Time Domain Random Wind Response of Cooling Tower
Publication: Journal of Engineering Mechanics
Volume 110, Issue 10
Abstract
Random wind response analysis of a cooling tower is performed using the Monte‐Carlo simulation approach. A 48 d.o.f. quadrilateral shell element is used. The response analysis capability is first verified by finding the deterministic response of a cooling tower due to an artificial wind load. Five different wind simulation models are then tested, based on quasi‐steady aerodynamics and ARIMA models derived from measured data, all with different correlation assumptions in the meridional and circumferential directions. Time domain responses of a cooling tower for the five wind models are obtained and compared. For generating random shocks an equation relating the variances of pressure and velocity, and other quantities to the variance of random shocks is derived to provide input to the ARIMA velocity‐pressure transfer function model. The assumption of ergodicity is made. Results are presented in the form of time‐history response, mean, RMS values, peak values, and gust factors. Frequency domain results are also obtained for the most realistic example to compare with the time‐domain results. Favorable agreement is found.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abu‐Sitta, S. H., and Hashish, M. G., “Dynamic Wind Stresses in Hyperbolic Cooling Towers,” Journal of the Structural Division, ASCE, Vol. 99, No. ST9, Paper 9989, Sept., 1973, pp. 1823–1835.
2.
Armitt, J., “Wind Loading on Cooling Towers,” Journal of the Structural Division, ASCE, Vol. 106, No. ST3, Paper 15242, Mar., 1980, pp. 623–641.
3.
Basu, P. K., and Gould, P. L., “Cooling Towers Using Measured Wind Data,” Journal of the Structural Division, ASCE, Vol. 106, No. ST3, Paper 15259, Mar., 1980, pp. 579–600.
4.
Bathe, K. J., and Wilson, E. L., Numerical Methods in Finite Element Analysis, Prentice‐Hall, Inc., Englewood Cliffs, N.J., 1976.
5.
Bendat, J. S., and Piersol, A. G., Random Data: Analysis and Measurement Procedures, Wiley Interscience, New York, N.Y., 1971.
6.
Billington, D. P., and Abel, J. F., “Design of Cooling Towers for Wind,” Proceedings of the Specialty Conference on Methods of Analysis, University of Wisconsin‐Madison, Aug. 22‐25, 1976, pp. 242–267.
7.
Box, G. E. P., and Jenkins, G. M., Time Series Analysis: Forecasting and Control, Holden Day, San Francisco, Calif., 1976.
8.
Caughey, T. K., and O'Kelly, M. E. J., “Classical Normal Modes in Damped Linear Dynamic Systems,” Journal of Applied Mechanics, ASME, Vol. 32, 1965, pp. 583–588.
9.
Chang, Y. B., Yang, T. Y., and Soedel, W., “Linear Dynamic Analysis of Revolutional Shells Using Finite Elements and Modal Expansion,” Journal of Sound and Vibration, Vol. 86, No. 4, 1983, pp. 523–538.
10.
Davenport, A. G., “Gust Loading Factors,” Journal of the Structural Division, ASCE, Vol. 93, No. ST3, Paper 5255, June, 1967, pp. 11–34.
11.
Farrel, C., Guven, O., and Maisch, F., “Mean Wind Loading on Rough‐Walled Cooling Towers,” Journal of the Engineering Mechanics Division, ASCE, Vol. 102, No. EM6, Paper 12647, Dec., 1976, pp. 1059–1081.
12.
Hashish, M. G., and Abu‐Sitta, S. H., “Response of Hyperbolic Cooling Towers to Turbulent Wind,” Journal of the Structural Division, ASCE, Vol. 100, No. ST5, Paper 10542, May, 1974, pp. 1037–1051.
13.
Lin, Y. K., Probabilistic Theory of Structural Dynamics, Robert E. Krieger Publishing Company, Huntington, N.Y., 1976, pp. 62–65.
14.
Miller, K. A. G., Chairman, Report of the Committee of Inquiry into the Collapse of the Cooling Tower at Ardeer Nylon Works, Ayrshire on Thursday, 27th September 1973, Imperial Chemical Industries Limited, Petrochemicals Division, available from Engineering Services Department, Imperial Chemical House, Millbank, London SWIP 3JF, no date.
15.
Newland, D. E., An Introduction to Random Vibrations and Spectral Analysis, Longman, London, England, 1975, pp. 113–165.
16.
Niemann, H. J., “Wind Effects on Cooling Tower Shells,” Journal of the Structural Division, ASCE, Vol. 106, No. ST3, Paper 15251, Mar., 1980, pp. 643–661.
17.
