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1.
Mohammad T. Islam 《Rheologica Acta》2006,45(6):1003-1009
We present a differential constitutive model of stress relaxation in polydisperse linear polymer melts and solutions that contains contributions from reptation, contour-length fluctuations, and chain stretching. The predictions of the model during fast start-up and steady shear flows of polymer melts are in accord with experimental observations. Moreover, in accordance with reported experimental literature (Osaki et al. in J Polym Sci B Polym Phys 38:2043–2050, 2000), the model predicts, for a range of shear rates, two overshoots in shear stress during start-up of steady shear flows of bidisperse polymer melts having components with widely separated molar masses. Two overshoots result only when the stretch or Rouse relaxation time of the higher molar mass component is longer than the terminal relaxation time of the lower molar mass component. The “first overshoot” is the first to appear with increasing shear rate and occurs as a result of the stretching of longer chains. Transient stretching of the short chains is responsible for the early time second overshoot. The model predictions in steady and transitional extensional flows are also remarkable for both monodisperse and bidisperse polymer solutions. The computationally efficient differential model can be used to predict rheology of commercial polydisperse polymer melts and solutions. 相似文献
2.
Uriel Goldberg 《International Journal of Computational Fluid Dynamics》2013,27(9):651-656
This paper introduces a two-equation turbulence model sensitized to deviations from simple shear flows. The closure is topography-parameter-free and is based on solving transport equations for the turbulence kinetic energy (k) and the turbulence length-scale (?). Brief model derivation details are given and test cases are presented to compare the model's performance to other closures and to experimental data. The flow examples demonstrate the advantage of the k–? model in non-simple shear flows. 相似文献
3.
This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress
and Reynolds-heat-flux equations. Several closure models have been investigated; the emphasis is placed on assessing the effect
of modeling the dissipation rate tensor in the Reynolds-stress equation. Three different approaches are considered; one is
an isotropic approach while the other two are anisotropic approaches. The isotropic approach is based on Kolmogorov's hypothesis
and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an
algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for
this tensor. In addition, within the former anisotropic approach, two different algebraic representations are examined; one
is a function of the Reynolds-stress anisotropy tensor, and the other is a function of the mean velocity gradients. The performance
of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows, pure buoyant
flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different
Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flux in a stratified shear flow can
be assessed. At low Ri, the isotropic model performs well in the predictions of stratified shear flows; however, its performance
deteriorates as Ri increases. At high Ri, the transport equation model for the dissipation rate tensor gives the best result.
Furthermore, the results also lend credence to the algebraic dissipation rate model based on the Reynolds stress anisotropy
tensor. Finally, it is found that Pr has an effect on the development of counter-gradient heat flux. The calculations show
that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
The Larson-Doi (LD) polydomain model is used to simulate orientation development along the centerline of slit-expansion and
slit-contraction flows of liquid crystalline polymers (LCPs). Orientation is computed using the LD structural evolution equations,
subject to an imposed velocity field that accounts for the spatial variation of both shear and extension rates characteristic
of this class of flows. Computed axial distributions of orientation averaged through the sample thickness are qualitatively
similar to birefringence and X-ray scattering measurements of molecular orientation in similar flows of lyotropic and thermotropic
LCPs. In slit-expansion flows, the simulations predict a 90∘ flip in orientation direction near the midplane due to transverse stretching in the expansion region. Far away from the midplane
where shear gradients dominate, orientation remains primarily along the flow direction. Within the LD model, tumbling and
flow aligning materials respond in a qualitatively similar manner to mixed shear and extension, although tumbling materials
are systematically more susceptible to the effects of extension.
Received: 22 October 1999/Accepted: 13 January 2000 相似文献
5.
6.
The purpose of thiswork is to introduce a complete and general one-equation model capable of correctly predicting a wide class
of fundamental turbulent flows like boundary layer, wake, jet, and vortical flows. The starting point is the mature and validated
two-equation k−ω turbulence model of Wilcox. The newly derived one-equation model has several advantages and yields better predictions than
the Spalart-Allmaras model for jet and vortical flows while retaining the same efficiency and quality of the results for near-wall
turbulent flows without using a wall distance. The derivation and validation of the new model using findings computed by the
Spalart-Allmaras and the k−ω models are presented and discussed for several free shear and wall-bounded flows. 相似文献
7.
Elastic effects on the hydrodynamic instability of inviscid parallel shear flows are investigated through a linear stability analysis. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. We study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet.The equation for stability is derived and solved numerically using the spectral Chebyshev collocation method. This algorithm is computationally efficient and accurate in reproducing the eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability. 相似文献
8.
David C. Venerus 《Rheologica Acta》2000,39(1):71-79
The behavior of a low-density polyethylene melt in exponential shear strain histories is examined and compared to its behavior
in constant rate planar elongation. A new set of shear stress and first normal stress difference data in exponential shear
are presented and used in several different material functions that have been previously proposed. Viscosities composed of
principal stress differences for the two flows showed no correspondence suggesting that, contrary to previous assertions,
exponential shear and constant rate planar elongation flows are fundamentally different. It is further suggested that the
presence of vorticity makes exponential shear a weak, rather than strong, flow.
