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Turbulent flow in smooth concentric annuli with small radius ratios

Published online by Cambridge University Press:  29 March 2006

K. Rehme
Affiliation:
Institut für Neutronenphysik und Reaktortechnik, Kernforschungszentrum, 75 Karlsruhe, Germany

Abstract

Fully developed turbulent flow through three concentric annuli was investigated experimentally for a Reynolds-number range Re = 2 × 104−2 × 105. Measurements were made of the pressure drop, the positions of zero shear stress and maximum velocity, and the velocity distribution in annuli of radius ratios α = 0.02, 0.04 and 0.1, respectively. The results for the key problem in the flow through annuli, the position of zero shear stress, showed that this position is not coincident with the position of maximum velocity. Furthermore, the investigation showed the strong influence of spacers on the velocity and shear-stress distributions. The numerous theoretical and experimental results in the literature which are based on the coincidence of the positions of zero shear stress and maximum velocity are not in agreement with reality.

Type
Research Article
Copyright
© 1974 Cambridge University Press

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References

Ball, H. D. & Azer, N. Z. 1972 Experimental investigations of eddy diffusivities of air in turbulent annular flow. Proc. 1972 Heat Transfer & Fluid Mech. Inst., San Fernando Valley, p 19. Stanford University Press.
Barrow, H., Lee, Y. & Roberts, A. 1965 The similarity hypothesis applied to turbulent flow in an annulus. Int. J. Heat Mass Transfer, 8, 1499.Google Scholar
Barthels, H. 1967 Darstellung des Wärmeübergangs in konzentrischen Ringspalten unter Benutzung der Analogie zwischen Impuls- und Wärmeaustausch. K.F.A. Jülich Rep. Jül-506-RB.Google Scholar
Brighton, J. A. 1963 The structure of fully developed turbulent flow in annuli. Ph.D. thesis, Purdue University.
Brighton, J. A. & Jones, J. B. 1964 Fully developed turbulent flow in annuli. J. Basic Engng, D 86, 835.Google Scholar
Clump, C. W. & Kwasnoski, D. 1968 Turbulent flow in concentric annuli. A.I.Ch.E. J. 14, 164.Google Scholar
Crookston, R. B. 1966 Heat and momentum transfer for turbulent flow in annuli with small cores. Ph.D. thesis, Carnegie Institute of Technology, Pittsburgh.
Crookston, R. B., Rothfus, R. R. & Kermode, R. I. 1968 Turbulent heat transfer in annuli with small cores. Int. J. Heat Mass Transfer, 11, 415.Google Scholar
Davis, E. S. 1943 Heat transfer and pressure drop in annuli. Trans. A.S.M.E. 65, 755.Google Scholar
Deissler, R. G. 1955 Analysis of turbulent heat transfer, mass transfer and fluid friction in smooth tubes at high Prandtl and Schmidt numbers. N.A.C.A. Rep. no. 1210.Google Scholar
Durst, F., Melling, A. & Whitelaw, J. H. 1971 The interpretation of hot wire signals in low turbulence flows, Imperial College Rep. ET/TN/B/5.Google Scholar
Eifler, W. 1968 Über die turbulente Geschwindigkeitsverteilung und Wandreibung in Strömungskanälen verschiedener Querschnitte. Ph.D. dissertation, Technische Hochschule, Darmstadt.
Eifler, W. 1969 Berechnung der turbulenten Geschwindigkeitsverteilung und der Wandreibung in konzentrischen Ringspalten. Wärme- & Stoffübertragung, 2, 36.Google Scholar
Eifler, W. 1970 Begrenzungen für die Anwendbarkeit von Preston-Rohren in Kanalströmungen. Wärme- & Stoffübertragung, 3, 58.Google Scholar
Goldstein, S. 1938 Modern Developments in Fluid Dynamics, vol. 2, p 331. Oxford University Press.
Gräber, H. 1970 Der Wärmeübergang in glatten Rohren, zwischen parallelen Platten, in Ringspalten und längs Rohrbündeln bei exponentieller Wärmefluzverteilung in erzwungener laminarer oder turbulenter Strömung, Int. J. Heat Mass Transfer, 13, 1645.Google Scholar
Ivey, C. M. 1965 The position of maximum velocity in annular flow. MSc thesis, University of Windsor, Canada.
Jonsson, V. K. 1965 Experimental studies of turbulent flow phenomena in eccentric annuli. Ph.D. thesis, University of Minnesota, Minneapolis.
