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 below 15 feet in height, and normally between 5 and10 feet high
(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 jumps that canoeists and kayakers find enticing to paddle over for a thrill. (Low
Dams)
Engineering Forensic Research Institute
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 requirements 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 Low Head 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.
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These are: 1) Concrete Gravity Dams, 2) Earth Dams, 3) Earth and Rock Fill Dams, and
4) Concrete Faced Rock Fill Dams. Concrete Gravity Dams rely on their own weight to
withstand the applied forces. (Woodward, “Types” 2004) If the water flowing over a 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). See Figures
2 and 3.
Figure 2: Concrete Gravity Dam (ASDSO)
Figure 3: Ogee spillway
Earth Dams consist completely of homogenous, impermeable earth material.
(Woodward,“Types” 2004) See Figure Below.
Figure 4: Earth Dam
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Earth and Rock Fill Dams have an impermeable earth or clay core, covered with a
permeable rock fill outer layer. (Woodward, “Types” 2004) See Figure 5.
Figure 5: Earth and Rock Fill Dam
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 6: Concrete Faced Rock Fill Dam
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1.4 Cost
The cost of construction varies widely due to the 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,
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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 7: 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
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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 prove to be more effective than others. Due
to IDNR’s wide range of needs, testing will be performed on two characteristic low-head
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.
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.
1.7 History of the Charles Mill Dam
The Charles Mill Dam is located in Marion Indiana. Originally built in 1855 by John
Secrist, the mill was called Marion Mills. The site consisted of a grist mill, powered by
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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. (“Low Hazard,” 2002) 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. (Simons, 1976)
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.
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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 recirculating current at the base of the dam, and
decreased buoyancy due to increased aeration from the reciriculating 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, and do not seem to acknowledge
the life-threatening nature of these structures.
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This section describes the previous research on hydraulic jumps and the recirculating
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:
V
gD
(1)
V = velocity of flow [m/s]
D = hydraulic depth [m]
g = gravitational acceleration [m/s2]
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In which:
Where:
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:
(3)
d1,d 2 = pair of sequent depths
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
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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
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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.
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Figure 8: 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.
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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
d
2
1
2g 
(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.
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2.4 Alternatives/Solutions
2.4.1 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).
2.4.2 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.
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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 9: Baffled Chute Basin. (Dam Safety, 1999)
2.4.3 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.
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Figure 10: Labyrinth Weir. (Physical Hydraulic, 2005)
2.4.4 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 (1993) 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
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(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 11: Four-step spillway. (Freeman 1996)
2.4.5 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).
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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 12: Rock Arch Dam Conversion (Aadland 2005).
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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, et.al., 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.
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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 C.
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Figure 13. Straight Dam
Figure 14. Ogee Dam
Flow rate was chosen as one of the independent variables in the controlled experiment. In
order to see the variation in flow properties, three discharge rates were utilized: low,
medium and high. The other independent variable selected 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 15: Tailwater Depth Control Panel
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The parameters measured were the flow height before the dam, the head on the dam,
tailwater depth, height of the downstream velocity, the reach of the roller, as well as the
surface and bottom velocity. The height of the 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 F)
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
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high flow rates. Within each of the flow rates five tailwater depths were set as 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 Flow-3D™ for each
set of experiments.
3.3.1 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 16.
Figure 16: 3D model Ogee and Flat Panel dams and their mesh system
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3.3.2 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.
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3.3.3 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.
3.3.4 Boundary conditions
The boundaries of the mesh were individually set to accurately represent the flow at those
areas (See Figure 17):
• 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 17. Boundary system
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3.3.5 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.
3.3.6 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.
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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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Validation of Flow-3D
4.1. Overview
When attempting to model phenomena using computer software it is important to know
that the data received from the software is valid. The first step in assuring data obtained
from numerical analysis is reasonable often boils down to entering reasonable values into
the software in the beginning. This step is something that most people with software
experience take seriously. There is a second component to ensure valid data is being
generated which can be easily overlooked by many. This component is the verification
that the program is capable of producing reliable data at all. Most people familiar with
the problems involved in software usage have heard the phrase, “garbage in, garbage
out”, however if the software is not capable of generating valid data in the first place you
can end up with, “good data in, garbage out”.
In our case it was important to verify the validity of the results Flow-3D™ provided.
While there have been some studies performed, which attempted to verify the data output
from Flow-3D, nothing has been done to verify that the software provides accurate
assessments of the actual hydraulic conditions developed at the base of a low-head dam
structure or ogee spillway.
4.2. Comparison of the two dimensional plots
The verification of the software was done in two steps. First, experimental data was
collected in the hydraulics laboratory at Rose-Hulman Institute of Technology, while the
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same scenarios were simulated in Flow-3D™ using dimensions and water conditions
identical to those in the laboratory. The illustrations below show the similarity between
the vector plots of the recirculating current and the path which was traced by our methods
in the laboratory. Below each vector plot is a picture which has been marked to show the
path of the dried pea which was introduced to show the recirculating current. The vector
plots, created using Flow-3D™, are simulations with the same conditions as the
situations pictured below directly below. See Figure 18. The vector paths appear to be
very similar to the traced paths from the lab. This information was the first indication
that Flow-3D™ could in fact accurately reproduce the hydraulic conditions created in the
laboratory.
Figure 18. Snapshots of the paths of a particle in the hydraulic
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4.3. Comparison of forward current velocity values
In order to get a more detailed representation of how well the parameters agree, the
physical data and the numerically modeled results were compiled on the basis of three
representative properties and analyzed. The three properties chosen were forward and
reverse current velocity as well as the reach of the roller. The analysis of the simulation
results provided 5 different values for each property. These values were then compared to
the numbers that were produced in the laboratory. The graphical comparison and
analysis of this data is provided below.
The first set of graphs illustrates the discrepancies in the forward current velocity values
for both experimental set-ups, the flat panel dam and ogee dam. Both plots contain two
series; one is a series that illustrates the velocity values obtained through numerically
modeling, and the other displays the values measured in the laboratory. Due to the fact
that the values obtained from both methods fall within a narrow range and vary similarly
from one trial to the next, we have determined that there is a good agreement between the
values (see Figure 19). Small differences, however, do exist. These discrepancies could
have been influenced by numerous factors; contributing factors may include: the limited
accuracy of the video analysis, the inconsistency in the horizontal location of velocity
determination and the inherent limitations of the software, which do not allow it to fully
capture all of the physical characteristics.
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Forward current velocity for flat panel dam
90.0
80.0
Velocity (cm/s)
70.0
60.0
50.0
Numerically modelled
40.0
Observed
30.0
20.0
10.0
0.0
1.0
2.0
5.0
7.0
13.0
Trial Num bers
Forward current velocity for ogee dam
90.0
80.0
Velocity (cm/s)
70.0
60.0
50.0
Numerically modelled
40.0
Observed
30.0
20.0
10.0
0.0
1b
2b
3b
7b
14b
Trial num bers
Figure 19. Comparison of the forward current velocity obtained through physical
experimentation and numerical modeling
The second set of graphs shows the discrepancies in the reverse current velocities for
both experimental set-ups. Again, the plots contain two series, one is a series that depicts
the velocity values obtained through numerical modeling, and the other uses the values
measured in the laboratory. Although the values fall within a narrow range they do not
vary similarly between trials (see Figure 20). It was observed that the reverse current
velocity varied along the width of the channel. Because the velocities were determined
through a 2 dimensional analysis, and we did not determine the location of the sample in
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relation to the flow channel walls, that variation was not accounted for. This limitation is
believed to be the major source of the seen discrepancies. Other sources of error are the
limited accuracy of the video analysis, the inconsistency in the location of velocity
determination in relation to the dam and the limitations of the software in fully capturing
all of the physical characteristics.
Reverse current velocity for flat panel dam
50.0
Velocity (cm/s)
45.0
40.0
35.0
30.0
Numerically modelled
25.0
Observed
20.0
15.0
10.0
5.0
0.0
1
2
5
7
13
Trial Num bers
Reverse current velocity for ogee dam
50.0
45.0
Velocity (cm/s)
40.0
35.0
30.0
Numerically modelled
25.0
Observed
20.0
15.0
10.0
5.0
0.0
1b
2b
3b
7b
14b
Trial num bers
Figure 20. Comparison of the reverse current velocity obtained through physical
experimentation and numerical modeling
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The third set of graphs depicts the difference in the obtained values for the reach of
rollers. There is good agreement between the values since they fall within a narrow range
and vary similarly between trials. (See Figure 21). Small differences, however, are
apparent. The ogee dam physical experiments consistently resulted in greater values for
the reach of the rollers. Because the discrepancy is somewhat uniform, it is suspected that
the numerical model was inefficient in delivering accurate values for this specific set-up.
Other factors that may have influenced the outcome were the limited accuracy of the
video analysis due to the fact that the velocity was not measured at a consistent distance
from the dam.
Reach of rollers for flat panel dam
60.0
Distance (cm/s)
50.0
40.0
Numerically modelled
30.0
Observed
20.0
10.0
0.0
1.0
2.0
5.0
7.0
13.0
Trial num bers
Reach of rollers for ogee dam
60.0
Distance (cm)
50.0
40.0
Numerically modelled
30.0
Observed
20.0
10.0
0.0
1b
2b
3b
7b
14b
Trial num bers
Figure 21. Comparison of the reach of rollers obtained through physical experimentation
and numerical modeling.
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Since we are concerned with the accuracy of the numerical modeling tool, it was crucial
to understand why the software failed to provide identical results to the measurements
obtained in the laboratory.
As it was mentioned earlier, the air entrainment is a
significant factor in the computation of variables. In order to activate the air entrainment
model, three properties needed to be specified; air density, surface tension coefficient,
and air entrainment coefficient. The first two properties are present in the literature,
however; the air entrainment coefficient for this specific water condition is not available.
One way to determine the coefficient is to calibrate the value through conducting a series
of controlled experiments. Unfortunately, that was not a viable option due to time
constraints. Because we kept the constant at 0.5, the accuracy of the results may have
been influenced. Among other possible limitations was the size of the mesh cells. An
increased number of cells resulted in longer simulation times; some accuracy was
sacrificed in order to keep the simulations reasonably short.
The 2-D numerical analysis of the hydraulic phenomenon gave results remarkably similar
to those observed in the laboratory. Further examination of fluid properties showed some
discrepancies between the numerical values obtained by the two methods; however, other
distinct similarities demonstrated the effectiveness and accuracy of Flow-3D™, a new
computational fluid dynamics tool, in the analysis of turbulent water conditions. The
results provided by the software were fairly close to the observed and measured
quantities, therefore we further utilized Flow-3D™ to obtain detailed qualitative and
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quantitative data to conduct a in-depth study on the recirculating current phenomenon,
and to verify the effectiveness of low head dams remediation options.
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Detailed Examination of Hydraulic
5.1. Reverse Current
When an object is trapped in the hydraulic at the base of a low-head dam it is obvious
that the object is being pulled toward the dam and held there by a strong force or some
combination of forces. It is not as obvious what that combination of forces is or how they
work together to create the high level of danger that exists at the base of low-head dam
structures. These unseen forces are what make these dams so dangerous and give them
the name, “drowning machines”.
The first force that traps an object and possibly the most obvious phenomena occurring at
low-head dams is the reverse current. The reverse current is an area, usually the entire
length of the dam, parallel with the face in which the velocity of the water is headed
upstream. This upstream velocity is counterintuitive because normally the velocity of a
moving body of water is directed downstream. Upstream velocity is what pulls
unsuspecting boating and fishing enthusiasts towards the face of the dam and begins a
series of events which creates one of the greatest hazards on water. The velocity of the
reverse current increases steadily as an objects location gets closer to the dam. It can be
seen from Figure 22 that the reverse velocity reaches its peak at the end of the reverse
current near the face of the dam. Due to the fact that velocity increases constantly until
the object reaches the face of the dam, the object will tend to have trouble escaping the
hydraulic.
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Sample
Location
0 velocity
Figure 22. Reverse current velocity measurement on the surface of downstream flow
5.2. Buoyancy
After an object is trapped by the reverse current the object is effected by two
overpowering forces, one pushing and the other pulling, both in a downward direction.
Water, typically with a high velocity (3-5 m/s) falls onto the trapped object and begins
forcing it downward. See simulation results of large scale model in Appendix B2. A
constant flow of water over the face of the dam creates a pushing force on the object. At
the same time the reverse current is hitting the base of the dam and being forced in the
downward direction. As the current moves downward it pulls the object down as it
begins to recirculate (see Appendix B2).
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As if two forces acting together pushing an object underwater is not daunting enough,
there is a property of the water at the base of the dam which works against the object as
well. The combination of the constant flow of water falling over the face of the dam and
turbulence from the recirculation causes a stark decrease in the density of the water. That
sharp decrease is then followed by a rapid increase to a value that becomes somewhat
steady for the entire area of the recirculating current. as demonstrated by Figure 23. The
decreased density at this area makes the object less buoyant and therefore tends to sink
instead of float.
Sample
location
Figure 23. Macroscopic density measurement of downstream flow
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5.3. Forward (bottom) velocity
Due to the combination of factors mentioned above the object ends up at the bottom of
the body of water with no real chance at getting back to the surface immediately. When
the object is at the base of the dam, submerged by water, it is carried out by the
downstream directed velocity which occurs at that point as illustrated by Figure 24. As
the object begins to be carried downstream by the current, the density of the water returns
to a more normal value. (See Figure 23). With a normal density value the object will
tend to float toward the surface due to buoyant effects. Also, at this point the velocity of
the recirculating current is directed upward, in the Z direction. This causes the object to
begin moving back toward the surface (see figure 24). The graph below shows that the
velocity of the water increases sharply until the bottom of the dam. Velocity then tapers
off with increasing distance from the dam. As stated before, once the object moves away
from the dam the velocity profile begins to develop a Z component to its velocity. This Z
component begins to appear just as the X component slows down to approximately
average velocity of the river. With less velocity to carry the object forward, it is carried
toward the top by the combination of the Z component of the velocity and is again caught
in the hydraulic. The combination of these two effects brings the object to the surface
where it is swept back into the face of the dam by the reverse current.
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0 Velocity
Sample
location
Figure 24. Reverse current velocity measurement on the surface of downstream flow
When considering how this dangerous condition is created at such an innocuous looking
structure it is seen that the situation is not nearly as simple as it first appears. There are
many variables which combine to create the right conditions for a hazard that is both
extremely dangerous and harmless looking at the same time.
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Numerical Analysis of Low Head Dam Retrofits
6.1. Baffled Blocks
After a detailed examination of the roller, two retrofit designs were chosen to be
numerically modeled. For the first retrofit, baffled blocks were placed on the downstream
end of the channel bed. The purpose of the blocks was to break up the recirculating
current by creating turbulence. The numerical model, however, showed that although
baffled blocks decreased the diameter of the hydraulic, they were unsuccessful in
eliminating it. As seen in Figure ###, the recirculating current is directed towards the
blocks, which ads additional hazards to the design. The figure also shows the decrease in
the magnitude of the velocity in the x direction is not significant.
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6.2. Four-Step Spillway
The second mode chosen was an already existing retrofit design that was presented by
Freeman and Garcia (1996). The model is a four-stepped spillway connected to an ogee
spillway. They claimed that their experimental data showed that the design completely
eliminates the hydraulic. The purpose of the numerical model was to validate their claim
by confirming the effectiveness of the four-stepped spillway. Figure 25 illustrates a 2
dimensional diagram of the simulation and a plot of x velocity on the surface. These
results did in fact confirm that the hydraulic is entirely eliminated using this remediation
option. The roller is no longer present and surface velocity is now directed downstream.
Sample
location
0 velocity
Figure 25. 2-D and 1-D plot of velocity at a four-stepped spillway retrofit.
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Laboratory Retrofit Analysis
7.1 Overview
While the efficiency of the stepped spillway retrofit has been established, the cost
involved in its implementation could make this option impractical. The Labyrinth Weir
is also deemed to possibly be financially impractical as a retrofit. Baffled Chutes have
been found unsatisfactory, and this leaves the Rock Arch Dam conversion as a viable
option for investigation. In seeking a more cost efficient solution, the basic idea of this
conversion was implemented only in the laboratory; since it was deemed too difficult to
numerically model this conversion. The data collected from the laboratory experiment is
available in Appendix E.
7.2. Observations
Shown below are two of the tests run to qualitatively discern the effects of rocks at
breaking up the dangerous rollers that form at the base of low-head dams. The first test
(Figure26)
under(RAD
known
initial conditions, and the same dam under
Figure # : is
4 ½an
inchogee
depth spillway
ogee recirculation
1A)
Figure # : 4 ½ inch Depth ogee retrofit (RAD 1B)
the same conditions, with the retrofit implemented.
Figure 26. Ogee dam with and without retrofit
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The second test is run on a straight dam, and once again the initial conditions are kept
Figure # : 4 5/8 inch depth straight dam recirculation (RAD 9A)
Figure # : 4 5/8 inch depth straight dam retrofit (RAD 9B)
during the implementation of the retrofit. See Figure 27.
Figure 27 . Straight Dam with and without the retrofit
Two different tailwater depths were measured for each flow rate, and the flow rate was
kept constant for four runs, two on the Ogee spillway, and two on the straight dam.
It
was observed that faster flow rates were the most efficient at remediation in our
scenarios. In our testing, optimum remediation occurs at high flow rates with greater
height differences between the rocks and the water surface. No remediation is seen to
occur at low flow rates, with high differences between the height of the rocks and water
above.
7.3. Data Analysis
From the data collected, it can be theorized that faster flow rates in coincidence with the
retrofit would be the most efficient at remediation. However, this may be due to the fact
that the water could be going too fast for a roller to develop. Also, when an object is put
into these conditions, it accelerates down the slope of the retrofit. It seems that the
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retrofit itself may reduce the hydraulic, but is a poor energy dissipater.
This type of
speed may be harmful to an object swept over the dam. Slower flow rates are very
unpredictable; the results vary greatly and depend mainly on the other parameters.
It was found that the optimum remediation occurs at high flow rates with high height
differences between the rocks and the water surface, and no remediation occurs at low
flow rates, with high differences between the height of the rocks and water above.
In accessing the remediation efficiency of the retrofit it is also necessary to consider the
initial strength of the roller, prior to implementation.
It would seem that a greater difference in the height of the dam and the height of the
rocks makes the retrofit less effective. Common sense would attest to this idea, but it is
only sparsely supported by our data. The greater the difference in height between the
surface of the water and the top of the rocks, the more one could expect the retrofit to
simulate a normal riverbed. More testing would be needed to confirm this theory. There
was no great difference in performance of the retrofit for either dam type, implying that
the shape of the original dam is not of great importance as long as a roller exists.
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7.4. Suggestions
It is suggested that in the implementation of this retrofit, the Rock Arch Dam conversion
should be followed. The larger boulders may create more turbulence and assist in energy
dissipation. Also, these larger boulders may help stabilize the rocks overall; during one
of the tests the rocks began to slip which is a valid concern with this retrofit. It is
similarly suggested that rocks not simply be dumped in front of a dam structure, though it
may be quite tempting to do so. Doing this may worsen the situation by disrupting the
energy dissipation and over time the rocks may be washed downstream. Also, the
decrease in energy dissipation may prove a threat to humans due to the high velocities
created and the dense nature of the rocks that they would be impacting.
A 5% incline is specified in the existing rock arch dam conversion; this has
environmental benefits in that this slope allows fish to migrate upstream. The purpose of
increasing the slope of this retrofit was to conserve the volume of construction material.
This was an attempt to lower the cost of the retrofit. If this cost effective solution has the
potential to reduce the hydraulic effectively, it may be implemented at sites where fish
migration is not an issue.
Retrofit Experimental Procedure (will be inserted to a different place next week)
It was deemed too difficult for the time period allotted, to create a numerical model of the
Rock Arch Dam conversion or any similar setup that utilizes rocks. In order to obtain
qualitative data a physical model was designed. We wanted to assess how critical the
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different size rocks and the specified slope were to the success of the retrofit. The
question highlighted was: Is it really necessary implement every detail of the Rock Arch
Dam Conversion or can one get similar results by merely sticking to its general idea?
A sturdy net material was obtained from a produce bag, this was cut, doubled over and
sewn together with fishing line, to make a rectangular pocket. By scaling down the
dimensions given in the report on the Rock Arch Dam conversion it was possible to
estimate the size of rocks needed to model realistic dimensions. Only the smaller size
rocks were used, not the larger boulders suggested.
The Ogee dam was tested first. Initial conditions were set, and after a roller developed,
the retrofit was tested under these same conditions. The same process was followed for
the straight dam. The slope of the retrofit was determined for each run. This was done by
measuring the height and length of the retrofit. An example of what the setup looks like is
shown in Figure #.
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Figure # : Straight Dam with retrofit implimented
Visual Data was collected in the form of video clips. The reach of the roller, if it
formed, the supercritical depth, the subcritical depth, and the height of the downstream
velocity were not deemed important in these tests. The objective of these tests was
purely to see if a hydraulic still formed with the use of the retrofit.
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