Berend van Wachem

Derivation and validation of a novel implicit second-order accurate immersed boundary method

A novel implicit second-order accurate immersed boundary method (IBM) for simulating the flow around arbitrary stationary bodies is developed, implemented and validated in this paper. The IBM is used to efficiently take into account the existence of bodies within the fluid domain. The flow domain consist of simple Cartesian cells whereas the body can be arbitrary. At the triangulated interface of the body and the fluid, the immersed boundary, the coefficients obtained from discretizing the Navier-Stokes equations are closed with a second-order accurate interpolation arising from the immersed boundary condition employed at the interface. Two different conditions are developed in this paper and it is shown that for the mirroring method the resulting coefficients lead to a well-posed and diagonally dominant system which can be efficiently solved with a preconditioned Krylov sub-space solver. The immersed boundary condition generates a fictitious reversed velocity field inside the immersed boundary, which is excluded from the continuity equation to account for the presence of the IB in the pressure correction equation, resulting in no mass flux over the IB. The force acting on the object from the fluid is determined by integrating the pressure and the viscous forces over the object. The method is validated by simulating the flow around a sphere for a range of Re numbers. It is shown that the drag is very well in agreement with experimental data. Accuracy and convergence studies are employed, proving the second-order accuracy of the method and showing the superiority in convergence rate compared to other IBM. Finally the drag force of a cluster of non-spherical particles is employed to show the generality and potential of the method.

Fully-Coupled Balanced-Force VOF Framework for Arbitrary Meshes with Least-Squares Curvature Evaluation from Volume Fractions

A fully-coupled balanced-force numerical framework for two-phase flows with surface tension on arbitrary collocated meshes is presented, including a novel method to evaluate the curvature from volume fractions. The presented framework reduces the imbalances at the interface to solver tolerance and provides stable and reliable results for density ratios of 106 and larger. The new method to evaluate the curvature is based on a least-squares fit, providing better or equal accuracy compared to implementations found in the literature, which are generally limited to structured meshes, and the accuracy on Cartesian and tetrahedral meshes is shown to be comparable.

Numerical time-step restrictions as a result of capillary waves

The propagation of capillary waves on material interfaces between two fluids imposes a strict constraint on the numerical time-step applied to solve the equations governing this problem and is directly associated with the stability of interfacial flow simulations. The explicit implementation of surface tension is the generally accepted reason for the restrictions on the temporal resolution caused by capillary waves. In this article, a fully-coupled numerical framework with an implicit treatment of surface tension is proposed and applied, demonstrating that the capillary time-step constraint is in fact a constraint imposed by the temporal sampling of capillary waves, irrespective of the type of implementation. The presented results show that the capillary time-step constraint can be exceeded by several orders of magnitude, with the explicit as well as the implicit treatment of surface tension, if capillary waves are absent. Furthermore, a revised capillary time-step constraint is derived by studying the temporal resolution of capillary waves based on numerical stability and signal processing theory, including the Doppler shift caused by an underlying fluid motion. The revised capillary time-step constraint assures a robust, aliasing-free result, as demonstrated by representative numerical experiments, and is in the static case less restrictive than previously proposed time-step limits associated with capillary waves.

Compressive VOF method with skewness correction to capture sharp interfaces on arbitrary meshes

The accurate and efficient modelling of two-phase flows is at present mostly limited to structured, unskewed meshes, due to the additional topological and numerical complexity of arbitrary, unstructured meshes. Compressive VOF methods which discretize the interface advection with algebraic differencing schemes are computationally efficient and inherently applicable to arbitrary meshes. However, compressive VOF methods evidently suffer severely from numerical diffusion on meshes with topological skewness. In this paper we present a compressive VOF method using a state-of-the-art donor-acceptor advection scheme which includes novel modifications to substantially reduce numerical diffusion on arbitrary meshes without adding computational complexity. The new methodology accurately captures evolving interfaces on any arbitrary, non-overlapping mesh and conserves mass within the limits of the applied solver tolerance. A thorough validation of the presented methods is conducted, examining the pure advection of the interface indicator function as well as the application to evolving interfaces with surface tension. Crucially, the results on equidistant Cartesian and arbitrary tetrahedral meshes are shown to be comparable and accurate.

TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness

Total variation diminishing (TVD) schemes are a widely applied group of monotonicity-preserving advection differencing schemes for partial differential equations in numerical heat transfer and computational fluid dynamics. These schemes are typically designed for one-dimensional problems or multidimensional problems on structured equidistant quadrilateral meshes. Practical applications, however, often involve complex geometries that cannot be represented by Cartesian meshes and, therefore, necessitate the application of unstructured meshes, which require a more sophisticated discretisation to account for their additional topological complexity. In principle, TVD schemes are applicable to unstructured meshes, however, not all the data required for TVD differencing is readily available on unstructured meshes, and the solution suffers from considerable numerical diffusion as a result of mesh skewness. In this article we analyse TVD differencing on unstructured three-dimensional meshes, focusing on the non-linearity of TVD differencing and the extrapolation of the virtual upwind node. Furthermore, we propose a novel monotonicity-preserving correction method for TVD schemes that significantly reduces numerical diffusion caused by mesh skewness. The presented numerical experiments demonstrate the importance of accounting for the non-linearity introduced by TVD differencing and of imposing carefully chosen limits on the extrapolated virtual upwind node, as well as the efficacy of the proposed method to correct mesh skewness.

