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Article

H. MADERS, Y. DEMAY and J.F. AGASSANT

In this study, the stationary flow of a polymeric fluid governed by the upper convected Maxwell law is computed in a 2‐D convergent geometry. A finite element method is…

Abstract

In this study, the stationary flow of a polymeric fluid governed by the upper convected Maxwell law is computed in a 2‐D convergent geometry. A finite element method is used to obtain non‐linear discretized equations, solved by an iterative Picard (fixed point) algorithm. At each step, two sub‐systems are successively solved. The first one represents a Newtonian fluid flow (Stokes equations) perturbed by known pseudo‐body forces expressing fluid elasticity. It is solved by minimization of a functional of the velocity field, while the pressure is eliminated by penalization. The second sub‐system reduces to the tensorial differential evolution equation of the extra‐stress tensor for a given velocity field. It is solved by the so‐called ‘non‐consistent Petrov‐Galerkin streamline upwind’ method. As with other decoupled techniques applied to this problem, our simulation fails for relatively low values of the Weissenberg viscoelastic number. The value of the numerical limit point depends on the mesh refinement. When convergence is reached, the numerical solutions for velocity, pressure and stress fields are similar to those obtained by other authors with very costly mixed methods.

Details

Engineering Computations, vol. 9 no. 3
Type: Research Article
ISSN: 0264-4401

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Article

Haohan Sun and Si Yuan

A general strategy is developed for adaptive finite element (FE) analysis of free vibration of elastic membranes based on the element energy projection (EEP) technique.

Abstract

Purpose

A general strategy is developed for adaptive finite element (FE) analysis of free vibration of elastic membranes based on the element energy projection (EEP) technique.

Design/methodology/approach

By linearizing the free vibration problem of elastic membranes into a series of linear equivalent problems, reliable a posteriori point-wise error estimator is constructed via EEP super-convergent technique. Hierarchical local mesh refinement is incorporated to better deal with tough problems.

Findings

Several classical examples were analyzed, confirming the effectiveness of the EEP-based error estimation and overall adaptive procedure equipped with a local mesh refinement scheme. The computational results show that the adaptively-generated meshes reasonably catch the difficulties inherent in the problems and the procedure yields both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm.

Originality/value

By reasonable linearization, the linear-problem-based EEP technique is successfully transferred to two-dimensional eigenproblems with local mesh refinement incorporated to effectively and flexibly deal with singularity problems. The corresponding adaptive strategy can produce both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm and thus can be expected to apply to other types of eigenproblems.

Details

Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0264-4401

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Article

A. Savini

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic…

Abstract

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 19 no. 2
Type: Research Article
ISSN: 0332-1649

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Article

J. Vuillon and D. Zeitoun

High‐power chemical lasers operating in high repetitive rate show a decrease of the output energy laser beam. In such lasers, the characteristic time which depends on the…

Abstract

High‐power chemical lasers operating in high repetitive rate show a decrease of the output energy laser beam. In such lasers, the characteristic time which depends on the laser output is short in comparison with those related to the flow. Consequently, shock waves, acoustic waves and thermal perturbations, induced by the strong electric energy deposition and remaining in the laser cavity between two pulses, may explain the decrease of output energy of the laser beam. For a better understanding of the flowfields, a numerical approach is carried out using flux corrected transport algorithms (FCT methods) associated with a Riemann solver on the computational domain boundaries. Under two‐dimensional assumptions, the inviscid flow in the convergent‐divergent laser cavity is computed to describe the creation and propagation of the wave system and the hot gas column in both single and multidischarge operating modes. Distortions of the contact surfaces are put into evidence through the study of flowfield instabilities. Finally, the limitations of the two‐dimensional modelization become apparent. The numerical resolution is extended to a 3D case in order to take into account the optical direction. This allows to study the influence of shock waves travelling between optics and being generated by a side effect developing at the electrodes. These waves have an effect of long duration on the flowfield and lead to a high residual perturbation level.

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International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 1
Type: Research Article
ISSN: 0961-5539

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Article

E.Y.K. NG and S.Z. LIU

This paper introduces a novel algorithm for solving the two‐dimensional Euler and Navier‐Stokes compressible equations using a one‐step effective flux vector‐splitting…

Abstract

This paper introduces a novel algorithm for solving the two‐dimensional Euler and Navier‐Stokes compressible equations using a one‐step effective flux vector‐splitting implicit method. The new approach makes a contribution by deriving a simple and yet effective implicit scheme which has the features of an exact factorization and avoids the solving of block‐diagonal system of equations. This results in a significant improvement in computational efficiency as compared to the standard Beam‐Warming and Steger implicit factored schemes. The current work has advantageous characteristics in the creation of higher order numerical implicit terms. The scheme is stable if we could select the correct values of the scalars (λ±ξ and λ±η) for the respective split flux‐vectors (F± and G±) along the ξ− and η−directions. A simple solving procedure is suggested with the discussion of the implicit boundary conditions, stability analysis, time‐step length and convergence criteria. This method is spatially second‐order accurate, fully conservative and implemented with general co‐ordinate transformations for treating complex geometries. Also, the scheme shows a good convergence rate and acceptable accuracy in capturing the shock waves. Results calculated from the program developed include transonic flows through convergence‐divergence nozzle and turbine cascade. Comparisons with other well‐documented experimental data are presented and their agreements are very promising. The extension of the algorithm to 3D simulation is straightforward and under way.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 8
Type: Research Article
ISSN: 0961-5539

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Article

Mubarak A.K. and Tide P.S.

The purpose of this paper is to design a double parabolic nozzle and to compare the performance with conventional nozzle designs.

