Ambit of Multiphase CFD in Modelling Transport Processes Related to Oil Spill Scenario and Microfluidics

During the ‘Deepwater Horizon’ accident in the deep sea in 2010, about 4.9 million barrels of oil was released into the Gulf of Mexico, making the spill one of the worst ocean spills in recent times. To mitigate the ill effects of the event on the environment, subsea injection of dispersants was carried out. Dispersant addition lowers the interfacial tension at oil/water interface and presence of local turbulence enhances the droplet disintegration process. The oil droplets contain a plethora of hydrocarbons which are soluble in water. In deep spill scenarios, droplets spend large amounts of time in water column; hence, the dissolution process of soluble hydrocarbons becomes important. In this study, our focus is to exploit the capabilities of multiphase CFD in developing an integrated numerical model which accounts for various transport processes and hence would effectively guide us in predicting the fate of oil mass. In the initial stages, studies were conducted to understand these transport processes at a very fundamental level where the effect of surfactant, on the dynamics of crude oil, droplet rising in a stagnant column, was investigated. To capture the subsurface dissolution of hydrocarbons from oil droplet, a unique experiment was devised wherein a binary organic mixture, representing a pseudo oil droplet comprising of volatile and non-volatile hydrocarbons, was employed to study the effect of unsteady mass transport on the overall dynamics of the droplet. In the next phase of project, we developed a numerical model, by integrating traditional multiphase CFD models and turbulence models, with a population balance (PB) approach, for predicting the droplet size distribution resulting from the interaction of turbulent oil jets with the surrounding quiescent environment. Apart from the simulations specific to oil spill related situations, the multiphase CFD was also employed to study the fluid flow in micro-channels. The mass transfer mechanisms in micro-channels for immiscible fluids in squeezing and dripping regimes were studied by employing the numerical model, which couples the features of the traditional Volume of fluid method and the Continuous Species transport approach for evaluating the concentration fields inside dispersed and continuous phase

Estimating pressure and internal-wave flux from laboratory experiments in focusing internal waves

Instantaneous measurements of pressure and wave flux in stratified incompressible flows are presented for the first time using combined time-resolved particle image velocimetry (PIV) and synthetic schlieren (SS). Corrections induced by variations of the refractive index in this strongly density-stratified fluid are also considered. The test case investigated here is a three-dimensional geometry consisting of a Gaussian ring-type topography forced by an oscillating tide representative of geophysical applications. Density and pressure are reconstructed from SS or PIV in combination with linear theories and combined SS-PIV. We perform a direct comparison between the experimental results and three-dimensional direct numerical simulations of the same flow conditions and control parameters. In particular, we show that the estimated velocity or density and the hence wave flux from linear theory solely based on SS or PIV can be flawed in regions of focusing internal waves. We also show that combined measurements of SS and PIV are capable of circumventing these limitations and accurately reproduce the results computed from the DNS

Scattering of internal gravity waves

Internal gravity waves play a fundamental role in the dynamics of stably stratified regions of the atmosphere and ocean. In addition to the radiation of momentum and energy remote from generation sites, internal waves drive vertical transport of heat and mass through the ocean by wave breaking and the mixing subsequently produced. Identifying regions where internal gravity waves contribute to ocean mixing and quantifying this mixing are therefore important for accurate climate and weather predictions. Field studies report significantly enhanced measurements of turbulence near ‘rough’ ocean topography compared with those recorded in the ocean interior or near more gradually varying topography (e.g. Toole et al. 1997, J. Geophys. Res. 102). Such observations suggest that interaction of waves with rough topography may act to skew wave energy spectra to high wavenumbers and hence promote wave breaking and fluid mixing. This thesis examines the high wavenumber scatter and spatial partitioning of wave energy at ‘rough’ topography containing features that are of similar scales to those characterising incident waves. The research presented here includes laboratory experiments using synthetic schlieren and PIV to visualise two-dimensional wavefields produced by small amplitude oscillations of cylinders within linear salt-water stratifications. Interactions of wavefields with planar slopes and smoothly varying sinusoidal topography are compared with those with square-wave, sawtooth and pseudo knife-edge profiles, which have discontinuous slopes. Far-field structures of scattered wavefields are compared with linear analytical models. Scatter to high wavenumbers is found to be controlled predominantly by the relative slopes and characterising length scales of the incident wavefield and topography, as well as the shape and aspect ratio of the topographic profile. Wave energy becomes highly focused and the spectra skewed to higher wavenumbers by ‘critical’ regions, where the topographic slope is comparable with the slope of the incident wave energy vector, and at sharp corners, where topographic slope is not defined. Contrary to linear geometric ray tracing predictions (Longuet-Higgins 1969, J. Fluid Mech. 37), a significant back-scattered field can be achieved in near-critical conditions as well as a forward scattered wavefield in supercritical conditions, where the slope of the boundary is steeper than that of the incident wave. Results suggest that interaction with rough benthic topography could efficiently convert wave energy to higher wavenumbers and promote fluid mixing in such ocean regions.This work was supported by the Natural Environment Research Council [grant number NER/S/A/2003/11205]

Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence

We consider the closure problem for turbulence in the dry convective atmospheric boundary layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large plumes in the well mixed middle part up to the inversion that separates the CBL from the stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02) that additionally includes a term for background turbulence. Thus an exact solution is derived and all higher order moments (HOMs) are explained by second order moments, correlation coefficients and the skewness. The solution provides a proof of the extended universality hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi- normality of FOM). This refined hypothesis states that CBL turbulence can be considered as result of a linear interpolation between the Gaussian and the very skewed turbulence regimes. Although the extended universality hypothesis was confirmed by results of field measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained unexplained. These are now answered by the new model including the reasons of the universality of the functional form of the HOMs, the significant scatter of the values of the coefficients and the source of the magic of the linear interpolation. Finally, the closures 61 predicted by the model are tested against measurements and LES data. Some of the other issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area coverage parameters of plumes (so called filling factors) with HOM will be discussed also

Triadic Resonance Instability in finite-width internal gravity wave beams

Through the use of both experiments and theoretical modelling, this thesis examines the weakly non-linear dynamics of an internal wave beam becoming unstable to Triadic Resonance Instability (TRI). To date, most theoretical work examines the instability in the context of monochromatic plane waves. In the ocean, however, waves seldom take this form, rather they manifest as beams that span the wavenumber spectra. With an aim of developing our understanding of the role of TRI in oceanic settings, this thesis focuses on how the instability evolves in finite-width internal wave beams. Experiments have been conducted using a new generation of wave maker, featuring a flexible horizontal bottom boundary driven by an array of independently controlled actuators. Using this wavemaker, finite-width internal wave beams of varying amplitude were generated in a linear stratification. Novel experimental results show that when one of these beams becomes unstable via TRI, the approach to a saturated equilibrium state for the triadic waves is not monotonic, rather their amplitudes continue to oscillate without reaching a steady equilibrium. Further diagnostics reveal how the frequencies of the two secondary waves involved in the resonant triad also modulate over time. This behaviour is shown to be a result of the finite spatial extent of the primary beam, which causes cyclic growth and decay of different triadic perturbations. As previously published literature does not consider the triadic energy exchange to be a function of space, it is unable to predict this oscillatory behaviour. Theoretical modelling is developed to capture the essence of the experimental setup. The model uses numerical solutions of a weakly non-linear system in a two-dimensional framework. A detailed study looks at how different wavenumbers and frequencies of the secondary waves affect the development of TRI in a finite-width beam. The results show how the orientation of the secondary waves has a strong influence on the evolution of the instability, as this determines the duration over which the triadic energy exchange can occur. By including multiple possible resonant waves in the system, the results also capture both the amplitude and frequency oscillations exhibited experimentally. This model not only recapitulates the experimental findings, but provides a tool for the community to dissect the underlying dynamics of the instability. Both the experimental and theoretical findings presented in this thesis reveal novel insights into how TRI evolves in finite-width internal wave beams. This work thus provides a key to understanding how this instability mechanism may manifest in oceanic scenarios and its potential role in global ocean circulation.National Environmental Research Council (NERC) grant no. NE/L002507/

Notes on the 1974 summer study program in geophysical fluid dynamics at the Woods Hole Oceanographic Institution

This year the central topic was the general circulation of the oceans. Some of the basic ideas used in wind-driven and thermohaline studies were presented in the introductory course of lectures and simple models that have guided our thinking in the development of the topic were discussed. As part of the introductory lectures Peter Niiler developed a model of the mixed layer, exploring the reasoning and the parameterization behind the theories of this important boundary region at the surface of the ocean. Dennis Moore gave a careful account of transient flows in equatorial regions and showed how dynamical conditions on the eastern and western boundaries are satisfied by a superposition of planetary, Kelvin and Yanai waves. Peter Rhines concluded the series with a discussion of topographically induced low frequency motions. At the request of the students Joseph B. Keller gave a lecture on "Solution of Partial Differential Equations by Ray Theory".National Science Foundatio