The receding front method applied to hexahedral mesh generation of exterior domains

Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.Peer ReviewedPostprint (author's final draft

Unstructured and semi-structured hexahedral mesh generation methods

Discretization techniques such as the finite element method, the finite volume method or the discontinuous Galerkin method are the most used simulation techniques in ap- plied sciences and technology. These methods rely on a spatial discretization adapted to the geometry and to the prescribed distribution of element size. Several fast and robust algorithms have been developed to generate triangular and tetrahedral meshes. In these methods local connectivity modifications are a crucial step. Nevertheless, in hexahedral meshes the connectivity modifications propagate through the mesh. In this sense, hexahedral meshes are more constrained and therefore, more difficult to gener- ate. However, in many applications such as boundary layers in computational fluid dy- namics or composite material in structural analysis hexahedral meshes are preferred. In this work we present a survey of developed methods for generating structured and unstructured hexahedral meshes.Peer ReviewedPostprint (published version

Frame Fields for Hexahedral Mesh Generation

As a discretized representation of the volumetric domain, hexahedral meshes have been a popular choice in computational engineering science and serve as one of the main mesh types in leading industrial software of relevance. The generation of high quality hexahedral meshes is extremely challenging because it is essentially an optimization problem involving multiple (conflicting) objectives, such as fidelity, element quality, and structural regularity. Various hexahedral meshing methods have been proposed in past decades, attempting to solve the problem from different perspectives. Unfortunately, algorithmic hexahedral meshing with guarantees of robustness and quality remains unsolved. The frame field based hexahedral meshing method is the most promising approach that is capable of automatically generating hexahedral meshes of high quality, but unfortunately, it suffers from several robustness issues. Field based hexahedral meshing follows the idea of integer-grid maps, which pull back the Cartesian hexahedral grid formed by integer isoplanes from a parametric domain to a surface-conforming hexahedral mesh of the input object. Since directly optimizing for a high quality integer-grid map is mathematically challenging, the construction is usually split into two steps: (1) generation of a feature-aligned frame field and (2) generation of an integer-grid map that best aligns with the frame field. The main robustness issue stems from the fact that smooth frame fields frequently exhibit singularity graphs that are inappropriate for hexahedral meshing and induce heavily degenerate integer-grid maps. The thesis aims at analyzing the gap between the topologies of frame fields and hexahedral meshes and developing algorithms to realize a more robust field based hexahedral mesh generation. The first contribution of this work is an enumeration of all local configurations that exist in hexahedral meshes with bounded edge valence and a generalization of the Hopf-Poincaré formula to octahedral (orthonormal frame) fields, leading to necessary local and global conditions for the hex-meshability of an octahedral field in terms of its singularity graph. The second contribution is a novel algorithm to generate octahedral fields with prescribed hex-meshable singularity graphs, which requires the solution of a large non-linear mixed-integer algebraic system. This algorithm is an important step toward robust automatic hexahedral meshing since it enables the generation of a hex-meshable octahedral field. In the collaboration work with colleagues [BRK+22], the dataset HexMe consisting of practically relevant models with feature tags is set up, allowing a fair evaluation for practical hexahedral mesh generation algorithms. The extendable and mutable dataset remains valuable as hexahedral meshing algorithms develop. The results of the standard field based hexahedral meshing algorithms on the HexMesh dataset expose the fragility of the automatic pipeline. The major contribution of this thesis improves the robustness of the automatic field based hexahedral meshing by guaranteeing local meshability of general feature aligned smooth frame fields. We derive conditions on the meshability of frame fields when feature constraints are considered, and describe an algorithm to automatically turn a given non-meshable frame field into a similar but locally meshable one. Despite the fact that local meshability is only a necessary but not sufficient condition for the stronger requirement of meshability, our algorithm increases the 2% success rate of generating valid integer-grid maps with state-of-the-art methods to 57%, when compared on the challenging HexMe dataset

Numerical Investigation of Liquid Film Dynamics and Atomisation in Jet Engine Fuel Injectors

