Elastic Turbulence Research Articles

The velocity studies in the pure viscoelastic liquid core in displacement flow with interfacial instabilities

The velocity profiles in the core of a pure viscoelastic liquid displacing a Newtonian oil in a 500 µm microchannel were measured with micro-particle image velocimetry (µPIV) to investigate the onset of elastic turbulence. During displacement, a film of the displaced phase remains on the channel wall while interfacial instabilities develop upstream of the displacing core. Two displacing phase flow rates were investigated at 0.1 ml/min and 0.2 ml/min, corresponding to elastic Mach numbers, Ma, of 0.43 and 0.86 respectively. It was found that the velocity profiles in the streamwise and wall-normal directions are almost symmetric with respect to the centre of the core phase, apart from the case at high Ma and at the position of maximum interface deformation. Velocity fluctuations are present for the 0.2 ml/min while they are almost zero for the 0.1 ml/min, indicating the presence of elastic turbulence at large flow rate. Similarly, the calculated turbulence strengths at different directions (which make up the turbulent kinetic energy) and the Reynolds stresses have significant values at 0.2 ml/min but are almost zero at the low flow rate. In both flow rates, a circulation pattern is formed below the interfacial instability.

Numerical investigation on the enhanced heat transfer characteristics of non-Newtonian viscoelastic fluids in microchannel with chip arrays

Elastic turbulence is an efficient heat transfer method at microscale. In this work, we conduct a systematic investigation on the flow and heat transfer performances of viscoelastic polymer solutions in microchannels with chip arrays by means of high-fidelity numerical simulations. Focusing on the effects of fluid elasticity [i.e. polymer relaxation time (λ)] and flow Reynolds number (Re), we find that the synergistic interplay between inertial and elastic forces is strategically exploited to amplify convection, thereby facilitating an enhanced heat transfer performance. For highly elastic fluid, the Nusselt number (Nu) can be improved by 76.13 % compared to that of less elastic fluid, while the pressure drop is reduced appropriately. In addition, as the fluid elasticity increases, the pressure drop decreases and eventually converges to a constant. In the zone of elastic turbulence, the fluid reinforces the convective heat transfer, which can be ascribe to the deformation of long-chain polymer molecules. Particularly, we consider the effect of temperature-dependent λ on the heat transfer performance. Our results demonstrate that the increased temperature-dependent λ decreases the value of Nu, and the variation between values of variable and constant λ is reduced with increasing Re or λ. Hence, in some cases of large fluid elasticity or high Re, it is possible to safely ignore the impact of temperature-dependent λ with an acceptable accuracy. The present work provides important insights into the enhanced heat transfer via elastic turbulence, which could guide the applications in the field of chip cooling.

Mixing in two-dimensional shear flow with smooth fluctuations.

Chaotic variations in flow speed up mixing of scalar fields via intensified stirring. This paper addresses the statistical properties of a passive scalar field mixing in a regular shear flow with random fluctuations against its background. We consider two-dimensional flow with shear component dominating over smooth fluctuations. Such flow is supposed to model passive scalar mixing, e.g., inside a large-scale coherent vortex forming in two-dimensional turbulence or in elastic turbulence in a microchannel. We examine both the decaying case and the case of the continuous forcing of the scalar variances. In both cases dynamics possesses strong intermittency, which can be characterized via the single-point moments and correlation functions calculated in our work. We present general qualitative properties of pair correlation function as well as certain quantitative results obtained in the framework of the model with fluctuations that are short correlated in time.

