Maciej Marek

Volume of Fluid (VOF) type advection methods in two-phase flow: A comparative study

Abstract In this paper, four distinct approaches to Volume of Fluid (VOF) computational method are compared. Two of the methods are the ‘simplified’ VOF formulations, in that they do not require geometrical interface reconstruction. The assessment is made possible by implementing all four approaches into the same code as switchable options. This allows to rule out possible influence of other parts of numerical scheme, be it the discretisation of Navier–Stokes equations or chosen approximation of curvature, so that we are left with conclusive arguments because only one factor differs the compared methods. The comparison is done in the framework of Coupled Level Set Volume of Fluid (CLSVOF), so that all four methods are coupled with Level Set interface, which is used to compute pressure jump via the Ghost Fluid Method (GFM). Results presented include static advections and full N–S solutions in both laminar and turbulent flows. The paper is aimed at research groups who are implementing VOF methods in their computations or intend to do it, and might consider a simplified approach as a preliminary measure, since the methods presented differ greatly in complication level, or ease of implementation expressed, e.g. in number of code lines.

A new approach to sub-grid surface tension for LES of two-phase flows

In two-phase flow, the presence of inter-phasal surface - the interface - causes additional terms to appear in LES formulation. Those terms were ignored in contemporary works, for the lack of model and because the authors expected them to be of negligible influence. However, it has been recently shown by a priori DNS simulations that the negligibility assumption can be challenged. In the present work, a model for one of the sub-grid two-phase specific terms is proposed, using deconvolution of the velocity field and advection of the interface using that field. Using the model, the term can be included into LES. A brief presentation of the model is followed by numerical tests that assess the models performance by comparison with a priori DNS results.

Modelling liquid redistribution in a packed bed

The paper is devoted to the computational fluid dynamics (CFD) simulation of liquid spreading process in a packed bed. The volume of fluid (VOF) approach was applied to simulate the flow in a realistic porous region composed of 6mm Raschig rings. Modelling results were used to determine the probability density function (PDF) distribution of liquid velocity vector orientation angle which was then implemented into 2-fluid Euler-Euler multiphase model of packing column. The simulation showed that the model is capable to simulate adequately the liquid redistribution in a porous region being, however, much more efficient computationally than the VOF method.

CFD modelling of gas flow through a fixed bed of Raschig rings

In this work, direct numerical simulation of incompressible gas flow through a complex geometrical structure of Raschig rings is performed. The bed structure is obtained in a separate simulation in which Raschig rings are added one by one and fall freely into a cylindrical container until mechanical equilibrium is reached. The gas is injected at the top of the container, flows through a packed layer of randomly oriented rings, then leaves the container at the bottom. The flow equations are solved with the use of classical second order solver and projection method for structured regular grid and the complexity of domain geometry is handled by a variant of immersed boundary technique. The model allows to study the characteristics of the flow within the bed, pressure distribution in particular, and can be applied to development and validation of simplified approaches. The simulations are performed for various grid resolutions and the results show good convergence to grid independent solution, especially for lower gas velocities. The obtained dependence of total pressure drop on the inlet velocity is in reasonable agreement with the literature data but the demand for grid resolution significantly increases with the gas velocity.

Comparison of the High-Order Compact Difference and Discontinuous Galerkin Methods in Computations of the Incompressible Flow

High-order compact difference scheme (CD) based on the half-staggered mesh is compared with discontinuous Galerkin method in computations of the incompressible flow. Assessment of the accuracy is performed based on the classical test cases: Taylor–Green vortices, Burggraf flow and also for temporally evolving shear layer. The CD method method provides very accurate results with expected order of accuracy, 4th and 6th. Similarly for the discontinuous Galerkin method provided that the number of degrees of fredom is close to the number of nodes in computations with CD method. Furthermore, it appeared that CD method is much more efficient than the discontinuous Galerkin method of comparable accuracy.

Simulation of the flow between rotating disks with Discontinuous Galerkin method

In this work Discontinuous Galerkin (DG) method is applied to the simulation of the incompressible, viscous flow between rotating disks. The code is based on the projection method and accepts unstructured meshes with hexahedral elements. It is explicit in time and allows for arbitrary partition of the computational domain between processors in parallel computing (communication patterns are automatically assigned). Two cases (configurations) are considered: flat disks (structured mesh) and disk with a step placed at the center of the cavity (unstructured mesh). In both configurations the upper disk is rotating, the other one and the remaining walls are stationary. The results for the flat disks are compared to DNS data and very good agreement is obtained. The second case shows capability of the new approach with handling complex geometries.