Frequently Asked Questions about Software Capabilities

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Cooling tower transfer characteristics is one of the most, if not the most important parameters in cooling tower thermal design. Unlike heat exchangers, where transfer coefficients for various configurations are widely published, cooling tower transfer characteristics are not commonly found in the open literature. One of the reasons for this is that fill manufacturer’s generally regard the transfer characteristics of their fills as confidential. The following two sources do give transfer coefficients of various fills:

• Lowe, H.J. and Christie, D.G., Heat Transfer and Pressure Drop Data on Cooling Tower Packings and Model Studies of the Resistance of Natural Draft Towers to Airflow, Proceedings of the International Heat Transfer Conference, Colorado, Part V, pp. 933-950, 1961.
• Johnson, B.M. (ed.), Cooling Tower Performance Prediction and Improvement, Volume 1, Applications Guide, EPRI Report GS-6370, Volume 2, Knowledge Base, EPRI Report GS-6370, EPRI, Palo Alto, 1989.

The fill transfer characteristics of the two sources above are available from a database in the software. The fill database of the software is expanded as fill manufacturers make the characteristic curves available. The fills characteristic of Brentwood is included in the software for counterflow fills.

The only way to be certain of what the transfer characteristics are for a fill, is to do an independent fill test. This can be a costly undertaking, but if you take the penalties involved if a cooling tower does not meet the guaranteed performance, this is a small price to pay. The only problem is that there are only a few facilities globally where tests like these can be conducted. 

The software package does not use multidimensional CFD, instead it is a one dimensional analytical model. The multi-dimentional effects are addressed in the semi-empirical equations of the transfer and pressure drop coefficients. These semi-empirical equations are derived from numerical and experimental studies. The software is therefore very cost effective when compared to CFD.

Accuracy

The big question is how do the accuracy of the software compare to the accuracy of CFD. Experience has shown that the analytical based models (like the current software) give results of the same order of magnitude than full-blown CFD simulations. The results of the software are, however, obtained at a fraction of the time and cost of the CFD simulations.

Why?

Why are CFD models of cooling towers not necessarily more accurate than analytical models? The geometry of a cooling tower is generally very complex. The water distribution system with the support structure, pipes and nozzles are difficult to accurately model in CFD. Add the water droplets, fill, fill support structure and fan to the CFD model and you can appreciate the increase in complexity of the model. CFD models are therefore simplified by employing many simplifying assumptions. Some transfer and loss coefficients are obtained from experimental research. These are the same semi-empirical models that are employed in the analytical models. Therefore, the same models are used in both CFD and the analytical models and the end results are therefore not too different.

CFD has its place

Having said the above, CFD is still a very powerful and useful tool to analyse cooling tower performance. It can run many scenarios that will be impossible to do with analytical tools. When you consider the cost and time to do CFD analyses, analytical models like the current software, will always be in demand.

The software is based on a semi-empirical analytical approach. The semi empirical equations are used to calculate the following:

• Airflow loss coefficients through the different components of the tower.
• Transfer characteristics (Merkel Numbers) in the different transfer zones and especially in the rain zone.

These semi-empirical equations are only valid for certain parameter ranges and operational conditions. The software may therefore not cater for all possible cooling tower sizes and operational conditions. The software will give an answer, but the equations will be extrapolated where the accuracy is unknown. The software will, however, warn the user if some equations are used outside the specified ranges for the design parameters. The software was specifically designed for relatively large industrial cooling towers and should work without any problem for these towers.

Many different numerical schemes are used in the software to obtain convergence of the equations. There may be some cases where numerical instabilities may occur, and the solution process will fail. There are, however, corrective measures implemented in the code that automatically prevents these instabilities. It must be stressed that these cases are relatively rare. A user familiar with the software can solve the numerical instabilities when they occur by changing the solution control parameters. This is similar to steps taken in CFD software packages to ensure stable convergence of solutions 

 The airflow through mechanical draft cooling towers can determined/specified in two different ways:

Firstly, the fan curve can be entered into the software by specifying up to a sixth order polynomial. This case is used when the fan curve is known. The polynomial (equation) that gives the fan static pressure vs volumetric flow can be entered into the software. The fan curve should be given by the fan manufacturer. The fan curve is only valid for one specific fan configuration, i.e. if the number of fan blades or the blade angle changes then a new curve should be entered into the software for the new configuration. Some fan manufacturers provide software with their fans which generate fan curves for all possible fan configurations. The polynomial that represents the fan curve should be determined by the user by using a curve fitting procedure. Microsoft Excel is commonly used for curve fitting. By using the fan curve the software will determine the operating point of the cooling tower by iteratively solving the draft and energy equations. The fan speed or other cooling tower parameters, like the fill height, can then be varied to achieve the required cooling load.

