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Article

B.P. LEONARD and SIMIN MOKHTARI

In 1982, Smith and Hutton published comparative results of several different convection‐diffusion schemes applied to a specially devised test problem involving…

Abstract

In 1982, Smith and Hutton published comparative results of several different convection‐diffusion schemes applied to a specially devised test problem involving near‐discontinuities and strong streamline curvature. First‐order methods showed significant artificial diffusion, whereas higher‐order methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of low‐order artificially diffusive schemes, especially in the numerical heat‐transfer industry. This paper presents an alternative strategy of using non‐artificially diffusive higher‐order methods, while maintaining strictly monotonic transitions through the use of simple flux‐limiter constraints. Limited third‐order upwinding is usually found to be the most cost‐effective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 5
Type: Research Article
ISSN: 0961-5539

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Article

Rhodri Bevan, P. Nithiarasu, Igor Sazonov, Raoul van Loon, Heyman Luckraz, Michael Collins and Andrew Garnham

The purpose of this paper is to numerically study blood flow through a subject‐specific carotid artery with a moderately severe stenosis, also to thoroughly analyse the…

Abstract

Purpose

The purpose of this paper is to numerically study blood flow through a subject‐specific carotid artery with a moderately severe stenosis, also to thoroughly analyse the wall shear stress (WSS), oscillatory shear index (OSI) and WSS angular deviation (WSSAD). One of the important aspects of this study is the investigation on the influence of the extensions attached to the domain outlets.

Design/methodology/approach

The segmentation of the carotid artery is carried out using a deformable model based on a level set method. A geometric potential force (GPF) is employed to deform the level set to obtain the carotid artery geometry. The initial surface meshing is generated using an advanced marching cubes (MC) method, before improving the quality of the surface mesh via a number of mesh cosmetic steps. The volume mesh generation has two parts. In the first part, a quasi‐structured, boundary layer mesh is generated in the vicinity of the geometry walls. The second part of the meshing involves unstructured tetrahedral meshing of the inner part of the geometry. After the meshing stage, the flow boundary conditions are generated by numerically solving the Helmholtz equation in both space and time. Finally, the explicit characteristic‐based split (CBS) method is employed in a parallel environment to produce a detailed analysis of wall quantities.

Findings

In general, WSS is very high in the vicinity of the carotid artery apex and in the proximity of the stenosis. From the results obtained, it is clear that the influence of outlet domain extension is marginal. While the peak instantaneous WSS differs by a maximum of 5.7 per cent, the time‐averaged WSS difference due to extended domain is only 1.3 per cent. Two other derived parameters are also examined in the paper, the oscillating shear index and the WSSAD. Both these quantities also display minor or negligible differences due to domain extension.

Originality/value

It has been perceived that domain extension is essential to avoid wrong application of boundary conditions. The results obtained, however, conclusively show that the outlet domain extension has only a moderate influence on WSS. Thus, outlet extension to the domains may not be essential for arterial blood flows. It is also observed that the dramatic values of peak WSS obtained near the stenosis is the result of high resolution mesh along with boundary layers used in this study. Both the outcomes represent the originality of this paper.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 8
Type: Research Article
ISSN: 0961-5539

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Article

D.C. Lo, Chih-Min Hsieh and D.L. Young

The main advantage of the proposed method is that the computations can be performed on a Cartesian grid with complex immersed boundaries (IBs). The purpose of this paper…

Abstract

Purpose

The main advantage of the proposed method is that the computations can be performed on a Cartesian grid with complex immersed boundaries (IBs). The purpose of this paper is to device a numerical scheme based on an embedding finite element method for the solution of two-dimensional (2D) Navier-Stokes equations.

Design/methodology/approach

Geometries featuring the stationary solid obstacles in the flow are embedded in the Cartesian grid with special discretizations near the embedded boundary to ensure the accuracy of the solution in the cut cells. To comprehend the complexities of the viscous flows with IBs, the paper adopts a compact interpolation scheme near the IBs that allows to satisfy the second-order accuracy and the conservation property of the solver. The interpolation scheme is designed by virtue of the shape function in the finite element scheme.

