Viscous laminar axially symmetric free mixing with large swirl is investigated by a boundary-layer type of analysis with integral methods. Large swirl generates axial pressure gradients as well as large radial pressure gradients, and therefore alters the streamwise flow. Examples calculated for both incompressible and compressible flow show that the wake may be significantly lengthened by large swirl. However, this effect is shown to be diminished in the compressible case where higher free-stream Mach numbers lead to decreased densities, and to decreased centrifugal effects, decreased radial pressure gradients, and decreased axial pressure gradients. In the limiting special case of small or moderate swirl the results agree with those previously obtained by Steiger and Bloom [1] in analysis wherein the induced pressure gradients were neglected a priori.
A linearized model of an ideal diatomic gas with diffusion processes and rate reaction is applied to one-dimensional unsteady motion generated by initial nonuniformities of state and velocity. The time-dependent system resembles that of steady free-mixing of jet or wake type, with two space coordinates. The temporal and spatial character of the profiles of flow variables is studied analytically under two sets of conditions. First considered is the case of unit Lewis number and for this case the investigation is subdivided as follows: (i) Zero mass motion with state nonuniformities for planar, cylindrical, and spherical configurations; and (ii) nonzero mass motion with state nonuniformities for the planar and cylindrical configurations. Secondly, the case of arbitrary, but constant, Lewis number is considered. In this instance, the investigation is limited to nonzero mass motion with state nonuniformities in the planar geometry. In all cases the Prandtl number is assumed to be an arbitrary constant. Analytic solutions are obtained for all cases and various parametric effects discussed.
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