Flow Of Dilute Polymer Solutions Research Articles

Some experimental results for converging flow of dilute polymer solution

This paper presents the results of experimental studies of the flow of a dilute polymer solution in a converging pipe. Three geometries with restriction rates are considered: 2.41, 3.92, and 5.65. A water–glycerin solution of 0.1% polyacrylamide was used as a working fluid. Point velocity measurements are made by using the smoke image velocimetry technique, which previously was proved by the construction of velocity profiles corresponding to the laminar viscoelastic flow in a straight pipe. The influence of the Weissenberg number and the restriction rate of the channel on the velocity profiles are established for both transverse and longitudinal directions. For small Weissenberg numbers, the experimental results are compared with the numerical results obtained using the Giesekus and exponential form of Phan-Thien–Tanner rheological models. Three flow regimes are identified: flow without vortex, vortex enhancement, and divergent flow, which is consistent with published results on the abrupt contraction and converging flows. Vortex length for a wide range of Weissenberg numbers is well predicted by a logarithm function. Modified expression of stretch rate with location of detachment plane can predict the flow regimes and the onset of unsteady flow in converging channels.

Transition to turbulence in viscoelastic channel flow of dilute polymer solutions

The transition to turbulence in a plane Poiseuille flow of dilute polymer solutions is studied by direct numerical simulations of a finitely extensible nonlinear elastic fluid with the Peterlin closure. The range of Reynolds number ( $Re$ ) $2000 \le Re \le 5000$ is studied but with the same level of elasticity in viscoelastic flows. The evolution of a finite-amplitude perturbation and its effects on the transition dynamics are investigated. A viscoelastic flow begins transition at an earlier time than its Newtonian counterparts, but the transition time appears to be insensitive to polymer concentration in the dilute and semi-dilute regimes studied. Increasing polymer concentration, however, decreases the maximum attainable energy growth during the transition process. The critical or minimum perturbation amplitude required to trigger transition is computed. Interestingly, both Newtonian and viscoelastic flows follow almost the same power-law scaling of $Re^\gamma$ with the critical exponent $\gamma \approx -1.25$ , which is in close agreement with previous studies. However, a shift downward is observed for viscoelastic flow, suggesting that smaller perturbation amplitudes are required for the transition. A mechanism of the early transition is investigated by the evolution of wall-normal and spanwise velocity fluctuations and flow structure. The early growth of these fluctuations and the formation of quasi-streamwise vortices around low-speed streaks are promoted by polymers, hence causing an early transition. These vortical structures are found to support the critical exponent $\gamma \approx -1.25$ . Once the transition process is completed, polymers play a role in dampening the wall-normal and spanwise velocity fluctuations and vortices to attain a drag-reduced state in viscoelastic turbulent flows.

Kinetic Energy Budget in Turbulent Flows of Dilute Polymer Solutions

Direct numerical simulation of a turbulent pipe flow of a realistic solution of 108\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^8$$\\end{document} polymers, modelled as finitely extensible nonlinear elastic (FENE) dumbbells, and directly momentum coupled with the incompressible Navier–Stokes equations, are performed by means of an Eulerian-Lagrangian approach. Besides the drag reduction, the polymers significantly modify mean and turbulent kinetic energy budgets. The polymer backreaction to the solvent reduces the Reynolds stress and thus decreases the turbulent production and, at large Weissenberg number, the polymers act as a source of turbulent kinetic energy for y+>40\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y^+> 40$$\\end{document}, leading to an increase in the dissipation. This effect is peculiar to large Weissenberg polymers and it is particularly apparent at a small Reynolds number. At a smaller Weissenberg number, the effect of the polymers remains confined in the buffer layer, with the kinetic energy budget not significantly altered elsewhere.

Large is different: Nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers.

