Computers & Fluids 68 (2012) 168–185
Contents lists available at SciVerse ScienceDirect
Computers & Fluids
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m p fl u i d
Evaluation of operational strategies to minimize gas supersaturation downstream
of a dam
M. Politano a,⇑, A. Arenas Amado a, S. Bickford b, J. Murauskas b, D. Hay c
a
IIHR – Hydroscience & Engineering, The University of Iowa, 300 South Riverside Dr., Iowa City, IA 52242-1585, USA
Public Utility District No. 1 of Douglas County, 1151 Valley Mall Parkway, East Wenatchee, WA 98802-4497, USA
c
Oakwood Consulting, Inc., 237 Turtlehead Rd., Belcarra, BC, Canada
b
a r t i c l e
i n f o
Article history:
Received 2 June 2010
Received in revised form 1 August 2012
Accepted 2 August 2012
Available online 20 August 2012
Keywords:
Total dissolved gas
Two-phase flow
Dissolution
Hydropower
TDG
Bubbles
a b s t r a c t
Bubble dissolution downstream of spillways may create zones of high total dissolved gas (TDG) concentration, which can be detrimental to fish. This paper presents the use of a numerical model to identify
dam operational strategies that mitigate elevated TDG production. A mixture model takes into account
the effect of the bubbles on the hydrodynamics. The model calculates bubble dissolution considering bubble size change due to dissolution and pressure. The model is validated using field velocity and TDG data.
Several simulations are performed to understand the physical phenomena leading to supersaturated
water under different operational configurations. According to the model, concentrating the spillway flow
in one bay causes bubbles to travel closer to the free surface and thus lower TDG production and more
degasification. In order to obtain the lowest TDG concentration, it is best to concentrate most of the flow
in a central spillway bay. If additional water needs to be spilled, the use of a western bay is recommended.
An additional simulation using compliance conditions indicates that, using the proposed configuration,
the dam meets TDG water quality standards. Moreover, statistical analysis performed on inert particles
released in the spillway and turbines demonstrates that, after 2 h, 83.9% of the time particles are exposed
to TDG values lower than 110%. If hydrostatic compensation is considered, particles are in undersaturated
water 70% of the time.
Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
1.1. Total dissolved gas in tailraces
Total dissolved gas (TDG) refers to the total amount of gases
present in water, which depends on pressure and temperature.
The main source of elevated TDG on the Columbia River Basin is
the dissolution of air from bubbles entrained during spill events.
When bubbles are carried down to deep, high pressure regions in
the stilling basin, the solubility increases and air is transferred
from the bubbles to the water.
The capability of bubbles to travel to depth depends on the
spillway jet regime, which in turn depends on the spillway geometry and tailwater elevation (TWE). Fig. 1 shows possible spillway
regimes in a hydrocombine structure. In skimming flow, bubbles
travel near the free surface with minimum TDG production. On
the other hand, at lower TWE, plunging jets can carry bubbles to
depth increasing bubble dissolution. At high TWE, a submerged
jump flow, with potential of air entrainment at depth, is possible.
⇑ Corresponding author. Tel.: +1 319 335 6393; fax: +1 319 335 5238.
E-mail addresses: [email protected] (M. Politano), antonio-arenasa
[email protected] (A. Arenas Amado), [email protected] (S. Bickford), joshm
@dcpud.org (J. Murauskas), [email protected] (D. Hay).
0045-7930/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.compfluid.2012.08.003
For the same spillway regime, the amount of bubbles at depth depends on bubble size, which is a function of air entrainment processes in the plunging region, breakup, and coalescence.
The TDG concentration in tailraces also depends on mixing, and
degasification at the free surface. TDG mixing is governed by the
tailrace hydrodynamics and turbulence. Spillway jet regimes
strongly affect the tailrace hydrodynamics. Spillway surface jets
in skimming flow, found in dams with hydrocombine structures
or retrofitted with spillway deflectors, attract water toward the
jet region, a phenomenon called water entrainment. Water entrainment is important in TDG prediction because it increases dilution
by powerhouse flows but can also increase TDG downstream if
water is undersaturated at local conditions and bubbles are present.
