Drowning Machines: Low Head Dam Hydraulics and Hazard
Remediation Options
Anita Rogacs, Cole Marr, Anizka Garcia
Rose-Hulman Institute of Technology, Terre Haute, Indiana
Introduction
1.1 Introduction
A father and two sons set out for a day of excitement as they head off to Licking River,
Kentucky. Chad, the youngest, has never been kayaking and this is his big chance to
‘learn the ropes’. With life jackets fastened, all three embark on their quest for fun as
they start into the water. Slipping through the waves, there are bright smiles on their
faces and excitement in their eyes, when the father, Larry Ratliff, catches sight of a
menacing horizon up ahead. He recognizes the danger and looks for his sons. Chad is
too far away to be warned and as his father watches in horror, his youngest son drops out
of sight. In a panic Larry paddles over the low-head dam after his son, thinking that
somehow he will save Chad. Larry is immediately pulled into the hydraulic as well.
Both father and son struggle, but ultimately lose their battle. Both are pronounced dead
at the scene. (“Kentucky”)
Many other tragic events such as the one described above occur every year, and have
been occurring since the construction of low-head dams began. A low head dam is a
water control structure usually below 10 feet in height (Elverum, 2003). Low-head dams
were constructed for many reasons, including; ensuring a constant water supply in low
flow conditions (White River, 2005), water quality control, aesthetics, and protection for
utility crossings. They also serve recreational purposes; they provide pools of water in
the river for fishing and boating, and end up being jumps that canoeists and kayakers find
enticing to paddle over for a thrill. (Low Dams)
Figure 1: Rafters at low-head dam ( Popular Mechanics)
1.2 History
One of the main reasons for the construction of low-head dams was to turn the water into
a source of power for mills. Water wheels were used to power mills in the 19th century,
and these wheels required a constant supply of water. Low head dams fulfilled this need
because they enable the storage of water for use in low flow conditions. (Colley)
Low-head dams also came into use as early settlers became concerned with the storage of
irrigation water. Originally local water supplies held enough water for their limited
needs. Unfortunately, this dependence on natural water resources forced them to cope
with the varying seasonal discharge.
Agricultural needs created the need for more
elaborate irrigation works and an increased need for storage of water. Low-head dams
created this reservoir of water needed to supply the increased irrigation.
1.3 Types of Dams
Dams consist of timber, rock, earth, masonry, concrete, or a combination of the afore
mentioned materials. (dam, 2005) Four basic types of dams will now be considered.
These are: 1) Concrete Gravity Dams, 2) Earth Dams, 3) Earth and Rock Fill Dams, and
4) Concrete Faced Rock Fill Dams. These structures can be as simple as a flat-topped
weir or as complicated as a multiple arch dam. Concrete Gravity Dams rely on their own
weight to withstand the applied forces. (Woodward, “Types” 2004) If the water flowing
over the dam produces any cavitation or turbulence, it will slowly erode the structure, to
reduce this effect, many of these dams are made in an Ogee style. ( Encyclopedia:Dam)
Earth Dams consist completely of homogenous, impermeable earth material. Earth and
Rock Fill Dams have an impermeable earth or clay core, covered with a permeable rock
fill outer layer. Concrete Faced Rock Fill dams mainly consist of permeable rock fill,
which is then covered on the upstream face with an impermeable concrete slab.
(Woodward, “Types” 2004)
Figure 4: Concrete Gravity Dam (ASDSO)
Figure 5: Ogee spillway
Figure 6: Earth Dam
Figure 7: Earth and Rock Fill Dam
Figure 8: Concrete Faced Rock Fill Dam
1.4 Cost
The cost of construction varies widely due to many variables involved with a given
project. In the case of an Earth and Rock Fill Dam or a Concrete Faced Rock Fill Dam,
many times the most economical way to obtain the large volume of rock needed is to use
the rock that needs to be excavated during the building of the spillway.
Another
important variable to take into account is the distance that the construction materials must
be hauled to get them to the work site. (Woodward, “Construction” 2004) Also, the river
on site has to be redirected in order to be able to build the dam. This cost depends on
