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Kybernetes, vol. 41 no. 7/8
Type: Research Article
ISSN: 0368-492X

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Article

S. Askari, M.H. Shojaeefard and K. Goudarzi

The purpose of this paper is to carry out a comprehensive study of compressible flow over double wedge and biconvex airfoils using computational fluid dynamics (CFD) and

Abstract

Purpose

The purpose of this paper is to carry out a comprehensive study of compressible flow over double wedge and biconvex airfoils using computational fluid dynamics (CFD) and three analytical models including shock and expansion wave theory, Busemann's second‐order linearized approximation and characteristic method (CHM).

Design/methodology/approach

Flow over double‐wedge and biconvex airfoils was investigated by the CFD technique using the Spalart‐Allmaras turbulence model for computation of the Reynolds stresses. Flow was considered compressible, two dimensional and steady. The no slip condition was applied at walls and the Sutherland law was used to calculate molecular viscosity as a function of static temperature. First‐order upwind discretization scheme was used for the convection terms. Finite‐volume method was used for the entire solution domain meshed by quadratic computational cells. Busemann's theory, shock and expansion wave technique and CHM were the analytical methods used in this work.

Findings

Static pressure, static temperature and aerodynamic coefficients of the airfoils were calculated at various angles of attack. In addition, aerodynamic coefficients of the double‐wedge airfoil were obtained at various free stream Mach numbers and thickness ratios of the airfoil. Static pressure and aerodynamic coefficients obtained from the analytical and numerical methods were in excellent agreement with average error of 1.62 percent. Variation of the static pressure normal to the walls was negligible in the numerical simulation as well as the analytical solutions. Analytical static temperature far from the walls was consistent with the numerical values with average error of 3.40 percent. However, it was not comparable to the numerical temperature at the solid walls. Therefore, analytical solutions give accurate prediction of the static pressure and the aerodynamic coefficients, however, for the static temperature; they are only reliable far from the solid surfaces. Accuracy of the analytical aerodynamic coefficients is because of accurate prediction of the static pressure which is not considerably influenced by the boundary layer. Discrepancies between analytical and numerical temperatures near the walls are because of dependency of temperature on the boundary layer and viscous heating. Low‐speed flow near walls causes transformation of the kinetic energy of the free stream into enthalpy that leads to high temperature on the solid walls; which is neglected in the analytical solutions.

Originality/value

This paper is useful for researchers in the area of external compressible flows. This work is original.

Details

Engineering Computations, vol. 28 no. 4
Type: Research Article
ISSN: 0264-4401

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Article

Chongbin Zhao, B.E. Hobbs, A. Ord, Ge Lin and H.B. Mühlhaus

In many scientific and engineering fields, large‐scale heat transfer problems with temperature‐dependent pore‐fluid densities are commonly encountered. For example, heat…

Abstract

Purpose

In many scientific and engineering fields, large‐scale heat transfer problems with temperature‐dependent pore‐fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large‐scale heat transfer problems with temperature‐dependent pore‐fluid densities in the lithosphere and crust scales.

Design/methodology/approach

The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts.

Findings

From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive‐and‐advective lithosphere with variable pore‐fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere.

Originality/value

The present analytical solutions can be used to: validate numerical methods for solving large‐scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large‐scale heat transfer problems with temperature‐dependent fluid densities.

Details

Engineering Computations, vol. 22 no. 2
Type: Research Article
ISSN: 0264-4401

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Article

W. Song and B.Q. Li

This paper describes the finite element solution of conjugate heat transfer problems with and without the use of gap elements. Direct and iterative methods to incorporate…

