Marangoni flows are free-surface flows driven by gradients of surface tension. Because surface tension depends on chemical composition, Marangoni flows may be generated by the uneven distribution of surface-active species at an interface. The primary goal of this thesis is to develop a rigorous computational framework for the simulation of the fluid dynamical and interfacial phenomena underlying the physics of Marangoni flows. The focus is on characterizing the different dynamical regimes generated by the presence of surface-active species (surfactants) at an interface. The computational framework was developed using direct numerical simulation, that is, by simultaneously solving the full system of partial differential equations governing the free-surface flow and the surfactant transport on a continually deforming interface. Results from the simulations enabled detailed examination of the interfacial mechanisms of surfactant transport and provided a comprehensive picture of the free-surface flow. Analysis of the results established limits of applicability of scaling solutions previously proposed in the literature, calculated the necessary corrections, and also lead to the discovery of previously unobserved scaling laws in viscous Marangoni flows. New findings from this research not only enhance the fundamental understanding of the physics of Marangoni flows, but also the ability to accurately predict the behaviour of Marangoni flows and the associated transport of surface-active species, which is critical to the understanding of important natural and biomedical processes, ranging from the surfactant-driven propulsion of insects and microorganisms to the spreading of drugs and natural surfactants (proteins) in the eye and lungs. Controlled Marangoni transport of chemical species is also relevant to a wide range of environmental and technological processes, with applications ranging from cleaning of oil spills to coating of microfluidic devices.

Results from direct numerical simulations (DNS) of multiphase bubbly flows in vertical and horizontal channels were compared to averaged models of multiphase flows (two-fluid model etc.). The data from the direct numerical simulation were also used to calibrate and improve the averaged models. Steady state laminar flow in a vertical channel was analyzed first. Results from direct numerical simulations are compared with prediction of the steady-state two-fluid model of Antal, Lahey, and Flaherty (1991). The simulations are done assuming a two-dimensional system and the model coefficients are adjusted slightly to match the data for upflow. The model is then tested by comparisons with different values of flow rate and gravity, as well as down flow. Results agree reasonably in the middle of the channel. However, for upflow, model performs poorly near the no-slip wall. To better understand the flow with rising bubbles hugging the no-slip wall, detailed direct numerical simulations of the problem were performed in three dimensions. Deformability of the bubbles was found to play a significant role in the flow structure and averaged flow rate. Finally, the transient buoyancy driven motion of two-dimensional bubbles across a domain bounded by two horizontal walls is studied by. The bubbles are initially released next to the lower wall and as they rise, they disperse. Eventually all the bubbles collect at the top wall. The goal of the study is to examine how a simple one-dimensional model for the averaged void fraction captures the unsteady bubble motion. By using void fraction dependent velocities, where the exact dependency is obtained from simulations of homogeneous bubbly flows, the overall dispersion of the bubbles is predicted. Significant differences remain, however. Results suggest that bubble dispersion by the bubble induced liquid velocity must be included, and by using a simple model for the bubble dispersion improved agreement is found.

Direct numerical simulations (DNS) of an initially quiescent coupled air-water interface driven by an air flow with free stream speed of 5 m/s have been conducted. The DNS solves a scalar advection-diffusion equation for dissolved gas (or scalar) concentration in order to determine the impact of the water-side turbulence on scalar (mass) transfer from the air side to the water side and subsequent vertical transport in the water column. Two simulations are compared: one with a freely deforming interface and a second one with a flat interface. In the first simulation, the deforming interface evolves in the form of gravity-capillary waves generating aqueous Langmuir turbulence characterized by small-scale (centimeter-scale) Langmuir cells (LCs). The second simulation is characterized by pure shear-driven turbulence in the absence of LCs as the interface is intentionally held flat. It is concluded that the Langmuir turbulence serves to enhance vertical transport of the scalar in the water side and in the process increases scalar transfer efficiency relative to the shear-dominated turbulence in the flat interface case. Furthermore, transition to Langmuir turbulence was observed to be accompanied by a spike in scalar flux via molecular diffusion across the interface characterized by an order of magnitude increase. Such episodic flux increases, if linked to gusts and overall unsteadiness in the wind field, are expected to be an important contributor in determining the long-term average of the air-sea gas fluxes. The effectiveness of popular transfer velocity models, namely the small eddy model and the surface divergence model, in predicting this spike is evaluated via the DNS. In addition to LCs, DNS reveals that the water side turbulence is characterized by smaller, shear-driven turbulent eddies at the surface embedded within the LCs. LES with momentum equation augmented with the well-known Craik-Leibovich (C-L) vortex force is used to understand the roles of the wave and shear-driven LCs (i.e. the Langmuir turbulence) and the smaller shear-driven eddies (i.e. the shear turbulence) in determining molecular diffusive scalar flux from the air side to the water side and vertical scalar transport beneath. The C-L force consists of the cross product between the Stokes drift velocity (induced by the interfacial waves) and the flow vorticity. It is observed that Stokes drift shear intensifies the smaller eddies (with respect to purely wind-driven flow, i.e. without wave effects) leading to enhanced diffusive scalar flux at the air-water interface. LC leads to increased vertical scalar transport at depths below the interface and thus greater scalar transfer efficiency.

