Search results

1 – 10 of 18
To view the access options for this content please click here
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.

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

Keywords

To view the access options for this content please click here
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…

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

Keywords

To view the access options for this content please click here
Article
Publication date: 3 April 2007

M. Pons and P. Le Quéré

This paper aims to present and then resolve the thermodynamic inconsistencies inherent in the usual Boussinesq model, especially with respect to the second law, and to…

Abstract

Purpose

This paper aims to present and then resolve the thermodynamic inconsistencies inherent in the usual Boussinesq model, especially with respect to the second law, and to highlight the effects of the correction.

Design/methodology/approach

The Boussinesq model (i.e. still assuming ▽v=0) is made thermodynamically consistent by maintaining in the heat equation, primarily the work of pressure forces, secondarily the heat generated by viscous friction. Numerically speaking, the modifications are very easy and hardly affect the computing time. However, new non‐dimensional parameters arise, especially the non‐dimensional adiabatic temperature gradient, ϕ.

Findings

There are presented and interpreted results of systematic numerical simulations done for a two‐dimensional square differentially‐heated cavity filled with air at 300K, with Rayleigh number ranging from 3,000 to 108 and ϕ ranging from 10−3 to 2. All configurations are stationary and the fluid is far from its critical state. Nevertheless, the pressure‐work effect (similar to the piston effect) enhances the heat transfer while diminishing the convection intensity. The magnitude of this effect is non‐negligible as soon as ϕ reaches 0.02.

Practical implications

The domain where the thermodynamic Boussinesq model must be used encompasses configurations relevant to building engineering.

Originality/value

Exact second‐law analyses can be developed with the so‐corrected model.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article
Publication date: 1 December 2003

Marcos de Souza, Ricardo Fortes de Miranda and Humberto Araujo Machado

The generalized integral transform technique (GITT) is an hybrid numerical‐analytical method that has been successfully applied in convection‐diffusion problems, where the…

Abstract

The generalized integral transform technique (GITT) is an hybrid numerical‐analytical method that has been successfully applied in convection‐diffusion problems, where the original potentials are replaced by eigenexpansion series, and the system of partial differential equations is transformed into a finite system of ordinary differential equations, allowing to obtain an error controlled solution without any kind of grid generation. This paper aims at the application of GITT to the transient version of the classical differentially heated square cavity problem, considering fluid properties as functions of temperature. Comparing results to some previously reported data for constant fluid properties validates the computational procedure. The solution for variable fluid properties with Boussinesq approximation is presented for several values of inclinations, at Rayleigh number of 103 and a Prandtl number of 0.71, demonstrating GITT capability of capturing circulating cells formation and evolution at a low Rayleigh number. New correlations for leaning angle and aspect ratio are presented.

Details

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

Keywords

To view the access options for this content please click here
Article
Publication date: 4 September 2017

Santiago Francisco Corzo, Damian Enrique Ramajo and Norberto Marcelo Nigro

The purpose of this paper is to assess the Boussinesq approach for a wide range of Ra (10 × 6 to 10 × 11) in two-dimensional (square cavity) and three-dimensional (cubic…

Abstract

Purpose

The purpose of this paper is to assess the Boussinesq approach for a wide range of Ra (10 × 6 to 10 × 11) in two-dimensional (square cavity) and three-dimensional (cubic cavity) problems for air- and liquid-filled domains.

Design/methodology/approach

The thermal behavior in “differentially heated cavities” filled with air (low and medium Rayleigh) and water (high Rayleigh) is solved using computational fluid dynamics (CFDs) (OpenFOAM) with a non-compressible (Boussinesq) and compressible approach (real water properties from the IAPWS database).

Findings

The results from the wide range of Rayleigh numbers allowed for the establishment of the limitation of the Boussinesq approach in problems where the fluid has significant density changes within the operation temperature range and especially when the dependence of density with temperature is not linear. For these cases, the symmetry behavior predicted by Boussinesq is far from the compressible results, thus inducing a transient heat imbalance and leading to a higher mean temperature.

Research limitations/implications

The main limitation of the present research can be found in the shortage of experimental data for very high Rayleigh problems.

Practical implications

Practical implications of the current research could be use of the Boussinesq approach by carefully observing its limitations, especially for sensible problems such as the study of pressure vessels, nuclear reactors, etc.

Originality/value

The originality of this paper lies in addressing the limitations of the Boussinesq approach for high Rayleigh water systems. This fluid is commonly used in numerous industrial equipment. This work presents valuable conclusions about the limitations of the currently used models to carry out industrial simulations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article
Publication date: 7 April 2015

Abdelraheem Mahmoud Aly

Modeling of multi-phase flows for Rayleigh-Taylor instability and natural convection in a square cavity has been investigated using an incompressible smoothed particle…

Abstract

Purpose

Modeling of multi-phase flows for Rayleigh-Taylor instability and natural convection in a square cavity has been investigated using an incompressible smoothed particle hydrodynamics (ISPH) technique. In this technique, incompressibility is enforced by using SPH projection method and a stabilized incompressible SPH method by relaxing the density invariance condition is applied. The paper aims to discuss these issues.

