PhD Thesis Work
The hot-dip galvanisation process
My PhD involved the development of optimal numerical modelling methods for the impact of water droplets onto hot galvanised steel surfaces. The solidification of the molten zinc layer (galvanisation) on top of the sheet while being impinged by water droplets within a spray gave rise to a cratered or roughened surface which best binds to other materials such as concrete. The thesis concentrated on the difficult problem of three phase flow, areas of specific concern were how best to:
· impose boundary conditions at a fluid-fluid interface and track it
accurately while it undergoes severe deformation and disruption
· maintain and impose incompressibility within each fluid as well as the
boundaries over the whole solution time
· model fluid advection and viscosity in the presence of high density ratio
fluid-fluid interfaces
Research Contributions
The solution of this problem was formulated within a one-field model using an Eulerian-Lagrangian mesh-particle discretisation of immersed fluid-fluid interfaces avoiding the need to separately impose interfacial boundary conditions and taking advantage of each of these techniques. This is categorised in terms of interface tracking and as a general multiphase flow solver:
Lagrangian Interface Tracking: this research possesses some unique advantages over other previously developed interface tracking methods:
· Particles were assigned to track only fluid phase information this avoids the various instabilities
which persist in pure particle methods but possesses several advantages.
· Fluid colour is assigned permanently to each fluid so that fluid identity is maintained throughout the
flow.
· Colour information is interpolated to the underlying grid in only one direction avoiding artificial
numerical diffusion of fluid interfaces.
· Fluid identity is conserved at smaller than grid resolution thereby avoiding artificial numerical surface
tension which results in the non-physical clumping of fluid blobs.
· The method is of second order accuracy while maintaining a constant interfacial transition width no
matter the severity of interface disruption. These results were published in Computers & Fluids.
Eulerian Multiphase Flow Solver: The interface tracking method I developed in the previous paper was combined with an approximate projection method to ensure incompressibility up to second order while avoiding grid decoupling in the pressure and velocity. The Godunov method was used to accurately advect fluid velocities without inducing instabilities during rapid changes of material properties across fluid interfaces. Pressure correction is implemented within the variable density solver so that artificial numerical boundary layers are not present. The method showed promising behaviour when measured against the experimentally determined radial spread factor for the droplet-solid impact and cavity depth for the droplet-liquid impact problem.
· impose boundary conditions at a fluid-fluid interface and track it
accurately while it undergoes severe deformation and disruption
· maintain and impose incompressibility within each fluid as well as the
boundaries over the whole solution time
· model fluid advection and viscosity in the presence of high density ratio
fluid-fluid interfaces
Research Contributions
The solution of this problem was formulated within a one-field model using an Eulerian-Lagrangian mesh-particle discretisation of immersed fluid-fluid interfaces avoiding the need to separately impose interfacial boundary conditions and taking advantage of each of these techniques. This is categorised in terms of interface tracking and as a general multiphase flow solver:
Lagrangian Interface Tracking: this research possesses some unique advantages over other previously developed interface tracking methods:
· Particles were assigned to track only fluid phase information this avoids the various instabilities
which persist in pure particle methods but possesses several advantages.
· Fluid colour is assigned permanently to each fluid so that fluid identity is maintained throughout the
flow.
· Colour information is interpolated to the underlying grid in only one direction avoiding artificial
numerical diffusion of fluid interfaces.
· Fluid identity is conserved at smaller than grid resolution thereby avoiding artificial numerical surface
tension which results in the non-physical clumping of fluid blobs.
· The method is of second order accuracy while maintaining a constant interfacial transition width no
matter the severity of interface disruption. These results were published in Computers & Fluids.
Eulerian Multiphase Flow Solver: The interface tracking method I developed in the previous paper was combined with an approximate projection method to ensure incompressibility up to second order while avoiding grid decoupling in the pressure and velocity. The Godunov method was used to accurately advect fluid velocities without inducing instabilities during rapid changes of material properties across fluid interfaces. Pressure correction is implemented within the variable density solver so that artificial numerical boundary layers are not present. The method showed promising behaviour when measured against the experimentally determined radial spread factor for the droplet-solid impact and cavity depth for the droplet-liquid impact problem.