Jonsson, V. K. & Sparrow, E. M. 1966 Experiments on turbulent-flow phenomena in eccentric annular ducts. J. Fluid Mech. 25, 65.Google Scholar
Kays, W. M. & Leung, E. Y. 1963 Heat transfer in annular passages — hydrodynamically developed turbulent flow with arbitrarily prescribed heat flux. Int. J. Heat Mass Transfer, 6, 537.Google Scholar
Kjellström, B. & Hedberg, S. 1966 On shear stress distributions for flow in smooth or partially rough annuli. AB Atomenergi, Stockholm Rep. AE-243.Google Scholar
Kjellström, B. & Hedberg, S. 1968 Calibration experiments with a DISA hot-wire anemometer. AB Atomenergi, Stockholm, Rep. AE-338.Google Scholar
Kjellström, B. & Hedberg, S. 1970 Die Eichung eines DISA Hitzdrahtanemometers und Bestätigung der Eichung durch Messungen in einem zylindrischen Kanal. DISA Inf. 9, 8.Google Scholar
Knudsen, J. G. & Katz, D. L. 1950 Velocity profiles in annuli. Proc. Midwest. Conf. Fluid Dynamics, 1st Conf. Univ. Illinois, Ann Arbor, p 175.Google Scholar
Knudsen, J. G. & Katz, D. L. 1958 Fluid Dynamics and Heat Transfer. McGraw-Hill.
Koch, R. & Feind, K. 1958 Druckverlust und Wärmeübergang in Ringspalten. Chem. Ing.-Tech. 30, 577.Google Scholar
Laufer, J. 1954 The structure of turbulence in fully developed pipe flow. N.A.C.A. Tech. Note, no. 1174.Google Scholar
Lawn, C. J. & Elliott, C. J. 1971 Fully developed turbulent flow through concentric annuli. C.E.G.B. Rep. RD/B/N 1878.Google Scholar
Lawn, C. J. & Elliott, C. J. 1972 Fully developed turbulent flow through concentric annuli. J. Mech. Eng. Sci. 14, 195.Google Scholar
Lee, J. 1965 On von Kármán's eddy viscosity in bounded flow. Appl. Sci. Res. A 14, 250.Google Scholar
Lee, Y. 1964 Turbulent flow and heat transfer in concentric and eccentric annuli. Ph.D. thesis, University of Liverpool.
Leung, E. Y., Kays, W. M. & Reynolds, W. C. 1962 Heat transfer with turbulent flow in concentric and eccentric annuli with constant and variable heat flux. Stanford Rep. AHT-4.Google Scholar
Levy, S. 1967 Turbulent flow in an annulus. J. Heat Transfer, 89, 25.Google Scholar
Lorenz, F. R. 1932 Über turbulente Strömung durch Rohre mit kreisringförmigem Querschnitt. Mitt. Inst. Strömungsmaschinen, TH Karlsruhe, no. 2.Google Scholar
Macagno, E. O. & McDougall, D. W. 1966 Turbulent flow in annular pipes. A.I.Ch.E.J. 12, 437.Google Scholar
MacMillan, F. A. 1956 Experiments on Pitot-tubes in shear flow. Aero. Res. Counc. R. & M. no. 3028.Google Scholar
Marek, J., Maubach, K. & Rehme, K. 1973 Heat transfer and pressure drop performance of rod bundles arranged in square arrays. Int. J. Heat Mass Transfer, 16, 2215.Google Scholar
Maubach, K. 1969 Reibungsgesetze turbulenter Strömungen in geschlossenen, glatten und rauhen Kanälen von beliebigem Querschnitt. Ph.D. dissertation. University of Karlsruhe. (Kernforschungszentrum Karlsruhe Ext. Rep. INR-4/69-22.)
Maubach, K. 1970 Reibungsgesetze turbulenter Strömungen. Chem.-Ing.-Tech. 42, 995.Google Scholar
Maubach, K. 1972 Rough annulus pressure-drop: interpretation of experiments and recalculation for square ribs. Int. J. Heat Mass Transfer, 15, 2489.Google Scholar
Maubach, K. & Rehme, K. 1972 Negative eddy diffusivities for asymmetric turbulent velocity profiles? Int. J. Heat Mass Transfer, 15, 425.Google Scholar
Maubach, K. & Rehme, K. 1973 Pressure drop for parallel flow through a roughened rod cluster. Nucl. Engng Design, 25, 369.Google Scholar
Michiyoshi, I. & Nakajima, T. 1968 Fully developed turbulent flow in a concentric annulus. J. Nucl. Sci. Tech. 5, 354.Google Scholar
Min, T. C., Hoffman, H. W. & Peebles, F. N. 1971 A bilateral approach to the analysis of turbulent flow in an annulus. Nucl. Engng Design, 15, 65.Google Scholar
Nicol, A. A. & Medwell, J. O. 1964 Velocity profiles and roughness effects in annular pipes. J. Mech. Engng Sci. 6, 110.Google Scholar
Nikuradse, J. 1932 Gesetzmäzigkeiten der turbulenten Strömung in glatten Rohren. Forsch.-Arb. Geb. Ing.-Wes., VDI-Forschungsheft, no. 356.Google Scholar
