Normal stress difference and drag reduction mechanism in Johnson-Segalman viscoelastic turbulence

ORAL

Abstract

The mechanism of turbulent drag reduction in the polymer- diluted flow is studied using the DNS data for homogeneous isotropic turbulence and pipe flow. The polymer stress $\tau$ is obtained by solving the non-affine Johnson-Segalman constitutive equation. The drag reduction is maximal when non- affinity is either minimum or maximum, but the largest reduction is achieved when non-affinity is maximum. The pressure force due to $\tau$, $\nabla p_\tau$, tends to oppose to that due to the solvent $\nabla p_s$, e.g., in the core of the vortex tube in which $p_s$ is minimal, $p_\tau$ bulges out. The normal-stress difference (NSD) is obtained on the basis of new eigenvectors which span the isosurfaces of vortex tube and sheet. It is shown in both flows that the first NSD is predominantly positive and the second is negative along the sheets and tubes. Thus, an extra tension is exerted on the sheet and tube. With an increase of effective viscosity by an addition of elongation viscosity, resistance of the sheet and tube to their stretching is enhanced. When non-affinity is maximum, the transformation of the sheet into the tube is restrained because the sheet tends to snap back to the original flat form due to viscoelastic effect. When non-affinity is minimum, the tubes are created but its stretching is suppressed. In both cases, cascade of the energy into the small scales is restricted leading to the reduction of drag.

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Authors

  • Kiyosi Horiuti

    Tokyo Institute of Technology, Japan

  • Sanjeeb Bose

    University of Alberta, Canada, Nagoya Institute of Technology, Japan, Case Western Reserve University, NASA GRC, The Dow Chemical Company, MIT, McGill University, Center for Soft Matter Research, New York University, IUSTI-CNRS UMR 6595 - Polytech Marseille - Aix-Marseille Universit\'e, University of Chicago, Multiscale Modeling and Simulation, Faculty EEMCS, University of Twente, The Netherlands, University of California, Irvine, University of California, Los Angeles, University of Toronto, University of Cambridge, ENS Lyon, Northwestern University, Politecnico di Milano, Emory University, University of Washington, Department of Mechanical and Aeronautical Engineering, Clarkson University, Korea Advanced Institute of Science and Technology (KAIST), Dept. of Civil and Environmental Engineering, University of Texas at San Antonio, U. S. Army, ARDEC, Picatinny Arsenal, The University of Tokyo, Old Dominion University, Syracuse University, Texas A\&M University Corpus Christi, University of Bristol, University of Exeter, Dept. of Mechanical Engineering, National Chiao Tung University, Taiwan, Tokyo University of Science, ForWind, Institute of Physics - University of Oldenburg, University of Puerto Rico, California Institute of Technology, Naval Research Laboratory, DAMTP, University of Cambridge, Department of Physics, University of Arizona, IMEDEA, Spain, Ecole Polytecnique, Grupo de Mecanica de Fluidos, ESI, Universidad de Sevilla, SPAIN, Drexel University, Ewha University, Konkuk University, Departamento de Fisica, FCFM, Universidad de Chile, Departamento de Fisica, Universidad del Bio-Bio, Laboratoire de Physique Statistique, Ecole Normale Superieure, Brown U., UTRC, Georgia Institute of Technology, University of Minnesota, Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061, USA, Department of Power Engineering, Jadavpur University, Kolkata 700032, India, Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA, UCSD, Stanford University, Duke University, Molecular and Cellular Biology, UC Berkeley, Dept. of Physics, CU Boulder, Integrative Biology, UC Berkeley, Dept. of Mathematics, UC Berkeley, Masschusetts Institute of Technology, New York University, Massachusetts Institute of Technology, Brigham Young University, Sandia National Laboratories, Mechanical and Aerospace Engineering, Princeton University, The Chinese University of Hong Kong, Universita Tor Vergata, CSU Chico, University of Illinois, Urbana-Champaign, St. Anthony Falls Laboratory, University of Minnesota, Norwegian Defence Research Establishment (FFI), Department of Mechanical Engineering, Royal Military College of Canada, Department of Chemical Engineering, University of California, Santa Barbara, Department of Chemical Engineering, Imperial College London, University of Maryland, University of Maryland and University of Texas at Austin, Johns Hopkins University, Princeton Plasma Physics Laboratory, Nova Photonics, Hokkaido University, Ilmenau University of Technology, Universite Pierre et Marie Curie, University of Cincinnati, ETH Zurich, Orbital Technologies Corp, Yonsei University, Defence Science and Technology Organisation, Institute of High Performance Computing, University of Melbourne, The University of Texas at Austin, Austin, TX, University of New Hampshire, Dept. of Physics, Eindhoven University of Technology, P.O.Box 513, 5600MB Eindhoven, The Netherlands, Eindhoven University of Technology, Eindhoven, The Netherlands, ESPCI ParisTech, LOF, Indian Institute of Technology Madras, University of Pennsylvania, University of Delaware, Nanjing University, China, National Science Foundation and University of Massachusetts Amherst, University of Massachusetts Amherst, Military Technical College, Cairo, Egypt, Center for Turbulence Research, Stanford University, Tokyo Institute of Technology, Nanyang Technological University, University of Illinois, University of Texas-Brownsville, The University of New Mexico, The University of Manchester, Lawrence Livermore National Laboratory, Mazda Motor Corporation, Hiroshima University, Arizona State University, Max Planck Institute of Colloids and Interfaces, D-14476 Potsdam, Germany, Cornell University, Combustion Research Facility, Sandia National Laboratory, Livermore, CA, Stanford University; 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