how large the river is and how accessible a place to redirect it is. If, for example, we
looked at a 15 ft. wide by 5’ tall dam, with access but no materials at the site (all material
and equipment has to be brought in), the price for the dam construction might be around
$50,000. If one was to try to use this same dam as a power source, the construction
including a power house, could cost around $300,000-$500,000. Or, if one were to
consider a bigger dam, one 200 ft. wide and 15 ft. high, also with access to a road, and
material or equipment on site, and about 70 miles from the materials, the construction
cost could amount to 1-2 million dollars. (Desrochers, 2005)
1.5 Description of Hydraulic Phenomena
Low-head dams are found throughout the United States and pose a considerable safety
risk to the general public. The safety risk arises from the fact that the structures often
look harmless or even inviting to the recreational water user. The danger of these
overflow structures is that the downstream side of a low-head dam contains a submerged
hydraulic jump or “hydraulic” as it is referred to in the boating community (Tschantz,
2003). The hydraulic jump creates a recirculating current which can trap water-goers in a
seemingly endless cycle of being pulled under, struggling back to the surface, being
pushed back toward the falling water, and once again being pushed under (Elverum &
Smalley, 2003). These low-head dams put an unsuspecting public in danger time and
time again.
Figure 9: Roller Effect (Curry, Reed)
The exact number of low-head dam structures throughout the United States is somewhat
vague. Some states do keep track of these structures, but even in these cases the numbers
can be inaccurate. Pennsylvania maintains a list of 280 low-head structures and Virginia
estimates between 50 and 100 in their state (Tschantz, 2003). Some confusion also arises
from the fact that there are no universal definitions or dimensions available to define a
“low-head” dam. According to Leutheusser and Birk (1991), in order to “drownproof” or
completely eliminate the hydraulic, for one of these structures the weir height would have
to be increased to approximately seven times the original height. The fact that there have
been no easy or inexpensive retrofits developed for these structures means that year after
year low-head dams are claiming lives throughout the world.
1. 6 Project Description
The Indiana Department of Natural Resources (IDNR) Engineering and Dam Safety
Group and the IDNR Division of Law Enforcement appointed our research group to
conduct an intensive investigation on low head dam hydraulics and affordable hazard
remediation alternatives. Since the hazards of low head dams have been recognized, over
the last few decades, various attempts have been made to eliminate the dangerous
hydraulics at these structures. However, some proving to be more effective than others.
Due to IDNR’s wide range of needs, testing will be performed on two characteristic lowhead dams, one will be a model of the Charles Mill Dam. The goal of this investigation is
to obtain measurements of physical characteristics of the roller and use those parameters
to validate the solutions to our numerical analysis in Flow-3D™. When the software is
verified it will be used to analyze the effectiveness of existing retrofits. Along with the
reduction of dangerous hydraulic features, implementation cost of any remediation option
is also of concern.
Despite the fact that the presented retrofit design will be applicable to similar low-head
dams, only those that have the same design as the models tested can be expected to
follow the experimental results. The standards for classification of low-head dams,
fatality statistics, final retrofit solution, and guidelines for implementation will be
provided to IDNR in the final report.
1.7 History of the Charles Mill Dam
The Charles Mill Dam is located in Marion Indiana. Originally the mill was called
Marion Mills. The site was a grist mill, powered by the dam built at its side. The
building, one of the oldest in Grant County, is still in use after more than a century. The
dam on the site today is called the Old Mill Dam and was built in 1936 by the Work
Projects Administration (US Government) as a recreation area. Over time the ownership
of Charles Mill Dam, like countless others, was lost in paperwork. With no apparent
owner, these structures fall into disrepair and become the property of the state. The
