Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session F37: NonNewtonian Flows: Instability and TurbulenceNonNewtonian Turbulence

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Chair: Yves Dubief, University of Vermont Room: 303 
Monday, November 20, 2017 8:00AM  8:13AM 
F37.00001: Quantifying polymer deformation in viscoelastic turbulence: the geometric decomposition and a Riemannian approach to scalar measures Ismail Hameduddin, Charles Meneveau, Tamer Zaki, Dennice Gayme We develop a new framework to quantify the fluctuating behaviour of the conformation tensor in viscoelastic turbulent flows. This framework addresses two shortcomings of the classical approach based on Reynolds decomposition: the fluctuating part of the conformation tensor is not guaranteed to be positive definite and it does not consistently represent polymer expansions and contractions about the mean. Our approach employs a geometric decomposition that yields a positivedefinite fluctuating conformation tensor with a clear physical interpretation as a deformation to the mean conformation. We propose three scalar measures of this fluctuating conformation tensor, which respect the nonEuclidean Riemannian geometry of the manifold of positivedefinite tensors: fluctuating polymer volume, geodesic distance from the mean, and an anisotropy measure. We use these scalar quantities to investigate dragreduced viscoelastic turbulent channel flow. Our approach establishes a systematic method to study viscoelastic turbulence. It also uncovers interesting phenomena that are not apparent using traditional analysis tools, including a logarithmic decrease in anisotropy of the mean conformation tensor away from the wall and polymer fluctuations peaking beyond the buffer layer. [Preview Abstract] 
Monday, November 20, 2017 8:13AM  8:26AM 
F37.00002: Flow and stability of a viscoelastic liquid curtain Antoine Gaillard, Luc Lebon, Matthieu Roche, Cyprien Gay, Sandra Lerouge, Laurent Limat We experimentally investigate the flow of a sheet of viscoelastic liquid falling freely from a thin slit under gravity. We observe new phenomena that are not described by the Newtonian curtain theory derived by Brown and Taylor. For lowviscosity elastic fluids, the mean falling velocity does not reduce to a free fall, even far downstream from the slit: we observe a shift towards subgravity accelerations. This corresponds to a dramatic increase of the length of the transient regime where gravity is balanced by internal stress instead of inertia. The flow in the curtain is stable for dilute and semidilute aqueous solutions of polyethylene oxide (PEO), a flexible polymer, but it becomes time dependent and horizontally modulated for aqueous solutions of partially hydrolyzed polyacrylamide (HPAM), a semirigid polyelectrolyte. In the latter case, the curtain becomes varicose. This extrusion instability results from the existence of large vortices at the entrance of the slit, where the liquid undergoes a strong planar contraction, which creates overfed and underfed regions. Finally, we show that the varicose curtain is prone to hole opening in its thinner parts and may cease to exist. [Preview Abstract] 
Monday, November 20, 2017 8:26AM  8:39AM 
F37.00003: Stabilizing effect of elasticity on the inertial instability of submerged viscoelastic liquid jets. Bavand Keshavarz, Gareth McKinley The stability of submerged Newtonian and viscoelastic liquid jets is studied experimentally using flow visualization. Precise control of the amplitude and frequency of the imposed linear perturbations is achieved through a piezoelectric actuator attached to the nozzle. By illuminating the jet with a strobe light driven at a frequency slightly less than the frequency of the perturbation we slow down the apparent motion by large factors ($\sim 100,000$) and capture the phenomena with high temporal and spatial resolution. Newtonian liquid jets become unstable at moderate Reynolds numbers ($Re_j\sim 150$) and sinuous or varicose patterns emerge and grow in amplitude. As the jet moves downstream, the varicose waves gradually pile up in the sinuous ones due to the difference in their corresponding wave speeds, leading to a unique chevronlike morphology. Experiments with model viscoelastic polymer solutions show that this inertial instability is fully stabilized sufficiently large levels of elasticity. We compare our experimental results with the theoretical predictions of an elastic Rayleigh equation for an axisymmetric jet and show that the presence of streamline tension is indeed the stabilizing effect for inertioelastic jets. [Preview Abstract] 
Monday, November 20, 2017 8:39AM  8:52AM 
