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Article
Publication date: 1 September 2003

X. Wen and K. Manik

A boundary integral technique is developed to study the free surface flow of a steady, two‐dimensional, incompressible, irrotational and inviscid fluid flow which is produced by…

Abstract

A boundary integral technique is developed to study the free surface flow of a steady, two‐dimensional, incompressible, irrotational and inviscid fluid flow which is produced by two submerged sinks (or sources) which are of equal strength, placed along a solid horizontal boundary with a stagnation point on the free surface in a two layer stratified fluid in the presence of gravity. A special form of the Riemann‐Hilbert problem, namely the Dirichlet boundary problem, is applied in the derivation of the governing non‐linear boundary integral‐differential equations which are solved for the fluid velocity on the free surface and this involves the use of an interpolative technique and an iterative process. Results have been obtained for the free surface flow for various values of the Froude number and sink locations on the solid horizontal boundary and we have also studied the largest value of the Froude number for which no convergent solutions are possible, namely the critical Froude number. We have found that the free surface profile is dependent on two parameters, namely the Froude number on the free surface and the non‐dimensional distance between the two sinks.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 September 2005

M.J. Chern, A.G.L. Borthwick and R. Eatock Taylor

The research is directed at development of an efficient and accurate technique for modelling incompressible free surface flows in which viscous effects may not be neglected. The…

1093

Abstract

Purpose

The research is directed at development of an efficient and accurate technique for modelling incompressible free surface flows in which viscous effects may not be neglected. The paper describes the methodology, and gives illustrative results for simple geometries.

Design/methodology/approach

The pseudospectral matrix element method of discretisation is selected as the basis for the CFD technique adopted, because of its high spectral accuracy. It is implemented as a means of solving the Navier‐Stokes equations coupled with the modified compressibility method.

Findings

The viscous solver has been validated for the benchmark cases of uniform flow past a cylinder at a Reynolds number of 40, and 2D cavity flows. Results for sloshing of a viscous fluid in a tank have been successfully compared with those from a linearised analytical solution. Application of the method is illustrated by the results for the interaction of an impulsive wave with a surface piercing circular cylinder in a cylindrical tank.

Research limitations/implications

The paper demonstrates the viability of the approach adopted. The limitation of small amplitude waves should be tackled in future work.

Practical implications

The results will have particular significance in the context of validating computations from more complex schemes applicable to arbitrary geometries.

Originality/value

The new methodology and results are of interest to the community of those developing numerical models of flow past marine structures.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 10 August 2015

Filippo Berto and Alberto Campagnolo

Accordingly to the recent multi-scale model proposed by Sih and Tang, different orders of stress singularities are related to different material dependent boundary conditions…

Abstract

Purpose

Accordingly to the recent multi-scale model proposed by Sih and Tang, different orders of stress singularities are related to different material dependent boundary conditions associated with the interaction between the V-notch tip and the material under the remotely applied loading conditions. This induces complex three-dimensional stress and displacement fields in the proximity of the notch tip, which are worthy of investigation. The paper aims to discuss these issues.

Design/methodology/approach

Starting from Sih and Tang’s model, in the present contribution the authors propose some analytical expressions for the calculation of the strain energy density (SED) averaged over a control volume embracing the V-notch tip. The expressions vary as a function of the different boundary conditions. Dealing with the specific crack case, the results from the analytical frame are compared with those determined numerically under linear-elastic hypotheses, by applying different constraints to the through-the-thickness crack edges in three-dimensional discs subjected to Mode III loading. Free-free and free-clamped cases are considered.

Findings

Due to three-dimensional effects, the application of a nominal Mode III loading condition automatically provokes coupled Modes (I and II). Not only the intensity of the induced modes but also their degree of singularity depend on the applied conditions on the crack flanks. The variability of local SED through the thickness of the disc is analysed by numerical analyses and compared with the theoretical trend.

Originality/value

The capability of the SED to capture the combined three-dimensional effects is discussed in detail showing that this parameter is particularly useful when the definition of the stress intensity factors (SIFs) is ambiguous or the direct comparison between SIFs with odd dimensionalities is not possible.

Details

International Journal of Structural Integrity, vol. 6 no. 4
Type: Research Article
ISSN: 1757-9864

Keywords

Article
Publication date: 9 August 2011

Yvonne Stokes and Graham Carey

The purpose of this paper is to extend the penalty concept to treat partial slip, free surface, contact and related boundary conditions in viscous flow simulation.

542

Abstract

Purpose

The purpose of this paper is to extend the penalty concept to treat partial slip, free surface, contact and related boundary conditions in viscous flow simulation.

Design/methodology/approach

The penalty partial‐slip formulation is analysed and related to the classical Navier slip condition. The same penalty scheme also allows partial penetration through a boundary, hence the implementation of porous wall boundaries. The finite element method is used for investigating and interpreting penalty approaches to boundary conditions.

