Session K12: Non-Newtonian Flows: Instability and Turbulence (8:45am - 9:30am CST)

Onset of elasto-inertial turbulence in Taylor-Couette flow

We study the Taylor-Couette flow of a constant viscosity (Boger fluid) viscoelastic polymer solution using a flow visualisation method [1]. We report evidence of a new route to elasto-inertial turbulence (EIT) caused by merging and splitting of base Taylor vortices --named merge-split transition (MST) hereafter-when crossed by elastic axial waves (RSW). Vortex merging and splitting events are not due to transient behaviour, finite aspect ratio or shear thinning behaviour. They are random in nature and increase in frequency with Re. They cause abrupt changes in the axial spatial wavelength, leading to the transition from RSW to the EIT state. We identify MST as an inertial feature solely triggered by elasticity. The final EIT state resembles inertial turbulence in that it is highly disordered and has a broadband spectral signature, but occurs at much lower Re [2,3]. Its existence could be of great interest for mixing applications. [1] N. Cagney and S. Balabani, Phys. Fluids, vol. 31, no. 5, p. 053102, 2019. [2] N. Liu and B. Khomami, J. Fluid Mech., vol. 737, p. R4, 2013 [3] N. Latrache, N. Abcha, O. Crumeyrolle, and I. Mutabazi, Phys. Rev. E, vol. 93, no. 4, p. 043126, 2016   

Wavelet analysis of spectral energy transfer in viscoelastic turbulent channel flow

Direct numerical simulation (DNS) database of a viscoelastic turbulent channel flow is analyzed using the wavelet multiresolution analysis (WMRA) to study drag-reduction mechanisms by polymer additives. At the friction Reynolds number $Re_{\tau}$ = 145, DNS of a viscoelastic channel flow is conducted using the finitely extensible nonlinear elastic-Peterlin (FENE-P) model. A Newtonian channel flow is also simulated at the same Reynolds number to examine the effects of viscoelasticity and validate the analysis framework. For the viscoelasticity, different Weissenberg numbers, which is the product of a polymer relaxation time and a characteristic strain rate in the flow, are considered. In-plane WMRA is performed to evaluate wavelet statistics of turbulence kinetic energy (TKE) and spectral energy transfer as a function of wall-normal distance. Spectrally and spatially local wavelet statistics show distinctly different characteristics of turbulence between the viscoelastic and Newtonian channel flows. Strong amplification of spectral energy is observed for viscoelastic flows, as well as substantially increased anisotropy and near-wall intermittency. Cross-scale transfer of TKE by the triadic interactions further characterizes the roles of polymer additives in turbulence modulation.   

The maximum drag reduction of turbulent flows with flexible and rigid polymer solutions in semi-dilute concentrations

Polymer solutions in the semi-dilute regime are commonly employed in transport of fluids in industrial applications. For instance, the high viscosities compared to the solvent allow for particle suspension, and the viscoelasticity of the solutions contributes to weaken eddies in turbulent flows, leading to the drag reduction phenomenon. Increasing the polymer concentration leads to more drag reduction until the maximum drag reduction (MDR) limit, which is universal in terms of average drag reduction, even for polymers with distinct drag reduction mechanisms prior to MDR. However, to the best of our knowledge, the similarities and differences between the dynamics of turbulence at MDR with flexible and rigid polymers remain unclear. In this work, we present an experimental investigation of turbulent flows with semi-dilute polymer solutions of xanthan gum (rigid polymer) and partially hydrolyzed polyacrylamide (flexible polymer) at high Reynolds numbers in a rectangular channel. The MDR state with each solution is analyzed with Laser Doppler Anemometry measurements of velocity profiles, turbulent intensities and energy spectra of velocity fluctuations, to explain similarities and potential differences in the drag reduction mechanism.   

Transitional Flow of Herschel-Bulkley Fluids in Pipes

This study aims to elucidate transitional flow characteristics of shear-thinning Herschel-Bulkley fluids using direct numerical simulation. Unlike Newtonian fluids where transition point can be described by a single Reynolds number, Herschel-Bulkley fluids require specification of a Reynolds number, Hedstrom number, and power law index to characterize the transition point. Computational studies are carried out using a second order accurate, unstructured, open-source finite volume solver over a limited range of parameters to identify transition points and flow behavior. Comparisons of statistics are made with literature whenever applicable, and results show excellent agreement. Results indicate strong increase in transition Reynolds number with increasing Hedstrom number. The mean flow properties support existence of the linear profile in the viscous sublayer. On the other hand, a universal logarithmic law does not generally hold. Turbulent fluctuation profiles also indicate strong variability with varying Hedstrom number. The analysis of instantaneous structures clearly reveal the transition delaying behavior due to yield stress and shear thinning.   

Non-asymptotic Elastoinertial Turbulence for Asymptotic Drag Reduction

Polymer-induced drag reduction is bounded by an asymptotic limit of maximum drag reduction (MDR). For decades, researchers have presumed that MDR reflects the convergence to an ultimate flow state that is not further changed by polymers. Our simulation shows that, as drag reduction converges to its invariant limit, the underlying dynamics continues to evolve with no sign of convergence. The stage of asymptotic drag reduction is not represented by any single flow state, but encompasses states with varying dynamical patterns, all of which are partially sustained by polymer elasticity.   

Self-sustained elastoinertial Tollmien-Schlichting waves

Direct simulations of 2D channel flow of a viscoelastic fluid at Re$=$3000 reveal the existence of a family of attractors that closely resembles the linear Tollmien-Schlichting (TS) mode, and exhibits localized stress fluctuations at the critical layer position. At the parameter values chosen, this solution branch represents a solution family that is nonlinearly self-sustained by viscoelasticity and connected through an unstable solution branch to 2D elastoinertial turbulence (EIT). This ``baby-EIT'' state displays tilted sheetlike structures that originate with the hyperbolic stagnation points of the ``Kelvin cat's eye'' kinematics of the TS wave. Tilted sheets of polymer stretch are also a feature of EIT. Further, at Re$=$10000, we show that the attractor associated with the viscoelastic extension of the Newtonian nonlinear TS branch is directly connected to 2D EIT. At intermediate levels of viscoelasticity, this attractor goes from intermittently displaying TS-like structures to EIT-like structures, shedding insights into viscoelastic self-sustenance. These results suggest that, in the parameter range considered here, the transition leading to EIT is mediated by nonlinear amplification and self-sustenance of perturbations that excite the TS mode.   

Pathways to Elasto-inertial Turbulence in Polymer Jets

We report experiments on the spatio-temporal evolution of flow structures in a jet of dilute polymer solution entering a quiescent bath of Newtonian fluid. High-speed digital Schlieren imaging is used to follow the evolution of local Lagrangian features revealing a rich sequence of transitional and turbulent states. A comprehensive state diagram constructed using the Reynolds number $Re$, elasticity number and polymer extensibility shows that increasing the fluid viscoelasticity at fixed Re initially destabilizes and then re-stabilizes the flow. At high elasticity numbers, we identify a distinct transitional pathway to elasto-inertial turbulence (EIT) which stabilizes the conventional turbulent bursts observed in Newtonian jets and instead a shear layer instability leads to elongated filaments of elastic fluid, termed elasto-inertial streaks. Within the family of jet flows studied here, we find that the temporal features of EIT far from the nozzle are universal and characterized by a power-law spectral decay $f^{-3}$, independent of fluid properties or flow parameters, whilst the spatial features of the turbulent structures in the jet strongly depend on polymer microstructure and concentration.