Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session M8: Non-Newtonian Flows II |
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Chair: Radhakrishna Sureshkumar, Syracuse University Room: 311 |
Tuesday, November 22, 2011 8:00AM - 8:13AM |
M8.00001: Re-examing the logarithmic dependence of the mean velocity distribution in polymer drag reduced wall-bounded flow Christopher White, Yves Dubief, Joe Klewicki The logarithmic dependence of the mean velocity distribution in polymer drag reduced wall-bounded flows is re-examined to study the effect of drag-reducing polymers on the von K\'{a}rm\'{a}n constant and to determine if the ``ultimate profile,'' corresponding to the state of maximum drag reduction, is truly logarithmic. The results of our findings show very different behaviors of the mean velocity distribution in polymer drag reduced flows than the classical view. First it is shown that at low drag reduction (DR) the slope of the logarithmic overlap region increases with increasing DR. Next, at some relatively high DR (which likely depends on Re), the inertially dominated logarithmic overlap region is eradicated. After which, the mean velocity distribution has a similar shape as a laminar flow and the perceived logarithmic scaling behavior corresponds to a thickened buffer layer and is not truly logarithmic. [Preview Abstract] |
Tuesday, November 22, 2011 8:13AM - 8:26AM |
M8.00002: Elastic turbulence in high Reynolds number polymer drag reduced flows Yves Dubief, Christopher White The present study discusses the existence of small scale dynamics resembling elastic turbulence in polymeric transitional and maximum drag reduction (MDR) flows. The observed flow patterns are driven by elastic stress and occur in regions of very low turbulence found before and after the breakdown of nonlinear instabilities in polymeric transitional flows leading to MDR. A state of polymer-dominated spanwise instabilities was found, resulting in a structure of the wall shear quite different than the structures observed in transitional Newtonian flow. Similar instabilities are observed in the wake of the head of hairpin vortices in simulated MDR flows, an extended region of extensional flow of the order of the Kolmogorov scale in the normal direction . The important Reynolds number is not that of flow ($Re_\tau=300$ and 600 for the Newtonian flows) but that of the local turbulent flow, which according to Kolmogorov approaches unity in the above mentioned flows, a reasonable magnitude for elastic turbulence. The existence of small scale elastic turbulence in transitional and MDR flows explains the phenomenon of early turbulence first observed in the 70s and challenges the notion that, in drag reduced flows, the energy flows only from large to small scales and never goes back from polymers to flow. [Preview Abstract] |
Tuesday, November 22, 2011 8:26AM - 8:39AM |
M8.00003: Elastic turbulence in Taylor-Couette Flow of Dilute Polymeric Solutions: A Direct Numerical Simulation Study Nansheng Liu, Bamin Khomami Despite tremendous progress in development of numerical techniques and constitutive theories for polymeric fluids in the past decade, Direct Numerical Simulation (DNS) of elastic turbulence has posed tremendous challenges to researchers engaged in developing first principles models and simulations that can accurately and robustly predict the dynamical behavior of polymeric flows. In this presentation, we report the first DNS of elastic turbulence in the Taylor-Couette (TC) flow. Specifically, our computations with prototypical constitutive equations for dilute polymeric solutions, such as the FENE-P model are capable of reproducing the essential features of the experimentally observed elastic turbulence in TC flow of this class of fluids, namely, randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales, and a significant increase of the flow resistance. Moreover, the experimentally measured Power Spectral Density of radial velocity fluctuations, i.e., two contiguous regions of power-law decay, -1.1 at lower frequencies and -2.2 at high-frequencies is accurately computed. [Preview Abstract] |
Tuesday, November 22, 2011 8:39AM - 8:52AM |
