Monte Carlo Method applied to Radiation Heat Transfer of a Solar Parabolic Collector - PowerPoint PPT Presentation

1 / 23
About This Presentation
Title:

Monte Carlo Method applied to Radiation Heat Transfer of a Solar Parabolic Collector

Description:

Monte Carlo Method applied to Radiation Heat Transfer of a Solar Parabolic Collector Jeffrey Chang 4/15/09 – PowerPoint PPT presentation

Number of Views:302
Avg rating:3.0/5.0
Slides: 24
Provided by: Jeffre261
Category:

less

Transcript and Presenter's Notes

Title: Monte Carlo Method applied to Radiation Heat Transfer of a Solar Parabolic Collector


1
Monte Carlo Method applied to Radiation Heat
Transfer of a Solar Parabolic Collector
  • Jeffrey Chang
  • 4/15/09

2
Proposal and Goals
  • Investigate an alternate approach to
    approximating radiative heat transfer of a solar
    collector for a given geometry.
  • The Monte Carlo Method can be used calculate the
    geometric configuration factor
  • Validate results to the analytical approach.
  • Attempt optimization via parametric study
  • MC numerical method written in FORTRAN code.

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 Solels Mojave Solar Park (MSP-1)
    becomes operational in 2011 with 553 MW capacity.

4
Solar One -towers absorb energy reflected by
Heliostat mirrors
Solar Energy Generating plants utilize parabolic
collectors to heat pipes
5
The Parabolic Solar Collector
  • Mirrors used to reflect sunlight
  • Concentrates energy
  • 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
6
Solar collectors substitute for nuclear process
for generating electricity
7
Using the Monte Carlo Method
  • Requires physical governing equations of physical
    phenomena.
  • Applies probability distribution combining
    behavior of individual players.
  • Use a pseudo-random number generator (PRNG) to
    produce uniform distribution of inputs for any
    single parameter.
  • Use the Inverse Transform method to transform
    random numbers into parameter inputs for
    analysis.

8
Applying Monte Carlo Method to calculate
efficiency
  • Assume that solar energy can be modeled as
    packets of energy or photons.
  • Use ITM to transform pseudo-random numbers to
    represent the photon emission locations
    reflecting off the mirror.
  • Track the probability of various parameters.
  • Hitting or missing the target
  • Absorbed by gas before hitting the target.

9
Validating MC for example of two perpendicular
infinitely long plates
Schematic of two infinitely long plates of
unequal lengths
Target
Emission surface
Analytical equation
(where Hh/w)
10
Validating MC for example of photon absorption
and attenuation
where I0 is initial photon intensity I is
attenuated intensity of photon S is the finite
flight distance of the photon K is the gas
absorption coefficient
  • Use Beers Law to calculate the fraction of
    transmittance of photons through a gaseous medium
  • Use ITM to convert random number generated to a
    usable parameter (attenuated photon flight
    distance S).
  • Track distances of photons traveled.

11
MC approximation is close to analytical results
Study to calculate photon absorption at 1-ft.
intervals
exact solution for photon traveling at interval
photons N15,000
12
Next Step Validating MC for Semicircular Geometry
Schematic of infinitely long concentric
semicylinder and cylinder
Analytical equations
  • Set target geometry (semicircle)
  • x2(y-H)2R22
  • H is the center of target.
  • R1 is the radius of the target.
  • R2 is radius of the collector.
  • P is angle of tangent line wrt to x-axis.

Use ITM to convert random numbers generated for
following parameters - q (photon flight
angle) - X1 (photon emission location)
13
MC approximation for configuration factor is
close to analytical results
MC approximation must be modified to EFFECTIVE
EFFICIENCY for blockage factor
Max efficiency is only about 25
14
Next Step Applying MC for Parabolic Geometry
Configuration factor 5 more efficient than
semicircular geometry
Collector
  • Develop 2-D model for analysis
  • Set mirror geometry (parabola)
  • y2Cx2
  • C determines the width of the mirror

15
Results show that both C1 and C2 are acceptable
shapes for effective efficiency
16
Attenuated efficiencies reduced by 10 (C1 and
C2 still acceptable cases)
17
Summary
  • MC method successfully validates exact solutions
    for 2 examples. Very useful for approximating
    solutions for simple models.
  • Parametric optimization analysis concludes that
    narrower parabolas are more efficient
    (non-attenuated and attenuated)
  • More detailed models can be examined (i.e.,
    additional parabolic geometries, secondary
    reflections, focal point validation)

18
Y
Target Half-tube
Semi circular Collector
19
7 The reciprocity rule requires that
8 Solving for F2-1
9 The areas of the target and collector are
10a,b Substituting 6 and 9a,b into 8
results in
11
12
20
(No Transcript)
21
Approach
X3,Y3
Target Half-tube
Photon Flight Path
L2
S
L3
q
X2,Y2
L1
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 Beers Law
  • Q is selected using RNG
  • X1 is selected using RNG

Line tangent to starting point 1
22
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)

23
(No Transcript)
Write a Comment
User Comments (0)
About PowerShow.com