David W. Mikolaitis

The interaction of flame curvature and stretch, part 1: The concave premixed flame

Premixed flames with radii of curvature on the order of the preheat zone thickness are studied with activation energy asymptotics. The changes in flame speed caused by varying the flame stretch as the flame radius is held fixed are calculated. The result of this calculation is that the decrease in flame speed due to flame stretch is amplified by more highly curved flames. When there is no flame stretch, the flame speed is independent of the flame radius, and so flame curvature in and of itself does not alter flame speed, but is important in determining the changes in flame speed when stretch is present.

Flow Control in a Driven Cavity Incorporating Excitation Phase Differential

Control of fluid flow is particularly difficult because of inherent nonlinearity in the Navier‐Stokes equations and high dimensionality of typical approximations of these equations. A control design is demonstrated for flow restricted to creeping flow within a driven cavity. Such a restriction allows linear reduced-order models to be generated as state-space systems. In particular, these models are generated as subspaces of the flow where each model represents modes associated with phase differential between exogenous disturbances. A linear parametervarying controller is designed to account for the range of dynamics introduced by the phase differential among subspaces. The controller is introduced to the reduced-order models, which contain individual phase-differential subspaces, and the full-order model, which contains all phase-differential subspaces, for disturbance attenuation. These closed-loop simulations show that the gain-scheduled controller, designed for individual subspaces, is able to reduce the flow velocity along the centerline of the cavity significantly for the full-order flow.

The interaction of flame curvature and stretch, part 2: The convex premixed flame

Abstract Premixed flames with radii of curvature of the order of the preheat zone thickness are studied with activation energy asymptotics. The flames studied are convex to the fresh mixture and the flame stretch is negative as in Bunsen burner flame tips. Solutions are found which correspond to flame speeds well in excess of the adiabatic flame speed.

Adiabatic Flame Speeds and the Zeldovich-Li[nbar]án Model

Abstract The Zeldovich-Li[nbar]an model, originally proposed by Zeldovich and analyzed asymptotically by Li[nbar]an, has recently been analyzed by Joulin et al. (1985) under a particular distinguished limit. The limit considered by Joulin et al. only has solutions with algebraically small concentrations of radicals in the neighborhood of a particular flame temperature. For flame temperatures above this, the concentration of radicals becomes 0(1) whereas for flame temperatures below the pivotal value the concentration of radicals become exponentially small. Joulin et al. do not discuss this aspect of the problem but it is demonstrated here. Flame structures with only algebraically small radical concentrations can be found for all reasonable flame temperatures under the limit of large activation energy and large heat release. Such a limit does not predict gross qualitative changes in the flame structure as the flame temperature crosses a pivotal value. This limit also predicts adiabatic flame speeds without...

The cylindrical stretched flame

For sufficiently cool remote gases, the cylindrical stretched flame shows classical ignition-extinction behavior. For remote gas temperatures close to the adiabatic flame temperature, the flame response is qualitatively different, with negative flame speed solutions which may be physically accessible.

Stretched spherical cap flames

Abstract Convex spherical cap flames with negative flame stretch and concave spherical cap flames with positive flame stretch are analyzed using activation energy asymptotics. A minimum flame radius is calculated for concave flames and this results is favorably compared with experimental data on quenching diameters.

The unsteady propagation of premixed flames through nonhomogeneous mixtures and thermal gradients

Abstract Recent advances in the mathematical study of unsteady laminar premixed flames have required the imposition of nearly constant flame temperature. This condition disallows investigations into such fundamentally important problems as flame propagation into thermal gradients and regions of varying equivalence ratio. Here a rational method of analysis is presented to derive asymptotic solutions for one-dimensional unsteady propagation of deflagration waves with O(1) flame temperature variations. The propagations of premixed flames down thermal and concentration gradients are studied as example problems.

An Asymptotic Analysis of the Induction Phases of Hydrogen-Air Detonations

An analysis of the induction stages for near stoichiometric and very lean hydrogen-air detonations is given under the limit of large activation energy. The asymptotic results are then compared to numerical calculations of the complete mechanism for a 30 percent and a 10 percent H2-air detonation wave.

LINEAR PARAMETER-VARYING FLOW CONTROL FOR A DRIVEN CAVITY USING REDUCED-ORDER MODELS

Flow control can potentially impact many engineering applications; however, the design of such controllers is extremely challenging. Some of the reasons for the challenging nature of this control design problem is the complexity of the uid dynamics, inherent nonlinearity and the associated numerical cost of computation. The degree of dicult y is increased when the boundary conditions or functional parameters change through control intervention during the normal evolution of the system. This paper presents a method to model uid dynamics and design associated o w controllers using the linear parameter-varying framework. The formulation of a model which is amenable to control design makes use of proper orthogonal decomposition to derive reduced-order representations of the open-loop uid dynamics. The resulting representations are shown to depend anely on a parameter, which is dened as the product of the Strouhal number and the Reynolds number, in a linear parameter-varying fashion. Controllers are then designed for this special model that are scheduled to work across a range of the parameter. A disturbance rejection problem is solved to demonstrate how this method generates controllers that achieve desired levels of performance even acting on the full-order nonlinear system.

Strained Laminar Premixed Flames

Abstract Plane, strained premixed flames governed by one-step Arrhenius kinetics are analyzed under conditions where the activation temperature of the reaction is large compared to the temperature of the remote reactants but is comparable to the temperature of the product gas stream. This gives rise to a problem where the activation energy non-dimensionalized with respect to the remote reactant temperature is large but the Zeldovich number is 0( I). In such a formulation the mass burning rate found at the inflection point of the temperature profile and the mass burning rate at the point where the second derivative of the temperature profile is minimized are distinctly different functions of the flame stretch.