M8.00004: Turbulence structure and statistics in polymer-induced low vs. high drag reduction regimes: the origin of the maximum drag reduction asymptote Kyoungyoun Kim, Radhakrishna Sureshkumar Turbulent statistics and structure in polymer-induced low (20{\%}) and high (66{\%}) drag reduction (DR) regimes are studied via channel flow DNS at $Re_\tau $ =395. The initial hairpin eddy extracted from the conditional averages of the Q2 events is self-consistently evolved in the presence of polymer stresses using the FENE-P model. For low DR (Weissenberg number $We_\tau $ defined as the ratio of the polymer relaxation time $\lambda $ to the viscous time scale = 50), large counter polymer torque is observed only near the vortex legs. This suppresses the auto-generation of new vortices primarily only in the inner layer. For high DR ($We_\tau \ge $100), large counter polymer torque appears near the hairpin head and legs. This modifies both the inner and outer layer dynamics. When the Elasticity number $E$, defined as the ratio of $\lambda $ to the eddy turnover time, approaches unity, the effect of the polymer encompasses the whole channel and DR approaches an asymptotic value. This distinction between low and high DR dynamics is not robustly captured by low $Re$ simulations in which $E$ remains $O(1)$. [Preview Abstract] |
Tuesday, November 22, 2011 8:52AM - 9:05AM |
M8.00005: The maximum drag reduction asymptote Bj\"orn Hof, Devranjan Samanta, Christian Wagner Addition of a small amount of long chain polymers to a Newtonian solvent can lead to a dramatic drag reduction in turbulent flows. This effect has been extensively studied since its discovery in the late 1940's. The drag reduction at first is proportional to the polymer concentration (Weisenberg number) but then saturates to the maximum drag reduction (MDR) asymptote. It is commonly believed that drag reduction results from an adjustment of the turbulent flow structure due to the action of the polymers. We here present experimental results of turbulent pipe flows using dilute polyacrylamid solutions at relatively large Weisenberg numbers ($\sim$10). Our results show that for relatively low polymer concentrations transition to turbulence is postponed to higher Reynolds numbers. However when the Weisenberg number is increased further we find that the subcritical transition to turbulence, typical for Newtonian pipe flow disappears. Instead a supercritical instability is found at much lower Reynolds numbers which gives rise to a disordered flow. The observed drag of this disordered flow is identical to the well known MDR asymptote. [Preview Abstract] |
Tuesday, November 22, 2011 9:05AM - 9:18AM |
M8.00006: Grid Turbulence in PEO solutions Peter Monkewitz, Richard Vonlanthen Grid turbulence in dilute PEO solutions is studied experimentally in a small, closed loop hydraulic tunnel. To attain higher Reynolds numbers based on the Taylor microscale of the order of 100 and an inertial range of about one decade, a novel passive grid with tethered spheres has been developed. By carefully studying the evolution of turbulence spectra as function of the age of the PEO solution, i.e. of the degradation of polymer molecules, it has been possible to clearly identify a time-dependent ``Lumley'' wave number $\kappa_L$ where the fluid behavior switches abruptly from Newtonian to visco-elastic. This switch is characterized by a rather sharp transition from the Kolmogorov $\kappa^{-5/3}$ slope of the energy spectrum to a $\kappa^{-3}$ slope. Dimensional analysis shows that this corresponds to a switch from constant down-scale energy flux to a self-regulated constant eddy rate of strain. A simple model is proposed for the time-dependence of the Lumley scale $\kappa_L$. [Preview Abstract] |
Tuesday, November 22, 2011 9:18AM - 9:31AM |
M8.00007: Draw resonance in non-isothermal non-Newtonian viscous sheets Zheming Zheng, Chunfeng Zhou, Olus Boratav In this presentation, we will discuss the instability known in literature as the ``draw resonance'' for a non-Newtonian viscous sheet of glass with non-isothermal conditions. Both eigen-solutions and transient solutions are used in the stability analysis. We will focus our discussion on the effects of viscoelasticity and thermal conditions (local or global variations) on the draw resonance stability. Our study found that the stability can be enhanced by both viscoelastic effect and thermal heating. It also demonstrated that the critical draw ratio is increasing significantly with the Deborah number and is sensitive to how the sheet is heated or cooled. We will also present stability results comparing sheet draw and fiber draw. [Preview Abstract] |