Stronger turbulence leads to mixing and weaker surface jets. Bubbles play an important role in the spillway jet regimes. Since the
effective density and viscosity of the water–air mixture is smaller
than pure water, bubbles favor the formation of surface jets. In
addition, bubbles can, depending on their size, increase or attenuate
the turbulence.
1.2. Total dissolved gas prediction
Reduced-scale models are limited to represent the hydrodynamics and TDG distribution in tailraces since they are scaled with
M. Politano et al. / Computers & Fluids 68 (2012) 168–185
Fig. 1. Flow regimes in a hydrocombine structure.
Fig. 2. Hydrocombine and typical mesh used for the VOF simulations.
169
170
M. Politano et al. / Computers & Fluids 68 (2012) 168–185
Fig. 3. Study area for the TDG model with bathymetry and location of the TDG transects.
the Froude number and therefore the Reynolds and Weber numbers are not honored. Smaller levels of turbulence and fewer and
bigger bubbles (in dimensionless terms) are observed in the laboratory than in the prototype. This results in weaker surface jets and
less water entrainment in the laboratory than in the prototype. Reduced-scale models are then used to infer TDG production through
observed spillway jet regimes.
Some attempts to predict TDG reported in literature are based
on mass transfer processes principles without solving the tailrace
hydrodynamics [9,7,23]. These approaches can be effective but imply obtaining empirical correlations for the transport of TDG that
need to be determined on a case-by-case basis. Numerical simulations offer a very attractive tool to simulate TDG production and
transport. An appropriate model to predict TDG distribution in tailraces should capture the hydrodynamics, bubble transport, and
dissolution. The model also needs to adequately predict the spillway jet regime in order to capture both water entrainment and
bubble transport to depth.
Single-phase isotropic Reynolds-averaged Navier–Stokes
(RANS) models demonstrated to be overpredict the turbulence
and therefore predict a more diffusive weaker surface jet and smaller water entrainment than observed at prototype scale [11,22].
Turan et al. [22] demonstrated that an anisotropic model, which
considers the attenuation of the turbulence at the free surface, is
needed to capture the measured water entrainment induced by a
surface jet.
Although the model used by Turan et al. [22] predicted the
water entrainment considerably better than isotropic single-phase
models, it still underpredicted the water entrainment observed in a
prototype scale tailrace.
Fig. 4. 3D view of a typical grid used for the rigid-lid model simulations.
171
M. Politano et al. / Computers & Fluids 68 (2012) 168–185
Table 1
Operating conditions used in the simulations. FB = Forebay. TW = Tailwater.
Calibration
Validation
FBS
7Q10-A
7Q10-B
7Q10-C
CS
June 4
June 5
May 14
May 17
June 17
111.8
237.6
218.6
12.0
111.5
237.3
219.5
12.0
109.1
237.3
216.9
12.0
110.4
236.9
218.1
12.0
113.9
237.8
219.0
12.0
–
238.0
219.1
13.0
113.0
237.6
219.9
13.0
113.0
237.6
219.9
13.0
113.0
237.6
219.9
13.0
115.0
237.6
219.9
15.5
Powerhouse discharge (m3/s)
Unit 1
0.0
Unit 2
416.3
Unit 3
416.3
Unit 4
407.8
Unit 5
416.3
Unit 6
416.3
Unit 7
419.1
Unit 8
419.1
Unit 9
407.8
