Turbulent flow and convection: The prediction of turbulent flow and convection in a round tube

Advances in Heat Transfer

Volumn 34, Issue C, 2001, Pages 255-361

  Churchill, Stuart W ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

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[No Author keywords available]

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EID: 77956759390     PISSN: 00652717     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0065-2717(01)80013-7     Document Type: Article

References (122)

1. Lamb H. Hydrodynamics. 1st American ed (1945), Dover Publications, New York 663
2. In: Richter J.P. (Ed). The Notebookds of Leonardo da Vinci Vol. 1 (1970), Dover Publications, New York
3. Chandrasekhar S. On Heisenberg's elementary theory of turbulence. Proc. Roy. Soc. (London) A 200 (1949) 20-33
4. Einstein A. Engl. transl. On the motion required by the molecular kinetic theory of heat of particles suspended in fluids at rest. Ann. Phys. 17 (1905) 549-560
5. Heisenberg W. Über Stabilität und Turbulenz von Flüssigkeitsströmen. Ann. Phys. 74 (1924) 577-627
6. Kapitsa P.L. Theoretical and empirical formulas for heat transfer in two-dimensional turbulent flow. Doklady AN SSSR 55 (1947) 595-602
7. Landau L.D. Turbulence. Doklady AN SSSR 44 (1944) 339-342
8. Lorentz H.A. Über die Entstehung turbulenter Flüssigkeitsbewegungen und über den Einfluss dieser Bewegungen bei der Strömung durch Rohren. Abh. Theor. Phys., Leipzig 1 (1907) 43-71
9. Newton I. Scala graduum Caloris. Philos. Trans. Roy. Soc. (London) 22 (1701) 824-829
10. Rayleigh L., and Strutt J.W. On the stability or instability of certain fluid motions. Proc. London Math. Soc. 11 (1880) 51-70
11. Sommerfeld A. A Contribution to the Hydrodynamical Explanation of Turbulent Fluid Motions. Atti del IV. Cong. intern. dei matematici. Roma (1909) 116-124
12. Uhlenbeck G. Some notes on the relation between fluid mechanics and statistical physics. Ann. Rev. Fluid Mech. 12 (1980) 1-9
13. Mises R.v. Some remarks on the laws of turbulent motion in channels and circular tubes. Th. von Kármán Anniversary Volume (1941), Calif. Inst. Techn. Press, Pasadena, CA 317-327
14. Weizsäcker C.F.v. Das Spectrum der Turbulenz bei grossen Reynolds'schen Zahlen. Z. Phys. 124 (1948) 614-627
15. Zel'dovich Ya.B. Limiting laws for turbulent flows in free convection. Zh. Eksp. Teor. Fiz. 7 (1937) 1463-1465
16. translated by J. Kestin. Schlichting H. Boundary Layer Theory. 7th ed. (1979), McGraw-Hill Book Co., New York xxii
17. Reynolds O. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos. Trans. Roy. Soc. (London) 186 (1895) 123-161
18. Reynolds O. On the extent and action of the heating surface of steam boilers. Proc. Lit. Soc. Manchester 14 (1874) 7-12
19. Navier C.-L.M.N. Mémoire sur les lois du mouvement des fluides. Mém. Acad. Roy. Sci. 6 (1822) 389-416
20. Stokes G.G. On the theories of internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. Trans. Cambridge Philos. Soc. 8 (1845) 287-319
21. Barenblatt G.I., and Goldenfeld N. Does fully developed turbulence exist? Reynolds number independence versus asymptotic covariance. Phys. Fluids 7 (1995) 3078-3082
22. Abbrecht P.H., and Churchill S.W. The thermal entrance region in fully developed turbulent flow. AIChE J. 6 (1960) 268-273
23. Fourier J.B. Théorie analytique de la chaleur (1822), Gauthiér-Villais, Paris