Design/methodology/approach

The Rayleigh-Taylor instability is introduced in two and three phases by using ISPH method. The author simulated natural convection in a square/cubic cavity using ISPH method in two and three dimensions. The solutions represented in temperature, vertical velocity and horizontal velocity have been studied with different values of Rayleigh number Ra parameter (103=Ra=105). In addition, characteristic based scheme in Finite Element Method is introduced for modeling the natural convection in a square cavity.

Findings

The results for Rayleigh-Taylor instability and natural convection flow had been compared with the previous researches.

Originality/value

Modeling of multi-phase flows for Rayleigh-Taylor instability and natural convection in a square cavity has been investigated using an ISPH technique. In ISPH method, incompressibility is enforced by using SPH projection method and a stabilized incompressible SPH method by relaxing the density invariance condition is introduced. The Rayleigh-Taylor instability is introduced in two and three phases by using ISPH method. The author simulated natural convection in a square/cubic cavity using ISPH method in two and three dimensions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article
Publication date: 2 November 2015

Abdelraheem M. Aly, Mitsuteru Asai and Ali J. Chamkha

The purpose of this paper is to model mixed convection in a square cavity included circular cylinders motion using an incompressible smoothed particle hydrodynamics (ISPH…

Abstract

Purpose

The purpose of this paper is to model mixed convection in a square cavity included circular cylinders motion using an incompressible smoothed particle hydrodynamics (ISPH) technique.

Design/methodology/approach

The problem is solved numerically by using the ISPH method.

Findings

The SPH tool shows robust performance to simulate the rigid body motion in the mixed convective flow with heat transfer, and it may apply easily to complicated problems in 2D and 3D problem without difficulties.

Originality/value

The application of the SPH method to mixed convective flow with heat transfer and its potential application easily to complicated 3D problems is original.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article
Publication date: 25 November 2019

Shihua Lu, Jianqi Zhu, Dongyan Gao, Weiwei Chen and Xinjun Li

This study aims to show the importance of natural convection of supercritical fluid in an inclined cavity. The heat transfer performance of natural convection can be improved.

Abstract

Purpose

This study aims to show the importance of natural convection of supercritical fluid in an inclined cavity. The heat transfer performance of natural convection can be improved.

Design/methodology/approach

A model of an inclined cavity was set up to simulate the natural convection of supercritical fluid. The influence of inclined angles (30 to approximately 90°) and pressures (8 to approximately 12 MPa) are analyzed. To ascertain flow and heat transfer of supercritical fluid natural convection, this paper conducts a numerical investigation using the lattice Boltzmann method (LBM), which is proven to be precise and convenient.

Findings

The results show that the higher heat transfer performance can be obtained with an inclined angle of 30°. It is also presented that the heat transfer performance under pressure of 10 MPa is the best. In addition, common criterion number correlations of average Nusselt number are also fitted.

Originality/value

These study results can provide a theoretical reference for the study of heat transfer of supercritical fluid natural convection in engineering.

Details

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

Keywords

To view the access options for this content please click here
Article
Publication date: 5 March 2018

Minh Tuan Nguyen, Abdelraheem M. Aly and Sang-Wook Lee

This paper aims to conduct numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions…

Abstract

Purpose

This paper aims to conduct numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the incompressible smoothed particle hydrodynamics (ISPH) method.

Design/methodology/approach

In the ISPH method, the pressure evaluation is stabilized by including both of divergence of velocity and density invariance in solving pressure Poisson equation. The authors prevented the particles anisotropic distributions by using the shifting technique.

Findings

The proposed ISPH method exhibited good performance in natural/mixed convection in a cavity with fixed, moving and free-falling rigid body. In natural convection, the authors investigated the effects of an inner sloshing baffle as well as fixed and moving circular cylinders on the heat transfer and fluid flow. The heated baffle has higher effects on the heat transfer rate compared to a cooled baffle. In the mixed convection, a free-falling circular cylinder over a free surface cavity and heat transfer in the presence of a circular cylinder in a lid-driven cavity are simulated. Fixed or moving rigid body in a cavity results in considerable effects on the heat transfer rate and fluid flow.

Originality/value

The authors conducted numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the ISPH method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

To view the access options for this content please click here
Article
Publication date: 1 March 1992

J. FRÖHLICH and R. PEYRET

The low Mach number approximation of the Navier—Stokes equations is of similar nature to the equations for incompressible flow. A major difference, however, is the…

Abstract

The low Mach number approximation of the Navier—Stokes equations is of similar nature to the equations for incompressible flow. A major difference, however, is the appearance of a space‐ and time‐varying density that introduces a supplementary non‐linearity. In order to solve these equations with spectral space discretization, an iterative solution method has been constructed and successfully applied in former work to two‐dimensional natural convection and isobaric combustion with one direction of periodicity. For the extension to other geometries efficiency is an important point, and it is therefore desirable to devise a direct method which would have, in the best case, the same stability properties as the iterative method. The present paper discusses in a systematic way different approaches to this aim. It turns out that direct methods avoiding the diffusive time step limit are possible, indeed. Although we focus for discussion and numerical investigation on natural convection flows, the results carry over for other problems such as variable viscosity flows, isobaric combustion, or non‐homogeneous flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 18