arXiv subjects

Berend van Wachem

Publications and source records attributed to Berend van Wachem.

At least 19 recordsLinked to original sources

arXiv2026

Orientation-dependent drag, lift, and torque correlations for regular Platonic polyhedral particles

In this work, particle-resolved direct numerical simulations are performed to investigate flow past the five Platonic solids, which represent a progression in particle sphericity with an increasing number of faces. The simulations cover particle Reynolds numbers in the range 0.1 <= Re_p <= 300 and multiple particle orientations relative to the incoming flow. Based on the numerical data, new correlations are developed for the drag, lift, and torque coefficients. The proposed drag correlation explicitly accounts for both Reynolds number and particle orientation, whereas the lift and torque coefficients are represented by orientation-dependent trigonometric and exponential basis functions whose coefficients vary with Reynolds number. The simulations are conducted using the immersed boundary method, and the resulting drag correlation accurately reproduces the numerical data. The lift and torque correlations capture the principal trends observed in the numerical simulations, including the strong dependence on particle orientation. The proposed correlations provide a computationally efficient framework for incorporating orientation-dependent hydrodynamic forces and torques into Euler--Lagrange and point-particle simulations, enabling a more realistic representation and predictions of non-spherical particle transport in multiphase flows.

physics.flu-dyn↗

arXiv2026

An integral surface tension scheme for three-dimensional front tracking frameworks

Surface tension is central to many two-phase flows, making accurate numerical schemes essential for predicting its effects. The integral formulation introduced by Popinet and Zaleski (1999) provides a natural discretisation that conserves momentum locally and globally and extends directly to variable surface tension, including Marangoni flows. However, to the authors' knowledge, only two-dimensional formulations have been reported, mainly because robust implementation in three dimensions is challenging for interfaces with complex geometries. This work presents the first three-dimensional integral surface tension scheme, implemented within a sharp front-tracking framework. The method is tested for static and translating spherical droplets, oscillating droplets, thermocapillary motion, and rising bubbles. Results are compared with analytical solutions, experimental data, and established approaches, including the continuous surface force (CSF) and smoothing-based methods. The proposed scheme produces spurious velocities comparable to CSF, while providing greater accuracy in all other tests. The largest improvements occur for droplets oscillating at low Ohnesorge numbers, variable-surface-tension flows, and strongly deforming rising bubbles. For a thermocapillary-driven droplet, terminal-velocity errors are reduced by up to five orders of magnitude relative to smoothing-based methods. The predicted steady-state shapes of rising bubbles also agree substantially better with experiments, particularly at low Morton numbers.

physics.flu-dyn↗

arXiv2026

Consistent closure modeling in large eddy simulations by direct approximation of the filtered advection term

This article addresses the widely overlooked conceptual inconsistency of the large eddy simulation (LES) framework, namely that the commonly used advection term introduces higher wave numbers in the filtered Navier-Stokes equations than consistent with the definition of a filtered equation. It is explained how this inconsistency is the reason that flux limiters, stabilization terms, or dealiasing is often required and that the LES solution is typically mesh dependent. A consistent alternative is the direct approximation of the filtered advection term, for which we derive an exact expression based on an infinite series expansion with terms of increasing order in the filter width. We show that truncating the series expansion after few terms gives an expression that is highly correlated with the filtered advection term and a suitable LES model. A posteriori studies with decaying turbulence and a turbulent shear flow are conducted that reveal that the proposed approximation of the filtered advection term predicts improved kinetic energy spectra and filtered velocity correlations compared to classical LES.

physics.flu-dyn↗

arXiv2026

Fully coupled implicit finite-volume algorithm for viscoelastic interfacial flows

