Holger Marschall

Numerical and experimental analysis of local flow phenomena in laminar Taylor flow in a square mini-channel

The vertically upward Taylor flow in a small square channel (side length 2 mm) is one of the guiding measures within the priority program “Transport Processes at Fluidic Interfaces” (SPP 1506) of the German Research Foundation (DFG). This paper presents the results of coordinated experiments and three-dimensional numerical simulations (with three different academic computer codes) for typical local flow parameters (bubble shape, thickness of the liquid film, and velocity profiles) in different cutting planes (lateral and diagonal) for a specific co-current Taylor flow. For most quantities, the differences between the three simulation results and also between the numerical and experimental results are below a few percent. The experimental and computational results consistently show interesting three-dimensional flow effects in the rear part of the liquid film. There, a local back flow of liquid occurs in the fixed frame of reference which leads to a temporary reversal of the direction of the wall shear stress during the passage of a Taylor bubble. Notably, the axial positions of the region with local backflow and those of the minimum vertical velocity differ in the lateral and the diagonal liquid films. By a thorough analysis of the fully resolved simulation results, this previously unknown phenomenon is explained in detail and, moreover, approximate criteria for its occurrence in practical applications are given. It is the different magnitude of the velocity in the lateral film and in the corner region which leads to azimuthal pressure differences in the lateral and diagonal liquid films and causes a slight deviation of the bubble from the rotational symmetry. This deviation is opposite in the front and rear parts of the bubble and has the mentioned significant effects on the local flow field in the rear part of the liquid film.

A comparison of stabilisation approaches for finite-volume simulation of viscoelastic fluid flow

In this work we compare different stabilisation approaches currently used in the simulation of viscoelastic fluid flow. These approaches are: the both-sides diffusion, the positive definiteness preserving scheme, the log-conformation tensor representation and the symmetry factorisation of the conformation tensor. The evaluation of these approaches is done regarding their implementation complexity, stability, accuracy, efficiency and applicability to complex problems. Their performances are examined for an Oldroyd-B fluid in the test cases of lid-driven cavity, flow past a cylinder and 4:1 contraction flow. We summarise the situations in which the different approaches can be recommended.

Boundedness-preserving implicit correction of mesh-induced errors for VOF based heat and mass transfer

Abstract Spatial discretisation of geometrically complex computational domains often entails unstructured meshes of general topology for Computational Fluid Dynamics (CFD). Mesh skewness is then typically encountered causing severe deterioration of the formal order of accuracy of the discretisation, or boundedness of the solution, or both. Particularly methods inherently relying on the accurate and bounded transport of sharp fields suffer from all types of mesh-induced skewness errors, namely both non-orthogonality and non-conjunctionality errors. This work is devoted to a boundedness-preserving strategy to correct for skewness errors arising from discretisation of advection and diffusion terms within the context of interfacial heat and mass transfer based on the Volume-of-Fluid methodology. The implementation has been accomplished using a second-order finite volume method with support for unstructured meshes of general topology. We examine and advance suitable corrections for the finite volume discretisation of a consistent single-field model, where both accurate and bounded transport due to diffusion and advection is crucial. In order to ensure consistency of both the volume fraction and the species concentration transport, i.e. to avoid artificial heat or species transfer, corrections are studied for both cases using distorted 2D meshes. The cross interfacial jump and adjacent sharp gradients of species concentration render the correction for skewness-induced diffusion and advection errors additionally demanding and has not so far been addressed in the literature.

Experimental and Computational Analysis of Fluid Interfaces Influenced by Soluble Surfactant

The present contribution is the result of a collaboration between the Max Planck Institute of Colloids and Interfaces and the Technical University of Darmstadt (MMA group). The main objective is to give a quantitative description of fluid interfaces influenced by surfactants, comparing experimental and computational results. Surfactants are amphiphilic molecules subject to ad- and desorption processes at fluid interfaces. In fact, they accumulate at the interface, modifying the respective interfacial properties. Since these interfaces are moving, continuously deforming and expanding, the local time-dependent interfacial coverage is the most relevant quantity. The description of such processes poses severe challenges both to the experimental and to the simulation sides. Two prototypical problems are considered for comparison between experiments and simulations: the formation of droplets under the influence of surfactants and rising bubbles in aqueous solutions contaminated by surfactants. Direct Numerical Simulations (DNS) provide valuable insights into local quantities such as local surfactant distribution and surface tension, but at high computational costs and restricted to short time frames. On the other hand, experiments can give global quantities necessary for the validation of the numerical procedures and can afford longer time frames. The two methodologies thus yield complementary results which help to understand such complex interfacial phenomena.

Investigation of Elementary Processes of Non-Newtonian Droplets Inside Spray Processes by Means of Direct Numerical Simulation

Binary droplet collisions play an important role as an essential elementary process in sprays. They significantly influence the droplet size distribution. In order to give an improved prediction of the outcome of droplet collisions, understanding of the influence of the liquid rheology on the collisions as well as on the flow dynamics inside the colliding droplets is necessary. In this work, we have investigated binary droplet collisions by means of Direct Numerical Simulation (DNS) of two-phase incompressible Navier–Stokes equations using the Volume-of-Fluid (VOF) code Free Surface 3D (FS3D). A pivotal aim of the study is to derive mechanistic models for the outcome of collisions which can be used for scale-reduced simulations such as Euler–Euler and Euler–Lagrange simulations. In order to reach this goal, we have investigated various kinds of collisions, such as collisions of shear-thinning, non-isoviscous, and viscoelastic droplets. We have also developed and implemented various numerical algorithms to overcome the numerical difficulties in simulating different kinds of collisions.