Unit 10
416.3
0.0
535.2
509.7
523.9
518.2
538.0
572.0
555.0
563.5
515.4
0.0
424.8
424.8
419.1
0.0
0.0
0.0
0.0
419.1
430.4
0.0
535.2
540.9
529.5
543.7
0.0
0.0
0.0
529.5
543.7
0.0
368.1
368.1
365.3
368.1
368.1
371.0
371.0
362.5
371.0
0.0
583.6
583.6
583.6
583.6
583.6
583.6
583.6
583.6
583.6
0.0
566.3
566.3
566.3
566.3
566.3
566.3
566.3
566.3
566.3
0.0
566.3
566.3
566.3
566.3
566.3
566.3
566.3
566.3
566.3
0.0
566.3
566.3
566.3
566.3
566.3
566.3
566.3
566.3
566.3
0.0
623.0
623.0
623.0
623.0
623.0
623.0
623.0
623.0
623.0
Total
4830.9
2118.1
3222.5
3313.1
5252.8
5097.0
5097.0
5097.0
5606.7
Spillway discharge (m /s)
Bay 1
0.0
Bay 2
45.3
Bay 3
152.9
Bay 4
147.2
Bay 5
152.9
Bay 6
147.2
Bay 7
152.9
Bay 8
147.2
Bay 9
152.9
Bay 10
45.3
0.0
36.8
0.0
62.3
0.0
62.3
1203.5
62.3
0.0
36.8
0.0
36.8
0.0
62.3
0.0
62.3
1002.4
62.3
0.0
36.8
0.0
25.5
0.0
62.3
0.0
62.3
965.6
62.3
0.0
25.5
0.0
48.1
0.0
62.3
0.0
62.3
843.8
563.5
843.8
48.1
0.0
0.0
0.0
0.0
0.0
0.0
651.3
0.0
0.0
0.0
0.0
48.1
0.0
62.3
0.0
226.5
1217.6
226.5
0.0
48.1
0.0
48.1
339.8
62.3
0.0
62.3
1217.6
62.3
0.0
48.1
0.0
48.1
0.0
62.3
1217.6
62.3
0.0
62.3
339.8
48.1
0.0
48.1
0.0
62.3
0.0
62.3
1047.7
62.3
0.0
48.1
Total
1144.0
1464.0
1262.9
1203.5
2472.1
651.3
1829.3
1840.6
1840.6
1330.9
River (m3/s)
4879.0
6294.8
3381.0
4425.9
5785.1
5904.1
6926.3
6937.6
6937.6
6937.6
FB TDG (%)
FBE (m)
TWE (m)
T (°C)
3735.0
3
The first 3D anisotropic mixture model capable of predicting the
tailrace hydrodynamics, including both water entrainment and
TDG distribution, is presented in Politano et al. [19]. The authors
validated their model in the tailrace of Wanapum Dam. Politano
et al. [19] used the anisotropic model proposed by Turan et al.
[22] and included the effect of the bubbles on the hydrodynamics
using a mixture model. The model considered interfacial forces exerted by bubbles on the liquid phase and the effect of the bubbles
on the turbulence field.
1.3. Effect of total dissolved gas in fish
Elevated TDG concentrations can be detrimental, or even lethal,
to fish [24]. High TDG can induce gas bubble disease (GBD), in
which bubbles are formed in the body cavities of fish. The effect
of TDG supersaturation on fish depends on TDG levels, exposure
time, and swimming depth.
Substantial research in the Columbia River Basin was performed
to understand the biological effects of TDG supersaturation
[24,4,1,20,3,6]. Fish exposed to elevated TDG during a short period
of time will likely only experience slight effects unless the level of
supersaturation is extremely high. Fish moving up and down daily
with at least one third of the time at depths of several meters will
probably experience minor effects for TDG in the range of 120–
140% [25]. However, mathematical expressions relating fish injury
with TDG exposure do not exist and general behavioral patterns,
swimming strategies, and energetic demands on migrating fish in
tailraces are not well understood [21].
TDG levels are usually reported with reference to atmospheric
pressure rather than to the depth at which measurements are taken
or at which fish reside. The compensation depth (or hydrostatic
compensation) is the water depth at which equilibrium between total pressure and the sum of the partial pressure of all air constituent
dissolved gases exists.