Today’s aerospace industry continues to exploit liquid hydrocarbon fossil fuels. Motivated by operational considerations, continued availability and cost, this is likely to be the case for many years, despite the obvious environmental concerns. The interplay of liquid atomisation, spray vaporisation and the combustion process are intricately linked. However, the physical process of fuel injection and its atomisation into tiny droplets prior to combustion remains poorly understood. Because atomisation governs the size of the fuel droplets, and therefore their subsequent evaporation rate, adjusting the injection sequence is of paramount importance and will have far-reaching repercussions on many aspects of the combustion process, for example pollutant formation. In the context of jet engines, kerosene is usually injected in its liquid form via an airblast-type fuel injector. A coflowing high-speed airstream destabilises the liquid fuel, which is thus sprayed into fine droplets into the combustion chamber. The prediction of this phenomenon for various operating conditions relevant to the aeronautical industry requires a deeper understanding of the mechanisms involved in the interaction of the two fluids. A key element in predicting the complex behaviour of spray formation and evolution in jet engines is accurate modelling of fuel atomisation. Atomisation represents one of the key challenges that remains to be undertaken to make predictive computational simulations possible. However, the inherent multi-physics and multi-scale nature of this process limits numerical investigations. Thanks to the steady progress in computer power and Computational Fluid Dynamics (CFD) methods, computational modelling of injection systems emerges as a promising tool that can drive the design of future devices. This research project sets out to investigate the atomisation process in detail, in particular in providing physical insight into the fundamental physics of the phenomenon, in conjunction with an analysis on wetting behaviours and liquid droplet tracking. High-fidelity numerical simulations are performed using a novel in-house state-of-the-art multiphase flow modelling capability, RCLSFoam. The performance of the numerical scheme is demonstrated on typical two-dimensional and three-dimensional benchmark test cases relevant to both multiphase flow modelling and atomisation, and validated against other computational methods. An informed and systematic qualitative assessment of the topological variations of the phase interface during primary atomisation of a liquid film is made through dynamical analysis, while investigating an extensive domain of operating conditions at ambient and aero-engine injection conditions relevant to industry. This analysis demonstrated the influence of shear-driven instabilities on the atomisation process. The shear stress and difference in inertia between liquid and gas are observed to play a significant role in the atomisation process. In addition, the key physical mechanisms and their competing effects have been mapped out in order to predict the evolution of the process according to the operating conditions of the injection system. The proposed cartography gathers four different atomisation mechanisms. In particular, for sufficiently high liquid injection speeds, three-dimensional wave modes were observed to co-exist (the “3-D wave mode” regime). For very low liquid flow rates, accumulated liquid at the atomising edge undergoes deformation by which droplets are generated (the “accumulation” regime). For an increasing gas injection speed and a fixed liquid velocity, the effects of surface tension were observed to result in the generation of streamwise ligaments only, which tend to pair up (the “ligament-merging” regime). Finally, “vortex action” is another observed mechanism by which the liquid film is fragmented. Overall, this research project culminated in (i) the study of dynamic wetting behaviours, with the implementation and validation against experimental data of the Kistler dynamic contact model; and (ii) the demonstration of an algorithm for droplet capture and subsequent post-processing analysis of the droplet characteristics.Rolls Royce plc. and EPSR

Numerical Modeling of Deformation, Oscillation, Spreading and Collision Characteristics of Droplets in an Electric Field

Electric field induced flows, or electrohydrodynamics (EHD), have been promising in many fast-growing technologies, where droplet movement and deformation can be controlled to enhance heat transfer and mass transport. Several complex EHD problems existing in many applications were investigated in this thesis. Firstly, this thesis presents the results of numerical simulations of the deformation, oscillation and breakup of a weakly conducting droplet suspended in an ambient medium with higher conductivity. It is the first time that the deformation of such a droplet was investigated numerically in a 3D configuration. We have determined three types of behavior for the droplets, which are less conducting than ambient fluid: 1) oblate deformation (which can be predicted from the small perturbation theory), 2) oscillatory oblate-prolate deformation and 3) breakup of the droplet. Secondly, a numerical study of droplet oscillation placed on different hydrophobic surfaces under the effect of applied AC voltage including the effect of ambient gas was investigated. The presented algorithm could reproduce droplet oscillations on a surface considering different contact angles. It has been found that the resonance frequency of the water droplet depends on the surface property of the hydrophobic materials and the electrostatic force. Thirdly, a new design of an electrowetting mixer using the rotating electric field was proposed which offers a new method to effectively mix two droplets over a different range of AC frequencies. Two regimes were observed for droplet coalescence: 1) coalescence due to the high droplet deformation, 2) coalescence due to the interaction of electrically induced dipoles. Fourthly, the spreading and retraction control of millimetric water droplets impacting on dry surfaces have been investigated to examine the effect of the surface charge density and electric field intensity. The effect of the surface charge on the spreading of droplets placed gently on surfaces was investigated in the first part. It was found that the maximum spreading diameter increases with an increasing charge. In the second part, the impact of a droplet on a ground electrode was considered. It was also found that in order to keep the maximum diameter after the impact, less charge is needed for surfaces with lower contact angle. Finally, the interaction between two identical charged droplets was investigated numerically. The effects of the impact velocity, drop size ratio and electric charge on the behavior of the combined droplet were investigated. It was shown that two conducting droplets carrying charges of the same polarity under some conditions may be electrically attracted. The formation of charged daughter droplets has been investigated and it was found that the number of the satellite droplets after collision appears to increase with an increase in the droplet charge

