Engineering Project Progress Report #1

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. Fluid in pipe Solar energy Parabolic mirror

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. • Hitting vs missing the mirror. • Absorbed vs reflected by the mirror • Absorbed by the air/gas before hitting the mirror. • 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 1 – e^(KS) = % Intensity Photons/energy packets x • 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

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

11. Next Step: Developing Code Target: Half-tube Y • 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 X-min X-max Mirror

12. Approach X3,Y3 Target: Half-tube Photon Flight Path L2 S L3 q L1 X2,Y2 X1,Y1 X1,Y1 • 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 Line tangent to starting point 1

13. Hit or Miss? C1 L3 X1,Y1 • 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)