Charles Mill Dam is currently the property of the city of Marion and is still in use as a
recreational site, and the mill itself is used for shops and apartments. (“Low Hazard,”
2002)
Unfortunately, this historic landmark has tragedies in its past. For example, on June 15,
2003, Neil W. Cornell (45 yrs. Old) died after diving into the Mississinewa River at the
Charles Mill Dam to save his twin 11 year old sons who became trapped in the reverse
roller at the base of the dam. The sons were rescued, unfortunately the father could not be
saved.( Ross, 2005) This is why Charles Mill Dam was chosen by the IDNR as a model
study for this project.
Literature Review
2.1 Introduction
In the last two decades attention has been drawn to the dangers that exist at low-head
dams throughout the country. The dangers include being pushed toward the dam face
and pulled under, being caught in the recirrculating current at the base of the dam, and
decreased buoyancy due to increased aeration from the recirriculating current. State
governments have published several brochures and papers warning recreational users of
these dangers. Newspaper articles show up all too often detailing the tragic drownings
that take place at low-head dams every summer; yet, to date little has been done to rectify
the problem. Some states, such as Minnesota, have started documenting low-head dam
accidents. During the 29-year period ending in 2002, The Boat and Water Safety Section
of the Minnesota Department of Natural Resources reported 53 deaths and 50 injuries at
low-head dams throughout the state (Tschantz 2003). While this is an alarming figure,
many states do not keep such specific statistics, so the aggregate effect of these
dangerous hydraulic structures can not be adequately quantified. However, it is clear that
safety concerns at low-head dams must be addressed.
Research into the components of the hydraulic characteristics found at low-head dam
structures has taken place as far back as about a half century ago. Early investigations on
the subject were chiefly concerned with the characterization of the submerged hydraulic
jump which forms at most of these low-head dam sites. The initial investigations on this
subject do not seem to acknowledge the life-threatening nature of these structures. They
simply try to characterize the phenomena occurring in these locations.
This section describes the previous research on hydraulic jumps and the recirrculating
currents produced at low-head dams. Previous research and the pertinent equations
needed to understand and control these hydraulic characteristics will be presented. In
addition proposed retrofits or alteration plans to eliminate the dangers will be discussed.
2.2 Hydraulic Jump
Hydraulic jumps occur most commonly in man-made channels as a way to dissipate
energy, often gained as water flows down an overflow structure. A hydraulic jump
occurs when flow changes from a supercritical level at the base of the dam to a subcritical
level after the hydraulic jump. According to Hwang and Houghtalen (1996), critical flow
is the flow at which a flow rate, Q, can be passed with minimum energy. This occurs at
the critical depth. Therefore, it follows that if the water level in the structure drops, the
velocity must increase in order to convey the same flow. This situation is called
supercritical flow. When the water depth is greater than the critical depth the flow is
called subcritical, which results in a lower velocity necessary to handle the same Q. The
flow regime can be characterized by a comparison of the unit inertial reaction to the unit
gravitational force or Froude number, F, (Forester & Skrinde 1949). It is defined by
Hwang and Houghtalen (1996) as follows:
F
Where:
In which:
Where:
V
gD
(1)
V = velocity of flow [m/s]
D = hydraulic depth [m]
g = gravitational acceleration [m/s2]
D = A/T
(2)
A = cross-sectional area of flow
T = top width of channel
When a rectangular channel is used for the idealization of the phenomenon, as is
common, hydraulic depth, D, is equal to d, the depth of flow in the section.
By definition when F=1 the flow is critical, when F>1 supercritical flow has developed,
and when F<1 the flow is subcritical. The water levels before and after the hydraulic
jump, or, the change from supercritical to subcritical flow, is defined by the Belanger
equation (Foster and Skrinde 1949; Leutheusser and Birk 1991; and Leutheusser and Fan
2001) :
d2 1 
2
  1  8F1  1

