On steady flows of fluids with pressure– and shear–dependent viscosities

Franta, Michal; Málek, Josef; Rajagopal, K. R.

doi:10.1098/rspa.2004.1360

Cited by 56 publications

(68 citation statements)

References 27 publications

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“…In [8], [11], some further generalizations are provided. The proof of existence presented here derives from the one developed in [16], where the existence theory was established for steady flows subject to homogeneous Dirichlet boundary condition only.…”

Section: Definition Of the Problem And The Main Resultsmentioning

confidence: 99%

“…For more details on models of the type (2.1), we refer the reader to [16], [27], [29], [30]. Simple flows and numerical simulations are discussed in [21], [22].…”

Section: Definition Of the Problem And The Main Resultsmentioning

confidence: 99%

“…The proof of (i) has the same structure as the proof given in [16] for the problem with the homogeneous Dirichlet boundary condition on ∂Ω: In 3.1, we define an approximate problem (P ε ), derive energy estimates and show the existence of a weak solution to (P ε ) via Galerkin approximations. Also, (ii) follows from the estimates derived in here.…”

Section: The Existence Of a Weak Solutionmentioning

confidence: 99%

“…In such case the value of the pressure affects the whole solution of the equations. In previous theoretical studies, such as [10], [16], [26], the mean value of the pressure either over the whole domain or over its nontrivial subdomain was prescribed as one of the input parameters. A difficulty of this approach lies in the fact that the pressure mean value is not a proper quantity from the practical point of view, i.e.…”

Section: Introductionmentioning

confidence: 99%

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On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

Lanzendörfer

Stebel

2011

Appl Math

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Section: Definition Of the Problem And The Main Resultsmentioning

confidence: 99%

“…For more details on models of the type (2.1), we refer the reader to [16], [27], [29], [30]. Simple flows and numerical simulations are discussed in [21], [22].…”

Section: Definition Of the Problem And The Main Resultsmentioning

confidence: 99%

Section: The Existence Of a Weak Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

Lanzendörfer

Stebel

2011

Appl Math

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“…Franta et al [126] considered a class of incompressible fluids where viscosity depends not only on pressure but also on shear rate. They considered the following forms for the kinematic viscosity:  is given by any of the relationships: 29 a,b,c) where α and q are constants.…”

Section: Pressure Effectsmentioning

confidence: 99%

Slag Behavior in Gasifiers. Part II: Constitutive Modeling of Slag

Massoudi

Wang

2013

Energies

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Abstract:The viscosity of slag and the thermal conductivity of ash deposits are among two of the most important constitutive parameters that need to be studied. The accurate formulation or representations of the (transport) properties of coal present a special challenge of modeling efforts in computational fluid dynamics applications. Studies have indicated that slag viscosity must be within a certain range of temperatures for tapping and the membrane wall to be accessible, for example, between 1,300 °C and 1,500 °C, the viscosity is approximately 25 Pa·s. As the operating temperature decreases, the slag cools and solid crystals begin to form. Since slag behaves as a non-linear fluid, we discuss the constitutive modeling of slag and the important parameters that must be studied. We propose a new constitutive model, where the stress tensor not only has a yield stress part, but it also has a viscous part with a shear rate dependency of the viscosity, along with temperature and concentration dependency, while allowing for the possibility of the normal stress effects. In Part I, we reviewed, identify and discuss the key coal ash properties and the operating conditions impacting slag behavior.

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A numerical study of fluids with pressure‐dependent viscosity flowing through a rigid porous medium

Nakshatrala

Rajagopal

2011

Numerical Methods in Fluids

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Abstract. Much of the work on flow through porous media, especially with regard to studies on the flow of oil, are based on "Darcy's law" or modifications to it such as Darcy-Forchheimer or Brinkman models. While many theoretical and numerical studies concerning flow through porous media have taken into account the inhomogeneity and anisotropy of the porous solid, they have not taken into account the fact that the viscosity of the fluid and drag coefficient could depend on the pressure in applications such as enhanced oil recovery. Experiments clearly indicate that the viscosity varies exponentially with respect to the pressure and the viscosity can change, in some applications, by several orders of magnitude. The fact that the viscosity depends on pressure immediately implies that the "drag coefficient" would also depend on the pressure.In this paper we consider modifications to Darcy's equation wherein the drag coefficient is a function of pressure, which is a realistic model for technological applications like enhanced oil recovery and geological carbon sequestration. We first outline the approximations behind Darcy's equation and the modifications that we propose to Darcy's equation, and derive the governing equations through a systematic approach using mixture theory. We then propose a stabilized mixed finite element formulation for the modified Darcy's equation. To solve the resulting nonlinear equations we present a solution procedure based on the consistent Newton-Raphson method. We solve representative test problems to illustrate the performance of the proposed stabilized formulation. One of the objectives of this paper is also to show that the dependence of viscosity on the pressure can have a significant effect both on the qualitative and quantitative nature of the solution.

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On steady flows of fluids with pressure– and shear–dependent viscosities

Cited by 56 publications

References 27 publications

On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

Slag Behavior in Gasifiers. Part II: Constitutive Modeling of Slag

A numerical study of fluids with pressure‐dependent viscosity flowing through a rigid porous medium

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