A fully coupled implicit finite-volume algorithm for incompressible viscoelastic interfacial flows is proposed, whereby the viscoelasticity of the flow is described by an upper-convected Maxwell constitutive model, including limited extensibility and shear-thinning behaviour. The governing equations describing the conservation of continuity and momentum, as well as the constitutive model are discretized using standard finite-volume methods and are solved for pressure, velocity and the polymer stress tensor in a single linear system of equations. Treating all terms of the linearized and discretized governing equations implicit in velocity, pressure and/or the components of the polymer stress tensor, a tightly coupled system of equations is obtained. The interface separating the interacting bulk phases and the surface tension acting at the fluid interface are modelled using a state-of-the-art front-tracking method. We demonstrate the capabilities of the proposed numerical framework with four representative test cases, including the deformation of a viscoelastic droplet in shear flow at large Weissenberg numbers of up to Wi=10^4, and the jump discontinuity of the rise velocity of a bubble rising in a viscoelastic liquid as a result of a "negative wake". Contrary to previous studies using segregated algorithms, the proposed fully coupled implicit algorithm does not apply or require a log-conformation approach to predict these flows. Overall, the fully implicit coupled front-tracking formulation provides a robust framework to reliable numerical predictions of strongly elastic interfacial flows at large Weissenberg numbers.

physics.flu-dyn↗

arXiv2025

Drag modelling for flows through assemblies of spherical particles with machine learning: A comparison of approaches

Drag forces on particles in random assemblies can be accurately estimated through particle-resolved direct numerical simulations (PR-DNS). Despite its limited applicability to relatively small assemblies, data obtained from PR-DNS has been the driving force for the development of drag closures for much more affordable simulation frameworks, such as Eulerian-Lagrangian point particle methods. Recently, more effort has been invested in the development of deterministic drag models that account for the effect of the structure of the particle assembly. Current successful deterministic models are mainly black-box neural networks which: 1) Assume pairwise superposition of the neighbours' effect on the drag, and 2) Are trained on PR-DNS data for a wide range of particle concentrations and flow regimes. To alleviate the black-box nature of neural networks, we use genetic programming (GP) to develop interpretable models. In our previous research, this has been proven successful in the Stokes regime. In the current contribution, we extend the application of GP to higher particle Reynolds number regimes. This is done by training a graph neural network (GNN) on the PR-DNS data to learn the pairwise interactions among the particles that constitute the drag variation. The significance of the input features of the GNN is assessed via a feature permutation approach. Then, the estimated pairwise interactions as extracted from the GNN are fed to a GP algorithm, which searches for symbolic expressions that fit the input data. A comparison between the trained GNN model and the resulting symbolic expressions is presented, to assess whether the symbolic expression can capture the underlying patterns learnt by the GNN. The comparison demonstrates the potential of GP in finding relatively simple symbolic models. At the same time, the accuracy of the symbolic models slightly fall behind the GNN.

physics.comp-ph↗

arXiv2025

A marching cubes based method for topology changes in three-dimensional two-phase flows with front tracking

The handling of topology changes in two-phase flows, such as breakup or coalescence of interfaces, with front tracking is a well-known problem that requires an additional effort to perform explicit manipulations of the Lagrangian front. In this work, we present an approach that allows to perform topology changes with interfaces made of connected triangular elements. The methodology consists of replacing the fluid entities that undergo breakup/coalescence with the iso-surface corresponding to the indicator function value I = 0.5, which automatically returns the shape of the bodies after topology changes. The generation and triangulation of such surface is obtained by exploiting the marching cubes algorithm. Since we perform the reconstruction of the interface only for the bodies that experience breakup/coalescence, the increase in computational cost with respect to a classic front tracking scheme without topology changes is small. Using validation cases, we show that the proposed reconstruction procedure is second-order accurate for volume conservation and able to capture the physics of several two-phase flow configurations undergoing topology changes. The validation cases include the breakup of a droplet in simple shear flow and two rising bubbles in different regimes (peripheral and central breakups). Coalescence is tested by modelling the binary collision between two droplets. For the selected validation cases, an excellent agreement between the numerical results and experiments is observed. The proposed methodology is able to capture the details of such interfacial flows, by predicting accurately the coalescence/breakup dynamics, as well as the number, size and shapes of satellite droplets/bubbles after topology changes.

