1. BEM simulation of compressible fluid flow in an enclosure induced by thermoacoustic wavesLeopold Škerget, Jure Ravnik, 2009, original scientific article Abstract: 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 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. Keywords: compressible fluid flow, boundary element method, thermoacoustic waves, velocity-vorticity fomulation Published: 31.05.2012; Views: 1326; Downloads: 62 Link to full text |
2. Fast single domain-subdomain BEM algorithm for 3D incompressible fluid flow and heat transferJure Ravnik, Leopold Škerget, Zoran Žunič, 2009, original scientific article Abstract: In this paper acceleration and computer memory reduction of an algorithm for the simulation of laminar viscous flows and heat transfer is presented. The algorithm solves the velocity-vorticity formulation of the incompressible Navier-Stokes equations in 3D. It is based on a combination of a subdomain boundary element method (BEM) and single domain BEM. The CPU time and storage requirements of the single domain BEM are reduced by implementing a fast multipole expansion method. The Laplace fundamental solution, which is used as a special weighting function in BEM, is expanded in terms of spherical harmonics. The computational domain and its boundary are recursively cut up forming a tree of clusters of boundary elements and domain cells. Data sparse representation is used in parts of the matrix, which correspond to boundary-domain clusters pairs that are admissible for expansion. Significant reduction of the complexity is achieved. The paper presents results of testing of the multipole expansion algorithm by exploring its effect on the accuracy of the solution and its influence on the non-linear convergence properties of the solver. Two 3D benchmark numerical examples are used: the lid-driven cavity and the onset of natural convection in a differentially heated enclosure. Keywords: boundary element method, fast multipole method, fluid flow, heat transfer, velocity-vorticity fomulation Published: 31.05.2012; Views: 1322; Downloads: 52 Link to full text |
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4. Laminar flow of a shear-thickening fluid in a 90° pipe bendJure Marn, Primož Ternik, 2006, original scientific article Abstract: The non-Newtonian fluid flow in a sharp 90 curved pipe is studied numerically to obtain the pressure loss coefficient prompted by disagreement between the existing empirical correlations and results obtained by computer codes. This disagreement results from presumption of fully developed flow throughout the curvature (correlations) while the actual flow is partially developed for the Newtonian and sharp 90 curved bend non-Newtonian flows, and fully developed for slightly bent 90 curvature non-Newtonian flow. The Quadratic model is employed to accommodate the shear-thickening behavior of an electrostatic ash and water mixture. Numerical results are obtained for different values of Reynolds number. Finally, results for local pressure loss coefficient are compared with values obtained for the Power law rheological model. Keywords: shear-thickening fluid, fluid dynamics, rheological model, pipe bend flow, numerical modelling, pressure losses Published: 30.05.2012; Views: 1160; Downloads: 57 Link to full text |
5. 3D multidomain BEM for solving the Laplace equationMatjaž Ramšak, Leopold Škerget, 2007, original scientific article Abstract: An efficient 3D multidomain BEM for solving problems governed by the Laplace equation is presented. Integral boundary equations are discretized using mixed boundary elements. The field function is interpolated using a continuous linear function while its derivative in a normal direction is interpolated using a discontiuous constant function over surface boundaey elements. Using amultidomain approach, also known as the subdomain technique, sparse system matrices similar to FEM are obtained. Interface boundary conditions between subdomains leads to an over-determined system matrix which is solved using a fast iterative linear least square solver. The accuracy and the robustness of the developed algorithm is presented on a scalar diffusion problem using simple cube geometry and various types of meshes. The efficiency is demonstrated with potential flow around a complex geometry of a fighter airplane using a tetrahedral mesh with over 100.000 subdomains on a personal computer. Keywords: fluid mechanics, aerodynamics, multidomain boundary element method, Laplace equation, mixed boundary elements, potential flow Published: 31.05.2012; Views: 1367; Downloads: 63 Link to full text |
6. The influence of rotating domain size in a rotating frame of reference approach for simulation of rotating impeller in a mixing vesselMatej Zadravec, Sani Bašič, Matjaž Hriberšek, 2007, original scientific article Abstract: This paper presents simulation of rotating impeller in a mixing vessel by means of Computational Fluid Dynamics (CFD). A special emphasis is devoted to the study of influence of the choice of numerical model for simulation of rotation of impeller when mixing a Newtonian fluid in a vessel equipped with Rushton impeller, and operating under turbulent flow conditions. In order to determine the best simulation approach experimental validation of the selected problem is done by means of Particle Image Velocimetry (PIV) system. When using the rotating frame of reference approach, the stirring vessel geometry has to be split into a stationary and rotating part, and the questionarises where to position the interface between both regions in order to avoid numerical errors, originating in numerical approximations at the interface. To answer this question, a comparison between the CFD based numerical results and experimental results, was made. Keywords: fluid mechanics, turbulent flow, Computational Fluid Dynamics, Particle Image Velocimetry, rotating frame of reference Published: 31.05.2012; Views: 1250; Downloads: 34 Link to full text |