The second approach is to specify the air flow through the cooling tower that will achieve the required cooling load. The pressure drop through the cooling tower is calculated by the software. The pressure drop and flow rate can then be used to specify a fan that will meet all the geometrical and operational requirements.

Over the years, the software was enhanced to cater for numerical instability. However, in some rare cases (especially those at extreme operating and atmospheric conditions) numerical instability may still occur during program execution.  There are however many measures that can be taken to fix the problem. Here is a short summary of steps to follow to obtain solutions (numerical convergence):

• Try different initial conditions for the design parameters. Select “Auto” initialization so that the initial parameters are calculated by the software. 
• If the problem still persist then change the values of the relaxation parameters.  
• If the software runs successfully for the Merkel model but not the Poppe model (and you have already tried the steps above with no success) then try the following: 
• Run the software with the Merkel model. Use the applicable outputs as new initial values. Rerun the software with the Poppe model selected. 

The following sources were consulted in the development of the software. They are presented in chronological order of the publication date.

• Lewis, W.K., The Evaporation of a Liquid into a Gas, Transactions of ASME, Vol. 44, pp. 325-340, May, 1922.
• Merkel, F., Verdunstungskühlung, VDI-Zeitchrift, Vol. 70, pp. 123-128, January 1925.
• Lewis, W.K., The Evaporation of a Liquid into a Gas – A Correction, Mechanical Engineering, Vol. 55, pp. 567-573, 1933.
• Hutchison, W.K. and Spivey, E., Design and Performance of Cooling Towers, Transactions of the Institute of Chemical Engineers, Vol. 20, pp. 14-29, 1942.
• Zivi, S.M. and Brand, B.B., An Analysis of the Crossflow Cooling Tower, Refrigerating Engineering, Vol. 64, pp. 31-34 & 90-92, 1956.
• McKelvey, K.K. and Brooke, M., The Industrial Cooling Tower, Elsevier Publishing Company, Amsterdam, 1959.
• Baker, D.R. and Shryock, H.A., A Comprehensive Approach to the Analysis of Cooling Tower Performance, Transactions of the ASME, Journal of Heat Transfer, pp. 339-350, 1961.
• Berman, L.D., Evaporative Cooling of Circulating Water, 2nd Edition, Chapter 2, pp. 94-99, ed. Sawistowski, H., Translated from Russian by R. Hardbottle, Pergamon Press, New York, 1961.
• Lowe, H.J. and Christie, D.G., Heat Transfer and Pressure Drop Data on Cooling Tower Packings and Model Studies of the Resistance of Natural Draft Towers to Airflow, Proceedings of the International Heat Transfer Conference, Colorado, Part V, pp. 933-950, 1961.
• Bosnjacovic, F., Technische Thermodinmik, Theodor Steinkopf, Dresden, 1965.
• CTI, Cooling Tower Performance Curves, The Cooling Tower Institute, Houston, 1967.
• Nahavandi, A. N., Kershah, R.M. and Serico, B.J., The Effect of Evaporation Losses in the Analysis of Counterflow Cooling Towers, Journal of Nuclear Engineering and Design, Vol. 32, pp. 29-36, 1975.
• Kelly, N.W., Kelly’s Handbook of Crossflow Cooling Tower Performance, Kansas City, Missouri, Neil W. Kelly and Associates, 1976.
• Kelly, N.W., A Blueprint for the Preparation of Crossflow Cooling Tower Characteristic Curves, Paper Presented before the Cooling Tower Institute Annual Meeting, January, 1976.
• Montakhab, A., Waste Heat Disposal to Air with Mechanical and Draft – Some Analytical Considerations, Heat Transfer Division of the ASME, Winter Annual Meeting, San Francisco, 1978.
• Cale, S.A., Development of Evaporative Cooling Packing, Commission of European Communities, Report EUR 7709 EN, Luxembourg, 1982.
• Missimer, J. and Wilber, K., Examination and Comparison of Cooling Tower Component Heat Transfer Characteristics, IAHR Cooling Tower Workshop, Hungary, October 12-15, 1982.