Okiishi, T. H. & Serovy, G. K. 1964 Experimental velocity profiles for fully developed turbulent flow of air in concentric annuli. A.S.M.E. Paper, 64-WA/FE-32 (1964).Google Scholar
Patel, V. C. 1965 Calibration of the Preston tube and limitation on its use in pressure gradients. J. Fluid Mech. 23, 185.Google Scholar
Patel, V. C. 1973 A unified view of the law of the wall using mixing-length theory. Aero. Quart. 24, 55.Google Scholar
Preston, J. H. 1954 The determination of turbulent skin friction by means of Pitot tubes. J. Roy. Aero. Soc. 58, 109.Google Scholar
Quarmby, A. 1967a On the use of the Preston tube in concentric annuli. Aeron. J. Roy. Aero. Soc. 71, 47.Google Scholar
Quarmby, A. 1967b An experimental study of turbulent flow through concentric annuli. Int. J. Mech. Sci. 9, 205.Google Scholar
Quarmby, A. 1968a The ratio of the wall shear stresses in concentric annuli. Aeron. J. Roy. Aero. Soc. 72, 345.Google Scholar
Quarmby, A. 1968b An analysis of turbulent flow in concentric annuli. Appl. Sci. Res. 19, 250.Google Scholar
Quarmby, A. 1969 Improved application of the von Kármán similarity hypothesis to turbulent flow in ducts. J. Mech. Engng Sci. 11, 14.Google Scholar
Quarmby, A. & Anand, R. K. 1970 Turbulent heat transfer in concentric annuli with constant wall temperatures. J. Heat Transfer, 92, 33.Google Scholar
Rao, G. N. V. & Keshavan, N. R. 1972 Axisymmetric boundary layers in zero pressure-gradient flows. J. Appl. Mech. 39, 25.Google Scholar
Ratkowsky, D. A. 1966 Fluid friction and heat transfer in plain, concentric annuli. Can. J. Chem. Engng, 44, 8.Google Scholar
Rehme, K. 1972a Untersuchungen der Turbulenz- und Schubspannungsverteilung an einem Kreisrohr mit einem Hitzdraht-Anemometer. Kernforschungszentrum Karlsruhe Rep. KFK 1642.Google Scholar
Rehme, K. 1972b Pressure drop performance of rod bundles in hexagonal arrangements. Int. J. Heat Mass Transfer, 15, 2499.Google Scholar
Rehme, K. 1973 Simple method of predicting friction factors of turbulent flow in non-circular channels. Int. J. Heat Mass Transfer, 16, 933.Google Scholar
Roberts, A. 1967 A comment on the turbulent flow velocity profile in a concentric annulus. Int. J. Heat Mass Transfer, 10, 709.Google Scholar
Rothfus, R. R. 1948 Velocity gradients and friction in concentric annuli. Ph.D. thesis, Carnegie Institute of Technology.
Rothfus, R. R., Monrad, C. C. & Senecal, K. E. 1950 Velocity distribution and fluid friction in smooth concentric annuli. Ind. Engng Chem. 42, 2511.Google Scholar
Rothfus, R. R., Monrad, C. C., Sikchi, K. G. & Heideger, W. J. 1955 Isothermal skin friction in flow through annular sections. Ind. Engng Chem. 47, 913.Google Scholar
Rothfus, R. R., Sartory, W. K. & Kermode, R. I. 1966 Flow in concentric annuli at high Reynolds numbers. A.I.Ch.E. J. 12, 1086.Google Scholar
Rothfus, R. R., Walker, J. E. & Whan, G. A. 1958 Correlation of local velocities in tubes, annuli, and parallel plates. A.I.Ch.E. J. 4, 240.Google Scholar
Sartory, W. K. 1962 Turbulent flow in annular ducts. Ph.D. thesis, Carnegie Institute of Technology, Pittsburgh.
Smith, S. L., Lawn, C. J. & Hamlin, M. J. 1968 The direct measurement of wall shear stress in an annulus. C.E.G.B. Rep. RD/B/N 1232.Google Scholar
Tiedt, W. 1966 Bereehnung des laminaren und turbulenten Reibungswiderstandes konzentrischer und exzentrischer Ringspalte. Chem.-Ztg./Chem. Appl. 90, 813.Google Scholar
Tiedt, W. 1967 Berechnung des laminaren und turbulenten Reibungswiderstandes konzentrischer und exzentrischer Ringspalte. Chem.-Ztg./Chem. Appl. 91, 17, 149, 299, 569, 968.Google Scholar
Tiedt, W. 1968 Berschnung des laminaren und turbulenten Reibungswiderstandes konzentrischer und exzentrischer Ringspalte. Chem.-Ztg./Chem. Appl. 92, 76.Google Scholar
Wilson, N. W. & Medwell, J. O. 1968 An analysis of heat transfer for fully developed turbulent flow in concentric annuli. J. Heat Transfer, 90, 43.Google Scholar