Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session R19: Non-Newtonian Flows IV: Turbulence |
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Chair: Yves Dubief, University of Vermont Room: 28E |
Tuesday, November 20, 2012 1:00PM - 1:13PM |
R19.00001: The onset of elasto-inertial turbulence Bjorn Hof, Devranjan Samanta, Yves Dubief, Markus Holzner, Christof Schaefer, Alexander Morozov, Christian Wagner, Jose Manuel Gallardo Ruiz A new type of turbulence is discovered for elastic fluids such as dilute solutions of long chain polymers and surfactants. Experiments are carried out in channel and pipe flows with diameters ranging from a few centimeters to a few hundred microns. At large enough shear rates an instability is found giving rise to disordered motion. For sufficiently large concentrations this instability already occurs at very low Reynolds numbers, where for Newtonian fluids flows are always laminar. The data for different pipe diameters reveal that the onset of the instability is governed by the shear rate and not by the Reynolds number. The ensuing disordered flow has a larger drag than the laminar one. The friction scaling coincides with the well known maximum drag reduction asymptote inferring that this asymptote is the characteristic friction scaling of elasto-inertial turbulence. [Preview Abstract] |
Tuesday, November 20, 2012 1:13PM - 1:26PM |
R19.00002: A new state of turbulence: Elasto-inertial turbulence Yves Dubief, Devranjan Samanta, Markus Holzner, Cristof Schafer, Alexander Morozov, Christian Wagner, Bjorn Hof, Vincent Terrapon, Julio Soria The elasticity of polymer solutions is found to generate a new state of turbulence, elasto-inertial turbulence (EIT), characterized by an interplay between elastic and flow instabilities. Experiments and direct numerical simulations (DNS) in pipe and channel flows demonstrate the emergence of EIT at Reynolds numbers much lower than the critical Reynolds number for transition to turbulence in Newtonian flows. EIT causes the friction factor to deviate from the laminar solution and subsequently transition to the maximum drag reduction asymptote around Re=1800. EIT is a self-sustained mechanism that arises from the interactions between fluctuations of extensional viscosity, velocity and pressure. The polymer solution elasticity controls the growth of flow instability, resulting in transitional-like flows at high Reynolds numbers. The existence of EIT is not limited to pipe, channel or boundary layer flows, and evidence of EIT will be discussed in other flows, including natural convection using DNS. [Preview Abstract] |
Tuesday, November 20, 2012 1:26PM - 1:39PM |
R19.00003: Experimental measurements of turbulent polymer solutions Alexandre de Chaumont Quitry, Douglas H. Kelley, Nicholas H. Ouellette Complex fluids modify turbulent flows over a broad range of scales, including scales much larger than the physical size of the fluid microstructure. Models have attempted to explain this phenomenon on the basis of assumptions such as enhanced effective viscosity or a critical length scale separating different flow regimes. We attempt to constrain such models with experimental measurements of bulk turbulence in a dilute solution of long-chain polyacrylamide in water. We use high-speed cameras and Lagrangian Particle Tracking Velocimetry to image the central region of a von K\'{a}rm\'{a}n swirling flow, in which counter-rotating impellers inject kinetic energy inertially. We observe that concentrations as low as a few parts per million can drastically modify the energy cascade. [Preview Abstract] |
Tuesday, November 20, 2012 1:39PM - 1:52PM |