We use direct numerical simulations to study homogeneous and isotropic turbulent flows of dilute polymer solutions at high Reynolds and Deborah numbers. We find that for small wave numbers k, the kinetic energy spectrum shows Kolmogorov-like behavior that crosses over at a larger k to a novel, elastic scaling regime, E(k) ∼ k-ξ, with ξ ≈ 2.3. We study the contribution of the polymers to the flux of kinetic energy through scales and find that it can be decomposed into two parts: one increase in effective viscous dissipation and a purely elastic contribution that dominates over the nonlinear flux in the range of k over which the elastic scaling is observed. The multiscale balance between the two fluxes determines the crossover wave number that depends nonmonotically on the Deborah number. Consistently, structure functions also show two scaling ranges, with intermittency present in both of them in equal measure.

Linear stability analysis of purely elastic travelling-wave solutions in pressure-driven channel flows

Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a subcritical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded in sufficiently wide three-dimensional domains. Our work demonstrates that studies of purely elastic and elasto-inertial turbulence in straight channels require three-dimensional simulations, and no reliable conclusions can be drawn from studying strictly two-dimensional channel flows.

Direct numerical simulation of elastic turbulence in the Taylor–Couette flow: transition pathway and mechanistic insight

Three-dimensional elastic turbulence in Taylor–Couette flows of dilute polymer solutions has been realized and thoroughly investigated via direct numerical simulations. A novel flow transition pathway from elastically dominated turbulence to solitary vortex pairs (or diwhirls) and eventually to elastic turbulence is observed by decreasing the fluid inertia ( $Re$ ) over seven orders of magnitude, i.e. from $Re=1000$ to $0.0001$ . The dominant spatio-temporal flow features in the elastic turbulence regime are those of large-scale unsteady diwhirls and small-scale axial and azimuthal travelling waves in the outer and inner halves of the gap, respectively. Moreover, it is conclusively shown that production of turbulent kinetic energy in purely elastic turbulence solely arises due to the stochastic nature of polymer stretch/relaxation. Overall, based on this comprehensive numerical investigation, the differences in the underlying fluid physics that give rise to turbulent fluctuations in elastically dominated and purely elastic turbulence have been delineated.

Coherent Structures in Plane Channel Flow of Dilute Polymer Solutions with Vanishing Inertia.

When subjected to sufficiently strong velocity gradients, solutions of long, flexible polymers exhibit flow instabilities and chaotic motion, often referred to as elastic turbulence. Its mechanism differs from the familiar, inertia-driven turbulence in Newtonian fluids and is poorly understood. Here, we demonstrate that the dynamics of purely elastic pressure-driven channel flows of dilute polymer solutions are organized by exact coherent structures that take the form of two-dimensional traveling waves. Our results demonstrate that no linear instability is required to sustain such traveling wave solutions and that their origin is purely elastic in nature. We show that the associated stress profiles are characterized by thin, filamentlike arrangements of polymer stretch, which is sustained by a solitary pair of vortices. We discuss the implications of the traveling wave solutions for the transition to elastic turbulence in straight channels and propose ways for their detection in experiments.

Similarity between the turbulent transports of heat and momentum in viscoelastic channel flows

This study examined the heat transfer reduction in drag-reduced turbulent flows of dilute polymer solutions. To this end, direct numerical simulations of fully developed viscoelastic turbulent channel flows (Reτ = 125 and Pr = 5) were conducted under a constant heat flux boundary condition. The polymer stress was modeled using the finitely extensible nonlinear elastic-Peterlin constitutive model, and low (15%), intermediate (34%), and high drag reduction (52%) cases were examined. In drag-reduced flows, the turbulent transport of momentum and heat were still analogous, similar to the case of Newtonian flow; however, the Colburn analogy cannot be applied. Further, the two-point correlations between the temperature fluctuations and velocity components were almost identical to those of the streamwise velocity fluctuations. In addition, the spectral density distribution of the turbulent heat flux was found to be similar to that of the Reynolds shear stress in both Newtonian and drag-reduced flows. The conditionally averaged fields for the events that considerably contributed to the wall-normal turbulent heat flux were quite similar to those for the second quadrant events most contributing the Reynolds shear stress in both Newtonian and viscoelastic flows. The results of the study indicated that the turbulent transport of momentum and heat are associated with approximately identical flow structures in drag-reduced and Newtonian flows. Furthermore, an analysis of the three-dimensional joint probability density function clearly confirmed that the turbulent motions contributing to the Reynolds shear stress contributed equivalently to the turbulent heat flux in both Newtonian and drag-reduced flows.