• Stoecker, W.F. and Jones, J.W., Refrigeration and Air Conditioning, McGraw-Hill Book Co., Singapore, 1982.
• Bourillot, C., TEFERI, Numerical Model for Calculating the Performance of an Evaporative Cooling Tower, EPRI Report CS-3212-SR, August 1983.
• Bourillot, C., On the Hypothesis of Calculating the Water Flowrate Evaporated in a Wet Cooling Tower, EPRI Report CS-3144-SR, August 1983.
• Majumdar, A.K., Singhal, A.K. and Spalding, D.B., Numerical Modeling of Wet Cooling Towers – Part 1: Mathematical and Physical Models, Transactions of the ASME, Journal of Heat Transfer, Vol. 105, pp. 728-735, November 1983.
• Majumdar, A.K., Singhal, A.K., Reilly, H.E. and Bartz, J.A., Numerical Modeling of Wet Cooling Towers – Part 2: Application to Natural and Mechanical Draft Towers, Transactions of the ASME, Journal of Heat Transfer, Vol. 105, pp. 736-743, November 1983.
• Majumdar, A.K., Singhal, A.K. and Spalding., D.B., VERA2D: Program for 2-D Analysis of Flow, Heat, and Mass Transfer in Evaporative Cooling Towers, EPRI Report CS 2923, Volume 1 and 2, March 1983.
• Sutherland, J.W., Analysis of Mechanical-Draught Counterflow Air/Water Cooling Towers, Transactions of the ASME, Journal of Heat Transfer, Vol. 105, pp. 576-583, August 1983.
• Poppe, M. and Rögener, H., Berechnung von Rückkühlwerken, VDI-Wärmeatlas, pp. Mh1-Mh15, 1984.
• Li, K.W. and Priddy, A.P., Power Plant System Design, John Wiley & Sons, 1985.
• Wilber, K.R., Yost, J.G. and Wheeler, D.E, An Examination of the Uncertainties in the Determination of Natural Draft Cooling Tower Performances, Joint AMSE/IEEE Power Generation Conference, Milwaukee, Wisconsin, October 20-24, 1985.
• Hoffmann, J.E., Bedryfspunt Voorspelling vir Nat Koeltorings, M.Eng Thesis, University of Stellenbosch, Stellenbosch, South Africa, 1987.
• British Standard 4485, Water Cooling Towers, Part 2: Methods for Performance Testing, 1988.
• Dreyer, A.A., Analysis of Evaporative Coolers and Condensers, M.Eng Thesis, University of Stellenbosch, Stellenbosch, South Africa, 1988.
• Jaber, H. and Webb, R.L., Design of Cooling Towers by the Effectiveness-NTU Method, Journal of Heat Transfer, Vol. 111, pp. 837-843, November 1989.
• Johnson, B.M. (ed.), Cooling Tower Performance Prediction and Improvement, Volume 1, Applications Guide, EPRI Report GS-6370, Volume 2, Knowledge Base, EPRI Report GS-6370, EPRI, Palo Alto, 1989.
• Cooling Tower Institute, CTI Code Tower, Standard Specifications, Acceptance Test Code for Water-Cooling Towers, Part I, Part II and Part III, CTI Code ATC-105, Revised, February 1990.
• Surridge, A.D., Swanepoel, D.J.deV., Held, G., Research on Thermal Feedback Caused by Dry-Cooling Power Generating Stations, Confidential Report, EMA-C 9086, CSIR, Pretoria, 1990.
• Feltzin, A.E. and Benton D., A More Exact Representation of Cooling Tower Theory, Cooling Tower Institute Journal, Vol. 12, No. 2, pp. 8-26, 1991.
• Osterle, F., On the Analysis of Counter-Flow Cooling Towers, International Journal of Heat and Mass Transfer, Vol. 34, No. 4/5, pp. 1313-1316, 1991.
• Poppe, M. and Rögener, H., Berechnung von Rückkühlwerken, VDI-Wärmeatlas, pp. Mi 1-Mi 15, 1991.
• Hensley, J., Maximize Tower Power, Chemical Engineering, pp. 74-82, February, 1992.
• Willa, J.L., Evolution of the Cooling Tower, CTI Journal, Vol. 13, No. 1, pp. 40-49, 1992.
• Becker, B.R. and Burdick, L.F., Drift Eliminators and Cooling Tower Performance, ASHRAE Journal, pp. 28-36, June 1993.
• Kranc, SC, Performance of Counterflow Cooling Towers with Structured Packings and Maldistributed Water Flow, Numerical Heat Transfer, Part A, Vol. 23, pp. 115-127, 1993.
• Mirsky, G.R. and Bauthier, J., Evolution of Cooling Tower Fill, CTI Journal, Vol. 14, No. 1, pp. 12-19, 1993.
• Du Preez, A.F. and Kröger, D.G., The Influence of a Buoyant Plume on the Performance of a Natural Draft Cooling Tower, 9th IAHR Cooling Tower and Spraying Pond Symposium, Brussels, 1994.
