Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session L19: Non-Newtonian Flows II: Turbulence and Instabilities |
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Chair: Jeff Oishi, University of New Hampshire Room: 250 C |
Monday, November 25, 2024 8:00AM - 8:13AM |
L19.00001: Machine Learning Period-Doubling in Inertialess Viscoelastic Kolmogorov Flow Muhammad Abdullah, Becca Thomases, Paulo E. Arratia The flow of dilute polymer solutions can exhibit highly complex spatio-temporal chaos, even at vanishing inertia, a phenomenon commonly referred to as purely elastic turbulence. Curiously, however, the mechanism of transition to such dynamical states is thus far poorly understood, particularly in rectilinear geometries. Recently, it has been demonstrated that the inertialess Kolmogorov flow of an Oldroyd-B fluid can achieve elastic turbulence -- even in two dimensions -- following a series of period-doubling bifurcations driven by narwhal-like coherent structures in the elastic stress. Here, we attempt to construct low-dimensional models of this behavior, leveraging Sparse Identification of Nonlinear Dynamics (SiNDy) to reduce the flow trajectory to that described by a small set of energetically efficient POD modes. Similar approaches have also been adopted for extensional geometries, such as the canonical four-roll mill configuration. Our work has implications for low-order representations of non-Newtonian flow dynamics captured via machine learning techniques. |
Monday, November 25, 2024 8:13AM - 8:26AM |
L19.00002: Influence of Carreau number on relaminarization of turbulent Shear Thickening channel flow Emanuele Milocco, Georgios Giamagas, Francesco Zonta, Alfredo Soldati We investigate numerically the relaminarization of a turbulent non-Newtonian shear thickening fluid in a channel geometry. The flow of a shear thickening fluid is characterized by the Carreau number which is the ratio between, λ, the fluid characteristic time constant and the flow characteristic timescale based on the shear rate of the channel. Using Direct Numerical Simulation (DNS), we start from an initial Newtonian turbulent channel flow at shear Reynolds number Re=180 and we investigate the effect of increasing Carreau number on the turbulent statistics and coherent structures. The shear dependent rheology is modelled via a Carreau viscosity model, and we range Cu over three orders of magnitude: Cu = 0.1, 1,5,10. For the same mean pressure gradient ∇p, we obtain an effective shear Reynolds number based on the wall viscosity of Re=111,76,58,52 respectively. Results show that the mean flow velocity decreases and velocity fluctuations become more isotropic, leading to increased Reynolds stresses, relative to the Newtonian case. Increasing Cu, we observe a general decrease in the turbulence activity, induced by an increase in the wall viscosity, corresponding to a more rare presence of vortical structures and reflected by the turbulence modules. However, we observe that at the same low effective shear Reynolds, at which a Newtonian fluid would flow in laminar condition, the shear thickening flow still exhibits turbulence, without a logarithmic layer. |
Monday, November 25, 2024 8:26AM - 8:39AM |
L19.00003: Elastic and elasto-inertial turbulence in channel flows Moritz F Linkmann, Alexander N Morozov Turbulence production in wall-bounded parallel shear flows of Newtonian fluids is mostly located close to the bounding walls. In contrast, our recent work demonstrates [1] that in purely elastic turbulence the production is concentrated along the centre plane of the channel away from the walls. This begs the question as to what type of production occurs in turbulent flows of Non-Newtonian fluids at finite Reynolds number, that is, in elasto-inertial turbulence. Observations suggesting wall-mode production have been made from numerical simulations, however, recent experimental results suggest a co-existence of wall- and centre-mode activity. |
Monday, November 25, 2024 8:39AM - 8:52AM |
