| Abstract: | The classical stability theory for multiphase flows, based on an analysis of one (most unstable) mode, is generalized. A method
for studying an algebraic (non-modal) instability of a disperse medium, which consists in examining the energy of linear combinations
of three-dimensional modes with given wave vectors, is proposed. An algebraic instability of a dusty-gas flow in a plane channel
with a nonuniform particle distribution in the form of two layers arranged symmetrically with respect to the flow axis is
investigated. For all possible values of governing parameters, the optimal disturbances of the disperse flow have zero wavenumber
in the flow direction, which indicates their banded structure (“streaks”). The presence of dispersed particles in the flow
increases the algebraic instability, since the energy of optimal disturbances in the disperse medium exceeds that for the
pure-fluid flow. It is found that for a homogeneous particle distribution the increase in the energy of optimal perturbations
is proportional to the square of the sum of unity and the particle mass concentration and is almost independent of particle
inertia. For a non-uniform distribution of the dispersed phase, the largest increase in the initial energy of disturbances
is achieved in the case when the dust layers are located in the middle between the center line of the flow and the walls. |
