Abstract
A modified Rayleigh equation has been derived for the study of spatial instability of gas–particle two-phase mixing layers. The particles are assumed to have a material density much greater than the carrier fluid. The mathematical model is based on the assumptions that the mean flow profile can be approximated as that of the particle-free single-phase mixing layer and that the two phases are in dynamic equilibrium at the start of the perturbation. The resulting eigenvalue problem was solved numerically. The major finding from the analysis is that the presence of the particles enhances the stability of the two-phase flow and decreases the amplification rate of perturbations in the flow. The results show that the stability of the flow is enhanced with increased particle loading and decreased free-stream velocity ratio. For a given free-stream velocity ratio, the most amplified growth rates decrease almost linearly with the particle loading. The most amplified growth rate, however, occurs near the same angular frequency as that of the particle-free flow. The effect of particle on the perturbation phase velocity is most significant for smaller values of the angular frequency. However, the presence of particles does not change the phase velocity at the angular frequency corresponding to the most amplified rate for the single-phase flow. The phase velocity of the perturbations is slower compared to particle-free flows for modes with frequencies below the maximum amplified frequency, while it is the opposite for modes at frequencies above the maximum amplified frequency. The profiles of streamwise and cross-stream velocity fluctuations are also modified by the existence of particles. The magnitude of effects is related closely to the particle loading. For temporal instability of a two-phase mixing layer, the growth rate in time decreases linearly with increasing particle loading, which is consistent with the spatial instability results.
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