Non-isothermal viscoelastic flow computations in an axisymmetric contraction at high Weissenberg numbers by a finite volume method

Wachs, Anthony; Clermont, Jean‐Robert

doi:10.1016/s0377-0257(00)00176-2

Cited by 33 publications

(29 citation statements)

References 28 publications

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“…It was shown that the use of the usual exponents (Eqs. (12) and (13)) in the property ratio method can result in large errors in predicting Nu and C f , especially when viscous dissipation is weak, and alternative values are presented as a function of the Brinkman number and a non-dimensionless number quantifying elastic effects, e We 2 . However, the use of these values is rather complex as the problem is highly non-linear.…”

Section: Discussionmentioning

confidence: 99%

“…Table 5 Values of exponents n and m for correcting Nu and C f using Eqs. (12) and (13) C f , determines an equivalent temperature to calculate properties to be used in the theoretical expressions for constant properties. Values of this normalised equivalent temperature were quantified and the method was seen to be a better alternative than the property ratio method, except under weak viscous dissipation conditions where it still did not provide a simple correction technique.…”

Section: Discussionmentioning

confidence: 99%

“…Nonetheless, we identify the numerical simulation of Davies and Li [10] with a White-Metzner fluid in a journal bearing and, more recently, the numerical simulations of Shin et al [11] using an explicit viscoelastic model which is much easier to solve. Other recent works on non-isothermal flow of viscoelastic fluids having temperature-dependent fluid properties are the simulations of Wachs and Clermont [12] and Marduel and Kunisch [13] in the 4:1 contraction benchmark flow. Whereas the former was basically aimed at assessing the performance of a numerical method under non-isothermal conditions, the latter developed a simple flow control strategy to reduce the size of recirculation zones.…”

Section: Introductionmentioning

confidence: 99%

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Accounting for temperature-dependent properties in viscoelastic duct flows

Nóbrega

Pinho

Oliveira

et al. 2004

International Journal of Heat and Mass Transfer

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A numerical and theoretical study is conducted to evaluate the effect of temperature-dependent properties on the hydrodynamic and thermal characteristics of viscoelastic fluid flow. The rheological constitutive equation of the fluid under consideration follows a common form of the PTT model, which embodies both influences of elasticity and shearthinning in viscosity. A large number of simulations were carried out for a developing channel flow with an imposed constant wall temperature by varying the parameters controlling elasticity (Weissenberg number) and viscous dissipation (Brinkman number). The resulting Nusselt number and friction factor were determined from the numerical results, for both conditions of constant and temperature-dependent properties. The properties that were allowed to vary with temperature were the viscosity, thermal conductivity, specific heat and relaxation time of the PTT model. From the results it was possible to determine how the usual correlations for Nu and C f have to be modified, following the property-correction method, in order to represent variable-property flow of this viscoelastic fluid. An alternative method to account for variable properties, based on the definition of an equivalent temperature to be used with the constant property Nu and C f expressions, is also proposed and shown to be less sensitive to the influence of viscous dissipation. The corrections are highly non-linear and strongly depend on e We 2 and Br especially when viscous dissipation is weak.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Accounting for temperature-dependent properties in viscoelastic duct flows

Nóbrega

Pinho

Oliveira

et al. 2004

International Journal of Heat and Mass Transfer

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“…The formulation ( v, p, ) is replaced by a new one involving the additional term 2 0 D/ t in the constitutive equation. This quantity is taken into account either by integrating by parts or introducing the rate-of-deformation tensor as a supplementary unknown [3]. Thus, the system of momentum, mass and constitutive equations to be solved can be written as [20,21] …”

Section: Specific Formulations For the Ucm And Ptt Viscoelastic Equatmentioning

confidence: 99%

“…More particularly, these studies have concerned simulations of flows of fluids obeying more sophisticated constitutive equations than the Newtonian model [2][3][4], besides the finite element techniques [5,6] widely used in such problems. In the field of non-Newtonian flow computations, various numerical approaches have been proposed [6].…”

Section: Introductionmentioning

confidence: 99%

Nonisothermal two‐ and three‐dimensional flow simulations of inelastic and viscoelastic fluids by a finite‐volume method

Khalifeh

Clermont

2011

Numerical Methods in Fluids

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SUMMARYThis paper applies the finite-volume method to computations of steady flows of viscous and viscoelastic incompressible fluids in complex two and three-dimensional geometries. The materials adopted in the study obey different constitutive laws: Newtonian, purely viscous Carreau-Yasuda as also Upper-Convected Maxwell and Phan-Thien/Tanner differential models, with a Williams-Landel-Ferry (WLF) equation for temperature dependence. Specific analyses are made depending on the rheological model. A staggered grid is used for discretizing the equations and unknowns. Stockage possibilities allow us to solve problems involving a great number of degrees of freedom, up to 1 500 000 unknowns with a desk computer. In relation to the fluid properties, our numerical simulations provide flow characteristics for various 2D and 3D configurations and demonstrate the possibilities of the code to solve problems involving complex nonlinear constitutive equations with thermal effects.

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Nonisothermal comprehensive 3D analysis of polymer melt flow in a coat‐hanger die

Jiang

et al. 2006

Polymer Engineering & Sci

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The nonisothermal flow of Carreau fluid in a coat-hanger die is studied. A general three-dimensional finite volume code is developed for the purpose of flow analysis. The isobars, the isotherms, and the velocity distribution are obtained. Simulation results illustrated that the highest temperature occurred by the center of manifold, rather than the die-lip region because of the combined effects of high shear rate and poor heat conduction, which is important for processing those heat-sensitive materials. In the regions where die gap is relatively small, the wall temperature plays a key role in deciding temperature distribution in the melt. The validity of simulation results is verified experimentally. POLYM. ENG. SCI., 46:406 -415, 2006. ANALYSISThe polymer melt flow in a coat-hanger die is examined by means of three-dimensional computational fluid dynamics techniques. A schematic of the die considered here is shown in Fig. 1. The flow simulation is full 3D and nonisothermal. Hence, the momentum and energy conservation equations should be coupled through temperature-dependent constitutive equations. For numerical analysis of extrusion die, the Carreau model has been employed here, considering its better representations of the entire viscosity curve. The temperature-shifting function is used to illustrate the temperature effects on the rheological aspects of polymer fluid.

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Non-isothermal viscoelastic flow computations in an axisymmetric contraction at high Weissenberg numbers by a finite volume method

Cited by 33 publications

References 28 publications

Accounting for temperature-dependent properties in viscoelastic duct flows

Accounting for temperature-dependent properties in viscoelastic duct flows

Nonisothermal two‐ and three‐dimensional flow simulations of inelastic and viscoelastic fluids by a finite‐volume method

Nonisothermal comprehensive 3D analysis of polymer melt flow in a coat‐hanger die

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