Generalized breakup and coalescence models for population balance modelling of liquid-liquid flows

Population balance framework is a useful tool that can be used to describe size distribution of droplets in a liquid-liquid dispersion. Breakup and coalescence models provide closures for mathematical formulation of the population balance equation (PBE) and are crucial for accu- rate predictions of the mean droplet size in the ow. Number of closures for both breakup and coalescence can be identi ed in the literature and most of them need an estimation of model parameters that can di er even by several orders of magnitude on a case to case basis. In this paper we review the fundamental assumptions and derivation of breakup and coalescence ker- nels. Subsequently, we rigorously apply two-stage optimization over several independent sets of experiments in order to identify model parameters. Two-stage identi cation allows us to estab- lish new parametric dependencies valid for experiments that vary over large ranges of important non-dimensional groups. This be adopted for optimization of parameters in breakup and co- alescence models over multiple cases and we propose a correlation based on non-dimensional numbers that is applicable to number of di erent ows over wide range of Reynolds numbers

A non-inertial two-phase model of wax transport in a pipeline during pigging operations

The removal of wax deposit from pipelines is commonly accomplished using pigs. In order to avoid the formation of wax plugs in pipes, bypass pigs, which create a liquid jet to disperse the scraped deposit, are employed. Despite many One-Dimensional (1D) models have been developed to predict the dynamics of bypass pigs, the details of the interaction between the liquid jet and the debris have not been investigated numerically yet. In this work the fluid dynamics of a wax-in-oil slurry in front of a moving bypass pig is studied by means of three-dimensional (3D) numerical simulations. A mathematical model which couples the pig and the wax-in-oil slurry dynamics, solved in the pig frame of reference, has been developed. The results show that the pig quickly reaches an equilibrium velocity, and the pig acceleration is proportional to the square of the mixture relative velocity. Comparing the present with previous sealing-pig results it appears that the bypass flow is more effective in deterring plug formation. Moreover, the 3D fields have the advantage of showing the wax distribution in each pipe section whereas the 1D model cannot distinguish between deposited and suspended wax

A computational framework for modelling infectious disease policy based on age and household structure with applications to the COVID-19 pandemic

The widespread, and in many countries unprecedented, use of non-pharmaceutical interventions (NPIs) during the COVID-19 pandemic has highlighted the need for mathematical models which can estimate the impact of these measures while accounting for the highly heterogeneous risk profile of COVID-19. Models accounting either for age structure or the household structure necessary to explicitly model many NPIs are commonly used in infectious disease modelling, but models incorporating both levels of structure present substantial computational and mathematical challenges due to their high dimensionality. Here we present a modelling framework for the spread of an epidemic that includes explicit representation of age structure and household structure. Our model is formulated in terms of tractable systems of ordinary differential equations for which we provide an open-source Python implementation. Such tractability leads to significant benefits for model calibration, exhaustive evaluation of possible parameter values, and interpretability of results. We demonstrate the flexibility of our model through four policy case studies, where we quantify the likely benefits of the following measures which were either considered or implemented in the UK during the current COVID-19 pandemic: control of within- and between-household mixing through NPIs; formation of support bubbles during lockdown periods; out-of-household isolation (OOHI); and temporary relaxation of NPIs during holiday periods. Our ordinary differential equation formulation and associated analysis demonstrate that multiple dimensions of risk stratification and social structure can be incorporated into infectious disease models without sacrificing mathematical tractability. This model and its software implementation expand the range of tools available to infectious disease policy analysts

Mathematical and computational methods of non-Newtonian, multiphase flows

The research presented in this thesis is concerned with the development of numerical techniques and mathematical models for non-Newtonian uids and two-phase ows in pipes and channels. Single phase, turbulent ow calculations of non-Newtonian uids were performed initially. Based on the literature a revised approach to wall modelling is proposed and implemented. The approach uses analytical and experimental analyses of the turbulent boundary layer structure. A comparison with the standard approach is presented. The interaction between turbulence and non-Newtonian behaviour is studied by examining the rate of strain induced by uctuating components of velocity. The statistical analysis of published DNS data is performed. Finally, a model is proposed where the turbulent rate of strain is determined from turbulence quantities used by the Reynolds-averaged Navier{Stokes model and used in the calculation of molecular viscosity. For two-phase ow, the solution procedure using periodic boundary conditions was developed under an assumption of a at interface. The numerical technique was veri ed by comparing to an analytical result obtained for laminar ow in a channel. An extension to three dimensional ow is performed. With periodic boundary conditions standard turbulence models are applied to two-phase strati ed ow. Several models and their corrections for twophase ow are assessed and a new model is proposed. The numerical studies were carried out primiarily in the open-source code OpenFOAM, but initial attempts were made in commercial packages such as STAR-CD and FLUENT. Experimental data collected from the literature are used to verify the results showing good agreement in pressure drops and phase fractions

Uncertainty Quantification at the Molecular–Continuum Model Interface †

Non-equilibrium molecular dynamics simulations are widely employed to study transport fluid properties. Observables measured at the atomistic level can serve as inputs for continuum calculations, allowing for improved analysis of phenomena involving multiple scales. In hybrid modelling, uncertainties present in the information transferred across scales can have a significant impact on the final predictions. This work shows the influence of force-field variability on molecular measurements of the shear viscosity of water. In addition, the uncertainty propagation is demonstrated by quantifying the sensitivity of continuum velocity distribution to the particle-based calculations. The uncertainty is modelled with polynomial chaos expansion using a non-intrusive spectral projection strategy. The analysis confirms that low-order polynomial basis are sufficient to calculate the dispersion of observables

Thermal Transients in a U-Bend

We study numerically the propagation of a hot thermal transient through a U-bend via an ensemble of wall-resolved large eddy simulations. Conjugate heat transfer between fluid and solid domains is accounted for. The flow is in a fully turbulent mixed convection regime, with a bulk Reynolds number of $10,000$, a Richardson number of $2.23$, and water as the working fluid (Prandtl number = $6$). These conditions lead to strong thermal stratification, with buoyancy-induced secondary flows, and the generation of a large and persistent recirculation region. The evolution of Dean vortices as the thermal transient passes is studied. It is found that baroclinic vorticity generation dominates over a large period of the transient, due to the thermal inertia of the wall. Gravitational buoyancy leads to a reversal of the counter-rotating vortex pair. The impact of this reversal on the swirl-switching and secondary-current losses is assessed. It is found that low frequency modes are suppressed in the reversed-vortex state.Comment: Accepted manuscrip