1. Flux Mapping of the Beam Down Solar Thermal Concentrator at Masdar City
Steven Meyers, Marwan Mokhtar, Peter Armstrong, Matteo Chiesa
Laboratory of Energy and Nano-Science (LENS)
Solar Energy Group

2. Outline Flux Mapping Basics Beam Down Solar Thermal Concentrator
Initial Results
Forward Optical Model
Bidirectional Reflectivity Distribution Function
Convolution
Model Results
Discussion

3. Flux Mapping Basics
Flux Mapping – A method to determine the distribution and quantity of concentrated solar radiation generated by a CSP facility
Three Basic Tools
CCD Camera
Diffuse Reflector (Lambertian)
Heat Flux Sensor (HFS)
CCD Camera –Luminance Map (cd/m2) nm
HFS – Discrete flux measurement (kW/m2) nm
Conversion ratio (kW/cd)
Yields a continuous flux map of (kW/m2)
Kaluza and Neumann, 1998
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4. Source: www.odforce.net
Diffuse Surface
Lambert’s Cosine Law (Lambertian surface)
The measured radiation intensity by an ideal diffusing surface is directly proportional to the cosine of the angle between the observer’s line of sight and the surface normal (Photometria, 1760).
If the surface obeys Lambert’s Cosine Law, the radiation angle of incidence (AOI) and azimuth are inconsequential
However, if the surface does not perfectly follow the Law, the reflected radiation to a stationary observer will change based on the radiation AOI and azimuth
Source:
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5. The Beam Down Solar Thermal Concentrator (BDSTC)
Central Reflector
Structure
CCD Camera Location
Heliostat Field
Target Receiver 1 5
HFS Location N E W 3 7
Designed by Tokyo Tech, constructed by MES
100 kW/m2 peak flux at a net incident energy of 100 kWt
Flux measurement instrumentation
Thermally regulated CCD camera (Konika Minolta CS-2000)
Eight in-situ calibrated (Mokhtar et al. 2011) Head Flux Sensors (Medtherm - Gardon, Schmidt-Boelter)
Diffuse Reflecting Target (sandblasted unglazed tile)
Goal – Determine the conversion coefficient to generate a flux map (HFS/CCD)
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6. Initial Results
Increasing trend due to spectral sensitivity differences between CCD camera and HFS
(Kaluza and Neumann. 1998, Ulmer et al. 2002)
AM (blue) PM (red)
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7. Beam Down Optics
The 360 degree field of heliostats contribute significantly different radiation quantities over the day
Not observed in north field dominant towers and dishes due limited changes in cosine loss
Needed to quantify the changing levels of radiation contribution from each heliostat over the day
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8. Optical Model Combined heliostat efficiency
Radiation Angle of Incidence on the Receiver
Radiation Azimuth direction
Mean AOI and Azimuth
Assumed Gaussian flux profile (no astigmatism)
CCD Camera
HFS
X HFS
Y HFS
Y CR
X CR
Z CR
AOI rec
φrec CR
Mirror
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9. Optical Model
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10. BRDF Lambertian assumption?
A Bidirectional Reflectance Distribution Function (BRDF) was constructed
Source: NIST
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11. BRDF
Results indicated a significant backscatter reflectance, consistent with a rough diffuse surface
(Oren-Nayar model)
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12. BRDF θ South East North West L L Sun – Afternoon CCD Camera
Peak Reflection
Reflected Ray Measured
by CCD Camera
South East
North West L L
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13. Convolution
By convoluting the optical forward model with the BRDF, we can estimate the quantity of light which is measured by the CCD camera (Fmodel )and compare that to predicted light assuming a true Lambertian surface (Flambertian)
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14. Results Fmodel / (Flambertian) Original Data West East West East
AM (blue) PM (red)
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15. Discussion
The AM/PM trend correlates to the HFS located on the East or West side of the Diffuse Surface
By applying this methodology to many points across receiver (x,y), compensation for any non-Lambertian reflections allows for proper extraction of the flux levels on the surface and not the light levels reflected to and measured by the CCD camera
A homogeneous Diffuse Surface BRDF is critical to the success of this method
𝑘𝑊 𝐶𝑑 𝑥,𝑦, 𝜔 𝑠 = 𝐻𝐹𝑆 𝐶𝐶𝐷 𝜔 𝑠 ∗ 𝐹 𝑚𝑜𝑑𝑒𝑙 𝑥,𝑦, 𝜔 𝑠 𝐹 𝑙𝑎𝑚𝑏𝑒𝑟𝑡𝑖𝑎𝑛 𝑥,𝑦, 𝜔 𝑠
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16. Limitations Assumed Gaussian flux distribution and no astigmatism
Modeled BRDF function valid for only one location, not entire surface
Inconsistent inter-HFS/CCD ratios due to non-uniform tile surface (poor conditioning)
HFS 2 had minimal AM/PM difference
Measured BRDF was very Lambertian
HFS 5 had significant AM/PM difference
Measured BRDF showed large back scattering reflection
Due to non-uniform tile surface, we were unable to generate an accurate flux map
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17. Conclusion
Method can be used to minimize errors caused by non-ideal Lambertian surfaces
Simple forward optical model and BRDF can provide significant insight into the changing radiation measured by the CCD camera
Allows for less precise (cheaper, more rugged) surfaces to be used for flux analysis, as long as they are homogeneous
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18. Thank you
Questions?