BEM simulation of compressible fluid flow in an enclosure induced by thermoacoustic waves

Škerget, L.; Ravnik, Jure

doi:10.1016/j.enganabound.2008.08.003

Cited by 11 publications

(4 citation statements)

References 29 publications

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“…Ravnik and Skerget [12] proposed a boundary-domain integral formulation for diffusion-convection equations with variable coefficient and velocity and considered the energy equation with variable material properties, [13]. Boundary-domain integral method for compressible fluid flow was proposed by Škerget and co-workers [15,16].…”

Section: Introductionmentioning

confidence: 99%

Boundary-domain integral method for vorticity transport equation with variable viscosity

Ravnik¹,

Tibaut²

2018

Int. J. CMEM

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In this paper, we derive a boundary-domain integral formulation for the vorticity transport equation under the assumption that the viscosity of the fluid, through which the vorticity is transported by diffusion and convection, is spatially changing. The vorticity transport equation is a second order partial differential equation of a diffusion-convection type. The final boundary-domain integral representation of the vorticity transport equation is discretized using a domain decomposition approach, where a system of linear equations is setup for each sub-domain, while subdomains are joint by compatibility conditions. The validity of the method is checked using several analytical examples. Convergence properties are studied yielding that the proposed discretization technique is second order accurate for constant and variable viscosity cases.

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Section: Introductionmentioning

confidence: 99%

Boundary-domain integral method for vorticity transport equation with variable viscosity

Ravnik¹,

Tibaut²

2018

Int. J. CMEM

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“…Boundary-domain integral formulation of the kinematics equation and the compressible vorticity equations has been presented by Skerget and Ravnik [8].…”

Section: Velocity-vorticity Formulation Of Navier-stokes Equationsmentioning

confidence: 99%

Implementation of the Rosseland and the P1 Radiation Models in the System of Navier-Stokes Equations with the Boundary Element Method

Crnjac¹,

Škerget²,

Ravnik³

et al. 2017

Int. J. CMEM

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The objective of this article is to develop a boundary element numerical model to solve coupled problems involving heat energy diffusion, convection and radiation in a participating medium. In this study, the contributions from radiant energy transfer are presented using two approaches for optical thick fluids: the Rosseland diffusion approximation and the P1 approximation. The governing NavierStokes equations are written in the velocity-vorticity formulation for the kinematics and kinetics of the fluid motion. The approximate numerical solution algorithm is based on a boundary element numerical model in its macro-element formulation. Validity of the proposed implementation is tested on a one-dimensional test case using a grey participating medium at radiative equilibrium between two isothermal black surfaces. Keywords: compressible fluid flow, radiation models, boundary element method INTRODUCTIONThe Navier-Stokes equations set is commonly used as a frame for the solution of transport phenomena in a fluid flow. It provides a mathematical model of physical conservation laws of mass, momentum and energy considering specific rheological models describing non-convective fluxes of momentum and energy. In general, all three physically different mechanisms of heat transport can occur, that is diffusion, convection and radiation. The energy radiation phenomenon, which is a complex non-linear mode of heat transfer, gains importance at sufficiently high temperature [1]. At temperatures which are high enough these processes are essentially interdependent; energy transfer by one mechanism can influence heat exchange by the other mechanism and vice versa. The objective of this article is to develop a boundary element numerical simulation model to solve coupled problems involving heat energy diffusion, convection and radiation in a participating viscous compressible fluid flow.The governing equation for radiative heat transfer is the radiative transfer equation [2], which is based on an energy balance for radiation passing through a differential volume in a participating medium in local thermo-dynamic equilibrium.The radiation impact on overall heat transfer is conveyed in the energy equation, where, in the non-convective energy flux, besides the diffusion heat flux the radiative heat flux also needs to be taken into consideration. This is done in such a way that we include the term for the divergence of the radiative flux vector into the energy equation as the radiative energy source [3,4]. The radiative transfer equations (RTE) is an integro-differential equation presenting a serious issue in computational fluid dynamics. Applying the chosen radiation model means, under the given physical circumstances, a simplification of the radiative transfer equation. In this study, the contributions from radiant energy transfer are presented using two approaches for optical thick fluids, that is the Rosseland diffusion approximation and the P1 approximation.

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“…In the present paper the boundary element method (BEM) is used. Previous studies of Lin and Farouk [3], Aktas and Farouk [4],Škerget and Ravnik [5], observed strong thermoacoustic waves as a consequence of impulsive heating. Horizontal velocity component reverses sign after reflection from the side walls.…”

Section: Introductionmentioning

confidence: 99%

Influence of linear and non-linear constitutive models on thermoacoustic waves in an enclosure

Škerget¹,

Ravnik²

2008

Advances in Fluid Mechanics VII

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The problem of unsteady compressible fluid flow in an enclosure induced by thermoacoustic waves is studied numerically. Full compressible set of Navier-Stokes equations are considered and numerically solved by boundary-domain integral equations approach, coupled with wavelet compression and domain decomposition to achieve numerical efficiency. The thermal energy equation is written in its most general form including the Rayleigh and reversible expansion rate terms. Both the classical Fourier heat flux model and wave heat conduction model are investigated. The momentum flux is modelled using standard Newtonian viscous model and linear viscoelastic Maxwell model.The velocity-vorticity formulation of the governing Navier-Stokes equations is employed, while the pressure field is evaluated from the corresponding pressure Poisson equation. Material properties are taken to be for the perfect gas and assumed to be pressure and temperature dependent.

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BEM simulation of compressible fluid flow in an enclosure induced by thermoacoustic waves

Cited by 11 publications

References 29 publications

Boundary-domain integral method for vorticity transport equation with variable viscosity

Boundary-domain integral method for vorticity transport equation with variable viscosity

Implementation of the Rosseland and the P1 Radiation Models in the System of Navier-Stokes Equations with the Boundary Element Method

Influence of linear and non-linear constitutive models on thermoacoustic waves in an enclosure

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