physics.flu-dyn↗

arXiv2025

Sharp front tracking with geometric interface reconstruction

This paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4-5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency.

physics.flu-dyn↗

arXiv2025

A new paradigm for computing hydrodynamic forces on particles in Euler-Lagrange point-particle simulations

Accurate prediction of the hydrodynamic forces on particles is central to the fidelity of Euler-Lagrange (EL) simulations of particle-laden flows. Traditional EL methods typically rely on determining the hydrodynamic forces at the positions of the individual particles from the interpolated fluid velocity field, and feed these hydrodynamic forces back to the location of the particles. This approach can introduce significant errors in two-way coupled simulations, especially when the particle diameter is not much smaller than the computational grid spacing. In this study, we propose a novel force correlation framework that circumvents the need for undisturbed velocity estimation by leveraging volume-filtered quantities available directly from EL simulations. Through a rigorous analytical derivation in the Stokes regime and extensive particle-resolved direct numerical simulations (PR-DNS) at finite Reynolds numbers, we formulate force correlations that depend solely on the volume-filtered fluid velocity and local volume fraction, parametrized by the filter width. These correlations are shown to recover known drag laws in the appropriate asymptotic limits and exhibit a good agreement with analytical and high-fidelity numerical benchmarks for single particle cases, and, compared to existing correlations, an improved agreement for the drag force on particles in particle assemblies. The proposed framework significantly enhances the accuracy of hydrodynamic force predictions for both isolated particles and dense suspensions, without incurring the prohibitive computational costs associated with reconstructing undisturbed flow fields. This advancement lays the foundation for robust, scalable, and high-fidelity EL simulations of complex particulate flows across a wide range of industrial and environmental applications.

physics.flu-dyn↗

arXiv2025

Self-sorting of bidisperse particles in evaporating sessile droplets

This study investigates the dispersion and self-sorting dynamics of bidisperse particles, i.e., a mixture of two distinct particle sizes, during the evaporation of ethanol droplets on a heated substrate, focusing on the influence of surface wettability, Marangoni stresses, and relative particle density. To this end, numerical simulations are carried out using a two-stage numerical approach: the first stage simulates the gas-liquid flow along with the heat and vapor distribution, while the second stage models the particle behavior using Lagrangian particle tracking. The results reveal that for an ethanol droplet evaporating with a constant contact angle in the absence of thermocapillary Marangoni stresses, the flow induced by the receding motion of the contact line supersedes the capillary flow, moving the fluid from the contact line to the apex of the droplet. This flow moves the particles from the bulk of the droplet to the apex of the droplet and suppresses size-based self-sorting of the particles. However, in the presence of Marangoni stresses, a flow along the interface near the apex of the droplet promotes the self-sorting of particles based on their size, whereby smaller particles concentrate near the droplet apex and larger particles form an outer shell around them.

physics.flu-dyn↗

arXiv2025

Steady undisturbed velocity correction scheme for Euler-Lagrange simulations near planar walls

Euler-Lagrange (EL) point-particle simulations rely on hydrodynamic force closure models to accurately predict particle dynamics in flows. The closure models currently employed for dilute particle-laden flows require the undisturbed fluid velocity estimated at the particle center. Recovering this undisturbed velocity necessitates modeling the particle-induced disturbance on the flow. In this work, we present a new framework for velocity disturbance modeling near no-slip walls, suited for dilute gas-solid flows characterized by large Stokes numbers. For small disturbance Reynolds numbers, the velocity disturbance governing equations reduce to the steady Stokes equations. To exactly satisfy the no-slip and no-penetration boundary conditions for the velocity disturbance at the location of the planar wall, we employ the method of images to derive the Green's functions of the Stokes equations for Wendland and Gaussian force regularization kernels. An additional convolution product with a mesh-spacing dependent Gaussian kernel is performed to match the solution produced by a discrete flow solver. We verify the proposed analytical model by comparing the velocity disturbance generated on a computational mesh with the model predictions. An extension of the model for finite particle Reynolds numbers is proposed by multiplying an Oseen correction factor in an unbounded domain. The correction scheme is validated using canonical test cases involving the motion of a single particle parallel and perpendicular to a wall at various Stokes numbers, particle Reynolds numbers, and particle diameter to mesh-spacing ratios. Owing to the polynomial representation of the velocity disturbance for a Wendland force regularization, the current model is computationally efficient and well-suited for large-scale, two-way coupled EL simulations.