Findings

The generalised penalty approach is verified by means of a novel variant of the circular‐Couette flow problem, having partial slip on one of the cylindrical boundaries, for which an analytic solution is derived. Further verificationis provided by consideration of viscous flow over a sphere with partial slip on the surface, and comparison of numerical and classical solutions. Numerical studies illustrate the versatility of the approach.

Research limitations/implications

The penalty approach is applied to some different boundaries: partial slip and partial penetration with no/full slip/penetration as limiting cases; free surface; space‐ and time‐varying boundary conditions which allow progressive contact over time. Application is made to curved and inclined boundaries. Sensitivity of flow to penalty parameters is an avenue for continued research, as is application of the penalty approach for non‐Newtonian flows.

Originality/value

This is the first work to show the relation between penalty formulation of boundary conditions and physical boundary conditions. It provides a method that overcomes past difficulties in implementing partial slip on boundaries of general shape, and which handles progressive contact. It also provides useful benchmark problems for future studies.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 July 2017

Qingshan Wang, Dongyan Shi, Qian Liang and Fuzhen Pang

The purpose of this work is to apply the Fourier–Ritz method to study the vibration behavior of the moderately thick functionally graded (FG) parabolic and circular panels and…

187

Abstract

Purpose

The purpose of this work is to apply the Fourier–Ritz method to study the vibration behavior of the moderately thick functionally graded (FG) parabolic and circular panels and shells of revolution with general boundary conditions.

Design/methodology/approach

The modified Fourier series is chosen as the basis function of the admissible functions of the structure to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges, and the vibration behavior is solved by means of the Ritz method. The complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of FG parabolic and circular panels at the common meridian of θ = 0 and 2π. The convergence and accuracy of the present method are verified by other contributors.

Findings

Some new results of FG panels and shells with elastic restraints, as well as different geometric and material parameters, are presented and the effects of the elastic restraint parameters, power-law exponent, circumference angle and power-law distributions on the free vibration characteristic of the panels are also presented, which can be served as benchmark data for the designers and engineers to avoid the unpleasant, inefficient and structurally damaging resonant.

Originality/value

The paper could provide the reference for the research about the moderately thick FG parabolic and circular panels and shells of revolution with general boundary conditions. In addition, the change of the boundary conditions can be easily achieved by just varying the stiffness of the boundary restraining springs along all the edges of panels without making any changes in the solution procedure.

Article
Publication date: 1 June 2002

M.S. Chandio and M.F. Webster

This article is concerned with the numerical simulation of a reverse roller‐coating process, which involves the computation of Newtonian viscous incompressible flows with free

Abstract

This article is concerned with the numerical simulation of a reverse roller‐coating process, which involves the computation of Newtonian viscous incompressible flows with free‐surfaces. A numerical scheme is applied of a transient finite element form, a semi‐implicit Taylor‐Galerkin/pressurecorrection algorithm. For free‐surface prediction, we use kinematic boundary adjustment with a mesh‐stretching algorithm. In the present work, an alloy sheet (foil) passes over a large roller and then a smaller applicator roller, which provides the in‐feed. In combination, the applicator roller, the foil and the fluid form part of the underside coating mechanism. The aim of this study is to investigate fundamental aspects of the process, to ultimately address typical coating instabilities. These may take the form of chatter and starvation. A uniform coating thickness is the desired objective. A mathematical model is derived to describe the solvent coating applied to the underside of the sheet, assuming that the lacquer is a Newtonian fluid. In particular, the work has concentrated on the flow patterns that result and a parameter sensitivity analysis covering the appropriate operating windows of applied conditions. Effects of independent variation in roll‐speed and foil‐speed are investigated, to find that maxima in pressure, lift and drag arise at the nip and are influenced in a linear fashion.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 12 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 14 May 2019

Ravisha M., I.S. Shivakumara and Mamatha A.L.

The onset of convection in a ferrofluid-saturated porous layer has been investigated using a local thermal nonequilibrium (LTNE) model by allowing the solid phase to transfer heat…

Abstract

Purpose

The onset of convection in a ferrofluid-saturated porous layer has been investigated using a local thermal nonequilibrium (LTNE) model by allowing the solid phase to transfer heat via a Cattaneo heat flux theory while the fluid phase to transfer heat via usual Fourier heat-transfer law. The flow in the porous medium is governed by modified Brinkman-extended Darcy model. The instability of the system is discussed exactly for stress-free boundaries, while for rigid-ferromagnetic/paramagnetic boundaries the results are obtained numerically using the Galerkin method. The presence of Cattaneo effect introduces oscillatory convection as the preferred mode of instability contrary to the occurrence of instability via stationary convection found in its absence. Besides, oscillatory ferroconvection is perceived when the solid thermal relaxation time parameter exceeds a threshold value and increase in its value is to hasten the oscillatory onset. The effect of different boundary conditions on the instability of the system is noted to be qualitatively same. The paper aims to discuss these issues.

