管内堆積層の滑動について
管路における堆積層を伴うスラリーの流動に関する研究
1986 年 102 巻 1176 号 p. 77-83
詳細
1986 年 102 巻 1176 号 p. 77-83
In a slurry pipeline deposition occurs on the bottom of the pipe at flow velocities below the critical deposit velocity. If the discharge is then gradually increased, particles at the surface of the bed are removed by flow to reduce the height of the bed. However, at certain flow conditions the bed begins to slip at the pipe wall, giving rise to a sliding bed flow.
The object of this paper is to provide accurate predictions of mechanical friction forces which must be overcome in order to set the bed in motion. The forces which act on the pipe wall were analysed, assuming that the state of stress in the bed is on a condition of plastic equilibrium and that the driving forces of the bed are equivalent to the mechanical friction forces which hold the bed in place. As a result, driving forces of the bed FT for θb <π/2 were given by
Ft=2r2μwγ∫0θbE(Ksin2θ+cos2θ)dθ dE/dθ={1+(K-1)sin2θ}μwE-sinθ
where μw is the friction coefficient between solids and the pipe wall, and K is the coefficient of particles (or earth) pressure at rest; the dimensionless number E with respect to pressure Pv is defined with the pipe radius r and the specific weight of the bed γ by E=Pv/(γ-r), and θb is a half of the center angle against a surface of the bed taken as a chord. The solution of these equations was provided numerically, and also analytically as in approximate one.
Experimental verification for this theoretical analysis was then performed.
The granular material used in the tests was a sand of specific gravity 2.66 and mean diameter 1.71 mm. Friction forces occurring between the sands and the pipe wall were measured in 3.2cm and 4.0cm transparent plastic pipes with a pair of cell keeping the bed at any height within it. Comparison between experimental results and theoretical values for the friction forces showed good agreement if 7 was calculated by the following equation:γ=C γ s+ (1-C)γ w
where Cis the volumetric fraction of solids in the bed;γs and γw are specific weights of solids and water, respectively.
