Identification of non-newtonian rheological parameter through an inverse formulation

Nascimento, Shirley Cristina Cabral; Naccache, Mônica F.; Rochinha, Fernando A.

doi:10.1590/s1678-58782010000200013

Cited by 7 publications

(4 citation statements)

References 23 publications

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“…Following this type of approach, identification of rheological parameters based on cross-section velocity measurements can be found in [3,4]. A similar approach using measurement of a pressure drop is proposed by [5]. In [6], attention is also payed to the identification of a scalar friction parameter.…”

Section: Introductionmentioning

confidence: 99%

Inverse rheometry and basal properties inference for pseudoplastic geophysical flows

Martin¹,

Monnier²

2015

European Journal of Mechanics - B/Fluids

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International audienceThe present work addresses the question of performing inverse rheometry and basal properties inferencefor pseudoplastic gravity-driven free-surface flows at low Reynolds’ number. The modeling of these flowsinvolves several parameters, such as the rheological ones or the state of the basal boundary (modeling aninterface between the base and the fluid). The issues of inverse rheometry are addressed in a generallaboratory flow context using surface velocity data. The inverse characterization of the basal boundary isproposed in a geophysical flow context where the parameters involved in the empirical effective slidinglaw are particularly difficult to estimate. Using an accurate direct and inverse model based on the adjointmethod combined with an original efficient solver, sensitivity analyses and parameter identification areperformed for a wide range of flow regimes, defined by the degree of slip and the non-linearity of theviscous sliding law considered at the bottom.The first result is the numerical assessment of the passive aspect of the viscosity singularity inherentto a power-law pseudoplastic (shear-thinning) description in terms of surface velocities. From this result,identification of the two parameters of the constitutive law, namely the power-law exponent and the con-sistency, are performed. These numerical experiments provide, on the one hand, a very robust identifica-tion of the power-law exponent, even for very noisy surface velocity observations and on the other hand, astrong equifinality problem on the identification of the consistency. This parameter has a minor influenceon the flow, in terms of surface velocities. Typically for temperature-dependent geophysical fluids, a lawdescribing a priori its spatial variability is then sufficient (e.g. based on a temperature vertical profile).This study then focuses on the basal properties interacting with the fluid rheology. An accuratejoint identification of the scalar valued triple ( n , m ; β) (respectively the rheological exponent, the nonlinear friction exponent and the friction coefficient) is achieved for any degree of slip, allowing tocompletely infer the flow regime. Next, in a geophysical flow context, identifications of a spatially varyingfriction coefficient are performed for various perturbed bedrock topography. The (2D-vertical) resultsdemonstrate a severely ill-posed problem that allows to compute a given set of surface velocity data withdifferent topography/friction pairs

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Section: Introductionmentioning

confidence: 99%

Inverse rheometry and basal properties inference for pseudoplastic geophysical flows

Martin¹,

Monnier²

2015

European Journal of Mechanics - B/Fluids

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“…In order to demonstrate the validity and also precision of the perturbation method, we solved numerically the Eqs. (15), (17), (19) with Runge-Kutta method and compared the results with that given by the perturbation method. Some results of calculated stream function are compared in Tables 1 and 2 where good agreements between the results can be observed.…”

Section: Validation Of the Methodsmentioning

confidence: 99%

“…Evans and Hagen [14] explored the two-dimensional sink flow in the wedges for the upper convected Maxwell and Oldroyd-B fluids, and showed that the local asymptotic structure near the apex consists of an outer core flow region and two thin elastic boundary layers at the walls. Nascimento et al [15], for providing an alternative method for estimation of flow properties, put forward an inverse formulation to identify a flow rheological parameter related to non-Newtonian fluids in a creeping flow through a 4:1 abrupt contraction. Rao et al [16] studied the boundary layer of an incompressible Jeffrey's viscoelastie fluid in a non-isothermal wedge.…”

Section: Introductionmentioning

confidence: 99%

Vortex behavior of particle suspension flow in a wedge for the second-order fluid

Wang

Lin

Zhang

2018

J Braz. Soc. Mech. Sci. Eng.

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Effect of Weissenberg number, Reynolds number, Stokes number and wedge angle on the vortex behavior of particle suspension flow is investigated numerically in a wedge for the second-order viscoelastic fluid. The results show that there exist symmetrical vortices near the walls close to apex for different wedge angles, and the vortex length is inversely proportional to the wedge angle. Increase of the Reynolds number not only increases the vortex length but also their dependence on the Weissenberg number. The vortex length increases with the increase of Weissenberg number and finally reaches an asymptotic value. The vortex gradually developed as the Stokes number is decreased, and the vortex length has a maximum for the single phase flow. The presence of particles will suppress the development of vortex, and the suppression degree is directly proportional to the Stokes number. The Reynolds number has a larger impact on the vortex length than the wedge angle in the parameter region studied here. Keywords Two-phase flow Á Second-order viscoelastic fluid Á Particles Á Wedge flow Á Vortex behavior Á Numerical simulation

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“…Their numerical simulations were capable of successfully capture the main features of the flow through an abrupt contraction. Nascimento et al [20] have employed a quasi-Newtonian flow-type dependent model in order to approximate flows of non-Newtonian through an axisymmetric abrupt contraction. These authors introduced a methodology to obtain nonNewtonian model parameters via an optimization strategy.…”

Section: Introductionmentioning

confidence: 99%

Finite element approximations for quasi-Newtonian flows employing a multi-field GLS method

Zinani

Frey

2011

Comput Mech

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This article concerns stabilized finite element approximations for flow-type sensitive fluid flows. A quasiNewtonian model, based on a kinematic parameter of flow classification and shear and extensional viscosities, is used to represent the fluid behavior from pure shear up to pure extension. The flow governing equations are approximated by a multi-field Galerkin least-squares (GLS) method, in terms of strain rate, pressure and velocity (D-p-u). This method, which may be viewed as an extension of the formulation for constant viscosity fluids introduced by Behr et al. (Comput Methods Appl Mech 104:31-48, 1993), allows the use of combinations of simple Lagrangian finite element interpolations. Mild Weissenberg flows of quasi-Newtonian fluidsusing Carreau viscosities with power-law indexes varying from 0.2 to 2.5-are carried out through a four-to-one planar contraction. The performed physical analysis reveals that the GLS method provides a suitable approximation for the problem and the results are in accordance with the related literature.

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Identification of non-newtonian rheological parameter through an inverse formulation

Cited by 7 publications

References 23 publications

Inverse rheometry and basal properties inference for pseudoplastic geophysical flows

Inverse rheometry and basal properties inference for pseudoplastic geophysical flows

Vortex behavior of particle suspension flow in a wedge for the second-order fluid

Finite element approximations for quasi-Newtonian flows employing a multi-field GLS method

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