Thermal boundary layer of laminar flow of dilute polymer solution

The thermal boundary layer flow is a canonical flow with characteristics that are present in most natural and industrial convection flows. An approximate self-similar solution is proposed for the first time for the thermal boundary layer of steady laminar flow of viscoelastic fluids, described by the finitely extensible nonlinear elastic constitutive equation with Peterlin's closure (FENE-P model). This semi-analytical thermal solution is obtained by performing an order of magnitude analysis and ensuing simplifications of the governing equations by assuming that the fluid properties are independent of temperature therefore decoupling the flow governing equations from the energy equation. The effects of viscoelasticity quantified with the Weissenberg number based on the streamwise coordinate (x) (Wix) up to Wix=1 and viscous dissipation (results are presented for Brinkman numbers between -40 and +40) on thermal boundary layer characteristics are investigated comprehensively for both constant wall temperature and constant wall heat flux. At low elasticity levels (Wix<0.01) the solution exhibits a global self-similar behavior in which flow and thermal quantities collapse on the corresponding Newtonian curves, and the polymer characteristics show a unique behavior if adequately normalized. However, by increasing flow elasticity the unique self-similar behavior of the approximate solution is lost, with the elasticity dependent results exhibiting local variations. In addition, the effects of elasticity are intensified by viscous dissipation. For the present study cases, it is observed that elasticity may change Nusselt numbers by more than 8%, and the thermal boundary layer thickens by up to 10%.

Vortex evolution patterns for flow of dilute polymer solutions in confined microfluidic cavities.

Flow instability in confined cavities has attracted extensive interest due to its significance in many natural and engineering processes. It also has applications in microfluidic devices for biomedical applications including flow mixing, nanoparticle synthesis, and cell manipulation. The recirculating vortex that characterizes the flow instability is regulated by the fluid rheological properties, cavity geometrical characteristics, and flow conditions, but there is a lack of quantitative understanding of how the vortex evolves as these factors change. Herein, we experimentally study the flow of dilute polymer solutions in confined microfluidic cavities and focus on a quantitative characterization of the vortex evolution. Three typical patterns of vortex evolution are identified in the cavity flow of dilute polymer solutions over a wide range of flow conditions. The geometrical characteristics of the cavity are found to have little effect on the patterns of vortex evolution. The geometry-independent patterns of vortex evolution provide us an intuitive paradigm, from which the interaction and competition among inertial, elastic and shear-thinning effects in these cavity-induced flow instabilities are clarified. These results extend our understanding of the flow instability of complex fluids in confined cavities, and provide useful guidelines for the design of cavity-structured microfluidic devices and their applications.

Convection Heat Transfer and Pressure Drop for Dilute Polymer Solutions Flow Inside Multi- Channels Flat Tube (Dept.M)

Convection heat transfer and pressure drop is investigated experimentally, for the flow of dilute polymer solutions (polyacrylamide) inside multi-channels flat tube and compared with water. An experimental apparatus equipped with the required measuring devices is designed and constructed to assess the effects of the operating parameters on convection heat transfer and pressure drop. The flat Aluminum multi-channels extruded tube composed of 22 parallel rectangular mini-channels (3.6 mm x 3.85 mm) with hydraulic diameter of 3.72 mm. Different polymer concentrations are considered; 10, 20, 50 and 100 ppm. This work covers a range of Reynolds number from 300 to 1200 and heat flux from 15 to 41kW/m2. The experimental measurements for flow rate, temperature, pressure, and pressure drop are taken to perform the required analysis. Therefore, the average value of convection heat transfer coefficient and friction factor for different operating parameters are computed. The obtained experimental results show that, the laminar-turbulent transition occurs in the range of Re=1100-2000. Pressure drop and in turn friction factor takes higher values for laminar flow of polymer solutions compared with water. Friction factor decreases with increasing Reynolds number for both polymer solutions and water flow inside the flat tube. Surface temperature of flat tube decreases with increasing Reynolds number for both polymer solutions and water. Accordingly, convection heat transfer coefficient and in tum Nusselt number are increased. When using polymer solutions, the surface temperature of flat tube increases compared with water. Therefore, Nusselt number is decreased. The reduction value in Nu increases with increasing concentration of polymer solution. The average value for this reduction in Nu was about 15%. An empirical correlation for Nusselt number is obtained in the range of the studied operating parameters. Comparison between the obtained experimental results with the previous data is done and gives the same trend.