Computational Fluid Dynamics for Engineers: Frontmatter

Computational fluid dynamics (CFD) has become an indispensable tool for many engineers. This book gives an introduction to CFD simulations of turbulence, mixing, reaction, combustion and multiphase flows. The emphasis on understanding the physics of these flows helps the engineer to select appropriate models with which to obtain reliable simulations. Besides presenting the equations involved, the basics and limitations of the models are explained and discussed. The book, combined with tutorials, project and Power-Point lecture notes (all available for download), forms a complete course. The reader is given hands-on experience of drawing, meshing and simulation. The tutorials cover flow and reactions inside a porous catalyst, combustion in turbulent non-premixed flow and multiphase simulation of evaporating sprays. The project deals with the design of an industrial-scale selective catalytic reduction process and allows the reader to explore various design improvements and apply best practice guidelines in the CFD simulations.

Computational Fluid Dynamics for Engineers by Bengt Andersson

Computational fluid dynamics (CFD) has become an indispensable tool for many engineers. This book gives an introduction to CFD simulations of turbulence, mixing, reaction, combustion and multiphase flows. The emphasis on understanding the physics of these flows helps the engineer to select appropriate models with which to obtain reliable simulations. Besides presenting the equations involved, the basics and limitations of the models are explained and discussed. The book, combined with tutorials, project and Power-Point lecture notes (all available for download), forms a complete course. The reader is given hands-on experience of drawing, meshing and simulation. The tutorials cover flow and reactions inside a porous catalyst, combustion in turbulent non-premixed flow and multiphase simulation of evaporating sprays. The project deals with the design of an industrial-scale selective catalytic reduction process and allows the reader to explore various design improvements and apply best practice guidelines in the CFD simulations.

Thermographic laser doppler velocimetry

We propose a point measurement technique for simultaneous gas temperature and velocity measurement based on thermographic phosphor particles dispersed in the fluid. The flow velocity is determined from the frequency of light scattered by BaMgAl10O17:Eu2+ phosphor particles traversing the fringes like in conventional laser Doppler velocimetry. Flow temperatures are derived using a two-color ratio method applied to the phosphorescence from the same particles. This combined diagnostic technique is demonstrated with a temperature precision of 4%-10% in a heated air jet during steady operation for flow temperatures up to 624 K. The technique provides correlated vector-scalar data at high spatial and temporal resolution.

Fully-coupled pressure-based finite-volume framework for the simulation of fluid flows at all speeds in complex geometries

Abstract A generalized finite-volume framework for the solution of fluid flows at all speeds in complex geometries and on unstructured meshes is presented. Starting from an existing pressure-based and fully-coupled formulation for the solution of incompressible flow equations, the additional implementation of pressure–density–energy coupling as well as shock-capturing leads to a novel solver framework which is capable of handling flows at all speeds, including quasi-incompressible, subsonic, transonic and supersonic flows. The proposed numerical framework features an implicit coupling of pressure and velocity, which improves the numerical stability in the presence of complex sources and/or equations of state, as well as an energy equation discretized in conservative form that ensures an accurate prediction of temperature and Mach number across strong shocks. The framework is verified and validated by a large number of test cases, demonstrating the accurate and robust prediction of steady-state and transient flows in the quasi-incompressible as well as subsonic, transonic and supersonic speed regimes on structured and unstructured meshes as well as in complex domains.

Estimation of curvature from volume fractions using parabolic reconstruction on two-dimensional unstructured meshes

Abstract This paper proposes a method to estimate the curvature of an interface represented implicitly by discrete volume fractions on an unstructured two-dimensional mesh. The method relies on the computation of local parabolic reconstructions of the interface. The parabolic reconstruction of the interface in a given computational cell is obtained by solving a local non-linear minimisation problem, and only requires additional information from two neighbouring cells. This compactness ensures a robust behaviour on poorly-resolved interfaces. The proposed method is proven to be analogous to the height-function method for Cartesian configurations with consistent heights, and can be interpreted as a generalisation of the height-function method to meshes of any type. Tests are conducted on a range of interfaces with known curvature. The method is shown to converge with mesh refinement with the same order of accuracy as the height-function method for all three types of meshes tested, i.e. Cartesian, triangular, and polygonal.