6,375 research outputs found
Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms
It is well known that the drag in a turbulent flow of a polymer solution is significantly reduced compared to Newtonian flow. Here we consider this phenomenon by means of a direct numerical simulation of a turbulent channel flow. The polymers are modelled as elastic dumbbells using the FENE-P model. In the computations the polymer model is solved simultaneously with the flow equations, i.e. the polymers are deformed by the flow and in their turn influence the flow structures by exerting a polymer stress. We have studied the results of varying the polymer parameters, such as the maximum extension, the elasticity and the concentration. For the case of highly extensible polymers the results of our simulations are very close to the maximum drag reduction or Virk (1975) asymptote. Our simulation results show that at approximately maximum drag reduction the slope of the mean velocity profile is increased compared to the standard logarithmic profile in turbulent wall flows. For the r.m.s. of the streamwise velocity fluctuations we find initially an increase in magnitude which near maximum drag reduction changes to a decrease. For the velocity fluctuations in the spanwise and wall-normal directions we find a continuous decrease as a function of drag reduction. The Reynolds shear stress is strongly reduced, especially near the wall, and this is compensated by a polymer stress, which at maximum drag reduction amounts to about 40% of the total stress. These results have been compared with LDV experiments of Ptasinski et al. (2001) and the agreement, both qualitatively and quantitatively, is in most cases very good. In addition we have performed an analysis of the turbulent kinetic energy budgets. The main result is a reduction of energy transfer from the streamwise direction, where the production of turbulent kinetic energy takes place, to the other directions. A substantial part of the energy production by the mean flow is transferred directly into elastic energy of the polymers. The turbulent velocity fluctuations also contribute energy to the polymers. The elastic energy of the polymers is subsequently dissipated by polymer relaxation. We have also computed the various contributions to the pressure fluctuations and identified how these change as a function of drag reduction. Finally, we discuss some cross-correlations and various length scales. These simulation results are explained here by two mechanisms. First, as suggested by Lumley (1969) the polymers damp the cross-stream or wall-normal velocity fluctuations and suppress the bursting in the buffer layer. Secondly, the ‘shear sheltering’ mechanism acts to amplify the streamwise fluctuations in the thickened buffer layer, while reducing and decoupling the motions within and above this layer. The expression for the substantial reduction in the wall drag derived by considering the long time scales of the nonlinear fluctuations of this damped shear layer, is shown to be consistent with the experimental data of Virk et al. (1967) and Virk (1975)
Multiscale structure of turbulent channel flow and polymer, dynamics in viscoelastic turbulence
This thesis focuses on two important issues in turbulence theory of wall-bounded
flows. One is the recent debate on the form of the mean velocity profile (is it a
log-law or a power-law with very weak power exponent?) and on its scalings with
Reynolds number. In particular, this study relates the mean flow profile of the
turbulent channel flow with the underlying topological structure of the fluctuating
velocity field through the concept of critical points, a dynamical systems concept that
is a natural way to quantify the multiscale structure of turbulence. This connection
gives a new phenomenological picture of wall-bounded turbulence in terms of the
topology of the flow. This theory validated against existing data, indicates that
the issue on the form of the mean velocity profile at the asymptotic limit of infinite
Reynolds number could be resolved by understanding the scaling of turbulent kinetic
energy with Reynolds number.
The other major issue addressed here is on the fundamental mechanism(s) of
viscoelastic turbulence that lead to the polymer-induced turbulent drag reduction
phenomenon and its dynamical aspects. A great challenge in this problem is the computation
of viscoelastic turbulent flows, since the understanding of polymer physics is
restricted to mechanical models. An effective numerical method to solve the governing
equation for polymers modelled as nonlinear springs, without using any artificial
assumptions as usual, was implemented here for the first time on a three-dimensional
channel flow geometry. The superiority of this algorithm is depicted on the results,
which are much closer to experimental observations. This allowed a more detailed
study of the polymer-turbulence dynamical interactions, which yields a clearer picture
on a mechanism that is governed by the polymer-turbulence energy transfers
Small scale statistics of viscoelastic turbulence
The small scale statistics of homogeneous isotropic turbulence of dilute
polymer solutions is investigated by means of direct numerical simulations of a
simplified viscoelastic fluid model. It is found that polymers only partially
suppress the turbulent cascade below the Lumley scale, leaving a remnant energy
flux even for large elasticity. As a consequence, fluid acceleration in
viscoelastic flows is reduced with respect to Newtonian turbulence, whereas its
rescaled probability density is left unchanged. At large scales the velocity
field is found to be unaffected by the presence of polymers.Comment: 7 pages, 4 figure
Finite element methods for deterministic simulation of polymeric fluids
In this work we consider a finite element method for solving the coupled Navier-Stokes (NS) and Fokker-Planck (FP) multiscale model that describes the dynamics of dilute polymeric fluids. Deterministic approaches such as ours have not received much attention in the literature because they present a formidable computational challenge, due to the fact that the analytical solution to the Fokker-Planck equation may be a function of a large number of independent variables. For instance, to simulate a non-homogeneous flow one must solve the coupled NS-FP system in which (for a 3-dimensional flow, using the dumbbell model for polymers) the Fokker-Planck equation is posed in a 6-dimensional domain. In this work we seek to demonstrate the feasibility of our deterministic approach. We begin by discussing the physical and mathematical foundations of the NS-FP model. We then present a literature review of relevant developments in computational rheology and develop our deterministic finite element based method in detail. Numerical results demonstrating the efficiency of our approach are then given, including some novel results for the simulation of a fully 3-dimensional flow. We utilise parallel computation to perform the large-scale numerical simulations
Thermodynamics of viscoelastic rate-type fluids with stress diffusion
We propose thermodynamically consistent models for viscoelastic fluids with a
stress diffusion term. In particular, we derive variants of
compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion
term in the evolution equation for the extra stress tensor. It is shown that
the stress diffusion term can be interpreted either as a consequence of a
nonlocal energy storage mechanism or as a consequence of a nonlocal entropy
production mechanism, while different interpretations of the stress diffusion
mechanism lead to different evolution equations for the temperature. The
benefits of the knowledge of the thermodynamical background of the derived
models are documented in the study of nonlinear stability of equilibrium rest
states. The derived models open up the possibility to study fully coupled
thermomechanical problems involving viscoelastic rate-type fluids with stress
diffusion.Comment: The benefits of the knowledge of the thermodynamical background of
the derived models are now documented in the study of nonlinear stability of
equilibrium rest state
Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids
In this review, we describe and analyze a mesoscale simulation method for
fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now
called multi-particle collision dynamics (MPC) or stochastic rotation dynamics
(SRD). The method consists of alternating streaming and collision steps in an
ensemble of point particles. The multi-particle collisions are performed by
grouping particles in collision cells, and mass, momentum, and energy are
locally conserved. This simulation technique captures both full hydrodynamic
interactions and thermal fluctuations. The first part of the review begins with
a description of several widely used MPC algorithms and then discusses
important features of the original SRD algorithm and frequently used
variations. Two complementary approaches for deriving the hydrodynamic
equations and evaluating the transport coefficients are reviewed. It is then
shown how MPC algorithms can be generalized to model non-ideal fluids, and
binary mixtures with a consolute point. The importance of angular-momentum
conservation for systems like phase-separated liquids with different
viscosities is discussed. The second part of the review describes a number of
recent applications of MPC algorithms to study colloid and polymer dynamics,
the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of
viscoelastic fluids
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