Commenced in January 2007
Paper Count: 30835
Heat Transfer Dependent Vortex Shedding of Thermo-Viscous Shear-Thinning Fluids
Abstract:Non-Newtonian fluid properties can change the flow behaviour significantly, its prediction is more difficult when thermal effects come into play. Hence, the focal point of this work is the wake flow behind a heated circular cylinder in the laminar vortex shedding regime for thermo-viscous shear thinning fluids. In the case of isothermal flows of Newtonian fluids the vortex shedding regime is characterised by a distinct Reynolds number and an associated Strouhal number. In the case of thermo-viscous shear thinning fluids the flow regime can significantly change in dependence of the temperature of the viscous wall of the cylinder. The Reynolds number alters locally and, consequentially, the Strouhal number globally. In the present CFD study the temperature dependence of the Reynolds and Strouhal number is investigated for the flow of a Carreau fluid around a heated cylinder. The temperature dependence of the fluid viscosity has been modelled by applying the standard Williams-Landel-Ferry (WLF) equation. In the present simulation campaign thermal boundary conditions have been varied over a wide range in order to derive a relation between dimensionless heat transfer, Reynolds and Strouhal number. Together with the shear thinning due to the high shear rates close to the cylinder wall this leads to a significant decrease of viscosity of three orders of magnitude in the nearfield of the cylinder and a reduction of two orders of magnitude in the wake field. Yet the shear thinning effect is able to change the flow topology: a complex K´arm´an vortex street occurs, also revealing distinct characteristic frequencies associated with the dominant and sub-dominant vortices. Heating up the cylinder wall leads to a delayed flow separation and narrower wake flow, giving lesser space for the sequence of counter-rotating vortices. This spatial limitation does not only reduce the amplitude of the oscillating wake flow it also shifts the dominant frequency to higher frequencies, furthermore it damps higher harmonics. Eventually the locally heated wake flow smears out. Eventually, the CFD simulation results of the systematically varied thermal flow parameter study have been used to describe a relation for the main characteristic order parameters.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1131305Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 522
 Andrade, E. N. D.: A theory of the viscosity of liquids. part 1. Philosophical Magazine, Vol. 17, pp. 497-511, 1934.
 CentaurSoftware, http://www.centaursoft.com.
 Bird, R. B.: Non-Newtonian behavior of polymeric liquids. Physica A: Statistical and Theoretical Physics, Vol. 118, No. 1-3, pp. 3-16, 1983.
 Bird, R. B., Curtiss, C. F.: Nonisothermal polymeric fluids. Rheol. Acta, 35:103109, 1983.
 Bird, R. B., Hassager, O.: Dynamics of Polymeric Liquids: Vol.1: Fluid Mechanics. Series: Dynamics of Polymeric Liquids, London, New York, John Wiley & Sons, 1987.
 Bogn´ar, G., Kov´acs, J.: Non-isothermal steady flow of power-law fluids between parallel plates. International Journal of Mathematical Models and Methods in Applied Science, 6(1), 2012.
 Carreau, P. J.: Rheological equations from molecular network theories. J. Rheol., Vol. 16, No. 1, pp. 99-127, 1972.
 Chabral, B.; Leedom, L. C.: Imaging Vector Fields Using Line Integral Convolution. In: Proceedings of SIGGRAPH 93. pp. 263-270, New York, 1993.
 Coelho, P. M.; Pinho, F. T. Vortex shedding in cylinder flow of shear-thinning fluids. II. Flow characteristics. J. Non-Newtonian Fluid Mech. Vol. 110, pp. 177-193, 2003.
 Eisenlohr, H., Eckelmann, H.: Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds number. Phys. Fluids A 1 (2), pp. 189192, 1989.
 Ferry, J. D.: Viscoleastic Properties of Polymers. Third edition, New York; John Wiley & Sons, 1980.
 Fey, U., K¨onig, M., Eckelmann, H.: A new Strouhal Reynolds number relationship for the circular cylinder in the range 47 ¡ Re ¡ 2 105. Phys. Fluids 10, pp. 15471549, 1998.
 von Ka´rma´n, Th.: U¨ ber den Mechanismus des Widerstandes, den ein bewegter K¨orper in einer Fl¨ussigkeit erf¨ahrt. Nachrichten der K. Gesellschaft der Wissenschaften zu G¨ottingen, Mathematisch-physikalische Klasse, 1911.
 von Ka´rma´n, Th., Rubach. H.: U¨ ber den Mechanismus des Flu¨ssigkeitsund Luftwiderstandes. Physikalische Zeitschrift, 13, pp. 4959, 1911.
 Knopp, T., Zhang, X., Kessler, R. and Lube, G.: Enhancement of an industrial finite-volume code for large-eddy-type simulation of incompressible high Reynolds number flow using near-wall modelling. Journal of Computer Methods in Applied Mechanics and Engineering, Vol. 199, pp. 890-902, 2010.
 Monkewitz P. A., Williamson, C. H. K., Miller, G. D.: Phase dynamics of K´arm´an vortices in cylinder wakes, Phys. Fluids 8, pp. 9196, 1996.
 Ostwald, W.: Ueber die rechnerische Darstellung des Strukturgebietes der Viskosit¨at, Kolloid Zeitschrift 47 (2), pp. 176-187, 1929.
 Owens, R. G.,Phillips, T. N.: Computational Rheology. Computational Rheology. Imperial College Press, ISBN 9781860941863, 2002.
 Skelland, A. H. P.: Non-Newtonian flow and heat transfer. John Wiley & Sons, New York, 1967.
 Soares, A. A., Ferreira, J. M., Chhabra, R. P.: Flow and Forced Convection Heat Transfer in Crossflow of Non-Newtonian Fluids over a Circular Cylinder. Ind. Eng. Chem. Res. Vol. 44, pp. 5815-5827, 2003.
 V´ıt, T., Ren, M., Tr´avn´ıˇcek, Z.,: Marˇs´ık, F.: The influence of temperature gradient on the StrouhalReynolds number relationship for water and air. Experimental Thermal and Fluid Science, Vol. 31, pp. 751-760, 2007.
 Wang, A.-B. , Tr´avn´ıˇcek, Z., Chia, K.-C.: On the relationship of effective Reynolds number and Strouhal number for the laminar vortex shedding of a heated circular cylinder. Phys. Fluids 12 (6), pp. 1401-1410, 2000.
 Wendt, J. F. (Ed.): Computational Fluid Dynamics - An Introduction. Third edition, Berlin, Heidelberg; Springer, 2009.
 Williams, M. L., Landel, R. F., Ferry, J. D: The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids. Journal of the American Chemical Society, Vol. 77, pp. 3701-3707, 1955.
 Williamson, C. H. K.: Vortex dynamics in the cylinder wake, Ann. Rev. Fluid. Mech. 28, pp. 477539, 1996.