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Numerical Modelling of Natural Draft Wet-Cooling Towers

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Abstract

Numerical modelling of natural draft wet-cooling towers is considered in this paper. Development of a complete CFD model capable of predicting cooling tower performance under various operating conditions is presented. A step-by-step approach is employed, thus one-dimensional numerical modelling of counterflow heat and mass exchangers is extensively presented first. This is followed by reduced order modelling of heat and mass transfer in cooling tower fills by means of proper orthogonal decomposition radial basis function networks. Then the approaches in modelling of droplet zones (rain and spray zones) are discussed. Finally the two and three-dimensional CFD models are discussed.

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References

  1. Al-Waked R (2010) Crosswinds effect on the performance of natural draft wet cooling towers. Int J Therm Sci 49:218–224

    Article  Google Scholar 

  2. Al-Waked R, Behnia M (2006) CFD simulation of wet cooling towers. Appl Therm Eng 26:382–395

    Article  Google Scholar 

  3. Al-Waked R, Behnia M (2007) Enhancing performance of wet cooling towers. Energy Convers Manag 48:2638–2648

    Article  Google Scholar 

  4. Alkidas A (1981) The influence of size-distribution parameters on the evaporation of polydisperse dilute sprays. Int J Heat Mass Transf 24(12):1913–1923

    Article  MATH  Google Scholar 

  5. Bai Z, Demmel J, Dongarra J, Ruhe A, van der Vorst H (2000) Templates for the solution of algebraic eigenvalue problems: a practical guide. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  6. Baker D, Shryock H (1961) A comprehensive approach to the analysis of cooling tower performance. J Heat Transf, 339–350. doi:10.1115/1.3682276

  7. Benton D, Waldrop W (1988) Computer simulation of transport phenomena in evaporative cooling towers. Trans Am Soc Mech Eng 80(236):347–352

    Google Scholar 

  8. Białecki R, Kassab A, Fic A (2005) Proper orthogonal decomposition and modal analysis for acceleration of transient FEM thermal analysis. Int J Numer Methods Eng 62:774–797

    Article  MATH  Google Scholar 

  9. Bird R, Stewart W, Lightfoot E (2006) Transport phenomena, 2nd edn. Wiley, India

    Google Scholar 

  10. Bourillot C (1983) On the hypothesis of calculating the water flowrate evaporated in a wet cooling tower. EPRI report CS-3144-SR

  11. Bošnjaković F (1965) Technical thermodynamics. Holt, Rinehart & Winston, New York. Translated by PL Blackshear Jr

    Google Scholar 

  12. Buhmann M (2003) Radial basis functions: theory and implementations. Cambridge monographs on applied and computational mathematics. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  13. Caudron L (1991) Les réfrigérants atmosphériques industriales. Eyrolles, New York

    Google Scholar 

  14. Chatterjee A (2000) An introduction to the proper orthogonal decomposition. Curr Sci 78(7):808–817

    Google Scholar 

  15. Erens P, Merker J, Dreyer A (1994) Evaporation from accelerating droplets. In: Proceedings of international heat transfer conference, pp 305–310

    Google Scholar 

  16. Ergun S (1952) Fluid flow through packed columns. Chem Eng Prog 48:89–94

    Google Scholar 

  17. Ferziger J, Perić M (2002) Computational methods for fluid dynamics, 3rd edn. Springer, Berlin

    Book  MATH  Google Scholar 

  18. Fic A, Białecki R, Kassab A (2004) Solving transient nonlinear heat conduction problems by proper orthogonal decomposition and FEM. In: Proceedings of CHT-04 ICHMT international symposium on advances in computational heat transfer, Norway. Paper No CHT-04-173 (full text on CD)

    Google Scholar 

  19. Fic A, Białecki R, Kassab A (2005) Solving transient nonlinear heat conduction problems by proper orthogonal decomposition and the finite-element method. Numer Heat Transf, Part B 48(2):103–124

    Article  Google Scholar 

  20. Fluent A (2011) Fluent 14.0 Users Guide. ANSYS, Inc, software documentation

  21. Golub G, Loan CV (1990) Matrix computations, 2nd edn. Johns Hopkins University Press, Baltimore

    Google Scholar 

  22. Hawlader M, Liu B (2002) Numerical study of the thermal-hydraulic performance of evaporative natural draft cooling towers. Appl Therm Eng 22:41–59

    Article  Google Scholar 

  23. Hobler T (1976) Dyfuzyjny ruch masy i absorbery, 2nd edn. WNT, Warszawa, in Polish

    Google Scholar 

  24. Hoffmann K, Chaing S (2000) Computational fluid dynamics, vol I, 4th edn. Engineering Education System, Wichita

    Google Scholar 

  25. Hollands K (1974) An analysis of a counterflow spray cooling tower. Int J Heat Mass Transf 17(10):1227–1239

    Article  Google Scholar 

  26. Holmes P, Lumley J, Berkoz G (1996) Turbulence, ccoherent structures, dynamical systems and symmetry. Cambridge monographs on mechanics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  27. Hotelling H (1933) Analysis of complex of statistical variables into principal components. J Educ Psychol 24:417–441