24. Rayleigh L., and Strutt J.W. The principle of similitude. Nature 95 (1915) 66-68
25. Rayleigh L., and Strutt J.W. On the question of the stability of the flow of fluids. Philos. Mag. 34 (1892) 59-70
26. Churchill S.W. The use of speculation and analysis in the construction of correlations. Chem. Eng. Commun. 9 (1981) 19-38
27. Churchill S.W. A new approach to teaching dimensional analysis. Chem. Eng. Educ. 30 (1997) 158-165
28. Reynolds O. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the law of resistance in parallel channels. Philos. Trans. Roy. Soc. (London) 174 (1883) 935-982
29. Prandtl L. Über die ausgebildete Turbulenz. Verhdl. 2. Kong. Techn. Mechanik. Zurich (1926) 62
30. Millikan C.B. A critical discussion of turbulent flows in channels and circular tubes. Proc. Fifth Intern. Congr. Appl. Mech. Cambridge. MA (1938) 386-392
31. Part 1. Kármán Th.v. Mechanische Ähnlichten und Turbulenz. Proc. Third Intern. Congr. Appl. Mech. Stockholm (1930) 85-93
32. Murphree E.V. Relation between heat transfer and fluid friction. Ind. Eng. Chem. 24 (1932) 726-736
33. Boussinesq J. Essai sur la théorie des eaux courantes. Mém. présents divers savants Acad. Sci. Inst. Fr. 23 (1877) 1-680
34. Prandtl L. Bericht über Untersuchungen zur ausgebildeten Turbulenz. Zeit. angew. Math. Mech. 6 (1925) 136-139
35. Bird R.B., Stewart W.E., and Lightfoot E.N. Transport Phenomena (1960), John Wiley & Sons, New York
36. Rotta J.C. Das in Wandnahe gultige Geschwindigkeitsgesetz turbulenter Strömungen. Ing. Arch. 18 (1950) 277-280
37. Prandtl L. Neuere Ergebnisse der Turbulenzforschung. Zeit. Vereines Deutscher Ingenieure 77 (1933) 105-114
38. van Driest E.R. On turbulent flow near a wall. J. Aeronaut. Sci. 13 (1956) 1007-1011
39. Kolmogorov A.N. The local structure of turbulence in an incompressible viscous fluid at very large Reynolds numbers. Doklady AN SSSR 30 (1941) 301-304
40. Prandtl L. Über ein neues Formelsystem für die ausgebildete Turbulenz. Nachr Ges. Wiss. Göttingen Math.-Phys. Klasse (1945) 6-19
41. Batchelor G.K. The Theory of Homogeneous Turbulence (1953), Cambridge Univ. Press
42. Launder B.E., and Spalding D.B. Mathematical Models of Turbulence (1972), Academic Press, London
43. Hanjalić K., and Launder B.E. A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech. 52 (1972) 609-638
44. Satake S., and Kawamura H. Large eddy simulation of turbulent flow in concentric annuli with a thin inner rod. In: Durst F., Kasagi N., Launder B.E., Schmidt F.W., Suzuki K., and Whitelaw J.N. (Eds). Turbulent Shear Flows 9 (1995), Springer, Berlin 259-281
45. Part 1. Nikuradse J. Widerstandgesetz und Geschwindigkeitsverteilung von turbulenten Wasserströmungen in glatten und rauhen Ŕohren. Proc. Third Intern. Congr. Appl. Mech. Stockholm (1930) 239-248
46. Nikuradse J. Gesetzmässigkeiten der turbulenten Strömung in glatten Rohren. Ver. Deutsch. Ing. Forschungsheft (1932) 356
47. Nikuradse J. Strömungs gesetze in rauhen Rohren. Ver. Deutsch. Ing. Forschungsheft 361 (1933)
48. Miller B. The laminar film hypothesis. Trans. ASME 71 (1949) 357-367
49. Robertson J.M., Martin J.D., and Burkhart T.H. Turbulent flow in rough pipes. Ind. Eng. Chem. Fundam. 7 (1968) 253-265
50. Lynn S. Center-line value of the eddy viscosity. AIChE J. 5 (1959) 566-567
51. Lindgren E.R., and Chao J. Average velocity distribution of turbulent pipe flow with emphasis on the viscous sublayer. Phys. Fluids 12 (1969) 1364-1371
