ApproachtothevoidfractiondistributionwithinahydraulicjumpinatypifiedUSBRIIstillingbasin.pdf

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Approach to the void fraction distribution within a hydraulic jump in a
typiﬁed USBR II stilling basin
Conference Paper · September 2019
DOI: 10.3850/38WC092019-0716
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E-proceedings of the 38th IAHR World Congress
September 1-6, 2019, Panama City, Panama
APPROACH TO THE VOID FRACTION DISTRIBUTION WITHIN A HYDRAULIC JUMP IN
A TYPIFIED USBR II STILLING BASIN
JUAN FRANCISCO MACIÁN-PÉREZ(1)
, RAFAEL GARCÍA-BARTUAL(2)
, BORIS HUBER(3)
, ARNAU BAYÓN(4)
& FRANCISCO J. VALLÉS MORÁN(5)
(1,2,4,5)
Research Institute of Water and Environmental Engineering (UniversitatPolitècnica de València), Valencia, Spain,
juamapre@cam.upv.es
(3)
Institute of Hydraulic Engineering and Water Resources Management (Technische Universität Wien), Vienna, Austria,
boris.huber@tuwien.ac.at
ABSTRACT
This research constitutes a first approach to analyze the void fraction distribution in a hydraulic jump taking
place within a typified USBR II stilling basin. In order to carry out this task both, a physical and a numerical
Computational Fluid Dynamics (CFD) model of the case study have been developed. Measurements of the
void fraction have been taken in different profiles throughout the hydraulic jump for both models and then, a
comparison of the results obtained has been made, taking also into account data from other authors regarding
void fraction distribution in classical hydraulic jumps. The results of this comparison show that the physical
model, in which an optical fibre probe has been used for the experimental campaign, is able to completely
reproduce the aeration of the hydraulic jump, whereas the numerical model misses to simulate certain
aeration mechanisms. The models developed also provide information on how the energy dissipation devices
from the USBR II stilling basin affect the void fraction distribution within the jump, which in turn can be useful
for the adaptation of dams to higher discharges than those considered in their design.
Keywords: Stilling basin; Hydraulic jump; Void fraction.
1 INTRODUCTION
The adaptation of existing dams to new standards derived from climate change effects and society
demands regarding flood protection arises as a key aspect in hydraulic structure engineering. This adaptation,
which implies accounting for larger discharges than those considered for the design of the dam, is especially
challenging for the energy dissipation structure. Consequently, important efforts have been devoted to
improve flow energy dissipation in dams. In particular, for dams with stilling basins, aeration of the incoming
flow to the dissipation structure is in the spotlight of the research dedicated to enhance the performance of the
basin, so that it can cope with the more demanding discharges associated to new scenarios.
On this basis, the research presented herein focuses on the aeration of the hydraulic jump taking place in
the stilling basin. Hence, the void fraction through a series of cross-sectional profiles of the hydraulic jump has
been analyzed using different techniques. To do so, a general case of spillway and stilling basin (USBR II)
has been designed and implemented into a numerical model in which the air entrainment is simulated. Next,
the same case has been used to build a physical model in which measures of the void fraction have been
taken using an optical fibre probe. This contrast between numerical and experimental techniques is crucial
when modelling hydraulic structures, due to their complementary nature (Wang and Chanson, 2015; Blocken
and Gualtieri, 2012), especially in those cases where aeration needs to be considered (Chanson, 2013).
Finally, the results obtained from these models have been compared with data form other authors, which
have measured the void fraction in classical hydraulic jumps. This comparison is intended to address the
effect of dissipation devices In the USBR II stilling basin, such as chute blocks and the end sill, on the void
fraction distribution through the hydraulic jump. Understanding these effects can be considered as an
important step towards an improved design of the dissipation structure, looking for the optimal number, size
and configuration of the dissipation devices in order to achieve an appropriate aeration of the flow, which in
turn, enhances the performance of the stilling basin.
2 CASE STUDY
In the selection of the case study, designing a general and representative case has been prioritized.