Computational analysis of single rising bubbles influenced by soluble surfactant

This paper presents novel insights about the influence of soluble surfactants on bubble flows obtained by Direct Numerical Simulation (DNS). Surfactants are amphiphilic compounds which accumulate at fluid interfaces and significantly modify the respective interfacial properties, influencing also the overall dynamics of the flow. With the aid of DNS local quantities like the surfactant distribution on the bubble surface can be accessed for a better understanding of the physical phenomena occurring close to the interface. The core part of the physical model consists in the description of the surfactant transport in the bulk and on the deformable interface. The solution procedure is based on an Arbitrary Lagrangian-Eulerian (ALE) Interface-Tracking method. The existing methodology was enhanced to describe a wider range of physical phenomena. A subgrid-scale (SGS) model is employed in the cases where a fully resolved DNS for the species transport is not feasible due to high mesh resolution requirements and, therefore, high computational costs. After an exhaustive validation of the latest numerical developments, the DNS of single rising bubbles in contaminated solutions is compared to experimental results. The full velocity transients of the rising bubbles, especially the contaminated ones, are correctly reproduced by the DNS. The simulation results are then studied to gain a better understanding of the local bubble dynamics under the effect of soluble surfactant. One of the main insights is that the quasi-steady state of the rise velocity is reached without ad- and desorption being necessarily in local equilibrium.

A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes

Summary A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full combinatorial flexibility between different kinds of rheological models on the one hand, and effective stabilization methods on the other hand. A special emphasis is put on the velocity-stress-coupling on co-located computational grids. Using special face interpolation techniques, a semi-implicit stress interpolation correction is proposed to correct the cell-face interpolation of the stress in the divergence operator of the momentum balance. Investigating the entry-flow problem of the 4:1 contraction benchmark, we demonstrate that the numerical methods are robust over a wide range of Weissenberg numbers and significantly alleviate the high Weissenberg number problem. The accuracy of the results is evaluated in a detailed mesh convergence study. This article is protected by copyright. All rights reserved.

CFD Simulation of Liquid Back Suction and Gas Bubble Formation in a Circular Tube with Sudden or Gradual Expansion

To avoid potential damage of the dosing unit in selective catalytic reduction by freezing urea-water-solution, the liquid is usually drained from the delivery line when the vehicle is out of operation. When liquid is sucked back counter to the normal delivery direction, the urea-water-solution is replaced by gas with the risk of air being sucked in. In this paper, we study the liquid back suction process and bubble formation numerically by interface-resolving simulations with a phase field method for a generic simplified geometry. We consider two connected circular tubes with sudden or gradual change of the diameter and provide guidelines for proper numerical setup of such flow problems in order to ensure physically reliable results. We study the influence of the geometry on the liquid draining process through variations of inner and outer tube diameters as well as transition inclination angle. The present numerical results indicate that geometrical modification is an effective means to control liquid draining in expanding pipes while preventing gas bubble formation.

An enhanced un-split face-vertex flux-based VoF method

Abstract Multiple advancements of the dimensionally un-split, flux-based geometrical Volume-of-Fluid method on unstructured meshes are proposed. A second-order accurate interface reconstruction algorithm for both two-and-three dimensions is developed on unstructured hexahedral meshes. A new triangulation algorithm is developed that results in an absolute increase in accuracy and can be directly applied to other geometrical Volume-of-Fluid methods on both structured and unstructured meshes. A second-order accurate interpolation of point displacements is proposed for unstructured meshes. A global parallel error re-distribution algorithm is developed, with no negative effects on the L 1 error convergence and computational costs. All algorithms are parallelized using the message passing parallel programming model, with a minimal parallel communication overhead. The results show L 1 errors to be exactly numerically bounded, second-order convergent and lower than the errors reported for other contemporary methods, volume conservation that is near machine tolerance, as well as execution times comparable to those of methods developed on structured Cartesian meshes, regardless of the increased algorithmic complexity introduced by the connectivity of unstructured meshes.

Direct Numerical Simulations of Taylor Bubbles in a Square Mini-Channel: Detailed Shape and Flow Analysis with Experimental Validation

The Priority Program SPP 1506 “Transport Processes at Fluidic Interfaces” by the German Research Foundation DFG has established a benchmark problem for validation of two-phase flow solvers by means of specifically designed experiments for Taylor Bubble Flow. This chapter is devoted to results from Direct Numerical Simulations (DNS) of a single rising Taylor bubble and of Taylor flow in a square channel, where both bubble shape and flow pattern around the bubble have been thoroughly analyzed. Comparisons have been accomplished to highly resolved experiments providing detailed and local benchmark data for validation. An interesting three-dimensional backflow effect of technological relevance has been revealed. A criterion to estimate its occurrence is deducted from thorough analysis of local simulation data.