In the finite element analysis with fast decoupled time integration scheme for viscoelastic fluid (the Leonov model) flow, we investigate strong nonlinear behavior in 2D creeping contraction flow. The algorithm is applicable in the whole range of the retardation parameter. In the analysis of steady solutions, there exists upper convergence limit of available numerical solutions in this contraction flow that is free from the frustrating mesh dependence when we incorporate the tensor-logarithmic formulation [Fattal and Kupferman, JNNFM, 2004]. With adjustment of a nonlinear parameter, 2 kinds of fluid have been chosen for flow modeling such as highly shear thinning and Boger-type liquids. According to the type of such property, the transient modeling has revealed distinct flow dynamics of elastic instability. With pressure difference imposed slightly below the steady limit, the result demonstrates fluctuating solution without approaching steady state for the shear thinning fluid. From it, we conclude that the existence of upper limit for convergent steady solution possibly implies transition to spatially as well as temporally varying flow field without steady asymptotic. Under the pressure fairly higher than the limit, the result expresses severe fluctuation of flowrate, oscillation of corner vortices and also asymmetric irregular wave propagation along the downstream wall. In addition, flow dynamics seems quite stochastic with almost no temporal correlation. For the Boger-type fluid, under the traction higher than steady limit the flowrate and corner vortices exhibit periodic oscillation with flow asymmetry. Both types of instability express purely elastic instability in this inertialess flow approximation.
We analyze transient dynamics during shear start-up in viscoelastic flows between two parallel plates, with a specific focus on the signatures for the onset of transient shear banding using the Johnson-Segalman, non-stretching Rolie-Poly and Giesekus models. We explore the dynamics of shear start-up in monotonic regions of the constitutive curves using two different methodologies: (i) the oft-used `frozen-time' linear stability (eigenvalue) analysis, wherein we examine whether infinitesimal perturbations imposed on instantaneous stress components (treated as quasi steady states) exhibit expone…
We study the development and decay of vortex in viscoelastic fluids between coaxial cylinders by means of experiments with solutions of polyacrylamide and glycerin and numerical simulations. The transient process is triggered when the inner cylinder is either abruptly started or stopped while the outer is kept fixed. The azimuthal velocity, obtained by means of digital particle velocimetry, exhibits oscillations before reaching the stationary state. The development of the vortex is characterized by means of the overshoot, i.e. the difference between the maximum and the stationary velocity. Ana…
Simulations of undulatory swimming in viscoelastic fluids with large amplitude gaits show concentration of polymer elastic stress at the tips of the swimmers.We use a series of related theoretical investigations to probe the origin of these concentrated stresses. First the polymer stress is computed analytically at a given oscillating extensional stagnation point in a viscoelastic fluid. The analysis identifies a Deborah number (De) dependent Weissenberg number (Wi) transition below which the stress is linear in Wi, and above which the stress grows exponentially in Wi. Next, stress and velocit…
A novel modeling approach for viscoelastic hydraulic cylinders, with negligible inertial forces, is proposed, based on the extended fractional-order Jeffreys model. Analysis and physical reasoning for the parameter constraints and order of the fractional derivatives are provided. Comparison between the measured and computed frequency response functions and time domain transient response argues in favor of the proposed four-parameter fractional-order model.
Lagrangian dynamics unveil polymer conformation in viscoelastic flows
Tufts University（塔夫茨大学）；Institute for Mechanobiology, Department of Bioengineering, College of Engineering, Northeastern University（东北大学生物工程学院机制生物学研究所）；Department of Mechanical Science and Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校机械科学与工程系）；Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania（宾夕法尼亚大学机械工程和应用力学系）
A wide and critical comparison of the capability of Method of Characteristics, Explicit Path-Conservative Finite Volume Method and Semi-Implicit Staggered Finite Volume Method is presented and discussed, in terms of accuracy and efficiency. The viscoelastic behaviour of the pipe wall, the effects of the unsteadiness of the flow on the friction losses, cavitation and cross-sectional changes are considered. The analyses are performed comparing numerical solutions obtained using the three models against experimental data and analytical solutions. Water hammer studies in high density polyethylene …
Viscoelastic flow through an abrupt planar contraction geometry above a certain Weissenberg number (Wi) is well known to become unstable upstream of the contraction plane via a central jet separating from the walls and forming vortices in the salient corners. Here, for the first time we consider three-dimensional (3D) viscoelastic contraction flows in a microfabricated glass square-square contraction geometry. We employ state-of-the-art microtomographic particle image velocimetry to produce time-resolved and volumetric quantification of the 3D viscoelastic instabilities arising in a dilute pol…