Received: 5 March 1999/Accepted: 1 September 1999 相似文献
9.
This paper presents a derivation of an explicit algebraic model for two-dimensional (2-D) buoyant flows. It is an extension of the work reported in Part I (So et al. [27]). The tensor representation method of Jongen and Gatski [14] is extended to derive an explicit algebraic Reynolds stress model (EASM) for 2-D buoyant flow invoking the Boussinesq approximation. The projection methodology is further extended to treat the heat flux transport equation in the derivation of an explicit algebraic heat flux model (EAHFM) for buoyant flow. Again, the weak equilibrium assumption is invoked for the scaled Reynolds stress and scaled heat flux equation. An explicit algebraic model for buoyant flows is then formed with the EASM and EAHFM. From the derived EAHFM, an expression for the thermal diffusivity tensor in buoyant shear flows is deduced. Furthermore, a turbulent Prandtl number (PrT) for each of the three heat flux directions is determined. These directional PrT are found to be a function of the gradient Richardson number. Alternatively, a scalar PrT can be derived; its value is compared with the directional PrT. The EASM and EAHFM are used to calculate 2-D homogeneous buoyant shear flows and the results are compared with direct numerical simulation data and other model predictions, where good agreement is obtained. Dedicated to the memory of the late Professor Charles G. Speziale of Boston University 相似文献
10.
The use of mixtures of pea protein isolate (PPI) and κ-carrageenan (κ-C) is increasing rapidly with the aim of increasing
the stability and viscosity of food products. Recent works have studied their textural and thermal properties but few have
studied the influence of the temperature and concentration on the rheological behavior of model systems. In the present work,
we study the thermo-rheological properties in the linear and non-linear viscoelastic regimes, in both shear and extensional
flows, of mixtures of PPI and κ-C with the aim of obtaining a model for the temperature-induced gelation of complex mixtures
of globular vegetable proteins under linear and non-linear deformations. We analyzed the influence of temperature and protein-to-polysaccharide
ratios and showed that there are strong changes in the mechanical properties. In shear flows, small-amplitude oscillatory
shear was used to study the linear regime and large-amplitude oscillatory shear was used for the non-linear regime. In extensional
flows, studies were carried out via the analysis of the dynamics of capillary thinning and breakup process in a filament-thinning
rheometer. 相似文献
11.
Nourdine Chikhi 《Theoretical and Computational Fluid Dynamics》2005,19(5):319-329
The aim of this article is to study the stability of shear flows in bubbly fluids. A mathematical model of bubbly fluids is
presented. The stability of shear flows is studied by two methods: by using a spectral approach and by solving the initial-value
problem. It is proved that the linear velocity profile is stable in the long wave approximation.
Communicated by R. Grimshaw 相似文献
12.
J. C. Dyre 《Rheologica Acta》1990,29(2):145-151
Based on the Cox-Merz rule and Eyring's expression for the nonlinear shear viscosity, a Wagner-type constitutive relation with no nontrivial adjustable parameters is proposed for simple shear viscoelasticity. The predictions for a number of non-steady shear flows are worked out analytically. It is shown that most features of shear viscoelasticity are reproduced by the model. 相似文献
13.
In this article, large eddy simulation is used to simulate homogeneous shear flows. The spatial discretization is accomplished by the spectral collocation method and a third‐order Runge–Kutta method is used to integrate the time‐dependent terms. For the estimation of the subgrid‐scale stress tensor, the Smagorinsky model, the dynamic model, the scale‐similarity model and the mixed model are used. Their predicting performance for homogeneous shear flow is compared accordingly. The initial Reynolds number varies from 33 to 99 and the initial shear number is 2. Evolution of the turbulent kinetic energy, the growth rate, the anisotropy component and the subgrid‐scale dissipation rate is presented. In addition, the performance of several filters is examined. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
14.
An extension of a mathematical model for non-isothermal multiphase materials to consider the dissolution of air in liquid
water and air mass sources during its desorption at lower water pressure is presented. The solid skeleton is assumed elasto-plastic;
heat, water and air flows and water phase changes are taken into account. Physics of air dissolution and desaturation due
to the air released from liquid water during cavitation in porous media are discussed. A numerical example where cavitation
develops during shear band development in undrained water-saturated dense sands is solved with the developed model as discretized
in space and time with the Finite Element Method. 相似文献
15.
A coarse-grained model developed for entangled polymeric systems and calibrated to represent melts in equilibrium (Rakshit,
Picu, J Chem Phys 125:164907(1)–(10), 2006) is used to model shear flows. The model is a hybrid between multimode and mean-field representations: chain inner blobs
are constrained to move along the chain backbone and the end blobs are free to move in 3D and continuously redefine the diffusion
path for the inner blobs. Therefore, contour length fluctuations and reptation are captured. Constraint release is implemented
by tracing the position of chain ends and performing a local relaxation of the chain backbones once end retraction is detected.
