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Article
Publication date: 1 February 2003

Bart Merci, Jan Vierendeels, Chris De Langhe and Erik Dick

A numerical scheme that has already proved to be efficient and accurate for laminar heat transfer is extended for turbulent, axisymmetric heat transfer calculations. The extended…

1129

Abstract

A numerical scheme that has already proved to be efficient and accurate for laminar heat transfer is extended for turbulent, axisymmetric heat transfer calculations. The extended scheme is applied to the steady‐state heat transfer of axisymmetric turbulent jets, impinging onto a flat plate. Firstly, the low‐Reynolds version of the standard k‐ε model is employed. As is well known, the classical k‐ε turbulence model fails to predict the heat transfer of impinging jets adequately. A non‐linear k‐ε model, with improved ε‐equation, yields much better results. The numerical treatment of the higher order terms in this model is described. The effect on the heat transfer predictions of a variable turbulent Prandtl number is shown to be small. It is also verified that the energy equation can be simplified, without affecting the results. Results are presented for the flow field and the local Nusselt number profiles on the plate for impinging jets with different distances between the pipe exit and the flat plate.

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International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 June 2001

Jan Vierendeels, Bart Merci and Erik Dick

Steady‐state two‐dimensional solutions to the full compressible Navier‐Stokes equations are computed for laminar convective motion of a gas in a square cavity with large…

966

Abstract

Steady‐state two‐dimensional solutions to the full compressible Navier‐Stokes equations are computed for laminar convective motion of a gas in a square cavity with large horizontal temperature differences. No Boussinesq or low‐Mach number approximations of the Navier‐Stokes equations are used. Results for air are presented. The ideal‐gas law is used and viscosity is given by Sutherland’s law. An accurate low‐Mach number solver is developed. Here an explicit third‐order discretization for the convective part and a line‐implicit central discretization for the acoustic part and for the diffusive part are used. The semi‐implicit line method is formulated in multistage form. Multigrid is used as the acceleration technique. Owing to the implicit treatment of the acoustic and the diffusive terms, the stiffness otherwise caused by high aspect ratio cells is removed. Low Mach number stiffness is treated by a preconditioning technique. By a combination of the preconditioning technique, the semi‐implicit discretization and the multigrid formulation a convergence behaviour is obtained which is independent of grid size, grid aspect ratio, Mach number and Rayleigh number. Grid converged results are shown for a variety of Rayleigh numbers.

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International Journal of Numerical Methods for Heat & Fluid Flow, vol. 11 no. 4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 31 July 2019

Mathieu Olivier and Olivier Paré-Lambert

This paper aims to present a fluid-structure coupling partitioned scheme involving rigid bodies supported by spring-damper systems. This scheme can be used with already existing…

122

Abstract

Purpose

This paper aims to present a fluid-structure coupling partitioned scheme involving rigid bodies supported by spring-damper systems. This scheme can be used with already existing fluid flow solvers without the need to modify them.

Design/methodology/approach

The scheme is based on a modified Broyden method. It solves the equations of solid body motion in which the external forces coming from the flow are provided by a segregated flow solver used as a black box. The whole scheme is implicit.

Findings

The proposed partitioned method is stable even in the ultimate case of very strong fluid–solid interactions involving a massless cylinder oscillating with no structural damping. The overhead associated with the coupling scheme represents an execution time increase by a factor of about 2 to 5, depending on the context. The scheme also has the advantage of being able to incorporate turbulence modeling directly through the flow solver. It has been tested successfully with URANS simulations without wall law, thus involving thin high aspect-ratio cells near the wall.

Originality/value

Such problems are known to be very difficult to solve and previous studies usually rely on monolithic approaches. To the authors' knowledge, this is the first time a partitioned scheme is used to solve fluid–solid interactions involving massless components.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 7 March 2016

Shainath Ramesh Kalamkar and Jadav Chandra Mandal

The purpose of this paper is to present two low diffusive convective-pressure flux split finite volume algorithms for solving incompressible flows in artificial compressibility…

326

Abstract

Purpose

The purpose of this paper is to present two low diffusive convective-pressure flux split finite volume algorithms for solving incompressible flows in artificial compressibility framework.