Elasto-inertial turbulence (EIT) is a new, two-dimensional chaotic flow state observed in polymer solutions with possible connections to inertialess elastic turbulence and drag-reduced Newtonian turbulence. In this Letter, we argue that the origins of EIT are fundamentally different from Newtonian turbulence by finding a dynamical connection between EIT and an elasto-inertial linear instability recently found at high Weissenberg numbers (Garg et al. Phys. Rev. Lett. 121, 024502, 2018). This link is established by isolating the first known exact coherent structures in viscoelastic parallel flow…
An extended volume of fluid method is developed for two-phase direct numerical simulations of systems with one viscoelastic and one Newtonian phase. A complete set of governing equations is derived by conditional volume-averaging of the local instantaneous bulk equations and interface jump conditions. The homogeneous mixture model is applied for the closure of the volume-averaged equations. An additional interfacial stress term arises in this volume-averaged formulation which requires special treatment in the finite-volume discretization on a general unstructured mesh. A novel numerical scheme…
We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). The numerical model is first benchmarked by characterizing the rheological behaviour of dilute homogeneous solutions in various configurat…
A semi-analytical solution for the lubrication force between two spheres approaching in viscoelastic fluids described by the Oldroyd-B model under small Deborah numbers
Recent experiments have reported a novel transition to elasto-inertial turbulence in the Taylor--Couette flow of a dilute polymer solution. Unlike previously reported transitions, this newly discovered scenario, dubbed vortex merging and splitting (VMS) transition, occurs in the centrifugally unstable regime and the mechanisms underlying it are two-dimensional: the flow becomes chaotic due to the proliferation of events where axisymmetric vortex pairs may be either created (vortex splitting) or annihilated (vortex merging). In this paper, we present direct numerical simulations, using the FENE…
Soft, low-friction particles in silos show peculiar features during their discharge. The outflow velocity and the clogging probability both depend upon the momentary silo fill height, in sharp contrast to silos filled with hard particles. The reason is the fill-height dependence of the pressure at the orifice. We study the statistics of silo discharge of soft hydrogel spheres. The outflow is found to become increasingly fluctuating and even intermittent with decreasing orifice size, and with decreasing fill height. In orifices narrower than two particle diameters, outflow can stop completely, …
Periodically-driven flows are known to generate non-zero, time-averaged fluxes of heat or solute species, due to the interactions of out-of-phase velocity and temperature/concentration fields, respectively. Herein, we investigate such transport (a form of the well-known Taylor--Aris dispersion) in the gap between two parallel plates, one of which oscillates vertically, generating a time-periodic squeeze flow of either a newtonian or Maxwellian fluid. Using the method of multiple time-scale homogenization, the mass/heat balance equation describing transport in this flow is reduced to a one-dime…
The rheological characterisation of complex fluids is mostly performed under simple shear flow in rotational rheometers. Their modern commercial versions are extremely sensitive instruments which are able to provide very accurate measurements of low values of different material functions, such as viscosity, viscoelastic moduli, etc., under certain ideal flow conditions. Nevertheless, they fail in providing reliable data when characterising the response of complex fluids at short time scales, due to artefacts induced by either instrument or fluid inertia. This is crucial in the analysis of the …
The accuracy and stability of implicit CFD codes are frequently impaired by the decoupling between variables, which can ultimately lead to numerical divergence. Coupled solvers, which solve all the governing equations simultaneously, have the potential to fix this problem. In this work, we report the implementation of coupled solvers for transient and steady-state electrically-driven flow simulations in the finite-volumes framework. The numerical method, developed in OpenFOAM, is generic for Newtonian and viscoelastic fluids and is formulated for the Poisson-Nernst-Planck and Poisson-Boltzmann…
Transport of electrolytic solutions under influence of electric fields occurs in phenomena ranging from biology to geophysics. Here, we present a continuum model for single-phase electrohydrodynamic flow, which can be derived from fundamental thermodynamic principles. This results in a generalized Navier-Stokes-Poisson-Nernst-Planck system, where fluid properties such as density and permittivity depend on the ion concentration fields. We propose strategies for constructing numerical schemes for this set of equations, where solving the electrochemical and the hydrodynamic subproblems are decoup…
Recent step strain experiments in well-entangled polymeric liquids demonstrated a bulk fracture-like phenomenon. We have studied this instability using a modern version of the Doi-Edwards theory for entangled polymers, and we find close quantitative agreement with the experiments. The phenomenon occurs because the viscoelastic liquid is sheared into a rubbery state that possesses an elastic constitutive instability (Marrucci and Grizzuti, 1983). The fracture is a transient manifestation of this instability, which relies on the amplification of spatially inhomogeneous fluctuations. This mechani…