Design/methodology/approach

The investigators would follow the procedure of Straughan (2013) to obtain the expression for Rayleigh number. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The investigators have used a Galerkin method to obtain the numerical results for rigid-ferromagnetic/paramagnetic boundaries, while the instability of the system is discussed exactly for stress-free boundaries.

Findings

The Cattaneo–LTNE porous ferroconvection has been analyzed for different velocity and magnetic boundary conditions. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The effect of different types of velocity and magnetic boundary conditions on the instability of the system has been highlighted. The instability of the system is discussed exactly for stress-free boundaries, while for rigid-ferromagnetic/paramagnetic boundaries the results are obtained numerically using the Galerkin method.

Originality/value

The novelty of the present paper is to combine LTNE and second sound effects in solids on thermal instability of a ferrofluid-saturated porous layer by retaining the usual Fourier heat-transfer law in the ferrofluid. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The effect of different types of velocity and magnetic boundary conditions on the instability of the system is discussed.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 21 February 2020

Changsheng Wang, Xiao Han, Caixia Yang, Xiangkui Zhang and Wenbin Hou

Numerous finite elements are proposed based on analytical solutions. However, it is difficult to find the solutions for complicated governing equations. This paper aims to present…

Abstract

Purpose

Numerous finite elements are proposed based on analytical solutions. However, it is difficult to find the solutions for complicated governing equations. This paper aims to present a novel formulation in the framework of assumed stress quasi-conforming method for the static and free vibration analysis of anisotropic and symmetric laminated plates.

Design/methodology/approach

Firstly, an initial stress approximation ruled by 17 parameters, which satisfies the equilibrium equations is derived to improve the performance of the constructed element. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the Timoshenko’s laminated composite beam functions are adopted as boundary string-net functions for strain integration.

Findings

Several numerical examples are presented to show the performance of the new element, and the results obtained are compared with other available ones. Numerical results have proved that the new element is free from shear locking and possesses high accuracy for the analysis of anisotropic and symmetric laminated plates.

Originality/value

This paper proposes a new QC element for the static and free vibration analysis of anisotropic and symmetric laminated plates. In contrast with the complicated analytical solutions of the equilibrium equations, an initial stress approximation ruled by 17 parameters is adopted here. The Timoshenkos laminated composite beam functions are introduced as boundary string-net functions for strain integration. Numerical results demonstrate the new element is free from shear locking and possesses high accuracy for the analysis of anisotropic and symmetric laminated plates.

Details

Engineering Computations, vol. 37 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 15 February 2020

Yunpeng Wang and Roger E. Khayat

The purpose of this study is to examine theoretically the axisymmetric flow of a steady free-surface jet emerging from a tube for high inertia flow and moderate surface tension…

Abstract

Purpose

The purpose of this study is to examine theoretically the axisymmetric flow of a steady free-surface jet emerging from a tube for high inertia flow and moderate surface tension effect.

Design/methodology/approach

The method of matched asymptotic expansion is used to explore the rich dynamics near the exit where a stress singularity occurs. A boundary layer approach is also proposed to capture the flow further downstream where the free surface layer has grown significantly.

Findings

The jet is found to always contract near the tube exit. In contrast to existing numerical studies, the author explores the strength of upstream influence and the flow in the wall layer, resulting from jet contraction. This influence becomes particularly evident from the nonlinear pressure dependence on the upstream distance, as well as the pressure undershoot and overshoot at the exit for weak and strong gravity levels, respectively. The approach is validated against existing experimental and numerical data for the jet profile and centerline velocity where good agreement is obtained. Far from the exit, the author shows how the solution in the diffusive region can be matched to the inviscid far solution, providing the desired appropriate initial condition for the inviscid far flow solution. The location, at which the velocity becomes uniform across the jet, depends strongly on the gravity level and exhibits a non-monotonic behavior with respect to gravity and applied pressure gradient. The author finds that under weak gravity, surface tension has little influence on the final jet radius. The work is a crucial supplement to the existing numerical literature.

Originality/value

Given the presence of the stress singularity at the exit, the work constitutes a superior alternative to a computational approach where the singularity is typically and inaccurately smoothed over. In contrast, in the present study, the singularity is entirely circumvented. Moreover, the flow details are better elucidated, and the various scales involved in different regions are better identified.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 November 2000

A.M.C. Janse, P.E. Dijk and J.A.M. Kuipers

The volume of fluid (VOF) method is a numerical technique to track the developing free surfaces of liquids in motion. This method can, for example, be applied to compute the…

1041

Abstract

The volume of fluid (VOF) method is a numerical technique to track the developing free surfaces of liquids in motion. This method can, for example, be applied to compute the liquid flow patterns in a rotating cone reactor. For this application a spherical coordinate system is most suited. The novel derivation of the extended VOF algorithms for this class of applications is presented here. Some practical limitations of this method, that are inherent in the geometry of the described system, are discussed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 10 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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