Matjaž Hriberšek

Natural convection flows in complex cavities by BEM

A numerical method for the solution of the 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 boundary‐domain integral formulation is developed and tested for natural convection flows in closed cavities with complex geometries.

Conjugate heat transfer by boundary-domain integral method

Abstract A novel approach to the numerical simulation of conjugate heat transfer is presented. Heat conduction in a solid is implicitly coupled with heat convection in viscous fluid flow. The frame of the solution is the Navier–Stokes equations set for viscous Newtonian fluid. A formulation for planar geometry is described in detail. The main advantage of the presented approach is implicit handling of the heat transfer conditions at the solid–fluid interface. Computed test examples include conjugate forced convection in a channel and conjugate natural convection in a cavity.

Experimental and numerical investigations of sedimentation of porous wastewater sludge flocs.

The paper studies the properties and sedimentation characteristics of sludge flocs, as they appear in biological wastewater treatment (BWT) plants. The flocs are described as porous and permeable bodies, with their properties defined based on conducted experimental study. The derivation is based on established geometrical properties, high-speed camera data on settling velocities and non-linear numerical model, linking settling velocity with physical properties of porous flocs. The numerical model for derivation is based on generalized Stokes model, with permeability of the floc described by the Brinkman model. As a result, correlation for flocs porosity is obtained as a function of floc diameter. This data is used in establishing a CFD numerical model of sedimentation of flocs in test conditions, as recorded during experimental investigation. The CFD model is based on Euler-Lagrange formulation, where the Lagrange formulation is chosen for computation of flocs trajectories during sedimentation. The results of numerical simulations are compared with experimental results and very good agreement is observed.

Preconditioned conjugate gradient methods for boundary-domain integral method

Abstract The paper deals with the iterative solution of systems of linear equations arising in viscous flow computation by the boundary-domain integral method (BDIM) with the subdomain technique. Three versions of conjugate gradient method — the bi-conjugate gradient method (bi-CG), conjugate gradients squared (CGS) and its variant bi-CGSTAB - are compared with the Gauss elimination direct method. Different types of preconditioning of matrices are tested including Jacobi and incomplete factorisation (ILU) preconditioners. A comparison of iterative and direct methods is done on a few test examples including Poiseuilles flow in a narrow channel and flow in a channel with circular obstacles. Special attention is given to behaviour of iterative methods in cases of fluid flows with higher Re numbers, where systems of linear equations become ill-conditioned. Whereas for low Re numbers all types of preconditioning used behave very well, this is not the case with higher Re numbers, where only ILU preconditioning preserves the stability and convergence of conjugate gradient methods. Among CG methods CGS and bi-CGSTAB are to be preferred since they reduce the error in the fastest and smoothest way. Computed test examples show that preconditioned CG methods can offer some major advantages over direct methods in the case of memory demands and computer time consumption.

Dual reciprocity BEM-BDIM technique for conjugate heat transfer computations

Numerical simulation of conjugate heat transfer problems by methods based on the boundary element method (BEM) promises great flexibility of the computational model. A combination of dual reciprocity BEM for computation of heat conduction in solid regions with boundary domain integral method for computation of heat transfer and fluid flow in fluid regions represents a promising way in numerical simulation of conjugate heat transfer. It combines boundary-only discretisation of solid parts and boundary and internal discretisation of fluid regions. In order to efficiently apply iterative solvers, the subdomain technique is used both in solid and in fluid parts of the computational domain. The results are compared with those of a thermal shock problem achieved by a pure boundary domain integral formulation and is verified on the test case of conjugate natural convection in a cavity with conducting side wall.

Advanced CFD modelling of air and recycled flue gas staging in a waste wood-fired grate boiler for higher combustion efficiency and greater environmental benefits

Grate-fired boilers are commonly used to burn biomass/wastes for heat and power production. In spite of the recent breakthrough in integration of advanced secondary air systems in grate boilers, grate-firing technology needs to be advanced for higher efficiency and lower emissions. In this paper, innovative staging of combustion air and recycled flue gas in a 13 MWth waste wood-fired grate boiler is comprehensively studied based on a numerical model that has been previously validated. In particular, the effects of the jet momentum, position and orientation of the combustion air and recycled flue gas streams on in-furnace mixing, combustion and pollutant emissions from the boiler are examined. It is found that the optimized air and recycled flue gas jets remarkably enhance mixing and heat transfer, result in a more uniform temperature and velocity distribution, extend the residence time of the combustibles in the hot zone and improve burnout in the boiler. Optimizing the air and recycled flue gas jet configuration can reduce carbon monoxide emission from the boiler by up to 86%, from the current 41.0 ppm to 5.7 ppm. The findings of this study can serve as useful guidelines for novel design and optimization of the combustion air supply and flue gas recycling for grate boilers of this type.

On Constitutive Models for the Momentum Transfer to Particles in Fluid-Dominated Two-Phase Flows

This contribution deals with fluid flow-particle interactions in fluid dominated two phase flows. Spherical as well as non-spherical particles in the form of are considered. In the case of ellipsoids, the hydrodynamic drag force model based on the Brenner-type resistance tensor is applied. As high shear flow regions are frequently encountered in complex flow patterns, special attention is devoted to the extension of established shear lift models, that are only valid for special cases of shear flows, to a general shear lift model based on permutations of the lift tensor, originally derived by Harper and Chang. A generalized lift vector, valid for ellipsoidal particles, is derived and implemented for the computation of the lift force in general shear flows. The derived generalized shear lift force model is validated against other numerical models for ellipsoids in Couette flow, and its influence on the translational motion of ellipsoidal particles in a three-dimensional lid-driven cavity flow is studied. The computational results confirm the correctness of the proposed generalized shear lift model.

Implementation of the Rosseland and the P1 radiation models in the system of Navier-stokes equations with the boundary element method

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 Navier– Stokes 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.

Two-step validation process of particle mixing in a centrifugal mixer with vertical axis

Two-step approach of validation is proposed to validate a numerical model, capable of accurate prediction of mixing power characteristics of a centrifugal mixer with vertical axis. Two sets of experiments and two sets of numerical simulations are presented—the first set to determine physical characteristics of the particles comparing the numerical simulations results with experimental data, and the second set to validate predicted behavior of anchor type vertical axis impeller for mixing of same particles. Zeolite particles were used for actual calculations. After determining shear modulus, coefficient of interaction, static friction coefficient, and rolling friction coefficient through optimization process based on numerical simulations with subject function of diameter and angle of repose derived from experiment, using these values in numerical simulation of impeller mixer mixing zeolite particles led to results, which were in good agreement with results of the second set of experiments. The obtained zeolite material parameter values can therefore serve as a solid basis for discrete elements method based numerical simulation of zeolite granular materials.

A Dual Reciprocity Boundary Element Formulation for Transient Non-Linear Conduction-Radiation Problems

A boundary-only formulation for transient temperature fields in bodies of non-linear material properties and arbitrary non-linear boundary conditions has been developed. The option for self-irradiating boundaries has been included in the formulation. Heat conduction equation has been partially linearized by Kirchhoff’s transformation. The result has been discretized by Dual Reciprocity Boundary Element Method. The integral equation of heat radiation has been discretized by standard boundary element method. The coupling of the resulting two sets of equations has been accomplished by eliminating the radiative heat fluxes arising in both sets. The final set of ordinary differential equations has been solved using Runge-Kutta solver with automatic time step adjustment. Another discussed problem is the coupling of transient conduction in a solid with natural convection in the surrounding fluid by discretizing the fluid itself.