Design/methodology/approach

The present method follows the framework similar to advection upwind splitting method of Liou and Steffen for compressible flows which is used by Vierendeels et al. to solve incompressible flow equations. Instead of discretizing the total inviscid flux using upwind scheme, the inviscid flux is first split into convective and pressure parts, and then discretized the two parts differently. The convective part is discretized using upwind method and the pressure part using central differencing. Since the Vierendeels type scheme may not be able to capture the divergence free velocity field due to the presence of artificial dissipation term, a strategy to progressively withdraw the dissipation with time step is proposed here that can ascertain the divergence free velocity condition to the level of residual error. This approach helps in reducing the amount of numerical dissipation due to upwind discretization, which is evident from the numerical test examples.

Findings

Upwind treatment of only the convective part of the inviscid flux terms, instead of the whole inviscid flux term, leads to more accurate solutions even at relatively coarse grids, which is substantiated by numerical test examples.

Research limitations/implications

The method is presently applicable to Cartesian grid.

Originality/value

Although similar formulation is reported by Vierendeels et al., no detailed study of the accuracy is presented. Discretization and solution reconstructions used in the present approach differ from the approach reported by Vierendeels et al. A modification to Vierendeels type scheme is proposed that can help in achieving divergence free velocity condition. Finally the efficacy of the present approach to produce very accurate solutions even on coarse grids is successfully demonstrated using a few benchmark problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 2
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 November 2003

Bart Merci and Erik Dick

The influence of computational aspects on simulation results is quantitatively investigated for the specific case of a turbulent piloted jet diffusion flame (Sandia Flame D). It…

387

Abstract

The influence of computational aspects on simulation results is quantitatively investigated for the specific case of a turbulent piloted jet diffusion flame (Sandia Flame D). It is illustrated that, with a fixed turbulence and chemistry model, the results can heavily depend on the numerical aspects. The influence of inlet boundary conditions has already been discussed in an earlier paper. In this work, attention is focused onto the order of accuracy of the spatial discretization in the numerical scheme and onto the position of the outlet boundary. It is stressed that the purpose is not to judge the quality of the applied models, but to illustrate the possible impact of numerical influence factors. The conclusion is a warning message and a demonstration that all numerical aspects must be completely described when calculation results are presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 December 2003

Jan Vierendeels, Bart Merci and Erik Dick

In this study, Benchmark solutions are derived for the problem of two‐dimensional laminar flow of air in a square cavity which is heated on the left, cooled on the right and…

1127

Abstract

In this study, Benchmark solutions are derived for the problem of two‐dimensional laminar flow of air in a square cavity which is heated on the left, cooled on the right and insulated on the top and bottom boundaries. The temperature differences between the hot and cold walls are large. Neither Boussinesq nor low‐Mach number approximations of the Navier‐Stokes equations are used. The ideal‐gas law is used and the viscosity is given by Sutherland's law. A constant Prandtl number is assumed. The computational method is completely described by Vierendeels et al. Grid converged results with an accuracy of 4 up to 5 digits are obtained for different Rayleigh numbers and temperature differences.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 7 August 2017

Hector Barrios-Piña, Stéphane Viazzo and Claude Rey

The purpose of this paper is to show a thermodynamic analysis to determine the contribution of each term of the total energy balance.

162

Abstract

Purpose

The purpose of this paper is to show a thermodynamic analysis to determine the contribution of each term of the total energy balance.

Design/methodology/approach

The thermodynamic analysis comprises a number of numerical simulations where some terms, typically ignored by the commonly used approximations, are removed from the total energy equation to quantify the effects in the flow and heat transfer fields. The case study is the differentially heated square cavity flow, in which the effects of work done by the pressure forces contribute significantly to the energy balance. Because local magnitudes are computed here for discussion, the dimensional form of the governing equations is preferred and a numerical model without any restrictive approximation about the role of the pressure is used.

Findings

The results show that the work of gravity forces term is in perfect balance with the work of pressure forces term, and thus, ignoring the contribution of one of them yields an incorrect solution. In addition, it is shown that the assumption of zero divergence of the Boussinesq approximation can be erroneous, even for a natural convection flow case where the temperature difference is very small.

Research limitations/implications

As the flow and heat transfer governing equations are complex, simplifying assumptions are generally used; that is, the Boussinesq and low Mach number approximations. These assumptions are systematically adopted without any validation process and without considering that they modify the physical meaning of one or more of the thermodynamic quantities, particularly the pressure. This fact results in inconsistencies of the different forms of energy.

