Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session D12: Non-Newtonian Flows: Turbulence |
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Chair: Yves Dubief, University of Vermont Room: 200 |
Sunday, November 22, 2015 2:10PM - 2:23PM |
D12.00001: Elasto-Inertial Turbulence: From Subcritical Turbulence to Maximum Drag Reduction Yves Dubief, Samir Sid, Raphael Egan, Vincent Terrapon Elasto Inertial Turbulence (EIT) is a turbulence state found so far in polymer solutions. Upon the appropriate initial perturbation, an autonomous regeneration cycle emerges between polymer dynamics, pressure and velocity fluctuations. This cycle is best explained by the Poisson equation derived from viscoelastic flow models such as FENE-P (used in this study). This presentation provides an overview of the structure of EIT in 2D channel flows for Reynolds numbers ranging from $Re_\tau=10$ to 100 and for 3D simulations up to $Re_tau=300$. For flows below the Newtonian critical Reynolds number, EIT increases the drag. For higher Reynolds numbers, EIT is surmised to be the energetic bound of Maximum Drag Reduction (MDR), the asymptotic state of drag reduction in polymer solutions. The very existence of EIT at low Reynolds numbers ($Re_\tau < 60$) highlights a backward energy transfer from the small scale polymer dynamics to larger flow scales. Similar dynamics is identified at higher Reynolds numbers, which could explain why polymer flows never become fully laminar. [Preview Abstract] |
Sunday, November 22, 2015 2:23PM - 2:36PM |
D12.00002: The maximum drag reduction asymptote George H. Choueiri, Bjorn Hof Addition of long chain polymers is one of the most efficient ways to reduce the drag of turbulent flows. Already very low concentration of polymers can lead to a substantial drag and upon further increase of the concentration the drag reduces until it reaches an empirically found limit, the so called maximum drag reduction (MDR) asymptote, which is independent of the type of polymer used. We here carry out a detailed experimental study of the approach to this asymptote for pipe flow. Particular attention is paid to the recently observed state of elasto-inertial turbulence (EIT) which has been reported to occur in polymer solutions at sufficiently high shear. Our results show that upon the approach to MDR Newtonian turbulence becomes marginalized (hibernation) and eventually completely disappears and is replaced by EIT. In particular, spectra of high Reynolds number MDR flows are compared to flows at high shear rates in small diameter tubes where EIT is found at Re $<$ 100. [Preview Abstract] |
Sunday, November 22, 2015 2:36PM - 2:49PM |
D12.00003: Spatial-Temporal dynamics of Newtonian and viscoelastic turbulence Sung-Ning Wang, Michael Graham Introducing a trace amount of polymer into liquid turbulent flows can result in substantial reduction of friction drag. This phenomenon has been widely used in fluid transport, such as the Alaska crude oil pipeline. However, the mechanism is not well understood. We conduct direct numerical simulations of Newtonian and viscoelastic turbulence in large domains, in which the flow shows different characteristics in different regions. In some areas the drag is low and vortex motions are quiescent, while in other areas the drag is higher and the motions are more active. To identify these regions, we apply a statistical method, k-means clustering, which partitions the observations into k clusters by assigning each observation to its nearest centroid. The resulting partition maximizes the between-cluster variance. In the simulations, the observations are the instantaneous wall shear rate. Regions with different levels of drag are automatically identified by the partitioning algorithm. We find that the velocity profiles of the centroids exhibit characteristics similar to the individual coherent structures observed in minimal domain simulations. In addition, as viscoelasticity increases, polymer stretch becomes strongly correlated with wall shear stress. [Preview Abstract] |
Sunday, November 22, 2015 2:49PM - 3:02PM |
