Spectrally accurate method for analysis of stationary flows of second‐order fluids in rough micro‐channels

Mohammadi, Alireza; Floryan, J. M.; Kaloni, P. N.

doi:10.1002/fld.2269

Cited by 7 publications

(7 citation statements)

References 31 publications

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“…more frequent variations in the surface profile) result in a significant larger incremental pressure loss, even if the relative roughness is the same. Mohammadi et al (2011) studied stationary flows of second-order fluids in rough microchannels by a spectral method. The algorithm models irregular roughness geometry using the Fourier expansions and enforces the flow boundary conditions on the rough wall by means of the immersed boundary method.…”

Section: Boundary Conditions and Wall Roughnessmentioning

confidence: 99%

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

Wörner

2012

Microfluid Nanofluid

372

197

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This article presents a comprehensive review of numerical methods and models for interface resolving simulations of multiphase flows in microfluidics and micro process engineering. The focus of the paper is on continuum methods where it covers the three common approaches in the sharp interface limit, namely the volumeof-fluid method with interface reconstruction, the level set method and the front tracking method, as well as methods with finite interface thickness such as color-function based methods and the phase-field method. Variants of the mesoscopic lattice Boltzmann method for two-fluid flows are also discussed, as well as various hybrid approaches. The mathematical foundation of each method is given and its specific advantages and limitations are highlighted. For continuum methods, the coupling of the interface evolution equation with the single-field Navier-Stokes equations and related issues are discussed. Methods and models for surface tension forces, contact lines, heat and mass transfer and phase change are presented. In the second part of this article applications of the methods in microfluidics and micro process engineering are reviewed, including flow hydrodynamics (separated and segmented flow, bubble and drop formation, breakup and coalescence), heat and mass transfer (with and without chemical reactions), mixing and dispersion, Marangoni flows and surfactants, and boiling.

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Section: Boundary Conditions and Wall Roughnessmentioning

confidence: 99%

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

Wörner

2012

Microfluid Nanofluid

372

197

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“…The additional attractiveness of the IBC method is associated with the precise mathematical formalism, high accuracy and sharp identification of the location of time-dependent physical boundaries. The method has been extended to two-dimensional unsteady problems [28], moving boundary problems involving Laplace [29] and biharmonic [30] operators, the complete Navier-Stokes system [31], to operators involving different classes of non-Newtonian fluids [32,33], to three-dimensional operators [34,35] as well as to operators expressed in cylindrical coordinate systems [36]. Its accuracy has been improved through the use of the overdetermined formulation [37].…”

Section: Introductionmentioning

confidence: 99%

Spectrally-accurate algorithm for the analysis of flows in two-dimensional vibrating channels

Zandi

Mohammadi

Floryan

2015

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

“…The additional attractiveness of this concept is associated with the precise mathematical formalism and high accuracy. The method has been implemented to study problems involving hydrodynamic instabilities induced by surface roughness [9,[16][17][18][19] and has been successfully extended to two-dimensional unsteady problems [37], moving boundary problems involving Laplace, biharmonic and Navier-Stokes operators [34][35][36][37], non-Newtonian fluid problems [38,39], and three-dimensional Laplace operator [40].The present work is focused on the development of spectrally accurate IBC algorithms suitable for accurate and computationally efficient analysis of flows in geometries described in terms of the cylindrical coordinate system. The problem is posed as the problem of determination of flows in annuli fitted with either transverse or longitudinal ribs with arbitrary cross-sections.…”

mentioning

confidence: 99%

Algorithm for analysis of flows in ribbed annuli

Moradi

Floryan

2011

Numerical Methods in Fluids

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SUMMARYSpectral methods for analyses of steady flows in annuli bounded by walls with either axi-symmetric or longitudinal ribs are developed. The physical boundary conditions are enforced using the immersed boundary conditions concept. In the former case, the Stokes stream function is used to eliminate pressure and to reduce system of field equations to a single fourth-order partial differential equation. The ribs are assumed to be periodic in the axial direction and this permits representation of the solution in terms of the Fourier expansion. In the latter case, the problem is reduced to the Laplace equations for the flow modifications that can be expressed in terms of the Fourier expansions. The modal functions, which are functions of the radial coordinate, are discretized using Chebyshev polynomials. The problem formulations are closed using either the fixed volume flow rate constraint or the fixed pressure gradient constraint. Various tests have been carried out in order to demonstrate the spectral accuracy of the discretizations, as well as the spectral accuracy of the enforcement of the flow boundary conditions at the ribbed walls using the immersed boundary conditions concept. Special linear solver that takes advantage of the matrix structure has been implemented in order to reduce computational time and memory requirements. It is shown that the algorithm has superior performance when one is interested in the analysis of a large number of geometries, as part of the coefficient matrix that corresponds to the field equation is always the same and one needs to change only the part of the matrix that corresponds to the boundary relations when changing geometry of the flow domain. Copyright

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Spectrally accurate method for analysis of stationary flows of second‐order fluids in rough micro‐channels

Cited by 7 publications

References 31 publications

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

Spectrally-accurate algorithm for the analysis of flows in two-dimensional vibrating channels

Algorithm for analysis of flows in ribbed annuli

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