Current Research
The bag break-up process
Multiphase flows
Research during my Cardiff postdoc has further expanded the previously developed multiphase flow code to take into account surface forces and the inclusion of outflow conditions to allow truncation of the computational domain. The new code has been applied to:
Droplet Break-Up: This problem is commonly encountered in diesel engine fuel sprays and in spray cooling or painting. Experimental observations demonstrate different break-up modes depending on critical Weber number including: vibrational, bag, sheet stripping and catastrophic break-up. The method was able to accurately model both vibrational and sheet stripping behaviour although the bag break-up process requires higher resolutions as this instability occurs at length scales below the resolution used. (published in International Journal for Numerical Methods in Fluids)
Mesh-free methods
It is thought that a mesh-free method is best able to model the break-up process of multiphase viscoelastic fluids. Smoothed Particle Hydrodynamics (SPH) method is a well developed technique for modelling the motion of fluids without recourse to an underlying grid. The earliest such methods were designed for use in astrophysics where domain boundaries such as the no-slip condition did not play a role. In order for this method to be able to accurately and robustly simulate multiphase flows confined within a limited domain it must be able to satisfy given boundary conditions to high accuracy.
The Treatment of Boundary Conditions in SPH: The particle deficiency problem in the presence of a rigid wall in SPH arises from insufficient information being available to perform accurate interpolation of data at particles located nearer to the boundary than the support of the interpolation kernel. I developed a consistent treatment of no-slip boundary conditions, utilising the momentum equation to obtain approximations to the velocity of image particles, is described. The method is validated for Poiseuille and Couette flow, for which analytical series solutions exist(published in Computer Methods in Applied Mechanics and Engineering)
Research during my Cardiff postdoc has further expanded the previously developed multiphase flow code to take into account surface forces and the inclusion of outflow conditions to allow truncation of the computational domain. The new code has been applied to:
Droplet Break-Up: This problem is commonly encountered in diesel engine fuel sprays and in spray cooling or painting. Experimental observations demonstrate different break-up modes depending on critical Weber number including: vibrational, bag, sheet stripping and catastrophic break-up. The method was able to accurately model both vibrational and sheet stripping behaviour although the bag break-up process requires higher resolutions as this instability occurs at length scales below the resolution used. (published in International Journal for Numerical Methods in Fluids)
Mesh-free methods
It is thought that a mesh-free method is best able to model the break-up process of multiphase viscoelastic fluids. Smoothed Particle Hydrodynamics (SPH) method is a well developed technique for modelling the motion of fluids without recourse to an underlying grid. The earliest such methods were designed for use in astrophysics where domain boundaries such as the no-slip condition did not play a role. In order for this method to be able to accurately and robustly simulate multiphase flows confined within a limited domain it must be able to satisfy given boundary conditions to high accuracy.
The Treatment of Boundary Conditions in SPH: The particle deficiency problem in the presence of a rigid wall in SPH arises from insufficient information being available to perform accurate interpolation of data at particles located nearer to the boundary than the support of the interpolation kernel. I developed a consistent treatment of no-slip boundary conditions, utilising the momentum equation to obtain approximations to the velocity of image particles, is described. The method is validated for Poiseuille and Couette flow, for which analytical series solutions exist(published in Computer Methods in Applied Mechanics and Engineering)
Multi-Droplet Interaction in Spray Impingement
Multiple droplet impact and film build up
It is often claimed that the characteristic impact behaviour of an individual spray droplet may be extrapolated to multiple droplets within the spray. However upon the simulation of up to three impacting droplets this is found to be very different. Provided the impacting droplets are within the influence zone of each other the droplets will interact significantly (published in proceedings of ILASS 08).
The Role of Neighbouring Droplets in the Spray Break-Up Process
The interaction between two impacting droplets
The surface to volume ratio of fuel droplets within a diesel engine determines combustion efficiency so that an understanding of spray break-up is to this process. The break-up of individual droplets follows well known behaviour although how nearby droplets in the spray influence this process is not well understood. The numerical simulation of the break-up behaviour of two equally sized droplets in two distinct geometrical configurations shows that the break up of each droplet is strongly influenced by the presence of the other (published in proceedings of ILASS 08).