Elastic Alfven waves in elastic turbulence

Speed of sound waves in gases and liquids are governed by the compressibility of the medium. There exists another type of non-dispersive wave where the wave speed depends on stress instead of elasticity of the medium. A well-known example is the Alfven wave, which propagates through plasma permeated by a magnetic field with the speed determined by magnetic tension. An elastic analogue of Alfven waves has been predicted in a flow of dilute polymer solution where the elastic stress of the stretching polymers determines the elastic wave speed. Here we present quantitative evidence of elastic Alfven waves in elastic turbulence of a viscoelastic creeping flow between two obstacles in channel flow. The key finding in the experimental proof is a nonlinear dependence of the elastic wave speed cel on the Weissenberg number Wi, which deviates from predictions based on a model of linear polymer elasticity.

Probing the strain-rotation balance in non-Newtonian turbulence with inertial particles

Experimental observations of the pair correlation function of small inertial particles in a turbulent flow of dilute polymer solutions shows that particle clustering increases with the concentration of polymers, possibly reflecting a reduction of vorticity relative to straining.

Viscoelastic Pipe Flow is Linearly Unstable.

Newtonian pipe flow is known to be linearly stable at all Reynolds numbers. We report, for the first time, a linear instability of pressure-driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used to model dilute polymer solutions. The instability is shown to exist at Reynolds numbers significantly lower than those at which transition to turbulence is typically observed for Newtonian pipe flow. Our results qualitatively explain experimental observations of transition to turbulence in pipe flow of dilute polymer solutions at flow rates where Newtonian turbulence is absent. The instability discussed here should form the first stage in a hitherto unexplored dynamical pathway to turbulence in polymer solutions. An analogous instability exists for plane Poiseuille flow.

Exploring the Molecular Distributions in Dilute Polymer Solutions Using a Multi-Scale Numerical Solver.

Simulating the rheological behaviors of polymer solutions is intrinsically a multi-scale problem. To study the macroscopic and microscopic characteristics in the fluid flow of dilute polymer solutions, we designed a multi-scale solver, which couples the Brownian Configuration Fields with the macroscopic hydrodynamic governing equations. Numerical simulation results using the multi-scale solver exhibited good accordance with the macroscopic only approach. Through a scalar field D we also quantitatively studied the flow behaviours in 2D planar channels, and analyzed the correlation between the molecular distribution and the macroscopic fluid flow in polymer solutions. Our results verified the correctness of the solver, which could provide valuable guidance for multi-scale simulations of complex fluids based on OpenFOAM.

Influence of polymer additive on flow past a hydrofoil: A numerical study

Flows of dilute polymer solutions past a hydrofoil (NACA0012) are examined by direct numerical simulation to investigate the modification of the wake pattern due to the addition of polymer. The influence of polymer additive is modeled by the FENE-P model in order to simulate a non-linear modulus of elasticity and a finite extendibility of the polymer macromolecules. Simulations were carried out at a Reynolds number of 1000 with the angle of attack varying from 0° to 20°. The results show that the influence of polymer on the flow behavior of the flow past a hydrofoil exhibits different flow regimes. In general, the addition of polymer modifies the wake patterns for all angles of attack in this study. Consequently, both drag and lift forces are changed as the Weissenberg number increases while the drag of the hydrofoil is enhanced at small angles of attack and reduced at large angles of attack. As the Weissenberg number increases, two attached recirculation bubbles or two columns of shedding vortices downstream tend to be symmetric, and the polymer tends to make the flow less sensitive to the variation of the angle of attack.