52. Hinze J.O. Turbulent pipe flow. Mécanique de la turbulence (1963), Editions CNRS, Paris 130-165
53. Blasius H. Das Ähnlichkeitsgesetz bei Reibungsvorgängen in Flüssigkeiten. Ver. Deutsch. Ing. Forsch-arb. Ing.-wes. No. 131 (1913)
54. Freeman J.R. Experiments upon the Flow of Water in Pipes and Fittings (1941), ASME, New York
55. (First mentioned in I. Lieferung (1921). Prandtl L. Über den Reibungswiderstand Strömender Luft. Ergebn. Aerodyn. Versanst. Göttingen 3 (1929) 1-5
56. Prandtl L. Über den Reibungswiderstand Strömender Luft. Ergebn. Aerodyn. Versanst., Göttingen 3 (1929) 136
57. Nunner W. Wärmeübertragung und Druckabfall in rauhen Rohren. Ver. Deutsch. Ing. Forschungsheft (1956) 455
58. Barenblatt G.I. Scaling laws for fully developed turbulent shear flows. Part 1. Basic hypotheses and analysis. J. Fluid Mech. 248 (1993) 513-520
59. Churchill S.W. An appraisal of new experimental data and predictive equations for fully developed turbulent flow in round tubes, in review (2000)
60. Rothfus R.R., and Monrad C.C. Correlation of turbulent velocities for tubes and parallel plates. Ind. Eng. Chem. 47 (1955) 1144-1149
61. MacLeod A.L. Liquid turbulence in a gas-liquid absorption system. Ph.D. Thesis (1951), Carnegie Institute of Technology, Pittsburgh, PA
62. Whan G.A., and Rothfus R.R. Characteristics of transition flow between parallel plates. AIChE J. 5 (1959) 204-208
63. Senecal V.E., and Rothfus R.R. Transition flow of fluids in smooth tubes. Chem. Eng. Progr. 49 (1955) 533-538
64. Colebrook C.F. Turbulent flow in pipes with particular reference to the transition region between smooth and rough pipe laws. J. Inst. Civ. Eng. 11 (1938-1939) 133-156
65. Churchill S.W. Empirical expressions for the shear stress in turbulent flow in commercial pipe. AIChE J. 19 (1973) 375-376
66. Churchill S.W., and Usagi R. A general expression for the correlation of rates of transfer and other phenomena. AIChE J. 18 (1972) 1121-1128
67. Orszag S.D., and Kells L.C. Transition to turbulence in plane Poiseuille and plane couette flow. J. Fluid Mech. 96 (1980) 159-205
68. Kim J., Moin P., and Moser R. Turbulence statistics in fully developed channel flow at low Reynolds numbers. J. Fluid Mech. 177 (1987) 133-166
69. Lyons S.L., Hanratty T.J., and McLaughlin J.B. Large-scale computer simulation of fully developed turbulent channel flow with heat transfer. Int. J. Num. Methods Fluids 13 (1991) 999-1028
70. Rutledge J., and Sleicher C.A. Direct simulation of turbulent flow and heat transfer in a channel. Part I. Smooth walls. Int. J. Num. Methods Fluids 16 (1993) 1051-1078
71. Eckelmann H. The structure of the viscous sublayer and the adjacent wall region in turbulent channel flow. J. Fluid Mech. 65 (1974) 439-459
72. Churchill S.W., and Chan C. Theoretically based correlating equations for the local characteristics of fully turbulent flow in round tubes and between parallel plates. Ind. Eng. Chem. Res. 34 (1995) 1332-1341
73. Groenhof H. Eddy diffusion in the central region of turbulent flow in pipes and between parallel plates. Chem. Eng. Sci. 25 (1970) 1005-1014
74. Zagarola M.V. Mean-flow scaling of turbulent pipe flow. Ph.D. Thesis (1966), Princeton University, Princeton, NJ
75. Spalding D.B. A single formula for the "Law of the Wall". J. Appl. Mech. 28E (1961) 455-458