L19.00004: The effectiveness of targeted polymer injection for turbulent drag redution Ryan Kelly, David B Goldstein, Saikishan Suryanarayanan, Robert a Handler, Anton Burtsev The effect of polymer drag reduction by targeted injection is studied in comparison to that of a uniform concentration (or polymer ocean) in a turbulent channel flow. Direct Numerical Simulations are performed using a pseudo-spectral method to solve the coupled equations of a viscoelastic fluid using the FENE-P model. Light and heavy particles are used to carry the polymer in some cases, and polymer is artificially injected into specific flow regions in the other cases. To study drag reduction, the global mass flux through the channel is computed over time and compared to a turbulent channel with no polymer. The overall effectiveness of targeted polymer injection is presented based on mass flux and its effect on turbulent structures. Various factors are discussed including relevant time scales and a correlation between polymer concentration and drag-producing structures. |
Monday, November 25, 2024 8:52AM - 9:05AM |
L19.00005: Josephson-Anderson Relation as Diagnostic of Turbulent Drag Reduction by Polymers Samvit Kumar, Simon S Toedtli, Tamer A Zaki, Gregory L Eyink The detailed Josephson-Anderson relation, which equates instantaneously the volume-integrated vorticity flux and the work by pressure-drop, has been the key to drag-reduction in superconductors and superfluids. We employ a classical version of this relation to investigate the dynamics of polymer drag-reduced channel flows, particularly in the High-extent Drag Reduction (HDR) regime which is known to exhibit strong space-time intermittency. We show that high drag is not created instantaneously by near-wall coherent vortex structures as assumed in prior works. The vorticity flux in turbulent channel flow is described by competing wall normal fluxes of spanwise vorticity, namely a drag-increasing "down-gradient" flux away from the wall and a drag-decreasing "up-gradient" flux towards the wall. The coherent vortex structures in HDR flows can produce a net ``up-gradient'' flux of vorticity toward the wall, which instead reduces instantaneous drag. Increase of wall-vorticity and skin friction due to this up-gradient flux occurs after an apparent lag of several advection times, increasing with Weissenberg number. This increasing lag appears due to polymer damping of up-gradient nonlinear vorticity transport arising from large-scale eddies in the logarithmic layer. The relatively greater polymer damping of down-gradient transport due to small-scale eddies results in lower net vorticity flux and hence lower drag. The Josephson-Anderson relation thus provides an exact tool to diagnose the mechanism of polymer drag-reduction in terms of vorticity dynamics and it explains also prior puzzling observations on transient drag-reduction, as for centerline-release experiments in pipe flow. |
Monday, November 25, 2024 9:05AM - 9:18AM |
L19.00006: Nested traveling waves underlying elastoinertial turbulence: simulations, SPOD analysis, theory, and reduced order model Manish Kumar, Michael David Graham Polymer additives are commonly used in pipeline transport of liquids such as crude oil transport, water heating and cooling systems, and airplane tank filling to reduce turbulent drag. The emergence of elastoinertial turbulence (EIT), a chaotic flow state resulting from the interplay between inertia and elasticity, sets a limit on the achievable drag reduction using polymer additives. We investigate the dynamics of simulated 2D EIT in a FENE-P fluid using Spectral Proper Orthogonal Decomposition (SPOD) and discover that the dynamics of EIT are predominantly made of a collection of self-similar nested traveling waves that exhibit wall-mode structure and shift-reflect symmetry similar to the Tollmien–Schlichting wave. A scaling theory quantitatively captures the distribution of dominant wave speeds. We also developed a data-driven reduced-order model of EIT which captures the dominant structures and dynamics O(106) times faster than the direct numerical simulation. The reduced-order model can be used to further investigate and also design control to manipulate its dynamics. |
Monday, November 25, 2024 9:18AM - 9:31AM |
