Finitely Extensible Nonlinear elastic-Peterlin Research Articles

Understanding Deformation and Breakup Tendency of Shear-Thinning Viscoelastic Drops in Constricted Microchannels.

The study of drop deformation in response to various stresses has long piqued the interest of several academics. The deformation behavior of cells, drug carriers, and even drug particles moving via microcapillaries inside the human body can be modeled using a viscoelastic drop model. A drop breakup study can also provide better design guidance for nanocarriers that can deliver on-demand burst drug releases at specific cancer sites. Thus, we attempted to investigate the deformation and breakup of a shear-thinning finitely extensible nonlinear elastic-peterlin (FENE-P) drop moving through the constricted microchannel. The computational simulation suggested that drop deformation and breakup can be manipulated by varying of parameters like channel confinement, Deborah number, solvent viscosity ratio, viscosity ratio, and capillary number. We attempted to find the critical capillary number for initiation of drop breakup. Observations from present study will give valuable insights into deformation and breakup patterns of drug carriers inside constricted microcapillaries. The simulations of the two-phase viscoelastic drop─Newtonian matrix system were performed on an open-source solver, Basilisk.

Vortex merging and splitting events in viscoelastic Taylor–Couette flow

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 finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive equation to model the polymer dynamics, which reproduce the experimental observations with great accuracy and elucidate the reasons for the onset of this surprising dynamics. Starting from the Newtonian limit and increasing progressively the fluid's elasticity, we demonstrate that the VMS dynamics is not associated with the well-known Taylor vortices, but with a steady pattern of elastically induced axisymmetric vortex pairs known as diwhirls. The amount of angular momentum carried by these elastic vortices becomes increasingly small as the fluid's elasticity increases and it eventually reaches a marginal level. When this occurs, the diwhirls become dynamically disconnected from the rest of the system and move independently from each other in the axial direction. It is shown that vortex merging and splitting events, along with local transient chaotic dynamics, result from the interactions among diwhirls, and that this complex spatio-temporal dynamics persists even at elasticity levels twice as large as those investigated experimentally.

Mathematical Analysis of Peristaltic Pumps for Fene-P model subject to Hall and Joule impact

A mathematical model is developed to discuss the impact of the Hall current and the Joule heating on the peristaltic flux of finitely extensible nonlinear elastic Peterlin (FENE-P) fluid in a tapered tube with mild stenosis. The fluid movement along the wall surface resulted from the sinusoidal wave flowing with constant speed. Conditions of velocity and thermal slip are applied. Lubrication approximation is adopted to modify the governing flow problem. To discover the solution to a system of equations, the regular perturbation approach is used. The effects of the different physical parameters are debated and graphically shown in a set of figures. It is discovered that as the Hall current parameter is increased and the Hartman number is decreased, the fluid velocity increases. It is also worth noting that the Dufour number causes the fluid temperature to rise, whilst the Hall current parameter causes the temperature to fall. In the meantime, both the Hall current parameter and the Soret number have the opposite effect on concentration. The trapping phenomenon is thoroughly investigated.

Influence of FENE-P fluid on drag reduction and heat transfer past a magnetized surface

This paper presents the finitely extensible nonlinear elastic-Peterlin (FENE-P) fluid model to analyze how polymeric fluid affects drag and heat transfer over a magnetized stretching surface. The FENE-P is one of the viscosity models used to study the behavior of polymeric fluids. The governing boundary layer equations based on physical laws are transformed into a similar form using appropriated transformation. To discuss the impacts of polymers and magnetic fields on flow and heat transfer, the resulting equations are numerically solved using the shooting method, and the outcomes are presented graphically. The role of magnetic fields and polymers as drag-reducing and heat transfer enhancing agents is also thoroughly discussed.

Response of Viscoelastic Turbulent Pipeflow Past Square Bar Roughness: The Effect on Mean Flow

The influence of viscoelastic polymer additives on response and recovery of turbulent pipeflow over square bar roughness elements was examined using Direct Numerical Simulations at a Reynolds number of 5×103. Two different bar heights for the square bar roughness elements were examined, h/D=0.05 and 0.1. A Finitely Extensible Non-linear Elastic-Peterlin (FENE-P) rheological model was employed for modeling viscoelastic fluid features. The rheological parameters for the simulation corresponded to a high concentration polymer of 160 ppm. Recirculation regions formed behind the bar elements by the viscoelastic fluid were shorter than those associated with Newtonian fluid, which was attributed to mixed effects of viscous and elastic forces due to the added polymers. The recovery of the mean viscoelastic flow was faster. The pressure losses on the surface of the roughness were larger compared to the Newtonian fluid, and the overall contribution to local drag was reduced due to viscoelastic effects.