Thermal convection of viscoelastic fluids in concentric rotating cylinders: Elastic turbulence and kinetic energy budget analysis

Thermal convection of viscoelastic fluids in concentric rotating cylinders: Elastic turbulence and kinetic energy budget analysis

Enhanced heat transfer in a two-dimensional serpentine micro-channel using elastic polymers

Elastic turbulence has emerged as a promising method to enhance heat transfer performance at the microscale. However, previous studies have mainly focused on the overall convective heat transfer performance in curved channels, overlooking the fact that the chaotic flow intensity varies along the streamline, leading to diverse local heat transfer characteristics. In this study, we systematically investigate the hydraulic and thermal properties of a dilute polymer solution under elastic turbulence conditions, where the inflow conditions exhibit a vanishing Reynolds number (Re) and high Weissenberg number (Wi), enabling a comprehensive understanding of the influence of polymers on the system. Through extensive direct numerical simulations using Rheotool, a two-dimensional curvilinear channel flow of an Oldroyd-B viscoelastic fluid is analyzed. By examining the variations of the friction factor and Nusselt number along the serpentine channel, we unveil both global and local characteristics of elastic turbulence. Based on the Wi value, we identify three distinct regimes. In the first regime (0<Wi≤3), we observe approximately 10% heat transfer enhancement accompanied by a roughly 5% reduction in the friction factor compared to laminar flow, known as polymer-induced thermal conductivity enhancement. In the second regime (3<Wi≤5), we observe a steep linear increase in heat transfer (around 30%) at the expense of up to 15% enhanced friction factor. Finally, in the fully developed elastic turbulence regime (Wi>5), we observe a remarkable heat transfer enhancement of up to 60% along with a reduced friction factor. The significant enhancement of heat transfer with increasing Wi can be attributed to the intensifying elastic instability resulting from the balance between normal stresses and streamlined curvatures.

Comparison of viscoelastic flows in two- and three-dimensional serpentine channels.

Polymer solutions in the dilute regime play a significant role in industrial applications. Due to the intricate rheological properties of these highly viscoelastic fluids, especially in complex flow geometries, a thorough numerical analysis of their flow dynamics is imperative. In this research, we present a numerical investigation of purely elastic instability occurring in two- and three-dimensional serpentine channels under conditions where fluid inertia is negligible and across a broad spectrum of polymer relaxation times. Our findings reveal a strong qualitative agreement between the existing experimental results obtained from dilute solutions of flexible polymers in microfluidic devices and the numerical simulations conducted in two and three dimensions using the Oldroyd-B model. Spatial flow observations and statistical analysis of temporal flow features indicate that this purely elastic turbulent flow exhibits nonhomogeneous, non-Gaussian, and anisotropic characteristics across all scales. Additionally, our comparison of two- and three-dimensional simulations demonstrates that the elastic instability is primarily driven by the curvature of the streamlines induced by the flow geometry, rather than the weak secondary flow in the azimuthal direction. Therefore, our two-dimensional numerical simulations successfully replicate, at least qualitatively, the features observed in three-dimensional experiments. Furthermore, spectral analysis suggests that, in comparison to elastic turbulence in the dilute regime, the range of scales for the excited fluctuations is narrower.

Intermittency in the not-so-smooth elastic turbulence.

Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ( ) numbers. Our direct numerical simulations show that elastic turbulence, though a low phenomenon, has more in common with classical, Newtonian turbulence than previously thought. In particular, we find power-law spectra for kinetic energy E(k) ~ k-4 and polymeric energy Ep(k) ~ k-3/2, independent of the Deborah (De) number. This is further supported by calculation of scale-by-scale energy budget which shows a balance between the viscous term and the polymeric term in the momentum equation. In real space, as expected, the velocity field is smooth, i.e., the velocity difference across a length scale r, δu ~ r but, crucially, with a non-trivial sub-leading contribution r3/2 which we extract by using the second difference of velocity. The structure functions of second difference of velocity up to order 6 show clear evidence of intermittency/multifractality. We provide additional evidence in support of this intermittent nature by calculating moments of rate of dissipation of kinetic energy averaged over a ball of radius r, εr, from which we compute the multifractal spectrum.

