Fluid Flow and Heat Transfer Structures of Oscillating Pipe Flows

Authors: Yan Su, Jane H. Davidson, F. A. Kulacki

Abstract:

The RANS method with Saffman-s turbulence model was employed to solve the time-dependent turbulent Navier-Stokes and energy equations for oscillating pipe flows. The method of partial sums of the Fourier series is used to analyze the harmonic velocity and temperature results. The complete structures of the oscillating pipe flows and the averaged Nusselt numbers on the tube wall are provided by numerical simulation over wide ranges of ReA and ReR. Present numerical code is validated by comparing the laminar flow results to analytic solutions and turbulence flow results to published experimental data at lower and higher Reynolds numbers respectively. The effects of ReA and ReR on the velocity, temperature and Nusselt number distributions have been di scussed. The enhancement of the heat transfer due to oscillating flows has also been presented. By the way of analyzing the overall Nusselt number over wide ranges of the Reynolds number Re and Keulegan- Carpenter number KC, the optimal ratio of the tube diameter over the oscillation amplitude is obtained based on the existence of a nearly constant optimal KC number. The potential application of the present results in sea water cooling has also been discussed.

Keywords: Keulegan-Carpenter number, Nusselt number, Oscillating pipe flows, Reynolds number

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078360

References:

[1] Falcão, A.F.O. (2010). "Wave energy utilization: A review of the technologies." Renewable and Sustainable Energy Reviews, vol. 14, pp. 899-918.
[2] Harish, R., Subhramanyan, E.E., Madhavan, S. and Vidyanand, S. (2010). "Theoretical model for evaluation of variable frequency drive for cooling water pumps in sea water based once through condenser cooling water systems." Applied Thermal Engineering, vol. 30, pp. 2051-2057.
[3] Orazov, B., Savas, O., O-Reilly, O.M. (2010). "On the dynamics of a novel ocean wave energy converter" Journal of Sound and Vibration, vol. 329, n 24, pp. 5058-5069.
[4] Prudell, J., Stoddard, M., Amon, E., Brekken, T. K. A., Von Jouanne, A., (2010) "A permanent-magnet tubular linear generator for ocean wave energy conversion" Transactions on Industry Applications, vol. 46, no. 6, pp. 2392-2400.
[5] Sergeev, S. I. (1966). "Fluid oscillations in pipes at moderate Reynolds numbers" Fluid Dynamics, vol. 1, no. 1, pp. 121-122.
[6] Merkli, P. and Thomann, H. (1975). "Transition to turbulence in oscillating pipe flow" Journal of Fluid Mechanics, vol. 68, part 3, pp. 567-575.
[7] Hino, M., Sawamoto, M. and Takasu, S. (1976). "Experiments on transition to turbulence in an oscillatory pipe flow." Journal of Fluid Mechanics, vol. 75, part 2, pp. 193-207.
[8] Ohmi, M., Iguchi, M., Kakehachi, K. and Masuda, T. (1982). "Transition to turbulence and velocity distribution in an oscillating pipe flow," Bulletin of the JSME, vol. 25, no. 201, pp. 365-371.
[9] Ramaprian, B. R. and Tu, S. W. (1983). "Fully developed periodic turbulent pipe flow. Part 2. The detailed structure of the flow." Journal of Fluid Mechanics, vol. 137, pp. 59-81.
[10] Ohmi, M., Iguchi, M. and Akao, F. (1984). "Laminar-turbulent transition and velocity profiles of oscillatory rectangular duct flows." Bulletin of the JSME, vol. 27, no. 229, pp. 1399-1406.
[11] Akhavan, R., Kamm, R. D. and Shapiro, A. H. (1991). "An investigation of transition to turbulence in bounded oscillatory Stokes flows. Part 1. Experiments" Journal of Fluid Mechanics, vol. 225, pp. 395-422.
[12] Blondeaux, P. (1987). "Turbulent boundary layer at the bottom of gravity waves." Journal of Hydraulic Research, vol. 25, no. 4, pp. 447- 464.
[13] Saffman, P. G. (1970). "A model for inhomogeneous turbulent flow" Proceedings of the Royal Society of London, Series A, vol. 317, pp. 417-433.
[14] Saffman, P. G. and Wilcox, P. C. (1974). "Turbulence-model predictions for turbulent boundary layers." AIAA Journal, vol. 12, no. 4, pp. 541-546.
[15] Koehler, W.J., Patankar, S.V. and Ibele, W. E., (1990) "Numerical prediction of turbulent oscillating flow in a circular pipe." Proceedings of the Intersociety Energy Conversion Engineering Conference, vol. 5, pp. 398-406.
[16] Hsu, C. T., Lu, X. and Kwan, M. K. (2000). "LES and RANS studies of oscillating flows over flat plate." Journal of Engineering Mechanics, vol. 126, no. 2, pp. 186-193.
[17] Hsu, C. T. and Kwan, M. K. (2001). "On the structure of oscillating channel flows" Technical Report of Hong Kong University of Science and Technology.
[18] Chai, B., Li, X., Zhou, S., Liu, D., Shao, M. and Peng, L. (2010). "Experimental study on energy saving of fluidized bed dryer with selfexcited mode oscillating-flow heat pipe heat exchanger", International Journal of Food Engineering, vol. 6, no. 2, Article 5.
[19] Wang, L. and Lu, X. (2003). "An investigation of turbulent oscillatory heat transfer in channel flows by large eddy simulation." International Journal of Heat and Mass Transfer, vol. 47 pp. 2161-2172
[20] Yamanaka, G., Kikura, H., Takeda, Y. and Aritomi, M. (2002). "Flow measurement on an oscillating pipe flow near the entrance using the UVP method." Experiments in Fluids, vol.32, pp. 212-220.
[21] Gerrard, J. and Hughes, M. (1971). "The flow due to an oscillating piston in a cylindrical tube: a comparison between experiment and a simple entrance flow theory." Journal of Fluid Mechanics, vol. 50, pp. 97-106.
[22] Dec, J. E., Keller, J. O. and Arpaci, V. S., (1992) "Heat transfer enhancement in the oscillating turbulent flow of a pulse combustor tail pipe." International Journal of Heat and Mass Transfer, vol. 35, n 9, pp. 2311-2325.
[23] Jacobs, S. J. (1984). "Mass transport in a turbulent boundary layer under a progressive water wave." Journal of Fluid Mechanics, vol. 146, pp. 303-312.
[24] Rush, T.A., Newell, T.A., and Jacobi, A.M. (1999). "An experimental study of flow and heat transfer in sinusoidal wavy passages." International Journal of Heat and Mass Transfer, vol. 42, pp. 1541- 1553.