physics.flu-dyn↗

arXiv2024

Correlations for aerodynamic force coefficients of non-spherical particles in compressible flows

This study presents particle-resolved direct numerical simulations using three-dimensional body-fitted hexahedral meshes to investigate the aerodynamic force and torque coefficients of non-spherical particles in compressible flows. The simulations focus on three particle shapes: a prolate spheroid, an oblate spheroid, and a rod-like particle, across a range of Mach numbers (0.3 to 2.0), angles of attack (0 degrees to 90 degrees), and particle Reynolds numbers (100 to 300). Results indicate that the particle shape significantly impacts the aerodynamic forces on a particle in a compressible flow, with oblate spheroids exhibiting the highest drag, lift, and torque values. Correlations for these aerodynamic coefficients of the particles in a compressible flow are developed and validated. These correlations advance multiphase flow modeling by improving the accuracy of point-particle simulations for non-spherical particles in compressible flows.

physics.flu-dyn↗

arXiv2024

A new paradigm for wall-modeled large eddy simulations using the volume-filtering framework

In the present paper, we apply the framework of volume-filtering for particle-laden flows, to large eddy simulations (LES) of wall-bounded flows leading to a new perspective on wall-modeled LES (WMLES) that we refer to as volume-filtered WMLES (VF-WMLES). In contrast to existing wall-models, the VF-WMLES framework does not rely on temporal averaging, does not make a priori assumptions on the pressure gradient, and can be used with a uniform spatial filter, which avoids the appearance of commutation closures in spatial derivatives of the filtered momentum and continuity equation. Volume-filtering is well-defined, even close to the wall, and it is shown that a non-zero slip and penetration velocity at the wall is a direct consequence of volume-filtering the flow. With the VF-WMLES concept, new wall models can be directly assessed in a priori and a posteriori studies by comparing the predicted slip and penetration velocities at the wall with the velocities from explicitly volume-filtered direct numerical simulations (DNS). Based on the VF-WMLES concept, we derive an LES modeling strategy that is based on the recently proposed PC-IBM, a modeling framework based on volume-filtering allowing to couple the flow with arbitrarily shaped solid boundaries using relatively coarse Cartesian fluid meshes. The proposed VF-WMLES is validated with two cases, a turbulent channel flow and a turbulent flow over periodic hills, and shown to accurately predict the mean velocity profiles for both cases.

physics.flu-dyn↗

arXiv2024

A fully-coupled algorithm with implicit surface tension treatment for interfacial flows with large density ratios

The stability of most surface-tension-driven interfacial flow simulations is governed by the capillary time-step constraint. This concerns particularly small-scale flows and, more generally, highly-resolved liquid-gas simulations with moderate inertia. To date, the majority of interfacial-flow simulations are performed using an explicit surface-tension treatment, which restrains the performance of such simulations. Recently, an implicit treatment of surface tension able to breach the capillary time-step constraint using the volume-of-fluid (VOF) method was proposed, based on a fully-coupled pressure-based finite-volume algorithm. To this end, the interface-advection equation is incorporated implicitly into the linear flow solver, resulting in a tight coupling between all implicit solution variables (colour function, pressure, velocity). However, this algorithm is limited to uniform density and viscosity fields. Here, we present a fully-coupled algorithm for interfacial flows with implicit surface tension applicable to interfacial flows with large density and viscosity ratios. This is achieved by solving the continuity and momentum equations in conservative form, whereby the density is treated implicitly with respect to the colour function, and the advection term of the interface-advection equation is discretised using the THINC/QQ algebraic VOF scheme, yielding a consistent discretisation of the advective terms. This new algorithm is tested by considering representative surface-tension-dominated interfacial flows, including the Laplace equilibrium of a stationary droplet and the three-dimensional Rayleigh-Plateau instability of a liquid filament. The presented results demonstrate that interfacial flows with large density and viscosity ratios can be simulated and energy conservation is ensured, even with a time step larger than the capillary time-step constraint.

