
    • Gtotal [i.e. 856W/m2] represents the total solar flux incident upon the collector.
      • Gtotal=Gbeam+Gdiffuse
    • Thermal losses () are typically lumped into a 2nd order polynomial which is dependent upon the temperature difference of the fluid circulating in the collector and air temperature.
      • tm represents the mean temperature of the fluid that is traveling through the collector. tm=(tinlet+toutlet)/2, [°C or °K].
      • ta represents the ambient temperature that the collector is placed in (i.e. how hot or cold it is outside), [°C or °K].
      • a1 and a2 are experimentally determined constants, representing the thermal losses of the collector, with units of and respectively.
        • Experimentally determined constants assume certain orientation, wind speed, mounting frame temperature, etc.. Actual values will vary slightly depending upon configuration and environment.
      • ThermalLosses/UnitArea== a1*(tm-ta)+a2*(tm-ta)2, [W/m2].
      • Care must be taken to ensure one knows which area base a1 and a2 refer to (gross, aperture, or absorber area). This affects what area base the thermal losses, and power refer to.
    • optical efficiency
      • nominal optical efficiency, η0(unit-less) is determined with direct radiation normal to the collector surface.
        • Care must be taken to ensure that η0 refers to the same area base as a1 and a2.
      • Incident Angle Modifiers (IAM) are unit-less multipliers used to represent the angle dependence of the optical efficiency of a solar collector.
        • Evacuated tube solar thermal collectors typically have biaxial incident angle modifiers
          • k=k(ΘLT)≈kLL)*kTT), [unit-less] (see McIntire, 1982)
            • ΘL represents the longitudinal incidence angle
            • ΘT represents the translational incidence angle
              • Please note: In many evacuated tube collectors, translational incidence angle rises above 1.00 for incidence angles greater than 0°. This is typically due to gaps between tubes which collect no solar energy when incidence angles is equal to 0°. Once an incidence angle is increased beyond 0° the gaps can "close up" if the absorber surface is curved. Many collectors with high translational incidence angles have low gross area nominal optical efficiency due to large gaps between the tubes.
            • values of kLL) and kTT) are typically presented in a tabular or graphical form.
        • Flat plate solar thermal collectors IAMs are typically only dependent upon the incidence angle
          • k=k(Θ), [unit-less]
          • values of k(Θ) are typically presented in a tabular or graphical form.
        • IAMs are characteristic of each individual collector and can be determined through standardized test procedures.
        • A separate value for k exists for beam radiation and diffuse radiation (kbeam & kdiffuse).
      • OpticalEfficiency~=η0*k, [unit-less].
      • OpticalEfficiency will change as the collector gets dirty or obstructed.
    • Power/UnitArea=0*(kbeam*Gbeam + kdiffuse*Gdiffuse)- , [W/m2]
      • Care must be taken to understand that UnitArea must refer to the same dimensions as a1, a2, & η0 .
    • Efficiency=η=/(Gtotal)=(η0*(kbeam*Gbeam + kdiffuse*Gdiffuse)-(a1*(tm-ta)+a2*(tm-ta)2))/(Gbeam+Gdiffuse)
  • Efficiency for parabolic trough, dish, and freznel style reflectors is more complex to calculate, and because these are not widely used by consumers, but rather industrial settings, there is not a widely standardized rating system.
How is solar thermal collector performance determined?
  • Several testing standards and certifications exist to characterize the thermal and mechanical performance of solar thermal collectors.
    • Europe
      • Most evolved and mature solar thermal market.
      • EN12975 is a popular standard, developed by CEN, the European Committee for Standardization
      • Several testing agencies exist which follow EN12975 standard testing procedure.
        • ITW
        • SPF
          • SPF publishes "typical solar yields" for domestic hot water, water pre-heating, and space heating. Great care must be taken when interpreting this data, as solar collector performance varies greatly with location and climate. Typical solar yields published by SPF are for Central Switzerland.
          • Provides a database of solar collectors which they have tested.
      • Well known agencies such as DinCertco acknowledge the validity of the test performed by a testing agency
      • CPC1512 and CPC1518 evacuated tubes have been tested by ITW according to EN12975, and the test has been certified by DinCertco
    • U.S.A.
      • Solar Rating Certification Corporation (SRCC)
        • Has developed a testing standard comprised of ISO, ASHRAE, and SRCC standards.
        • Certifies testing laboratories
        • Certifies test reports
        • Provides a database of certified solar thermal collectors.
        • SRCC publishes a "Collector Thermal Performance Rating", described in MJ/panel/day, for various operating temperatures, and "Clear Day (23MJ/m2/day)", "Mildly Cloudy (17MJ/m2/day)", and "Cloudy Day (11MJ/m2/day)". Although this can be used as a comparison of panel to panel, it is misleading, because all panels are not of the same surface area. One should be sure to use this as a comparison tool only, and not a system sizing tool. Performance varies significantly based upon climate, geography, and collector orientation. SRCC does not indicate what location and collector orientation their performance ratings are defined for. Additionally, choosing the number clear, mildly cloudy, and cloudy days cannot be performed arbitrarily
      • CPC1512 and CPC1518 evacuated tubes have not completed testing with SRCC.
      • In order to receive residential federal subsidies via IRS Form 5695, the solar thermal collectors must be certified by SRCC. Individuals are encouraged to deeply search their conscience before making decisions based on artificial market forces established by subsidies which erode the principles of laissez-faire capitalism.
    • Reciprocity does not currently exist between U.S.A. & European standards & certifications, however, both define nominal optical efficiency & incidence angle modifiers, and constants for the heat loss as a second order polynomial.




©2007 - Andy Schroder