Therefore, a series of existing dams in the Júcar River Basin (Spain) have been studied. From this review, the
dimensions and discharge of the case have been chosen and the design of the structure has been determined
too (Figure 1). On the one hand, a Creager profile spillway has been designed (Şentürk, 1994) and the
corresponding calculations have been made in order to obtain the reservoir water level that fits the chosen
discharge (Vischer and Hager, 1998; Şentürk,1994; Thompson, 1987; USBR,1987). On the other hand, a
typified USBR II stilling basin has been designed, following the patterns and recommendations of the United

States Bureau of Reclamation (Peterka, 1964) not only for the dimensions of the basin, but also for the size,
distribution and configuration of the energy dissipation devices. It is important to highlight that both, the
Creager profile and the USBR II typified stilling basin are widely spread in existing dams all around the world,
and therefore they have been chosen, along with the dimensions and hydraulics parameters coming from the
previously mentioned review, to achieve a representative case study.
Figure 1.Sketch of the designed case study (Creager profile spillway and USBR II typified stilling basin) with
the basic dimensions.
3 NUMERICAL MODEL
Modeling a hydraulic jump implies taking into account intense turbulence with large velocity and pressure
fluctuations and significant flow aeration and energy dissipation. The complexity arising from these factors has
increased the amount of numerical methods, and in particular Computational Fluid Dynamics (CFD) models,
used to study the hydraulic jump (Bayón et al., 2016; Bayón and López-Jiménez, 2015; Castillo et al., 2014).
In this particular research, FLOW-3D, a commercial software package developed by FlowScience, Inc., has
been used to develop the CFD model, at prototype scale, of the hydraulic jump taking place in the USBR II
basin. This software, based on Navier-Stokes equations numerical resolution, uses the Finite Volume Method
(McDonald, 1971) to discretize the conservation laws in the case study domain and, in order to address the
treatment of the free surface between air and water, the Volume Of Fluid method (VOF) described by Hirt and
Nichols (1981) is employed.
FLOW-3D software and the methods for the numerical resolution of the flow governing equations
bounded to this code have been widely used for hydraulic engineering applications, proving their efficiency
and reliability (Caishui, 2012; Sarafaz and Attari, 2011; Ho and Riddette, 2010).
3.1 Turbulence modeling
Turbulence modeling is not only a key aspect of CFD applications, but also indispensable to study the
performance of a stilling basin. When dealing with a highly turbulent flow, such as the one developed in a
hydraulic jump, the intense and multi-scale fluctuations of velocity and pressure in time and space, along with
computer memory and processing limitations, lead to a statistic treatment of the turbulence. To do so, the
most popular approach for engineering problems consists of carrying out a time average of Navier-Stokes
equations which leads to the Reynolds Averaged Navier-Stokes (RANS) equations. This approach implies a
new unknown term (Reynolds stresses) for the equations and, consequently, a closure problem arises. The
closure problem can be solved by the addition of a turbulence model including transport equations for
variables related to the turbulent viscosity, which in turn is related to the Reynolds stresses through the
Boussinesq approximation.
For the CFD model here presented, a two equations RNG κ-ε turbulence model (Yakhot et al., 1992),
which includes transport equations for the turbulent kinetic energy (κ) and its dissipation rate (ε), has been
used. This turbulence model was chosen since it has proven a good performance when modeling swirling
flows (Bayón et al., 2016) like the one addressed in the present research.
3.2 Flow aeration
The research here presented is focused on the study of void fraction distribution through the hydraulic
jump taking place in a USBR II stilling basin and its comparison to the one described by other authors in a
classical hydraulic jump. Therefore, air entrainment becomes an essential phenomenon to consider in the
numerical model.

Air entrainment is modeled in FLOW-3D through a balance between destabilizing forces (turbulent kinetic
energy) and stabilizing forces (gravity and surface tension) in order to carry out an estimation of the air
entrainment rate to the flow. Furthermore, density fluxes due to this air entrained to the flow, and the
movement of air bubbles within the fluid, are also modeled by considering the bulking and buoyancy options
available in FLOW-3D. Figure 2 shows the void fraction provided by the CFD FLOW-3D model for our case
study.
Figure 2.Volume fraction of entrained air in the flow displayed by the CFD numerical model of the Creager
spillway and the USBR II stilling basin.
3.3 Mesh convergence analysis
A structured rectangular hexahedral mesh has been used in this numerical model, in which the
corresponding boundary conditions have been implemented, so that the desired hydraulic jump location within
the stilling basin is achieved and taking advantage of the symmetry of the problem.