F37.00004: Viscoelastic fluidstructure interactions between flexible circular cylinder and wormlike micelle solution: Role of structural natural frequency Anita Dey, Yahya ModarresSadeghi, Jonathan Rothstein It is well known that when a flexible or flexiblymounted structure is placed perpendicular to a Newtonian fluid flow, it can oscillate due to the shedding of separated vortices at high Reynolds numbers. Unlike Newtonian fluids, the flow of viscoelastic fluids can become unstable even at infinitesimal Reynolds numbers due to a purely elastic flow instability. We have recently shown that these elastic flow instabilities can drive the motion of different flexible structures including sheets and cylinders. In this talk, we will present an investigation into the influence of a varying natural frequency of a flexible circular cylinder on the form, frequency and amplitude of the viscoelastic fluidstructure interactions with the goal of understanding lockin behavior for these interactions. The static and dynamic responses of the cylinder will be presented for a range of flow velocities for wormlike micelle solutions with varying viscosity and relaxation time. The time variation and state of stress of the flow field will be shown using particle image velocimetry and flowinduced birefringence images. Finally, the nonlinear dynamics of the structural motion will be investigated to understand an observed transition from a symmetric to an asymmetric flow field and oscillation behavior. [Preview Abstract] 
Monday, November 20, 2017 8:52AM  9:05AM 
F37.00005: Role of ElastoInertial Turbulence in Polymer Drag Reduction Yves Dubief, Samir Sid, Vincent Terrapon ElastoInertial Turbulence (EIT) is a peculiar state of turbulence found in dilute polymer solutions flowing in parallel wall flows over a wide range of Reynolds numbers. At subcritical Reynolds numbers, appropriate boundary conditions trigger EIT, a selfsustaining cycle of energy transfers between thin sheets of stretched polymers and velocity perturbations, which translates into an increase of friction drag. For critical and supercritical Reynolds numbers, polymer additives may lead to significant drag reduction, bounded by the asymptotic state known as Maximum Drag Reduction (MDR). The present research investigates the role of EIT in the dynamics of critical and supercritical Reynolds number wall flows. Using highfidelity direct numerical simulations of channel flows and the FENEP model, we establish that (i) EIT is twodimensional, (ii) the scales essential to the existence of EIT are subKolmogorov, and (iii) EIT drives MDR at low and possibly moderate Reynolds number turbulent flows. These findings were validated in two different codes and using unprecedented resolutions for polymer flows. [Preview Abstract] 
Monday, November 20, 2017 9:05AM  9:18AM 
F37.00006: On the Link Between Kolmogorov Microscales and Friction in WallBounded Flow of Viscoplastic Fluids Fabio Ramos, Hamid Anbarlooei, Daniel Cruz, Atila Silva Freire, Cecilia M. Santos Most discussions in literature on the friction coefficient of turbulent flows of fluids with complex rheology are empirical. As a rule, theoretical frameworks are not available even for some relatively simple constitutive models. In this work, we present a new family of formulas for the evaluation of the friction coefficient of turbulent flows of a large family of viscoplastic fluids. The developments combine an unified analysis for the description of the Kolmogorov's microscales and the phenomenological turbulence model of Gioia and Chakraborty (Phys. Rev. Lett. 96 044502 2006). The resulting Blasiustype friction equation has only Blasius' constant as a parameter, and tests against experimental data show excellent agreement over a significant range of Hedstrom and Reynolds numbers. The limits of the proposed model are also discussed. We also comment on the role of the new formula as a possible benchmark test for the convergence of DNS simulations of viscoplastic flows. The friction formula also provides limits for the Maximum Drag Reduction (MDR) for viscoplastic flows, which resembles MDR asymptote for viscoelastic flows. [Preview Abstract] 
Monday, November 20, 2017 9:18AM  9:31AM 
F37.00007: Elastoinertial turbulence in straight pipes at low Reynolds numbers George Choueiri, Bj\"orn Hof An early point of contention in the study of polymer drag reduction had been whether polymers delay transition to turbulence or cause it to occur at earlier Reynolds numbers (Re). Recent results have shown that at low polymer concentrations, the subcritical transition to Newtonian type turbulence (NTT) is delayed; however at higher concentrations an elastic instability is encountered which results in a distinct flow state dubbed elastoinertial turbulence (EIT). Here transition is continuous, fluctuation and friction levels are considerably lower than those for NTT and flow structures are qualitatively different. Several factors can influence the necessary Re for transition to occur for a specific polymer concentration; these include the type of polymer, its molecular weight, the solution viscosity and the proximity of the wall boundaries. By controlling these factors, we have found that chaotic motions can be measured at Re of the order of 1 even in straight smooth pipes as opposed to curved microchannels where curved streamlines cause a purely elastic instability. Furthermore we found that lowRe EIT is closely connected to turbulence that exists on the maximum drag reduction asymptote for polymer solutions with Re several orders of magnitude higher. [Preview Abstract] 
