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A head loss model for slurry transport in the heterogeneous regime
Sape A. Miedema
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Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
article info
Article history:
Received 20 July 2014
Accepted 10 July 2015
Keywords:
Dredging
Slurry transport
Heterogeneous transport
Multi-phase flow
Head loss
Hydraulic gradient
abstract
Although sophisticated 2 and 3 layer models exist for slurry flow (here the flow of sand/gravel water
mixtures), the main Dutch and Belgium dredging companies still use modified Durand and Condolios
(1952) and Fuhrboter (1961) models, while the main companies in the USA use a modified Wilson et al.
(1992) model for heterogeneous transport. These older models use one term for the excess pressure
losses, the pressure losses resulting from the solids, with an empirical character. A new model has been
developed based on energy considerations. The model consists of two terms for the excess pressure
losses, one for the potential energy losses and one for the kinetic energy losses. This gives more
flexibility matching experimental results. Although the model is derived fundamentally, the slip velocity
of the particles is still an unknown in the model. An equation for this slip velocity is derived, based on
physical parameters. The resulting model is validated with numerous experimental data from the
literature and from the Delft Dredging Laboratory and matches very well. The advantage of this model is,
that it requires the parameters known to the dredging industry and is thus easy to use.
&2015 Elsevier Ltd. All rights reserved.
1. Introduction
Although sophisticated 2 and 3 layer models exist for slurry
flow (here the flow of sand/gravel water mixtures), the main
Dutch and Belgium dredging companies still use modified Durand
and Condolios (1952) and Fuhrboter (1961) models, while the
main dredging companies in the USA use a modified Wilson et al.
(1992) model for heterogeneous transport. When asked why these
companies do not use the more sophisticated models, they answer
that they require models that match their inputs and they feel that
the 2 and 3 layer models are still in an experimental phase,
although these models give more insight in the physics. Usually
the companies require a model based on the particle size dis-
tribution or d
50
, the pipe diameter D
p
, the line speed v
ls
, the
relative submerged density R
sd
and the temperature (the viscosity
of the carrier liquid
ν
l
). Parameters like the bed associated
hydraulic radius are not known in advance and thus not suitable.
Usually the dredging companies operate at high line speeds above
the limit deposit velocity (LDV) in the heterogeneous or homo-
geneous regime. This implies that the bed has dissolved and 2 and
3 layer models are not applicable anyway.
Still there is a need for improvement, since the existing models
give reasonably good predictions for small diameter pipes, but not
for large diameter pipes as used in dredging. Recent projects
require line lengths up to 35 km with 5 to 6 booster pumps and
large diameter pipes. Choosing the number of booster pumps and
the location of the booster pumps depends on the head losses.
However it should be considered that the slurry transport process
is not stationary. Densities may vary from a water density of 1 t/m
3
to densities of 1.6 t/m
3
and particle size distributions will change
over time. This results in a dynamic process where pumps, pump
drives and slurry transport interact. The fundamental 2 and 3 layer
models require a stationary approach, while the more empirical
equations may take the dynamic effects as time and place
averaged effects into account. The question is whether a semi
empirical approach is possible, covering the whole range of pipe
diameters and giving the empirical equations a more physical
background, but still using the parameters available to the dred-
ging industry.
The paper first gives a short introduction of the DHLLDV model,
followed by the derivation of the slip velocity equation. Simplified
models for small, medium and coarse particles are derived for
sands and gravels, followed by a comparison with the Durand and
Condolios (1952) equation. Finally the application of the model
derived for graded sands and gravels is shown.
2. The Delft Head Loss &Limit Deposit Velocity model
The Delft Head Loss & Limit Deposit Velocity (DHLLDV) model
is such a model (see Miedema and Ramsdell, 2013, 2014b). The
model is based on constant spatial volumetric concentration C
vs
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/oceaneng
Ocean Engineering
http://dx.doi.org/10.1016/j.oceaneng.2015.07.015
0029-8018/&2015 Elsevier Ltd. All rights reserved.
n
Tel.: þ31 15 2788359.
E-mail address: s.a.miedema@tudelft.nl
Ocean Engineering 106 (2015) 360–370