The Drop Formation Process
The drop formation process: drop pinch-off
During a previous postdoc in 2010-2011 working at the University of Leeds I modified existing Lagrangian finite element code, originally designed to simulate the inkjet process, in order to model the drop formation process which occurs at the larger length and time scales required for the pill printing process:
Operability Windows in the Industrial Drop Formation Process: GlaxoSmithKline has developed a way of printing active pharmaceutical ingredients onto tablets. Printing onto pre-formed tablets speeds up and improves quality control, as each tablet contains exactly the correct dose as well as being faster acting. This study developed a computational tool to accurately predict the behaviour of the printing process, subject to the operating conditions of the plant equipment and the properties of the fluid itself. These operability diagrams are an important tool for use in the industrial process. (poster at the GSK Process Modelling Conference, 2010)
Operability Windows in the Industrial Drop Formation Process: GlaxoSmithKline has developed a way of printing active pharmaceutical ingredients onto tablets. Printing onto pre-formed tablets speeds up and improves quality control, as each tablet contains exactly the correct dose as well as being faster acting. This study developed a computational tool to accurately predict the behaviour of the printing process, subject to the operating conditions of the plant equipment and the properties of the fluid itself. These operability diagrams are an important tool for use in the industrial process. (poster at the GSK Process Modelling Conference, 2010)
Research Agenda
My experience in engineering and industrial research has shown me the importance of two aspects in the modelling process. Firstly, in model methodology: the development of new mathematical models and the construction of innovative numerical methods and secondly: the application of these newly developed models/methods in the solution of complex natural, engineering and industrial problems.
Research Directions
Eulerian-Lagrangian Model Methodology
Physical modelling & numerical compatibility: typically such mathematical models involve the modelling of complex physical systems and the solution of the associated partial differential equations for reasons (i) involving the interaction of continuous (Eulerian) and discrete (Lagrangian) media, e.g. soil erosion through water-drop impact, and (ii) of numerical compatibility, e.g. the interaction of multiphase flows in an Eulerian medium involving the solution of multiple material advection equations for which a Lagrangian description is ideal.
One-Field Models, Variational Principles & Optimised EL Systems: a fuller development ofthe one-field approach as a general tool for multi-physics problems which allows the interaction of multiple physical forces within a single framework incorporating multiple materials: solid, elastic, fluid while still allowing interfacial immersed boundaries conditions to be satisfied in a natural way. This involves the process whereby a continuous EL model is created so that many of the internal aspects of the model, such as immersed forces, may be constructed. A similar process is proposed in order to optimise a numerical discretisation of the original continuous EL system so that error growth is minimised.
Applications
Research Directions
Eulerian-Lagrangian Model Methodology
Physical modelling & numerical compatibility: typically such mathematical models involve the modelling of complex physical systems and the solution of the associated partial differential equations for reasons (i) involving the interaction of continuous (Eulerian) and discrete (Lagrangian) media, e.g. soil erosion through water-drop impact, and (ii) of numerical compatibility, e.g. the interaction of multiphase flows in an Eulerian medium involving the solution of multiple material advection equations for which a Lagrangian description is ideal.
One-Field Models, Variational Principles & Optimised EL Systems: a fuller development ofthe one-field approach as a general tool for multi-physics problems which allows the interaction of multiple physical forces within a single framework incorporating multiple materials: solid, elastic, fluid while still allowing interfacial immersed boundaries conditions to be satisfied in a natural way. This involves the process whereby a continuous EL model is created so that many of the internal aspects of the model, such as immersed forces, may be constructed. A similar process is proposed in order to optimise a numerical discretisation of the original continuous EL system so that error growth is minimised.
Applications
Phase Change
Boiling
The extension of one-field and mesh-particle models to compressible flows involving true phase change: solidification, e.g. the icing up of aircraft wings, boiling, e.g. the modelling of nucleate, transition and film boiling, combustion, e.g. ignition of fuel droplets, bubbles, e.g. the collapse of vapour bubbles near a ship’s propeller.
Biological Flows
Wind seed dispersal
for example: the wind dispersal of seeds is a function of the presence of wind to lift the seeds and the structures used by the seeds to remain aloft. These kinds of structures, immersed within an ambient fluid may be examined in order to determine the maximum dispersal of seed. Other examples of biological flows include cell motility in bacterial chemotaxis, as well as filter and suspension feeding.
Soil Erosion
Rainsplash erosion
the application of multi-physics, multi-phase one-field methods to the mathematical modelling of the poorly understood raindrop induced splash erosion (rainsplash) process. This involves a model able to capture all of the significant features of the process such as cratering, splashing and flow transport of loosened soil particles within a water-soil suspension flow.