    Article  Google Scholar 

  28. Hotelling H (1933) Analysis of complex of statistical variables into principal components. J Educ Psychol 24:498–520

    Article  Google Scholar 

  29. Institute CT (1990) CTI code tower, standard specifications, acceptance test for water-cooling towers, Part I, Part II, Part III. CTI code ATC-105, revised

  30. Jaber H, Webb R (1989) Design of cooling towers by the effectiveness-NTU method. J Heat Transf 111:837–843

    Article  Google Scholar 

  31. Kappagantu R, Feeny B (1999) An optimal modal reduction of a system with frictional excitation. J Sound Vib 224:863–877

    Article  Google Scholar 

  32. Karhunen K (1947) Über lineare Methoden in der Wahrscheinlichkeitsrechnung. Ann Acad Sci Fenn Ser A I, Math Phys 37:1–79

    MathSciNet  Google Scholar 

  33. Kerschen G, Golinval J (2002) Physical interpretation of the proper orthogonal modes using singular value decomposition. J Sound Vib 249(5):849–865

    Article  MathSciNet  MATH  Google Scholar 

  34. Kirby M, Sirovich L (1990) Application of Karhunen-Loéve procedure for characterization of human faces. IEEE Trans Pattern Anal Mach Intell 12(1):103–108

    Article  Google Scholar 

  35. Klimanek A (2010) Numerical modelling of heat, mass and momentum transfer in natural draft wet-cooling tower. PhD thesis, Faculty of Energy and Environmental Protection, Silesian University of Technology, Gliwice, Poland

  36. Klimanek A, Białecki R (2008) Modelling of flow, heat and mass transfer in natural drought wet-cooling towers. In: Proceedings of XVI mdzinárodná vedecká konferencia—aplikácia experimentalnych a numerických metód v mechanike tekutin, Žilinská Univerzita, Žilina-Terchová, Slovakia, pp 73–78

    Google Scholar 

  37. Klimanek A, Białecki R (2008) On a numerical model of a natural draught wet-cooling tower. Arch Thermodyn 29(4):63–72

    Google Scholar 

  38. Klimanek A, Białecki R (2009) A 3D CFD model of a natural draft wet-cooling tower. Arch Thermodyn 30(4):119–132

    Google Scholar 

  39. Klimanek A, Białecki R (2009) CFD analysis of fixed and varying fill height natural draft wet-cooling tower. In: Proceedings of 18th international conference on computer methods in mechanics CMM 2009, Zielona Gòra, Poland, pp 237–238

    Google Scholar 

  40. Klimanek A, Białecki R (2009) Solution of heat and mass transfer in counterflow wet-cooling tower fills. Int Commun Heat Mass Transf 36(6):547–553

    Article  Google Scholar 

  41. Klimanek A, Ostrowski Z, Białecki R (2008) Reduced order model of heat and mass transfer in wet cooling tower fills. In: Proceedings of ECOS 2008, vol 1, Cracow-Gliwice, Poland, pp 361–370

    Google Scholar 

  42. Klimanek A, Białecki R, Ostrowski Z (2010) CFD two scale model of a wet natural draft cooling tower. Numer Heat Transf, Part A, Appl 57(2):119–137

    Article  Google Scholar 

  43. Kloppers J (2003) A critical evaluation and refinement of the performance prediction of wet-cooling towers. University of Stellenbosch, Department of Mechanical Engineering, University of Stellenbosch, South Africa, doctoral thesis

  44. Kloppers J, Kröger D (2001) A critical cooling tower performance evaluation. In: 12th IAHR symposium in cooling tower and heat exchangers. UTS, Sydney, Australia, pp T-102

    Google Scholar 

  45. Kloppers J, Kröger D (2003) Loss coefficient correlation for wet-cooling tower fills. Appl Therm Eng 23:2201–2211

    Article  Google Scholar 

  46. Kloppers J, Kröger D (2004) A critical investigation into the heat and mass transfer analysis of crossflow wet-cooling towers. Numer Heat Transf, Part A, Appl 46:785–806

    Article  Google Scholar 

  47. Kloppers J, Kröger D (2005) Cooling tower performance evaluation: merkel, poppe, and e-NTU methods of analysis. J Eng Gas Turbines Power 127(1):1–7

    Article  Google Scholar 

  48. Kloppers J, Kröger D (2005) A critical investigation into the heat and mass transfer analysis of counterflow wet-cooling towers. Int J Heat Mass Transf 48:765–777

