Abstracts - KTH Mechanics

140
Stability of dusty gas flow in a vertical channel
S.A. Boronin a, A.N. Osiptsov a
The problem of laminar-turbulent transition in 2D dusty-gas flows was
considered in a number of studies using the Saffman 1 formulation or its small
modifications 2 , in which velocity slip of the phases in the basic flow was
ignored. It was shown that the presence of even a small amount of particles
can significantly change the limits of the laminar flow regime. In the present
study, dealing with the stability of a vertical channel flow with inertial particles,
we modify the Saffman formulation and focus on the role of phase velocity
slip in the basic flow (caused by the gravity force) in laminar-turbulent
transition.
We consider the linear stability of downward dusty-gas flow in a vertical
channel within the two-fluid model 3 with Stokes particles. The basic carrierphase
flow is given by the Poiseuille velocity profile, with the particle velocity
slip being equal to the gravitational settling velocity. The disturbances are
specified in the form of travelling waves. After the linearization, the problem is
reduced to a modified Orr-Sommerfeld equation with several extra terms. The
eigenvalues are calculated numerically at high accuracy using an
orthonormalization method.
The effect of the particles on the gas flow is described by three similarity
parameters: Froude number (which determines the velocity slip in the basic
flow), particle mass loading , and inverse Stokes number (ratio of the
channel width to the particle velocity relaxation length). A parametric study of
neutral curves was performed for fixed =0.1. It was shown that: (i) for <
0.075 (high-inertia particles), the critical Reynolds number decreases as
compared to horizontal channel flow and the effect of particles is most
pronounced at small Froude numbers (high gravity). (ii) For 0.075, the
instability region in the (Re, k) plane (Re – basic-flow Reynolds number, k –
wave number) becomes bounded and reduces (tending to a point) as the
Froude number decreases and tends to a threshold value Fr 0.. Accordingly, for
Fr < Fr 0 the flow is stable with respect to arbitrary small perturbations. The
work was supported by the RFBR (project 05-01-00502).
a
Institute of Mechanics Lomonosov Moscow State University, Michurinskii pr., 1 119899 Moscow,
Russia
1 Saffman, J. Fluid Mech. 13, 120 (1962).
2 Asmolov and Manuilovich, J. Fluid Mech. 365, 135 (1998)
3 Marble, Ann. Rev. Fluid Mech. 2, 397 (1970)