76. Churchill S.W., and Choi B. A simplified expresson for the velocity distribution in turbulent flow in smooth pipes. AIChE J. 19 (1973) 196-197
77. Reichardt H. Vollständige Darstellung der turbulenten Geschwindigkeitsver-teilung in glatten Leitungen. Zeit. angew. Math. Mech. 31 (1951) 201-219
78. Churchill S.W., and Chan C. Turbulent flow in channels in terms of local turbulent shear and normal stresses. AIChE. J. 41 (1995) 2513-2525
79. Churchill S.W., and Chan C. Improved correlating equations for the friction factor for fully developed turbulent flow in round tubes and between identical parallel plates, both smooth and rough. Ind. Eng. Chem Res. 33 (1994) 2016-2019
80. Churchill S.W. New simplified models and formulations for turbulent flow and convection. AIChE J. 42 (1997) 1125-1140
81. Churchill S.W. A critique of predictive and correlative models for turbulent flow and convection. Ind. Eng. Chem. Res. 35 (1996) 3122-3140
82. Kampé de Fériet J. Sur l'écoulement d'un fluide visqueux incompressible entre deux plaques parallélel indefinies. La Houille Blanche 3 (1948) 509-517
83. Pai S.I. On turbulent flow between parallel plates. J. Appl. Mech. 20 (1953) 109-114
84. Pai S.I. On turbulent flow in circular pipe. J. Franklin Inst. 236 (1953) 337-352
85. Notes. Churchill S.W. Chapter 5. Turbulent Flows. The Practical Use of Theory (1994), The University of Pennsylvania, Philadelphia
86. Wei T., and Willmarth W.W. Reynolds-number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204 (1980) 57-95
87. Danov S.N., Arai N., and Churchill S.W. Exact formulations and nearly exact solutions for convection in turbulent flow between parallel plates. Int. J. Heat Mass Transfer 43 (2000) 2767-2777
88. Churchill S.W. New wine in new bottles; unexpected findings in heat transfer. Part II. A critical examination of turbulent flow and heat transfer in circular annuli. Therm. Sci. Eng. 5 (1997) 1-12
89. Reichardt H. Die Grundlagen des turbulenten Wärmeüberganges. Arch. ges. Wärmetechn. 2 (1951) 129-142
90. Rohsenow W.M., and Choi H.Y. Heat, Mass, and Momentum Transfer (1961), Prentice-Hall, Englewood Cliffs, NJ 183
91. Yahkot V., Orszag S.A., and Yahkot A. Heat transfer in turbulent fluids-1. Pipe flow. Int. J. Heat Mass Transfer 30 (1987) 15-22
92. Page Jr. F., Schlinger W.G., Breaux D.K., and Sage B.H. Point values of eddy conductivity and eddy viscosity in uniform flow between parallel plates. Ind. Eng. Chem. 44 (1952) 424-430
93. CHurchill S.W. New wine in new bottles; unexpected findings in heat transfer. Part III. The prediction of turbulent convection with minimal explicit empiricism. Therm. Sci. Eng. 5 (1997) 13-30
94. Petukhov B.S. Heat transfer and friction in turbulent pipe flow with variable physical properties. Adv. Heat Transfer 6 (1970) 503-562
95. Seban R.A., and Shimazaki T.T. Heat transfer to a fluid flowing turbulently in a smooth pipe with walls at constant temperature. Trans. ASME 73 (1951) 803-808
96. Lyon R.N. Liquid metal heat-transfer coefficients. Chem. Eng. Progr. 47 (1951) 75-79
97. Reynolds A.J. The prediction of turbulent Prandtl and Schmidt numbers. Int. J. Heat Mass Transfer 18 (1975) 1055-1069
98. Kays W.M. Turbulent Prandtl number-Where are we?. J. Heat Transfer, Trans. ASME 116 (1994) 284-295
99. Jischa M., and Rieke H.B. About the prediction of turbulent Prandtl and Schmidt numbers from modified transport equations. Int. J. Heat mass Transfer 22 (1979) 1547-1555
