Spectral element method for viscoelastic flows in a planar contraction channel

Meng, Sha; Li, Xin Kai; Evans, G. A.

doi:10.1002/fld.524

Cited by 7 publications

(3 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Even though it has been recognized a posteriori that for non-Newtonian fluids this choice has been misguided, as many interesting flow characteristics are only apparent for contraction ratios beyond the specific ratio of 4:1 [52], most published numerical works are still concerned with the standard case of the 4:1 contraction ratio (e.g. [35,36,38,[56][57][58][59]). Some authors have used different values of the contraction ratio and there are a few, mainly experimental, studies in which variations of the contraction ratio are considered [1,10,15,17].…”

Section: The Contraction Ratiomentioning

confidence: 98%

Effect of contraction ratio upon viscoelastic flow in contractions: The axisymmetric case

Oliveira

Pinho

et al. 2007

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

A comprehensive numerical study of the effects of the contraction ratio upon viscoelastic flow through axisymmetric contractions was carried out. Six contraction ratios were examined (CR = 2, 4, 10, 20, 40 and 100) using the Oldroyd-B and Phan-Thien-Tanner (PTT) constitutive equations, under creeping-flow conditions and for a wide range of Deborah numbers (De). The results enabled the construction of vortex pattern maps, with CR and De as independent parameters, elucidating the role of these dimensionless groups in controlling vortex growth, vortex type (lip or corner vortices), and pressure-drop characteristics. The extensional parameter of the PTT model was also varied (ε = 0-0.5) and it was found that for small values of ε the Couette correction is a monotonic decreasing function of De, while for high ε values it is a monotonic increasing function.

show abstract

Section: The Contraction Ratiomentioning

confidence: 98%

Effect of contraction ratio upon viscoelastic flow in contractions: The axisymmetric case

Oliveira

Pinho

et al. 2007

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

show abstract

“…Meng et al . developed a new algorithm, which combines the spectral element method with elastic viscous splitting stress method. The system of spectral element approximations of the velocity, pressure, extra stress, and the rate of deformation variables is solved by a preconditioned conjugate gradient method based on the Uzawa iteration procedure.…”

Section: Introductionmentioning

confidence: 99%

Simulation of viscoelastic fluids in a 2D abrupt contraction by spectral element method

Jafari

Fiétier

Deville

2015

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYThis study presents the vortex structure and numerical instability increase occurring when the level of elasticity is enhanced in inertial flows in planar contraction configuration for finitely extensible nonlinear elastic model by Peterlin (FENE-P) fluid [1]. The re-entrant corner effect on corner vortices is also considered. The calculations are performed using extended matrix logarithm formulation described in a previous paper: A. Jafari et al. A new extended matrix logarithm formulation for the simulation of viscoelastic fluids by spectral elements. Computer & Fluids 2010; 39(9):1425-1438. In that reference, the proposed algorithm has been tested for simple geometry such as Poiseuille flow. In this study, we are interested in the capability of this algorithm for more complex geometry. This formulation helps to reach higher values of the Weissenberg number when compared with the classical one.

show abstract

“…In 1984, the spectral energy method (SEM) was developed by Patera [2]employing Chebyshev polynomials as basis functions to describe fluid flow in a channel expansion. SEM has been developed for many other problems in both fluid and solid mechanics, from the axisymmetric Navier-Stokes equation [3] to entry flow in a contraction channel [4] to plates reinforced by beams [5]. In 1985, Dowell and Kubota presented asymptotic modal analysis (AMA) [6], which reduces the complexity of the results of the Ritz method by identifying elements of system transfer functions that are slowly varying for high-frequency, broadband excitation.…”

Section: Introductionmentioning

confidence: 99%

High Frequency Analysis of a Point-Coupled Parallel Plate System

Culver

Dowell

2017

Journal of Vibration and Acoustics

View full text Add to dashboard Cite

The root-mean-square (RMS) response of various points in a system comprised of two parallel plates coupled at a point undergoing high frequency, broadband transverse point excitation of one component is considered. Through this prototypical example, asymptotic modal analysis (AMA) is extended to two coupled continuous dynamical systems. It is shown that different points on the plates respond with different RMS magnitudes depending on their spatial relationship to the excitation or coupling points in the system. The ability of AMA to accurately compute the RMS response of these points (namely, the excitation point, the coupling points, and the hot lines through the excitation or coupling points) in the system is shown. The behavior of three representative prototypical configurations of the parallel plate system considered is: two similar plates (in both geometry and modal density), two plates with similar modal density but different geometry, and two plates with similar geometry but different modal density. After examining the error between reduced modal methods (such as AMA) to classical modal analysis (CMA), it is determined that these several methods are valid for each of these scenarios. The data from the various methods will also be useful in evaluating the accuracy of other methods including statistical energy analysis (SEA).

show abstract

Spectral element method for viscoelastic flows in a planar contraction channel

Cited by 7 publications

References 33 publications

Effect of contraction ratio upon viscoelastic flow in contractions: The axisymmetric case

Effect of contraction ratio upon viscoelastic flow in contractions: The axisymmetric case

Simulation of viscoelastic fluids in a 2D abrupt contraction by spectral element method

High Frequency Analysis of a Point-Coupled Parallel Plate System

Contact Info

Product

Resources

About