Numerical Computation Of A Confined
Sediment–water Mixture In Uniform Flow
Author(s)
L. Sarno, R. Martino &M. N. Papa
Abstract
The purpose of this paper is to simulate a laminar mud flow confined in a
narrow rectangular open channel. The flow bed is an erodible layer made up
of the same material involved in the flow; the equilibrium condition between
the moving and non-moving layer is assumed. The mud mixture under study is
ruled by the Herschel–Bulkley’s (H–B) shear thickening rheological law. It is
supposed that the local volumetric concentration is linearly increasing with the
depth and it is constantly equal to its maximum value where the local velocity
is smaller than a threshold value. Relations among rheological parameters and
concentration have been obtained through laboratory rheometric tests. Turbulence
effects and Coulombian stresses have been ignored. The momentum equation has
to be integrated along the flow cross section for the flow velocity to be obtained.
Unfortunately, it is very difficult to integrate this equation using H–B rheological
law, since there are different stress functions and it is not possible to know a priori
the sub-domains of them (plug, non-plug and bed regions). In the present work
a modified rheological law, continuous over the whole domain of integration is
employed and the momentum equation is numerically integrated. This modified
law has been obtained by adding a constant correcting the denominator in the H–B
stress functions. Therefore, there are no longer any dead zones or plug regions.
However it is noteworthy that, using a small constant, the model produces a
good simulation of plug and dead zones: i.e. the velocity gradient is very small
there. The mathematical model has two parameters: maximum concentration and
threshold velocity. These parameters have been adjusted by back-analysis with
measurements from laboratory flume experiments in uniform flow conditions.
Keywords: mud flow, Herschel–Bulkley rheological law, equilibrium, plug.
Keywords
mud flow, Herschel–Bulkley rheological law, equilibrium, plug.
Related Book
Other papers in this volume
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