Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T08:38:56.311Z Has data issue: false hasContentIssue false
  • English
  • Français

A Lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation

Published online by Cambridge University Press:  25 February 2008

MARKUS HOLZNER ,
A. LIBERZON ,
N. NIKITIN ,
B. LÜTHI ,
W. KINZELBACH  and
A. TSINOBER
MARKUS HOLZNER
Affiliation:
International Collaboration for Turbulence Research Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Str. 15, 8093 Zurich, Switzerland
A. LIBERZON
Affiliation:
International Collaboration for Turbulence Research School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
N. NIKITIN
Affiliation:
Institute of Mechanics, Moscow State University, 119899 Moscow, Russia
B. LÜTHI
Affiliation:
International Collaboration for Turbulence Research Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Str. 15, 8093 Zurich, Switzerland
W. KINZELBACH
Affiliation:
International Collaboration for Turbulence Research Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Str. 15, 8093 Zurich, Switzerland
A. TSINOBER
Affiliation:
International Collaboration for Turbulence Research School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel Institute for Mathematical Sciences and Department of Aeronautics, Imperial College, SW7 2AZ London, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

We report an analysis of small-scale enstrophy ω2 and rate of strain s2 dynamics in the proximity of the turbulent/non-turbulent interface in a flow without strong mean shear. The techniques used are three-dimensional particle tracking (3D-PTV), allowing the field of velocity derivatives to be measured and followed in a Lagrangian manner, and direct numerical simulations (DNS). In both experiment and simulation the Taylor-microscale Reynolds number is Reλ = 50. The results are based on the Lagrangian viewpoint with the main focus on flow particle tracers crossing the turbulent/non-turbulent interface. This approach allowed a direct investigation of the key physical processes underlying the entrainment phenomenon and revealed the role of small-scale non-local, inviscid and viscous processes. We found that the entrainment mechanism is initiated by self-amplification of s2 through the combined effect of strain production and pressure--strain interaction. This process is followed by a sharp change of ω2 induced mostly by production due to viscous effects. The influence of inviscid production is initially small but gradually increasing, whereas viscous production changes abruptly towards the destruction of ω2. Finally, shortly after the crossing of the turbulent/non-turbulent interface, production and dissipation of both enstrophy and strain reach a balance. The characteristic time scale of the described processes is the Kolmogorov time scale, τη. Locally, the characteristic velocity of the fluid relative to the turbulent/non-turbulent interface is the Kolmogorov velocity, uη.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 598 , 10 March 2008 , pp. 465 - 475
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Balachandar, S. & Maxey, M. R. 1989 Methods for evaluating fluid velocities in spectral simulations of turbulence. J. Comput. Phys. 83, 96–125.CrossRefGoogle Scholar
Bisset, D. K., Hunt, J. C. R. & Rogers, M. M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383–410.CrossRefGoogle Scholar
Corrsin, S. 1943 Investigation of flow in an axially symmetric heated jet in air. NACA ACR 3L23 and Wartime Rep. W94.Google Scholar
Corrsin, S. & Kistler, A. L. 1954 The free-stream boundaries of turbulent flows. NACA TN-3133, TR-1244, pp. 1033–1064.Google Scholar
Moffatt, H. K. (1965) The interaction of turbulence %with rapid uniform shear. SUDAER Report No. 242, Stanford University.Google Scholar
Holzner, M., Liberzon, A., Guala, M., Tsinober, A. & Kinzelbach, W. 2006 An experimental study on the propagation of a turbulent front generated by an oscillating grid. Exps. Fluids 41, 711–719.CrossRefGoogle Scholar
Holzner, M., Liberzon, A., Nikitin, N., Kinzelbach, W. & Tsinober, A. 2007 Small scale aspects of flows in proximity of the turbulent/non-turbulent interface. Phys. Fluids 19, 071702.CrossRefGoogle Scholar
Hoyer, K., Holzner, M., Lüthi, B., Guala, M., Liberzon, A. & Kinzelbach, W. 2005 3D scanning particle tracking velocimetry. Exps. Fluids 39, 923–934.CrossRefGoogle Scholar
Hunt, J. C. R., Eames, I. & Westerweel, J. 2006 Mechanics of inhomogeneous turbulence and interfacial layers. J. Fluid Mech. 554, 449–519.CrossRefGoogle Scholar
Landau, L. D. & Lifshits, E. M. 1959 Fluid Mechanics. Pergamon.Google Scholar
Lüthi, B., Tsinober, A. & Kinzelbach, W. 2005 Lagrangian measurement of vorticity dynamics in turbulent flow. J. Fluid Mech. 528, 87–118.CrossRefGoogle Scholar
Mathew, J. & Basu, A. J. 2002 Some characteristics of entrainment at a cylindrical turbulence boundary. Phys. Fluids 14, 2065–2072.CrossRefGoogle Scholar
Mordant, N., Crawford, A. M. & Bodenschatz, E. 2004 Experimental Lagrangian acceleration probability density function measurement. Physica D, 193, 245–251.Google Scholar
Nikitin, N. 2006 Finite-difference method for incompressible Navier-Stokes equations in arbitrary orthogonal curvilinear coordinates. J. Comput. Phys. 217, 759–781.CrossRefGoogle Scholar
Ott, S. & Mann, J. 2000 An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. J. Fluid Mech. 422, 207–223.CrossRefGoogle Scholar
Poulain, C., Mazellier, N., Gervais, P., Gagne, Y. & Baudet, C. 2004 Spectral vorticity and Lagrangian velocity measurements in turbulent jets. Flow, Turb. Combust. 72, 245–271.CrossRefGoogle Scholar
Tritton, D. J. 1988 Physical Fluid Dynamics 2nd edn. Clarendon. ISBN 0198 544936.Google Scholar
Tsinober, A. 2001 An Informal Introduction to Turbulence. Springer. ISBN 140200110X.CrossRefGoogle Scholar
Voth, G. A., LaPorta, A. Porta, A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121–160.CrossRefGoogle Scholar
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. 2005 Mechanics of the turbulent/non-turbulent interface of a jet. Phys. Rev. Lett. 95, 174501.CrossRefGoogle Scholar
Westerweel, J., Hoffmann, T., Fukushima, C. & Hunt, J. C. R. 2002 The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet. Exps. Fluids 33, 873–878.CrossRefGoogle Scholar