• Grange, J.L., Calculating the Evaporated Water Flow in a Wet Cooling Tower, Paper presented at the 9th IAHR Cooling Tower and Spraying Pond Symposium, von Karman Institute, Brussels, Belgium, September 1994.
• Bernier, M.A., Thermal Performance of Cooling Towers, ASHRAE Journal, pp. 56-61, April 1995.
• Bland, C., A Cool Solution to a Hot Problem, Process Engineering, pp. 33, June, 1995.
• Conradie, A.E., Performance Optimization of Engineering Systems with Particular Reference to Dry-Cooled Power Plants, Ph.D. Thesis, University of Stellenbosch, South Africa, 1995.
• Ibrahim, G.A., Nabhan, M.B.W. and Anabtawi M.Z., An Investigation into a Falling Film Type Cooling Tower, International Journal of Refrigeration, Vol. 18, No. 8, pp. 557-564, 1995.
• Kintner-Meyer, M. and Emery, A.F., Cost-Optimal Design for Cooling Towers, ASHRAE Journal, pp. 46-55, April 1995.
• Mills, A.F., Basic Heat and Mass Transfer, Irwin, Chicago, 1995.
• Liffick, G.W. and Cooper, Jr, J.W., Thermal Performance Upgrade of the Arkansas Nuclear One Cooling Tower: A “Root Cause” Analysis Approach, Proceedings of the American Power Conference, Vol. 57, No. 2, pp. 1357-1362, 1995.
• Oosthuizen, P.C., Performance Characteristics of Hybrid Cooling Towers, M.Eng. Thesis, University of Stellenbosch, Stellenbosch, South Africa, 1995.
• Sadasivam, M. and Balakrishnan, A.R., On the Effective Driving Force for Transport in Cooling Towers, Transactions of the ASME, Journal of Heat Transfer, Vol. 117, pp. 512-515, May 1995.
• Mohiuddin, A.K.M. and Kant, K., Knowledge Base for the Systematic Design of Wet Cooling Towers. Part I: Selection and Tower Characteristics, International Journal of Refrigeration, Vol. 19, No. 1, pp. 43-51, 1996.
• Mohiuddin, A.K.M. and Kant, K., Knowledge Base for the Systematic Design of Wet Cooling Towers. Part II: Fill and other Design Parameters, International Journal of Refrigeration, Vol. 19, No. 1, pp. 52-60, 1996.
• Bowman, C.F. and Benton, D.J., Oriented Spray-Assisted Cooling Tower, CTI Journal, Vol. 18, No. 1, 1997.
• Cooling Tower Institute, CTI Code Tower, Standard Specifications, Acceptance Test Code for Water-Cooling Towers, Vol. 1, CTI Code ATC-105(97), Revised, February 1997.
• De Villiers, E. and Kröger, D.G., Analysis of Heat, Mass and Momentum Transfer in the Rain Zone of Counterflow Cooling Towers, Proceedings of the 1997 IJPGC, Vol.2, PWR-Vol. 32, pp. 141-149, Denver, November 1997.
• El-Dessouky, H.T.A., Al-Haddad, A. and Al-Juwayhel, F., A Modified Analysis of Counter Flow Wet Cooling Towers, Journal of Heat Transfer, Vol. 119, No. 3, pp. 617-626, 1997.
• Hoffmann, J.E., The Influence of Temperature Stratification in the Lower Atmospheric Boundary Layer on the Operating Point of a Natural Draft Dry-Cooling Tower, Ph.D Thesis, University of Stellenbosch, Stellenbosch, South Africa, 1997.
• Huser, A., Nilsen, P.J. and Skatun, H., Application of k-ε Model to the Stable ABL: Pollution in Complex Terrain, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 67 and 68, pp. 425-436, 1997.
• Al-Nimr, M.A., Dynamic Thermal Behaviour of Cooling Towers, Energy Conversion Management, Vol. 39. No. 7, pp. 631-636, 1998.
• Baard, T.W., Performance Characteristics of Expanded Metal Cooling Tower Fill, M.Eng Thesis, University of Stellenbosch, Stellenbosch, South Africa, 1998.
• Conradie, A.E., Buys, J.D. and Kroger, D.G., Performance Optimization of Dry-Cooling Systems for Power Plants through SQP Methods, Applied Thermal Engineering, Vol. 18, Nos. 1-2, pp. 25-40, 1998.
• Kröger, D.G., Air-Cooled Heat Exchangers and Cooling Towers Thermal-Flow Performance, Evaluation and Design, Begell House, Inc., New York, 1998.
• Streng, A., Combined Wet/Dry Cooling Towers of Cell-Type Construction, Journal of Energy Engineering, Vol. 124, No. 3, pp. 104-121, December 1998.
• De Villiers, E. and Kröger, D.G., Inlet Losses in Counterflow Wet-Cooling Towers, Joint Power Generation Conference, Vol.2, PWR-Vol. 34, ASME, 1999.
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