Francis E. Fendell

Asymptotic Analysis of Turbulent Channel and Boundary Layer Flow.

Abstract : Asymptotic expansion techniques are used in the limit of large Reynolds number, to study the structure of fully turbulent shear layers. Two cases examined are channel (or pipe) flow and two-dimensional boundary layer flow with an applied pressure gradient, upstream of any separation. Attention, for these two cases, is confined to the flow of incompressible constant-property fluids. Closure is effected through the introduction of an eddy viscosity model formulated with sufficient generality so that most existing models are special cases.

Wind-Aided Firespread Across Arrays of Discrete Fuel Elements. II. Experiment

Abstract Laboratory-scale experiments on wind-aided firespread across an array of very-small-diameter (1.3-4.4-mm), discrete fuel elements were carried out in a specially designed wind tunnel. The rate of firespread, ty, is inferred from the output of streamwise-disiributed, near-bed-surface thermocouples. The fuel consists of an array of identical, regularly arranged, wooden, toothpick-like Tuel elements, positioned upright in shallow holes drilled in a ceramic substrate. Adoption of this well-defined fuel bed facilitates repetition. Extensive testing suggests that νy ∼ (U/m)1/2 over a wide range of the uniform ambient wind speed U and the fuel-mass distribution m (fuel, per unit planform area of the bed, consumed with firefront passage). The effects on the firespread rate of other parameters investigated and reported include the type of wood species; fuel-element length; fuel-element diameter; fuel-bed width, including streamwise-varyjng width; enhanced moisture content of the substratum and/or fuel; sm...

Stoichiometry and Flameholder Effects on a One-Dimensional Flame

Abstract The steady one-dimensional isobaric combustion of a gaseous premixture of fuel and oxidant under a direct one-step irreversible Arrhenius-type exothermic chemical reaction is studied analytically for constant, but general, Lewis-Semenov number. Limit-process expansions are used to obtain solutions in the physically interesting limit of activation temperature large relative to the hot-boundary temperature. The eigenvalue or critical flow speed for an adiabatic system is established as a function of departure from stoichiometry. It is emphasized that, for relatively small departures from stoichiometry, the bimolecular system behaves as a monopropellant decomposition, to lowest order of approximation, because the richer reactant is effectively undepleted. The porous-disk-type flameholder for a flat-flame burner is modeled as a (nonadiabatic) heat source (supercritical flow speed) or heat sink (subcritical flow speed). The flame stand-off distance and the amount of departure of the hot-boundary tempe...

Laminar natural convection about an isothermally heated sphere at small Grashof number

The flow induced by gravity about a very small heated isothermal sphere introduced into a fluid in hydrostatic equilibrium is studied. The natural-convection flow is taken to be steady and laminar. The conditions under which the Boussinesq model is a good approximation to the full conservation laws are described. For a concentric finite cold outer sphere with radius, in ratio to the heated sphere radius, roughly less than the Grashof number to the minus one-half power, a recirculating flow occurs; fluid rises near the inner sphere and falls near the outer sphere. For a small heated sphere in an unbounded medium an ordinary perturbation expansion essentially in the Grashof number leads to unbounded velocities far from the sphere; this singularity is the natural-convection analogue of the Whitehead paradox arising in three-dimensional low-Reynolds-number forced-convection flows. Inner-and-outer matched asymptotic expansions reveal the importance of convective transport away from the sphere, although diffusive transport is dominant near the sphere. Approximate solution is given to the nonlinear outer equations, first by seeking a similarity solution (in paraboloidal co-ordinates) for a point heat source valid far from the point source, and then by linearization in the manner of Oseen. The Oseen solution is matched to the inner diffusive solution. Both outer solutions describe a paraboloidal wake above the sphere within which the enthalpy decays slowly relative to the rapid decay outside the wake. The updraft above the sphere is reduced from unbounded growth with distance from the sphere to constant magnitude by restoration of the convective accelerations. Finally, the role of vertical stratification of the ambient density in eventually stagnating updrafts predicted on the basis of a constant-density atmosphere is discussed.

Cyclic Absorption/Desorption of Gas in a Liquid Wall Film,

Abstract —The unsteady one-dimensional cyclic absorption and desorption of a dilute amount of gas in a thin (constant-thickness),isothermal (constant-property) liquid layer on an impervious noncatalytic wall is examined. The pertinent conditions are taken to be (1) thermodynamic equilibrium (such that Henrys law holds at the two-phase interface), and (2) diffusional resistance of the liquid layer being rate-controlling (such that the problems for the liquid layer, and for the bulk gas contiguous to it, decouple). Specifically, the mass fraction of the gaseous species of interest is taken to be known, and of square-wave periodic character, at the two-phase interface, so attention is concentrated on the total gaseous content of the liquid layer as a function of time. While start-up (in which the liquid layer is taken to be initially free of gaseous content) is considered, primary interest is in steady periodic operation in which no residual influence of the initial condition remains. The model is developed...