physics.flu-dyn↗

arXiv2024

Physically consistent immersed boundary method: a framework for predicting hydrodynamic forces on particles with coarse meshes

In the present paper, a fluid-particle coupling method is directly derived from the Navier-Stokes equations (NSE) by applying the concept of volume-filtering, yielding a physically consistent methodology to incorporate solid wall boundary conditions in the volume-filtered flow solution, thereby allowing to solve the governing flow equations on non-body conforming meshes. The resulting methodology possesses similarities with a continuous forcing immersed boundary method (IBM) and is, therefore, termed physically consistent IBM (PC-IBM). Based on the recent findings of arXiv:2402.05842v1, the closures arising in the volume-filtered NSE are closed by suitable models or even expressed analytically. The PC-IBM is fully compatible with the large eddy simulation framework, as the volume-filtered NSE converge to the filtered NSE away from solid boundaries. The potential of the PC-IBM is demonstrated by means of different particle-laden flow applications, including a dense packing of fixed particles and periodic settling of 500 particles. The new methodology turns out to be capable of accurately predicting the fluid forces on particles with relatively coarse mesh resolutions. For the flow around isolated spheres, a spatial resolution of six fluid mesh cells per diameter is sufficient to predict the drag force with less than 10% deviation from highly resolved simulation for the investigated particle Reynolds numbers ranging from 10 to 250.

physics.flu-dyn↗

arXiv2024

Drag, lift, and torque correlations for axi-symmetric rod-like non-spherical particles in linear wall-bounded shear flow

This paper presents novel correlations to predict the drag, lift, and torque coefficients of axi-symmetric non-spherical rod-like particles in a wall-bounded linear shear flow. The particle position and orientation relative to the wall are varied to systematically investigate the influence of the wall on the hydrodynamic forces. The newly derived correlations for drag, lift, and torque on the particle depend on various parameters, including the particle Reynolds number, the orientation angle between the major axis of the particle and the main local flow direction, the aspect ratio of the particle, and the dimensionless distance from the particle centre to the wall. The coefficients of the correlations are determined through a fitting process utilizing the data generated from our previous study on the interaction forces between a locally uniform flow and an axi-symmetric non-spherical rod-like particles, as well as from data of novel direct numerical simulations (DNS) performed in this work of flow past axi-symmetric rod-like particles near a wall. The proposed correlations exhibit a good agreement compared to the DNS results, with median errors of 2.89%, 5.37%, and 11.00%, and correlation coefficients of 0.99, 0.99, and 0.96 for the correlations accounting for changes in drag, lift, and torque coefficients due to the wall-bounded linear shear flow profile, respectively. These correlations can be used in large-scale simulations using an Eulerian-Lagrangian or a CFD/DEM framework to predict the behaviour of axi-symmetric rod-like non-spherical particles in wall-bounded flows, shear flows, as well as uniform flows.

physics.flu-dyn↗

arXiv2024

A semi-analytical transient undisturbed velocity correction scheme for wall-bounded two-way coupled Euler-Lagrange simulations

