1. Engineering Project Progress Report #1 Jeffrey Chang 2/18/09

2. Proposal Investigate different approaches to calculating the radiative heat transfer of a solar collector for a given geometry. The Monte Carlo Method can be used calculate the geometric configuration factor Compare results to the analytical approach.

3. Background Parabolic Solar collectors have been used for over 30 years Practice varies from domestic use to large scale power generation in the Southwestern states. Example: Solel’s Mojave Solar Park (MSP-1) becomes operational in 2011 with 553 MW capacity.

4. Solar towers absorb energy reflected by mirrors Solar Energy Generators utilize parabolic collectors to heat pipes

6. The Parabolic Solar Collector Mirrors used to reflect sunlight Concentrates energy at a focal point Energy heats a thermal fluid flowing through the pipe Thermal fluid interfaces with heat exchanger to create high pressure steam Steam drives turbine generators. Parabolic mirror Fluid in pipe Solar energy

7. Using the Monte Carlo Method to calculate efficiency Assume that solar energy can be modeled as packets of energy or photons. Use set of random numbers to represent the number of photons reflecting off the mirror. When set becomes large, we are guaranteed a probability distribution. Track the probability of various parameters. 1)Hitting vs missing the mirror. 2)Absorbed vs reflected by the mirror 3)Absorbed by the air/gas before hitting the mirror. 4)Hitting the focal point (pipe containing thermal fluid)

8. First Pass at Monte Carlo Analysis (Absorbed by the air) Start off simple in 1-D analysis Use Beer’s Law to calculate the fraction of transmittance of photons through a gaseous medium Track distances of photons traveled.

9. Beer’s Law – Determine how far photons will fly x Photons/energy packets Some will be absorbed by the gaseous medium. Use random number to determine flight distances. S = -LN(1-Rs)/AK S = Flight distance (dimensionless) Rs = Uniform Random Number AK= gas absorption coefficient 1 – e^(KS) = % Intensity

10. Results As # of packets increase, absorption % converges to analytical solution

11. Next Step: Developing Code Develop 2-D model for analysis – Set mirror geometry (parabola) y=2*C*x^2 C determines the width of the mirror – Set target geometry (semicircle) x^2+(y-H)^2=R^2 H is the center of target R is the radius of the target H R Mirror X-max Y Target: Half-tube X-min

12. Approach X1,Y1 Target: Half-tube X3,Y3 X1,Y1 S Line tangent to starting point 1 Photon Flight Path  X2,Y2 Point 1 (X1,Y1): Starting point of photon (emitting point). Point 2 (X2,Y2): Projected point of photon onto tangent line Point 3 (X3,Y3): End point of photon. S calculated using Beer’s Law Q is selected using RNG X1 is selected using RNG L2 L1 L3

13. Conditions for Hitting the Target: If point 3 (X3,Y3) remains on the edge or inside the target. If line equation L3 intercepts semicircle equation C1 And if point 3 lies above the mirror And if point 3 is in left quadrant of the mirror (given point is on the right side) Hit or Miss? X1,Y1 L3 C1