This thesis deals with numerical simulation of turbulentflows in geometrically simple cases. Both plane and cylindricalgeometries are used. The simplicity of the geometry allows theuse of spectral methods which yield a very high accuracy usingrelatively few grid points. A spectral method for planegeometries is implemented on a parallel computer. Thetransitional Reynolds number for plane Couette flow is verifiedto be about 360, in accordance with earlier findings. TurbulentCouette flow at twice the transitional Reynolds number isstudied and the findings of large scale structures in earlierstudies of Couette flow are substantiated. These largestructures are shown to be of limited extent and give anintegral length scale of six half channel heights, or abouteight times larger than in pressure-driven channel flow.Despite this, they contain only about 10 \% of the turbulentenergy. This is demonstrated by applying a very smallstabilising rotation, which almost eliminates the largestructures. A comparison of the Reynolds stress budget is madewith a boundary layer flow, and it is shown that the near-wallvalues in Couette flow are comparable with high-Reynolds numberboundary layer flow. A new spectrally accurate algorithm isdeveloped and implemented for cylindrical geometries andverified by studying the evolution of eigenmodes for both pipeflow and annular pipe flow. This algorithm is a generalisationof the algorithm used in the plane channel geometry. It usesFourier transforms in two homogeneous directions and Chebyshevpolynomials in the third, wall-normal, direction. TheNavier--Stokes equations are solved with a velocity-vorticityformulation, thereby avoiding the difficulty of solving for thepressure. The time advancement scheme used is a mixedimplicit/explicit second order scheme. The coupling between twovelocity components, arising from the cylindrical coordinates,is treated by introducing two new components and solving forthem, instead of the original velocity components. TheChebyshev integration method and the Chebyshev tau method isboth implemented and compared for the pipe flow case.

No description available.

Modern industrial society is based on combustion with ever increasing standards on the efficiency of burning. One of the main combustion characteristics is the burning rate, which is influenced by intrinsic flame instabilities, external turbulence and flame interaction with walls of combustor and sound waves. In the present work we started with the problem how to include combustion along the vortex axis into the general theory of turbulent burning. We demonstrated that the most representative geometry for such problem is a hypothetic “tube” with rotating gaseous mixture. We obtained that burning in a vortex is similar to the bubble motion in an effective acceleration field created by the centrifugal force. If the intensity of the vortex is rather high then the flame speed is determined mostly by the velocity of the bubble. The results obtained complement the renormalization theory of turbulent burning. Using the results on flame propagation along a vortex we calculated the turbulent flame velocity, compared it to the experiments and found rather good agreement. All experiments on turbulent combustion in tubes inevitably involve flame interaction with walls. In the present thesis flame propagation in the geometry of a tube with nonslip walls has been widely studied numerically and analytically. We obtained that in the case of an open tube flame interaction with nonslip walls leads to the oscillating regime of burning. The oscillations are accompanied by variations of the curved flame shape and the velocity of flame propagation. If flame propagates from the closed tube end, then the flame front accelerates with no limit until the detonation is triggered. The above results make a good advance in solving one of the most difficult problems of combustion theory, the problem of deflagration to detonation transition. We developed the analytical theory of accelerating flames and found good agreement with results of direct numerical simulations. Also we performed analytical and numerical studies of another mechanism of flame acceleration caused by initial conditions. The flame ignited at the axis of a tube acquires a “finger” shape and accelerates. Still, such acceleration takes place for a rather short time until the flame reaches the tube wall. In the case of flame propagating from the open tube end to the closed one the flame front oscillates and therefore generates acoustic waves. The acoustic waves reflected from the closed end distort the flame surface. When the frequency of acoustic mode between the flame front and the tube end comes in resonance with intrinsic flame oscillations the burning rate increases considerably and the flame front becomes violently corrugated.