This algorithm takes advantage of the multi-body nature of the model and requires no phenomenological parameters other than
the length of an entanglement segment. The model is used to study start-up and step strain shear flows and reproduces features
observed experimentally such as the overshoot during start-up shear flow, the Lodge–Meissner law, the monotonicity of the
steady state shear stress with the strain rate, and shear thinning at large . These simulations are performed in conditions in which using a fully refined model of the same system would have been extremely
computationally demanding or simply impossible with the current methods. 相似文献
16.
The pom-pom rheological constitutive equation for branched polymers proposed by McLeish and Larson is evaluated in step shear
strain flows. Semianalytic expressions for the shear-stress relaxation modulus are derived for both the integral and approximate
differential versions of the pom-pom model. Predictions from the thermodynamically motivated differential pompon model of
?ttinger are also examined. Single-mode integral and differential pom-pom models are found to give qualitatively different
predictions, the former displays time–strain factorability after the backbone stretch is relaxed, while the latter does not.
We also find that the differential pompon model gives quantitatively similar predictions to the integral pom-pom model in
step strain flows. Predictions from multimode integral and differential pom-pom models are compared with experimental data
on a widely characterized, low-density polyethylene known as 1810H. The experiments strongly support time–strain factorability,
while the multimode pom-pom model predictions show deviations from this behavior over the entire range of time that is experimentally
accessible. 相似文献
17.
The incompressible flow around bluff bodies (a square cylinder and a cube) is investigated numerically using turbulence models. A non‐linear k–ε model, which can take into account the anisotropy of turbulence with less CPU time and computer memory then RSM or LES, is adopted as a turbulence model. In tuning of the model coefficients of the non‐linear terms are adjusted through the examination of previous experimental studies in simple shear flows. For the tuning of the coefficient in the eddy viscosity (=Cμ), the realizability constraints are derived in three types of basic 2D flow patterns, namely, a simple shear flow, flow around a saddle and a focal point. Cμ is then determined as a function of the strain and rotation parameters to satisfy the realizability. The turbulence model is first applied to a 2D flow around a square cylinder and the model performance for unsteady flows is examined focussing on the period and the amplitude of the flow oscillation induced by Karman vortex shedding. The applicability of the model to 3D flows is examined through the computation of the flow around a surface‐mounted cubic obstacle. The numerical results show that the present model performs satisfactorily to reproduce complex turbulent flows around bluff bodies. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
18.
A. A. Chesnokov 《Journal of Applied Mechanics and Technical Physics》2006,47(6):800-811
The problem of the decay of an arbitrary discontinuity for the equations describing plane-parallel shear flows of an ideal
fluid in a narrow channel is considered. The class of particular solutions corresponding to fluid flows with piecewise constant
vorticity is studied. In this class, the existence of self-similar solutions describing all possible unsteady wave configurations
resulting from the nonlinear interaction of the specified shear flows is established.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 34–47, November–December, 2006. 相似文献
19.
Capability of the explicit algebraic stress models to predict homogeneous and inhomogeneous shear flows are examined. The importance of the explicit solution of the production to dissipation ratio is first highlighted by examining the algebraic stress models performance at purely irrotational strain conditions. Turbulent recirculating flows within sudden expanding pipes are further simulated with explicit algebraic stress model and anisotropic eddy viscosity model. Both models predict better stress–strain interactions, showing reasonable shear layer developments. The anisotropic stress field are also accurately predicted by the models, though the anisotropic eddy viscosity model of Craft et al. returns marginally better results. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
20.
Development of LBGK and incompressible LBGK‐based lattice Boltzmann flux solvers for simulation of incompressible flows
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This paper presents lattice Boltzmann Bhatnagar–Gross–Krook (LBGK) model and incompressible LBGK model‐based lattice Boltzmann flux solvers (LBFS) for simulation of incompressible flows. LBFS applies the finite volume method to directly discretize the governing differential equations recovered by lattice Boltzmann equations. The fluxes of LBFS at each cell interface are evaluated by local reconstruction of lattice Boltzmann solution. Because LBFS is applied locally at each cell interface independently, it removes the major drawbacks of conventional lattice Boltzmann method such as lattice uniformity, coupling between mesh spacing, and time interval. With LBGK and incompressible LBGK models, LBFS are examined by simulating decaying vortex flow, polar cavity flow, plane Poiseuille flow, Womersley flow, and double shear flows. The obtained numerical results show that both the LBGK and incompressible LBGK‐based LBFS have the second order of accuracy and high computational efficiency on nonuniform grids. Furthermore, LBFS with both LBGK models are also stable for the double shear flows at a high Reynolds number of 105. However, for the pressure‐driven plane Poiseuille flow, when the pressure gradient is increased, the relative error associated with LBGK model grows faster than that associated with incompressible LBGK model. It seems that the incompressible LBGK‐based LBFS is more suitable for simulating incompressible flows with large pressure gradients. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献