On designing a wavy sinusoidal micromixer for efficient mixing of viscoelastic fluids harnessing elastic instability and elastic turbulence phenomena

Effective mixing in microscale systems encounters difficulties due to the inherently low Reynolds numbers. This investigation delves into harnessing elastic instability and elastic turbulence phenomena to improve the mixing performance of viscoelastic fluids within a wavy sinusoidal micromixer with variable cross-sectional areas. Previous experiments demonstrated enhanced mixing efficiency, while our numerical simulations indicate that this enhancement is true up to a certain Weissenberg number. Beyond this threshold, a further increase in the Weissenberg number results in diminished mixing efficiency. Moreover, we observe that mixing efficiency increases with the Deborah number, albeit with an exponential increase in pressure drop. Conversely, mixing efficiency also increases with the number of turns in the micromixer, albeit with a linear increase in pressure drop. Hence, selecting a wavy micromixer with more turns and a relatively lower Deborah number is advisable for achieving comparable efficiency with reduced pressure drop. Additionally, the shear-thinning properties of viscoelastic fluids impede mixing efficiency by suppressing elastic instability and elastic turbulence phenomena. In conclusion, this study provides valuable insights for designing optimal wavy micromixers that effectively mix viscoelastic fluids by utilizing elastic instability and elastic turbulence phenomena.

Coherent structures in elastic turbulent planar jets

At low Reynolds numbers, the flow of a Newtonian planar jet remains laminar, thus easy to characterize. In contrast, the presence of elasticity (e.g., attained dissolving polymers in a Newtonian solvent) enables a highly-complex turbulent-like behavior termed elastic turbulence. In this work, we run data-driven modal decomposition algorithms on high-fidelity data collected from the simulation of an elastic turbulent planar jet. The large-scale motions are expressed as a finite expansion of modes that condense the dominant dynamics. The modes associated with lower frequencies weight the most on the reconstruction of the original data, thus they are further decomposed in space to investigate their implications on the sustainment of the elastic turbulent state. Our findings suggest that slower dynamics are crucial for the sustainment of elastic turbulence, which is connected to the interaction of spanwise-coherent structures, steady in space, with spanwise-periodic traveling waves, causing the breakdown of the structures close to the inlet.

Purely elastic turbulence in pressure-driven channel flows

Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behavior. When subjected to an external flow, dilute polymer solutions exhibit elastic turbulence-a unique, chaotic flow state absent in Newtonian fluids, like water. Unlike its Newtonian counterpart, elastic turbulence is caused by polymer molecules stretching and aligning in the flow, and can occur at vanishing inertia. While experimental realizations of elastic turbulence are well-documented, there is currently no understanding of its mechanism. Here, we present large-scale direct numerical simulations of elastic turbulence in pressure-driven flows through straight channels. We demonstrate that the transition to elastic turbulence is sub-critical, giving rise to spot-like flow structures that, further away from the transition, eventually spread throughout the domain. We provide evidence that elastic turbulence is organized around unstable coherent states that are localized close to the channel midplane.

A web of sticky strands: how localized stress controls spatio-temporal fluctuations in viscoelastic flows through a lattice of obstacles

Recent microfluidic experiments have evidenced complex spatio-temporal fluctuations in low-Reynolds-number flows of polymer solutions through lattices of obstacles. However, understanding the nonlinear physics of such systems remains a challenge. Here, we use high performance simulations to study viscoelastic flows through a hexagonal lattice of cylindrical obstacles. We find that structures of localized polymer stress – in particular birefringent strands – control the stability and the dynamics. We first show that, at steady state, strands act as a web of sticky flow barriers that induce channelization, multistability and hysteresis. We then demonstrate that a spontaneous destabilization of the strands drives the transition to unsteady flow with regimes of self-sustained oscillations, travelling waves and strand pulsations. We further show that these pulsations, which result from the destabilization of envelope patterns of stress with strands wrapped around multiple obstacles, are integral to the transition towards elastic turbulence in our two-dimensional simulations. Our study provides a new perspective on the role of birefringent strands and a framework for understanding experimental observations. We anticipate that it is an important step towards unifying existing interpretations of the nonlinear physics of viscoelastic flows through complex structures.

