2,894 research outputs found
Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows
In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids
Flow pattern transition accompanied with sudden growth of flow resistance in two-dimensional curvilinear viscoelastic flows
We find three types of steady solutions and remarkable flow pattern
transitions between them in a two-dimensional wavy-walled channel for low to
moderate Reynolds (Re) and Weissenberg (Wi) numbers using direct numerical
simulations with spectral element method. The solutions are called
"convective", "transition", and "elastic" in ascending order of Wi. In the
convective region in the Re-Wi parameter space, the convective effect and the
pressure gradient balance on average. As Wi increases, the elastic effect
becomes suddenly comparable and the first transition sets in. Through the
transition, a separation vortex disappears and a jet flow induced close to the
wall by the viscoelasticity moves into the bulk; The viscous drag significantly
drops and the elastic wall friction rises sharply. This transition is caused by
an elastic force in the streamwise direction due to the competition of the
convective and elastic effects. In the transition region, the convective and
elastic effects balance. When the elastic effect dominates the convective
effect, the second transition occurs but it is relatively moderate. The second
one seems to be governed by so-called Weissenberg effect. These transitions are
not sensitive to driving forces. By the scaling analysis, it is shown that the
stress component is proportional to the Reynolds number on the boundary of the
first transition in the Re-Wi space. This scaling coincides well with the
numerical result.Comment: 33pages, 23figures, submitted to Physical Review
Numerical simulation of combined mixing and separating flow in channel filled with porous media
Various flow bifurcations are investigated for two dimensional combined mixing and separating geometry. These consist of two reversed channel flows interacting through a gap in the common separating wall filled with porous media of Newtonian fluids and other with unidirectional fluid flows. The Steady solutions are obtained through an unsteady finite element approach that employs a Taylor-Galerkin/pressure-correction scheme. The influence of increasing inertia on flow rates are all studied. Close agreement is attained with numerical data in the porous channels for Newtonian fluids.Peer reviewedSubmitted Versio
Finite element methods for deterministic simulation of polymeric fluids
In this work we consider a finite element method for solving the coupled Navier-Stokes (NS) and Fokker-Planck (FP) multiscale model that describes the dynamics of dilute polymeric fluids. Deterministic approaches such as ours have not received much attention in the literature because they present a formidable computational challenge, due to the fact that the analytical solution to the Fokker-Planck equation may be a function of a large number of independent variables. For instance, to simulate a non-homogeneous flow one must solve the coupled NS-FP system in which (for a 3-dimensional flow, using the dumbbell model for polymers) the Fokker-Planck equation is posed in a 6-dimensional domain. In this work we seek to demonstrate the feasibility of our deterministic approach. We begin by discussing the physical and mathematical foundations of the NS-FP model. We then present a literature review of relevant developments in computational rheology and develop our deterministic finite element based method in detail. Numerical results demonstrating the efficiency of our approach are then given, including some novel results for the simulation of a fully 3-dimensional flow. We utilise parallel computation to perform the large-scale numerical simulations
Flow of non-Newtonian Fluids in Converging-Diverging Rigid Tubes
A residual-based lubrication method is used in this paper to find the flow
rate and pressure field in converging-diverging rigid tubes for the flow of
time-independent category of non-Newtonian fluids. Five converging-diverging
prototype geometries were used in this investigation in conjunction with two
fluid models: Ellis and Herschel-Bulkley. The method was validated by
convergence behavior sensibility tests, convergence to analytical solutions for
the straight tubes as special cases for the converging-diverging tubes,
convergence to analytical solutions found earlier for the flow in
converging-diverging tubes of Newtonian fluids as special cases for
non-Newtonian, and convergence to analytical solutions found earlier for the
flow of power-law fluids in converging-diverging tubes. A brief investigation
was also conducted on a sample of diverging-converging geometries. The method
can in principle be extended to the flow of viscoelastic and
thixotropic/rheopectic fluid categories. The method can also be extended to
geometries varying in size and shape in the flow direction, other than the
perfect cylindrically-symmetric converging-diverging ones, as long as
characteristic flow relations correlating the flow rate to the pressure drop on
the discretized elements of the lubrication approximation can be found. These
relations can be analytical, empirical and even numerical and hence the method
has a wide applicability range.Comment: 36 pages, 14 figures, 5 table
The fully-implicit log-conformation formulation and its application to three-dimensional flows
The stable and efficient numerical simulation of viscoelastic flows has been
a constant struggle due to the High Weissenberg Number Problem. While the
stability for macroscopic descriptions could be greatly enhanced by the
log-conformation method as proposed by Fattal and Kupferman, the application of
the efficient Newton-Raphson algorithm to the full monolithic system of
governing equations, consisting of the log-conformation equations and the
Navier-Stokes equations, has always posed a problem. In particular, it is the
formulation of the constitutive equations by means of the spectral
decomposition that hinders the application of further analytical tools.
Therefore, up to now, a fully monolithic approach could only be achieved in two
dimensions, as, e.g., recently shown in [P. Knechtges, M. Behr, S. Elgeti,
Fully-implicit log-conformation formulation of constitutive laws, J.
Non-Newtonian Fluid Mech. 214 (2014) 78-87].
The aim of this paper is to find a generalization of the previously made
considerations to three dimensions, such that a monolithic Newton-Raphson
solver based on the log-conformation formulation can be implemented also in
this case. The underlying idea is analogous to the two-dimensional case, to
replace the eigenvalue decomposition in the constitutive equation by an
analytically more "well-behaved" term and to rely on the eigenvalue
decomposition only for the actual computation. Furthermore, in order to
demonstrate the practicality of the proposed method, numerical results of the
newly derived formulation are presented in the case of the sedimenting sphere
and ellipsoid benchmarks for the Oldroyd-B and Giesekus models. It is found
that the expected quadratic convergence of Newton's method can be achieved.Comment: 21 pages, 9 figure
Multiscale structure of turbulent channel flow and polymer, dynamics in viscoelastic turbulence
This thesis focuses on two important issues in turbulence theory of wall-bounded
flows. One is the recent debate on the form of the mean velocity profile (is it a
log-law or a power-law with very weak power exponent?) and on its scalings with
Reynolds number. In particular, this study relates the mean flow profile of the
turbulent channel flow with the underlying topological structure of the fluctuating
velocity field through the concept of critical points, a dynamical systems concept that
is a natural way to quantify the multiscale structure of turbulence. This connection
gives a new phenomenological picture of wall-bounded turbulence in terms of the
topology of the flow. This theory validated against existing data, indicates that
the issue on the form of the mean velocity profile at the asymptotic limit of infinite
Reynolds number could be resolved by understanding the scaling of turbulent kinetic
energy with Reynolds number.
The other major issue addressed here is on the fundamental mechanism(s) of
viscoelastic turbulence that lead to the polymer-induced turbulent drag reduction
phenomenon and its dynamical aspects. A great challenge in this problem is the computation
of viscoelastic turbulent flows, since the understanding of polymer physics is
restricted to mechanical models. An effective numerical method to solve the governing
equation for polymers modelled as nonlinear springs, without using any artificial
assumptions as usual, was implemented here for the first time on a three-dimensional
channel flow geometry. The superiority of this algorithm is depicted on the results,
which are much closer to experimental observations. This allowed a more detailed
study of the polymer-turbulence dynamical interactions, which yields a clearer picture
on a mechanism that is governed by the polymer-turbulence energy transfers
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