Abstract

This paper describes the finite element solution of conjugate heat transfer problems with and without the use of gap elements. Direct and iterative methods to incorporate gap elements into a general finite element program are presented, along with their advantages and disadvantages of the two gap element treatments in the framework of finite elements. The numerical performance of the iterative gap element treatment is discussed in detail in comparison with analytical solutions for both 2‐ and 3‐D gap conductance problems. Numerical tests show that the number of iterations depends on the non‐dimensional number Bi = hL/k, and it increases approximately linearly with Bi for Bi≥0.6. Here, for gap heat transfer problems, h is taken to be the inverse of the contact resistance. This conclusion holds true for both 2‐ and 3‐D problems, for both linear and quadratic elements and for both transient and steady state calculations. Further numerical results for conjugate heat transfer problems encountered in heat exchanger and micro chemical reactors are computed using the gap element approach, the direct numerical simulations and analytical solutions whenever solvable. The results reveal that for the standard heat exchanger designs, an accurate prediction of temperature distribution in the moving streams must take into consideration the radial temperature distribution and the accuracy of the calculations depends on the non‐dimensional number Bi = hR/2k. From gap element calculations, it is found that classical analytical solutions are valid for a heat transfer analysis of an exchanger system, only when Bi<0.1. This important point so far has been neglected in virtually all the textbooks on heat transfer and must be included to complete the heat transfer theory for heat exchanger designs. Results also suggest that for thermal fluids systems with chemical reactions such as micro fuel cells, the gap element approach yields accurate results only when the heat transfer coefficient that accounts for the chemical reactions is used. However, when these heat transfer coefficients are not available, direct numerical simulations should be used for an accurate prediction of the thermal performance of these systems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 12 no. 1
Type: Research Article
ISSN: 0961-5539

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Article

A.A. Avramenko, N.P. Dmitrenko, I.V. Shevchuk, A.I. Tyrinov and V.I. Shevchuk

The paper aims to consider heat transfer in incompressible flow in a rotating flat microchannel with allowance for boundary slip conditions of the first and second order…

Abstract

Purpose

The paper aims to consider heat transfer in incompressible flow in a rotating flat microchannel with allowance for boundary slip conditions of the first and second order. The novelty of the paper encompasses analytical and numerical solutions of the problem, with the latter based on the lattice Boltzmann method (LBM). The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). An increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes a similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which takes into account the second-order boundary conditions.

Design/methodology/approach

The paper is based on the comparisons of an analytical solution and a numerical solution, which employs the lattice Boltzmann method. Both mathematical approaches used the first-order and second-order slip boundary conditions. The results obtained using both methods agree well with each other.

Findings

The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). The increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes the similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which considers the second-order boundary conditions.

Originality/value

The novelty of the paper encompasses analytical and numerical solutions of the problem, whereas the latter are based on the LBM.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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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.

Details

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.I. Ramos

The purpose of this paper is to determine both analytically and numerically the existence of smooth, cusped and sharp shock wave solutions to a one-dimensional model of…

Abstract

Purpose

The purpose of this paper is to determine both analytically and numerically the existence of smooth, cusped and sharp shock wave solutions to a one-dimensional model of microfluidic droplet ensembles, water flow in unsaturated flows, infiltration, etc., as functions of the powers of the convection and diffusion fluxes and upstream boundary condition; to study numerically the evolution of the wave for two different initial conditions; and to assess the accuracy of several finite difference methods for the solution of the degenerate, nonlinear, advection--diffusion equation that governs the model.

Design/methodology/approach

The theory of ordinary differential equations and several explicit, finite difference methods that use first- and second-order, accurate upwind, central and compact discretizations for the convection terms are used to determine the analytical solution for steadily propagating waves and the evolution of the wave fronts from hyperbolic tangent and piecewise linear initial conditions to steadily propagating waves, respectively. The amplitude and phase errors of the semi-discrete schemes are determined analytically and the accuracy of the discrete methods is assessed.

Findings

For non-zero upstream boundary conditions, it has been found both analytically and numerically that the shock wave is smooth and its steepness increases as the power of the diffusion term is increased and as the upstream boundary value is decreased. For zero upstream boundary conditions, smooth, cusped and sharp shock waves may be encountered depending on the powers of the convection and diffusion terms. For a linear diffusion flux, the shock wave is smooth, whereas, for a quadratic diffusion flux, the wave exhibits a cusped front whose left spatial derivative decreases as the power of the convection term is increased. For higher nonlinear diffusion fluxes, a sharp shock wave is observed. The wave speed decreases as the powers of both the convection and the diffusion terms are increased. The evolution of the solution from hyperbolic tangent and piecewise linear initial conditions shows that the wave back adapts rapidly to its final steady value, whereas the wave front takes much longer, especially for piecewise linear initial conditions, but the steady wave profile and speed are independent of the initial conditions. It is also shown that discretization of the nonlinear diffusion flux plays a more important role in the accuracy of first- and second-order upwind discretizations of the convection term than either a conservative or a non-conservative discretization of the latter. Second-order upwind and compact discretizations of the convection terms are shown to exhibit oscillations at the foot of the wave’s front where the solution is nil but its left spatial derivative is largest. The results obtained with a conservative, centered second--order accurate finite difference method are found to be in good agreement with those of the second-order accurate, central-upwind Kurganov--Tadmor method which is a non-oscillatory high-resolution shock-capturing procedure, but differ greatly from those obtained with a non-conservative, centered, second-order accurate scheme, where the gradients are largest.

