Hybrid Ray Tracing Model and Particle Swarm Optimization for the Performance of an Internally Reflecting Solar Still wit
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RESEARCH ARTICLE-MECHANICAL ENGINEERING
Hybrid Ray Tracing Model and Particle Swarm Optimization for the Performance of an Internally Reflecting Solar Still with a Booster Reflector N. U. Rehman1,2
· M. Uzair3
Received: 3 February 2020 / Accepted: 17 September 2020 © King Fahd University of Petroleum & Minerals 2020
Abstract The existing models for analyzing internally reflecting solar stills with external boosters are based on simple geometric relationships and are therefore not adequate for simulating and optimizing more complex arrangements. Therefore, this study presents a 3D hybrid ray-tracing-based model for designing and optimizing such stills. To validate the model, a geometrical arrangement was simulated, and a comparison was made with the output of a geometrical modeling package. To statistically sample a large number of solar rays to determine the irradiance received by the basin, the Latin hypercube sampling technique was used. A comparison was made with the results from a still with the same geometry but without the booster reflector. The model was then used to produce optimal optical-irradiance performance values for aspect ratio, cover angle, booster length ratio and booster angle. The effects of changing these parameters were shown using contour plots. Particle swarm optimization was then applied as an alternative method and was found to optimize the design in significantly less time. Keywords Hybrid ray tracing · Latin hypercube sampling · Aspect ratio · Booster angle · Particle swarm optimization
List of symbols A As c1 , c2 , c Dˆ F g g Best H h1 h2 I IN
B
Area of basin (m2 ) Area of all surfaces of still (m2 ) Learning rates Direction of propagating ray Performance factor Number of reflections Best solution of all particles Position of particle Height of back wall (m) Height of front wall (m) Irradiance at the basin (W/m2 ) Direct irradiance normal to the surface (W/m2 )
N. U. Rehman [email protected]
1
School of Engineering Trades and Technology, Southern Institute of Technology, Invercargill 9840, New Zealand
2
Department of Mechanical Engineering, Auckland University of Technology, Auckland, New Zealand
3
Department of Mechanical Engineering, NED University of Engineering and Technology, Karachi, Pakistan
i j k L Lˆ
Particle number Iteration number Surface Still length (m) Vector representing the direction of the incident ray Booster length (m) Lb N Number of samples generated in LHS Nˆ Normal vector to the surfaces n Number of rays the basin received Normal vector to basin Nˆ basin Source coordinate of the propagating ray P ∗ (x ∗ , y ∗ , z ∗ ) Point chosen on still surface for backPo (xo , yo , z o ) ward ray tracing Coordinate of intersection of ray and surPt (xt , yt , z t ) face P∞ (x∞ , y∞ , z ∞ ) Distant point for forward ray tracing p Best Best solution of a particle r Aspect ratio Booster length ratio rb Random numbers (used in PSO) r1 , r2 ˆS Direction vector for the incoming ray t Parameter to represent the intersection of ray and surface
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Arabia
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