Findings

Three numerical examples are selected to demonstrate the accuracy and flexibility of the proposed methodology. Simulation of flow past a circular cylinder for a range of Re=20-200 shows excellent agreements with other results using different numerical schemes. Flows around a pair of tandem cylinders and several bodies are particularly investigated. The paper simulates the time-based variation of the flow phenomena for uniform flow past a pair of cylinders with various streamwise gaps between two cylinders. The results in terms of drag coefficient and Strouhal number show excellent agreements with the results available in the literature.

Originality/value

Details of the flow characteristics, such as velocity distribution, pressure and vorticity fields are presented. It is concluded the combined embedding boundary method and FE discretizations are robust and accurate for solving 2D fluid flows with complex IBs.

Details

Engineering Computations, vol. 31 no. 4
Type: Research Article
ISSN: 0264-4401

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Article

Chongbin Zhao, B.E. Hobbs, K. Baxter, H.B. Mühlhaus and A. Ord

We present a numerical methodology for the study of convective pore‐fluid, thermal and mass flow in fluid‐saturated porous rock basins. In particular, we investigate the…

Abstract

We present a numerical methodology for the study of convective pore‐fluid, thermal and mass flow in fluid‐saturated porous rock basins. In particular, we investigate the occurrence and distribution pattern of temperature gradient driven convective pore‐fluid flow and hydrocarbon transport in the Australian North West Shelf basin. The related numerical results have demonstrated that: (1) The finite element method combined with the progressive asymptotic approach procedure is a useful tool for dealing with temperature gradient driven pore‐fluid flow and mass transport in fluid‐saturated hydrothermal basins; (2) Convective pore‐fluid flow generally becomes focused in more permeable layers, especially when the layers are thick enough to accommodate the appropriate convective cells; (3) Large dislocation of strata has a significant influence on the distribution patterns of convective pore‐fluid flow, thermal flow and hydrocarbon transport in the North West Shelf basin; (4) As a direct consequence of the formation of convective pore‐fluid cells, the hydrocarbon concentration is highly localized in the range bounded by two major faults in the basin.

Details

Engineering Computations, vol. 16 no. 2
Type: Research Article
ISSN: 0264-4401

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Article

Sara Rainieri, Fabio Bozzoli, Linda Schiavi and Giorgio Pagliarini

The aim of this paper is to investigate the convective heat transfer in swirl tubes, which are obtained by roto‐translating a circular section eccentric with respect to…

Abstract

Purpose

The aim of this paper is to investigate the convective heat transfer in swirl tubes, which are obtained by roto‐translating a circular section eccentric with respect to the rotation axis. The geometry is numerically investigated with the aim of evaluating the convective heat transfer enhancement effect due to the secondary flow induced by the centrifugal force.

Design/methodology/approach

The governing equations, i.e. continuity, momentum and energy equations, are integrated numerically within Comsol Multiphysics® environment, under the assumption of incompressible Newtonian and constant properties fluid and of periodically fully developed laminar flow for what concerns both the hydrodynamic and the thermal problem under the uniform wall heat flux thermal boundary condition.

Findings

The heat transfer performance of the geometry is discussed in relation to the flow pattern. In particular, the numerical results show that two different stable flow regimes may exist, according to the ratio of the Reynolds number to the dimensionless helix pitch. The Nusselt number augmentation becomes significant for high Prandtl number fluids when a critical Re/P* value, corresponding to the onset of the centrifugal forces induced secondary flow, is reached.

Originality/value

The geometry here investigated represents an interesting solution to enhance the convective heat transfer in situations in which the flow, although disturbed, persists in the laminar regime. This type of enhanced tubes shows then interesting heat transfer performances (which becomes particularly significant for high Prandtl number values) by thus suggesting convenient applications also for highly viscous fluids which are often treated under the laminar flow regime.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 5
Type: Research Article
ISSN: 0961-5539

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Article

Z.B. Xing, Xingchao Han, Hanbing Ke, Q.G. Zhang, Zhiping Zhang, Huijin Xu and Fuqiang Wang

A combination of highly conductive porous media and nanofluids is an efficient way for improving thermal performance of relevant applications. For precisely predicting the…

Abstract

Purpose

A combination of highly conductive porous media and nanofluids is an efficient way for improving thermal performance of relevant applications. For precisely predicting the flow and thermal transport of nanofluids in porous media, the purpose of this paper is to explore the inter-phase coupling numerical methods.

