Viscoelastic effects on higher order statistics and on coherent structures in turbulent channel flow

In this work we study, using the results of direct numerical simulations [Housiadas and Beris, “Polymer-induced drag reduction: Viscoelastic and inertia effects of the variations in viscoelasticity and inertia,” Phys. Fluids 15, 2369 (2003)], the effects of changes in the flow viscoelasticity and the friction Reynolds number on several higher order statistics of turbulence, such as the Reynolds stress, the enstrophy, the averaged equations for the conformation tensor, as well as on the coherent structures through a Karhunen–Loeve (K-L) analysis and selected flow and conformation visualizations. In particular, it is shown that, as the zero friction Weissenberg number Weτ0 increases (for a constant zero friction Reynolds number Reτ0) dramatic reductions take place in many terms in the averaged equations for the Reynolds stresses and in all terms of the averaged enstrophy equations. From a Karhunen–Loeve analysis of the eigenmodes of the flow we saw that the presence of viscoelasticity increases significantl...

[1]  A. B. Metzner,et al.  Turbulent flow characteristics of viscoelastic fluids , 1964, Journal of Fluid Mechanics.

[2]  F. A. Schraub,et al.  The structure of turbulent boundary layers , 1967, Journal of Fluid Mechanics.

[3]  John L. Lumley,et al.  Drag Reduction by Additives , 1969 .

[4]  A. B. Metzner,et al.  Turbulence phenomena in drag reducing systems , 1969 .

[5]  J. Lumley.  Stochastic tools in turbulence , 1970 .

[6]  John L. Lumley,et al.  Drag reduction in turbulent flow by polymer additives , 1973 .

[7]  P. S. Virk.  Drag reduction fundamentals , 1975 .

[8]  John L. Lumley,et al.  Drag reduction in two phase and polymer flows , 1976 .

[9]  A. B. Metzner.  Polymer solution and fiber suspension rheology and their relationship to turbulent drag reduction , 1977 .

[10]  Steven A. Orszag,et al.  Transition to turbulence in plane Poiseuille and plane Couette flow , 1980, Journal of Fluid Mechanics.

[11]  C. R. Smith,et al.  The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer , 1983, Journal of Fluid Mechanics.

[12]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[13]  R. Byron Bird,et al.  From molecular models to the solution of flow problems , 1988 .

[14]  Nadine Aubry,et al.  The dynamics of coherent structures in the wall region of a turbulent boundary layer , 1988, Journal of Fluid Mechanics.

[15]  R. Preisendorfer,et al.  Principal Component Analysis in Meteorology and Oceanography , 1988 .

[16]  W. G. Tiederman,et al.  Turbulent structure in low-concentration drag-reducing channel flows , 1988, Journal of Fluid Mechanics.

[17]  Parviz Moin,et al.  Characteristic-eddy decomposition of turbulence in a channel , 1989, Journal of Fluid Mechanics.

[18]  L. Sirovich,et al.  Plane waves and structures in turbulent channel flow , 1990 .

[19]  W. G. Tiederman.  The Effect of Dilute Polymer Solutions on Viscous Drag and Turbulence Structure , 1990 .

[20]  Albert Gyr,et al.  Structure of Turbulence and Drag Reduction , 1990 .

[21]  Knight,et al.  Kolmogorov inertial range for inhomogeneous turbulent flows. , 1990, Physical review letters.

[22]  Lawrence Sirovich,et al.  Propagating Structures in Wall-Bounded Turbulent Flows , 1991 .

[23]  S. K. Robinson,et al.  Coherent Motions in the Turbulent Boundary Layer , 1991 .

[24]  Lawrence Sirovich,et al.  Coherence and chaos in a model of turbulent boundary layer , 1992 .

[25]  Peter S. Bernard,et al.  Vortex dynamics and the production of Reynolds stress , 1993, Journal of Fluid Mechanics.

[26]  Thomas J. Hanratty,et al.  Origin of turbulence‐producing eddies in a channel flow , 1993 .

[27]  Sirovich,et al.  Dynamical model of wall-bounded turbulence. , 1994, Physical review letters.

[28]  Lawrence Sirovich,et al.  The Karhunen–Loéve decomposition of minimal channel flow , 1997 .

[29]  Robert A. Handler,et al.  Direct numerical simulation of the turbulent channel flow of a polymer solution , 1997 .

[30]  Antony N. Beris,et al.  Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: effect of the variation of rheological parameters , 1998 .

[31]  John Kim,et al.  DIRECT NUMERICAL SIMULATION OF TURBULENT CHANNEL FLOWS UP TO RE=590 , 1999 .

[32]  Ahmet Omurtag,et al.  On Low-Dimensional Modeling of Channel Turbulence , 1999 .

[33]  R. Handler,et al.  Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow , 2001 .

[34]  Robert A. Handler,et al.  Energy dynamics in a turbulent channel flow using the Karhunen‐Loéve approach , 2002 .

[35]  Stefano Sibilla,et al.  Polymer stress statistics in the near-wall turbulent flow of a drag-reducing solution , 2002 .

[36]  Renzo Piva,et al.  DNS of wall turbulence: dilute polymers and self-sustaining mechanisms , 2002 .

[37]  Antony N. Beris,et al.  Polymer-induced drag reduction: Effects of the variations in elasticity and inertia in turbulent viscoelastic channel flow , 2003 .

[38]  Bo Yu,et al.  Effect of Weissenberg number on the flow structure: DNS study of drag-reducing flow with surfactant additives , 2003 .

[39]  Jung Yul Yoo,et al.  Drag reduction by polymer additives in a turbulent channel flow , 2003, Journal of Fluid Mechanics.

[40]  Jung Yul Yoo,et al.  Maximum drag reduction in a turbulent channel flow by polymer additives , 2002, Journal of Fluid Mechanics.

[41]  R. Fox.  Computational Models for Turbulent Reacting Flows , 2003 .

[42]  Drag reduction by polymers in turbulent channel flows: Energy redistribution between invariant empirical modes. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  van den Bhaa Ben Brule,et al.  Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms , 2003, Journal of Fluid Mechanics.

[44]  Q. Zhou,et al.  A comparison of FENE and FENE-P dumbbell and chain models in turbulent flow , 2003 .

[45]  K. Housiadas,et al.  Characteristic scales and drag reduction evaluation in turbulent channel flow of nonconstant viscosity viscoelastic fluids , 2004 .

[46]  Kostas D. Housiadas,et al.  An efficient fully implicit spectral scheme for DNS of turbulent viscoelastic channel flow , 2004 .