Asymptotics and numerics for the upper-convected Maxwell model describing transient curved viscoelastic jets

2016 ◽  
Vol 26 (03) ◽  
pp. 569-600 ◽  
Author(s):  
Nicole Marheineke ◽  
Björn Liljegren-Sailer ◽  
Maike Lorenz ◽  
Raimund Wegener
Keyword(s):  
Slenderness Ratio ◽  
Time Integration ◽  
Three Dimensional ◽  
String Model ◽  
Maxwell Model ◽  
Fiber Spinning ◽  
Implicit Time ◽  
Physical Parameters ◽  
Systematic Derivation ◽  
Upper Convected Maxwell Model

This work deals with the modeling and simulation of non-Newtonian jet dynamics as it occurs in fiber spinning processes. Proceeding from a three-dimensional instationary boundary value problem of upper-convected Maxwell equations, we present a strict systematic derivation of a one-dimensional viscoelastic string model by using asymptotic analysis in the slenderness ratio of the jet. The model allows for the unrestricted motion and shape of the jet’s curve, and its deduction extends the hitherto existing uniaxial asymptotic approaches. However, the system of partial differential equations with algebraic constraint has a varying character (hyperbolic, hyperbolic–elliptic, parabolic deficiency). Its applicability range turns out to be limited depending on the physical parameters and the boundary conditions (i.e. singular perturbation). Numerical results are discussed for the hyperbolic regime of gravitational inflow–outflow set-ups which become relevant in drawing and extrusion processes. The simulations are performed with a normal form total upwind scheme in space and an implicit time-integration ensuring convergence of first order.

scholarly journals Geometric scaling of a purely elastic flow instability in serpentine channels

2012 ◽  
Vol 712 ◽  
pp. 203-218 ◽  
Author(s):  
J. Zilz ◽  
R. J. Poole ◽  
M. A. Alves ◽  
D. Bartolo ◽  
B. Levaché ◽  
...  
Keyword(s):  
Flow Instability ◽  
Three Dimensional ◽  
Maxwell Model ◽  
Azimuthal Direction ◽  
Flexible Polymers ◽  
Good Qualitative Agreement ◽  
Geometric Scaling ◽  
Flow Geometry ◽  
Upper Convected Maxwell Model ◽  
Three Dimensional Simulations

AbstractA combined experimental, numerical and theoretical investigation of the geometric scaling of the onset of a purely elastic flow instability in serpentine channels is presented. Good qualitative agreement is obtained between experiments, using dilute solutions of flexible polymers in microfluidic devices, and three-dimensional numerical simulations using the upper-convected Maxwell model. The results are confirmed by a simple theoretical analysis, based on the dimensionless criterion proposed by Pakdel & McKinley (Phys. Rev. Lett., vol. 77, 1996, pp. 2459–2462) for onset of a purely elastic flow instability. Three-dimensional simulations show that the instability is primarily driven by the curvature of the streamlines induced by the flow geometry and not due to the weak secondary flow in the azimuthal direction. In addition, the simulations also reveal that the instability is time-dependent and that the flow oscillates with a well-defined period and amplitude close to the onset of the supercritical instability.

scholarly journals IMPACT: an implicit time integration scheme for chemical species and families

2000 ◽  
Vol 18 (3) ◽  
pp. 337-346 ◽  
Author(s):  
G. D. Carver ◽  
P. A. Stott
Keyword(s):  
Middle Atmosphere ◽  
Time Integration ◽  
Three Dimensional ◽  
Chemical Species ◽  
Atmospheric Composition ◽  
Implicit Time ◽  
Integration Scheme ◽  
Implicit Time Integration ◽  
Time Integration Scheme ◽  
Complex Chemistry