R19.00004: Nonlinear dynamics of turbulent drag reduction by polymers Michael Graham, Sung-Ning Wang, Friedemann Hahn Minimal channel flow of Newtonian and drag-reducing polymer solutions is studied computationally. Even in the Newtonian limit, intervals of ``active'' and ``hibernating'' turbulence exist, the latter displaying many features of the maximum drag reduction (MDR) asymptote observed in polymer solutions: weak streamwise vortices, nearly nonexistent streamwise variations and a mean velocity gradient that quantitatively matches experiments (i.e. the Virk log-law). Polymer stretching is very weak during hibernation. As viscoelasticity increases, the frequency of the hibernation intervals increases, leading to flows that increasingly resemble MDR. This observation can be explained with a simple mathematical model that posits that the lifetime of an active turbulence interval is the time that it takes for the turbulence to stretch polymer molecules to a certain threshold value beyond which the active turbulence is suppressed. An extended Karhunen-Loeve analysis is introduced and used to illustrate how the velocity and stress fields change as MDR is approached. These results and others indicate that the MDR dynamics are governed by an underlying Newtonian state -- a saddle point in phase space -- that is unmasked as viscoelasticity suppresses normal turbulent fluctuations. [Preview Abstract] |
Tuesday, November 20, 2012 1:52PM - 2:05PM |
R19.00005: Elastic turbulence of polymer solutions at low Re in a straight channel Laetitia Martinie, Julien Beaumont, Hugues Bodiguel, Hamid Kellay, Annie Colin At low Reynolds number (Re$<$1), elastic turbulence develops in polymer solutions flowing in curvilinear flows for Weissenberg numbers Wi beyond a given threshold Wic. Unlike inertial turbulence (Re$>>$1), elastic turbulence is due to their normal stress anisotropy [Groisman and Steinberg, Nature, 2000]. It has only been shown very recently, both theoretically [Morozov and van Saarlos, Phys. Report, 2007] and experimentally [Bonn et al., PRE 2011], that elastic turbulence could also occur in rectilinear flows, provided that the perturbation amplitude is sufficiently high. In this work, we aim to characterize the consequences of this turbulence on the velocity profile and the flow rate-pressure relationship of high molecular weight Polyaccrylamide solutions flowing in a straight channel. By varying both flow rate and polymer concentration, we are able to explore a wide range of Wi. Flows driven by a controlled pressure in a microfluidic straight channel are characterized using particle image velocimetry. For Wi $<$ Wic, the measured velocity field is well accounted for by the bulk flow curve of the shear thinning fluid. For Wi $>$ Wic, this prediction is not valid anymore and a high level of fluctuations is observed. In addition, velocity profiles can be described by a logarithmic behavior in areas where the fluid is highly sheared, similarly to what is observed in inertial turbulence in a rectilinear geometry. A model based on an Olroyd B fluid behavior has been developed to explain the experimental profiles observed. [Preview Abstract] |
Tuesday, November 20, 2012 2:05PM - 2:18PM |
R19.00006: Energy spectra in polymer-doped turbulent soap films Rory Cerbus, Walter Goldburg, Pinaki Chakraborty, Nathan Flynn, Chien-Chia Liu We investigate the energy spectra of turbulent soap films doped with a dilute amount of a very large molecular weight polymer ($>$ 1M). We perform experiments in a soap-film channel that in the absence of polymers manifests decaying turbulence and a direct enstrophy cascade: the energy spectrum E(k) $\propto$ k$^{-3}$. For polymer-doped flow, where the polymer is added gently to the soapy solution, we observe that the energy spectrum switches to E(k) $\propto$ k$^{-5/3}$, which is consistent with the inverse energy cascade of forced 2D turbulence. This switching of the spectral exponent from 3 to 5/3 occurs for polymer concentrations as low as 2 wppm. For lower concentrations, the spectral exponent is unaffected. We also find that our results are sensitive to the method of polymer doping. If we stir our polymer-doped solution repeatedly, the effect of the polymer diminishes: the exponent of the energy spectrum switches back from 5/3 to 3. [Preview Abstract] |
Tuesday, November 20, 2012 2:18PM - 2:31PM |
R19.00007: Elastic Energy Transfer in Turbulence of Dilute Polymer Solution Heng-Dong Xi, Eberhard Bodenschatz, Haitao Xu We present an experimental study of the energy transfer in the bulk of a turbulent flow with small amount long-chain polymer additives. By varying the Reynolds numbers $R_\lambda$, Wissenberg number $Wi$ and polymer concentration $\phi$. We test quantitively the elastic theory proposed by de Gennes and Tabor (Europhys. Lett., 1986; Physica A, 1986). The rate of energy transfer by polymer elasticity as inferred from the theory is consistent with that measured from the second order Eulerian structure functions. The unknown parameter $n$ in the theory, which represents the flow topology of the stretching field, is found to be nearly $1$. Based on energy transfer rate balance, We propose an elastic length scale, $r_\epsilon$, which describes the effect of polymer elasticity on turbulence energy cascade and captures the scale dependence of the elastic energy transfer rate. [Preview Abstract] |
