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 consideration is ruled by Herschel-Bulkley’s 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 are obtained through laboratory rheometric tests. Turbulence effects and Coulombian stresses are ignored. To get the flow velocity, the momentum equation has to be integrated along the flow cross section. 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 integrated numerically. This modified law is obtained by adding a constant correcting the denominator in the H-B stress functions: strictly speaking, there are not dead zones or plug any more. However it is noteworthy that, using a small constant, the model produces a good simulation of plug and dead zone: that is velocity gradient is very small there. The mathematical model has two parameters: maximum concentration and threshold velocity. These parameters are adjusted by back-analysis with measurements from laboratory flume experiments in uniform flow conditions.

Numerical computation of a confined sediment-water mixture in uniform flow

SARNO, Luca;PAPA, Maria Nicolina
2007

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 consideration is ruled by Herschel-Bulkley’s 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 are obtained through laboratory rheometric tests. Turbulence effects and Coulombian stresses are ignored. To get the flow velocity, the momentum equation has to be integrated along the flow cross section. 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 integrated numerically. This modified law is obtained by adding a constant correcting the denominator in the H-B stress functions: strictly speaking, there are not dead zones or plug any more. However it is noteworthy that, using a small constant, the model produces a good simulation of plug and dead zone: that is velocity gradient is very small there. The mathematical model has two parameters: maximum concentration and threshold velocity. These parameters are adjusted by back-analysis with measurements from laboratory flume experiments in uniform flow conditions.
9781845640798
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/1727208
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