Design/methodology/approach

Based on the lattice Boltzmann (LB) method, this study combines the convective flow, non-equilibrium thermal transport and phase interactions of nanofluids in porous matrix and proposes a new multi-phase LB model. The micro-scale momentum and heat interactions are especially analyzed for nanoparticles, base fluid and solid matrix. A set of three-phase LB equations for the flow/thermal coupling of base fluid, nanoparticles and solid matrix is established.

Findings

Distributions of nanoparticles, velocities for nanoparticles and the base fluid, temperatures for three phases and interaction forces are analyzed in detail. Influences of parameters on the nanofluid convection in the porous matrix are examined. Thermal resistance of nanofluid convective transport in porous structures are comprehensively discussed with the models of multi-phases. Results show that the Rayleigh number and the Darcy number have significant influences on the convective characteristics. The result with the three-phase model is mildly larger than that with the local thermal non-equilibrium model.

Originality/value

This paper first creates the multi-phase theoretical model for the complex coupling process of nanofluids in porous structures, which is useful for researchers and technicians in fields of thermal science and computational fluid dynamics.

Details

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

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Article

Leo Lukose and Tanmay Basak

The purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the…

Abstract

Purpose

The purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the bottom wall (isothermal/sinusoidal heating). Containers are categorized into three classes based on geometric configurations [Class 1 (square, tilted square and parallelogram), Class 2 (trapezoidal type 1, trapezoidal type 2 and triangle) and Class 3 (convex, concave and triangle with curved hypotenuse)].

Design/methodology/approach

The governing equations are solved by using the Galerkin finite element method for various processing fluids (Pr = 0.025 and 155) and Rayleigh numbers (103 ≤ Ra ≤ 105) involving nine different containers. Finite element-based heat flow visualization via heatlines has been adopted to study heat distribution at various sections. Average Nusselt number at the bottom wall ( Nub¯) and spatially average temperature (θ^) have also been calculated based on finite element basis functions.

Findings

Based on enhanced heating criteria (higher Nub¯ and higher θ^), the containers are preferred as follows, Class 1: square and parallelogram, Class 2: trapezoidal type 1 and trapezoidal type 2 and Class 3: convex (higher θ^) and concave (higher Nub¯).

Practical implications

The comparison of heat flow distributions and isotherms in nine containers gives a clear perspective for choosing appropriate containers at various process parameters (Pr and Ra). The results for current work may be useful to obtain enhancement of the thermal processing rate in various process industries.

Originality/value

Heatlines provide a complete understanding of heat flow path and heat distribution within nine containers. Various cold zones and thermal mixing zones have been highlighted and these zones are found to be altered with various shapes of containers. The importance of containers with curved walls for enhanced thermal processing rate is clearly established.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 7
Type: Research Article
ISSN: 0961-5539

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Article

Pratibha Biswal and Tanmay Basak

This paper is aimed to study natural convection in enclosures with curved (concave and convex) side walls for porous media via the heatline-based heat flow visualization approach.

Abstract

Purpose

This paper is aimed to study natural convection in enclosures with curved (concave and convex) side walls for porous media via the heatline-based heat flow visualization approach.

Design/methodology/approach

The numerical scheme involving the Galerkin finite element method is used to solve the governing equations for several Prandtl numbers (Prm) and Darcy numbers (Dam) at Rayleigh number, Ram = 106, involving various wall curvatures. Finite element method is advantageous for curved domain, as the biquadratic basis functions can be used for adaptive automated mesh generation.