    Article  MATH  Google Scholar 

  49. Kosambi D (1943) Statistics in function space. J Indian Math Soc 7:76–88

    MathSciNet  MATH  Google Scholar 

  50. Kozioł J, Stechman A (2006) Przemysłowa woda chłodzaca. Wydawnictwo Politechniki Ślaskiej, Gliwice, in Polish

    Google Scholar 

  51. Kröger D (2004) Air-cooled heat exchangers and cooling towers. PennWell Corporation, Oklahoma

    Google Scholar 

  52. Kurpisz K, Nowak A (1995) Inverse thermal problems. International series on computational engineering. Computational Mechanics, Southampton

    MATH  Google Scholar 

  53. Liang Y, Lee H, Lim S, Lin W, Lee K, Wu C (2002) Proper orthogonal decomposition and its applications—Part I: Theory. J Sound Vib 252(3):527–544

    Article  MathSciNet  MATH  Google Scholar 

  54. Long A, Long C (2001) Surface approximation and interpolation via matrix SVD. Coll Math J 32(1):20–25

    Article  MATH  Google Scholar 

  55. Lowe H, Christie D (1961) Heat transfer and pressure drop data on cooling tower packings, and model studies of the resistance of natural draught towers to airflow, Part V. International development in heat transfer. American Society of Mechanical Engineers, New York

    Google Scholar 

  56. Majumdar A, Singhal K, Spalding D (1983) Numerical modelling of wet cooling towers. Trans ASME J Heat Transf 105:728–735

    Article  Google Scholar 

  57. Majumdar A, Singhal K, Bartz J (1984) Effect of the plume on the performance of a natural draft cooling tower. AIChE Symp Ser 80(236):347–352

    Google Scholar 

  58. Matulewicz Ł, Pohl A, Sokł M, Białecki R (2005) Principal component analysis of in vivo 1H NMR spectra from patients postoperatively irradiated for malignant gliomas. In: Proceedings of Congress European society for magnetic resonance in medicine and biology, Basel, Switzerland

    Google Scholar 

  59. Merkel F (1925) Verdunstungskühlung. VDI-Z 70:123–128

    Google Scholar 

  60. Moler C (2004) Numerical computing with MATLAB, SIAM, Philadelphia, print edition: http://www.ec-securehost.com/SIAM/ot87.html. Electronic edition: the MathWorks, Natick, http://www.mathworks.com/moler

    Book  MATH  Google Scholar 

  61. Morsi S, Alexander A (1972) An investigation of particle trajectories in two-phase flow systems. J Fluid Mech 55(2):193–208

    Article  MATH  Google Scholar 

  62. Nag P (2001) Power plant engineering, 2nd edn. Tata McGraw-Hill, New Delhi

    Google Scholar 

  63. Osterle F (1991) On the analysis of counter-flow cooling towers. Int J Heat Mass Transf 34:1313–1316

    Article  Google Scholar 

  64. Ostrowski Z (2005) Application of proper orthogonal decomposition to the solution of inverse problems. Faculty of Energy and Environmental Protection, Silesian University of Technology, Gliwice, Poland, PhD thesis

  65. Ostrowski Z, Białecki R, Kassab A (2004) Application of the proper orthogonal decomposition to the inverse heat transfer problems. In: Proceedings of XII symposium of heat and mass transfer, vol 2. Polish Academy of Sciences, Committee for Thermodynamics and Combustion, Cracow, pp 625–636, in Polish

    Google Scholar 

  66. Ostrowski Z, Białecki R, Kassab A (2005) Estimation of constant thermal conductivity by use of proper orthogonal decomposition. Comput Mech 37(1):52–59. doi:10.1007/s00466-005-0697-y

    Article  MATH  Google Scholar 

  67. Ostrowski Z, Białecki R, Kassab A (2008) Solving inverse heat conduction problems using trained POD-RBF network inverse method. Inverse Probl Sci Eng 16(1):39–54

    Article  MATH  Google Scholar 

  68. Özişik M, Orlande H (2000) Inverse heat transfer. Taylor & Francis, New York

    Google Scholar 

  69. Pearson K (1901) On lines planes of closes fit to system of points in space. Philos. Mag. 2:559–572

    Google Scholar 

  70. Poppe M, Rögener H (1991) Berechnung von rückkühlwerken. VDI-Wärmeatlas 111:1–15

    Google Scholar 

  71. Press W, Teukolsky S, Vetterling W, Flannery B (1992) Numerical recipes in Cambridge University Press, 40 West 20th Street, New York, NY 10011-4211, USA

  72. Radosavljevic D (1990) The numerical simulation of direct-contact natural-draught cooling tower performance under influence of cross-wind. Imperial College of Science, Technology and Medicine, Exhibition Road. SW7 2BX London, doctoral thesis