Two-Phase Flow Simulation in Porous Media Geometries Reconstructed from micro CT Data : Application to Fluid Transport at Low Capillary Numbers

Liquid flow penetrating into porous media, such as rocks, metal foam, soil, and drug delivery, are often simulated as a single phase or multiphase continuum using Darcy’s law. Darcy’s law considered being the most used model of many approaches for simulating the flow through porous media, where the Darcy model assumes a simple proportional relationship between the instantaneous discharge rate through a porous medium, the viscosity of the fluid, and the pressure drop over a given distance. The law was formulated based on the results of experiments on the flow of water through beds of sand. It also forms the scientific basis of fluid permeability used in the earth sciences, particularly in hydrogeology. The underlying assumption with the Darcy method is that the microscopic concept of the liquid flow in any porous material will involve the use of the microscopic velocities associated with the actual paths of the liquid. However, in practice, it is challenging to measure the real microscopic velocities and for this reason, the average value of the real velocities is accepted. By averaging the steady-state Stokes equation this leads to Darcys law, which was introduced as an empirical relationship to describe flow in sand filters, as discovered by Darcy in 1856 and this served as a starting point for numerous practical applications and as a constant challenge for theoreticians. While the original conditions studied by Darcy are found in many practical situations, its extensions to more general cases that are especially designed for theoretical analysis are widely used to represent situations in which experiments are difficult to perform. While this form of Darcy’s law is used with great frequency, it is difficult to get experimental verification of the obvious terms representation of Darcy’s law. For example, the Darcy velocity, which is defined as a volume-average of the flow field, does not represent the real velocity inside the porous media, but rather, the volume of fluid flowing per unit area of the porous medium, including both solids and voids. Also, the pressure gradient does not represent the microscopic pore-level quantity, but rather, is defined over a representative elementary volume medium. To explore Darcy assumptions and to understand the controlling pore-scale mechanisms, a numerical framework has been developed that involves using a reconstructed real porous medium to present a detailed numerical domain for multiphase flow simulations. For the numerical multiphase flow methodology the Volume-of-Fluid (VoF) method combined with additional sharpening, smoothing and filtering algorithms is used as a basis for interface capturing. These algorithms help in the minimisation of the parasitic currents presented in flow simulations. The framework is implemented within a finite volume code (OpenFOAM) using a limited Multidimensional Universal Limiter with Explicit Solution (MULES) implicit formulation. This framework allows for more substantial time steps at low capillary numbers to be utilised compared to the standard solver. In addition, a novel adaptive interface compression scheme is introduced. This allows for dynamic estimation of the compressive velocity only at the areas of interest and thus, has the advantage of avoiding the use of a priori defined compression coefficient parameters. The adaptive method increases the numerical accuracy and reduces the sensitivity of the methodology to tuning parameters. The accuracy and stability of the proposed model are verified against different benchmark test cases. Moreover, the numerical results are compared against analytical solutions as well as available experimental data and this reveals improved predictions relative to the standard VoF solver. This thesis is focused on two different applications that involve porous media: first, flow and transport inside a porous structure, where the presented simulations results show the importance of liquid front invasion. Also, the salience of phase wettability on the residual phase using different wetting dynamic conditions is demonstrated. The results for simulations relating the pore-scale physics, thereby obtaining permeability values are presented. The overall results provide a detailed pore-scale analysis of multiphase flow, serving as a foundation for large-scale modelling and flow prediction. The second application is droplet impact on porous structures and the penetration physics on porous media. The work is focused on droplet spreading and absorption during the early stages of impact. Using the developed framework, the droplet penetrating the porous media is also studied. In addition, simulations of the penetration of different sizes of droplets with different fluid properties in the pore network with different porosities are performed to characterise the effect of the Re and We numbers on the penetration behaviour. The capability to estimate the key features of the flow dynamics has been investigated. For example, in order to relate the microscopic effects to the macroscopic ones, it is important to focus on the maximum spreading, while considering the influence of liquid properties, and wetting behaviour with relation to porous media properties such as porosity. Some conclusions regarding the relation between porosity and porous wall wetting conditions have been drawn using the developed numerical framework for studying the liquid spreading onto porous media. Also, in the thesis, the influence of the porous structure wetting behaviour, the morphology of porous surfaces and the effects of porosity on droplet penetration and spreading are presented. Using the proposed developed solver, a direct relation between penetration volume and the imposed dynamic contact angle was found. This would appear to contradict the expected behaviour in vertical liquid penetration that is obtained using the macroscopic multiphase Darcy’s law. The goals of this research have been achieved by deploying the complex flow physics using the two described applications and by showing the importance of the developed framework in relation to a wide range of applications. This provides evidence for the effectiveness of studying multiphase flows at the microscale level uisng interface tracking methods

