Simulation of flow inside differentially heated rotating cavity

J.C. Mandal (Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai, India)
C.R. Sonawane (Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai, India)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Publication date: 4 January 2013

Abstract

Purpose

The purpose of this paper is to simulate flow inside differentially heated rotating cavity using two different formulations; one using Navier‐Stokes (NS) equations derived in non‐inertial (rotating) frame of reference and the other using NS equations in inertial frame of reference. Then to compare the results obtained from these formulations to find their merits and demerits.

Design/methodology/approach

The NS equations for both non‐inertial and inertial formulations are written in artificial compressibility form before discretizing them by a high resolution finite volume method. The dual time steeping approach of Jameson is used for time accuracy in both the formulations. Arbitrary Lagrangian Eulerian (ALE) approach is used for taking care of moving boundary problem arising in the inertial formulation. A newly developed HLLC‐AC Riemann solver for discretizing convective fluxes and central differencing for discretizing viscous fluxes are used in the finite volume approach. Results for both the formulations are first validated with test cases reported in literature. Then the results of the two formulations are compared among themselves.

Findings

Results of the non‐inertial formulation obtained by the proposed method are found to match well with those reported in literature. The results of both the formulations match well for low rotational speeds of the cavity. The discrepancies between the results of the two formulations progressively increase with the increase in rotational speed. Implicit treatment of the source term is found to reduce the discrepancies.

Practical implications

The present approach is useful for accurate prediction of flow feature and heat transfer characteristic in case of applications such as manufacturing of single wafer crystal for semiconductor and in numerous metallurgical processes.

Originality/value

The ALE formulation is used for the first time to simulate a differentially heated rotating cavity problem. The attempt to compare non‐inertial and inertial formulations is also reported for the first time. Implicit treatment of the source term leading to change in solution accuracy is one of the important findings of the present investigation.

Keywords

Citation

Mandal, J. and Sonawane, C. (2013), "Simulation of flow inside differentially heated rotating cavity", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 1, pp. 23-54. https://doi.org/10.1108/09615531311289097

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Publisher

:

Emerald Group Publishing Limited

Copyright © 2013, Emerald Group Publishing Limited

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