Tuesday, November 20, 2012 2:31PM - 2:44PM |
R19.00008: Direct Numerical Simulation of Elastically Modified Turbulent Taylor-Couette Flow Nansheng Liu, Bamin Khomami Direct Numerical Simulations (DNS) of elastically modified turbulent Taylor-Couette (TC) flow are carried out to study the effect of polymer additives on the dynamics of the flow, using a fully spectral method in conjunction with the FENE-P model for the description of polymer chain dynamics. Significant polymer-induced drag increase is observed for the TC flow, which is strikingly different from the findings of drag reduction in the turbulent viscoelastic channel flow. Careful examination of turbulent, viscous and elastic stresses show that the elastically modified wall structures are mainly responsible for the polymer-induced drag increase. In addition, turbulence statistics are analyzed to develop the correlations between the polymer body force and velocity. The probability density functions (PDFs) of the velocity and polymer stress fluctuations are illustrated to reveal the stochastic characteristics of the flow. [Preview Abstract] |
Tuesday, November 20, 2012 2:44PM - 2:57PM |
R19.00009: Mechanics and characteristics of transition to turbulence in elasto-inertial turbulence Vincent Terrapon, Julio Soria, Yves Dubief Numerical experiments of transition in elasto-inertial turbulent channel flows are used to highlight the mechanisms of transition and characterize the MDR regime. Specifically, the pressure kernel from the generalized pressure Poisson equation is used to demonstrate the role of elastic instabilities in inducing and sustaining a turbulent-like flow. Additionally, dynamic mode decomposition is applied to statistically steady viscoelastic flows at different Reynolds number to identify the relative contributions of elastic and inertial instabilities. It is shown that elastic instabilities can be triggered through long-range interactions from disturbances in the free-stream, similarly to by-pass transition, and are then sufficient to self-sustain. When the Reynolds number is increased, the relative contribution of inertial instabilities becomes more important, and the flow demonstrates features that are characteristic to Newtonian turbulent flows (e.g., streaks, quasi-streamwise vortices), although at lower intensity. [Preview Abstract] |
Tuesday, November 20, 2012 2:57PM - 3:10PM |
R19.00010: Studying the Topology and Dynamics of Elasto-inertial Channel Flow Turbulence Using the Invariants of the Velocity Gradient Tensor and Dynamic Mode Decomposition Julio Soria, Vincent Terrapon, Yves Dubief Direct numerical simulations (DNS) of the transition to and fully developed elasto-inertial turbulence (EIT) of a polymer solution in a channel flow has been used as a basis for the study of the topology and dynamics of these flows. The Reynolds number in these DNS ranged from 500 to 5000. The topology of these flows was studied through the joint probability density functions (JPDFs) of the second and third invariants of the velocity gradient tensor (VGT), $Q_A$ and $R_A$ respectively and the JPDFs of the second invariants of the rate-of-strain tensor and the rate-of-rotation tensor, $Q_S$ and $Q_W$ respectively. The results suggest that these transitional and fully developed EIT flows are predominantly made up of vortex sheets. Dynamic mode decomposition has been undertaken on the second invariant of the VGT, $Q_A$, which reveals that the most amplified mode is a two-dimensional structure located in the near-wall region. A ``discontinuity'' is observed close to the wall, which corresponds closely to the location of extrema of the mean polymer extension and is hypothesized to be a critical layer. [Preview Abstract] |
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