Polymer diffusive instability leading to elastic turbulence in plane Couette flow

Polymer diffusive instability leading to elastic turbulence in plane Couette flow

Scalability of Viscoelastic Fluid Solvers Based on OpenFOAM-PETSc Framework in Large-Scale Parallel Computing

Enormous advances in physics of complex fluids/soft matter over last decades have rapidly transformed traditional industrial sectors in foods, personal care products, pharmaceuticals, paints, lubricants, ceramics, polymers, liquid crystals, high performance fibers, oil exploration and production into a digital era of formulation design and precision control over processing conditions from molecular viewpoint, and fertilizing a new industrial revolution. Development of high performance viscoelastic fluid solvers is of great significance for large scale digital manufacturing. In the present work, a portable and extensible scientific computing (PETSc) toolbox has been successfully integrated into the popular OpenFOAM CFD toolbox for carrying out large scale parallel computing of Turbulent Drag Reduction (TDR) and Elastic Turbulence (ET) in the isotropic turbulence flow. Its scalability has been evaluated and compared with the scalability of the OpenFOAM based viscoelastic fluid solvers. The results show that there are significant improvements.

Relative Influences of Inertia and Polymeric Viscoelastic Effects on Nusselt Numbers within Rotating Couette Flows

In past investigations of elastic instabilities and elastic turbulence, almost no attention has been devoted to the effects and influences of inertial phenomena. Within the present investigation, Nusselt number data are provided to illustrate the relative influences of inertia and polymeric viscoelastic phenomena within a rotating Couette flow (RCF) environment. Data are provided from experimental measurements of local surface heat transfer characteristics for different flow passage heights, one radial position, and different values of disk rotational speed for polyacrylamide polymer concentrations ρ of 0 ppm, 100 ppm, 150 ppm, and 300 ppm. With this approach, data for a wide range of shear rate γ˙ values, Weissenberg numbers, and first normal stress difference values are provided. Nusselt number data are provided as dependent upon a newly developed P′ parameter, equal to ReEI/Re0.22, which collapse into a single distribution over the range of P′ values considered which range from 0 to about 182. Such characteristics indicate that the P′ parameter provides an appropriate means to simultaneously account for the relative influences of inertia and polymeric viscoelastic effects. The use of such a power law dependence for Re additionally gives P′ values which are dominated by ReEI values when the Weissenberg number Wi is greater than the elastic instability transition onset value. The experimental conditions associated with this value correspond to the change from inertia domination (with buoyance influences) to polymeric viscoelastic domination which occurs for shear rates in the vicinity of 11 to 12 s−1. For Weissenberg numbers greater than the onset value, Nusselt numbers associated with H = 5 mm are generally the highest values measured, with magnitudes that steadily increase with γ˙. Associated Nusselt numbers become as high as about 3.0, whereas zero-shear rate values (obtained with zero rotation) are in the vicinity of 1.0. At lower Weissenberg number magnitudes (below the transition onset value), Nusselt numbers cover a wide range of values as experimental conditions and configuration are varied, as a consequence of the complicated and simultaneous influences of inertia, buoyancy, and dilute polymer presence.

Mixed lubrication performances of misaligned stern bearing considering turbulence and elastic deformation

PurposeThis study aims to investigate mixed lubrication performances of stern bearing in a misaligned state considering turbulence and bearing deformation impacts.Design/methodology/approachA mixed lubrication model of stern bearing is established. The generalized average Reynolds equation governing the turbulent flow of lubricant is analyzed by considering the interaction of bearing elastic deformation, asperity contact pressure and film pressure. The bearing behaviors including minimum film thickness, hydrodynamic pressure, asperity friction force and frictional coefficient are studied under different models. The correctness of this model is verified by comparing it with that of the published data.FindingsNumerical results indicate that elastic deformation noticeably decreases the maximum film pressure, the asperity contact force and the friction coefficient in the mixed lubrication stage. The effect of elastic deformation and turbulence reduces the transition speed from mixed to liquid lubrication.Originality/valueThis model includes both turbulence and bearing deformation impacts on journal bearing performances. It is expected that the numerical results can provide useful information to establish a stern bearing exposed to mixed lubrication conditions.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2022-0352/