Distinguishing thixotropy from viscoelasticity

Owing to nonlinear viscoelasticity, materials often show characteristic features that resemble those of thixotropy. This issue has been debated in the literature over the past several decades, and several experimental protocols have been proposed to distinguish thixotropy from viscoelasticity. In this work, we assess these protocols by carrying out experiments using polymer solutions, thixotropic clay dispersions, and modeling their behavior, respectively, using the finitely extensible nonlinear elastic—Peterlin (FENE-P) constitutive equation and a viscoelastic aging model. We find that the criteria proposed in the literature, such as a step-down jump in the shear rate and shear start-up at different waiting times elapsed since preshear, are inadequate to distinguish thixotropy from viscoelasticity. In marked contrast, we show that the application of step-strain or step-stress after cessation of the preshear serves as a useful discriminant between thixotropy and viscoelasticity. In thixotropic materials, we observe that the application of step strain (or step stress) after cessation of the preshear eventually leads to slowing down of relaxation dynamics as a function of waiting time. However, for viscoelastic materials, the relaxation modulus (creep compliance) curve shifts to lower modulus (higher compliance) values as a function of waiting time until equilibrium is reached. While the proposed criterion offers a robust distinction between viscoelasticity and thixotropy for the systems studied here, further experimental investigations based on other systems are needed to establish its versatility and will lead to a greater insight into this long-standing issue in rheological categorization.

A FENE-P k–ε Viscoelastic Turbulence Model Valid up to High Drag Reduction without Friction Velocity Dependence

A viscoelastic turbulence model in a fully-developed drag reducing channel flow is improved, with turbulent eddies modelled under a k–ε representation, along with polymeric solutions described by the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model. The model performance is evaluated against a wide variety of direct numerical simulation data, described by different combinations of rheological parameters, which is able to predict all drag reduction (low, intermediate and high) regimes with good accuracy. Three main contributions are proposed: one with a simplified viscoelastic closure for the NLTij term (which accounts for the interactions between the fluctuating components of the conformation tensor and the velocity gradient tensor), by removing additional damping functions and reducing complexity compared with previous models; second through a reformulation for the closure of the viscoelastic destruction term, Eτp, which removes all friction velocity dependence; lastly by an improved modified damping function capable of predicting the reduction in the eddy viscosity and thus accurately capturing the turbulent kinetic energy throughout the channel. The main advantage is the capacity to predict all flow fields for low, intermediate and high friction Reynolds numbers, up to high drag reduction without friction velocity dependence.

Reynolds-Averaged Simulation of the Fully Developed Turbulent Drag Reduction Flow in Concentric Annuli

AbstractReynolds-averaged modeling is performed for polymer-induced drag reduction (DR) fluid at the fully developed turbulent regime in a concentric annulus by using the commercial code, ansys-fluent. The numerical approach adopted in this study relies on a modified k–ε–v2¯–f model to characterize the turbulence and the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model to represent the rheological behavior of the polymer solution. The near-wall axial velocity, Reynolds stress, and turbulent kinetic energy (TKE) budget near both walls of the annulus (fixed radius ratio of 0.4) are compared in detail at a constant Reynolds number (Re=10,587) and various rheological parameters (Weissenberg number We in the range of 1–7 and the maximum polymer elongation L = 30 and 100). Current simulation has predicted the redistributions of turbulent statistics in the annulus, where the two turbulent boundary layers (TBLs) of the DR flow differ more compared to those of its Newtonian counterpart. The difference is also found to be highly dependent on the rheological properties of the viscoelastic fluid.

