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Post-transitional periodic flow in a straight square duct

Published online by Cambridge University Press:  23 November 2018

S. Gavrilakis*
Affiliation:
School of Environment and Geography, Harokopio University of Athens, Athens 17671, Greece
*
Email address for correspondence: [email protected]

Abstract

Direct numerical simulation of incompressible turbulence in a straight square duct finds the post-transition flow evolving substantially, and for Reynolds numbers based on the friction velocity and duct hydraulic radius greater than 600 a two-structure secondary flow regime has been established, suggesting the coexistence of two distinct sources of mean streamwise vorticity. The nominal source terms in the equation for the mean streamwise vorticity involve turbulent variables only, that allow us to identify the dominant dynamical process that marks and/or sustains the transverse mean flow. Close to the corner a mean profile instability is dominant, while farther away turbulent streamwise vorticity intensification is broadly distributed near the duct walls. The instability-driven secondary velocity maximum on the duct diagonals scales with the friction velocity. There is limited scaling of turbulent intensities on the wall bisectors.

Type
JFM Papers
Copyright
© 2018 Cambridge University Press 

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References

Biau, D., Soueid, H. & Bottaro, A. 2008 Transition to turbulence in duct flow. J. Fluid Mech. 596, 133142.Google Scholar
Deschamps, V.1988 Simulation numérique de la turbulence inhomogène incompressible dans un écoulement de canal plan. PhD thesis, Institut National Polytechnique de Toulouse.Google Scholar
Fang, X., Yang, Z., Wang, B.-C. & Bergstrom, D. J. 2017 Direct numerical simulation of turbulent flow in a spanwise rotating square duct at high rotation numbers. Intl J. Heat Fluid Flow 63, 8898.Google Scholar
Fischer, P. & Mullen, J. 2001 Filter-based stabilization of spectral element methods. C. R. Acad. Sci. Paris 332, 265270.Google Scholar
Gavrilakis, S. 1992 Numerical simulation of low-Reynolds number turbulent flow through a straight square duct. J. Fluid Mech. 244, 101129.Google Scholar
Hoagland, L. C.1960 Fully developed turbulent flow in straight rectangular ducts. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Huser, A. & Biringen, S. 1993 Direct numerical simulation of turbulent flow in a square duct. J. Fluid Mech. 257, 6595.Google Scholar
Karniadakis, G. Em. & Sherwin, S. J. 1999 Spectral/hp Element Methods for CFD. Oxford University Press.Google Scholar
Leriche, E., Perchat, L. E., Labrosse, G. & Deville, M. O. 2006 Numerical evaluation of the accuracy and stability properties of high-order direct Stokes solvers with or without temporal splitting. J. Sci. Comput. 26, 2543.Google Scholar
Lynch, R. E., Rice, J. R. & Thomas, D. H. 1964 Direct solution of partial difference equations by tensor product methods. Numer. Math. 6, 185199.Google Scholar
Marin, O., Vinuesa, R., Obabko, A. V. & Schlatter, P. 2016 Characterization of the secondary flow in hexagonal ducts. Phys. Fluids 28, 125101.Google Scholar
McKeon, B. J., Swanson, C. J., Zagarola, M. V., Donnelly, R. J. & Smits, A. J. 2004 Friction factors for smooth pipe flow. J. Fluid Mech. 511, 4144.Google Scholar
Moffat, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 118.Google Scholar
Owolabi, B. O., Dennis, D. J. C. & Poole, R. J. 2017 Turbulent drag reduction by polymer additives in parallel-shear flows. J. Fluid Mech. 827, R4.Google Scholar
Patera, A. T. 1984 A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54, 468488.Google Scholar
Pinelli, A., Uhlmann, M., Sekimoto, A. & Kawahara, G. 2010 Reynolds number dependence of mean flow structure in square duct turbulence. J. Fluid Mech. 644, 107122.Google Scholar
Sakai, Y.2016 Coherent structures and secondary motions in open duct flow. PhD thesis, Karlsruher Institut für Technologie.Google Scholar
Sharma, G.2004 Direct numerical simulation of particle-laden turbulence in a straight square duct. PhD thesis, Texas A&M University.Google Scholar
Timoshenko, S. & Goodier, J. N. 1951 Theory of Elasticity. McGraw-Hill.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Uhlmann, M., Pinelli, A., Kawahara, G. & Sekimoto, A. 2007 Marginally turbulent flow in a square duct. J. Fluid Mech. 588, 153162.Google Scholar
Yong, C. K.1988 Zur Wirkung von Polymer-Additiven auf die kohärente Struktur turbulenter Kanalströmungen. PhD thesis, University of Essen.Google Scholar
Zhang, H., Trias, F. X., Gorobets, A., Tang, Y. & Oliva, A. 2015 Direct numerical simulation of a fully developed turbulent square duct up to Re 𝜏 = 1200. Intl J. Heat Fluid Flow 54, 258267.Google Scholar