Air Entrainment - 01
Air Entrainment - 01
Air Entrainment - 01
DigitalCommons@USU
12-2009
Recommended Citation
Mortensen, Joshua D., "Factors Affecting Air Entrainment of Hydraulic Jumps within Closed Conduits"
(2009). All Graduate Theses and Dissertations. 531.
https://digitalcommons.usu.edu/etd/531
CLOSED CONDUITS
by
Joshua D. Mortensen
of
MASTER OF SCIENCE
in
Approved:
_________________________ _________________________
Steven L. Barfuss Blake P. Tullis
Major Professor Committee Member
_________________________ _________________________
Gary P. Merkley Byron R. Burnham
Committee Member Dean of Graduate Studies
2009
ii
ABSTRACT
by
While there has been a great deal of research on air entrainment at hydraulic
jumps within closed conduits, very little of the research has specifically addressed size
and temperature scale effects. Influences from jump location and changing length
characteristics on air entrainment have also received little attention from past research.
closed conduits, air flow measurements were taken in four different-sized circular pipe
models with similar Froude numbers. Each of the pipe models sloped downward and
created identical flow conditions that differed only in size. Additionally, specific
measurements were taken in one of the pipe models with various water temperatures to
identify any effects from changing fluid properties. To determine the significance of the
effects of changed length characteristics on air demand, air flow measurements were
taken with hydraulic jumps at multiple locations within a circular pipe with two different
together, the data from four different pipe models show that size-scale effects of air
entrained into hydraulic jumps within closed conduits are negligible. However, it was
determined that air entrainment was significantly affected by the water temperature.
Water at higher temperatures entrained much less air than water at lower temperatures.
Hydraulic jump location results showed that for both configurations the percentage of air
entrainment significantly increased as the hydraulic jump occurred near the point of air
release downstream. As the jump occurred nearer to the end of the pipe, its length
characteristics were shortened and air demand increased. However, jump location was
only a significant factor until the jump occurred some distance upstream where the length
characteristics were not affected. Upstream of this location the air demand was
(65 pages)
iv
CONTENTS
Page
ABSTRACT........................................................................................................................ ii
CHAPTER
I. INTRODUCTION .......................................................................................1
ABSTRACT.................................................................................... 5
INTRODUCTION .......................................................................... 6
LITERATURE REVIEW ............................................................... 7
RESULTS ..................................................................................... 13
DISCUSSION ............................................................................... 18
ABSTRACT.................................................................................. 23
INTRODUCTION ........................................................................ 24
v
LITERATURE REVIEW ............................................................. 25
EXPERIMENTAL SETUP AN PROCEDURE ........................... 28
RESULTS ..................................................................................... 30
DISCUSSION ............................................................................... 37
SUMMARY AND CONCLUSIONS ........................................... 38
REFERENCES ..................................................................................................................44
APPENDICES ...................................................................................................................46
Figure Page
2 Plan view of the model used for data collection at various temperatures ............. 12
3 Air demand vs. Froude number for each model size; (♦) 7.62 cm, (■) 17.7 cm,
(▲) 30.0 cm and (●) 59.1 cm diameters ............................................................... 13
4 Scale effects due to jump location near point of air release: (♦) 7.62 cm,
(▲) 30.0 cm and (●) 59.1 cm pipe diameters ....................................................... 14
5 Air demand vs. Froude number for each water temperature where (♦) 12.8°C,
(■) 29.4 °C, (▲) 48.9 °C and (●) 62.8 °C ............................................................. 15
6 Difference in air bubble size between (a) 12.8°C, (b) 29.4 °C, (c) 48.9 °C
and (d) 62.8 °C ...................................................................................................... 16
8 Cylindrical Air Capture Chamber (a) and Open Tank (b) air release
configurations ....................................................................................................... 28
9 Air demand vs. Froude of jumps located less than 17 diameters (♦), greater than
17 diameters (■) from the end of the pipe and Kalinske and Robertson’s curve
(solid line) ............................................................................................................. 30
10 Cases of altered characteristic lengths; Case 1 (a), Case 2 (b), and Case 3 (c) .... 32
11 Air demand vs. distance of the jump from the end of the pipe for (▲) 5.0 l/s,
(■) 4.4 l/s, and (♦) 3.8 l/s ...................................................................................... 33
17 12-inch pipe model and air capture chamber with vent ........................................ 49
vii
18 7-inch acrylic pipe model...................................................................................... 50
19 3-inch acrylic pipe and air intake just downstream of flow nozzle ...................... 51
20 Air capture chamber and vent on the 3-inch acrylic pipe ..................................... 51
21 Downstream control valve of 3-inch pipe and thermometer for size and
temperature scale tests .......................................................................................... 52
23 Roughened flow nozzle for rough water surface tests in 3 inch pipe ................... 53
25 Repeated runs for size and temperature tests to ensure repeatability of data ....... 56
26 Repeated runs for location tests in open tank to ensure repeatability of data ....... 56
viii
LIST OF SYMBOLS AND ABBREVIATIONS
List of Symbols
List of Abbreviations
INTRODUCTION
which entrains air into the flow due to its high level of turbulence at the air-water
interface. When a hydraulic jump occurs within a closed conduit and causes pressurized
flow downstream, the air that is entrained may cause problems within the conduit.
Pipelines with changing slopes, low-level outlet works of dams and other hydraulic
conduits have experienced choked flow, blow-back, negative pressures and other similar
problems due to air that was entrained through a hydraulic jump. Knowledge of the
amount of air that is entrained by a hydraulic jump is important for proper venting and air
release design.
Due to the many factors that may affect air entrainment, physical model studies
are often necessary to predict the amount of air entrained by a hydraulic jump (or air
demand of the jump). Great care must be taken when scaling results from models of two-
phase flows as size-scale effects may exist. Various model sizes may be necessary to
determine the significance of size-scale effects between the different sized structures.
An example of such a model study is a pipeline and air release system that was
modeled at the Utah Water Research Laboratory for MWH Global. This circular pipeline
was designed to transport treated effluent from the area of Las Vegas, Nevada to the
bottom of Lake Mead. Due to the slope of the pipe and the hydraulic grade line at the
lake surface, a hydraulic jump will always exist somewhere in the pipe. A passive air
venting system requiring no manual operation or maintenance was designed to capture all
2
of the free air entrained by the jump. This design consisted of air capture chambers
(short sections of larger diameter pipe with air vents near the top) placed in series down
the length of the pipe. This design was necessary to prevent any free air to be released
into the lake which could cause algae bloom and other environmental problems. Air
demand data was taken at hydraulic jumps in different sized pipe models to determine the
possibility and significance of size-scale effects between pipe sizes. Test results were
useful in optimizing the air release design, assuring that no free air would be released into
the lake.
This thesis studied size-scale, temperature and jump location effects of air
entrained by hydraulic jumps using a very similar pipe and air release design as the
MWH study. For size-scale effects, air entrainment rates were recorded in pipe sizes of
24-inch, 12-inch, 7-inch and 3-inch I.D. that were operated with common Froude
numbers. For water temperature effects, similar tests were performed in the 3-inch pipe
at four different water temperatures (55, 85, 120 and 145 °F). For the research on jump
location effects, air flow measurements were taken with hydraulic jumps located at
various distances from the pipe exit using two different air release structures at the end of
the pipe. One structure was the air capture chamber used in the size-scale effects study
and the other was an open tank. The roller and aeration lengths (characteristic lengths) of
the jump were expected to change with distance from the end of the pipe, possibly
guidance in this thesis. The research indicated that various factors may influence the air
demand of hydraulic jumps such as upstream Froude number (Kalinske and Robertson,
3
1943), jump location from an upstream air intake (Sharma, 1976), flow and exit
entrainment of hydraulic jumps in open channels showed that viscous and surface tension
effects can produce size-scale effects (Chanson, 2008a, 2008b, 2007, 2006, 1995).
jump location effects of air entrainment of hydraulic jumps within circular closed
conduits.
Specifics of the literature review, experimental set up, procedure and test results
are documented in Chapters II and III of this document. Chapter II addresses size-scale
effects from the four pipe sizes as well as temperature effects. Chapter III addresses
effects from jump location and changed characteristic lengths. Both chapters are journal
In summary, the main objective of this thesis was to determine how air demand of
• Size-scale effects
• Temperature effects
closed conduit and open channel flows have been reviewed and have been found useful.
However, results from these past studies do not specifically address the factors
investigated in the current research. The results obtained from the physical model studies
provide new insights into air entrainment processes of hydraulic jumps within closed
4
conduits. Hopefully, these results will be useful in future modeling processes and aid the
CLOSED CONDUITS 1
ABSTRACT
While there has been a great deal of research in air entrainment at hydraulic jumps
within closed conduits, very little of the research has specifically addressed size-scale
jumps in closed conduits, air flow measurements were taken in four different sized
circular pipe models with similar Froude numbers. Additionally, specific measurements
were taken in one of the models with various water temperatures to identify any effects
from changing fluid properties. Results showed that the percentage of air entrainment
was not affected by the size of the model. All together, the data from four different pipe
models show that scale effects of air entrained into hydraulic jumps within closed
conduits are negligible. However, it was determined that air entrainment was
1
Coauthored by Steven L. Barfuss P.E. and Michael C. Johnson Ph.D., P.E
6
1 Introduction
pressurized flow within a closed conduit will entrain air into the flow due to its high level
hydraulic jump is important for the proper design of pipelines, low-level outlet works of
dams, and other such conveyance systems. Past studies have shown that the amount of
air entrained and passed downstream by the jump within closed conduits is dependent on
many factors, including; Froude number (Kalinske & Robertson, 1943), and jump
location (Sharma, 1976). However, no studies were found that specifically addressed
scale effects of air entrainment of hydraulic jumps within closed conduits. Extensive
research by Chanson (2008a, 2008b, 2007) has shown that for open channel flows, scale
effects of air entrainment exist between different sized jumps with a common Froude
number. However, despite the many studies on air entrainment at hydraulic jumps
performed by Chanson, scale effects of air entrained by hydraulic jumps within closed
The primary objective of this study was to investigate size-scale effects of air
were taken at hydraulic jumps in four different sized pipe models that were operated with
common Froude numbers. A secondary objective of this research was to determine if air
models by recording air flow measurements at four different water temperatures. The
results of this study are important because the differences in conduit size and even water
temperature are often significant between model and prototype. It is expected that these
7
findings will give greater insight into air entrainment processes and will be valuable for
system design.
2 Literature Review
Kalinske and Robertson (1943) conducted some of the very first experiments of
air entrainment by measuring air entrainment rates at hydraulic jumps within a single
circular pipe at various slopes from 0 to 16.7 degrees. Their results showed that air
demand is dependent only on the Froude number immediately upstream of the jump and
not the slope of the pipe. From their data they developed the following air demand
relationship:
Qair
β= = 0.0066( Fr − 1)1.4 (1)
Qwater
In Eq. (1) β is the volumetric ratio of the air flow to water flow and Fr is the Froude
V
Fr = (2)
gye
In Eq. (2) g is the acceleration of gravity, V is the approach velocity and ye, the effective
depth, is the water cross-sectional flow area divided by the water surface width.
8
Kalinske and Robertson also found that for downward sloping pipes, multiple
hydraulic jumps may occur in series with a pressurized air pocket between them and that
the primary jump’s ability to entrain air is dependent the hydraulic features beyond the
jump (Estrada, 2007). Many others have built upon Kalinske and Robertson’s pioneering
conduit model for many different flow scenarios, including a hydraulic jump that fills the
conduit. After comparing his results to prototype data he found that Kalinske and
Robertson’s equation (Eq. 1) underestimated the air entrained by the hydraulic jump in
the prototype when the jump occurred at a considerable distance from the gate. He
claimed that prototype air demand was larger due a “pre-entrained” hydraulic jump which
pumps additional air that was entrained into the more turbulent upstream supercritical
flow. Sharma’s research indicates that jump location and water surface roughness
upstream of the jump may contribute to scale effects and should be accounted for when
measuring air entrainment rates. Despite the studies of Sharma and others, pipe size-
scale effects on air entrained into hydraulic jumps within circular closed conduits has not
circular pipe and compared her results to those found by Kalinske and Robertson (1943),
Wisner et al. (1975), Rajaratnam (1967), and Rabben et al. (1983). This comparison
showed significant differences of air demand between the various experiments. She
suggests that the different results may be due to differences in conduit geometry as well
as downstream flow and exit conditions. The comparison of Escarameia’s results with
9
other studies show that factors other than pipe size-scale effects may influence air
entrainment and great care should be taken to recognize the effect of each factor.
Hager et al. (1989 and 1990) have conducted many studies on a classical
hydraulic jump within open channels and reported that in addition to the Froude number
the Reynolds number also influences jump characteristics. They also defined the length
from the toe to the surface stagnation point as the surface roller length. Their
observations indicate that air bubbles intensively rise at the downstream end of the roller.
Although the characteristics of a hydraulic jump in a closed pipe may differ, knowledge
Chanson (2008a, 2008b, 2007, 2006, 1995) has extensively studied scale effects
of air entrainment in hydraulic jumps in open channel flows. His work shows that scale
effects may exist between two systems that are not dynamically similar. Complete
dynamic similitude is achieved only when each dimensionless parameter (Fr, Re, We) is
the same in both model and prototype (D.O.I., 1980). When comparing two hydraulic
jumps of different flume widths using Froude similitude, he found greater air entrainment
within the larger jump. Chanson determined that this was due to the jump’s greater
clearly shows the greater turbulence of the jump in the larger flume as well as a
difference in air bubble size. Greater incoming velocities and turbulence cause more
breakup of the air bubbles, resulting in smaller bubble size and greater air entrainment
tension effects do influence air entrainment because of their effect on turbulence and
bubble size. His results confirm that scale effects do exist for air entrainment of
hydraulic jumps in open channel flows. However, to date, Chanson’s research has not
In order to investigate the specific influence of model size and fluid properties on
air entrainment of hydraulic jumps in closed conduits, physical model studies were
conducted to compare results. Air entrainment rates were measured in four similar
circular pipe models with inside diameters of 7.62-cm, 17.7-cm, 30.0-cm and 59.1 cm
and lengths of 106, 120, 80, and 53 pipe diameters, respectively. Pipe length and
material varied due to space and visual constraints; each model was set at a 4%
downward slope. Air entrainment rates were obtained in each model by using a model
A031 Kanomax anemometer to measure air velocities through a 6.35 cm diameter air
intake located immediately downstream of an acrylic flow nozzle at the upstream end of
the pipe model. Pressure drop readings across the inlet of each air intake confirmed that
it would not limit the air flow for the range of air velocities measured. Water flow rates
were measured using a combination of calibrated magnetic, ultrasonic and venturi flow
meters.
Water entered each model through a flow nozzle which forced an open channel
flow condition with a smooth water surface. A gradually varied flow surface profile
developed down the length of the pipe until a hydraulic jump occurred downstream. At
11
the end of the pipe the water flowed through a larger diameter air capture chamber with
an air vent near the top to allow the free air to be released from the flow. A hydraulic
jump was forced to occur at a desired location by adjusting a control valve downstream
of the chamber. The air entrained by the jump was measured as it entered the system
through the acrylic intake inserted just downstream of the nozzle (Fig. 1).
For each model size, common Froude numbers (ranging 2.6 – 11.4) were obtained
by measuring the depth and velocity of the supercritical flow upstream of the jump
location. Due to the difficulty in acquiring an accurate depth measurement inside the
pipe, calculated Gradually Varied Flow (GVF) profiles of the water surface were used to
estimate the depth. Approximate visual measurements from the outside of the pipe were
made for verification. Once the hydraulic jump stabilized at the desired location, the air
entrainment for each run was quantified by averaging a three minute sample (180
velocity readings) of air velocity measurements and then calculating the volumetric air
flow rate (Qair). To ensure accuracy and repeatability, selected runs were repeated using
two identical anemometers and allowing data to be collected for up to ten minutes (600
3) (air demand) versus the respective Froude number for each model on the same graph.
Since the same range of Froude numbers was used for each model size, any existing scale
Qair
β= (100) (3)
Qwater
temperatures (12.8° C, 29.4° C, 48.9° C and 62.8° C) using the same procedure as the
size-scale effect data collection. The air was at room temperature (approximately 21.1°
C). The 7.62-cm I.D. model was used for the varied temperature tests. As with the size-
scale data, selected runs from each temperature were repeated using two anemometers
and allowing data to be collected for up to ten minutes (600 velocity readings).
through the system and pipe, then back into the tank as shown in Figure 2. Water
temperature was measured as the water left the capture chamber using a digital
thermometer and was kept within 2 degrees of the desired temperature during each test
series. Temperature effects were illustrated by plotting the percent air entrainment versus
the corresponding Froude number for each temperature on the same graph. Temperature
effects could be identified since a common Froude range was used for each temperature.
13
Figure 2 Plan view of the model used for data collection at various water temperatures
4 Results
Figure 3 shows air demand results of each pipe model compared to the Kalinske
and Robertson (1943) curve (Eq. 1). This curve was adjusted to fit the x-axis of Fr
instead of Fr-1 as presented in their article. The overlapping data from each model
shows that pipe size has very little effect on the percentage of air entrained by the
hydraulic jump. Air entrainment was dependent on the Froude number immediately
upstream of the jump, except when the hydraulic jump occurred near the air capture
chamber where the air is released from the flow. When the jump was located too near the
air capture chamber, the measured air entrainment increased. Jump lengths (from toe to
point where all air bubbles rose to surface) varied from about 15 to 20 pipe diameters.
Once the jump was more than about 20 pipe diameters upstream, the full length of the
jump was contained in the pipe and the influence of the air capture chamber was not a
factor.
14
25
20
15
β
10
0
0 1 2 3 4 5 6 7 8 9 10 11 12
Fr
Figure 3 Air demand vs. Froude number for each model size; (♦) 7.62 cm, (■) 17.7 cm,
observed in each pipe model where a primary hydraulic jump occurred followed by a
pressurized air pocket followed by a secondary hydraulic jump downstream. This almost
always occurred unless the primary jump was near the air capture chamber, and then only
one jump would occur. For some conditions, usually with greater water flow rates, the
air demand consistently oscillated. The primary hydraulic jump also oscillated about a
mean location in phase with the air demand, moving downstream as the air demand
increased and moved upstream as the air demand decreased. When this happened the
vent pipe out of the air capture chamber would fill with water and then be blown out in
phase with the oscillations of the air demand and hydraulic jump.
15
Figure 4 illustrates the difference in air entrainment at the hydraulic jump between
pipe sizes when a single hydraulic jump occurred too near the air capture chamber. For
this condition, jumps in the larger models entrained a greater amount of air. Figure 4
shows scale effects in air entrainment between the different model sizes for hydraulic
jumps at locations between 6 and 10 pipe diameters upstream of the air capture chamber.
It was determined that if the jump was further away from the air capture chamber than
about 20 pipe diameters, the effects illustrated in Figure 4 would not occur.
4
β
0
0 1 2 3 4 5 6 7
Fr
Figure 4 Scale effects due to jump location near point of air release: (♦) 7.62 cm, (▲)
temperature. As the temperature of the water increased, the amount of air entrained by
the hydraulic jump decreased (Fig. 5). There is only a slight difference between results
of 12.8 °C and 29.4 °C, but the trend becomes more significant with higher temperatures.
Primary and secondary hydraulic jumps were observed to be similar for all temperatures,
similar to the flow conditions of the size-scale data. As noted previously, a primary
hydraulic jump oscillated about a mean location and a secondary hydraulic jump occurred
25
20
15
β
10
0
2 4 6 8 10 12 14
Fr
Figure 5 Air demand vs. Froude number for each water temperature where (♦) 12.8°C,
It was noted that the size of the air bubbles entrained by the jump visually
increased with temperature. Figure 6 illustrates the difference in air bubble size between
hydraulic jumps with a common Froude number of 7.62. The air demand of each
temperature was 12.5 (a), 12.1 (b), 7.5 (c) and 3.2 (d).
Figure 6 Difference in air bubble size between (a) 12.8°C, (b) 29.4 °C, (c) 48.9 °C and
(d) 62.8 °C
Several factors may have contributed to the uncertainty and spread of the data.
These factors come from natural and experimental causes. First, the natural process of air
entrainment in a hydraulic jump is very unstable and erratic which is a significant cause
of the spread of the data. Additional uncertainty was introduced by estimating the depth
18
of the supercritical flow calculating a GVF profile. Depths were not steady as also
mentioned in Kalinske and Robertson’s (1943) study which also showed spread in their
data. Also, jump location and air demand oscillated about a mean value as previously
mentioned. Data points that were repeated several times with two anemometers and a 10
minute average (average of 600 velocity readings) produced similar results as the 3
minute average. While the results were similar, some uncertainty due to the anemometer
Despite the uncertainty of the data, definite trends and similarities were confirmed.
Tests in which data was collected for a longer period of time showed no significant
change of air demand or water depth over time. Data from these repeated runs added
confidence that the measured average air demand and estimated Froude number are
accurate representations of the actual values. They also showed that the air demand
trends were repeatable and consistent, despite the erratic nature of air entrainment at
5 Discussion
Results from the size-scale effect data show that for closed conduit flow, air
demand is not affected by pipe size. The data suggest that the absence of scale effects
between the different pipe model sizes was due to the confined flow downstream of the
hydraulic jump in which the air could not be immediately released from the flow. This
was true even when the downstream pipe was partially filled with air when multiple
experiment. Also, a correlation was found of results from different pipe sizes to Kalinske
19
and Robertson’s curve (Fig. 3). They did not indicate in their study where any of the
jumps occurred relative to the end of the pipe. The deviation from their curve,
particularly at lower Froude numbers, may be due to the close location of the hydraulic
jump to the end of the pipe. Also, Kalinske and Robertson did not indicate the
temperature of the water or if it was held constant for each run which may account for
slightly higher air demand results of this study in comparison to their curve.
The greater air demand that occurred when the hydraulic jump is located too near
the end of the pipe suggests that air entrainment is dependent on the extent that the
hydraulic jump is contained within the pipe. In other words, the jump’s location relative
to the point of air release downstream. For jumps 15 – 20 pipe diameters or closer to the
end of the pipe, air entrainment was dominated by the jump not being fully contained in
the pipe, despite the relatively low Froude number for these tests. This may be due to
reducing the length characteristics of the jump, or allowing the downstream end of the
jump roller to occur within the air capture chamber which would allow more air to be
freely released from the flow (Hager et al., 1990). The presence of scale effects for
jumps near the chamber suggests that size scaling effects may exist when the air is freely
released from the jump. This finding is consistent with Chanson’s (2008a, 2008b, 2007,
2006) work on scale effects of open channel hydraulic jumps in which the air can be
temperature was varied (Fig. 5). Since greater Reynolds numbers result from higher
20
temperatures one would expect greater air entrainment rates due to the increased
turbulence of the hydraulic jump as Chanson (2008b) described for open channel flow
hydraulic jumps. However, the opposite occurred when the jump was confined in a
closed conduit resulting in decreased air entrainment with increased water temperatures.
This may be explained by a visual inspection of the air bubbles entrained into the
hydraulic jump.
The bubbles within the air-water mixture expanded within the hydraulic jump and
were visually larger as temperature increased. Consequently, there was less breakup of
the larger air bubbles limiting the amount of air that could be entrained and passed
downstream. This may have been because of greater surface tension due to the increased
Weber number and surface area of the air bubbles. Also, the buoyant force is greater on a
bubble with more surface area which would keep it up in the recirculation region of the
jump roller, preventing it from being passed downstream. Also, air is less soluble in
water at higher temperatures. However, the majority of the air did not go into solution
but was passed downstream as air bubbles which rose to the pressurized air pocket at the
This trend of decreased air demand continued for rising temperatures even though
Reynolds and Weber numbers increased and Froude numbers remained the same for each
temperature. Photographs show a gradual increase of bubble size with temperature (Fig.
6). The visual inspection suggests that air entrained by a hydraulic jump is dependent on
Measurements were taken of air entrainment rates into four different sized pipe
models with similar Froude numbers and compared to identify any scaling effects.
determine if changing water properties would affect the amount of air entrained into a
hydraulic jump. Results showed that the percentage of air entrainment was not affected
by the size of the pipe model. However, results from the model with different water
temperatures.
From the comparison of air entrainment within the different sized models it may
be concluded that when the air is not immediately released downstream of the hydraulic
jump, the air demand is not dependent on the size of the conduit. Even though a larger
jump has more turbulence, it cannot entrain a greater percentage of air because the air
leaving the jump is not freely released and the fluid reaches a certain carrying capacity.
It can further be concluded that air entrainment is dependent on the jump’s location
relative to the point of air release on the downstream side of the hydraulic jump. When
the jump was near an air capture chamber, the air demand increased and scale effects
were detected between the different models. This is possibly due to the air being more
freely released from the hydraulic jump similar to open channel jumps which is in
After visually inspecting the air demand of different water temperatures, it was
concluded that air bubble size greatly affects the air demand of the hydraulic jump.
Higher water temperatures caused the air-water mixture to expand, forming larger air
22
bubbles. Consequently, larger air bubbles led to less breakup of the entrained air, causing
less air entrainment into the jump even though the Reynolds number had increased.
The findings from this study provide new insights into air entrainment processes
of hydraulic jumps within closed conduits. The absence of size-scale effects of air
entrained into hydraulic jumps in closed conduit flow should aid the practicing engineer
in predicting air entrainment rates for design purposes. Also, in addition to the other
factors that influence air entrainment, water temperature should be considered when
CLOSED CONDUITS 2
ABSTRACT
While there has been a great deal of research on air entrainment at hydraulic
jumps within closed conduits, very little of the research has specifically addressed how
the jump’s location from the point of downstream air release may influence the amount of
air it can entrain. To determine the significance of the effects of jump location on air
entrained by hydraulic jumps in closed conduits, air flow measurements were taken in a
7.62-cm circular pipe with two different air release configurations at the end of the pipe.
Results showed that for both configurations the percentage of air entrainment was
significantly affected by the hydraulic jump’s proximity to the point of air release
downstream. As the hydraulic jump occurred closer to the air release at the end of the
pipe air entrainment increased because characteristic lengths of the jump were shortened
allowing more air to be freely released. However, this was only a significant factor until
the jump occurred some distance upstream where it was then dependent only on the
2
Coauthored by Steven L. Barfuss, P.E., and Blake P. Tullis, Ph.D., P.E.
24
1 Introduction
transition from open channel to pressurized flow due to elevation changes or other
occurrences which cause the hydraulic grade line to be greater than the pipe diameter. A
hydraulic jump will entrain air into the flow due to its high level of turbulence at the air-
important for the proper design of pipelines, dam low-level outlet works, and other such
conveyance systems requiring air venting. Past studies have shown that the rate of air
entrained and passed downstream by the hydraulic jump, or air demand of the jump
within closed conduits is dependent on many factors, including; Froude number, flow and
exit conditions, jump and conduit geometry and jump location relative to the air supply.
However, no studies were found that specifically addressed how the location of the jump
in closed conduits relative to the point of air release downstream influences the rate of air
entrainment. It is suspected that the location of the hydraulic jump relative to the point of
downstream air release may affect the characteristics lengths of the jump which may also
The objective of this study was to investigate how air entrainment rates are
the point where the air is released from the flow. To accomplish this, air flow
measurements were made in conjunction with hydraulic jumps that completely fill the
conduit (open to pressurized flow) located at various positions within a circular pipe.
The measurements were made with two different air release structures at the end of the
pipe, one a pipe expansion with an air vent and the other an open tank to determine if
25
vented or free air release influences the amount of air entrained. Jump location was
defined by the distance from the jump toe to the end of pipe for each air release test
configuration. The results from this study are important because length characteristics
are suspected to influence air entrainment within a hydraulic jump and specific studies
are not found in the literature. It is expected that these findings will give greater insight
into air entrainment processes and will be valuable for system design.
2 Literature Review
Kalinske and Robertson (1943) conducted some of the very first experiments of
air entrainment within circular pipes by measuring air entrainment rates at hydraulic
jumps at open channel to pressurized flow at various slopes from 0 to 16.7 degrees. Their
results showed that air demand varied only with the Froude number immediately
upstream of the jump. Additionally they found that air demand was not dependent on the
slope of the pipe. From their data they developed the following air demand relationship
Qair
β= = 0.0066( Fr − 1)1.4 (1)
Qwater
In Eq. (1) β is the volumetric ratio of the air flow to water flow and Fr is the Froude
V
Fr = (2)
gye
26
In Eq. (2) g is the acceleration of gravity, V is the approach velocity and ye, the effective
depth, is the water area divide by the surface width upstream of the jump.
Others have built upon Kalinske and Robertson’s pioneering work by performing
similar air entrainment experiments of closed conduit flow. Sharma (1976) collected air
demand data in a lab-scale rectangular conduit model with a vertical gate under high
upstream head conditions for many different flow scenarios, including a hydraulic jump
that fills the conduit. After comparing his results to prototype data he determined that
hydraulic jump in the prototype when the jump occurred at a considerable distance from
the gate. He claimed that prototype air demand was larger due a “pre-entrained”
hydraulic jump which pumps additional air that was entrained into the more turbulent
upstream supercritical flow. Sharma’s research indicates that distance to a jump and
water surface roughness upstream of the jump may influence air entrainment and should
Wisner et al. (1975), Rajaratnam (1967), and Rabben et al. (1983) also developed
air demand relationships for hydraulic jumps. Escarameia (2007) compared the air
demand relationship from her results to those found by Kalinske and Robertson (1943),
Wisner et al., Rajaratnam, and Rabben et al. This comparison showed significant
differences of air demand between the various experiments which may be due to
Escarameia’s comparison with other studies shows that many factors may influence air
entrainment and great care should be taken to recognize the effect of each factor.
27
For hydraulic jumps in open channel flows Chanson (2008a, 2008b, 2007, 1995)
has extensively studied air entrainment. Chanson showed that in addition to Fr, Re and
Chanson’s studies may also be helpful in understanding air entrainment of closed conduit
hydraulic jumps.
rectangular channel and observed a turbulent recirculation region in which unsteady flow
reversals occurred. This region from the toe to the stagnation point was defined as the
surface roller length (Lr). It was observed that air bubbles intensively rise at the
downstream end of the roller. Hager also defined the aeration length (La) of an open
channel hydraulic jump (Fig. 7) as the length from the toe to the point where all the air
bubbles have risen to the surface (Chanson, 1995). Later Stahl and Hager (1999)
observed that in a circular pipe when the upstream depth is greater than 1/3 of the pipe
diameter, a hydraulic jump is similar to the classical hydraulic jump with a turbulent
surface roller. While these definitions do not address rates of air entrainment, they may
Figure 7 Schematic of open channel hydraulic jump roller (Lr) and aeration (La) lengths
28
3 Experimental Setup and Procedure
acrylic circular pipe with an inside diameter of 7.62 cm and a length of 8 m. The model
was set at a 4% downward slope. Air entrainment rates were obtained using a model
diameter air intake located at the upstream end of the pipe (Fig. 8). Pressure drop
readings across the inlet of the air intake confirmed that it was sufficiently large to not
limit the air flow. Water flow rates approaching the pipe model were measured using a
Water entered the conduit test section through a flow nozzle which created an
open channel flow condition with a smooth water surface (Fig 8). Primarily, the flow
nozzle eliminated the possibility for air entrainment near an upstream control valve or
slide gate which would create spray and disturb flow at the upstream end. Downstream
of the flow nozzle a gradually varied flow surface profile formed until a hydraulic jump
occurred downstream. At the end of the pipe the water flowed through a larger diameter
cylindrical air capture chamber with an air vent near the upstream top to allow the free air
to be released from the flow (Fig. 8a). A hydraulic jump was forced to occur at a desired
location by adjusting a control valve downstream of the chamber. Tests were repeated
using an open rectangular tank at the end of the pipe with a slide gate to control the jump
location (Fig. 8b). The air entrained by the jump was measured as it entered the system
through the acrylic intake inserted just downstream of the flow nozzle.
29
(a)
(b)
Figure 8 Cylindrical Air Capture Chamber (a) and Open Tank (b) air release
configurations
the depth and velocity of the upstream supercritical flow. Due to the difficulty in
acquiring an accurate depth measurement inside the pipe, Gradually Varied Flow (GVF)
profiles of the open water surface were used to estimate the depth. Approximate visual
measurements from the outside of the pipe were also made to validate this method.
30
Velocities were obtained by conservation of mass using the known flow rate and water
surface depth.
Once the hydraulic jump stabilized at the desired location, the air entrainment for
each run was quantified by averaging a three minute sample (180 readings) of air velocity
at the air intake and then calculating the volumetric air flow rate (Qair). The volumetric
ratio of air to water, or air demand, was then calculated (Eq. 5) and compared to the
upstream Froude number. The location of the hydraulic jump was defined by the
distance from the toe of the jump to the downstream end of the pipe.
Qair
β= (100) (5)
Qwater
To ensure accuracy and repeatability, selected runs were repeated using two
identical anemometers and allowing data to be collected for up to ten minutes (600
readings). Also, to determine if a rough upstream water surface would increase air
4 Results
air demand of a hydraulic jump vs. the upstream Froude number. It includes results from
both air release structures and shows that the air demand was dependent only on Froude
number except when the jump occurred too near the end of the pipe. For this particular
pipe and GVF profile, the Froude numbers decreased as the flow approached the pipe
exit. The largest aeration length observed was about 17 pipe diameters. When the jump
31
toe occurred closer than 17 pipe diameters from the end of the pipe, the downstream end
of the jump was not contained in the pipe and air entrainment increased despite the
Froude number, causing the vertical trend. When the jump toe occurred further upstream
than 17 pipe diameters the full length of the jump was contained in the pipe and flow
differences in air demand results were found between the air capture chamber and open
tank except when a jump occurred within 2 diameters of the end of the pipe at which
point a greater amount of air was entrained into the open tank configuration. A turbulent
roller was observed within the hydraulic jumps where much of the air was rising within
the jump at the downstream end of the roller, similar to Hager’s (1990) description.
25
20
15
β
10
0
0 2 4 6 8 10 12
Fr
Figure 9 Air demand vs. Froude of jumps located less than 17 diameters (♦), greater than
17 diameters (■) from the end of the pipe and Kalinske and Robertson’s curve (solid line)
32
Roller lengths (Lr) of 4 to 5 pipe diameters were observed as well as aeration
lengths (La) of 13 to 17 pipe diameters depending on the Froude number. Lr and La had
similar hydraulic characteristics as the classical open channel hydraulic jump but differed
in length. Results showed that altered characteristic lengths directly influenced the
Three separate cases of altered jump characteristic lengths were identified as well
as their specific influence on the air demand of the hydraulic jump. Each case is
illustrated in Figure 10 which defines Lj as the distance from the jump toe to the end of
the pipe, La as the original (undisturbed) aeration length, and Lr as the original
Case 1: Lj > La; the full length of the hydraulic jump is fully contained within the
conduit. Characteristic lengths are unchanged and air demand is dependent on Froude
number only.
Case 2: La > Lj > Lr; the actual aeration length is shortened by the end of the pipe. Air
Case 3: Lr > Lj; the actual roller length is shortened by the end of the pipe. Air demand
greatly increases and is dominated by this feature. Froude number is not significant.
33
(a)
(b)
(c)
Figure 10 Cases of altered characteristic lengths; Case 1 (a), Case 2 (b), and Case 3 (c)
34
Figure 11 illustrates how air demand was influenced by the distance (Lj/La) of the
jump toe from the end of the pipe. The three data sets are different water flow rates that
were tested. The greater flow rates naturally have higher Froude numbers which
correlate to greater air entrainment which is most apparent in Case 1. The alignment of
flow rate trends as the jump moves closer to the end of the pipe (right to left) indicates
that the Froude number is no longer a significant influence because the characteristic
lengths of the jump have been shortened. There is no significant change in air demand
until Case 3 which shows a drastic increase of air demand as the jump occurred closer to
the pipe exit. The line separating Case 3 and Case 2 corresponds to the original roller
lengths of the jumps tested. Similarly, the line between Case 2 and Case 1 corresponds to
8
Case 1
7
Case 2
6
5
β
0
0.0 0.5 1.0 1.5
Lj / La
Figure 11 Air demand vs. distance of the jump from the end of the pipe for (▲) 5.0 l/s,
toe occurred 10 diameters from the end of the pipe which allowed the full roller to form.
However, since a fully formed aeration length would be about 17 diameters for this
condition, it was cut short by the end of the pipe causing slightly increased air demand.
For Case 3 (Fig. 12a), the roller length, which is about 4-5 diameters when fully
developed, was cut short and the increase in air demand was even more significant. Air
demand continued to increase as the toe of the jump occurred closer to the end of the
pipe.
demand results. The supercritical flow upstream was visually roughened but air
entrainment rates were similar to the runs using the smooth flow nozzle. This indicates
that the hydraulic jump itself dominated the air entrainment rate and that the roughened
Several factors may have contributed to the uncertainty and spread of the data.
These factors come from natural and experimental causes. First, the natural process of air
entrainment in a hydraulic jump is very unstable and erratic which is a significant cause
of the spread of the data. Additional uncertainty was introduced by estimating the depth
of the supercritical flow calculating a GVF profile. Depths were not steady as also
mentioned in Kalinske and Robertson’s (1943) study which also showed spread in their
data. Also, jump location and air demand oscillated about a mean value as previously
mentioned. Data points that were repeated several times with two anemometers and a 10
minute average (average of 600 velocity readings) produced similar results as the 3
minute average. While the results were similar, some uncertainty due to the anemometer
Despite the uncertainty of the data, definite trends and similarities were
confirmed. Tests in which data was collected for a longer period of time showed no
significant change of air demand or water depth over time. Data from these repeated runs
added confidence that the measured average air demand and estimated Froude number
are accurate representations of the actual values. They also showed that the air demand
trends were repeatable and consistent, despite the erratic nature of air entrainment at
For both air release configurations results of air demand vs. Froude number
correlated with Kalinske and Robertson’s (1943) results when the hydraulic jump was
greater than 17 diameters from the end of the pipe. It is not indicated in the Kalinske
study the location of hydraulic jumps in relation to the end of the pipe or if the jump’s
characteristic lengths were changed. Although the Kalinske data does indicate a greater
spread at lower Froude numbers, the spread in the present data at lower Froude numbers
is due to the changing of the hydraulic jump’s characteristic lengths because of its
lengths were identified. In Case 1 the characteristic lengths of the jump were allowed to
fully form and are completely contained within the pipe. For this case, the flow reached a
certain carrying capacity due to the pressurized air pocket that formed at the crown of the
pipe. Air demand was dependent on the Froude number only. For Case 2, La was cut
short and less air downstream of the jump was confined to the pressurized air pocket at
the crown of the pipe. This may have caused the slight increase in air demand for this
condition. However, there was not a significant difference of air demand in Cases 1 and
2.
Case 3 was the most interesting because of the drastic increase of air demand
compared to Cases 1 and 2. Due to Lr being shortened, the portion of air that was
normally re-circulated by the reversed velocities within the roller was instead passed
downstream. Since a great deal of air bubbles rise at the downstream end of the roller as
described by Hager et al. (1990), this caused a significant increase in air demand despite
38
the low Froude number. The closer the jump toe occurred to the end of the pipe, the
greater amount of air was allowed to short-cut through the jump and was released at the
end of the pipe. The characteristic lengths of each jump were estimated by observation
only. To date, there is no mathematical relationship that can accurately predict these
lengths for the specific case of a hydraulic jump that completely fills a circular conduit.
There was no significant increase in air demand during the tests with a roughened
upstream water surface, which is not consistent with the results from Sharma’s study.
This may be due to pipe scale size, upstream approach length differences and/or physical
disturbances near the upstream control gate. Again, this study installed a hydraulically
smooth nozzle at the upstream end to eliminate all disturbed flow allowing for the
Measurements were taken of air entrainment rates into a circular pipe with two
different air release configurations at the end of the pipe. The results of both air release
configurations showed that air entrainment rates were greatly influenced by altered jump
length characteristics due to the jump’s location to the downstream air release point.
Three cases or conditions were identified to show how characteristic lengths were altered
The first case was when the jump occurred far enough away from the end of the
pipe that the length characteristics were not affected. For this condition, the air demand
of the jump was dependent only on the Froude number as shown by Kalinske and
39
Robertson (1943). In the second case the jump occurred close enough to the end of the
pipe to shorten the aeration length of the jump. For this specific study, this occurred if
the jump toe was closer than 17 pipe diameters from the end of the pipe. In this condition
not all of the air downstream of the jump was confined to the air pocket at the crown of
the pipe and air demand slightly increased despite the Froude number.
The third case occurred when the jump was close enough to the end of the pipe to
shorten the jump roller. For this condition the air that was normally re-circulated within
the jump roller was passed downstream and the air demand increased significantly. Since
the downstream end of the roller was no longer confined within the pipe the air was
freely released from the jump. These results correspond with Hager’s (1990)
observations of air bubbles intensively rising at the downstream end of the jump roller.
The findings from this study provide new insights into additional factors which
influence air entrainment of hydraulic jumps within closed conduits. Understanding how
a hydraulic jump’s length characteristics are affected by the location to a downstream air
release and its effect on air demand should aid the practicing engineer in predicting air
prototype pipeline, the Utah Water Research Laboratory performed a physical model
study to obtain results from four different sized circular pipes. The data from these tests
helped determine the significance of size-scale effects and use the air demand prediction
to optimize the design of the prototype air release structure. Additional research was
of hydraulic jumps. Hydraulic jump location from the air release point and its effects on
jump characteristic lengths and air demand was also investigated by obtaining data from
a circular pipe with two different air release structures. Test results for each of these
Results from the size-scale effect data showed that air demand was not affected
by the size of the pipe. This was true as long as the jump occurred far enough upstream
from the air release structure so the free air would not be immediately released from the
flow. From the comparison of data from different sized pipes it may be concluded that
when the air is not immediately released downstream of the hydraulic jump, the air
demand is not dependent on the size of the conduit. Even though a larger jump has more
turbulence, it cannot entrain a greater percentage of air because the air leaving the jump is
not freely released and the fluid reaches a certain carrying capacity.
Temperature results showed that the air demand was significantly affected by the
water temperature. The data confirmed that the jump was able to entrain less air with
41
higher water temperatures. After visually inspecting the air demand of different
temperatures, it was concluded that air bubble size greatly affects the air demand of the
hydraulic jump. Higher water temperatures caused the air-water mixture to expand,
forming larger air bubbles. Consequently, larger air bubbles led to less breakup of the
entrained air, causing less air to be entrained into the jump even though the Reynolds and
Weber numbers had increased. Surface tension and buoyancy of the larger bubbles may
have also influenced how air was passed downstream through the jump.
Data from various hydraulic jump locations showed that air demand significantly
increased when the jump occurred close enough to the end of the pipe to change its
hydraulic length characteristics. If the toe of the jump occurred at a distance less than its
roller length (Lr) air demand drastically increased (Case 3). Visual observations suggest
this increase was due to the downstream end of the roller, where much of the air rises to
the surface, being cut short by the end of the pipe which allowed the air to be
immediately released from the flow. Similarly, if the jump occurred at a distance less the
aeration length of the jump (La) the increase in air demand was significant but not as
drastic (Case 2). It was concluded that this was due to the aeration length of the jump
being shortened by the end of the pipe where the air bubbles were still rising and were
not confined by the downstream flow. If the jump occurred further upstream than its
aeration length, the free air that rose to the surface was confined to a pressurized air
pocket and the air demand became a function of the Froude number only (Case 1). It
may be concluded that air entrainment rates increase as the free air is more immediately
• Size-scale effects
• Temperature effects
For this purpose physical model studies have been conducted and results
documented to provide new insights into air entrainment processes of hydraulic jumps
within closed conduits. It is expected that these results will be useful in aiding the
practicing engineer in predicting air entrainment rates and will be valuable for system
design.
43
CHAPTER V
FUTURE RESEARCH
Due to the unstable and erratic nature of air entrainment at hydraulic jumps there
is still much that is unknown. Additional research is needed to better understand the
processes of air entrained by hydraulic jumps and the factors that influence those
processes. Specifically, for the case of a hydraulic jump at a transition from open
• Comparison of air demand data from prototypes to model results for the same
flow conditions, air release structure and pipe geometry as it becomes available
• Additional data from a greater range of temperatures (less than 40 ˚F and greater
• Dynamics of released air flow through various air removal structures and their
influence air entrainment processes through closed conduit hydraulic jumps but were not
addressed in the current research. Any insights provided from future research, especially
information of how model results compare to prototype results, would be of great value
Chanson, H., Murzyn, F. (2008a). Froude similitude and scale effects affecting air
entrainment in hydraulic jumps. World Environmental and Water Resources Congress
2008 Ahupua’a ASCE.
Chanson, H., Gualtieri, C. (2008b). Similitude and scale effects of air entrainment in
hydraulic jumps. J. Hydr. Res. 46(1), 35-44.
Chanson, H., Gualtieri, C. (2007). Experimental analysis of Froude number effect on air
entrainment in the hydraulic jump. Environ. Fluid Mech. 7, 217-238.
Chanson, H. (2006). Air bubble entrainment in hydraulic jumps. Similitude and scale
effects. Report No. CH57/05, Dept. of Civil Engineering, The University of Queensland,
Brisbane, Australia, (ISBN 1864998423)
Chanson, H. (1995). Air-water gas transfer at hydraulic jump with partially developed
inflow. Water Res., IAWPRC, 29(10), 2247-2254 (ISSN 0043-1354).
Escarameia, M. (2007). Investigating hydraulic removal of air from water pipelines. The
institution of Civil Engineers Water Management I60, issue WMI, pg. 25-34.
Hager, W.H., Bremen, R., Kawagoshi N. (1990). Classical hydraulic jump: length of
roller. J. of Hydr. Res. 28(5), 591-608.
Hager, W.H., Bremen, R. (1989). Classical hydraulic jump: sequent depths. J. Hydr. Res.
27(5), 565-585.
Kalinske, A.A., Robertson, J.M. (1943). Closed conduit flow. Transactions, ASCE, 108,
1435-1447.
Rabben S. L., Els, H., Rouve, G. (1983). Investigation on flow aeration at offsets
downstream of high-head control structures. Proceedings of the 20th IAHR Congress,
Moscow, USSR, 4, 354–360.
Sharma, H.R., (1976). Air-Entrainment in high head gated conduits. Journal of the
Hydraulics Division, Proceedings of the American Society of Civil Engineers,
102(HY11), 1629-1646.
45
Stahl, H., Hager, W.H. (1999). Hydraulic jump in circular pipes. Can. J. Civil
Engineering, 26, 368-373.
Wisner, P.E., Mohsen, F.N., Kouwen, N. (1975). Removal of air from water lines by
hydraulic means. Journal of the Hydraulics Division, Proceedings of the American
Society of Civil Engineers, 101(HY2), 243-257.
46
APPENDICES
47
Figure 17 12-inch pipe model and air capture chamber with vent
51
Figure 19 3-inch acrylic pipe and air intake just downstream of flow nozzle
Figure 20 Air capture chamber and vent on the 3 inch acrylic pipe
53
Figure 21 Downstream control valve of 3-inch pipe and thermometer for size and
Figure 23 Roughened flow nozzle for rough water surface tests in 3-inch pipe
55
Figure 24 Example of spreadsheet used to calculated distance to jump, Fr, V, Qwater and
Qair using GVF water surface profiles (red text indicates values entered in spread sheet)
57
25
20
55 Anemometer 1
15
Anemometer 2
β
Original Run
10
10 minutes of data
5
145
0
2 3 4 5 6 7 8 9 10 11 12 13 14
Fr
Figure 25 Repeated runs for size and temperature tests to ensure repeatability of data
25
20
15 Anemometer 1
Anemometer 2
β
10 Original Run
10 min. of data
0
2 4 6 8 10
Fr
Figure 26 Repeated runs for location tests in open tank to ensure repeatability of data