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Non-Unique Solutions in Turbulent Curved Pipe Flow

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Direct and Large-Eddy Simulation II

Part of the book series: ERCOFTAC Series ((ERCO,volume 5))

Abstract

The mean flow and turbulent statistics obtained from the direct numerical simulation of a fully developed turbulent flow through a curved pipe with circular cross-section are reported. The Reynolds number based on the bulk velocity and the pipe diameter is approximately 5500, the radius of curvature is equal to five pipe diameters. In the cross-section of the pipe a strong secondary motion is observed. It is shown that in the turbulent case multiple time mean solutions of governing equations exist.

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References

  • Batchelor, G.K., 1967, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Boersma, B.J. & Nieuwstadt, F.T.M., 1996a, Large Eddy simulation of turbulent flow in a curved pipe, J. Fluids Eng.

    Google Scholar 

  • Boersma, B.J. & Nieuwstadt, F.T.M., 1996b, Direct Numerical Simulation of the flow in a bend, In the Proceedings of: 3rd International Symposium on Engineering Turbulence Modelling and Measurements, Elsevier.

    Google Scholar 

  • Bradshaw, P., 1987, Turbulent secondary flows, Ann. Rev. Fluid Mech., 19, 53–74.

    Article  ADS  Google Scholar 

  • Eggels, J.G.M., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J., Friedrich R., & Nieuwstadt, F.T.M., 1994, Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175–209

    Article  ADS  Google Scholar 

  • Collins, W.M., & Dennis, S.C.R., 1975, The steady motion of a viscous fluid in a curved tube, Q. J. Mech. Appl. Math., 28, 133–156.

    Article  MATH  Google Scholar 

  • Germano, M., 1989, The Dean equations extended to a helical pipe flow. J. Fluid Mech., 203, 289–305.

    Article  ADS  MATH  Google Scholar 

  • Gavrilakis, S., 1992, Numerical simulation of low Reynolds-number turbulent flow through a straight square duct, J. Fluid Mech., 244, 101–129.

    Article  ADS  Google Scholar 

  • Ito, H., 1987, Flow in curved pipes, JSME International Journal, 30, 543–552.

    Article  Google Scholar 

  • Kim, J., Moin, P., and Moser, R., 1987 Turbulence statistics in fully developped channel flow at low Reynolds number, J. Fluid Mech., 177, 133–166.

    Article  ADS  MATH  Google Scholar 

  • Morse, P.M., & Feshbach, H., 1953, Methods of Theoretical Physics, McGraw-Hill, New York

    MATH  Google Scholar 

  • Orlandi, P. & Fatica, M., 1995, Direct simulation of a turbulent pipe rotating along the axis, Submitted to: J. Fluid Mech.

    Google Scholar 

  • Ramshankar, R. & Sreenivasan, K.R., 1988, A paradox concerning the extended Stokes series solution for the pressure drop in coiled pipes. Phys. Fluids, 31, 1339–1347.

    Article  ADS  Google Scholar 

  • Swarztrauber, P., 1977, The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson’ s equation on a rectangle, SIAM Review, 19,490–501.

    Article  MATH  MathSciNet  Google Scholar 

  • Taylor, G.I., 1929, The criterion for turbulence in curved pipes, Proc. R. Soc. London Ser. A., 124, 243–249. (also in: The collected paper of G.I. Taylor).

    Article  ADS  MATH  Google Scholar 

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© 1997 Springer Science+Business Media Dordrecht

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Boersma, B.J., Nieuwstadt, F.T.M. (1997). Non-Unique Solutions in Turbulent Curved Pipe Flow. In: Chollet, JP., Voke, P.R., Kleiser, L. (eds) Direct and Large-Eddy Simulation II. ERCOFTAC Series, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5624-0_24

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  • DOI: https://doi.org/10.1007/978-94-011-5624-0_24

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6370-8

  • Online ISBN: 978-94-011-5624-0

  • eBook Packages: Springer Book Archive

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