Abstract. The implicit time integration scheme of Stott and Harwood (1993) was proposed as an efficient scheme for use in three-dimensional chemical models of the atmosphere. The scheme was designed for chemistry schemes using `chemical families', in which species with short lifetimes are grouped into longer-lived families. Further study with more complex chemistry, more species and reactions showed the scheme to be non-convergent and unstable under certain conditions; particularly for the perturbed chemical scenarios of polar stratospheric winters. In this work the scheme has been improved by revising the treatment of families and the convergence properties of the scheme. The new scheme has been named IMPACT (IMPlicit Algorithm for Chemical Time-stepping). It remains easy to implement and produces simulations that compare well with integrations using more accurate higher order schemes.Key words: Atmospheric composition and structure (middle atmosphere - composition and chemistry; lioposphere - composition and chemistry; instruments and techniques)

scholarly journals An investigation of stress inaccuracies and proposed solution in the material point method

2019 ◽  
Vol 65 (2) ◽  
pp. 555-581 ◽  
Author(s):  
José Leόn González Acosta ◽  
Philip J. Vardon ◽  
Guido Remmerswaal ◽  
Michael A. Hicks
Keyword(s):  
Shape Function ◽  
Time Integration ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Material Point Method ◽  
Material Point ◽  
Point Method ◽  
Implicit Time ◽  
Integration Scheme ◽  
Time Integration Scheme

AbstractStress inaccuracies (oscillations) are one of the main problems in the material point method (MPM), especially when advanced constitutive models are used. The origins of such oscillations are a combination of poor force and stiffness integration, stress recovery inaccuracies, and cell crossing problems. These are caused mainly by the use of shape function gradients and the use of material points for integration in MPM. The most common techniques developed to reduce stress oscillations consider adapting the shape function gradients so that they are continuous at the nodes. These techniques improve MPM, but problems remain, particularly in two and three dimensional cases. In this paper, the stress inaccuracies are investigated in detail, with particular reference to an implicit time integration scheme. Three modifications to MPM are implemented, and together these are able to remove almost all of the observed oscillations.

Modeling of 3D Magnetostrictive Systems with Application to Galfenol and Terfenol-D Actuators

2012 ◽  
Vol 77 ◽  
pp. 11-28
Author(s):  
Marcelo J. Dapino ◽  
Suryarghya Chakrabarti
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Three Dimensional ◽  
Nonlinear Dynamic System ◽  
Element Model ◽  
Implicit Time ◽  
Integration Scheme ◽  
Modeling Framework ◽  
Time Integration Scheme ◽  
Parametric Analyses

This work presents a unified approach to model three dimensional magnetostrictive transducers. Generalized procedures are developed for incorporating nonlinear coupled constitutive behavior of magnetostrictive materials into an electro-magneto-mechanical finite element modeling framework. The finite element model is based on weak forms of Maxwell's equations for electromagnetics and Navier's equations for mechanical systems. An implicit time integration scheme is implemented to obtain nonlinear dynamic system responses. The model is implemented into a finite element (FE) solver and applied to two case studies, a Galfenol unimorph actuator and a magnetohydraulic Terfenol-D actuator for active engine mounts. Model results are compared with experiments, and parametric analyses are conducted which provide guidelines for optimization of actuator design.

A Non-Linear Aeroelasticity Analysis of a Fan Blade Using Unstructured Dynamic Meshes

1996 ◽  
Vol 210 (6) ◽  
pp. 549-564 ◽  
Author(s):  
M Vahdati ◽  
M Imregun
Keyword(s):  
Time Integration ◽  
Three Dimensional ◽  
Leading Edge ◽  
Element Model ◽  
Mode Shapes ◽  
Implicit Time ◽  
Integration Scheme ◽  
Central Difference ◽  
Basic Fluid ◽  
Fan Blade