Book of Abstracts 15th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering and 3rd Conference on Imaging and Visualization

In this edition, the two events will run together as a single conference, highlighting the strong connection with the Taylor & Francis journals: Computer Methods in Biomechanics and Biomedical Engineering (John Middleton and Christopher Jacobs, Eds.) and Computer Methods in Biomechanics and Biomedical Engineering: Imaging and Visualization (JoãoManuel R.S. Tavares, Ed.). The conference has become a major international meeting on computational biomechanics, imaging andvisualization. In this edition, the main program includes 212 presentations. In addition, sixteen renowned researchers will give plenary keynotes, addressing current challenges in computational biomechanics and biomedical imaging. In Lisbon, for the first time, a session dedicated to award the winner of the Best Paper in CMBBE Journal will take place. We believe that CMBBE2018 will have a strong impact on the development of computational biomechanics and biomedical imaging and visualization, identifying emerging areas of research and promoting the collaboration and networking between participants. This impact is evidenced through the well-known research groups, commercial companies and scientific organizations, who continue to support and sponsor the CMBBE meeting series. In fact, the conference is enriched with five workshops on specific scientific topics and commercial software.info:eu-repo/semantics/draf

Numerical and experimental investigation of droplet actuation by surface acoustic waves

Surface acoustic waves (SAWs) technology for manipulating small volumes of liquids has received much attention in recent years. SAW-based manipulation can be used for different bio-sampling functions, such as mixing, heating, pumping, jetting, separation, and atomization of droplets with volumes in the scale of microliters. Most studies in recent years have mainly focused on investigating SAW potential in different real-world microfluidics applications. However, the underlying physics of the droplet deformation by SAW still remains controversial. This thesis aims to investigate droplet deformations subjected to SAWs using both numerical and experimental methods. Different types of SAW devices with various resonant frequencies and different substrates are fabricated to carry out droplet actuation experiments. The experimental models are developed for three main reasons. First, to analyse the droplet deformation; second, to accurately define the contact angle boundary condition needed for simulations; and third, to validate the computational model. A Coupled Level Set Volume of Fluid (CLSVOF) mathematical model is developed to investigate the large deformation of sessile droplet induced by SAWs. A dynamic contact angle boundary condition is implemented to model the droplet three-phase contact line (TPCL) movement. The numerical and experimental results are quantitatively and qualitatively compared, and a remarkable agreement is achieved, which proves that the developed computational model can be used to simulate different droplet actuation scenarios. After validation of the computational model, it is used for analysing the physics of the droplet jetting and pumping. The effects of important factors such as droplet volume and SAW frequency and power on droplet pumping are investigated. Moreover, the model is used to analyse the energy budget of a droplet jetting. An investigation into the optimization of the interdigital transducers (IDT) location of the SAW devices for different microfluidic applications is also carried out using the computational model. The experimental and computational models are then employed to investigate a novel application of SAW devices to control the droplet impact. SAWs devices are used to manipulate and control the droplet dynamics. The experimental results revealed that characteristic impact parameters such as impact regime, contact time, maximum spreading and re-bouncing angle could be modified and controlled by SAWs. By changing the SAW direction and power, droplets impact behaviour can be altered. The maximum reduction of contact time up to ∼50% can be achieved, along with alterations of droplet spreading, re-bouncing angle, and movement along the inclined surfaces. On the other hand, numerical results revealed that the SAWs could be used to modify and control the internal velocity fields inside the droplet. By breaking the symmetry of the internal recirculation patterns inside the droplet during the impact on flat surfaces, the kinetic energy recovered from interfacial energy during the retraction process is increased, and the droplet can be entirely separated from the surface with a much shorter contact time. Also, numerical results revealed that applying SAWs modifies the energy budget inside the liquid medium on both flat and inclined surface, leading to different impact behaviours. This innovative paradigm opens up new opportunities to actively program and controls the droplet impact on smooth or planar and curved surfaces, as well as rough or textured surfaces