D12.00004: Scaling of energy amplification in the weak and strong elastic limits of viscoelastic shear flows Ismail Hameduddin, Tamer Zaki, Dennice Gayme We investigate energy amplification in viscoelastic parallel shear flows in terms of the steady-state variance maintained in the velocity and polymer stresses when either quantity is excited with white noise. We derive analytical expressions that show how this amplification scales with both Reynolds (Re) and Weissenberg (Wi) numbers. The analysis focuses on the streamwise-constant fields in the limits of high and low elasticity. By introducing stochastic forcing in both the velocity and the polymer stress dynamics, we show that at low elasticity the scaling retains a form similar to the well-known O(Re$^3$) relationship but with an added elastic correction. At high elasticity, however, the scaling is O(Wi$^3$) with a viscous correction. Our results demonstrate that energy amplification in a viscoelastic flow can be considerable even at low Re, correlating well with recent observations of elastic turbulence in creeping flows. We also note that forcing in the polymer stress dynamics can contribute significantly to the energy amplification. [Preview Abstract] |
Sunday, November 22, 2015 3:02PM - 3:15PM |
D12.00005: Streak instability in viscoelastic Couette flow Luca Biancofiore, Luca Brandt, Tamer Zaki The secondary instability of streaks and transition to turbulence in viscoelastic Couette flow are studied using direct numerical simulations (DNS). Viscoelasticity is modeled using the FENE-P constitutive equations, and both the polymer concentration and Weissenberg number are varied in order to assess their effect on transition at moderate Reynolds number, $Re=400$.The base streaks are obtained from nonlinear simulations of the Couette flow response to a streamwise vortex, and can be classified as quasi-Newtonian streaks according to the terminology introduced by Page \& Zaki (2014). At every streak amplitude of interest, harmonic forcing is introduced to trigger the secondary instability and breakdown to turbulence. The critical amplitude of this forcing decreases at higher Weissenberg number and also with increasing polymer concentration. The results demonstrate the destabilizing effect of elasticity at moderate Reynolds numbers. [Preview Abstract] |
Sunday, November 22, 2015 3:15PM - 3:28PM |
D12.00006: Elastic Turbulence in Parallel Shear Flows at Low Re Boyang Qin, Paulo Arratia In this talk, the flow of a viscoelastic fluid is experimentally investigated using particle velocimetry methods in a microfluidic device. The device is a long and straight microchannel that is 100-$\mu$m wide and deep; the channel has a short 3-mm region that contains an linear array of cylinders (perturbation region) followed by a 3-cm long and straight region (parallel shear region). We find that, both in the wake of the cylinders and far downstream in the parallel shear region, the flow is excited over a broad range of frequencies and wavelengths. These velocity fluctuations are consistent with the main features that characterize elastic turbulence at low Re. In the wake of the cylinder, we find that the decay in velocity temporal and spatial spectra is approximately -2.7 and -3.0, respectively. These fluctuations persist far downstream in the parallel shear flow region, but with a different power law for the spatial spectrum, -2.0. Our velocimetry measurements indicate that, as the flow moves from the perturbation to the parallel shear region, there is substantial decrease in large length scale fluctuations. Temporally, there is an increase in low frequency fluctuations (and decrease in high frequency velocity fluctuations). [Preview Abstract] |
Sunday, November 22, 2015 3:28PM - 3:41PM |
D12.00007: Transition to asymmetry in pipe flow of shear-thinning fluids: a linear instability? David Dennis, Chaofan Wen, Robert Poole Previous studies of shear-thinning fluids in pipe flow discovered that, although the time-averaged velocity profile was axisymmetric when the flow was laminar or fully turbulent, contrary to expectations it was asymmetric in the laminar-turbulent transition regime. We reveal that in fact the asymmetry is not induced by the laminar-turbulent transition process, but is an instability of the laminar state. Furthermore, the transition process is responsible for returning symmetry to the flow (i.e. the opposite to what was previously believed), which explains why the fully turbulent case is axisymmetric. The experiment was performed using an aqueous solution of xanthan gum (0.15\%), an essentially inelastic shear-thinning polymer solution. Stereoscopic particle image velocimetry was used to measure the 3C velocity vectors over the entire circular cross-section of the pipe, 220 pipe diameters downstream of the inlet. The deviation from the axisymmetric laminar state is observed to develop in the form of a supercritical bifurcation with square-root dependence on Reynolds number. The asymmetry is non-hysteretic and reversible, not only having a favoured location, but a preferred route between axisymmetry and asymmetry, which it adheres to regardless of the direction of the transition. [Preview Abstract] |
