A theoretical formulation and analysis is presented for a study of
the stability and interaction of coherent structure in reacting
free shear layers. The physical problem under investigation is a
premixed hydrogen-oxygen reacting shear layer in the wake of a thin
flat plate. The coherent structure is modeled as a periodic
disturbance and its stability is determined by the application of
linearized hydrodynamic stability theory which results in a
generalized eigenvalue problem for reactive flows. Detailed
stability analysis of the reactive wake for neutral, symmetrical
and antisymmetrical disturbance is presented. Reactive stability
criteria is shown to be quite different from classical non-reactive
stability. The interaction between the mean flow, coherent
structure and fine-scale turbulence is theoretically formulated
using the von-Kaman integral technique. Both time-averaging and
conditional phase averaging are necessary to separate the three
types of motion. The resulting integro-differential equations can
then be solved subject to initial conditions with appropriate shape
functions. In the laminar flow transition region of interest, the
spatial interaction between the mean motion and coherent structure
is calculated for both non-reactive and reactive conditions and
compared with experimental data wherever available. The fine-scale
turbulent motion determined by the application of integral analysis
to the fluctuation equations. Since at present this turbulence
model is still untested, turbulence is modeled in the interaction
problem by a simple algebraic eddy viscosity model. The
applicability of the integral turbulence model formulated here is
studied parametrically by integrating these equations for the
simple case of self-similar mean motion with assumed shape
functions. The effect of the motion of the coherent structure is
studied and very good agreement is obtained with previous
experimental and theoretical works for non-reactive flow.
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