Jet Buckling Research Articles

Numerical investigation of non-Newtonian power law flows using B-spline material point method

• A weakly compressible BSMPM method for simulating non-Newtonian flow is proposed. • Complex free surface flow and fluid structure interaction problems for power law fluid are studied. • Shear thickening/thinning, jet buckling/splashing, and vortex whirling are well represented. • Results demonstrate the efficacy of the proposed method for non-Newtonian power law flow problems. Simulating the complex flow with free surface and large deformation of non-Newtonian fluid is a challenging problem and plays a significant role in many industrial areas. In this paper, a weakly compressible B-spline material point method (WC-BSMPM) is presented and extended to solve the complex free surface flow of non-Newtonian fluid with a power law rheology model. Numerical examples including two-dimensional problems of plane Poiseuille, dam break, and container filling flow as well as three-dimensional sphere water entry problems are adopted to demonstrate the effectiveness and capabilities of the proposed method. The simulated results show good agreements with analytical solutions or published experimental data. Moreover, significant flow features for non-Newtonian power law fluid, including shear thickening, shear thinning, jet buckling, jet splashing, vortex whirling, and fluid-structure interactions can be well captured. Meanwhile, the numerical noise of the traditional MPM can be eliminated by the proposed method, which confirms that the WC-BSMPM method is a promising alternative to simulate the complex free surface flow and fluid-structure interactions for the non-Newtonian power law fluid.

Numerical and dimensional analysis for the jet buckling of highly viscous fluid

Jet buckling of highly viscous fluid is a common phenomenon both in nature and industry. In order to effectively understand this phenomenon, experiments, numerical simulation and dimensional analysis are employed with the jet buckling of rubber melt and in injection molding. To begin with the construction of two high-resolution discretization schemes for convection terms, a three dimensional algorithm for liquid jet buckling phenomenon is established based on two phase flow model and discretization via finite volume method. The developed algorithm shows its good accuracy and stability for jet buckling simulation. The numerical results are in good agreement with experimental results obtained by camera directly and short shot experiments. It is found shear rate and gravity have an effect on jet buckling. Compared to non-buckling, buckling of liquid occurs at high shear rate. Direction of gravity influences the length of jet and the pattern of buckling. Furthermore, dimensional analysis of buckling is carried out based on experimental and numerical results. Results reveal that the influence of gravity on buckling is greater when gravity is vertical than parallel to velocity. Dimensional analysis illustrates that shear rate has a greater effect on buckling frequency than hydraulic radius of inlet, length of cavity, gravitational force, viscous force and kinematic viscosity. The buckling frequency is approximately proportional to the square of the shear rate.

High Weissenberg number simulations with incompressible Smoothed Particle Hydrodynamics and the log-conformation formulation

Viscoelastic flows occur widely, and numerical simulations of them are important for a range of industrial applications. Simulations of viscoelastic flows are more challenging than their Newtonian counterparts due to the presence of exponential gradients in polymeric stress fields, which can lead to catastrophic instabilities if not carefully handled. A key development to overcome this issue is the log-conformation formulation, which has been applied to a range of numerical methods, but not previously applied to Smoothed Particle Hydrodynamics (SPH). Here we present a 2D incompressible SPH algorithm for viscoelastic flows which, for the first time, incorporates a log-conformation formulation with an elasto-viscous stress splitting (EVSS) technique. The resulting scheme enables simulations of flows at high Weissenberg numbers (accurate up to Wi=85 for Poiseuille flow). The method is robust, and able to handle both internal and free-surface flows, and a range of linear and non-linear constitutive models. Several test cases are considerd included flow past a periodic array of cylinders and jet buckling. This presents a significant step change in capabilties compared to previous SPH algorithms for viscoelastic flows, and has the potential to simulate a wide range of new and challenging applications.

Extension rate and bending behavior of electrospinning jet: The role of solution conductivity

Two model solutions, one containing organic salt and the other none, of poly(N-isopropylacrylamide) (PNIPAM) in DMF solvent with the same concentration of 17 wt% were electrospun to investigate the extension rate profile in the straight jet as well as the subsequent jet bending (whipping) behavior. Both model solutions have identical rheological properties, while the solution with added salt possesses electrical conductivity 16 fold higher than the other. At a given flow rate of Q, light scattering experiments were carried out to derive the jet diameters of the straight segment dj at different jet positions z so that the z-dependence of jet velocity (vj, = 4Q/πdj2) was feasibly calculated, from which the profile of extension rate (ε˙) was obtained by dvj/dz. Using high speed video imaging, the onset of jet bending was observed, and the motion of the first bend was traced, from which the extension rate of the bending jet could be also estimated.Compared to the neat solution, the solution with salt exhibits a bigger Taylor cone and a shorter straight segment with a larger jet-end diameter to proceed the subsequent jet bending process. Moreover, the magnitudes of ε˙ in the straight jet and in the bending jet are all dramatically enhanced with solution conductivity, yielding PNIPAM fibers with a smaller diameter on the grounded collector. Our results show that it is the extension rate developed in the spin line plays an important role in determining the final fiber diameter. The onset of bending instability is attributed to the local buckling in the end section of the straight jet, which is unambiguously observed by video imaging with a high frame rate of 104 fps. The formation of jet buckling is due to the compressive forces associated with the air drag to resist the electric stretching force induced by the setup electric field. The dynamics of bending jet was elucidated in this work.