d1 2 
Where:
d1,d 2 = pair of sequent depths
(3)
F1 = Froude number at supercritical depth
The Belanger equation applies only to rectangular channels, but provides the only method
for analysis of the jump phenomenon.
Velocity of the flow rate per unit width, q, is determined by:
V
Where:
q
d
(4)
V = velocity of flow [m/s]
q = flow rate per unit width [m2/s]
d = depth of flow
The flow rate per unit width of overflow, q, can be determined using the head on the
overflow (Leutheusser and Birk 1991; and Leutheusser and Fan 2001 :
q
Where:
3
2
Cw 2 g H 2
3
(5)
Cw = Rehbock weir discharge coefficient
H = head on weir [m]
g = gravitational acceleration [m/s2]
C w  .611  .075
In which:
H
P
(6)
H = head on weir [m]
P = height of weir [m]
According to Foster and Skrinde (1949) and Leutheusser and Birk (1991) a hydraulic
jump will form when the downstream depth, d2, satisfies equation 3. From equation 3 it
can be seen that there is an ideal manner for the jump to form. In reality these conditions
do not occur readily in the field.
2.3 Submerged Hydraulic Jump
While it is know how to produce an optimal hydraulic jump, the ideal situation does not
usually occur at low-head dams. The phenomenon which takes place at these structures
is referred to as a submerged hydraulic jump. When the tail water, dt, rises to become
higher than the ideal condition would require in eq.3 the jump becomes submerged. A
submerged hydraulic jump sweeps back on itself and creates a vortex (Leutheusser &
Fan, 2001). “Vortex” is one term of many used to describe the phenomenon. Other
terms for what occurs at a submerged hydraulic jump include “hydraulic”, ‘recirrculating
current”, and “roller” which will be used throughout this paper. According to
Leutheusser and Fan (2001) this roller swirls on a horizontal axis parallel to the dam
creating a strong upstream surface velocity, pushing whatever it comes in contact with
back into the dam. Rajaratnam (1965) and Leutheusser and Fan (2001) have described
the behavior in terms of submergence of the jump using the following relationship:
S
Where:
dt  d 2
d2
(7)
dt = local tailwater depth
d2 = second in pair of sequent depths [m]
The optimal jump occurs when S = 0, the jump is swept downstream if S < 0, and the
dangerous submerged jump happens when S > 0 (Leutheusser & Fan 2001). This relation
illustrates the fact that the submerged jump occurs if the tailwater depth downstream of
an overflow structure exceeds the subcritical depth of the hydraulic jump (Leutheusser &
Fan 2001).
The diagram below shows three possible conditions that develop at the base of a low
head dam. Condition A illustrates a low tailwater depth, which results in an optimum
hydraulic jump. Condition B depicts a medium tailwater depth, for which a submerged
hydraulic jump is developed, and a reverse roller is produced. For Condition C the flow
is purely directed downstream due to the high tailwater depth.
Figure ??. Possible flow regimes
Early modeling of the horizontal surface velocity of the upstream directed wave was
performed by Leutheusser and Birk (1991). With their initial investigation they
developed an estimate of the surface velocity. In accordance with predicted results the
velocity directed upstream decreased as the tailwater increased (Leutheusser and Birk
1991). Generally, the velocity at low-head dams is calculated to be near this maximum
swimming velocity. It is also important to remember that a 2 m/s swimming velocity is
only achievable by Olympic class athletes and would probably not be possible over the
extended period of time necessary to escape the recirculating current.
In 2001 Leutheusser and Fan developed a more comprehensive method to predict the free
surface velocity:

Vs 
16Edm d1


V1  S  1 1  8F12  1 F12 


3


Where:
1
(8)
Vs = free surface velocity [m/s]
V1 = average velocity of supercritical jump inflow [m/s]
Edm = change in energy defined in Leutheusser & Fan 2001
d1 = first in pair of sequent depths
 = Experimental constant found in Table 1 of Leutheusser & Fan 2001
S = submergence as defined in equation 5
F1 = Froude number at supercritical depth
The change in energy, Edm , is calculated using the equation:
E dm
Where:



d1 
4

2
2

2  S  1 1  8 F1  1  F1 1  C L  
 (9)
2
2
2
2 

S  1 1  8F1  1 



CL = empirical loss coefficient
CL is defined as:
In which:


CL 
E p

q 2 d12 2 g

(10)

E p  P  H   d1  q 2 d12 2 g

(11)
The experimentation of Leutheusser and Fan supports their statement that the free surface
velocity, Vs in equation 8, is about one-third the unsubmerged jump supercritical inflow
velocity V1 (2001). Using general hydraulic methods as well as the relationships
determined by previous research it should be possible to quantify the dangerous hydraulic
features occurring at low-head dam structures.
2.4 Alternatives/Solutions
Increased Spillway Elevation
According to Leutheusser and Birk (1991) many overflow structures are constructed too
low to produce a hydraulic jump that effectively dissipates the increased kinetic energy of
the flow. Although the operational requirements of the low-head dams were satisfied,
Leutheusser and Birk claimed that engineers failed to notice that the low overflow
structures did not allow the flow to go through the optimal, free hydraulic jump. The
faulty hydraulic condition, therefore, posed great danger. The suggested method for
eliminating the dangerous rollers, produced at the base of low-overflow structures, was to
simply elevate the height of the dam. It was theorized that by using the combination of
tailwater depth and the rate of flow at the downstream end of the roller, it would be
possible to determine the required height of the overflow structure that would produce the
optimal hydraulic jump. However, Leutheusser and Birk , realized that the required
height in many cases would be so great that this design option would be impractical
(1991).
Baffled Chutes
Leutheusser and Birk (1991) suggested an alternative retrofit to eliminate the “hydraulic”
of overflow structures completely, see Figure 1. It was thought that “baffled chute
spillways” would provide “continuous energy dissipation by cascade action”
(Leutheusser & Birk 1991). Hotchkiss and Comstock (1992) later experimented with
baffled chutes and found the claim flawed. Baffled chutes dissipated energy by creating
a turbulence that presented a new safety hazard for boaters navigating through the baffles.
Physical models of the baffled chutes showed that scale model boats were often trapped
in the baffled chutes. Furthermore, the collected floating and suspended debris may
result in the overtopping of the basin and damage to the baffle blocks. This occurrence
would require regular cleaning of the blocks.
Figure 1. Baffled Chute Basin. (Dam Safety 1999)
Labyrinth Weir
Hauser et. al. (1991) proposed an alternative design, called a labyrinth weir (Figure 2),
for low-head hydropower dams. The new structure increases minimum flow between
generating periods. Hauser et. al. claim rollers are created when the discharge per unit
width is high. By enlarging the crest length the labyrinth weir has a lower discharge per
unit width reducing the chance of roller formation. Disadvantages of the design include
the difficulty of increasing the crest length and the non-navigable nature of the labyrinth.
Such disadvantages have precluded the Labyrinth Weir from becoming a viable solution.
Figure 2. Labyrinth Weir. (Physical Hydraulic 2005)
Stepped Spillways
Stepped spillways are also used as energy dissipaters for low overflow structures (Figure
3). The flow over the steps can be defined as either nappe flow or skimming flow. In
nappe flow, as water hits each step, it dissipates energy by either breaking up the water
flow in air or mixing the flow on each step. This process may or may not form partial
hydraulic jump on the step (Rajaratnam 1990). In the skimming flow, the flow from each
step travels as a consistent stream, “skimming” over each step creating recirculating
rollers. The momentum transfer to these rollers enhances the energy dissipation over the
structure. Christodoulou (1992) conducted experiments to validate Rajaratnam’s
estimates on the energy loss over stepped spillways. It was found that the amount of
energy lost is mainly governed by the ratio of the critical depth of the water flow passing
over the spillway to the step height (dc/h), and the number of steps N. Furthermore,
greater number of steps and decreasing values of dc/h result in increased energy
dissipation over the spillway. With further experimentation Chamani and Rajaratnam
(1994) were able to present a method to estimate the energy loss within the nappe region
flow and find a relationship for the variation of energy loss at each step. To retrofit a low
head dam, Freeman and Garcia (1996) constructed a four- and a six-step spillway. The
conclusion reached was that even though the six-step spillway performed better, the fourstep arrangement is more cost effective and a more feasible solution.
Figure 3. Four-step spillway. (Freeman 1996)
Rock Arch Dam Conversion
Rock arch rapids are a new retrofit for low-head dams that is currently being investigated
by Dr. Luther Aadland, who is currently taking data at multiple locations where the
design has been implemented. The retrofit design uses three different sized field stones,
which are placed as seen in Figure 4. The downstream end of the rock arch rapids curves
and then becomes flat as it approaches the dam crest. The slope of the rapid is
approximately 5%, which allows fish to swim upstream. The slope of the weirs varies to
match the grade. “Weirs are integrated into the bank and gaps between the large boulders
near the bank are filled with smaller stones to reduce leakage and create pools” (Aadland
2005).
The rock arch dam conversion utilizes varying sized stones. The different sizes are
necessary since each serves a specific purpose. Boulders function as strengthening
elements that add stability to the flow and direct the rapids towards the mid-channel,
therefore, reducing the flow velocity and stress on the river banks. The size of the field
stones or boulders range between three and six feet in diameter. They are set one foot
above the grade and are spaced according to the slope for a maximum of one foot head
loss per weir (Aadland 2005). “Cobble” is used for filling voids near the crest. The size
of these smaller field stones change from one foot to three feet depending on the shear
stress exerted on the rocks due to the varying flow rates. The size of a cobble can be
between one and six inches in diameter.
Aadland claims that the retrofit completely eliminates the “hydraulic” and provides a
pathway for migrating fish. The primary concern with the design is the mobile nature of
stones, which has led to questions regarding the permanence of the structure.
30o ANGLE OF WIER TO BANK
FLOW
SLOPE
5% slope
or lower
D
A
M
C
R
E
S
T
Figure 4. Rock Arch Dam Conversion (Aadland 2005).
2.5 Numerical Modeling Tools
In the past, physical models have been built to study the transition of supercritical flow to
subcritical flow at overflow structures, but their construction and accurate scaling was
very costly and time-consuming. With the latest advances in computational fluid
dynamics (CFD), that solve the Reynolds-averaged Navier-Stokes equations, a new tool
has evolved to accurately depict and quantify the behavior of hydraulic structures.
Between 2000 and 2004, the Utah Water Research Laboratory (Savage & Johnson, 2001)
and the NSW Department of Commerce (Ho, Boyes, Donohoo, Cooper, 2003) has
conducted studies to validate the accuracy of a CFD method, called Flow-3D, (Flow
Science Inc.), in solving multiple significant fluid parameters at these structures. Both
studies have compared the flow parameters over a standard ogee-crested spillway using
numerical modeling and published data. The results from both sources confirmed that
there is a strong agreement between the physical and numerical models for pressures,
discharges and average velocities.
Project Approach
3.1 Overview
To carry out our project successfully, we first conducted an intensive literature search on
low head dam structures, hazards and fatality statistics. After obtaining the necessary
background information, two characteristic low head dams were chosen for
experimentation. The phenomenon was tested by numerical modeling using Flow-3D, a
fluids modeling software that utilizes finite element analysis. Both quantitative and
qualitative testing was conducted on the velocities and flow direction of the recirculating
current using different flow rates and tailwater depths. A physical model was then built to
verify the accuracy of the numerical model. Furthermore, effective retrofits identified
during the literature search were simulated to investigate their ability to reduce the
dangerous hydraulics.
3.2 Experimental Procedure
Two types of dams were tested in the laboratory, an ogee style dam, and a flat panel
dam. To see the dimensions and composition details of these models see Appendix # .
Figure 14: Straight Dam
Figure 15: Ogee Dam
Flow rate was chosen as one of the dependent variables in the controlled experiment. In
order to see the dependence flow parameters, three discharge rates were utilized; low,
medium and high. The other dependent variable was the tailwater depth. Varying the
tailwater depth allowed us to measure its affect on the hydraulic characteristics at the
base of the dam. The tailwater depth was controlled using a flat panel, which was slid up
and down to alter the outflow of the channel.
Figure 16: Tailwater Depth Control Flat Panel
The parameters which are measured are the flow height before the dam, the head on the
dam, tailwater depth, height of downstream velocity, the reach of the roller, as well as
surface and bottom velocity. The height of downstream velocity is where the current
changes from a reverse current to a forward flowing current. This was estimated using an
air pump connected through a tube to a fine pointed syringe. The small bubbles created
were used to determine the direction of the flow deeper in the water. The reach of the
roller is the distance from the base of the dam to the end of the boil. In order to
determine the reach of the roller, styrofoam was placed in the water to determine the
position at which the surface velocity changes direction. In order to accurately determine
the flow rate, the water pump was calibrated. A series of tests were conducted yielding
data which was used to create a calibration curve. This calibration curve was then used
to adjust the flow rate reading.(See Appendix# )
3.3 Numerical Modeling
