Skip to main content Accessibility help
×
Home

The structure and budget of turbulent kinetic energy in front of a wall-mounted cylinder

  • Wolfgang Schanderl (a1), Ulrich Jenssen (a1), Claudia Strobl (a1) and Michael Manhart (a1)
  • Please note a correction has been issued for this article.

Abstract

We investigate the flow and turbulence structure in front of a cylinder mounted on a flat plate by a combined study using highly resolved large-eddy simulation and particle image velocimetry. The Reynolds number based on the bulk velocity and cylinder diameter is $Re_{D}=39\,000$ . As the cylinder is placed in an open channel, we take special care to simulate open-channel flow as the inflow condition, including secondary flows that match the inflow in the experiment. Due to the high numerical resolution, subgrid contributions to the Reynolds stresses are negligible and the modelled dissipation plays a minor role in major parts of the flow field. The accordance of the experimental and numerical results is good. The shear in the approach flow creates a vertical pressure gradient, inducing a downflow in the cylinder front. This downflow, when deflected in the upstream direction at the bottom plate, gives rise to a so-called horseshoe vortex system. The most upstream point of flow reversal at the wall is found to be a stagnation point which appears as a sink instead of a separation point in the symmetry plane in front of the cylinder. The wall shear stress is largest between the main (horseshoe) vortex and the cylinder, and seems to be mainly governed by the strong downflow in front of the cylinder as turbulent stresses are small in this region. Due to a strong acceleration along the streamlines, a region of relatively small turbulent kinetic energy is found between the horseshoe vortex and the cylinder. When passing under the horseshoe vortex, the upstream-directed jet formed by the deflected downflow undergoes a deceleration which gives rise to a strong production of turbulent kinetic energy. We find that pressure transport of turbulent kinetic energy is important for the initiation of the large production rates by increasing the turbulence level in the upstream jet near the wall. The distribution of the dissipation of turbulent kinetic energy is similar to that of the turbulent kinetic energy. Large values of dissipation occur around the centre of the horseshoe vortex and near the wall in the region where the jet decelerates. While the small scales are nearly isotropic in the horseshoe vortex centre, they are anistotropic near the wall. This can be explained by a vertical flapping of the upstream-directed jet. The distribution and level of dissipation, turbulent and pressure transport of turbulent kinetic energy are of crucial interest to turbulence modelling in the Reynolds-averaged context. To the best of our knowledge, this is the first time that these terms have been documented in this kind of flow.