Particle-based fluids for viscous jet buckling

In this paper, we introduce a novel meshfree framework for animating free surface viscous liquids with jet buckling effects, such as coiling and folding. Our method is based on Smoothed Particle Hydrodynamics (SPH) fluids and allows more realistic and complex viscous behaviors than the previous SPH frameworks in computer animation literature. The viscous liquid is modeled by a non-Newtonian fluid flow and the variable viscosity under shear stress is achieved using a viscosity model known as Cross model. We demonstrate the efficiency and stability of our framework in a wide variety of animations, including scenarios with arbitrary geometries and high resolution of SPH particles. The interaction of the viscous liquid with complex solid obstacles is performed using boundary particles. Our framework is able to deal with different inlet velocity profiles and geometries of the injector, as well as moving inlet jet along trajectories given by cubic Hermite splines. Moreover, the simulation speed is significantly accelerated by using Computer Unified Device Architecture (CUDA) computing platform.

Melt electrospinning in a parallel electric field

ABSTRACTElectrospinning is an efficient and direct method of fabricating nanofibers. Fibers are frequently unstable in the electrospinning process, and the uneven distribution of the electric field is an important factor leading to instability. Experimental and finite element simulation studies are conducted on the process of melt electrospinning in a parallel electric field. Two parallel metal disks are used to successfully generate a uniform electric field. Electric field intensity on the edges of the metal disk is always stronger than the field at the center of the disk or at the spinneret bottom. The diameters, distances, and relative areas of these disks significantly affect the distribution of the electric field. Thus, the parallel electric field effectively reduces jet buckling in melt electrospinning. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014, 52, 946–952

A SPH-based particle method for simulating 3D transient free surface flows of branched polymer melts

In this article we present a particle method based on smoothed particle hydrodynamics (SPH) for simulating three-dimensional (3D) transient free surface flows of branched polymer melts which are governed by the single equation version of the eXtended Pom-Pom (XPP) model. In order to remedy the so-called tensile instability which results in particle clustering and unphysical fracture in the state of fluid stretching, both artificial stress and artificial viscosity are incorporated into the momentum equation. For facilitating the implementation of the wall boundary condition in 3D space, an enhanced treatment of solid boundaries is proposed in this paper. The proposed SPH algorithm is validated by the excellent agreement between the numerical and the analytical solutions of Hagen-Poiseuille flow of an Oldroyd-B fluid. To demonstrate the ability of the numerical method in simulating free surface flows of branched polymer melts, the fall and impact on a rigid plate of a XPP fluid droplet is investigated for a wide range of the relevant parameters. Specifically, the convergence of the numerical results is discussed by three particle sizes of different levels of refinement. To provide some additional applications of 3D free surface flows of branched polymer melts, the challenging jet buckling and rod-climbing effect of viscoelastic fluids are further simulated and analyzed. All numerical results establish the capability of the SPH-based particle method to simulate 3D transient free surface flows of branched polymer melts in an entirely mesh-free framework.

SPH simulations of three-dimensional non-Newtonian free surface flows

In this paper, the smoothed particle hydrodynamics (SPH) method is extended to deal with three-dimensional (3D) non-Newtonian flows with complex free surfaces, in which the viscosity is modeled using the Cross model. In order to alleviate the so-called tensile instability which leads to particle clustering and unphysical fracture in fluid stretching, an artificial stress term is particularly incorporated into the momentum equation. For convenience in implementation of wall boundary condition in 3D, an enhanced treatment of solid boundaries is proposed to improve the computational performance. Parallelization is also developed to ensure affordable computational time of simulations involving millions of particles. The proposed SPH algorithm is validated by solving the Hagen–Poiseuille flow and comparing the SPH results with the available analytical solutions. To demonstrate the ability of the numerical method in simulating 3D non-Newtonian flows with free surfaces, three challenging engineering applications, including the impacting droplet, molding injection of a thin plate mold and a Z-shaped mold, and jet buckling, are investigated. It is found that the shear-thinning behavior can be well displayed in all cases, and the proposed SPH algorithm is stable and fairly accurate and agrees well with the available data.