Monday, November 20, 2017 9:31AM  9:44AM 
F37.00008: An investigation of the linear mechanisms in polymer dragreduced turbulence using resolvent analysis Ryan McMullen, Beverley McKeon It is wellknown that small amounts of highmolecular weight polymers can drastically reduce turbulent drag in a liquid (Toms, 1948). Furthermore, recent work has shown that studying polymers in turbulence can shed light on the nature of the selfsustaining mechanisms of wall turbulence (White and Mungal, 2008; Graham, 2014). The focus of this talk is an investigation of the linear mechanisms at play in polymer dragreduced turbulent channel flow. The resolvent framework introduced by McKeon and Sharma (2010) for Newtonian turbulence is extended to the viscoelastic case in order to study the mostamplified velocity and polymer stretching modes, explored in the case of creeping flow by Jovanovi\'{c} and coworkers (Jovanovi\'{c} and Kumar, 2010; Lieu et al., 2013). Particular attention is given to the role of critical layers, which have been shown to be important in the dynamics of Newtonian turbulence (McKeon and Sharma, 2010). Additionally, comparisons will be made with the lower branch of the P4 family of exact coherent states, which closely reproduce statistical features of polymer dragreduced turbulence close to maximum drag reduction (Park and Graham, 2015). [Preview Abstract] 
Monday, November 20, 2017 9:44AM  9:57AM 
F37.00009: Drag reduction in plane Couette flow of dilute polymer solutions Nansheng Liu, Hao Teng, Xiyun Lu, Bamin Khomami Drag reduction (DR) in the plane Couette flow (PCF) by the addition of flexible polymers has been studied by direct numerical simulation (DNS) in this work. Special interest has been directed to explore the similarity and difference in the DR features between the PCF and the plane Poiseuille flow (PPF), and to clarify the effects of largescale structures (LSSs) on the nearwall turbulence. It has been demonstrated that in the nearwall region the dragreduced PCF shares typical DR features similar to those reported for the dragreduced PPF (White & Mungal 2008; Graham 2014), however in the core region intriguing differences are found between these two DR shear flows of polymeric solution. Specifically, in the core region of the dragreduced PCF, the polymer chains are stretched substantial and absorb kinetic energy from the turbulent fluctuations. In commensurate, peak values of conformation tensor components $\bm{C}_{yy}$ and $\bm{C}_{zz}$ occur in the core region. This finding is strikingly different from that of the dragreduced PPF. For the dragreduced PCF, the LSSs are found to have monotonically increasing effects on the nearwall flow as the Weissenberg number increases, and have their spanwise length scale unchanged. [Preview Abstract] 
Monday, November 20, 2017 9:57AM  10:10AM 
F37.00010: Simultaneous Rotational and Axial Flow of Nonlinear Fluids Nariman Ashrafi, Mehdi Yektapour, Mehdi Shafahi An axial flow is introduced to the rotational flow of pseudoplastic fluids in the gap between concentric cylinders. The outer cylinder is fixed while the inner one has simultaneous and independent rotational and translational motions. The fluid follows the CarreauBird model and mixed boundary conditions are imposed. The fourdimensional loworder equations resulted from Galerkin projection of the conservation of mass and momentum equations, includes highly nonlinear terms in the velocity components. Without axial flow, stability of the base radial flow is lost to the vortex structure at a lower critical Taylor number, with increase of the fluid pseudoplasticity. The vortices imply onset of a supercritical bifurcation which occurs in the rotational flow of linear fluids as well. In contrast to the Newtonian case, pseudoplastic Taylor vortices lose their stability at a second critical Taylor number is reached a second critical number that corresponds to the onset of a Hopf bifurcation. The axial flow, caused by the translational motion of the inner cylinder advance each critical point on the bifurcation diagram. The flow field and viscosity maps are provided for major stability regions [Preview Abstract] 
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