Effect of thermal expansion on the stability of two-reactant flames

The full problem of flame stability for the two-reactant model, which takes into account thermal expansion effects for all disturbance wave lengths, is examined. It is found that the stability problem for the class of two-reactant flames is equivalent to the stability problem for the class of one-reactant flames with an appropriate interpretation of Lewis numbers

An asymptotic analysis of supersonic reacting mixing layers

The purpose of this paper is to present an asymptotic analysis of the laminar mixing of the simultaneous chemical reaction between parallel supersonic streams of two reacting species. The study is based on a one-step irreversible Arrhenius reaction and on large activation energy asymptotics. Essentially it extends the work of Linan and Crespo to include the effect of free shear and Mach number on the ignition regime, the deflagration regime and the diffusion flame regime. It is found that the effective parameter is the product of the characteristic Mach number and a shear parameter

Absolute/convective instabilities and the convective Mach number in a compressible mixing layer

Two aspects of the stability of a compressible mixing layer: Absolute/Convective instability and the convective Mach number were considered. It was shown that, for Mach numbers less than one, the compressible mixing layer is convectively unstable unless there is an appreciable amount of backflow. Also presented was a rigorous derivation of a convective Mach number based on linear stability theory for the flow of a multi-species gas in a mixing layer. The result is compared with the heuristic definitions of others and to selected experimental results

Inviscid spatial stability of a compressible mixing layer. Part 3: Effect of thermodynamics

The results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow are reported. The models are: (1) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; (2) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (3) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity temperature relation and arbitrary but constant Prandtl number. The purpose was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the quantative features of the stability characteristics are quite similiar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, it is shown that the stability characteristics are sensitive to the value of the Prandtl number

Inviscid spatial stability of a compressible mixing layer. Part 2: The flame sheet model

The results of an inviscid spatial calculation for a compressible reacting mixing layer are reported. The limit of infinitive activation energy is taken and the diffusion flame is approximated by a flame sheet. Results are reported for the phase speeds of the neutral waves and maximum growth rates of the unstable waves as a function of the parameters of the problem: the ratio of the temperature of the stationary stream to that of the moving stream, the Mach number of the moving streams, the heat release per unit mass fraction of the reactant, the equivalence ratio of the reaction, and the frequency of the disturbance. These results are compared to the phase speeds and growth rates of the corresponding nonreacting mixing layer. We show that the addition of combustion has important, and complex effects on the flow stability

Zero wavenumber modes of a compressible supersonic mixing layer

It is shown that there exists a family of supersonic neutral modes for a compressible mixing layer in an unbounded domain. These modes have zero wavenumber and frequency with nonzero phase speed. They are analogous to the supersonic neutral modes of the compressible vortex sheet found by Miles. The results presented give a more complete picture of the spectrum of the disturbances in this flow

Stability of a non-orthogonal stagnation flow to three dimensional disturbances

A similarity solution for a low Mach number nonorthogonal flow impinging on a hot or cold plate is presented. For the constant density case, it is known that the stagnation point shifts in the direction of the incoming flow and that this shift increases as the angle of attack decreases. When the effects of density variations are included, a critical plate temperature exists; above this temperature the stagnation point shifts away from the incoming stream as the angle is decreased. This flow field is believed to have application to the reattachment zone of certain separated flows or to a lifting body at a high angle of attack. Finally, the stability of this nonorthogonal flow to self similar, 3-D disturbances is examined. Stability properties of the flow are given as a function of the parameters of this study; ratio of the plate temperature to that of the outer potential flow and angle of attack. In particular, it is shown that the angle of attack can be scaled out by a suitable definition of an equivalent wavenumber and temporal growth rate, and the stability problem for the nonorthogonal case is identical to the stability problem for the orthogonal case

Effect of heat release on the spatial stability of a supersonic reacting mixing layer

A numerical study of the stability of compressible mixing layers in which a diffusion flame is embedded is described. The mean velocity profile has been approximated by a hyperbolic tangent profile and the limit of infinite activation energy taken, which reduces the diffusion flame to a flame sheet. The addition of combustion in the form of a flame sheet was found to have important, and complex, effects on the flow stability

Ignition and structure of a laminar diffusion flame in a compressible mixing layer with finite rate chemistry

The ignition and structure of a reacting compressible mixing layer is considered using finite rate chemistry lying between two streams of reactants with different freestream speeds and temperatures. Numerical integration of the governing equations show that the structure of the reacting flow can be quite complicated depending on the magnitude of the Zeldovich number. An analysis of both the ignition a diffusion flame regimes is presented using a combination of large Zeldovich number asymptotics and numerics. This allows to analyze the behavior of these regimes as a function of the parameters of the problem