Vortex generation in a finitely extensible nonlinear elastic Peterlin fluid initially at rest

AbstractIt is well known that the mixing of two or more species in flows at low Reynolds numbers cannot be easily achieved since inertial effects are essentially absent and molecular diffusion is slow. To achieve mixing in Newtonian fluids under these circumstances requires innovative new ideas such as the use of external body forces (eg, electromagnetic mixers) or the stretching and folding of fluid elements (eg, chaotic advection). For non‐Newtonian fluids with elasticity, mixing can be achieved by enabling the emergence of elastic instabilities that results in chaotic flows in which mixing is significantly enhanced. In this work, our goal is to demonstrate that clearly identifiable vortical structures (eg, vortex rings) can be generated in a viscoelastic fluid initially at rest by the release of elastic stresses. In turn, these vortex motions promote bulk mixing by transporting fluid elements from one location to another more efficiently than diffusion alone. We demonstrate this first theoretically by using the finitely extensible nonlinear elastic Peterlin (FENE‐P) model to show that elastic forces can generate torque. Using this model, we derive an expression for the time rate of change of vorticity in an elastic fluid initially at rest caused by a sudden release of stored elastic stress. This process can be thought of as the release of elastic energy from a stretched rubber band that is suddenly cut at its center. We confirm this ansatz by performing a series of direct numerical simulations based on an in‐house pseudo‐spectral code that couples the FENE‐P model to the equations of motion for an incompressible fluid. The simulations reveal that a pair of vortex rings traveling in opposite directions, with Reynolds numbers on the order of one, is generated from the sudden release of elastic stresses. Secondary vortical structures are also generated. In the concluding section of this work, we address the potential for vortex motions generated by elastic stresses to promote mixing in microflows, and we describe a possible experiment that may demonstrate this effect.

Combined Influence of Fluid Viscoelasticity and Inertia on Forced Convection Heat Transfer From a Circular Cylinder

AbstractIn this study, the combined influence of fluid viscoelasticity and inertia on the flow and heat transfer characteristics of a circular cylinder in the steady laminar flow regime have been studied numerically. The momentum and energy equations together with an appropriate viscoelastic constitutive equation have been solved numerically using the finite volume method over the following ranges of conditions: Reynolds number, 0.1≤Re≤20; elasticity number (= Wi/Re, where Wi is the Weissenberg number), 0≤El≤0.5; Prandtl number, 10≤Pr≤100 for Oldroyd-B and finitely extensible nonlinear elastic-Peterlin (FENE-P) (with two values of the chain extensibility parameter L2, namely 10 and 100) viscoelastic fluid models including the limiting case of Newtonian fluids (El = 0). New extensive results are presented and discussed in terms of the streamline and isotherm profiles, drag coefficient, distribution of the local and surface averaged Nusselt number. Within the range of conditions embraced here, the separation of boundary layers (momentum and thermal) is seen to be completely suppressed in an Oldroyd-B fluid whereas it is accelerated for a FENE-P fluid in comparison with that seen for a Newtonian fluid otherwise under identical conditions. At a fixed elasticity number, both the drag coefficient and average Nusselt number are seen to be independent of the Reynolds number beyond a critical value for an Oldroyd-B fluid. In contrast, the drag coefficient decreases and the average Nusselt number increases with Reynolds number for a FENE-P fluid at a constant value of the elasticity number. Finally, a simple correlation for the average Nusselt number for a FENE-P fluid is presented which facilitates the interpolation of the present results for the intermediate values of the governing parameters and/or its a priori estimation in a new application.

A turbulent duct flow investigation of drag-reducing viscoelastic FENE-P fluids based on different low-Reynolds-number models

Drag reduction of viscoelastic fluids under turbulent flow regime is an important phenomenon and well observed by many researchers. In this paper, turbulent flow characteristics under drag reduction condition are compared using four different low-Reynolds number k- ε models namely, Lam–Bremhorst, Launder–Sharma, Nagano–Hishida and Chien. The viscoelastic turbulence closure of Resende et al. (2011) is adopted. Time-averaged momentum and rheological constitutive equations based on finitely extensible nonlinear elastic-Peterlin (FENE-P) model are used and a polymeric contribution to the eddy viscosity equation is considered. The simulations are conducted for two sets of rheological parameters identified by Reτ0 = 395, β=0.9, L2 = 900 and Weτ0 = 25, 100 corresponding to drag reductions of 18% and 37%. Validation against DNS data is carried out for profiles of mean velocity, viscoelastic stress tensor, turbulent kinetic energy and its rate of dissipation. The differences are mainly limited to the viscous and buffer layer regions. While Nagano–Hishida and Chien models overpredict the DNS drag reduction results in both cases, the two other models underpredict them. The Lam–Bremhorst has the most accurate drag reduction results as a consequence of better capturing the near-wall effects.