Modeling of complex fluids using micro-macro approach with transient network dynamics

In this work, the micro-macro approach is used to simulate the flow of dilute polymer solutions by means of a kinetic model coupled with the dynamics of a transient network. The transient network modeling is based on the original formulation, in which the kinetics of microstates describes the complexity of interactions among the macromolecules suspended in a Newtonian solvent (Rincon et al, J Non-Newton Fluid 131:64–77, 2005). The average concentration of microstates, at a given time, defines a variable maximum segment length (variable extensibility) of the molecular FENE model. The non-Newtonian contribution to the extra stress tensor is computed according to the Brownian configuration-fields method. Comparisons with the Oldroyd-B model validates its limiting behavior. Numerical results show the influence of the solvent to total viscosity ratio and shear rate, on the transient and steady rheological phenomena of complex fluids with microstates.

Fluttering conditions of an energy harvester for autonomous powering

Flapping states of an energy harvesting device have been investigated by means of experiments, numerical simulations and a phenomenological model. The main aim is to predict the geometrical/physical properties of the system allowing sustained flapping limit cycles to emerge. These latter regimes are interesting when the system is used to harvest energy from flows. The main argument to identify flapping states is based on a simple resonance condition between the characteristic (elastic) time of the system and the flow time-scale. Similar arguments have been successful in other fields of fluid dynamics and fluid-structure interactions including turbulent flows of dilute polymer solutions and interactions between the wake originated by bluff bodies and elastic structures. The predictions of the geometrical/physical properties associated to critical conditions (i.e. those separating stable stages from flapping regimes) have been compared against the results of experiments, numerical simulations and a phenomenological model based on a set of ordinary differential equations. Results clearly confirm the expectations from the resonance condition. Discussions on how to extend our analysis in situations where the extraction stage is taken into account are also provided: this latter is indeed expected to influence the flapping stage and thus the critical conditions for flapping.

A RANS model for heat transfer reduction in viscoelastic turbulent flow

Direct numerical simulations (DNS) were carried out to investigate turbulent heat transfer in a channel flow of homogenous polymer solutions described by the Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) constitutive model at intermediate and high Prandtl numbers (Pr=1.25 and 5). Time-averaged statistics of temperature fluctuations, turbulent heat fluxes, thermal turbulent diffusivity, and of budget terms of the temperature variance are reported and compared with those of the Newtonian fluid cases at the same Prandtl and Reynolds numbers. Moreover, twenty one sets of DNS data of fluid flow are utilized to improve existing k–ε–v2‾–f models for FENE-P fluids to deal with turbulent flow of dilute polymer solutions up to the high drag reduction regime; specifically the dependency of closures on the wall friction velocity is removed. Furthermore, five sets of recent DNS data of fluid flow and heat transfer of FENE-P fluids were used to develop the first RANS model capable of predicting the heat transfer rates in viscoelastic turbulent flows. In this model, an existing closure for calculating the turbulent Prandtl number for Newtonian fluids is extended to deal with heat transfer in turbulent viscoelastic fluids. Predicted polymer stresses, velocity profiles, mean temperature profiles, and turbulent flow characteristics are all in good agreement with the DNS data, and show improvement over previous RANS models.

Simple framework for understanding the universality of the maximum drag reduction asymptote in turbulent flow of polymer solutions.

Self-consistent direct numerical simulations of turbulent channel flows of dilute polymer solutions exhibiting friction drag reduction (DR) show that an effective Deborah number defined as the ratio of polymer relaxation time to the time scale of fluctuations in the vorticity in the mean flow direction remains O(1) from the onset of DR to the maximum drag reduction (MDR) asymptote. However, the ratio of the convective time scale associated with streamwise vorticity fluctuations to the vortex rotation time decreases with increasing DR, and the maximum drag reduction asymptote is achieved when these two time scales become nearly equal. Based on these observations, a simple framework is proposed that adequately describes the influence of polymer additives on the extent of DR from the onset of DR to MDR as well as the universality of the MDR in wall-bounded turbulent flows with polymer additives.