Inviscid Dynamics of Two-Dimensional Shear Layers

Abstract

The dynamics of unconfined, spatially developing shear layers is studied by numerical solutions of the time-dependent Euler equations using a second-order Godunov scheme. Effects of density and velocity variations between the two streams of the shear layer are studied and color graphics is used to show more clearly the entrainment process of the surrounding streams. The calculations demonstrated that the evolution of the mean flow was dominated by two-dimensional, inviscid effect.s. The I.m.s. fluctuating velocity and density profiles were found to be in good agreement with the measurements of Oster and \\'ygnanski and of Konrad, except for the peak value of the v' profile.

A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier–Stokes Equations

“…These profiles are the same profiles as were used by Chien et al [13], expect for the inclusion of the random perturbation in the density field. The inflow velocity profile as a function of time was…”

“…Consequently this disagreement may be an artifact of the small number of temporal samples. (Chien et al [13] report needing several thousand samples to compute accurate statistics.) The perturbational density profile matches the overall structure of the experimental profile.…”

“…The data for the problem were chosen to model the conditions studied by Brown and Roshko [12] and Konrad [18] who were studying the effects of density variation on low speed shear layers. Although the experimental shear layer was unforced, we have added forcing, using frequencies taken from Monkewitz and Huerre [22] as was done by Chien et al [13] for their two-dimensional simulations of shear layers.…”

“…However, the projection as defined by Eqs. (13) and (14) is a discrete orthogonal projection onto a larger velocity space (in the finite element sense) which is then averaged onto the grid. The resulting approximate projection satisfies the divergence constraint to second-order accuracy and the overall algorithm is stable.…”

Heterogeneous Continuum Model of Aluminum Particle Combustion in Explosions

“…The scheme ability to follow vorticity intensification during the transition to a turbulent flow was described by Bell and Marcus [35]. The scheme was also used to predict the transition in the Kelvin-Helmholtz shear layers; the computed mean and second-moment profiles were found to be in good agreement with the measured profiles [36].…”