Originality/value

This is the first time that the terms of the total energy balance are quantified in such a way, in a differentially heated square cavity flow, which is a case study addressed by several authors.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 23 October 2023

Shengxian Huang, Huihe Qiu and Ying Wang

Since most of the existing literature do not disclose the node coordinate data of its fixed-wing aircraft airfoil, in order to develop and obtain a practical and suitable…

139

Abstract

Purpose

Since most of the existing literature do not disclose the node coordinate data of its fixed-wing aircraft airfoil, in order to develop and obtain a practical and suitable deformation airfoil for fixed-wing micro air vehicle (MAV), this paper proposes an improved airfoil design method of fixed-wing MAV based on the profile data of S5010 airfoil.

Design/methodology/approach

Combined with the body shape variation of the stingray in the propulsion process, the parametric study of the aerodynamic shape of the original design airfoil is carried out to explore the influence of a single parameter change on the aerodynamic performance of the airfoil. Then, according to the influence law of single parameter variation on the aerodynamic performance of the airfoil, the original airfoil is synthetically deformed by changing multiple parameters.

Findings

By comparing the aerodynamic performance of the multi-parameter deformed airfoil with the original airfoil, it is found that the lift coefficient of the multi-parameter deformed airfoil changes from negative to positive value when AOA = 0°. When AOA = 2°, the lift coefficient growth rate is the largest, which is 47.27%, and the lift-to-drag ratio is increased by 50.00%. At other angles of attack, the lift, drag, and torque coefficients of the multi-parameter deformed airfoil are optimized to some extent.

Originality/value

Combined the body shape variation of the stingray in the propulsion process, the parametric study of the aerodynamic shape of the original design airfoil is carried out to explore the influence of a single parameter change on the aerodynamic performance of the airfoil.

Details

Engineering Computations, vol. 40 no. 9/10
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 August 2002

E. Theuns, J. Vierendeels and P. Vandevelde

This paper describes a one dimensional moving grid model for the pyrolysis of charring materials. In the model, the solid is divided by a pyrolysis front into a char and a virgin…

424

Abstract

This paper describes a one dimensional moving grid model for the pyrolysis of charring materials. In the model, the solid is divided by a pyrolysis front into a char and a virgin layer. Only when the virgin material reaches a critical temperature it starts to pyrolyse. The progress of the front determines the release of combustible volatiles by the surface. The volatiles, which are produced at the pyrolysis front, flow immediately out of the solid. Heat exchange between those volatiles and the char layer is taken into account. Since the model is used here as a stand‐alone model, the external heat flux that heats up the solid, is assumed to be known. In the future, this model will be coupled with a CFD code in order to simulate fire spread. The char and virgin grid move along with the pyrolysis front. Calculations are done on uniform and on non‐uniform grids for the virgin layer. In the char layer only a uniform grid is used. Calculations done with a non‐uniform grid are about 3 times faster than with a uniform gird. The moving grid model is compared with a faster but approximate integral model for several cases. For sudden changes in the boundary conditions, the approximate integral model gives significant errors.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 12 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 27 May 2014

Artur Tyliszczak

Variable density flows play an important role in many technological devices and natural phenomena. The purpose of this paper is to develop a robust and accurate method for low…

212

Abstract

Purpose

Variable density flows play an important role in many technological devices and natural phenomena. The purpose of this paper is to develop a robust and accurate method for low Mach number flows with large density and temperature variations.

Design/methodology/approach

Low Mach number approximation approach is used in the paper combined with a predictor-corrector method and accurate compact scheme of fourth and sixth order. A novel algorithm is formulated for the projection method in which the boundary conditions for the pressure are implemented in such a way that the continuity equation is fulfilled everywhere in the computational domain, including the boundary nodes.

Findings

It is shown that proposed implementation of the boundary conditions considerably improves a solution accuracy. Assessment of the accuracy was performed based on the constant density Burggraf flow and for two benchmark cases for the natural convection problems: steady flow in a square cavity and unsteady flow in a tall cavity. In all the cases the results agree very well with exemplary solutions.

Originality/value

A staggered or half-staggered grid arrangement is usually used for the projection method for both constant and low Mach number flows. The staggered approach ensures stability and strong pressure-velocity coupling. In the paper a high-order compact method has been implemented in the framework of low Mach number approximation on collocated meshes. The resulting algorithm is accurate, robust for large density variations and is almost free from the pressure oscillations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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