Michael Booty

Interaction of pulsating and spinning waves in condensed phase combustion

We employ a nonlinear stability analysis in the neighborhood of a multiple bifurcation point to describe the interaction of pulsating and spinning modes of condensed phase combustion. Such phenomena occur in the synthesis of refractory materials. In particular, we consider the propagation of combustion waves in a long thermally insulated cylindrical sample and show that steady, planar combustion is stable for a modified activation energy/melting parameter less than a critical value. Above this critical value primary bifurcation states, corresponding to time-periodic pulsating and spinning modes of combustion, emanate from the steadily propagating solution. By varying the sample radius, we split a multiple bifurcation point to obtain bifurcation diagrams which exhibit secondary, tertiary, and quaternary branching to various types of quasi-periodic combustion waves.

Influence of insoluble surfactant on the deformation and breakup of a bubble or thread in a viscous fluid

The influence of surfactant on the breakup of a prestretched bubble in a quiescent viscous surrounding is studied by a combination of direct numerical simulation and the solution of a long-wave asymptotic model. The direct numerical simulations describe the evolution toward breakup of an inviscid bubble, while the effects of small but non-zero interior viscosity are readily included in the long-wave model for a fluid thread in the Stokes flow limit. The direct numerical simulations use a specific but realizable and representative initial bubble shape to compare the evolution toward breakup of a clean or surfactant-free bubble and a bubble that is coated with insoluble surfactant. A distinguishing feature of the evolution in the presence of surfactant is the interruption of bubble breakup by formation of a slender quasi-steady thread of the interior fluid. This forms because the decrease in surface area causes a decrease in the surface tension and capillary pressure, until at a small but non-zero radius, equilibrium occurs between the capillary pressure and interior fluid pressure. The long-wave asymptotic model, for a thread with periodic boundary conditions, explains the principal mechanism of the slender threads formation and confirms, for example, the relatively minor role played by the Marangoni stress. The large-time evolution of the slender thread and the precise location of its breakup are, however, influenced by effects such as the Marangoni stress and surface diffusion of surfactant.

Steady deformation and tip-streaming of a slender bubble with surfactant in an extensional flow

Slender-body theory is used to investigate the steady-state deformation and time-dependent evolution of an inviscid axisymmetric bubble in zero-Reynolds-number extensional flow, when insoluble surfactant is present on the bubble surface. The asymptotic solutions reveal steady ellipsoidal bubbles covered with surfactant, and, at increasing deformation, solutions distinguished by a cylindrical surfactant-free central part, with stagnant surfactant caps at the bubble endpoints. The bubble shapes are rounded near the endpoints, in contrast to the pointed shapes found for clean inviscid bubbles. Simple expressions are derived relating the capillary number Q to the steady bubble slenderness ratio e

Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid

In a previous study [M. Hameed et al., J. Fluid Mech. 594, 307 (2008)] the authors investigated the influence of insoluble surfactant on the evolution of a stretched, inviscid bubble surrounded by a viscous fluid via direct numerical simulation of the Navier–Stokes equations, and showed that the presence of surfactant can cause the bubble to contract and form a quasisteady slender thread connecting parent bubbles, instead of proceeding directly toward pinch-off as occurs for a surfactant-free bubble. Insoluble surfactant significantly retards pinch-off and the thread is stabilized by a balance between internal pressure and reduced capillary pressure due to a high concentration of surfactant that develops during the initial stage of contraction. In the present study we investigate the influence of surfactant solubility on thread formation. The adsorption-desorption kinetics for solubility is in the diffusion controlled regime. A long-wave model for the evolution of a capillary jet is also studied in the St...

Synthetic fuel for imitation of municipal solid waste in experimental studies of waste incineration

Synthetic fuel is prepared to imitate municipal solid waste (MSW) in experimental studies of incineration processes. The fuel is composed based on the Environmental Protection Agency reports on the materials contained in MSW. Uniform synthetic fuel pellets are prepared using available and inexpensive components including newsprint, hardwood mulch, low density polyethylene, iron, animal feed, sand, and water to imitate paperbound, wood, yard trimming, plastic, metal, food wastes, and other materials in MSW. The synthetic fuel preparation procedure enables one to reproduce and modify the fuel for a wide range of experiments in which the mechanisms of waste incineration are addressed. The fuel is characterized using standard ASTM tests and it is shown that its parameters, such as combustion enthalpy, density, as well as moisture, ash and fixed carbon contents are adequate for the representation of municipal solid waste. In addition, chlorine, nitrogen, and sulfur contents of the fuel are shown to be similar to those of MSW. Experiments are conducted in which the synthetic fuel is used for operation of a pilot-scale incinerator research facility. Steady-state temperature operation regimes are achieved and reproduced in these experiments. Thermodynamic equilibrium flame conditions are computed using an isentropic one-dimensional equilibrium code for a wide range of fuel/air ratios. The molecular species used to represent the fuel composition included cellulose, water, iron, polyethylene, methanamine, and silica. The predicted concentrations of carbon monoxide, nitric oxides, and oxygen in the combustion products are compared with the respective experimental concentrations in the pilot-scale incinerator exhaust.