Abstract

Purpose

The purpose of this paper is to design a double parabolic nozzle and to compare the performance with conventional nozzle designs.

Design/methodology/approach

The throat diameter and divergent length for Conical, Bell and Double Parabolic nozzles were kept same for the sake of comparison. The double parabolic nozzle has been designed in such a way that the maximum slope of the divergent curve is taken as one-third of the Prandtl Meyer (PM) angle. The studies were carried out at Nozzle Pressure Ratio (NPR) of 5 and also at design conditions (NPR = 3.7). Experimental measurements were carried out for all the three nozzle configurations and the performance parameters compared. Numerical simulations were also carried out in a two-dimensional computational domain incorporating density-based solver with RANS equations and SST k-ω turbulence model.

Findings

The numerical predictions were found to be in reasonable agreement with the measured experimental values. An enhancement in thrust was observed for double parabolic nozzle when compared with that of conical and bell nozzles.

Research limitations/implications

Even though the present numerical simulations were capable of predicting shock cell parameters reasonably well, shock oscillations were not captured.

Practical implications

The double parabolic nozzle design has enormous practical importance as a small increase in thrust can result in a significant gain in pay load.

Social implications

The thrust developed by the double parabolic nozzle is seen to be on the higher side than that of conventional nozzles with better fuel economy.

Originality/value

The overall performance of the double parabolic nozzle is better than conical and bell nozzles for the same throat diameter and length.

Details

Aircraft Engineering and Aerospace Technology, vol. 91 no. 1
Type: Research Article
ISSN: 1748-8842

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Article

Y.T. Feng, K. Han, D.R.J. Owen and J. Loughran

The main purpose of this paper is to derive a set of similarity principles for discrete element modelling so that a numerical model can exactly reproduce the physical…

Abstract

Purpose

The main purpose of this paper is to derive a set of similarity principles for discrete element modelling so that a numerical model can exactly reproduce the physical phenomenon concerned.

Design/methodology/approach

The objective is achieved by introducing the concepts of particle “strain” and “stress” so that some equivalence between the physical system and the numerical model can be established.

Findings

Three similarity principles, namely geometric, mechanical and dynamic, under which the numerical model can exactly reproduce the mechanical behaviour of a physical model are proposed. In particular, the concept of the scale invariant interaction law is further introduced. The scalability of a number of most commonly used interaction laws in the discrete element modelling is examined.

Research limitations/implications

This is a preliminary research for a very important and challenging topic. More research, particularly in the understanding of the convergent properties of discrete element models, is needed.

Originality/value

The paper provides some important theoretical guidances to computational modelling of particle systems using discrete element techniques.

Details

Engineering Computations, vol. 26 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

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Article

Dongliang Qi, Dongdong Wang, Like Deng, Xiaolan Xu and Cheng-Tang Wu

Although high-order smooth reproducing kernel mesh-free approximation enables the analysis of structural vibrations in an efficient collocation formulation, there is still…

Abstract

Purpose

Although high-order smooth reproducing kernel mesh-free approximation enables the analysis of structural vibrations in an efficient collocation formulation, there is still a lack of systematic theoretical accuracy assessment for such approach. The purpose of this paper is to present a detailed accuracy analysis for the reproducing kernel mesh-free collocation method regarding structural vibrations.

Design/methodology/approach

Both second-order problems such as one-dimensional (1D) rod and two-dimensional (2D) membrane and fourth-order problems such as Euler–Bernoulli beam and Kirchhoff plate are considered. Staring from a generic equation of motion deduced from the reproducing kernel mesh-free collocation method, a frequency error measure is rationally attained through properly introducing the consistency conditions of reproducing kernel mesh-free shape functions.

Findings

This paper reveals that for the second-order structural vibration problems, the frequency accuracy orders are p and (p − 1) for even and odd degree basis functions; for the fourth-order structural vibration problems, the frequency accuracy orders are (p − 2) and (p − 3) for even and odd degree basis functions, respectively, where p denotes the degree of the basis function used in mesh-free approximation.

Originality/value

A frequency accuracy estimation is achieved for the reproducing kernel mesh-free collocation analysis of structural vibrations, which can effectively underpin the practical applications of this method.

Details

Engineering Computations, vol. 36 no. 3
Type: Research Article
ISSN: 0264-4401

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Article

A.A. Polynkine, F. Van Keulen and V.V. Toropov

Presents an approach for optimal design of geometrically non‐linear structures, using adaptive mesh refinement (AMR). The optimization technique adopted is based on the…

Abstract

Presents an approach for optimal design of geometrically non‐linear structures, using adaptive mesh refinement (AMR). The optimization technique adopted is based on the multi‐point approximation method. The finite element method is used for the structural analysis. Reformulation of the optimal design problem is applied to circumvent complications caused by the non‐linear behaviour of the structure. The latter may lead to bifurcations, limit points and/or significant reduction of the structural stiffness for individual intermediate designs generated by an optimization algorithm. Discretization errors are controlled using AMR. To reduce computational costs, the requested global and local discretization errors are not taken as fixed values but are specified on the basis of the current status of the optimization process. In the beginning relatively large errors are accepted, while as the process progresses discretization errors are reduced. The method is applied to thin‐walled structures with geometrically non‐linear behaviour.

Details

Engineering Computations, vol. 13 no. 2/3/4
Type: Research Article
ISSN: 0264-4401

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Article

Jaroslav Mackerle

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view…

Abstract

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Details

Engineering Computations, vol. 20 no. 4
Type: Research Article
ISSN: 0264-4401

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