Numerical simulation of 3D-unsteady viscoelastic free surface flows by improved smoothed particle hydrodynamics method

In this paper, a working smoothed particle hydrodynamics (SPH) method is introduced to solve three-dimensional (3D) transient viscoelastic flows with complex free surfaces. In order to alleviate the unphysical behavior of fracture and particle clustering in fluid stretching which is the so-called tensile instability, an artificial stress term is incorporated into the momentum equation. To facilitate the enforcement of 3D wall boundaries, a new boundary treatment technique, which can observably improve the computational efficiency, is proposed. The proposed SPH method is validated by solving the Hagen–Poiseuille flow of an Oldroyd-B fluid and comparing the SPH results with the available analytical solutions. Two challenging fluid flow problems, namely, a viscoelastic drop impacting on a rigid plate and jet buckling, are simulated to demonstrate the capability of the proposed SPH method in handing 3D viscoelastic free surface flows. Results for a Newtonian fluid are also shown for comparison. All numerical results obtained are in agreement with the available data.

The SPH approach to the process of container filling based on non-linear constitutive models

In this work, the transient free surface of container filling with non-linear constitutive equation’s fluids is numerically investigated by the smoothed particle hydrodynamics (SPH) method. Specifically, the filling process of a square container is considered for non-linear polymer fluids based on the Cross model. The validity of the presented SPH is first verified by solving the Newtonian fluid and Oldroyd-B fluid jet. Various phenomena in the filling process are shown, including the jet buckling, jet thinning, splashing or spluttering, steady filling. Moreover, a new phenomenon of vortex whirling is more evidently observed for the Cross model fluid compared with the Newtonian fluid case.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom–Pom model

This work presents numerical simulations of two fluid flow problems involving moving free surfaces: the impacting drop and fluid jet buckling. The viscoelastic model used in these simulations is the eXtended Pom–Pom (XPP) model. To validate the code, numerical predictions of the drop impact problem for Newtonian and Oldroyd-B fluids are presented and compared with other methods. In particular, a benchmark on numerical simulations for a XPP drop impacting on a rigid plate is performed for a wide range of the relevant parameters. Finally, to provide an additional application of free surface flows of XPP fluids, the viscous jet buckling problem is simulated and discussed.

Numerical simulations of mounding and submerging flows of shear-thinning jets impinging in a container

Continuous jets of non-Newtonian fluids impinging on a fluid surface exhibit instabilities from jet buckling and coiling at low Reynolds numbers to delayed die swell, mounding, and air entrainment at higher Reynolds numbers. Filling containers with complex fluids is an important process for many industries, where the need for high throughput requires operating at high Reynolds numbers. In this regime, air entrainment can produce a visually unappealing product, causing a major quality control issue. Just prior to the onset of air entrainment, however, there exists an ideal filling regime which we term “planar filling,” as it is characterized by a relatively flat free surface that maintains its shape over time. In this paper, we create a steady-state, 2-D axisymmetric finite element model to study the transition from planar filling to the onset of air entrainment in a container filling process with generalized-Newtonian fluids. We use this model to explore the operating window for Newtonian and shear-thinning (or, more generally, deformation-rate-thinning) fluids, demonstrating that the flow behavior is characterized by a balance between inertial, viscous, and gravitational forces, as characterized by the Reynolds and Froude numbers. A scaling analysis suggests that the relevant parameters for calculating these dimensionless numbers are located where the jet impacts the liquid surface, and simulations show that the transition from planar filling to air entrainment often occurs when Re ∼ O ( 10 ) . We found that the bottom and side surfaces of the container drastically influence this transition to entrainment, stabilizing the flow.

Improved SPH Approach to Branched Polymer Free Surface Flows Based on the XPP Model

In this work, an improved smoothed particle hydrodynamics (IMSPH) method is presented to simulate a polymer-free surface based on XPP model. The IMSPH is a coupled approach between smoothed particle hydrodynamics (SPH) method and the finite particle method (FPM), which possesses higher accuracy and better stability than SPH, especially on boundary. An artificial stress term is added to IMSPH for removing the unphysical phenomenon. The examples of impacting drop and jet buckling are investigated, and the influence of the physical parameters on moving free surface with high Weissenberg number is considered. All the numerical results agree well with the available data.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

A finite difference technique for solving the Oldroyd-B model for 3D-unsteady free surface flows

This work presents a numerical method for solving three-dimensional (3D) viscoelastic unsteady free surface flows governed by the Oldroyd-B constitutive equation. It is an extension of the two-dimensional (2D) technique introduced by Tomé et al. [M.F. Tomé, N. Mangiavacchi, J.A. Cuminato, A. Castelo, S. McKee, A numerical technique for solving unsteady viscoelastic free surface flows, J. Non-Newt. Fluid Mech. 106 (2002) 61–106]. The governing equations are solved by a finite difference method on a 3D-staggered grid. Marker particles are employed to describe the fluid providing both visualization and the location of the free surface. The numerical technique is validated by using an exact solution of the flow of an Oldroyd-B fluid inside a 3D-pipe. Numerical results include the simulation of the transient extrudate swell and jet buckling.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5].

