Download Engineering Project Progress Report #1

Engineering Project Progress
Report #1
Jeffrey Chang
2/18/09
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.
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.
Solar towers absorb energy
reflected by mirrors
Solar Energy Generators utilize
parabolic collectors to heat pipes
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
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)
2)
3)
4)
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)
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.
Beer’s Law – Determine how far photons will fly
Photons/energy
packets
1 – e^(KS) = % Intensity
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
Results
Absorption coefficient
# packets
Distance (m/m)
# packets absorbed
Calculated Absorption
Exact Absorption
total Absorption
0.1
15000
1
2
3
4
5
6
7
8
9
10
1389
1212
1160
1071
984
905
786
719
677
578
9.260% 8.080% 7.733% 7.140% 6.560% 6.033% 5.240% 4.793% 4.513% 3.853%
9.516% 8.611% 7.791% 7.050% 6.379% 5.772% 5.223% 4.726% 4.276% 3.869%
63.207%
As # of packets increase,
absorption % converges to
analytical solution
Next Step: Developing Code
Target:
Half-tube
Y
• Develop 2-D model for analysis
– Set mirror geometry (parabola)
R
• C determines the width of the mirror
H
• y=2*C*x^2
– Set target geometry (semicircle)
• x^2+(y-H)^2=R^2
• H is the center of target
• R is the radius of the target
X-min
X-max
Mirror
Approach
X3,Y3
Photon Flight Path
L2
S
L3
Target:
Half-tube
q
L1
X2,Y2
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
X1,Y1
Line tangent to
starting point 1
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)