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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/10779
Title: A fourth-order accurate finite difference method to evaluate the true transient behaviour of natural convection flow in enclosures
Authors: Balam N.B.
Gupta A.
Published in: International Journal of Numerical Methods for Heat and Fluid Flow
Abstract: Purpose: Modelling accurately the transient behaviour of natural convection flow in enclosures been a challenging task because of a variety of numerical errors which have limited achieving the higher order temporal accuracy. A fourth-order accurate finite difference method in both space and time is proposed to overcome these numerical errors and accurately model the transient behaviour of natural convection flow in enclosures using vorticity–streamfunction formulation. Design/methodology/approach: Fourth-order wide stencil formula with appropriate one-sided difference extrapolation technique near the boundary is used for spatial discretisation, and classical fourth-order Runge–Kutta scheme is applied for transient term discretisation. The proposed method is applied on two transient case studies, i.e. convection–diffusion of a Gaussian Pulse and Taylor Vortex flow having analytical solution. Findings: Error magnitude comparison and rate of convergence analysis of the proposed method with these analytical solutions establish fourth-order accuracy and prove the ability of the proposed method to truly capture the transient behaviour of incompressible flow. Also, to test the transient natural convection flow behaviour, the algorithm is tested on differentially heated square cavity at high Rayleigh number in the range of 103-108, followed by studying the transient periodic behaviour in a differentially heated vertical cavity of aspect ratio 8:1. An excellent comparison is obtained with standard benchmark results. Research limitations/implications: The developed method is applied on 2D enclosures; however, the present methodology can be extended to 3D enclosures using velocity–vorticity formulations which shall be explored in future. Originality/value: The proposed methodology to achieve fourth-order accurate transient simulation of natural convection flows is novel, to the best of the authors’ knowledge. Stable fourth-order vorticity boundary conditions are derived for boundary and external boundary regions. The selected case studies for comparison demonstrate not only the fourth-order accuracy but also the considerable reduction in error magnitude by increasing the temporal accuracy. Also, this study provides novel benchmark results at five different locations within the differentially heated vertical cavity of aspect ratio 8:1 for future comparison studies. © 2019, Emerald Publishing Limited.
Citation: International Journal of Numerical Methods for Heat and Fluid Flow (2019), (): -
URI: https://doi.org/10.1108/HFF-06-2019-0519
http://repository.iitr.ac.in/handle/123456789/10779
Issue Date: 2019
Publisher: Emerald Group Publishing Ltd.
Keywords: Finite difference method
Natural convection
Navier–Stokes equation
Streamfunction
Vorticity
ISSN: 9615539
Author Scopus IDs: 57193856184
55491955100
Author Affiliations: Balam, N.B., Efficiency of Buildings Group, C.S.I.R. – Central Building Research Institute, Roorkee, India
Gupta, A., Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee, India
Corresponding Author: Balam, N.B.; Efficiency of Buildings Group, C.S.I.R. – Central Building Research InstituteIndia; email: nagesh.balam@gmail.com
Appears in Collections:Journal Publications [ME]

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