William B. Bush

Asymptotic Analysis of Laminar Flame Propagation for General Lewis Numbers

Abstract The structure of a steady one-dimensional isobaric deflagration is examined for the case of a direct first-order one-step irreversible exothermic unimolecular decomposition under Arrhenius kinetics. In particular, the eigenvalue giving the speed of propagation of the laminar flame into the unburned gas is sought for constant Lewis number of order unity. The method of matched asymptotic expansion is invoked in the physically interesting limit of activation temperature large relative to the adiabatic flame temperature. The leading approximation for the eigenvalue is found to be a generalization of the result given by Zeldovich, Frank-Kamenetski, and Semenov for Lewis number unity. The first two terms in the asymptotic expansion for the eigenvalue yield an expression superior to any previously published.

On the viscous hypersonic blunt-body problem

The viscous hypersonic flow past an axisymmetric blunt body is analysed based upon the Navier-Stokes equations. It is assumed that the fluid is a perfect gas having constant specific heats, a constant Prandtl number, P , whose numerical value is of order one, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied as the free-stream Mach number, M , and the free-stream Reynolds number based on the body nose radius, R , go to infinity, and e = (γ − 1)/(γ + 1), where γ is the ratio of the specific heats, and δ = 1/(γ − 1) M 2 go to zero.

Asymptotic Analysis of the Structure of a Steady Planar Detonation

Abstract The structure of a steady planar Chapman-Jouguet detonation, which is supported by a direct firstorder one-step irreversible exothermic unimolecular reaction, subject to Arrhenius kinetics, is examined. Solutions are studied, by means of a limit process expansions analysis, valid for A, proportional to the ratio of the reaction rate to the flow rate, going to zero, and fl, proportional to the ratio of the activation temperature to the maximum flow temperature, going to infinity, with the product Aβ going to zero. The results, essentially in agreement with the Zeldovich-von Neumann.Doring model, show that the detonation consists of ( 1) a two region upstream

Asymptotic Analysis of Turbulent Channel Flow for Mixing-Length Theory.

Limit process expansion techniques are used to analyze fully developed turbulent incompressible flow in an infinitely long channel with plane parallel walls. Closure of the Reynolds time-averaged equations of motion is effected through the introduction of a model for the eddy viscosity that is a generalization and modification of the model of mixing length theory. Expansions are carried out in the limit of the turbulent Reynolds number (the ratio of the eddy viscosity to the molecular viscosity) going to infinity. To leading orders of approximation, it is determined that the flow divides into : a relatively thick turbulent centerline defect layer, where the Reynolds turbulent stress dominates the Newton laminar stress ; and a thin viscous wall layer, where the Reynolds and Newton stresses are of comparable magnitude. By proceeding to higher orders of approximation, however, it is determined that this two-layer formulation for the flow is not uniformly valid. For completeness, a very thin laminar wall laye...

Asymptotic Analysis of Turbulent Channel Flow for Mean Turbulent Energy Closures.

The Reynolds time‐averaged equations are adopted for fully turbulent two‐dimensional flow of an incompressible fluid through a channel with plane smooth walls. Closure is effected by means of so‐called second‐order methods based on the conservation of mean turbulent kinetic energy. In particular, generalizations of the turbulent shear flow models due to Bradshaw and co‐workers and to Spalding and co‐workers, are adopted as representative of recent differential closure models. The models are treated in the limit of large turbulent Reynolds number by means of limit‐process expansions. The principal division of the flow is into a relatively thick defect layer near the center of the channel (in which the channel half‐width characterizes the layer thickness, the velocity may be linearized about its centerline speed, and the Reynolds stress dominates the Newtonian stress to lowest order), and the relatively thin viscous sublayer near the wall (in which a viscous length scale is appropriate, the velocity is smal...

On Diffusion Flames in Turbulent Shear Flows: Modeling Reactant Consumption in a Planar Fuel Jet†

Abstract The turbulent portion of the planar fuel jet, for isobaric subsonic flow, under fast direct one-step irreversible reaction between unpremixed fuel and oxidant, is analyzed. Mean spatial profiles for the dependent variables are found numerically and analytically from the governing nonlinear partial differential equations, based on an explicit eddy diffusion and on a mean rate of reactant consumption proportional to the product of the mean mass fraction of fuel, the mean mass fraction of oxidant and the appropriate local characterization of the mean rate of strain. Results from the model are qualitatively, and, in many cases, quantitatively, compatible with experimental data.

An Asymptotic Analysis of Strong Radiation-Resisted Normal Shock Waves

An asymptotic analysis is presented for the structure of a strong radiation-resisted normal shock wave in a gray gas. Previous solutions for the weak and strong radiation cases are reviewed and modified; then, new analytical and numerical solutions for the moderate radiation case are developed. Analytical solutions for the flow quantities at the imbedded discontinuity as functions of the radiation parameter, valid over the range of the parameter, are derived.

THE SLIP-DOMINATED MERGED LAYER REGIME FOR NEWTONIAN HYPERSONIC FLOW PAST A FLAT PLATE*

The rarefied uniform hypersonic flow past the leading edge of a sharp flat plate at zero angle of attack is analyzed on the basis of a continuum model consisting of the Navier–Stokes equations and the velocity-slip and temperature-jump plate boundary conditions. The model fluid is a perfect gas having constant specific heats, a constant Prandtl number of order unity, and first and second viscosity coefficients varying as a power of the absolute temperature. For this flow, it is taken that the Newtonian parameter,

Hypersonic strong-interaction similarity solutions for flow past a flat plate

\varepsilon = ( {\gamma - 1} )/( {\gamma + 1} )

Continuum theory of spherical electrostatic probes (frozen chemistry)

, goes to zero, and that the freestream Mach number,