7. Velocity vorticity-based large eddy simulation with the bounadr element methodJure Ravnik, Leopold Škerget, Matjaž Hriberšek, 2006, published scientific conference contribution (invited lecture) Abstract: A large eddy simulation using the velocity-vorticity formulation of the incompressible Navier-Stokes equations in combination with the turbulent heat transfer equation is proposed for the solution of the turbulent natural convection drive flow in a 1:4 enclosure. The system of equations is closed by an enthropy-based subgrid scale model.The Prandtl turbulent number is used to estimate turbulent diffusion in the heat transfer equation. The boundary element method is used to solve the kinematics equation and estimate the boundary vorticity values. The vorticity transport equation is solved by FEM. The numerical example studied in this paper is the onset of a turbulent flow regime occuring at high Rayleigh number values ▫$(Ra=10^7-10^10)$▫. The formation of vortices in the boundary layer is observed, along with buoyancy driven diffusive convective transport. Quantitative comparison with the laminar flow model and the worh of other authors is also presented in terms of Nusselt number value oscillations. Keywords: fluid mechanics, incompressible viscous fluid, turbulent flow, velocity vorticity formulation, finite element method, large eddy simulation Published: 31.05.2012; Views: 1248; Downloads: 18 Link to full text |
8. Velocity-vorticity formulation for 3D natural convection in an inclined enclosure by BEMJure 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: 1534; Downloads: 66 Link to full text |
9. Simulation of unsteady fluid flow and heat transfer by BEMJure Ravnik, Leopold Škerget, 2011, published scientific conference contribution Abstract: A boundary element method based solver for simulation of unsteady laminar viscous flow and heat transfer in three-dimensions has been developed. The algorithm solves the incompressible Navier- Stokes equations written in velocity-vorticity form and coupled with energy equation. Buoyancy is modelled within the Boussinesq approximation. The solver has recently been adapted for simulation of unsteady phenomena. The governing set of equations consists of the kinematics equation and transport equations for vorticity and temperature. Velocity and temperature boundary conditions are known, vorticity boundary conditions are calculated during the simulation by single domain BEM applied on the kinematics equation. The transport equations are solved by a domaindecomposition BEM approach, which yields sparse integral matrices and enables simulation using large computational grids. Rayleigh-Benard convection is used for a test case. In this case fluid is heated flow below, thus making it highly unstable. Already at low driving temperature of the bottom wall, the fluid becomes unstable. Vortices are formed above the hot bottom wall and travel up by buoyancy forces. Flow exhibits oscillatory behaviour, which at higher temperatures leads to chaotic and turbulent flow. The phenomenon was simulated using different driving temperatures of the bottom wall, observing the change of flow characteristics for steady to unsteady oscillatory regime and at even higher temperature to chaotic behaviour. Time series of heat flux and field functions were examined by phase portraits to determine the flow regime. A grid independence study and time step analysis was performed to asses the algorithms capability of simulation of unsteady behaviour. Keywords: boundary element method, heat transfer, unsteady fluid flow, transport equations Published: 01.06.2012; Views: 985; Downloads: 15 Link to full text |
10. Boundary domain integral method for high Reynolds viscous fluid flows in complex planar geometriesMatjaž Hriberšek, Leopold Škerget, 2005, original scientific article Abstract: The article presents new developments in boundary domain integral method (BDIM) for computation of viscous fluid flows, governed by the Navier-Stokes equations. The BDIM algorithm uses velocity-vorticity formulation and is basedon Poisson velocity equation for flow kinematics. This results in accurate determination of boundary vorticity values, a crucial step in constructing an accurate numerical algorithm for computation of flows in complex geometries, i.e. geometries with sharp corners. The domain velocity computations are done by the segmentation technique using large segments. After solving the kinematics equation the vorticity transport equation is solved using macro-element approach. This enables the use of macro-element based diffusion-convection fundamental solution, a key factor in assuring accuracy of computations for high Reynolds value laminar flows. The versatility and accuracy of the proposed numerical algorithm is shown for several test problems, including the standard driven cavity together with the driven cavity flow in an L shaped cavity and flow in a Z shaped channel. The values of Reynolds number reach 10,000 for driven cavity and 7500 for L shapeddriven cavity, whereas the Z shaped channel flow is computed up to Re = 400. The comparison of computational results shows that the developed algorithm is capable of accurate resolution of flow fields in complex geometries. Keywords: fluid mechanics, numerical methods, boundary domain integral method, algorithms, incompressible fluid flow, Navier-Stokes equations, velocity vorticity formulation, segmentation technique, driven cavity flow Published: 01.06.2012; Views: 1139; Downloads: 50 Link to full text |