In order to determine the appropriate cell size for the case study, a mesh convergence analysis has been
carried out, with the objective of achieving the independence of the numerical model results from the cell size
employed. For this analysis, developed following the ASME’s criterion (Celik et al., 2008), four different
meshes have been tested and for each of these meshes, ten basic variables (velocities and pressures) have
been analyzed as indicators. The cell sizes in the tested set of meshes range from 0.8 to 0.135 meters, with a
refinement ratio always above the minimum value of 1.3 established by Celik et al. (2008). Finally, the chosen
mesh consists of a refined block with a cell size of 0.18 meters for the area of the USBR II stilling, where the
hydraulic jump takes place, and a coarser mesh block, in which the cell size is 0.36 meters, for the rest of the
domain. The indicators resulting from the convergence analysis behind the mesh choice are a model apparent
order (p) of 2.78, which approaches the model formal order, and a Grid Convergence Index (GCI) of 6.02%,
considered as an acceptable value for problems involving flows with the complexity of the case here
presented.
4 PHYSICAL MODEL
Experimental contrast remains crucial when modeling complex hydraulic structures (Wang and Chanson,
2015), due to the still existing limitations in numerical models for the simulation of certain hydraulic
phenomena (Blocken and Gualtieri, 2012). Consequently, an undistorted physical model with Froude similarity
of the case study was built in the hydraulics laboratory of the Institute of Hydraulic Engineering and Water
Resources Management from Technische Universität Wien (TUWien).
The design of the physical model was made following the limiting criteria to avoid significant scale effects
presented by Heller (2011). Taking into account these criteria and the available resources at the TUWien
hydraulics laboratory the scale factor used for the design process was 1:25, resulting into a physical model
whose dimensions are displayed in Table 1.
Table 1.Dimensions of the physical model built in the TUWien hydraulics laboratory, following Figure 1
nomenclature.
Dimensions Prototype Physical model
Hd(m) 25.5 1.02
h (m) 20 0.8

Ls (m) 21.94 0.88
Lii (m) 47.8 1.91
d1(m) 1.33 0.05
d2(m) 2.33 0.09
Width (m) 12.25 0.49
Q (m
3
/s) 357 0.11
In regards to the construction of the model, it was placed in a rectangular section open flow channel,
equipped with a downstream gate which was maneuvered in order to locate the hydraulic jump into the
desired position within the USBR II stilling basin model. The feeding system is a pressure flow with enough
pumping capacity to meet the discharge requirements displayed in Table 1. Then, the transition to free
surface flow takes place at the entrance of the channel, which has a glass wall in the area of interest for
experimental purposes (Figure 3).
Figure 3.Creager profile spillway and USBR II stilling basin physical model at the TUWien hydraulics
laboratory.
4.1 Optical fibre probe
In order to obtain the void fraction distribution in the hydraulic jump performed in the physical model, an
experimental campaign was carried out using a dual-tip optical fibre probe at six different profiles along the
jump. In particular, the probe used for the campaign is a RBI dual-tip optical phase detection device, which
works on the basis described by Boyer et al. (2002), Cartellier and Barrau (1998) and Cartellier and Achard
(1991). Hence, phase discrimination rests on the discrete variation of the refraction index between flow
components. At a given emission of light, the quantity reflected by the wall of an optical probe sensitive tip
depends exclusively on the refraction index of the medium surrounding the wall. Then, the conversion of the
optical signal (i.e. quantity of light reflected) into an electrical signal is made by a photo-sensitive element.
Following this technique, the void fraction comes from a reduction of the portion of time in which gas phase is
in contact with the sensitive tip of the optical probe, in relation with the full observation time (RBI
instrumentation). More information on the characteristics of this probe can be found at Murzyn et al. (2005).
The six profiles studied in the experimental campaign are placed along the longitudinal axis of the
channel. For each of these profiles, whose location can be observed in Figure 4, a number of points (9 to 12),
were measured in the same vertical line. The collection data time, chosen because of the expected velocities
in the model, was 200 seconds for each point.

Figure 4.Left: Profiles for the void fraction measurement experimental campaign in the physical model. Right:
Optical fibre probe equipment, including probe, opto-electronic unit, oscilloscope, acquisition box and
software.
5 RESULTS AND DISCUSSION
The aim of the research here presented is to gather information concerning the void fraction distribution
throughout a hydraulic jump taking place in a typified USBR II stilling basin, and to compare it with the void
fraction distribution in classical hydraulic jumps. In order to carry out this task, which implies comparing, not
only the information coming from the numerical and the experimental models previously described, but also
other authors’ experimental data, it is important to unify criteria and work with normalized parameters.