Numerical simulation of a viscoelastic RANS turbulence model in a diffuser

One of the newest viscoelastic RANS turbulence models for drag reducing flows with polymer additives is studied considering different rheological properties. A finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model is used to describe the viscoelastic effect of the polymer solutions and the $$k - \varepsilon - \overline {{v^2}} - f$$ turbulence framework is applied for turbulence modelling. The geometry in this study is a twodimensional diffuser. The finite volume method (FVM) with a non-uniform collocated mesh is used to solve the momentum and constitutive equations. In order to evaluate the turbulence model, the flow is simulated with different parameters such as the Weissenberg number and the maximum polymer extensibility and compared with the experimental results qualitatively. The velocity profiles, pressure distribution, reattachment length, and the amount of the drag reduction predicted by the turbulence model are in line with the experimental results.

Analytical Upper Limit of Drag Reduction With Polymer Additives in Turbulent Pipe Flow

Flow drag reduction induced by chemical additives, more commonly called drag-reducing agents (DRAs), has been studied for many years, but few studies can manifest the mechanism of this phenomenon. In this paper, a new mathematical model is proposed to predict the upper limit of drag reduction with polymer DRAs in a turbulent pipe flow. The model is based on the classic finitely extensible nonlinear elastic-Peterlin (FENE-P) theory, with the assumption that all vortex structures disappear in the turbulent flow, i.e., complete laminarization is achieved. With this model, the maximum drag reduction by a DRA at a given concentration can be predicted directly with several parameters, i.e., bulk velocity of the fluid, pipe size, and relaxation time of the DRA. Besides, this model indicates that both viscosity and elasticity contribute to the drag reduction: before a critical concentration, both viscosity and elasticity affect the drag reduction positively; after this critical concentration, elasticity still works as before but viscosity affects drag reduction negatively. This study also proposes a correlation format between drag reduction measured in a rheometer and that estimated in a pipeline. This provides a convenient way of pipeline drag reduction estimation with viscosity and modulus of the fluids that can be easily measured in a rheometer.

Dynamics of a single buoyant plume in a FENE-P fluid

The dynamics of a single laminar buoyant plume in a FENE-P (finitely extensible nonlinear elastic-Peterlin) fluid has been investigated by performing a series of direct simulations over a range of Weissenberg numbers. Examination of this flow has given insight into the heat transfer reduction phenomenon observed recently in more complex Rayleigh-Benard turbulence. The simulations, which were performed with a Rayleigh number of 2.53×106 and a maximal polymeric extension of L = 100, show that the wall heat flux is reduced by about 28% at a Weissenberg number of 20, which is in reasonable agreement with the results obtained in Rayleigh-Benard turbulence. In addition, the global flow kinetic energy was reduced by about one order of magnitude.

Parametric study of a viscoelastic RANS turbulence model in the fully developed channel flow

One of the newest of viscoelastic RANS turbulence models for drag reducing channel flow with polymer additives is studied in different flow and rheological properties. In this model, finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model is used to describe the viscoelastic effect of polymer solution and turbulence model is developed in the k-ϵ-(ν^2 ) -f framework. The geometry in this study is two-dimensional channel flow and finite volume method (FVM) with a non-uniform collocated mesh is used to solve the momentum and constitutive equations. In order to evaluate this turbulence model, several cases with different parameters such as Reynolds numbers, Weissenberg number, maximum polymer extensibility and concentration of polymer are simulated and assessed against direct numerical simulation (DNS) data. The velocity profiles, shear stress profiles and the percentage of friction drag reduction predicted by this turbulence model are in good agreement with DNS data at moderate to high Reynolds numbers. However, in low Reynolds numbers, the results of model are reliable only for low 〖 L〗^2 value. Moreover, in case of high concentration of polymer, the accuracy of the model is lost.