The main objective of this paper is to present a methodology for the three-dimensional aeroelasticity analysis of turbomachinery blades using an unstructured compressible Navier-Stokes solver for the fluid and a modal model for the structure. The basic fluid solver is constructed in the form of a central difference scheme with explicitly added artificial dissipation which is based upon the fourth- and second-order differences of the solution. The temporal discretization uses an implicit time integration scheme based on a Jacobi relaxation procedure. The structural modes of vibration are determined via a finite element model and the mode shapes are interpolated on to the fluid mesh in a manner that is consistent with general unstructured tetrahedral grids. A spring analogy algorithm that can move the mesh according to the instantaneous shape of a deforming blade has been developed for the accurate tracking of the solid boundaries without creating excessive grid distortions. The performance of the resulting system was examined by considering the aeroelastic behaviour of NASA Rotor 67 fan blade and predictions were compared to experimental results wherever possible. Using a three-dimensional cyclic symmetry model, the tip leading edge time histories were predicted under peak-efficiency and near-stall conditions, and the corresponding aeroelastic natural frequencies and aerodynamic damping values were determined. The blade was found to be stable in all cases considered.

Nonlinear Transient Motion of Deep Ocean Mining Pipe

1981 ◽  
Vol 103 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. S. Chung ◽  
A. K. Whitney ◽  
W. A. Loden
Keyword(s):  
Time Integration ◽  
Three Dimensional ◽  
Deep Ocean ◽  
Time Domain Analysis ◽  
Implicit Time ◽  
Force Coefficient ◽  
Transient Motion ◽  
Realistic Representation ◽  
Nonlinear Transient ◽  
Stratified Ocean

For accurate and economic time-domain analysis of deep ocean pipes, a realistic representation of hydrodynamic forces along the pipe and an efficient numerical method are required. A transient analysis procedure is formulated and implemented for the numerical determination of nonlinear transient motion of pipes using, as an initial condition, the nonlinear static configuration. The pipe is modeled by three-dimensional beam finite elements which account for coupled axial, bending and torsional deformations. We used 1) vertical variation of seawater properties and hydrodynamic force in the stratified ocean, 2) relative pipe velocity and response for each state in the force computation, and 3) an implicit time-integration method. Several cases are presented for accelerating, turning, and oscillatory motions of the ship and an 18,000-ft pipe, bottom end free. The subsurface environment and force coefficient selection greatly affects the results. The method can be directly applied to the analysis of deepsea risers and OTEC pipes.

Modeling Slab Track for Vehicle –Track-Coupled Dynamics Analysis Using Spline Function Method

2020 ◽  
Vol 20 (02) ◽  
pp. 2050026
Author(s):  
Jianjin Yang ◽  
Shengyang Zhu ◽  
Wanming Zhai
Keyword(s):  
Spline Function ◽  
Time Integration ◽  
Three Dimensional ◽  
Computational Time ◽  
Implicit Time ◽  
Response Analysis ◽  
Slab Track ◽  
Time Integration Method ◽  
Modeling Process ◽  
Track System

This paper presents a new approach for modeling the slab tracks by using the spline function to derive an element that is capable of describing the vertical motions of the entire slab. The accuracy and advantages of the method are verified through comparison with the finite element method (FEM) by the frequency response analysis for the CRTS-III slab track system. With this, a three-dimensional train–slab track-coupled dynamic (TSTCD) model is developed and solved by a hybrid explicit–implicit time integration method. Finally, the characteristics and feasibility of the developed TSTCD model are demonstrated through two typical case studies together with the comparison made for verifications. The results indicate that the proposed method provides an alternative approach for modeling the slabs, by simplifying the modeling process and decreasing the computational time without losing accuracy, with respect to the FEM. Besides, the modes of the slab appear many dips and peaks above the first resonant frequency, leading to complicated frequency responses of the CRTS-III slab. Moreover, the developed TSTCD model is not only feasible, but also capable of describing the slab vibrations at medium-high frequencies.

scholarly journals Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2288
Author(s):  
Hongming Luo ◽  
Guanhua Sun
Keyword(s):  
Structural Dynamics ◽  
Interpolation Method ◽  
Mass Matrix ◽  
Time Integration ◽  
Partition Of Unity ◽  
Implicit Time ◽  
Lumped Mass ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Consistent Mass Matrix

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

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