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ERDC TN-DOER-N7
August 2000
A Reynolds number (R) criteria for the turbulent-laminar transition has been proposed for Bingham
plastic materials (Liu and Mei 1990), and found to be applicable to mud flows. R is composed of
viscous (R)and yield-stress components (Rτ) depending on underflow conditions, and:
1
R=
(1)
d1 R + 1 Rτ i
where
R = 4 ρ q and
Rτ = 8ρ q2 τ yh2
where
ρ = the underflow density, the overbar indicates a layer-averaged density
q = the underflow discharge per unit width
= the apparent viscosity
τy = the yield stress
h = the underflow thickness.
The yield stress is defined here as the stress below which no flow occurs, but in practice it is
dependent on the stress history of the material and flow conditions for the case at hand. Measured
values are method-depend. Experimental evidence indicates that the turbulent-laminar transition
occurs at R's of about 2,100 (Liu and Mei 1990; Van Kessel and Kranenburg 1997).
Fluid Mud Underflow Models. To predict underflow behavior, a set of equations must be solved
that is appropriate to its classification. The study of fluid mud flow properties is known as rheology,
and two notable flow features are plasticity and shear-thinning. Deformation in a plastic material
is limited to conditions where the imposed shear stress is greater than some threshold value, a yield
stress. A Bingham model is usually used to represent the stress-strain relationship of a plastic
material. A shear-thinning material's apparent viscosity decreases with increased shear-rate (Teeter
1992a). A Newtonian fluid such as water has a linear stress-strain relationship. Both yield stress
and shear thinning are non-Newtonian characteristics of fluid muds.
Recent studies on laminar fluid mud underflows have used Bingham (Liu and Mei 1990; Van Kessel
and Kranenburg 1997) or Herschel-Bulkley (Coussot and Proust 1996; Huang and Garcia 1998)
rheological models where shear stress (τ) is:
&
τ = τ y + γ n , τ > τ y
(2)
5

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