Kinetics and Morphology of Flow Induced Polymer Crystallization in 3D Shear Flow Investigated by Monte Carlo Simulation

To explore the kinetics and morphology of flow induced crystallization of polymers, a nucleation-growth evolution model for spherulites and shish-kebabs is built based on Schneider rate model and Eder model. The model considers that the spherulites are thermally induced, growing like spheres, while the shish-kebabs are flow induced, growing like cylinders, with the first normal stress difference of crystallizing system being the driving force for the nucleation of shish-kebabs. A two-phase suspension model is introduced to describe the crystallizing system, which Finitely Extensible Non-linear Elastic-Peterlin (FENE-P) model and rigid dumbbell model are used to describe amorphous phase and semi-crystalline phase, respectively. Morphological Monte Carlo method is presented to simulate the polymer crystallization in 3D simple shear flow. Roles of shear rate, shear time and shear strain on the crystallization kinetics, morphology, and rheology are analyzed. Numerical results show that crystallization kinetics, morphology and rheology in shear flow are qualitatively in agreement with the theoretical, experimental and other numerical works which verifies the validity and effectiveness of our model and algorithm. To our knowledge, this is the first time that a model and an algorithm revealing the details of crystal morphology have been applied to the flow induced crystallization of polymers.

Hall Effect on Falkner—Skan Boundary Layer Flow of FENE-P Fluid over a Stretching Sheet

The Falkner—Skan boundary layer steady flow over a flat stretching sheet is investigated in this paper. The mathematical model consists of continuity and the momentum equations, while a new model is proposed for MHD Finitely Extensible Nonlinear Elastic Peterlin (FENE-P) fluid. The effects of Hall current with the variation of intensity of non-zero pressure gradient are taken into account. The governing partial differential equations are first transformed to ordinary differential equations using appropriate similarity transformation and then solved by Adomian decomposition method (ADM). The obtained results are validated by generalized collocation method (GCM) and found to be in good agreement. Effects of pertinent parameters are discussed through graphs and tables. Comparison with the existing studies is made as a limiting case of the considered problem at the end.

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.

Grid and subgrid-scale interactions in viscoelastic turbulent flow and implications for modelling

ABSTRACTUsing direct numerical simulations of turbulent plane channel flow of homogeneous polymer solutions, described by the Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) rheological constitutive model, a-priori analyses of the filtered momentum and FENE-P constitutive equations are performed. The influence of the polymer additives on the subgrid-scale (SGS) energy is evaluated by comparing the Newtonian and the viscoelastic flows, and a severe suppression of SGS stresses and energy is observed in the viscoelastic flow. All the terms of the transport equation of the SGS kinetic energy for FENE-P fluids are analysed, and an approximated version of this equation for use in future large eddy simulation closures is suggested. The terms responsible for kinetic energy transfer between grid-scale (GS) and SGS energy (split into forward/backward energy transfer) are evaluated in the presence of polymers. It is observed that the probability and intensity of forward scatter events tend to decrease in the presence of polymers.

Simulation of polymer filling process by an improved smoothed particle hydrodynamics method based on higher-order Taylor expansion

In this work, an improved smoothed particle hydrodynamics (SPH) method based on higher order Taylor expansion (CSPH_HT) is proposed and tentatively applied to the filling process of the viscoelastic fluid. Owing to the disadvantages of the traditional SPH method and the presented corrected SPH methods, the CSPH_HT method based on the higher order Taylor expansion is proposed and described in detail. In order to illustrate the validity and merits of the CSPH_HT method, two benchmark problems are simulated and discussed. The numerical results show that the proposed CSPH_HT method has higher numerical accuracy and better stability. Subsequently, the proposed improved SPH method is extended to simulate the filling processes of the viscoelastic fluid in the ring-shaped mold, for the purpose of exhibiting the capacity of the proposed method. The extended pom-pom (XPP) model and finitely extensible nonlinear elastic-Peterlin (FENE-P) model fluid are all considered in this case, in which the viscoelastic fluid flow and extra stress are shown. The differences in fluid flow between the XPP model and FENE-P model are also discussed. Finally, the filling process of the viscoelastic fluid in the square mold with single inlet or two inlets are tentatively simulated. The differences between the filling process of XPP fluid and the filling process of FENE-P fluid are shown, and the influences of the parameters of the mold on the flow are analyzed. Especially, the influences of locations and sizes of two inlets on the filling process of viscoelastic fluid are illustrated. The XPP model fluid and FENE-P model fluid show different characteristics in the filling process and small change of the size of the mold can lead to obvious change of the flow.