In the present paper, we model the velocity disturbance generated by a regularized forcing near a planar wall, which, along with the temporal nature of the forcing, provides an estimate of the unsteady velocity disturbance of the particle near a planar wall. We use the analytical solution for a singular in-time transient Stokeslet near a planar wall (Felderhof, 2009) and derive the corresponding time-persistent Stokeslets. The velocity disturbance due to a regularized forcing is then obtained numerically via a discrete convolution with the regularization kernel. The resulting Green's functions for parallel and perpendicular regularized forcing to the wall are stored as pre-computed temporal correction maps. By storing the time-dependent particle force on the fluid as fictitious particles, we estimate the unsteady velocity disturbance generated by the particle as a scalar product between the stored forces and the pre-computed Green's functions. Since the model depends on the analytical Green's function solution of the singular Stokeslet near a planar wall, the obtained velocity disturbance exactly satisfies the no-slip condition and does not require any fitted parameters to account for the rapid decay of the disturbance near the wall. The numerical evaluation of the convolution integral makes the present method suitable for arbitrary regularization kernels. Additionally, the generation of parallel and perpendicular correction maps enables to estimate the velocity disturbance due to particle motion in arbitrary directions relative to the local flow. The convergence of the method is studied on a fixed particle near a planar wall, and verification tests are performed on a settling particle parallel to a wall and a free-falling particle perpendicular to the wall.

physics.flu-dyn↗

arXiv2024

Undisturbed velocity recovery with transient and weak inertia effects in volume-filtered simulations of particle-laden flows

In volume-filtered Euler-Lagrange simulations of particle-laden flows, the fluid forces acting on a particle are estimated using reduced models, which rely on the knowledge of the local undisturbed flow for that particle. Since the two-way coupling between the particle and the fluid creates a local flow perturbation, the filtered fluid velocity interpolated to the particle location must be corrected prior to estimating the fluid forces, so as to subtract the contribution of this perturbation and recover the local undisturbed flow with good accuracy. In this manuscript, we present a new model for estimating a particle's self-induced flow disturbance that accounts for its transient development and for inertial effects related to finite particle Reynolds numbers. The model also does not require the direction of the momentum feedback to align with the direction of the particle's relative velocity, allowing force contributions other than the steady drag force to be considered. It is based upon the linearization of the volume-filtered equations governing the particle's self-induced flow disturbance, such that their solution can be expressed as a linear combination of regularized transient Stokeslet contributions. Tested on a range of numerical cases, the model is shown to consistently estimate the particle's self-induced flow disturbance with high accuracy both in steady and highly transient flow environments, as well as for finite particle Reynolds numbers.

physics.comp-ph↗

arXiv2024

Study and derivation of closures in the volume-filtered framework for particle-laden flows

The volume-filtering of the Navier-Stokes equations allows to consider the effect that particles have on the fluid without further assumptions, but closures arise of which the implications are not fully understood. In the present paper, we carefully study every closure in the volume-filtered fluid momentum equation and investigate their impact on the momentum and energy transfer dependent on the filtering characteristics. We provide an analytical expression for the viscous closure that arises because filter and spatial derivative in the viscous term do not commute. An analytical expression for the regularization of the particle momentum source of a single sphere in the Stokes regime is derived. Furthermore, we propose a model for the subfilter stress tensor, which originates from filtering the advective term. The model for the subfilter stress tensor is shown to agree well with the subfilter stress tensor for small filter widths relative to the size of the particle. We show that the subfilter stress tensor requires modeling and should not be neglected. For small filter widths, we find that the commonly applied Gaussian regularization of the particle momentum source is a poor approximation of the spatial distribution of the particle momentum source, but for larger filter widths the spatial distribution approaches a Gaussian. Furthermore, we propose a modified advective term in the volume-filtered momentum equation that consistently circumvents the common stability issues observed at locally small fluid volume fractions and identify inconsistencies in previous studies of the phase-averaged kinetic energy of the volume-filtered fluid velocity. Finally, we propose a generally applicable form of the volume-filtered momentum equation and its closures based on clear and well-founded assumptions and propose guidelines for point-particle simulations based on the new findings.

physics.flu-dyn↗