Numerical simulation of 3D viscoelastic flows with free surfaces

A numerical model is presented for the simulation of viscoelastic flows with complex free surfaces in three space dimensions. The mathematical formulation of the model is similar to that of the volume of fluid (VOF) method, but the numerical procedures are different. A splitting method is used for the time discretization. The prediction step consists in solving three advection problems, one for the volume fraction of liquid (which allows the new liquid domain to be obtained), one for the velocity field, one for the extra-stress. The correction step corresponds to solving an Oldroyd-B fluid flow problem without advection in the new liquid domain. Two different grids are used for the space discretization. The three advection problems are solved on a fixed, structured grid made out of small cubic cells, using a forward characteristics method. The Oldroyd-B problem without advection is solved using continuous, piecewise linear stabilized finite elements on a fixed, unstructured mesh of tetrahedrons. Efficient post-processing algorithms enhance the quality of the numerical solution. A hierarchical data structure reduces the memory requirements. Convergence of the numerical method is checked for the pure extensional flow and the filling of a tube. Numerical results are presented for the stretching of a filament. Fingering instabilities are obtained when the aspect ratio is large. Also, results pertaining to jet buckling are reported.

A numerical method for solving three-dimensional generalized Newtonian free surface flows

This work presents a numerical technique for solving three-dimensional generalized Newtonian free surface flows. It is an extension to three dimensions of the technique introduced by Tomé et al. [M.F. Tomé, B. Duffy, S. McKee, A numerical technique for solving unsteady non-Newtonian free surface flows, J. Non-Newtonian Fluid Mech. 62 (1996) 9–34] but additionally includes many other features. The governing equations are solved by a finite difference method on a staggered grid. It uses marker particles to describe the fluid; these particles provide the location and visualization of the fluid free surface. As currently implemented, the present method can simulate generalized Newtonian flow in which the viscosity is modelled using the Cross model. The numerical technique presented in this paper is validated by using exact solutions for the flow of a Cross model fluid inside a pipe and convergence is demonstrated by means of grid refinement for the problem of a spreading drop. Numerical results showing the flow of a generalized Newtonian fluid jet impinging onto a flat surface and that of a jet buckling are given.

GENSMAC3D: a numerical method for solving unsteady three‐dimensional free surface flows

AbstractA numerical method for solving three‐dimensional free surface flows is presented. The technique is an extension of the GENSMAC code for calculating free surface flows in two dimensions. As in GENSMAC, the full Navier–Stokes equations are solved by a finite difference method; the fluid surface is represented by a piecewise linear surface composed of quadrilaterals and triangles containing marker particles on their vertices; the stress conditions on the free surface are accurately imposed; the conjugate gradient method is employed for solving the discrete Poisson equation arising from a velocity update; and an automatic time step routine is used for calculating the time step at every cycle. A program implementing these features has been interfaced with a solid modelling routine defining the flow domain. A user‐friendly input data file is employed to allow almost any arbitrary three‐dimensional shape to be described. The visualization of the results is performed using computer graphic structures such as phong shade, flat and parallel surfaces. Results demonstrating the applicability of this new technique for solving complex free surface flows, such as cavity filling and jet buckling, are presented. Copyright © 2001 John Wiley & Sons, Ltd.

Numerical simulation of viscous flow: Buckling of planar jets

The phenomenon of viscous fluid buckling has a long and distinguished history, dating back to Taylor (1968). This paper is concerned with demonstrating that a numerical method, GENSMAC, is capable of simulating this physical instability. A table of the parameter values (e.g. the Reynolds number, the Froude number, inlet width, inlet velocity and aspect ratio) is provided giving details of when buckling occurs and when it does not. This allows the deduction of a possible buckling condition in terms of the Reynolds number and the ratio of height of the jet to the inlet width, modifying a previous hypothesis. Visualization of jet buckling is provided. This work has been motivated by the need of industry to understand jet filling of containers; jet buckling can lead to air entrapment and this is undesirable. Copyright © 1999 John Wiley & Sons, Ltd.