engineering project progress report #1 jeffrey chang 2/18/09

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

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

Engineering Project Progress Report #1

Jeffrey Chang2/18/09

Page 2: 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.

Page 3: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09

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

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
Page 6: Engineering Project Progress Report #1 Jeffrey Chang 2/18/09

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

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

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

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

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

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

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

•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