The relative dispersion of one fluid particle with respect to another is fundamentally related to the transport and mixing of contaminant species in turbulent flows. The most basic consequence of Kolmogorov's 1941 similarity hypotheses for relative dispersion, the Richardson-Obukhov law that mean-square pair separation distance grows with the cube of time at intermediate times in the inertial subrange, is notoriously difficult to observe in the environment, laboratory, and direct numerical simulations (DNS). Inertial subrange scaling in size parameters like the mean-square pair separation requires careful adjustment for the initial conditions of the dispersion process as well as a very wide range of scales (high Reynolds number) in the flow being studied. However, the statistical evolution of the shapes of clusters of more than two particles has already exhibited statistical invariance at intermediate times in existing DNS. This invariance is identified with inertial-subrange scaling and is more readily observed than inertial-subrange scaling for seemingly simpler quantities such as the mean-square pair separation Results from dispersion of clusters of four particles (called tetrads) in large-scale DNS at grid resolutions up to 4096 points in each of three directions and Taylor-scale Reynolds numbers from 140 to 1000 are used to explore the question of statistical universality in measures of the size and shape of tetrahedra in homogeneous isotropic turbulence in distinct scaling regimes at very small times (ballistic), intermediate times (inertial) and very late times (diffusive). Derivatives of fractional powers of the mean-square pair separation with respect to time normalized by the characteristic time scale at the initial tetrad size constitute a powerful technique in isolating cubic time scaling in the mean-square pair separation. This technique is applied to the eigenvalues of a moment-of-inertia-like tensor formed from the separation vectors between particles in the tetrad. Estimates of the proportionality constant "g" in the Richardson-Obukhov law from DNS at a Taylor-scale Reynolds number of 1000 converge towards the value g=0.56 reported in previous studies. The exit time taken by a particle pair to first reach successively larger thresholds of fixed separation distance is also briefly discussed and found to have unexplained dependence on initial separation distance for negative moments, but good inertial range scaling for positive moments. The use of diffusion models of relative dispersion in the inertial subrange to connect mean exit time to "g" is also tested and briefly discussed in these simulations. Mean values and probability density functions of shape parameters including the triangle aspect ratio "w," tetrahedron volume-to-gyration radius ratio, and normalized moment-of-inertia eigenvalues are all found to approach invariant forms in the inertial subrange for a wider range of initial separations than size parameters such as mean-square gyration radius. These results constitute the clearest evidence to date that turbulence has a tendency to distort and elongate multiparticle configurations more severely in the inertial subrange than it does in the diffusive regime at asymptotically late time. Triangle statistics are found to be independent of initial shape for all time beyond the ballistic regime. The development and testing of different schemes for parallelizing the cubic spline interpolation procedure for particle velocities needed to track particles in DNS is also covered. A "pipeline" method of moving batches of particles from processor to processor is adopted due to its low memory overhead, but there are challenges in achieving good performance scaling.

<p>This thesis deals with numerical simulation of turbulentflows in geometrically simple cases. Both plane and cylindricalgeometries are used. The simplicity of the geometry allows theuse of spectral methods which yield a very high accuracy usingrelatively few grid points. A spectral method for planegeometries is implemented on a parallel computer. Thetransitional Reynolds number for plane Couette flow is verifiedto be about 360, in accordance with earlier findings. TurbulentCouette flow at twice the transitional Reynolds number isstudied and the findings of large scale structures in earlierstudies of Couette flow are substantiated. These largestructures are shown to be of limited extent and give anintegral length scale of six half channel heights, or abouteight times larger than in pressure-driven channel flow.Despite this, they contain only about 10 \% of the turbulentenergy. This is demonstrated by applying a very smallstabilising rotation, which almost eliminates the largestructures. A comparison of the Reynolds stress budget is madewith a boundary layer flow, and it is shown that the near-wallvalues in Couette flow are comparable with high-Reynolds numberboundary layer flow. A new spectrally accurate algorithm isdeveloped and implemented for cylindrical geometries andverified by studying the evolution of eigenmodes for both pipeflow and annular pipe flow. This algorithm is a generalisationof the algorithm used in the plane channel geometry. It usesFourier transforms in two homogeneous directions and Chebyshevpolynomials in the third, wall-normal, direction. TheNavier--Stokes equations are solved with a velocity-vorticityformulation, thereby avoiding the difficulty of solving for thepressure. The time advancement scheme used is a mixedimplicit/explicit second order scheme. The coupling between twovelocity components, arising from the cylindrical coordinates,is treated by introducing two new components and solving forthem, instead of the original velocity components. TheChebyshev integration method and the Chebyshev tau method isboth implemented and compared for the pipe flow case.</p>

No description available.

abstract: Many methods of passive flow control rely on changes to surface morphology. Roughening surfaces to induce boundary layer transition to turbulence and in turn delay separation is a powerful approach to lowering drag on bluff bodies. While the influence in broad terms of how roughness and other means of passive flow control to delay separation on bluff bodies is known, basic mechanisms are not well understood. Of particular interest for the current work is understanding the role of surface dimpling on boundary layers. A computational approach is employed and the study has two main goals. The first is to understand and advance the numerical methodology utilized for the computations. The second is to shed some light on the details of how surface dimples distort boundary layers and cause transition to turbulence. Simulations are performed of the flow over a simplified configuration: the flow of a boundary layer over a dimpled flat plate. The flow is modeled using an immersed boundary as a representation of the dimpled surface along with direct numerical simulation of the Navier-Stokes equations. The dimple geometry used is fixed and is that of a spherical depression in the flat plate with a depth-to-diameter ratio of 0.1. The dimples are arranged in staggered rows separated by spacing of the center of the bottom of the dimples by one diameter in both the spanwise and streamwise dimensions. The simulations are conducted for both two and three staggered rows of dimples. Flow variables are normalized at the inlet by the dimple depth and the Reynolds number is specified as 4000 (based on freestream velocity and inlet boundary layer thickness). First and second order statistics show the turbulent boundary layers correlate well to channel flow and flow of a zero pressure gradient flat plate boundary layers in the viscous sublayer and the buffer layer, but deviates further away from the wall. The forcing of transition to turbulence by the dimples is unlike the transition caused by a naturally transitioning flow, a small perturbation such as trip tape in experimental flows, or noise in the inlet condition for computational flows. / Dissertation/Thesis / M.S. Mechanical Engineering 2011