Originality/value

A new, one-dimensional model for microfluidic droplet transport, water flow in unsaturated flows, infiltration, etc., that includes high-order convection fluxes and degenerate diffusion, is proposed and studied both analytically and numerically. Its smooth, cusped and sharp shock wave solutions have been determined analytically as functions of the powers of the nonlinear convection and diffusion fluxes and the boundary conditions. These solutions are used to assess the accuracy of several finite difference methods that use different orders of accuracy in space, and different discretizations of the convection and diffusion fluxes, and can be used to assess the accuracy of other numerical procedures for one-dimensional, degenerate, convection--diffusion equations.

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

Zaatar Makni and Richard Demersseman

The purpose of this paper is to present an optimal sizing methodology. It is applied to a foil-coil powder core power inductor used in new generation inverters designed…

Abstract

Purpose

The purpose of this paper is to present an optimal sizing methodology. It is applied to a foil-coil powder core power inductor used in new generation inverters designed for hybrid and full-electric vehicles. The methodology includes a preliminary analytical calculation and a numerical optimization aimed at minimizing the component size.

Design/methodology/approach

Unlike bulk magnetic alloys or ferrites, the magnetic non-linearity of powder materials cannot be neglected in the analytical calculation. This non-linearity requires the use of an iterative calculation to search the set of parameters for which the target inductance value and the minimum volume are simultaneously reached. The numerical optimization process is based on 2D Finite Element (FE) analysis carried out with FEMM software tool and a simplex-type algorithm run in Scilab software. These two freewares are coupled using the scifemm.sci script which is included in the FEMM distribution.

Findings

The association of analytical and FE approaches provides a relevant and quick sizing methodology. It was successfully applied to size a new power inductor.

Originality/value

The strong non-linearity of the powder material is correctly taken into account in the analytical model thanks to an iterative calculation process. Thus, the preliminary analytical solution is quite relevant. Consequently, a local FE-based optimization is enough to find the optimal solution close by the analytical one. No global optimization is required. A local optimum is sufficient.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

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Article

L. Kadinski and M. Perić

The paper presents a numerical technique for the simulation of theeffects of grey‐diffusive surface radiation on fluid flow using a finitevolume procedure for…

Abstract

The paper presents a numerical technique for the simulation of the effects of grey‐diffusive surface radiation on fluid flow using a finite volume procedure for two‐dimensional (plane and axi‐symmetric) geometries. The governing equations are solved sequentially, and the non‐linearities and coupling of variables are accounted for through outer iterations (coefficients updates). In order to reduce the number of outer iterations, a multigrid algorithm was implemented. The radiating surface model assumes a non‐participating medium, semi‐transparent walls and constant elementary surface temperature and radiation fluxes. The calculation of view factors is based on the analytical evaluation for the plane geometry and numerical integration for axi‐symmetric geometry. Ashadowing algorithm was implemented for the calculation of view factors in general geometries. The method for the calculation of view factors was first tested by comparison with available analytical solutions for a complex geometric configuration. The flow prediction code combined with radiation heat transfer was verified by comparisons with analytical one‐dimensional solutions. Further test calculations were done for the flow and heat transfer in a cavity with a radiating submerged body. As an example of the capabilities of the method, transport processes in metalorganic chemical vapour deposition (MOCVD) reactors were simulated.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 3
Type: Research Article
ISSN: 0961-5539

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Article

K. Aboubi, L. Robillard, E. Bilgen and P. Vasseur

The present study deals with two‐dimensional convective motion due tothe effect of a centrifugal force field on a fluid contained between twohorizontal concentric…

Abstract

The present study deals with two‐dimensional convective motion due to the effect of a centrifugal force field on a fluid contained between two horizontal concentric cylinders, for the particular case of an adiabatic inner boundary (zero heat flux) and a constant heat flux imposed on the outer boundary. The normal terrestrial gravity is considered negligible. Governing equations for a two‐dimensional flow field are solved using analytical and numerical techniques. Based on a concentric flow approximation, the analytical solution is obtained in terms of the Rayleigh number and the radius ratio. The numerical solution is based on a finite difference method. Results indicate that the flow field always consists of two symmetrical cells at incipient convection even at radius ratios near unity. A good agreement is found between the analytical and numerical solutions at finite amplitude convection.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 5 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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