100. Notter R.H., and Sleicher C.A. A solution to the turbulent Graetz problem-III. Fully developed and entry region heat transfer rates. Chem. Eng. Sci. 27 (1972) 2073-2093
101. Elperin T., Kleeorin N., and Rogachevskii I. Isotropic and anisotropic spectra of passive sealer fluctuations in turbulent film flow. Phys. Rev. E 53 (1996) 3431-3441
102. Papavassiliou D.V., and Hanratty T.J. Transport of a passive scalar in a turbulent channel flow. Int. J. Heat Mass Transfer 40 (1997) 1303-1311
103. Shaw D.A., and Hanratty T.J. Turbulent mass transfer to a wall for large Schmidt numbers. AIChE J. 23 (1978) 28-37
104. Heng L., Chan C., and Churchill S.W. Essentially exact characteristics of turbulent convection in a round tube. Chem. Eng. J. 71 (1998) 163-173
105. Yu B., Ozoe H., and Churchill S.W. The characteristics of fully developed turbulent convection in a round tube, in review (2000)
106. Kays W.M., and Leung R.Y. Heat transfer in annular passages-Hydrodynamically developed turbulent flow with arbitrarily prescribed heat flux. Int. J. Heat Mass Transfer 6 (1963) 537-557
107. Nusselt W. Der Wärmeübergang in Rohrleitungen. Mitt. Forsch.-Arb. Ing.-wes. 89 (1909) 1750-1787
108. Dittus R.W., and Boelter L.M.K. Heat Transfer in Automobile Radiators of the Tubular Type, University of California Publications in Engineering 2 (1930) 443-461
109. Sherwood T.K., and Petrie J.M. Heat transmission to liquids flowing in pipes. Ind. Eng. Chem. 24 (1932) 736-748
110. Coulson J.M., and Richardson J.F. Chemical Engineering Vol. 1 (1954), McGraw-Hill Book Co., New York 166
111. Colburn A.P. A method for correlating forced convection heat transfer data and a comparison with fluid friction. Trans. AIChE 29 (1933) 174-210
112. Martinelli R.C. Heat transfer to molten metals. Trans. ASME 69 (1947) 947-959
113. Lubarsky B., and Kaufman S.J. Review of experimental investigations of liquid-metal heat transfer. Nat. Advisory Comm. Aeronaut. Report 1270, Washington, D.C. (1956)
114. Sleicher C.A., and Tribus M. Heat transfer in a pipe with turbulent flow and arbitrary wall-temperature distribution. Trans. ASME 79 (1957) 789-797
115. Notter R.H., and Sleicher C.A. The eddy diffusivity in the turbulent boundary layer near a wall. Chem. Eng. Sci. 26 (1971) 161-172
116. Notter R.H., and Sleicher C.A. A Solution to the turbulent Graetz problem by matched asymptotic expansions-II. The case of uniform heat flux. Chem. Eng. Sci. 26 (1971) 559-565
117. Churchill S.W. Comprehensive correlating equations for heat, mass, and momentum transfer in fully developed flow in smooth tubes. Ind. Eng. Chem. Fundam. 16 (1977) 109-116
118. Prandtl L. Eine Beziehung zwischen Wärmeaustausch and Strömungswiderstand der Flüssigkeiten. Phys. Z. 11 (1910) 1072-1078
119. Thomas L.C., and Fan L.T. Heat and momentum analogy for incompressible boundary layer flow. Int. J. Heat Mass Transfer 14 (1971) 715-717
120. Higbie R. The rate of pure gas into a still liquid during short periods of exposure. Trans. Amer. Inst. Chem. Engrs. 31 (1935) 365-389
121. Danckwerts P.V. Significance of liquid film coefficients in gas absorption. Ind. Eng. Chem. 43 (1957) 1460-1467
122. in press. Churchill S.W., Shinoda M., and Arai N. A new concept of correlation for turbulent convection. Thermal Sci. Eng. (2000)