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Natural convection of micropolar fluid in an enclosure with boundary element method
Matej Zadravec, Matjaž Hriberšek, Leopold Škerget, 2009, original scientific article

Abstract: The contribution deals with numerical simulation of natural convection in micropolar fluids, describing flow of suspensions with rigid and underformable particles with own rotation. The micropolar fluid flow theory is incorporated into the framework of a velocity-vorticity formulation of Navier-Stokes equations. The governing equations are derived in differential and integral form, resulting from the application of a boundary element method (BEM). In integral transformations, the diffusion-convection fundamental solution for flow kinetics, including vorticity transport, heat transport and microrotation transport, is implemented. The natural convection test case is the benchmark case of natural convection in a square cavity, and computations are performed for Rayleigh number values up to 107. The results show, which microrotation of particles in suspension in general decreases overall heat transfer from the heated wall and should not therefore be neglected when computing heat and fluid flow of micropolar fluids.
Keywords: natural convection, micropolar fluid, boundary element method
Published: 31.05.2012; Views: 1481; Downloads: 71
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Two-dimensional velocity-vorticity based LES for the solution of natural convection in a differentially heated enclosure by wavelet transform based BEM and FEM
Jure Ravnik, Leopold Škerget, Matjaž Hriberšek, 2006, original scientific article

Abstract: A wavelet transform based boundary element method (BEM) numerical scheme is proposed for the solution of the kinematics equation of the velocity-vorticityformulation of Navier-Stokes equations. FEM is used to solve the kinetics equations. The proposed numerical approach is used to perform two-dimensional vorticity transfer based large eddy simulation on grids with 105 nodes. Turbulent natural convection in a differentially heated enclosure of aspect ratio 4 for Rayleigh number values Ra=107-109 is simulated. Unstable boundary layer leads to the formation of eddies in the downstream parts of both vertical walls. At the lowest Rayleigh number value an oscillatory flow regime is observed, while the flow becomes increasingly irregular, non-repeating, unsymmetric and chaotic at higher Rayleigh number values. The transition to turbulence is studied with time series plots, temperature-vorticity phase diagrams and with power spectra. The enclosure is found to be only partially turbulent, what is qualitatively shown with second order statistics-Reynolds stresses, turbulent kinetic energy, turbulent heat fluxes and temperature variance. Heat transfer is studied via the average Nusselt number value, its time series and its relationship to the Rayleigh number value.
Keywords: numerical modelling, boundary element method, discrete wavelet transform, large eddy simulation, velocity-vertocity formulation, natural convection
Published: 31.05.2012; Views: 1602; Downloads: 55
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Boundary domain integral method for the study of double diffusive natural convection in porous media
Janja Kramer Stajnko, Renata Jecl, Leopold Škerget, 2007, original scientific article

Abstract: The main purpose of this paper is to present a boundary domain integral method(BDIM) for the solution of natural convection in porous media driven by combining thermal and solutal buoyancy forces. The Brinkman extension of the classical Darcy equation is used for the momentum conservation equation. The numerical scheme was tested on a natural convection problem within a square porous cavity, where different temperature and concentration values are applied on the vertical walls, while the horizontal walls are adiabatic and impermeable. The results for different governing parameters (Rayleigh number, Darcy number, buoyancy ratio and Lewis number) are presented and compared withpublished work. There is a good agreement between those results obtained using the presented numerical scheme and reported studies using other numerical methods.
Keywords: double diffusive natural convection, porous medium, velocity-vorticity formulation, Brinkman extended Darcy formulation, boundary domain integrated method
Published: 31.05.2012; Views: 1187; Downloads: 59
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Velocity-vorticity formulation for 3D natural convection in an inclined enclosure by BEM
Jure Ravnik, Leopold Škerget, Zoran Žunič, 2008, original scientific article

Abstract: A natural convection phenomenon is studied in cubic and parallelepipedal inclined enclosures. The simulation of coupled laminar viscous flow and heat transfer is performed using a novel algorithm based on a combination of singledomain Boundary element method (BEM) and subdomain BEM. The algorithm solves the velocity-vorticity formulation of the incompressible Navier-Stokes equations coupled with the energy equation using the Boussinesq approximation.The subdomain BEM is used to solve the kinematics equation, the vorticity transport equation and the energy equation. The boundary vorticity values, which are needed as boundary conditions for the vorticity transport equation, are calculated by singe domain BEM solution of the kinematics equation. Simulation results are compared with benchmark results for a cubic inclined enclosure for Rayleigh number values ▫$10^3Keywords: podobmočna metoda robnih elementov, hitrostno-vrtinčna formulacija, laminarni tok viskozne tekočine, naravna konvekcija, nagnjena kotanja, fluid mechanics, subdomain boundary element method, velocity-vorticity formulation, laminar viscous fluid flow, natural convection, inclined enclosure
Published: 31.05.2012; Views: 1607; Downloads: 70
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BEM for the two-dimensional plane compressible fluid dynamics
Leopold Škerget, Niko Samec, 2005, original scientific article

Abstract: In this study, the boundary element method, which has been established for theviscous incompressible fluid motion, is modified and extended to capture the compressible fluid state. The velocity-vorticity formulation of the time dependent set of equations is employed, where the kinematics is given with thePoisson velocity vector equation, while the kinetics is represented with the vorticity transport equation, and the pressure field function is governed by the Poisson pressure scalar equation. The method is applied to consider buoyancy driven flow in closed cavity, differentially heated under large temperature gradients. The ideal gas law is used and viscosity is given by Sutherland law.
Keywords: fluid mechanics, compressible viscous fluid, natural convection, boundary element method, fluid dynamics
Published: 01.06.2012; Views: 992; Downloads: 65
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The wavelet transform for BEM computational fluid dynamics
Jure Ravnik, Leopold Škerget, Matjaž Hriberšek, 2004, original scientific article