Findings

Smooth end-to-end heatlines are seen at the low Dam involving all the cases. At the high Dam, the intense heatline cells are seen for the Cases 1-2 (concave) and Cases 1-3 (convex). Overall, the Case 1 (concave) offers the largest average Nusselt number ( Nur¯) at the low Dam for all Prm. At the high Dam, Nur¯ for the Case 1 (concave) is the largest involving the low Prm, whereas Nur¯ is the largest for Case 1 (convex) involving the high Prm.

Practical implications

Thermal management for flow systems involving curved surfaces which are encountered in various practical applications may be complicated. The results of the current work may be useful for the material processing, thermal storage and solar heating applications

Originality/value

The heatline approach accompanied by energy flux vectors is used for the first time for the efficient heat flow visualization during natural convection involving porous media in the curved walled enclosures involving various wall curvatures.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 7
Type: Research Article
ISSN: 0961-5539

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Article

C. RamReddy and P. Naveen

The purpose of this paper is to analyze the combined effects of thermal radiation and activation energy with a chemical reaction on the quadratic convective flow of a…

Abstract

Purpose

The purpose of this paper is to analyze the combined effects of thermal radiation and activation energy with a chemical reaction on the quadratic convective flow of a micropolar fluid over an inclined plate. Convective thermal boundary condition and suction/injection effects are considered at the surface of an inclined plate.

Design/methodology/approach

The convection along with nonlinear Boussinesq approximation (i.e. quadratic convection or nonlinear convection) and usual boundary layer assumptions is employed in the mathematical formulation. Highly coupled nonlinear governing equations are tackled by a combined local non-similarity and successive linearization techniques.

Findings

The behavior of various pertinent parameters on the fluid flow characteristics is conferred through graphs and it reveals that the qualitative behaviors of velocity, temperature, skin friction and heat transfer rates of a micropolar fluid are similar for Biot number and radiation parameters. The suction/injection and activation energy parameters increase the concentration of the micropolar fluid within the boundary layer, while the chemical reaction parameter reduces the concentration in the same region. Further, this quadratic convection shows a strong influence on the fluid flow characteristics and then the impact of pertinent parameters is more prominent on the physical quantities, compared therewith results of the linear convection.

Practical implications

This kind of investigation is useful in the mechanism of combustion, aerosol technology, high-temperature polymeric mixtures and solar collectors which are operated at moderate to very high temperatures.

Originality/value

This attempt is a unique contribution to the establishment of both micropolar fluid and activation energy. This kind of study even in the absence of quadratic convection is not yet noted.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 1
Type: Research Article
ISSN: 1573-6105

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Article

Siya Jiang and Song Fu

The purpose of the paper is to propose some modifications to the SIMPLE (semi-implicit method for pressure-linked equations) algorithm. These modifications can ensure the…

Abstract

Purpose

The purpose of the paper is to propose some modifications to the SIMPLE (semi-implicit method for pressure-linked equations) algorithm. These modifications can ensure the numerical robustness and optimize computational efficiency. They remarkably promote the ability of the SIMPLE algorithm for incompressible DNS (direct numerical simulation) of multiscale problems, such as transitional flows and turbulent flows, by improving the properties of dispersion and dissipation.

Design/methodology/approach

The MDCD (minimized dispersion and controllable dissipation) scheme and MMIM (modified momentum interpolation method) are introduced. Six typical test cases are used to validate the modified algorithm, including the linear convective flow, lid-driven cavity flow, laminar boundary layer, Taylor vortex and DHIT (decaying homogenous isotropic turbulence). Particularly, a highly unsteady DNS of separated-flow transition in turbomachinery is precisely predicted by the modified algorithm.

Findings

The numerical examples show the distinct superiority of the modified algorithm in both internal flows and external flows. The advantages of the MDCD scheme and MMIM make the SIMPLE algorithm a promising method for DNS.

Originality/value

Some effective modifications to the SIMPLE algorithm are addressed. It is the first attempt to introduce the MDCD approach into the SIMPLE-type algorithms. The new algorithm is especially suitable for the incompressible DNS of convection-dominated flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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