Wind-Aided Flame Spread Along a Horizontal Fuel Slab

Abstract The American Society of Testing and Materials test E84 is widely employed in North America to characterize the rate of flame spread along samples of material proposed for use in construction of buildings; by this test, materials, in part, are qualified with respect to fire safety for classes of application. In this ten-minute-duration test, an 8 meter slab of the material comprises the ceiling of a sealed duct (termed a Steiner tunnel) through which hot vitiated air (up to about 1150 K) flows after time zero at about 1.2 m/s. Materials are rated according to the distance from the leading edge that the wind-aided flame propagates (or, alternatively for samples that become totally involved, by the elapsed time to flameover at the downwind end). An unsteady two-spatial-dimensional model of this test has been undertaken, as a first step toward the goal of anticipating behavior of a sample from knowledge of its chemical and physical properties. In the formulation, at any fixed position along the sampl...

On diffusion flames in turbulent shear flows

Abstract For control and safety, combustion in engineering devices often concerns the burning of highly reactive, initially unmixed fuel and oxidant. The rate-controlling step is then the mixing of the reactants; further, turbulent mixing is known to be more rapid than laminar mixing. Thus, diffusion flames in turbulent shear flows arise in a wide variety of combustion problems, including propulsion and continuous chemical lasers. Toor has suggested a method by which the time-averaged solutions for the passive scalars in turbulent shear flows with the Lewis-Semenov number unity can be used to obtain the time-averaged solutions for the reactant mass fractions and the temperature in turbulent diffusion flames. This method is the turbulent analogue of that of Burke and Schumann, who have shown how solutions for the convection-diffusion of inert species in laminar flows can be used to obtain the reactant mass fractions and the temperature in laminar diffusion flames. Toors method does require knowledge of the probability distribution function for the states available to the fluctuating portion of the passive scalars involved. Because many lasers and propulsion devices are operated with mixing-rate-controlled combustion, because finite-rate reactions in turbulent flows necessitate adoption of speculative closures of the time-averaged law of mass action, and because the frozen and equilibrium limits are taken to bound the behaviors of unpremixed systems, there is motivation to implement the method of Toor. Closure schemes for turbulent shear layers should permit analytic prediction for the required mean fields of the passive scalars. Although these time-averaged boundary-value problems are usually solved numerically, recently, multiple-scaling techniques have been employed successfully in the limit of large turbulent Reynolds number to display important properties of the solutions. While experiment is necessary for the determination of the probability distribution functions, arguments can be made that these distribution functions depart significantly from frequently assumed Gaussian-type forms, so that predictions based on such normal distributions are of dubious accuracy.

Effect of Boundary Thermal Constraint on Planar Premixed-Flame/Wall Interaction

Abstract The unsteady one-dimensional laminar isobaric propagation of a flame toward a wall, through a homogeneous fuel-lean premixture, characterized by large activation temperature, is examined under a Shvab-Zeldovich-type formulation, via numerical integration by the method of lines with spline interpolation. In particular, the effect of the boundary thermal constraint and of the Lewis-Semenov number, on the propagation in the immediate vicinity of a noncatalytic impervious planar wall parallel to the flame, is examined. Both an isothermal-wall constraint, for a series of values ranging from the initial cold temperature of the unburned premixture to the bulk-burned-gas temperature, and also an adiabatic-wall constraint, are considered. Persistence of unburned residual fuel, and occurrence of either large wall temperature or large wall heat transfer, are insights of interest in the context of current and proposed internal-combustion automotive engines. It is found that the largest gas-phase temperatures...

Towards Wind-Aided Flame Spread Along a Horizontal Charring Slab: The Steady-Flow Problem

Abstract The spread of fire across the ceiling of a large room (or long corridor) is modeled as wind-aided flame spread along a horizontal char-forming thick slab, in the presence of significant convective, diffusive, and radiative transport. The goal is to predict the rate of streamwise advance of the site on the solid-gas interface at which the pristine solid undergoes endothermic degradation to a combination of (I) a porous carbonaceous heat-retaining matrix, and (2) a mixture of (partially combustible) vapors that move through the matrix to the outer gas. This rate of advance of the thermal-degradation site is sought as a function of normally available data concerning the thermodynamic and physical properties of the solid; the thermodynamic and dynamic state of the hot vitiated bulk gas that abruptly starts, and then continues, to flow over the slab; and the initial thermodynamic state of the slab. Downwind of the interfacial degradation site, hot product gases flowing over the slab preheat it from it...

On Diffusion Flames in Turbulent Shear Flows— the Two-Step Symmetrical Chain Reaction

Abstract Often in combustion engineering, when unpremixed gaseous reactants are burned in a low-speed shear flow, product formation is controlled by the rate of mixing, rather than by the rate of reaction. The reaction mechanism is usually modeled as a direct one-step irreversible reaction, with Lewis-Semenov number taken as unity. For laminar flow, Burke and Schumann suggested how knowledge of a passive scalar in the same flow field as the reactants, satisfying similar boundary conditions, and possessing identical diffusion coefficients, furnishes the diffusion-flame solution. Analogously, for the turbulent case, under almost identical constraints, Toor indicated how knowledge of the mean field and probability density function for a passive scalar in an inert flow yields the mean-field behavior of the turbulent diffusion flame in the same flow. The only additional condition is that, in general, the heat associated with chemical reaction must not alter the dynamics. Here, Toors method is extended to the ...