  73. Ranz W, Marshall J WR (1952) Evaporation from drops, Part I. Chem Eng Prog 48(3):141–146

    Google Scholar 

  74. Ranz W, Marshall J WR (1952) Evaporation from drops, Part II. Chem Eng Prog 48(4):173–180

    Google Scholar 

  75. Reuter H, Kröger D (2010) A new two-dimensional CFD model to predict the performance of natural draught wet-cooling towers packed with trickle or splash fills. In: 2010 14th international heat transfer conference, IHTC14, ASME, Washington, DC, USA, pp 589–598

    Google Scholar 

  76. Rish R (1961) The design of a natural draught cooling tower. In: Proceedings of 2nd international heat transfer conference, Boulder, Colorado

    Google Scholar 

  77. Rosten H, Spalding D (1989) The PHOENICS Reference Manual. CHAM TR/99, CHAM Ltd, Wimbledon, London, software documentation

  78. Sadasivam M, Balakrishnan A (1995) On the effective driving force for transport in cooling towers. J Heat Transf 117:512–515

    Article  Google Scholar 

  79. Schiller L, Naumann Z (1935) Z Ver Deutsch Ing 77:318

    Google Scholar 

  80. Sirovich L (1987) Turbulence and dynamics of coherent structures. Part I: Coherent structures. Comput Mech XLV:561–571

    MathSciNet  Google Scholar 

  81. Standards BB (1988) Water cooling towers. Methods for performance testing, vol BS 4485-2:1988

  82. Stechman A (2006) Sposób eksploatacji chłodni kominowych w warunkach zimowych. Wydział Inzynierii Środowiska i Energetyki, Politechnika Ślaska w Gliwicach, Gliwice, PhD thesis, in Polish

  83. Terblanche R, Reuter H, Kröger D (2009) Drop size distribution below different wet-cooling tower fills. Appl Therm Eng 29:1552–1560

    Article  Google Scholar 

  84. The MathWorks, Inc (2009) MATLAB Documentation. Online: http://www.mathworks.com

  85. Tieszen S, Ooi A, Durbin P, Behnia M (1998) Modeling of natural convection heat transfer. In: Proceedings of the 1998 summer program, Center for Turbulence Research, Stanford University, Stanford, CA 94305-3035, USA, pp 287–302. Online: http://www.stanford.edu/group/ctr/Summer/SP98.html

    Google Scholar 

  86. Uytterhoeven G (1999) Wavelets: software and applications. Department of Computer Science, Katholieke Universiteit Leuven, Belgium, PhD thesis

  87. Versteeg H, Malalasekera W (1995) An introduction to computational fluid dynamics. Longman Scientific and Technical, Harlow, Essex, UK

    Google Scholar 

  88. Whitaker S (1972) Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles. AIChE J 18(2):361–371

    Article  Google Scholar 

  89. Wilcox D (2006) Turbulence modeling for CFD, 3rd edn. DCW Industries, La Cañada

    Google Scholar 

  90. Williamson N, Behnia M, Armfield S (2004) Numerical simulation of heat and mass transfer in a natural draft wet cooling tower. In: Behnia M, Lin W, McBain GD (eds) Proceedings of the fifteenth Australasian fluid mechanics conference, paper AFMC00237. The University of Sydney, Sydney, 2006. ISBN 1-864-87695-6 (CD-ROM)

    Google Scholar 

  91. Williamson N, Armfield S, Behnia M (2008) Numerical simulation of flow in a natural draft wet cooling tower the effect of radial thermofluid fields. Appl Therm Eng 28:178–189

    Article  Google Scholar 

  92. Williamson N, Behnia M, Armfield S (2008) Comparison of a 2D axisymmetric CFD model of a natural draft wet cooling tower and a 1D model. Int J Heat Mass Transf 51(9–10):2227–2236

    Article  Google Scholar 

  93. Williamson N, Behnia M, Armfield S (2008) Thermal optimization of a natural draft wet cooling tower. Int J Energy Res 32:1349–1361

    Article  Google Scholar 

  94. Wu C, Liang Y, Lin W, Lee H, Lim S (2003) A note on equivalence of proper orthogonal decomposition methods. J Sound Vib 265:1103–1110

    Article  MathSciNet  MATH  Google Scholar 

  95. Zembaty W (1993) Systemy i urzdzenia chodzce elektrowni cieplnych. WNT, Warszawa, in Polish

    Google Scholar 

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Acknowledgements

This work has been partially supported by RECENT 7FP project, grant No. 245819.

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Klimanek, A. Numerical Modelling of Natural Draft Wet-Cooling Towers. Arch Computat Methods Eng 20, 61–109 (2013). https://doi.org/10.1007/s11831-013-9081-9

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