Optimum Shape and Design of Cooling Towers

The aim of the current study is to develop a numerical tool that is capable of achieving an optimum shape and design of hyperbolic cooling towers based on coupling a non-linear finite element model developed in-house and a genetic algorithm optimization technique. The objective function is set to be the minimum weight of the tower. The geometric modeling of the tower is represented by means of B-spline curves. The finite element method is applied to model the elastic buckling behaviour of a tower subjected to wind pressure and dead load. The study is divided into two main parts. The first part investigates the optimum shape of the tower corresponding to minimum weight assuming constant thickness. The study is extended in the second part by introducing the shell thickness as one of the design variables in order to achieve an optimum shape and design. Design, functionality and practicality constraints are applied.

Authors:

• A. M. El Ansary
• A. A. El Damatty
• A. O. Nassef

Keywords:

• B-splines
• Cooling towers
• Finite element
• Genetic algorithm
• Optimization

References:

[1] O.C. Zienkiewicz, J.C. Campbell, "Shape optimization and sequential
linear programming", in: R.A. Gallagher, O.E. Zienkiewicz (Eds.),
Optimum Structural Design, Wiley, New York, pp. 109-126, 1973.
[2] C.V. Ramakrishnan, A. Francavilla, "Structural shape optimization
using penalty functions", J. Struct. Mech. 3 (4), 403-422, 1975.
[3] R.J. Yang, D.L. Dewhirst, J.E. Allison, A. Lee, "Shape optimization of
connecting rod pin end using a generic model", Finite element Analysis.
257-264, 1992.
[4] K.H. Chang, K.K. Choi, "A geometry-based parameterization method
for shape design of elastic solids", Mech. Struct. And Mach. 215-252,
1992.
[5] P.L. Gould, and S.L. Lee, "Bending of hyperbolic cooling towers", J.
Struct. Div. ASCE 93 (ST5) 125-146, 1967.
[6] J. Pieczara, "Optimization of cooling tower shells using a simple genetic
algorithm", Struct Multidisc Optim 19, 311-316, 2000.
[7] W. B. Kratzig, W. Zerna, "Resistance of hyperbolic cooling towers to
wind and earthquake loading", In: Pister KS, editor. Structural
engineering and structural mechanics. Englewood Cliffs, NJ: Prentice-
Hall; P. 419-45, 1980.
[8] ACI-ASCE Committee 334, "Recommended Practice for the Design and
Construction of Reinforced Concrete Cooling Towers", ACI J., 74(1),
22-31, 1977.
[9] H. J. Niemann, "Wind effects on cooling-tower shells", Journal of
Structural Engineering, ASCE; 106(3):643-61, 1980.
[10] ASCE, "Minimum design loads for Buildings and other structures",
ASCE 7-98, Reston, Va, 1999.
[11] B. J. Vickery, J. Galsworthy, and A. A. El Damatty, BLWT-SS46-2007.
"Wind loads and Interference effects for the cooling tower at the
Cardinal #3 Plant", November, 2007.
[12] A. M. El Ansary, "Optimum Design of Shell Structures" Ph.D.
dissertation. The University of Western Ontario, London, Ontario,
Canada. 2010.
[13] L. Piegl, W. Tiller, "The NURBS book", Berlin, Heidel-berg, New
York:Springer, 1995.
[14] B. Koziey, F. A. Mirza, "Consistent thick shell element", Computers and
Structures, 65(12):531-41, 1997.
[15] A. A. El Damatty, F. A. Mirza, R. M. Korol, "Large displacements
extension of consistent shell element for static and dynamic analysis",
Computers and Structures; 62(6):943-60, 1997.
[16] D. E. Goldberg, "Genetic Algorithms in search", Optimization and
Machine Learning. Addison-Wesley Publishing Company, Inc., New
York, 1989.
[17] L. Davis, Handbook of Genetic Algorithms, Van Nostrand Reinhold,
New York, 1991.
[18] P. L. Gould, W. B. Kratzig "Cooling tower structures", In: Chen W,
editor. Handbook of structural engineering. Boca Raton, FL: CRC Press
Inc. P. 473-504, 1998.
[19] D. Busch, R. Harte, W. B. Kratzig, U. Montag, "New natural draft
cooling tower of 200 m of height", Eng.Struct. 12;24(12):1509-21, 2002.
[20] Z. Michalewicz, D. B. Fogel, "How to solve it: modern heuristics", 2nd
Ed. New York, 2004.