Niemann, H. J., and Propper, H., “Some Properties of Fluctuating Wind Pressure on a Full‐Scale Cooling Tower,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 1, 1975–1976, pp. 349–359.
18.
Niemann, H. J., and Ruhwedel, J., “Full‐Scale and Model Tests on Wind‐Induced, Static and Dynamic Stresses in Cooling Tower Shells,” Engineering Structures, Vol. 2, Apr., 1980, pp. 81–89.
19.
Reed, D. A., and Scanlan, R. H., “Time‐Series Analysis of Cooling Tower Wind Loading,” Journal of Structural Engineering, ASCE, Vol. 109, No. ST2, Paper 17735, Feb., 1983, pp. 538–554.
20.
“Reinforced Concrete Cooling Tower Shell: Practice and Commentry,” Report of ACI‐ASCE Committee 334, American Concrete Institute Journal, No. 1, Jan., 1977, pp. 22–31.
21.
Report of the Committee on Inquiry into the Collapse of the Cooling Tower at Ferrybridge, Monday, November 1, 1965, Central Electricity Generating Board, Her Majesty's Stationary Office, London, England, 1966.
22.
Ruscheweyh, H., “Wind Loading on Hyperbolic Natural Draught Cooling Towers,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 1, 1975–76, pp. 335–340.
23.
Shinozuka, M., “Monte‐Carlo Solution of Structural Dynamics,” Computers and Structures, Vol. 2, 1972, pp. 855–874.
24.
Simiu, E., and Scanlan, R. H., Wind Effects on Structures: An Introduction to Wind Engineering, John Wiley & Sons, Inc., New York, N.Y., 1978, pp. 54–61.
25.
Singh, M. P., and Gupta, A. K., “Gust Factors for Hyperbolic Cooling Towers,” Journal of the Structural Division, ASCE, Vol. 102, No. ST2, Paper 11894, Feb., 1976, pp. 371–386.
26.
Sollenberger, N. J., and Scanlan, R. H., “Pressure Difference Across the Shell of a Hyperbolic Natural Draft Cooling Tower,” Proceedings of the International Conference on Full Scale Testing of Wind Effects, London, Ontario, Canada, June, 1974.
27.
Sollenberger, N. J., Scanlan, R. H., and Billington, D. P., “Wind Loading and Response of Cooling Towers,” Journal of the Structural Division, ASCE, Vol. 106, No. ST3, Paper 15281, Mar., 1980, pp. 601–621.
28.
Spanos, P. T. D., “Numerical Simulation of a Van Der Pol Oscillator,” Computers and Mathematics With Applications, Vol. 6, 1980, pp. 135–145.
29.
Steinmetz, R. L., Billington, D. P., and Abel, J. F., “Hyperbolic Cooling Tower Dynamic Response to Wind,” Journal of the Structural Division, ASCE, Vol. 104, No. ST1, Paper 13484, Jan., 1978, pp. 35–53.
30.
Suryoutomo, H., Gould, P. L., and Basu, P. K., “Direct Dynamic Analysis of Shells of Revolution Using High‐Precision Finite Elements,” Computers and Structures, Vol. 7, 1977, pp. 425–433.
31.
Vaicaitis, R., Shinozuka, M., and Takeno, M., “Response Analysis of Tall Buildings to Wind Loading,” Department of Civil Engineering and Engineering Mechanics, Technical Report No. 1, Columbia University, New York, N.Y., July, 1973.
32.
Yang, T. Y., and Kapania, R. K., “Shell Elements for Cooling Tower Analysis,” Journal of Engineering Mechanics, ASCE, Vol. 109, No. 5, Paper 18296, Oct., 1983, pp. 1270–1289.
33.
Yang, T. Y., and Kapania, R. K., “Finite Element Random Response Analysis of a Cooling Tower,” Journal of Engineering Mechanics, ASCE, Vol. 110, No. 4, Paper 18738, Apr., 1984, pp. 589–609.
34.
Yang, T. Y., and Kapania, R. K., Dynamic Response Analysis of Complex Thin Shell Structures, report submitted to the National Science Foundation, School of Aeronautics and Astronautics, Purdue University, West Lafayette, Ind., Nov., 1983.
35.
Yeh, C. H., “Nonlinear Dynamic Analysis of Cooling Tower,” Journal of the Power Division, ASCE, Vol. 99, No. PO2, Paper 10141, Nov., 1973, pp. 339–347.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 110 • Issue 10 • October 1984
Pages: 1524 - 1543
Copyright
Copyright © 1984 ASCE.
History
Published online: Oct 1, 1984
Published in print: Oct 1984
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.