engineering project progress report #1 jeffrey chang 2/18/09
TRANSCRIPT
![Page 1: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/1.jpg)
Engineering Project Progress Report #1
Jeffrey Chang2/18/09
![Page 2: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/2.jpg)
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.
![Page 3: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/3.jpg)
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.
![Page 4: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/4.jpg)
Solar towers absorb energy reflected by mirrors
Solar Energy Generators utilize parabolic collectors to heat pipes
![Page 5: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/5.jpg)
![Page 6: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/6.jpg)
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
![Page 7: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/7.jpg)
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 mirror3) Absorbed by the air/gas before hitting the mirror.4) Hitting the focal point (pipe containing thermal fluid)
![Page 8: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/8.jpg)
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.
![Page 9: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/9.jpg)
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)/AKS = Flight distance (dimensionless)Rs = Uniform Random NumberAK= gas absorption coefficient
1 – e^(KS) = % Intensity
![Page 10: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/10.jpg)
ResultsAbsorption coefficient 0.1
# packets 15000Distance (m/m) 1 2 3 4 5 6 7 8 9 10
# packets absorbed 1389 1212 1160 1071 984 905 786 719 677 578Calculated Absorption 9.260% 8.080% 7.733% 7.140% 6.560% 6.033% 5.240% 4.793% 4.513% 3.853%
Exact Absorption 9.516% 8.611% 7.791% 7.050% 6.379% 5.772% 5.223% 4.726% 4.276% 3.869%total Absorption 63.207%
As # of packets increase, absorption % converges to analytical solution
![Page 11: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/11.jpg)
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
YTarget: Half-tube
X-min
![Page 12: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/12.jpg)
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
![Page 13: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09](https://reader033.vdocuments.site/reader033/viewer/2022051401/56649ea35503460f94ba7e41/html5/thumbnails/13.jpg)
•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
L3C1