Therefore, the nomenclature and expressions proposed by Murzyn et al. (2005) in the analysis of void fraction
profiles within a hydraulic jump are used in this section. This formulation is based on the division of the flow
into two different regions separated by the turbulent shear layer. For the lower region, the void fraction C
should satisfy a diffusion equation (Chanson, 1996) which leads to the following void fraction profile on a given
vertical (Murzyn et al., 2005):
𝐶 = 𝐶𝑚𝑚𝑚 exp �−
1
4
𝑈
𝐷
(𝑧 − 𝑧𝐶𝐶𝐶𝐶)2
𝑥
�
[1]
In Eq. [1] C is the void fraction, U the flow velocity upstream of the hydraulic jump toe, D a diffusion
coefficient and the void fraction reaches its maximum Cmax at zCmax. On the other hand, for the upper region,
similar conditions to the edge of water jets freely discharging into air are assumed and, consequently, the
following expression proposed by Brattberg et al. (1998) is adopted:
𝐶 =
1
2
�1 + 𝑒𝑒𝑒 �
𝑧 − 𝑧𝐶50
2�𝐷𝐷 𝑈
⁄
��
[2]
Where void fraction is C=0.5 at z=zC50. It is important to highlight that whereas U is the same for Eq. [1]
and [2] as a result of its definition, D is different since the air entrainment mechanism varies from one region to
another. Hence, the expressions displayed in Eq. [1] and [2] have been adjusted to the data obtained from the
six different profiles analyzed in the physical and the numerical model, using the incoming flow depth to the
hydraulic jump h to normalize both, the height of the measurement points and the distance of the profiles to
the hydraulic jump toe (Table 2).
Table 2.Information of the profiles for void fraction measurement in the physical and numerical models.
h (m) U (m/s) Fr1 x1/h x2/h x3/h x4/h x5/h x6/h
Numerical model 1.62 16.00 4.01 1.23 5.48 10.49 19.37 24.92 31.87
Physical model 0.07 3.20 4.01 1.14 5.07 9.71 17.93 23.07 29.50
The parameters resulting from this analysis have been compared and discussed taking into account not
only the physical and numerical models, but also data from Murzyn et al. (2005) and Chanson and Brattberg
(2000) regarding void fraction profiles in classical hydraulic jumps, with an incoming Froude number of 3.7 and
6.3 respectively (Figures 5 and 6). However, before starting with the discussion, it is important to remark that
the adjustment process has revealed that the first of the profiles where void fraction was measured in the

physical model shows an anomalous behavior, with few physical sense, probably because of the proximity to
the hydraulic jump toe, where important turbulence and fluctuations, which may have affected the
performance of the optical fibre probe, take place. Therefore, this section has not been considered in the
analysis. In addition to this, data coming from the numerical model is not able to reproduce the influence of the
upper region and only the values belonging to the lower region seem to follow the expression from Eq. [1] and
consequently, the numerical model has only been considered in the analysis of the parameters for the lower
region. The limitations showed by the numerical model when reproducing the air entrainment process to the
hydraulic jump, may be explained because of the complexity of this phenomenon, which often results into
reliability problems for this kind of models (Blocken and Gualtieri, 2012). Furthermore, modeling air
entrainment in FLOW-3D implies adjusting a series of parameters which affect the balance between stabilizing
and destabilizing forces governing the aeration process. As this research is a first approach to the air
entrainment study in a typified USBR II stilling basin, the numerical model has not been calibrated yet using
the physical model and other authors´ data, which remains as future work in order to improve the capacity of
the model to reproduce air entrainment.
Figure 5.Void fraction parameters for the lower region obtained by fitting Eq. [1].
In respect with Cmax, which is the first of the lower region parameters displayed in Figure 5, Murzyn et al.
(2005) proposes an adjustment of the form: Cmax~exp (-Ax). For the results obtained in this research, the
values from the physical model follow the expression Cmax=0.3641exp(-0.08x) with a R2
=97.12%, whereas for
the numerical model, the expression Cmax=0.65exp(-0.01x) yields a R2
=80.5%. In addition to this, it can be
observed that the values for the physical model fit with the data gathered by other authors for similar Froude
numbers, whereas the numerical model seems to overestimate the parameter Cmax.
Looking at the normalized height at which Cmax is achieved, this parameter seems to be proportional to x
with a gradient 0.1085 for the data coming from the physical model, very close to the gradient of 0.108 found
by Chanson & Brattberg (2000) and not far from the 0.102 proposed by Murzyn et al. (2005).This gradient is
slightly higher (0.118) for the values extracted from the numerical model. For this parameter, the magnitude of
the values obtained from both models is in the line of the observations from other authors.