Mechanism of vorticity amplification by elastic waves in a viscoelastic channel flow

Inertia-less viscoelastic channel flow displays a supercritical nonnormal mode elastic instability due to finite-size perturbations despite its linear stability. The nonnormal mode instability is determined mainly by a direct transition from laminar to chaotic flow, in contrast to normal mode bifurcation leading to a single fastest-growing mode. At higher velocities, transitions to elastic turbulence and further drag reduction flow regimes occur accompanied by elastic waves in three flow regimes. Here, we demonstrate experimentally that the elastic waves play a key role in amplifying wall-normal vorticity fluctuations by pumping energy, withdrawn from the mean flow, into wall-normal fluctuating vortices. Indeed, the flow resistance and rotational part of the wall-normal vorticity fluctuations depend linearly on the elastic wave energy in three chaotic flow regimes. The higher (lower) the elastic wave intensity, the larger (smaller) the flow resistance and rotational vorticity fluctuations. This mechanism was suggested earlier to explain elastically driven Kelvin-Helmholtz-like instability in viscoelastic channel flow. The suggested physical mechanism of vorticity amplification by the elastic waves above the elastic instability onset recalls the Landau damping in magnetized relativistic plasma. The latter occurs due to the resonant interaction of electromagnetic waves with fast electrons in the relativistic plasma when the electron velocity approaches light speed. Moreover, the suggested mechanism could be generally relevant to flows exhibiting both transverse waves and vortices, such as Alfven waves interacting with vortices in turbulent magnetized plasma, and Tollmien-Schlichting waves amplifying vorticity in both Newtonian and elasto-inertial fluids in shear flows.

Theoretical and experimental investigation on effective length-to-diameter ratio of misaligned water-lubricated bearings

An effective length-to-diameter ratio (ELDR) of the misaligned water-lubricated bearing is investigated in this paper. Firstly, the influence of the length-to-diameter ratio (LDR) on the misaligned bearing is explored theoretically and experimentally. In the theoretical model, liner elastic deformation, local turbulence, and journal misalignment are considered. In the experimental research, the bearing frictional force and hydrodynamic pressure are measured. The results show that an increasing effect of LDR on load-carrying capacity is remarkably weakened for misaligned bearings. On this basis, a concept of effective length-to-diameter ratio is defined. The results show that the bearing part exceeding ELDR has a minor effect on increasing the load-carrying capacity. Thus, the proposed concept of ELDR can be used to evaluate the rationality of bearing length. Finally, the variation law of ELDR with respect to key bearing parameters is analyzed.

Origin of steady state stress fluctuations in a shear-thinning worm-like micellar system

Large, irregular stress fluctuations under a constant applied shear rate are observed during the flow of dilute worm-like micellar solutions even at low Reynolds numbers. Statistical properties of such fluctuations showing signatures of chaos and elastic turbulence have been studied extensively. Although the mechanisms like boundary slippage, dynamics of shear band interface, time-dependent secondary flows, and inertio-elastic effects are conceived as the possible factors for such striking flow properties, their contributions in different non-linear flow regimes remain poorly understood. Here, we study the Taylor–Couette flow of a well-characterized aqueous worm-like micellar system formed by 2 wt. % cetyltrimethylammonium tosylate and 100 mM sodium chloride (2 wt. % CTAT + 100 mM NaCl). For a fixed applied shear-rate just beyond the onset of shear-thinning, high-speed optical imaging in the flow-gradient plane reveals spatiotemporally varying velocity gradients in the system. In this regime, the magnitude of stress fluctuations remains insignificant. However, the fluctuation becomes substantial beyond a critical shear rate deep inside the non-linear regime of the flow curve when significant free-surface undulations, sustained stick-slip, and elastic recoil events are observed. Imaging in the flow-vorticity and the gradient-vorticity plane indicates that such dynamics are primarily driven by the elasticity-induced turbulent flows in the system. Furthermore, in this regime, we find that the characteristic persistent time of stress fluctuations matches well with the time scales of the stick-slip events, as well as the micellar breaking time, indicating a possible connection between the striking stress dynamics and the micellar kinetics.

