Modified equation of state laws for heat transfer and natural convection in smoothed particle hydrodynamics

Peacock, P.H., and Holmes, D.W. (2014) Modified equation of state laws for heat transfer and natural convection in smoothed particle hydrodynamics. In: Proceedings of the 19th Australasian Fluid Mechanics Conference. From: AFMC 2014: 19th Australasian Fluid Mechanics Conference, 8-11 December 2014, Melbourne, VIC, Australia.

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Abstract

In this paper we present a modified equation of state law for use within Smoothed Particle Hydrodynamics (SPH). We then compare this to existing solutions for convection problems, specifically those obtained using the Boussinesq approximation. These developments are required in order to accurately model complex and thermally driven problems, such as natural convection and other applications particularly seen in geophysics. In SPH, practical examples of heat conduction and energy are scarce, when compared with fluid flow formulations that determine pressure simply from density and an artificial sound speed. Previous work has involved the inclusion of temperature and energy effects into the calculation of pressure to solve for simple problems where thermal buoyancy is the only source of dynamics.

While there are a number of heat transfer algorithms in use within SPH, it is uncommon in literature to couple the thermal energy of the system to the governing equations being used to determine the dynamics of the system. This work discusses conventional equations of state, previous work performed in this area in terms of introducing a thermal influence into the dynamics of the overall system and other approaches that have been identified to date in wider literature. The results produced from this new approach to the SPH equation of state are discussed and compared with traditional equations of state, as well as with other mechanisms for instigating thermally driven convective flow, such as the use of the Boussinesq approximation. The problem considered is that of a differentially heated cavity for a prescribed set of conditions. These developments facilitate future work towards a more overarching energy implementation of the governing equations to better represent the influence energy can have on a system when purely isothermal flows are no longer being considered for use in much more complex physical systems.

Item ID: 38994
Item Type: Conference Item (Refereed Research Paper - E1)
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ISBN: 978-0-646-59695-2
Funders: National Natural Science Foundation of China, Yunnan Natural Science Foundation, China, Australian Research Council (ARC)
Projects and Grants: National Natural Science Foundation of China (51469035, 51266016), Yunnan Natural Science Foundation (2011FA017)
Date Deposited: 21 May 2015 04:22
FoR Codes: 09 ENGINEERING > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics @ 50%
09 ENGINEERING > 0915 Interdisciplinary Engineering > 091502 Computational Heat Transfer @ 50%
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