On the other hand, for the diffusion coefficient D, the values are rather scattered for both models, as
pointed out by Murzyn et al. (2005) for their observations. Paying attention to the magnitude order, values
from the numerical model seem to be higher compared to physical model and bibliography data.
It can also be highlighted that the comparison between data from the experimental model and from
Murzyn et al. (2005), both with a very similar Froude number, shows that despite the high degree of
coincidence found, slightly higher values for Cmax can be observed for the physical model as we move
downstream from the hydraulic jump toe. Moreover, these Cmax values take place at higher normalized heights
for the physical model throughout the whole hydraulic jump. These observations could be explained because
of the energy dissipation devices present in the stilling basin, affecting the aeration when compared to a
classical hydraulic jump. However, a deeper study, testing different Froude numbers and devices, would be
required to confirm these results.

Figure 6.Void fraction parameters for the upper region obtained by fitting Eq. [2].
With regards to the parameters of the upper region, Murzyn et al. (2005) pointed out that for the
normalized height at which C=0.95 and for the one at which C=0.5, as well as for the normalized height where
the boundary between the upper and the lower region can be found (z*), the initial rates of increase with x
show that the region where interfacial aeration is the predominant aeration mechanism increases its thickness
with the distance from the hydraulic jump toe. In respect with this statement, the values obtained from the
physical model are in total agreement, as it can be observed from the higher gradient shown in the closer
profiles to the hydraulic jump toe. Moreover, the magnitude order for the physical model data is in the line of
the bibliographic results.
Finally, the diffusion coefficient D shows both, for the physical model and for the bibliographic results a
decay as the distance to the hydraulic jump toe increases, which was not observed for the lower region. For
this parameter, again, the values coming from the physical model are in good agreement with data from
Murzyn et al. (2005) and Chanson and Brattberg (2000).
6 CONCLUSIONS
The aim of the research here presented was to make a first approach to the void fraction distribution in
the hydraulic jump taking place within a typified USBR II stilling basin, in order to compare it to the one
observed in classical hydraulic jumps. In this sense, the physical model built for the study, where void fraction
measures using an optical fibre probe were taken, was able to reproduce the air entrainment process, leading
to void fraction profiles in good agreement with those found in the bibliography for a classical hydraulic jump.
On the other hand, the numerical model, which showed acceptable results for the lower region, was not able
to reproduce the aeration mechanism for the upper region, dominated by interactions with the free surface.
The information gathered also shows that despite the multiple similarities found in the void fraction distribution
for the case study and the classical hydraulic jump, the energy dissipation devices placed in the USBR II
stilling basin, namely chute blocks and end sill, result in a slight affection to the aeration in the jump, which
must be considered for confirmation with future research.
Hence, the works developed for this research are intended to be the basis for future works. On the one
hand, the good agreement between the physical model values and the bibliographic results must be employed
to calibrate the numerical model and to improve its performance so that it can completely reproduce the air
entrainment mechanisms existing within the hydraulic jump. On the other hand, more research needs to be
done regarding the definition of the lower and the upper region, the aeration processes taking place, their
mathematical formulation and the parameters involved.
In conclusion, this research looks for a better understanding of how air entrainment can affect hydraulic
jumps behavior and consequently, the performance of stilling basis. In this sense, more research can be
developed on how new versions of the existing typified stilling basins can enhance energy dissipation by
affecting the hydraulic jumps aeration. This information is crucial since the need for adaptation of dams to

higher discharges than those considered for their design is constantly increasing, as a result of climate
change effects and new society demands.
ACKNOWLEDGEMENTS
The research presented herein has been possible thanks to the ‘Generalitat Valenciana predoctoral
grants (Ref. [2015/7521]) ’, in collaboration with the European Social Funds and to the research project: ‘La
aireación del flujo y su implementación en prototipo para la mejora de la disipación de energía de la lámina
vertiente por resalto hidráulico en distintos tipos de presas’ (BIA2017-85412-C2-1-R), funded by the Spanish
Ministry of Economy. The authors also would like to acknowledge the collaboration of the hydraulics
laboratory of the Institute of Hydraulic Engineering and Water Resources Management from Technische
Universität Wien (TU Wien) and their technicians, in the construction and experimental campaign of the
physical model referred in the article.
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