Analysis of viscoelastic flow past a square cylinder in a channel with sudden contraction

The present study examines the effectiveness of the geometric modification in stabilizing the viscoelastic (VE) fluid flow through a planar channel with 5:1 sudden contraction. The geometric modification employed in this study includes a square cylinder positioned in front of the contraction plane. The square cylinder pre-deforms the fluid before entering the contraction region. The cylinder causes elongational flow in the wake region as well as shear and elongational flow between the channel and cylinder walls, significantly changing the nature of the flow. We used the open-source software OpenFoam, which is based on the finite volume method, to solve the mass, momentum, and rheological stress-constitutive equations. The Oldroyd-B model mimics the rheological characteristics of the VE fluid. Our research demonstrates that the pre-deformation of VE fluid stabilizes flow in the Wi range of 0–4. Additionally, the salient corner vortex size in the Wi range of 6–10 is effectively reduced by the square cylinder with a blockage ratio of 0.30. Furthermore, the Pakdel–Mckinley stability criterion demonstrates that an increase in Wi beyond the critical value initiates elastic turbulence in the flow.

Entrapment and mobilization dynamics during the flow of viscoelastic fluids in natural porous media: A micro-scale experimental investigation

Capillary desaturation process was investigated as a function of wetting phase rheological signatures during the injection of Newtonian and non-Newtonian fluids. Two sets of two-phase imbibition flow experiments were conducted on a water-wet sandstone core sample using brine and viscoelastic polymer solutions. During the experiments, a high-resolution micro-computed tomography scanner was employed to directly map pore-level fluid occupancies within the pore space. The results of the experiments revealed that at a given capillary number, the viscoelastic polymer was more efficient than the brine in recovering the non-wetting oil phase. At low capillary numbers, this is attributed to the improved accessibility of the viscoelastic polymer solution to the entrance of pore elements, which suppressed snap-off events and allowed more piston-like and cooperative pore-body filling events to contribute to oil displacement. For intermediate capillary numbers, the onset of elastic turbulence caused substantial desaturation, while at high capillary numbers, the superimposed effects of higher viscous and elastic forces further improved the mobilization of the trapped oil ganglia by the viscoelastic polymer. In the waterflood, however, the mobilization of oil globules was the governing recovery mechanism, and the desaturation process commenced only when the capillary number reached a threshold value. These observations were corroborated with the pore-level fluid occupancy maps produced for the brine and viscoelastic polymer solutions during the experiments. Furthermore, at the intermediate and high capillary numbers, the force balance and pore-fluid occupancies suggested different flow regimes for the non-Newtonian viscoelastic polymer. These regions are categorized in this study as elastic-capillary- and viscoelastic-dominated flow regimes, different from viscous-capillary flow conditions that are dominant during the flow of Newtonian fluids. Moreover, we have identified novel previously unreported pore-scale displacement events that take place during the flow of viscoelastic fluids in a natural heterogeneous porous medium. These events, including coalescence, fragmentation, and re-entrapment of oil ganglia, occurred before the threshold of oil mobilization was reached under the elastic-capillary-dominated flow regime. In addition, we present evidence for lubrication effects at the pore level due to the elastic properties of the polymer solution. Furthermore, a comparison of capillary desaturation curves generated for the Newtonian brine and non-Newtonian viscoelastic polymer revealed that the desaturation process was more significant for the viscoelastic polymer than for the brine. Finally, the analysis of trapped oil clusters showed that the ganglion size distribution depends on both the capillary number and the rheological properties of fluids.