Tuesday, November 22, 2011 9:31AM - 9:44AM |
M8.00008: Nonlinear elastic instabilities in parallel shear flows Lichao Pan, Alexander Morozov, Paulo Arratia It is a common assumption that, in the absence of inertia and curvature, the flow of a viscoelastic fluid is linearly stable to flow perturbations. Recent evidence, however, suggests that such flow may be unstable to a finite amplitude perturbation. In this talk, we present evidence of a subcritical nonlinear instability for the flow of a dilute polymeric solution in a straight microchannel (no curvature) at low \textit{Re}. The experimental configuration consists of a long, straight microchannel that is 100 $\mu $m deep, 100 $\mu $m wide and 3.0 cm long. The channel is divided into two main regions: a short ($\sim $0.3 cm) region where an array of cylinders is positioned in order to introduce perturbations in the flow, and a long ($\sim $2.7 cm) parallel flow region; a channel devoid of cylinders is also used for control. The flow is investigated using both dye advection and particle tracking velocimetry. Results show large velocity fluctuations far downstream (2 cm) away from the initial perturbation for strong enough and long lived disturbances. Small disturbances decay quickly under the same flow conditions (i.e. flow rate). A hysteresis loop, characteristic of subcritical instabilities, is observed. [Preview Abstract] |
Tuesday, November 22, 2011 9:44AM - 9:57AM |
M8.00009: Visco-plastic Lubrication: New Areas for Application Sarah Hormozi, Ian Frigaard Stable multi-layer flows can be achieved at high Reynolds numbers by using a yield stress fluids in a lubricating outer layer. These flows have been demonstrated to be linearly and nonlinearly stable as well as observable experimentally; see Frigaard (2001), Moyers-Gonzalez et al. (2004) and Huen et al. (2007). Recently, we have studied these flows computationally in the setting of a Newtonian core fluid surrounded by a Bingham lubricated fluid, within pipe and channel configurations; see Hormozi et al. (2011a) and Hormozi et al. (2011b). The results show that we are able to freeze in non-planar interface and form interesting patterns by retaining an unyielded plug region at the interface. Our studies open up new potential areas for application such as drop encapsulation and near net shape production of multi-layered products with axial variations. We give an overview of experimental results on establishing these exotic patterns.\\[0pt] References: I.A. Frigaard, J. Non-Newt. Fluid Mech., 100, (2001) 4976. M. Moyers-Gonzalez, I.A. Frigaard \& C. Nouar, J. Fluid Mech., 506, (2004) 117146. C.K. Huen, I.A. Frigaard \& D.M. Martinez, J. Non-Newt. Fluid Mech., 142, (2007) 150161. S. Hormozi, K. Wielage-Burchard \& I.A. Frigaard, J. Fluid Mech.,673, (2011) 432 467. S. Hormozi, K. Wielage-Burchard \& I.A. Frigaard, J. Non-Newt. Fluid Mech.,166, (2011) 262278. [Preview Abstract] |
Tuesday, November 22, 2011 9:57AM - 10:10AM |
M8.00010: Dynamics of inertialess flows of viscoelastic fluids: the role of uncertainty Mihailo Jovanovic, Binh Lieu, Satish Kumar We use techniques from control theory to demonstrate high sensitivity of inertialess channel flows of viscoelastic fluids. To counter this sensitivity we explicitly account for modeling imperfections, such as the approximate nature of polymer constitutive equations, by quantifying their influence on transient and asymptotic dynamics. Our approach has strong connections to the analysis of pseudospectra of linear operators, and it exhibits the importance of streamwise-elongated flow patterns in viscoelastic fluids. For streamwise-independent flows with high elasticity numbers and finite Weissenberg numbers, $W\!e$, we establish that the energy of velocity and polymer stress fluctuations scale as $O (W\!e^2)$ and $O (W\!e^4)$, respectively. This suggests that small amount of modeling uncertainty can destabilize nominally stable dynamics and promote transition to elastic turbulence. The underlying physical mechanism involves polymer stretching that introduces a lift-up of flow fluctuations similar to vortex tilting in inertia- dominated flows. The phenomenon examined here provides a possible route for the early stages of a bypass transition to elastic turbulence and might be exploited to enhance mixing in microfluidic devices. [Preview Abstract] |
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