Copyright

Corresponding author

Email address for correspondence: michael.manhart@tum.de

References

Hide All
Apsilidis, N., Diplas, P., Dancey, C. L. & Bouratsis, P. 2015 Time-resolved flow dynamics and Reynolds number effects at a wall–cylinder junction. J. Fluid Mech. 776, 475511.
Apsilidis, N., Khosronejad, A., Sotiropoulos, F., Dancey, C. L. & Diplas, P. 2012 Physical and numerical modeling of the turbulent flow field upstream of a bridge pier. In International Conference on Scour and Erosion 6, Paris, Ecole des Arts et Metiers - Paris Tech.
Baker, C. J. 1979 The laminar horseshoe vortex. J. Fluid Mech. 95, 347367.
Bruns, J., Dengel, P. & Fernholz, H. H.1992 Mean flow and turbulence measurements in an incompressible two-dimensional turbulent boundary layer. Part I: data. Tech. Rep., Herman-Föttinger-Institut für Thermo- und Fluiddynamik, TU Berlin.
Clauser, F. H. 1954 Turbulent boundary layer in adverse pressure gradients. J. Aero. Sci. 21, 91108.
Dargahi, B. 1989 The turbulent flow field around a circular cylinder. Exp. Fluids 8 (1–2), 112.
Demuren, A. O. & Rodi, W. 1984 Calculation of turbulence-driven secondary motion in non-circular ducts. J. Fluid Mech. 140, 189222.
Devenport, W. J. & Simpson, R. L. 1990 Time-dependent and time-averaged turbulence structure near the nose of a wing–body junction. J. Fluid Mech. 210, 2355.
Dey, S. & Raikar, R. V. 2007 Characteristics of horseshoe vortex in developing scour holes at piers. J. Hydraul Engng 133 (4), 399413.
Escauriaza, C. & Sotiropoulos, F. 2011 Reynolds number effects on the coherent dynamics of the turbulent horseshoe vortex system. Flow Turbul. Combust. 86 (2), 231262.
Fernholz, H. H. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32 (4), 245311.
Graf, W. H. & Istiarto, I. 2002 Flow pattern in the scour hole around a cylinder. J. Hydraul Res. 40 (1), 1320.
Gresho, P. M. & Lee, R. 1981 Don’t suppress the wiggles – they’re telling you something. Comput. Fluids 9, 223253.
Kähler, C. J., Scharnowski, S. & Cierpka, C. 2012 On the uncertainty of digital PIV and PTV near walls. Exp. Fluids 52 (6), 16411656.
Kähler, C. J., Scholz, U. & Ortmanns, J. 2006 Wall-shear-stress and near-wall turbulence measurements up to single pixel resolution by means of long-distance micro-PIV. Exp. Fluids 41 (2), 327341.
Kirkil, G. & Constantinescu, G. 2015 Effects of cylinder Reynolds number on the turbulent horseshoe vortex system and near wake of a surface-mounted circular cylinder. Phys. Fluids 27, 075102.
Kumar, A. & Kothyari, U. C. 2011 Three-dimensional flow characteristics within the scour hole around circular uniform and compound piers. J. Hydraul Engng 138 (5), 420429.
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical simulation experiments. In Proceedings of the IBM Scientific Computing Symposium on Environmental Sciences, IBM Form No. 320–1951, pp. 195210. IBM Data Processing Division.
Manhart, M. 2004 A zonal grid algorithm for DNS of turbulent boundary layers. Comput. Fluids 33 (3), 435461.
Melville, B. W. & Raudkivi, A. J. 1977 Flow characteristics in local scour at bridge piers. J. Hydraul. Res. 15 (4), 373380.
Nezu, I. & Nakagawa, H. 1993 Turbulence in Open-Channel Flows. A.A. Balkema.
Nicoud, F. & Ducros, F. 1999 Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62 (3), 183200.
Paik, J., Escauriaza, C. & Sotiropoulos, F. 2007 On the bimodal dynamics of the turbulent horseshoe vortex system in a wing–body junction. Phys. Fluids 19, 045107.
Peller, N.2010 Numerische Simulation turbulenter Strömungen mit Immersed Boundaries. PhD thesis, Technische Universität München.
Peller, N., Duc, A. L., Tremblay, F. & Manhart, M. 2006 High-order stable interpolations for immersed boundary methods. Intl J. Numer. Meth. Fluids 52, 11751193.
Pfleger, F.2011 Experimentelle Untersuchung der Auskolkung um einen zylindrischen Brückenpfeiler. PhD thesis, Technische Universität München.
Pope, S. B. 2011 Turbulent Flows. Cambridge University Press.
Raffel, M., Willert, C., Wereley, S. & Kompenhans, J. 2007 Particle Image Velocimetry – A Practical Guide, 2nd edn. Springer.
Roulund, A., Sumer, B. M., Fredsoe, J. & Michelsen, J. 2005 Numerical and experimental investigation of flow and scour around a circular pile. J. Fluid Mech. 534, 351401.
Ryu, S., Emory, M., Iaccarino, G., Campos, A. & Duraisamy, K. 2016 Large-eddy simulation of a wing–body junction flow. AIAA J. 54 (3), 793804.
Schanderl, W. & Manhart, M. 2015 Non-equilibrium near wall velocity profiles in the flow around a cylinder mounted on a flat plate. In 15th European Turbulence Conference, TU Delft.
Schanderl, W. & Manhart, M. 2016 Reliability of wall shear stress estimations of the flow around a wall-mounted cylinder. Comput. Fluids 128, 1629.
Schlichting, H. & Gersten, K. 2006 Boundary Layer Theory. Springer.
Simpson, R. L. 2001 Junction flows. Annu. Rev. Fluid Mech. 33, 415443.
Strobl, C., Jenssen, U. & Manhart, M.2016 Reconstructing velocity statistics from single pixel ensemble correlation PIV. Exp. Fluids (submitted).
Tanaka, T. & Eaton, J. K. 2007 A correction method for measuring turbulence kinetic energy dissipation rate by PIV. Exp. Fluids 42 (6), 893902.
Unger, J. & Hager, W. H. 2007 Down-flow and horseshoe vortex characteristics of sediment embedded bridge piers. Exp. Fluids 42, 119.
Werner, H.1991 Grobstruktursimulation der turbulenten Strömung über eine querliegende Rippe in einem Plattenkanal bei hoher Reynoldszahl. PhD thesis, Technische Universität München.
Westerweel, J., Geelhoed, P. F. & Lindken, R. 2004 Single-pixel resolution ensemble correlation for micro-PIV applications. Exp. Fluids 37 (3), 375384.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed

A correction has been issued for this article: