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Journal ArticleDOI

Total pressure fluctuations and two-phase flow turbulence in hydraulic jumps

05 Nov 2014-Experiments in Fluids (Springer Berlin Heidelberg)-Vol. 55, Iss: 11, pp 1847

AbstractThe large-scale turbulence and high air content in a hydraulic jump restrict the application of many traditional flow measurement techniques. This paper presents a physical modelling of hydraulic jump, where the total pressure and air–water flow properties were measured simultaneously with intrusive probes, namely a miniature pressure transducer and a dual-tip phase-detection probe, in the jump roller. The total pressure data were compared to theoretical values calculated based upon void fraction, water depth and flow velocity measured by the phase-detection probe. The successful comparison showed valid pressure measurement results in the turbulent shear region with constant flow direction. The roller region was characterised by hydrostatic pressure distributions, taking into account the void fraction distributions. The total pressure fluctuations were related to both velocity fluctuations in the air–water flow and free-surface dynamics above the roller, though the time scales of these motions differed substantially.

Topics: Total pressure (63%), Hydrostatic pressure (63%), Pressure measurement (59%), Flow measurement (59%), Hydraulic jump (59%)

Summary (1 min read)

1 Introduction

  • The jump toe, where the upstream flow impinges into the downstream region, is a singular locus with discontinuity in velocity and pressure fields (Rajaratnam 1967).
  • Any theoretical and numerical analyses of hydraulic jumps are based upon a large number of relevant equations to describe the two-phase turbulent flow motion and the interaction between entrained air and turbulence.
  • The phase-detection probe was excited by an electronic system designed with a response time less than 10 µs, and scanned at 5 kHz simultaneously with the total pressure probe and an acoustic displacement meter above the probe leading tip.
  • The simultaneous sampling of all instruments was performed for 180 s at each measurement location.

3 Results

  • 1 Basic flow patterns Observations showed some enhanced flow aeration and turbulent fluctuations with increasing Froude number.
  • Figure 4 shows a comparison between the vertical void fraction distributions in the present study and Wang & Chanson (2014) for identical flow conditions and longitudinal positions.
  • The instantaneous bubble distribution was highly affected by the turbulent flow structures, and bubbles tended to travel in clusters rather than in randomness (Chanson 2007).
  • The turbulence intensity Tu" deduced from the high-frequency signal component reflected the 'true' turbulence of the flow.

4 Discussion: characteristic total pressure fluctuation frequencies

  • The instantaneous total pressure signals exhibited some pseudo-periodic patterns.
  • The analysed characteristic total pressure fluctuation frequencies are summarised in Table 2.
  • The relatively high-frequency filtered signals (0 – 25 Hz) exhibited a range of typical fluctuation frequencies Fp(H) between 8 and 12 Hz, whereas the low-frequency filtered signals (0 – 5 Hz) gave a frequency Fp(L) about 2.6 Hz.
  • Figure 15a shows a smaller dimensionless frequency Fp(H)×d1/V1 for a higher Froude number, which decreased with increasing distance from the jump toe.
  • The comparable decreasing trends along the roller might suggest some correlation between the detected pressure fluctuations and the turbulent air-water flow features, of which the longitudinal decay was related to the diffusion and dispersion of bubbly flow structures as well as the turbulence dissipation.

4 Conclusion

  • The total pressure and air-water flow properties were measured simultaneously at adjacent locations in hydraulic jump rollers, together with the water level fluctuations above.
  • Four Froude numbers were investigated with the same intake aspect ratio and inflow length, corresponding to partiallydeveloped inflow conditions.
  • The bubble count rate was however underestimated when the Froude and Reynolds numbers were large.
  • The total pressure was predicted based upon the void fraction and velocity data, and the predictions agreed well with experimental results given by the total pressure probe.
  • This was supported by comparison between relative total pressure fluctuation and turbulence intensity, and a preliminary investigation of pressure fluctuation frequencies.

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WANG,H.,MURZYN,F.,andCHANSON,H.(2014)."TotalPressureFluctuationsandTwoPhaseFlowTurbulenceinHydraulicJumps."
ExperimentsinFluids,Vol.55,No.11,Paper1847,16pages(DOI:10.1007/s0034801418479)(ISSN07234864).
1
Total pressure fluctuations and two-phase flow turbulence in hydraulic
jumps
Hang Wang (
1
) (*), Frédéric Murzyn (
2
) and Hubert Chanson (
1
)
(
1
) The University of Queensland, School of Civil Engineering, Brisbane QLD 4072, Australia
(
2
) ESTACA Campus Ouest, Parc Universitaire de Laval Changé, BP 53061 Laval Cedex 9, France
(*) Corresponding author: hang.wang@uqconnect.edu.au
Abstract
The large-scale turbulence and high air content in a hydraulic jump restrict the application of many
traditional flow measurement techniques. This paper presents a physical modelling of hydraulic jump,
where the total pressure and air-water flow properties were measured simultaneously with intrusive
probes in the jump roller, namely a miniature pressure transducer and a dual-tip phase detection
probe. The total pressure data were compared to theoretical values calculated based upon void
fraction, water depth and flow velocity measured by the phase-detection probe. The successful
comparison showed valid pressure measurement results in the turbulent shear region with constant
flow direction. The roller region was characterised by hydrostatic pressure distributions, taking into
account the void fraction distributions. The total pressure fluctuations were related to both velocity
fluctuations in the air-water flow and free-surface dynamic above the roller, though the time scales of
these motions deferred substantially.
Keywords
Hydraulic jump, Total pressure, Two-phase flow, Turbulence, Physical modelling
List of symbols
C Time-averaged void fraction
C
max
Local maximum time-averaged void fraction in the shear flow region
D
#
Dimensionless diffusivity in the turbulent shear region
D* Dimensionless diffusivity in the free-surface region
d
1
Inflow water depth immediately upstream of the jump toe [m]
F Bubble count rate [Hz]
F
clu
Longitudinal bubble cluster count rate [Hz]
(F
clu
)
max
Maximum cluster count rate in the shear flow region [Hz]
F
fs
Characteristic free-surface fluctuation frequency [Hz]
F
max
Maximum bubble count rate in the shear flow region [Hz]
F
p
(H)
Upper total pressure fluctuation frequency [Hz]
F
p
(L)
Lower total pressure fluctuation frequency [Hz]
Fr
1
Inflow Froude number,
11 1
Fr = V g×d
g Gravity acceleration [m/s
2
]
h Upstream gate opening [m]
L
r
Length of jump roller [m]
P Time-averaged total pressure [Pa]
P
k
Kinetic pressure [Pa]
P
max
Maximum mean total pressure in the shear flow region [Pa]
P
o
Piezometric pressure [Pa]
p' Standard deviation of total pressure [Pa]
p'
max
Maximum total pressure fluctuation [Pa]
Q Flow rate [m
3
/s]

WANG,H.,MURZYN,F.,andCHANSON,H.(2014)."TotalPressureFluctuationsandTwoPhaseFlowTurbulenceinHydraulicJumps."
ExperimentsinFluids,Vol.55,No.11,Paper1847,16pages(DOI:10.1007/s0034801418479)(ISSN07234864).
2
Re
Reynolds number,
11
Re =ρ×V ×d μ
T Time lag for maximum cross-correlation coefficient [s]
T
0.5
Time lag for maximum auto-correlation coefficient [s]
Tu Turbulence intensity
Tu" Decomposed turbulence intensity of high-frequency signal component
U Free-stream velocity in upstream supercritical flow [m/s]
V Average air-water interfacial velocity [m/s]
V
max
Maximum interfacial velocity in the shear flow region [m/s]
V
recirc
Average recirculation velocity in the free-surface region [m/s]
V
1
Average inflow velocity [m/s]
v' Standard deviation of interfacial velocity [m/s]
W Channel width [m]
x Longitudinal distance from the upstream gate [m]
x
1
Longitudinal position of jump toe [m]
Y
Cmax
Characteristic elevation of local maximum void fraction in the shear region [m]
Y
Fmax
Characteristic elevation of maximum bubble count rate in the shear region [m]
Y
Pmax
Characteristic elevation of maximum mean total pressure in the shear region [m]
Y
p'max
Characteristic elevation of maximum total pressure fluctuation in the shear region
[m]
Y
Vmax
Characteristic elevation of maximum interfacial velocity in the shear region [m]
Y
0.5
Characteristic elevation of half maximum interfacial velocity [m]
Y
50
Characteristic elevation where C = 0.5 [m]
Y
90
Characteristic elevation where C = 0.9 [m]
y Vertical distance from the channel bed [m]
y* Characteristic elevation of local minimum void fraction [m]
z Transverse distance from the channel centreline [m]
Δx Longitudinal separation distance between two phase-detection probe sensors [m]
δ Inflow boundary layer thickness at channel bed [m]
μ Water dynamic viscosity [Pa×s]
ρ
Water density [kg/m
3
]
τ Time lag [s]
τ
0.5
Time lag between maximum and half maximum cross-correlation coefficient [s]
1 Introduction
A hydraulic jump is a rapidly-varied open channel flow characterised by a sudden transition from a
supercritical flow motion to a subcritical regime. The jump toe, where the upstream flow impinges
into the downstream region, is a singular locus with discontinuity in velocity and pressure fields
(Rajaratnam 1967). The transition region immediately downstream of the toe is named the jump
roller because of the presence of large-scale vortices and flow recirculation. The jump roller is a
turbulent two-phase flow region with coexistence of and interaction between air entrainment,
turbulence and flow instabilities.
The turbulent nature of hydraulic jump leads to an efficient energy dissipation rate. For example, an
inflow Froude number Fr
1
= 9 gives a theoretical energy dissipation rate exceeding 70%, where the
Froude number is defined as Fr
1
= V
1
×(g×d
1
)
-1/2
, V
1
being the average inflow velocity and d
1
the
inflow depth. Therefore hydraulic jumps are often generated in hydraulic structures for the purpose

WANG,H.,MURZYN,F.,andCHANSON,H.(2014)."TotalPressureFluctuationsandTwoPhaseFlowTurbulenceinHydraulicJumps."
ExperimentsinFluids,Vol.55,No.11,Paper1847,16pages(DOI:10.1007/s0034801418479)(ISSN07234864).
3
of energy dissipation (Fig 1). However, the large shear force and fluctuating motions of the flow may
challenge the strength of construction, e.g., on the bottom of the jump in a stilling basin. In the early
20
th
century, the attention to hydraulic jump was first triggered with the design of energy dissipators,
which was developed by USBR (U.S. Bureau of Reclamation) in 1940s and 1950s (Riegel and Beebe
1917, Peterka 1958). A number of studies contributed to the pressure quantification mainly beneath
hydraulic jumps (Vasiliev & Bukreyev 1967, Schiebe 1971, Abdul Khader & Elango 1974, Lopardo
& Henning 1985, Fiorotto & Rinaldo 1992, Yan & Zhou 2006, Lopardo & Romagnoli 2009). The
relationship between cavitation occurrence and pressure fluctuations was investigated (Narayanan
1980). The pressure fluctuations were further correlated with water level fluctuations and/or velocity
turbulence in some limited flow conditions with minor aeration (Onitsuka et al. 2009, Lopardo 2013).
In most prototype conditions with large inflow Froude number, the air entrainment in hydraulic jump
is significant. Air entrapped at the jump toe as well as through the rough roller surface is advected
downstream by large vortical structures (Long et al. 1991). The diffusive advection of air bubbles
interplays with the turbulence development. The studies of two-phase flow properties were
represented by Rajaratnam (1962), Resch & Leutheusser (1972) and Chanson (1995) describing the
air concentration and interfacial velocity characteristics using air-water interface detection
techniques. The turbulence characterisation was promoted by Chanson & Toombes (2002) and
Chanson & Carosi (2007) and recently developed by Wang et al. (2014) based upon statistical
analysis of interface detection signals. In a few attempts of numerical modelling, the air entrainment
was rarely taken into account together with the dynamic features of the flow (Richard & Gavrilyuk
2013). Physical modelling with consideration of simultaneous air entrainment and flow
turbulence/fluctuations included Cox & Shin (2003), Murzyn & Chanson (2009) and Wang &
Chanson (2014).
Direct pressure measurement in hydraulic jump flows with strong air entrainment are lacking despite
the significance in hydraulic engineering. This paper presents new experiments measuring the total
pressure distributions within the jump roller. The air-water flow properties were characterised at the
adjacent locations, and the water level fluctuations above were recorded as well. The application of
total pressure transducer in such turbulent bubbly flow was justified by a comparison between the
total pressure output and calculations based upon air-water flow measurement results. The present
work provides new information on the flow regime and fluctuating nature of hydraulic jumps, and
allows further investigation on the interactions between turbulence, aeration and flow instabilities in
such a flow.
2 Physical modelling and instrumentation
2.1 Dimensional considerations
Any theoretical and numerical analyses of hydraulic jumps are based upon a large number of
relevant equations to describe the two-phase turbulent flow motion and the interaction between
entrained air and turbulence. The outputs must be tested against a broad range of gas-liquid flow
measurements:"Unequivocally [...] no experimental data means no validation" (Roache 2009).
Physical modelling requires the selection of a suitable dynamic similarity (Liggett 1994).
Considering a hydraulic jump in a smooth horizontal rectangular channel, dimensional
considerations give a series of dimensionless relationships in terms of the turbulent two-phase flow
properties at a position (x,y,z) within the hydraulic jump roller as functions of the inflow properties,
fluid properties and channel configurations. Using the upstream flow depth d
1
as the characteristic
length scale, a dimensional analysis yields

WANG,H.,MURZYN,F.,andCHANSON,H.(2014)."TotalPressureFluctuationsandTwoPhaseFlowTurbulenceinHydraulicJumps."
ExperimentsinFluids,Vol.55,No.11,Paper1847,16pages(DOI:10.1007/s0034801418479)(ISSN07234864).
4
11 11
1
22
11111 111111
F×d x-x v ' x
Pp'Vv' yz W
, , , ,C, ,... = F , , ,Fr ,Re, , , ,...
0.5×ρ×V 0.5×ρ×V V V V d d d V d d



(1)
where P and V are the total pressure and velocity respectively, p' and v' are pressure and velocity
fluctuations, C is the void fraction, F is the bubble count rate, x
1
is the jump toe position, Re is the
Reynolds number, W is the channel width and the subscript 1 refers to the inflow conditions. In a
hydraulic jump, the momentum considerations demonstrated the significance of the inflow Froude
number, and the selection of the Froude similitude derives implicitly from basic theoretical
considerations (Lighthill 1978, Liggett 1994). Equation (1) shows that measurements in small size
models might be affected by viscous scale effects because the Reynolds number is grossly
underestimated. In the present study, the experiments were performed in a relatively large-size
facility to minimise scale effects (Murzyn & Chanson 2008, Chanson & Chachereau 2013).
2.2 Experimental setup and flow conditions
The experimental channel was 3.2 m long and 0.5 m wide, built with horizontal HDPE bed and 0.4 m
high glass sidewalls (Fig 1b). The inflow was supplied to the flume from a constant head tank. A
rounded undershoot gate of the head tank induced a horizontal impinging flow without contraction.
The gate opening was set at h = 0.02 m, and hydraulic jumps were generated at x
1
= 0.83 m
downstream of the gate. The inflow depth was measured using a point gauge right upstream of the
jump toe. The tailwater depth and jump toe position were controlled by an overshoot gate at the end
of the channel. The flow rate was measured with a Venturi meter in the supply line. While the flow
rate measurement was within an accuracy of 2%, the precision of the determination of inflow depth
and jump toe position relied largely on the fluctuation level of the flow.
Four inflow Froude numbers Fr
1
= 3.8, 5.1, 7.5 and 8.5 were tested, corresponding to Reynolds
numbers 3.5×10
4
< Re < 8.0×10
4
. The total pressure and two-phase flow properties were measured
locally with intrusive total pressure probe and phase-detection probe. The probes were placed side by
side with a 9 mm transverse distance between the sensor tips and sampled at a number of elevations
in a vertical cross-section on the channel centreline. The instantaneous water elevation above the
measurement location was measured non-intrusively with an acoustic displacement meter. The
instrumental setup is illustrated in Figure 2, and the flow conditions are summarised in Table 1 along
with the longitudinal positions of the scanned cross-sections. With an inflow length x
1
/h = 41.5, the
inflow conditions were characterised by partially-developed boundary layer at the channel bed (δ/d
1
< 1 at x = x
1
, Table 1, 7
th
column). Figure 3a presents typical inflow velocity profiles measured with
a Prandtl-Pitot tube along the channel centreline. A developing boundary layer was shown with a
constant free-stream velocity U. Figure 3b compares the free-stream velocity U with the average
inflow velocity V
1
for a broader range of flow conditions. The results indicated U 1.1×V
1
because
the velocities in boundary layers were lower than the cross-sectional average. Resch & Leutheusser
(1972) and Thandaveswara (1974) compared the air-water flow properties for different types of
inflow conditions (partially-developed, fully-developed and per-entrained). The presence of highly-
aerated shear flow region (see 3.2.1 below) was only observed for partially-developed inflow
conditions, with the shortest aeration length (Chanson 1997).
2.3 Instrumentation
The total pressure probe consisted of a silicon diaphragm sensor mounted on the probe tip. The
sensor was a miniature Micro-Electro-Mechanical-System technology based pressure transducer
(Model MRV21, by MeasureX, Australia). Such a diaphragm pressure sensor is not affected by the

WANG,H.,MURZYN,F.,andCHANSON,H.(2014)."TotalPressureFluctuationsandTwoPhaseFlowTurbulenceinHydraulicJumps."
ExperimentsinFluids,Vol.55,No.11,Paper1847,16pages(DOI:10.1007/s0034801418479)(ISSN07234864).
5
presence of bubbles and does not require to be purged. The sensor had a 5 mm outer diameter with 4
mm diameter sensor. The model provided a measurement range between 0 and 1.5 bars (absolute
pressures). The response frequency was in excess of 100 kHz. The sampling frequency was set at 5
kHz in the present study, though the signal was filtered by a signal amplification system to eliminate
noises above 2 kHz. A daily calibration was conducted and regularly checked, because the output
voltage appeared to be temperature and ambient-pressure sensitive. The largest uncertainty of the
total pressure measurements was thought to be introduced by the fluctuations in atmospheric
pressure reading.
The dual-tip phase-detection probe was designed to pierce bubbles and droplets with its two needle
sensors and worked based upon the difference in electrical resistance between air and water. The
needle sensor tips (0.25 mm inner diameter) were separated longitudinally by Δx = 7.25 mm. While
the signal of each sensor gave the local void fraction and bubble count rate data, a cross-correlation
between the signals provided an average time T of the air-water interfaces travelling over the
distance Δx, yielding a mean longitudinal interfacial velocity V = Δx/T. The phase-detection probe
was excited by an electronic system designed with a response time less than 10 µs, and scanned at 5
kHz simultaneously with the total pressure probe and an acoustic displacement meter above the
probe leading tip. A Microsonic
TM
Mic+25/IU/TC acoustic displacement meter measured the
instantaneous water elevation with a 50 Hz response frequency which was lower than the sampling
rate. The sensor height was carefully adjusted to ensure that the displacement meter measurement
range covered the maximum free-surface fluctuations, and the erroneous samples caused by
splashing droplets were removed from the signal.
The simultaneous sampling of all instruments was performed for 180 s at each measurement location.
3 Results
3.1 Basic flow patterns
Observations showed some enhanced flow aeration and turbulent fluctuations with increasing Froude
number. The large-scale turbulent structures inside the roller were visualised by the entrained air
bubbles (Fig 1b). The formation of large turbulent structures was linked to the oscillations of jump
toe position and free-surface fluctuations (Long et al. 1991, Wang & Chanson 2014, Wang et al.
2014). These motions were observed in a pseudo-periodic manner, together with the associated air
entrapment and macroscopic variation in velocity and pressure fields. For instance, the slow pressure
pulsations could be felt by placing a hand in the roller. Basically the pulse of increasing impinging
pressure appeared to correspond to the downstream ejection of large vortices.
The water elevation measured along the channel centreline outlined the time-averaged free-surface
profiles similar to the visual observations. The length of hydraulic jump roller L
r
is defined as the
longitudinal distance over which the water elevation increases monotonically. The roller length was
derived from the free-surface profile and found to be an increasing function of the Froude number. A
linear relationship was given by the dataset consisting of Murzyn et al. (2007), Kucukali & Chanson
(2008), Murzyn & Chanson (2009), Wang & Chanson (2014) and the present study:
r
1
1
L
= 6×(Fr -1)
d
for 2 < Fr
1
< 10 (2)

Citations
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TL;DR: A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number, where both CFD codes had good behavior, but special care is required with swirling flows.
Abstract: A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number. Turbulence is treated using RANS approach RNG k-e. A Volume Of Fluid (VOF) method is used to track the air-water interface, consequently aeration is modeled using an Eulerian-Eulerian approach. Structured meshes of cubic elements are used to discretize the channel geometry. The numerical model accuracy is assessed comparing representative hydraulic jump variables (sequent depth ratio, roller length, mean velocity profiles, velocity decay or free surface profile) to experimental data. The model results are also compared to previous studies to broaden the result validation. Both codes reproduced the phenomenon under study concurring with experimental data, although special care must be taken when swirling flows occur. Both models can be used to reproduce the hydraulic performance of energy dissipation structures at low Reynolds numbers. Two CFD models: OpenFOAM and FLOW-3D for hydraulic jump in low Reynolds numbers.Representative variables are compared for the two CFD results and experimental data.The model results are also compared to previous studies with good agreement.Both CFD codes had good behavior, but special care is required with swirling flows.A quantification of both models accuracy relating to studied variables is proposed.

102 citations


Journal ArticleDOI
Abstract: We present direct numerical simulation (DNS) of a stationary turbulent hydraulic jump with inflow Froude number of 2, Weber number of 1820 and density ratio of 831, consistent with ambient water–air systems, all based on the inlet height and inlet velocity A non-dissipative geometric volume of fluid (VOF) method is used to track the detailed interactions between turbulent flow structures and the nonlinear interface dynamics Level set equations are also solved concurrent with VOF in order to calculate the interface curvature and surface tension forces The mesh resolution is set to resolve a wide range of interfacial scales including the Hinze scale Calculations are compared against experimental data of void fraction and interfacial scales indicating, reasonable agreement despite a Reynolds number mismatch Multiple calculations are performed confirming weak sensitivity of low-order statistics and void fraction on the Reynolds number The presented results provide, for the first time, a comprehensive quantitative data for a wide range of phenomena in a turbulent breaking wave using DNS These include mean velocity fields, Reynolds stresses, turbulence production and dissipation, velocity spectra and air entrainment data In addition, we present the energy budget as a function of streamwise location by keeping track of various energy exchange processes in the wake of the jump The kinetic energy is mostly transferred to pressure work, potential energy and dissipation while surface energy plays a less significant role Our results indicate that the rate associated with various energy exchange processes peak at different streamwise locations, with exchange to pressure work flux peaking first, followed by potential energy flux and then dissipation The energy exchange process spans a streamwise length of order jump heights Furthermore, we report statistics associated with bubble transport downstream of the jump The bubble formation is found to have a periodic nature Meaning that the bubbles are generated in patches with a specific frequency associated with the roll-up frequency of the roller at the toe of the jump, with its footprint apparent in the velocity energy spectrum Our study also provides the ensemble-averaged statistics of the flow which we present in this paper These results are useful for the development and validation of reduced-order models such as dissipation models in wave dynamics simulations, Reynolds-averaged Navier–Stokes models and air entrainment models

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Abstract: In open channel, canals and rivers, a rapid increase in flow depth will induce a positive surge, also called bore or compression wave. The positive surge is a translating hydraulic jump. Herein new experiments were conducted in a large-size rectangular channel to characterise the unsteady turbulent properties, including the coupling between free-surface and velocity fluctuations. Experiments were repeated 25 times and the data analyses yielded the instantaneous median and instantaneous fluctuations of free-surface elevation, velocities and turbulent Reynolds stresses. The passage of the surge front was associated with large free-surface fluctuations, comparable to those observed in stationary hydraulic jumps, coupled with large instantaneous velocity fluctuations. The bore propagation was associated with large turbulent Reynolds stresses and instantaneous shear stress fluctuations, during the passage of the surge. A broad range of shear stress levels was observed underneath the bore front, with the probability density of the tangential stresses distributed normally and the normal stresses distributed in a skewed single-mode fashion. Maxima in normal and tangential stresses were observed shortly after the passage of a breaking bore roller toe. The maximum Reynolds stresses occurred after the occurrence of the maximum free-surface fluctuations, and this time lag implied some interaction between the free-surface fluctuations and shear stress fluctuations beneath the surge front, and possibly some causal effect.

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Abstract: The flow structure in the aerated region of the roller generated by breaking waves remains a great challenge to study, with large quantities of entrained air and turbulence interactions making it very difficult to investigate in details. A number of analogies were proposed between breaking waves in deep or shallow water, tidal bores and hydraulic jumps. Many numerical models used to simulate waves in the surf zone do not implicitly simulate the breaking process of the waves, but are required to parameterise the wave-breaking effects, thus relying on experimental data. Analogies are also assumed to quantify the roller dynamics and the energy dissipation. The scope of this paper is to review the different analogies proposed in the literature and to discuss current practices. A thorough survey is offered and a discussion is developed an aimed at improving the use of possible breaking proxies. The most recent data are revisited and scrutinised for the use of most advanced numerical models to educe the surf zone hydrodynamics. In particular, the roller dynamics and geometrical characteristics are discussed. An open discussion is proposed to explore the actual practices and propose perspectives based on the most appropriate analogy, namely the tidal bore.

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  • ...Further observations include the integral turbulent length scale Lt characterising the size of large turbulent eddies advecting the bubbles in the hydraulic jump roller [34, 179]....

    [...]


Journal ArticleDOI
Abstract: In an estuary, a tidal bore may be generated at the leading edge of the flood tidal wave during the early flood tide under spring tide conditions into a narrow funnelled channel. For Froude numbers greater than 1.4–1.6, the leading edge of the bore is characterised by a breaking roller. The roller is characterised by a sudden increase in water depth, a highly turbulent flow with large-scale vortical structures, some kinetic energy dissipation, a two-phase air–water flow region and strong turbulence interactions. New experiments were conducted in a large canal with a focus on breaking bore roller propagation. The upstream propagation of the roller toe was highly turbulent. The toe perimeter shape fluctuated rapidly with transverse distance and time. The celerity of the roller toe changed rapidly with time and space, although in a quasi-two-dimensional manner on average. The instantaneous longitudinal free-surface profile of the roller showed significant temporal and spatial fluctuations. New air–water flow measurements highlighted some distinctive air bubble entrainment at the toe of the roller. Bubbles with larger chord times were detected at higher vertical elevations in a more intermittent manner. Overall the study demonstrated that the propagation of breaking bore is a very turbulent, three-dimensional process.

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  • ...Hydraulic jump data gmax/d1: theoretical calculations [31], experimental data [22,26,23,27,17,28,4,35,36] (For interpretation of the references to colour in this...

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Book
01 Jan 1996
Abstract: In high velocity water flows, large quantities of air bubbles are entrained at the free-surfaces. Practical applications are found in Chemical, Civil, Environmental, Mechanical, Mining and Nuclear Engineering. Air-water flows are observed in small-scale as well as large-scale flow situations. E.g., thin circular jets used as mixing devices in chemical plants (Qw ~ 0.001 L/s, diameter ~ 1 mm), and spillway flows (Qw > 10,000 m3/s, flow thickness over 10 m). In each case, however, the interactions between the entrained air bubbles and the turbulence field are significant. This monograph investigates the "air bubble entrainment in free-surface turbulent shear flows". It develops an analysis of the air entrainment processes in free-surface flows. The air-water flows are investigated as homogeneous mixtures with variable density. The variations of fluid density result from the non-uniform air bubble distributions and the turbulent diffusion process. Several types of air-water free-surface flows are studied : plunging jet flows (Part II), open channel flows (Part III), and turbulent water jets discharging into air (Part IV). Each configuration can be characterised as a high-velocity free-surface flow with turbulent shear layer and large air bubble content. Experimental observations confirm the conceptual idea that the air-water mixture behaves as a homogeneous compressible fluid. The monograph presents numerous and recent experimental investigations with mean velocities up to 57 m/s and mean air contents up to 70%. The analysis of experimental studies provides new information on the air-water flow field : air bubble distributions, air-water velocity profiles, air bubble sizes and bubble-turbulence interactions. The results show a strong similarity between all the flow patterns. In each case the distributions of air concentration (i.e. void fraction) can be approximated by a simple advective diffusion theory. New analysis is developed for each flow configuration and compared successfully with model and prototype data. The velocity distributions in air-water flows have the same shape as for monophase flows. However the presence of air bubbles modifies some turbulence characteristics while the turbulence controls the mechanism of bubble breakup. The book presents new useful information for design engineers and research-and-development scientists who need a better understanding of the fluid mechanics of air-water flows. Both qualitative and quantitative information are provided. In some cases the limits of our knowledge are pointed out. The book consists of five parts. Part I introduces the topic and its relevance, develops a dimensional analysis and discusses the air-water gas transfer process. In each subsequent part, the distributions of air content and air-water velocity are described. The results are grouped as : plunging jet flows (Part II), open channel flows (Part III) and high-velocity water jets discharging into the atmosphere (Part IV). In Part V, an analogy between the various types of air-water flows is developed. In the appendices, tables of physical and chemical properties of fluids are provided in appendix A. The report presents results expressed in SI Units. A table of unit conversions is given in appendix B. Estimates of bubble rise velocity are discussed in appendix C. Appendix D develops sound celerity calculations in two-phase flows. Appendices E, G, H and I present complete calculations of the air bubble diffusion process. Boundary layer characteristics and jet trajectory calculations are detailed in appendices F and J respectively. Appendix K defines bubble size distribution characteristic parameters. Observations by LEONARDO DA VINCI are recounted in appendix L. 'Errare Humanum Est'. Appendix M presents a correction form. Readers who find an error or mistake are welcome to record the error on the page and to send a copy to the author. At the beginning of the book, the reader will find the table of contents, a list of symbols, a glossary and an album of colourful photographs of 'white waters'.

347 citations


"Total pressure fluctuations and two..." refers background in this paper

  • ...1 below) was only observed for partially developed inflow conditions, with the shortest aeration length downstream of the toe (Chanson 1997)....

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  • ...3.2.1 below) was only observed for partially developed inflow conditions, with the shortest aeration length downstream of the toe (Chanson 1997)....

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01 Jan 2016
TL;DR: The waves in fluids is universally compatible with any devices to read, and an online access to it is set as public so you can download it instantly.
Abstract: Thank you for reading waves in fluids. Maybe you have knowledge that, people have search hundreds times for their favorite books like this waves in fluids, but end up in infectious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some malicious bugs inside their desktop computer. waves in fluids is available in our book collection an online access to it is set as public so you can download it instantly. Our book servers spans in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the waves in fluids is universally compatible with any devices to read.

280 citations


"Total pressure fluctuations and two..." refers background in this paper

  • ...In a hydraulic jump, the momentum considerations demonstrated the significance of the inflow Froude number, and the selection of the Froude similitude derives implicitly from basic theoretical considerations (Lighthill 1978; Liggett 1994)....

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Book
29 Feb 1992
Abstract: Part 1: Hydraulic Jump 1 Introduction 2 Classical Hydraulic Jump 3 Sloping Jump 4 Hydraulic Jump in Non-Rectangular Channel 5 Submerged Hydraulic Jump References Part 1 Notation Part 1 Part 2: Stilling Basins 6 Introduction 7 Steps and Sills 8 Baffle Rock 9 Effect of Roughness and Discharge 10 Expanding Channel 11 Bucket-type Energy Dissipator 12 Various Aspects of Stilling Basins 13 Types of Stilling Basins 14 Experiences with Stilling Basins References Part 2 Notation Part 2 Subject Index Author Index

246 citations


Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "Total pressure fluctuations and two-phase flow turbulence in hydraulic jumps" ?

This paper presents a physical modelling of hydraulic jump, where the total pressure and air-water flow properties were measured simultaneously with intrusive probes in the jump roller, namely a miniature pressure transducer and a dual-tip phase detection probe.