Sunday, November 22, 2015 3:41PM - 3:54PM |
D12.00008: Investigation of the required length for fully developed pipe flow with drag-reducing polymer solutions Yasaman Farsiani, Brian Elbing Adding trace amounts of long chain polymers into a liquid flow is known to reduce skin friction drag by up to 80{\%}. While polymer drag reduction (PDR) has been successfully implemented in internal flows, diffusion and degradation have limited its external flow applications. A weakness in many previous PDR studies is that there was no characterization of the polymer being injected into the turbulent boundary layer, which can be accomplished by testing a sample in a pressure-drop tube. An implicit assumption in polymer characterization is that the flow is fully developed at the differential pressure measurement. While available data in the literature shows that the entry length to achieve fully developed flow increases with polymeric solutions, it is unclear how long is required to achieve fully developed flow for non-Newtonian turbulent flows. In the present study, the pressure-drop is measured across a 1.05 meter length section of a 1.04 cm inner diameter pipe. Differential pressure is measured with a pressure transducer for different entry lengths, flow and polymer solution properties. This presentation will present preliminary data on the required entrance length as well as characterization of polymer solution an estimate of the mean molecular weight. [Preview Abstract] |
Sunday, November 22, 2015 3:54PM - 4:07PM |
D12.00009: Natural transition to turbulence in polymeric channel flow Sang Jin Lee, Tamer Zaki Natural transition in viscoelastic channel flow is investigated using direct numerical simulations (DNS), where the polymer is modeled using the FENE-P constitutive equations. The computations capture the amplification of the primary two-dimensional Tollmien-Schlichting (TS) waves, their secondary instability and ultimately the onset of turbulence. Various Weissenberg numbers (Wi) are simulated in order to assess the influence of elasticity. As Wi is increased, the primary TS waves initially become more linearly unstable, but are subsequently stabilized at higher Wi. This trend suggests that elasticity can either promote or delay transition to turbulence, and the DNS substantiate this prediction. In order to isolate the effect of the polymer on the secondary instability process, simulations are performed for a set of elastic parameters where the primary TS wave has the same linear growth rate as the Newtonian configuration. As a result, while the linear disturbance amplification is similar in the viscoelastic and Newtonian flows, the nonlinear saturated state of the TS waves differs in the two cases, as well as their secondary instability and breakdown to turbulence. The changes in the transition process are examined by analyzing the disturbance energy budget and spectra. [Preview Abstract] |
Sunday, November 22, 2015 4:07PM - 4:20PM |
D12.00010: Energy transfer and drag reduction in elasto-inertial turbulence laden with elongated contravariant and covariant polymers Kiyosi Horiuti We study elongation and energy-transfer process of polymers released in the homogeneous isotropic turbulence by connecting mesoscopic Brownian description of elastic dumbbells to macroscopic description for the solvent (DNS). The dumbbells are allowed to be advected either affinely with the macroscopically-imposed deformation (contravariant) or completely non-affinely (covariant). We consider the elasto-inertial regime in which the relaxation time of polymer is in the order of the eddy turnover time. Highly-elongated contravariant polymers remove more energy from the large scales than they can dissipate and transfer the excess energy back into the solvent as in P.C. Valente {\it et al.} (2014). By deriving the approximate solution of the constitutive equation for the polymer stress (Horiuti {\it et al.} 2013), we identified the term responsible for causing this transfer. The skewness of the strain-rate tensor $(S_{ik} S_{kl} S_{li})$ in the elastic energy production term transfer the elastic energy back into the smallest scale of the solvent and increase the dissipation. In the covariant polymers, this trend is reversed and leads to enhancement of drag reduction, in accordance with the hypothesis that stretched polymers may behave like rods and exhibit rigidity (de Gennes 1986). [Preview Abstract] |
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