The accommodation of traveling waves of Fisher's type to the dynamics of the leading tail

Traveling wave solutions for equations of Fisher’s type are given by a connection from a saddle point to a node, and their velocity for large times is known to be determined by the spatial decay rate of the initial conditions far ahead of the wave. To understand this phenomenon in simple terms, initial conditions are considered that correspond to a traveling wave, but with an exponential decay rate far ahead of the wave that varies slowly in the region referred to as the leading tail. The wave that results is supersonic in the sense that the speed of the core of the traveling wave is greater than the velocity of the characteristics, or group velocity, in the leading tail. Consequently, the speed of the core adjusts to accommodate the slowly varying decay rate in the leading tail. A generalization is also considered that includes Fishers equation, for which traveling waves with a stable exponential tail corresponding to a node are supersonic.

Numerical simulation of drop and bubble dynamics with soluble surfactant

Numerical computations are presented to study the effect of soluble surfactant on the deformation and breakup of an axisymmetric drop or bubble stretched by an imposed linear strain flow in a viscous fluid. At the high values of bulk Peclet number Pe in typical fluid-surfactant systems, there is a thin transition layer near the interface in which the surfactant concentration varies rapidly. The large surfactant gradients are resolved using a fast and accurate “hybrid” numerical method that incorporates a separate, singular perturbation analysis of the dynamics in the transition layer into a full numerical solution of the free boundary problem. The method is used to investigate the dependence of drop deformation on parameters that characterize surfactant solubility. We also compute resolved examples of tipstreaming, and investigate its dependence on parameters such as flow rate and bulk surfactant concentration.

ANALYTICAL AND COMPUTATIONAL METHODS FOR TWO-PHASE FLOW WITH SOLUBLE SURFACTANT ∗

A hybrid method is used to determine the influence of surfactant solubility on two-phase flow by solution of a reduced transition layer equation near a fluid interface in the limit of large bulk Peclet number. The method is applied to finding the evolution of a drop of arbitrary viscosity that is deformed by an imposed linear strain or simple shear flow. A semianalytical solution of the transition layer equation is given that expresses exchange of surfactant between its bulk and interfacial forms in terms of a convolution integral in time. Results of this semianalytical solution are compared with the results of a spatially spectrally accurate numerical solution. Although both the hybrid method and its semianalytical solution are valid in three dimensions, the two-dimensional context of this study allows additional validation of results by comparison with those of conformal mapping techniques applied to inviscid bubbles.

REFLECTION AND TRANSMISSION FROM A THIN INHOMOGENEOUS CYLINDER IN A RECTANGULAR TE10 WAVEGUIDE

We study the scattering problem for a thin cylindrical target that is placed with arbitrary orientation in a rectangular TE10 waveguide and subjected to an imposed electromagnetic field. The scattered far-field is expressed in terms of the scattered field inside the target and the far-field expansion of the dyadic Greens function for the waveguide. In order to capture features of interest in microwave heating applications, we allow the target materials electrical properties to be arbitrary functions of position along the thin cylindrical targets axis. Reflection and transmission coefficients for such a target, and an expression for the rate of deposition of electromagnetic energy within it are derived.

Microwave-induced combustion: a one-dimensional model

A model for the heating and ignition of a combustible solid by microwave energy is formulated and analysed in the limit of small inverse activation energy and small Biot number B. The high activation energy limit implies that the heating process is effectively inert until the temperature within the material reaches a critical ignition value, while the small Biot number limit implies that during this stage spatial variations in temperature throughout the material are always small. Analysis of the inert stage includes determination of the dynamics of inert hot-spots. As the ignition temperature is approached chemical energy is released rapidly in the form of heat, and the evolution then enters an ignition stage which develops on a fast time-scale. A reduced system is derived governing small-amplitude departures of the temperature from the inert value during the ignition stage under the significant scaling relation between the expansion parameters, which is shown to be ~ B. This reduced system recovers both ...