Our experiment further advanced the analysis of low-head dam structures by numerically
investigating the hydraulic development at the base of an overflow structure using the
commercially available CFD program, Flow-3D™. The first objective was to confirm
the accuracy of the software by comparing the flow data of the roller using the numerical
and the physical models. Two types of dam were used to carry out this task. The first
model was a flat panel dam and the second model was an ogee-crested spillway. The
parameters used to examine the precision of the simulation results were: horizontal
downstream reach of hydraulic (roller), downstream bottom and surface velocity, and
subcritical and supercritical depths. These variables were compared at low, medium, and
high flow rates. Within each of the flow rates five tailwater depths were set as a
dependent variables. Since each flow condition had a constant upstream water depth and
head over the dam, those two parameters were used to assign the discharges on Flow3D™ for each set of experiments.
3-D model of Dams and Mesh
The flat panel model was created using the basic rectangle file within Flow-3D and was
assigned the exact dimensions of the physical model. The ogee spillway was constructed
using Solid Works™, a computer-aided 3-D modeling software. The dimensions of this
numerical model were also identical to the physical model used in the hydraulics
laboratory. To accurately depict the changes in the flow properties, a mesh was placed so
all necessary data would be computed and captured. The number of cells was set to
60,000.00. The accuracy that this number provided was sufficient for the purpose of this
experiment. See Figure ???.
Figure ???. 3D model Ogee and Flat Panel dams and their mesh system.
Global and Physics Parameters
Multiple models and parameters were activated universally on all 30 experiments. 25
seconds of flow was simulated in order to ensure that a steady state flow condition would
develop. Since the fluid of interest is water only, the interaction of water and air was
disregarded and the number of fluids was set to “one”. The flow mode was set to
“incompressible” and the interface tracking to “Free surface or sharp interference”. Since
the unit system was set to “cgs”, the gravitational constant assigned in the z direction was
-980 cm/s2. The turbulent behavior of the downstream flow made it necessary to activate
the viscous and turbulence flow model. Within the model the no-slip wall shear
boundary condition was set with a friction coefficient of -1.0. This setting accounted for
the no-slip boundary effects at the interface of the water, the walls of the channel and the
dam. Due to the effect of turbulence at the location of the hydraulic, the air entrainment
model was also activated by setting the air entrainment coefficient to 0.5 and adding the
constant value of the surface tension coefficient and the air density. Considering the
affect of increased volume fraction of air on constant water density, the density
evaluation model was turned on and set to “solve transport equation for density” with
first order differential equations using the results of the air entrainment model simulation.
This accounted for the variation in the macroscopic density at the location of the
hydraulic jump.
Fluid Selection
As mentioned before, the only fluid that was being considered in the experiments was
water. In the Fluids tab, “water at 20 C” was loaded, which automatically set the
necessary properties within the software.
Boundary conditions
The boundaries of the mesh were individually set to accurately represent the flow at those
areas (See Figure ??):
• Upstream boundary (Xmax): Hydrostatic stagnation pressure in z direction with zero
velocity and fluid height: du.
• Downstream boundary (Xmin): Hydrostatic stagnation pressure in the z direction with
zero velocity and fluid height: dt.
• Bottom (Zmin): Set to “Wall”. No flow is allowed through it.
•Top (Zmax): Set to “Symmetry”. No influence from this plane due to open channel.
•Edge of dam (Ymax): Set to “Wall”. No flow is allowed through it.
•Center plane of dam (Ymin): Since this plane is the symmetry plane of the dam, it is set
to “Symmetry”.
Figure ???. Boundary system.
Initial Settings
Since the flow condition is governed by the fluid heights set at the boundary conditions,
the initial pressure field was set to a hydrostatic pressure in the z direction. Two fluid
regions were added; one before the dam with the larger water depth and one region after
the dam with the lower water depth. The initial fluid velocities were kept at zero.
Output and Numerics
Each simulation was set to obtain data using a time step of 0.01 seconds. Because the
mesh cell sides had different values in all three directions, the GMRE implicit pressure
solver option was selected so the pressure iterations would converge at each time step.
Notation:
The following are used in the paper:
g = acceleration due to gravity
F = Froude number
F1 = Froude number at jump inflow
d1= supercritical depth
d2 = subcritical depth
dc = critical depth
N = number of steps
h = step height
H = head on weir
Cw = weir coefficient
q = flow rate per unit width
S = submergence
dt = local tailwater depth of channel
du= local upstream water depth (behind the dam)
Vs = surface velocity
Edm = change in energy defined in Leutheusser & Fan 2001
 = Experimental constant found in Table 1 of Leutheusser & Fan 2001
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