L19.00007: A Generalized Approach to the Linear Stability of Viscoelastic Shear-Flows Johannes Heinrich Conrad, Martin Oberlack Our talk revisits the linear stability theory of viscoelastic shear-flows, based upon a constitutive equation of fading-memory-type. The particular model was introduced by Kenneth Walters through the integration of classical rate-type fluids in a convected frame. Despite their broad applicability for various materials, their utilization in shear flow stability analysis has been insufficiently explored. Initial findings by Tackels and Crochet revealed promising agreement for small Weissenberg numbers but raised questions for larger values. The talk provides a concise formulation of these foundational results in terms of a displacement field, a well-known concept in the theory of linear elasticity, inheriting several advantages. Firstly, the analysis of Tackels and Crochet is extended to diverse material models, including those of rate-type without exact solutions in terms of convected integration. Furthermore, no assumptions on the kinematics of the base flow had to be imposed and the study is readily extended to the weakly non-linear stability analysis. |
Monday, November 25, 2024 9:31AM - 9:44AM |
L19.00008: Dueling rheology in a cross-slot flow instability Maliheh Teimouri, Louison Thorens, Jeffrey S Guasto In polymeric fluid flows, the dominance of elastic stresses over viscous stresses (large Weissenberg number, Wi) leads to viscoelastic instability, characterized by symmetry breaking and unsteady flow. Recently, the importance of shear-thinning in regulating viscoelastic instabilities has been highlighted, but the rheological conditions triggering the instability remain to be fully understood. Here, we begin to address this knowledge gap by probing the stability of a microfluidic cross-slot flow having two opposing fluids with contrasting rheological properties from either inlet. The fluids span purely elastic, purely shear thinning, viscoelastic, and Newtonian materials, where their respective properties are tuned and characterized using shear and extensional rheology. The flow topology and velocity fluctuations for different combinations of these miscible fluids are quantified using micro-PIV across a range of Weissenberg numbers (Wi) and shear thinning parameter values. Our results show that opposing flows of purely elastic and purely shear thinning fluids remain stable for the tested Wi, whereas the presence of one fluid exhibiting both shear-thinning and elasticity appears crucial to facilitating instability. These findings are potentially important for processes including remediation and mucus flows, where variations in fluid rheology have macro-scale implications for transport properties. |
Monday, November 25, 2024 9:44AM - 9:57AM |
L19.00009: Revisiting elastic turbulence in Kolmogorov flow: the centre-mode causes transition Theo Lewy, Rich R Kerswell Viscoelastic Kolmogorov flow is known to undergo an elastic linear instability at vanishing Reynolds numbers (Boffetta et al. 2005). We revisit this to confirm that the inertialess dynamics are entirely due to the centre-mode instability of Garg et al. 2018 in a pipe and Khalid et al. 2021 in a channel. The instability persists even when the solvent viscosity vanishes (i.e. in the Upper Convective Maxwell limit), and Floquet analysis shows that the preferred mode typically has a wavelength twice that of the forcing. It is also found that for a given streamwise domain size, the instability always disappears for sufficiently large Weissenberg number (W). The centre mode instability gives rise to familiar `arrowheads' (Page et al. 2020) which at sufficient W interact chaotically in 2D to give elastic turbulence. |
Monday, November 25, 2024 9:57AM - 10:10AM |
L19.00010: Linear stability of elastic and elasto-inertial pipe flows of viscoelastic fluids Jeff S Oishi, Keaton J Burns, Geoffrey Vasil, Moritz F Linkmann, Daniel Lecoanet, Benjamin P Brown, Alexander N Morozov Pipe flow is known to be linear stable at all Reynolds number when the fluid is Newtonian. However, when a dilute viscoelastic polymer is introduced, the flow can become linearly unstable. Prior linear stability analyses were carried out using the Oldroyd-B model [1,2]. These results suggest a critical Reynolds number of at least $\textrm{Re}_c \gtrsim 60$. Experiments show instability down to $\textrm{Re}_c \simeq 5$ in a shear-thinning viscoelastic polymer solutions [3]. Here, we include the effects of shear thinning in a linear stability calculation and find that instability persists to arbitrarily low $\textrm{Re}$. We will discuss the linear eigenfunctions and the effects of finite Schmidt number on the calculations. [1] Garg et al., Phys. Rev. Lett. 121, 024502 (2018) [2] Chaudhary et al., J. Fluid Mech. 908, A11 (2021) [3] Choueiri et al., Proc. Natl. Acad. Sci. U.S.A., 118, e2102350118 (2021) |
Monday, November 25, 2024 10:10AM - 10:23AM |
L19.00011: ABSTRACT WITHDRAWN
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