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HYDRAULIC MODELING OF OPEN CHANNEL FLOWS
OVER AN ARBITRARY 3-D SURFACE
AND ITS APPLICATIONS
IN AMENITY HYDRAULIC ENGINEERING
TRAN NGOC ANH
August, 2006
Acknowledgements
The research work presented in this manuscript was conducted in River System
Engineering Laboratory, Department of Urban Management, Kyoto University, Kyoto,
Japan.
First of all, I would like to convey my deepest gratitude and sincere thanks to Professor
Dr. Takashi Hosoda who suggested me this research topic, and provided guidance,
constant and kind advices, encouragement throughout the research, and above all, giving
me a chance to study and work at a World-leading university as Kyoto University.
I also wish to thank Dr. Shinchiro Onda for his kind assistance, useful advices especially
in the first days of my research life in Kyoto. His efforts were helping me to put the first
stones to build up my background in the field of computational fluid dynamics.
My special thanks should go to Professor Toda Keiichi and Associate Professor Gotoh
Hitoshi for their valuable commences and discussions that improved much this
manuscript.
I am very very grateful to my best foreign friend, Prosper Mgaya from Tanzania, for all
of his helps, discussions and strong encouragements since October, 2003.
In addition, my heartfelt gratitude is extended to all of my Vietnamese friends in Japan,
Kansai Football Club members, who helped me forget the seduced life in Vietnam,
particular Nguyen Hoang Long, Le Huy Chuan and Le Minh Nhat.
Last but not least, the most deserving of my gratitude is to my wife, Ha Thanh An, and
my family, parents and younger brother. This work might not be completed without their
constant support and encouragement. I am feeling lucky because my wife, my parents and
my younger brother are always by my side, and this work is therefore dedicated to them.
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Abstract
Two-dimensional (2D) description of the flow is commonly sufficient to analyze
successfully the flows in most of open channels when the width-to-depth ratio is large
and the vertical variation of the mean-flow quantities is not significant. Based on
coordinate criteria, the depth-averaged models can be classified into two groups namely:
the depth-averaged models in Cartesian coordinate system and the depth-averaged models
in generalized curvilinear coordinate system. The basic assumption in deriving these
models is that the vertical pressure distribution is hydrostatic; consequently, they possess
the advantage of reduction in computational cost while maintaining the accuracy when
applied to flow in a channel with linear or almost linear bottom/bed. But indeed, in many
cases, water flows over very irregular bed surfaces such as flows over stepped chute,
cascade, spillway, etc and the alike. In such cases, these models can not reproduce the
effects of the bottom topography (e.g., centrifugal force due to bottom curvature).
In this study therefore, a depth-averaged model for the open channel flows over an
arbitrary 3D surface in a generalized curvilinear coordinate system was proposed. This
model is the inception for a new class of the depth-averaged models, which was classified
by the criterion of coordinate system. In conventional depth-averaged models, the
coordinate systems are set based on the horizontal plane, then the equations are obtained
by integration of the 3D flow equations over the depth from the bottom to free surface
with respect to vertical axis. In contrary the depth-averaged equations derived in this
study are derived via integration processes over the depth with respect to the axis
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perpendicular to the bottom. The pressure distribution along this axis is derived from one
of the momentum equations as a combination of hydrostatic pressure and the effect of
centrifugal force caused by the bottom curvature. This implies that the developed model
can therefore be applied for the flow over highly curved surface. Thereafter the model
was applied to simulate flows in several hydraulic structures this included: (i) flow into a
vertical intake with air-core vortex and (ii) flows over a circular surface.
The water surface profile of flows into vertical intake was analyzed by using 1D steady
equations system and the calculated results were compared with an existing empirical
formula. The comparison showed that the model can estimate accurately the critical
submergence of the intake without any limitation of Froude number, a problem that most
of existing models cannot escape. The 2D unsteady (equations) model was also applied to
simulate the water surface profile into vertical intake. In this regard, the model showed its
applicability in computing the flow into intake with air-entrainment.
The model was also applied to investigate the flow over bottom surface with highly
curvature (i.e., flows over circular surface). A hydraulic experiment was conducted in
laboratory to verify the calculated results. For relatively small discharge the flow
remained stable (i.e., no flow fluctuations of the water surface were observed). The model
showed good agreement with the observations for both steady and unsteady calculations.
When discharge is increased, the water surface at the circular vicinity and its downstream
becomes unstable (i.e., flow flactuations were observed). In this case, the model could
reproduce the fluctuations in term of the period of the oscillation, but some discrepancies
could be still observed in terms of the oscillation’s amplitude.
In order to increase the range of applicability of the model into a general terrain, the
model was refined by using an arbitrary axis not always perpendicular to the bottom
surface. The mathematical equation set has been derived and some simple examples of
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dam-break flows in horizontal and slopping channels were presented to verify the model.
The model’s results showed the good agreement with the conventional model’s one.
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