Abstract: A wavelet matrix compression technique was used to solve systems of linear equations resulting from BEM applied to fluid dynamics. The governing equations were written in velocity-vorticity formulation and solutions of the resulting systems of equations were obtained with and without wavelet matrix compression. A modification of the Haar wavelet transform, which can transformvectors of any size, is proposed. The threshold, used for making fully populated matrices sparse, was written as a product of a user defined factor and the average value of absolute matrix elements values. Numerical tests were performed to assert, that the error caused by wavelet compression depends linearly on the factor , while the dependence of the error on the share of thresholded elements in the system matrix is highly non-linear. The results also showed that the increasing non-linearity (higher Ra and Re numbervalues) limits the extent of compression. On the other hand, higher meshdensity enables higher compression ratios.
Keywords: fluid mechanics, computational fluid dynamics, boundary element method, wavelet transform, linear systems of equations, velocity vorticity formulation, driven cavity, natural convection, system matrix compression
Published: 01.06.2012; Views: 1345; Downloads: 61
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Natural convection flows in complex cavities by BEM
Leopold Škerget, Matjaž Hriberšek, Zoran Žunič, 2003, original scientific article

Abstract: A numerical method for the solution of Navier-Stokes equations is developed using an integral representation of the conservation equations. The velocity- vorticity formulation is employed, where the kinematics is given with the Poisson equation for a velocity vector, while the kinetics is represented with the vorticity transport equation. The corresponding boundary-domain integral equations are presented along with discussions of the kinetics and kinematics of the fluid flow problem. THE BEM formulation is developed and tested for natural convection flows in closed cavities with complex geometries.
Keywords: fluid dynamics, natural convection, boundary element method, differential equations, closed cavity
Published: 01.06.2012; Views: 815; Downloads: 58
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Boundary element method for natural convection in non-Newtonian fluid saturated square porous cavity
Renata Jecl, Leopold Škerget, 2003, original scientific article

Abstract: The main purpose of this work is to present the use of the Boundary Element Method (BEM) in the analysis of the natural convection in the square porous cavity saturated by the non-Newtonian fluid. The results of hydrodynamic and heat transfer evaluations are reported for the configuration in which the enclosure is heated from a side wall while the horizontal walls are insulated.The flow in the porous medium is modelled using the modified Brinkman extended Darcy model taking into account the non-Darcy viscous effects. The governing equations are transformed by the velocity-vorticity variables formulation enabling the computation scheme to be partitioned into kinematic and kinetic parts. To analyse the effects of the available non-Newtonian viscosity and to evaluate the presented approach, the power law model for shear thinning fluids (n<1), for shear thickening fluids (n>1) and in the limit for the Newtonian fluids (n=1) is considered. Numerical model is tested also for the Carreau model adequate for many non-Newtonian fluids. Solutions for the flow and temperature fields and Nusselt numbers are obtainedin terms of a modified Rayleigh number Ra*, Darcy number Da, and the non-Newtonian model parameters. The agreement between the results obtained with finite difference method is very good indicating that BEM can be efficiently used for solving transport phenomena in saturated porous medium.
Keywords: natural convection, non-Newtonian fluid, porous medium, cavity flow, boundary element method, boundary domain integral method
Published: 01.06.2012; Views: 1036; Downloads: 62
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Numerical study of Rayleigh-Bénard natural-convection heat-transfer characteristics of water-based Au nanofluids
Primož Ternik, Rebeka Rudolf, Zoran Žunič, 2013, original scientific article

Abstract: The present work deals with the natural convection in a square cavity filled with a water-based Au nanofluid. The cavity is heated from the lower and cooled from the adjacent wall, while the other two walls are adiabatic. Theg overning differential equations have been solved with the standard finite volume method and the hydrodynamic and thermal fields have been coupled using the Boussinesq approximation. The main objective of this study is to investigate the influence of the nanoparticlesć volume fraction on the heat-transfer characteristics of Au nanofluids at a given base-fluid (i.e., water) Rayleigh number Rabf. Accurate results are presented over a wide range of the base-fluid Rayleigh numbers (102 £ Rabf £ 105) and the volume fraction of Au nanoparticles (0 % £ j £ 10 %). It is shown that adding nanoparticles to the base fluid delays the onset of convection. Contrary to what is argued by many authors, we show, with numerical simulations, that the use of nanofluids can reduce the heat transfer instead of increasing it.
Keywords: Rayleigh-Bénard natural convection, water-Au nanofluid, heat transfer, numerical modelling
Published: 10.07.2015; Views: 536; Downloads: 68
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Numerical study of heat-transfer enhancement of homogeneous water-Au nanofluid under natural convection
Primož Ternik, Rebeka Rudolf, Zoran Žunič, 2012, original scientific article

Abstract: A numerical analysis is performed to examine the heat transfer of colloidal dispersions of Au nanoparticles in water (Au nanofluids). The analysis used a two-dimensional enclosure under natural convection heat-transfer conditions and has been carried out for the Rayleigh number in the range of 103 < Ra < 105, and for the Au nanoparticles' volume-fraction range of 0 < j < 0.10. We report highly accurate numerical results indicating clearly that the mean Nusselt number is an increasing function of both Rayleigh number and volume fraction of Au nanoparticles. The results also indicate that a heat-transfer enhancement is possible using nanofluids in comparison to conventional fluids. However, low Rayleigh numbers show more enhancement compared to high Rayleigh numbers.
Keywords: natural convection, nanofluid, heat transfer, numerical modelling
Published: 10.07.2015; Views: 578; Downloads: 77
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