The first attempt to estimate TDG exposure is found in Johnson
et al. [10]. Fish migration paths were determined by tracking individual fish tagged with radio transmitters and TDG values were obtained using an empirical 2D depth-averaged model. The main
drawback of this approach is that a 2D depth-averaged model does
not provide the vertical TDG gradients required to calculate the level of uncompensated TDG.
1.4. Total dissolved gas regulations
Fig. 5. Evolution of the flow rate and talwater elevation for May 14, 2006.
Due to the adverse impacts of the gas supersaturation on aquatic resources, Federal and State regulations have established TDG
water quality standards [15,16,17,13]. State of Washington water
quality standards limit TDG levels to 110% at any point of measure-
172
M. Politano et al. / Computers & Fluids 68 (2012) 168–185
Fig. 6. Predicted flow field for May 14, 2006. (a) top view and (b) vertical slice through bay 7.
Fig. 7. Predicted flow field for June 4, 2006. (a) Top view and (b) vertical slice through bay 7.
ment. However, TDG levels are allowed to exceed the standard, up
to 120%, of saturation under two scenarios: (1) to pass a discharge
greater or equal than the 7Q10 or, (2) to pass voluntary spill to assist out-migrating juvenile salmonids. The 7Q10 discharge is defined as the highest average flow that occurs for seven
consecutive days in a once-in-10-year period.
1.5. Objective
The main focus of this paper is to present a numerical methodology to identify operational strategies that minimize TDG downstream of a dam. The model is applied to the Wells Hydroelectric
Project. The model proposed by Politano et al. [19] is used to
173
M. Politano et al. / Computers & Fluids 68 (2012) 168–185
Table 2
TDG predicted and measured data.
Calibration
TDG
Field data
Model results
Relative error (%)
Validation
7Q10-A
7Q10-B
7Q10-C
CS
June 4
June 5
May 14
May 17
June 17
T1
A
B
C
D
E
F
Average
119.7
120.0
117.8
117.3
–
–
118.7
115.9
115.8
118.0
120.0
–
–
117.4
116.8
116.3
118.7
118.1
116.7
116.7
117.2
115.3
114.9
117.3
116.6
116.1
116.3
116.1
122.2
121.7
126.0
128.2
125.6
–
124.7
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
T2
A
B
C
D
Average
117.9
117.4
117.2
–
117.5
118.3
118.2
118.1
–
118.2
118.0
117.5
117.0
116.7
117.3
116.7
117.2
116.8
–
116.9
123.3
126.1
126.1
–
125.2
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
T3
A
B
C
D
E
Average
118.8
117.9
117.1
116.5
–
117.6
118.2
118.2
117.8
117.3
–
117.9
117.0
117.3
116.4
116.5
115.1
116.5
116.1
116.9
116.2
116.4
115.3
116.2
123.8
124.8
124.9
124.3
–
124.5
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
T1
A
B
C
D
E
F
Average
119.0
122.4
126.5
123.8
–
–
122.9
115.2
115.3
115.5
116.0
–
–
115.5
116.6
117.3
117.6
117.0
115.9
115.5
116.7
116.8
117.7
118.8
118.3
115.6
114.7
117.0
125.9
128.4
134.3
139.8
118.8
–
130.5
118.2
118.9
119.9
120.2
118.9
118.9
119.2
122.6
122.8
120.2
116.8
115.3
115.0
118.8
121.0
120.9
118.7
118.4
117.2
117.1
118.9
116.9
117.4
118.1
117.6
115.1
115.1
116.7
T2
A
B
C
D
Average
123.3
123.0
120.4
–
122.2
115.1
115.2
115.1
–
115.1
116.4
116.3
116.2
116.2
116.3
116.7
117.1
116.8
–
116.9
126.5
126.5
126.1
–
126.4
119.7
120.2
120.0
119.8
119.9
120.4
118.2
116.6
116.1
117.8
120.0
118.8
118.3
118.1
118.8
117.6
117.6
116.9
116.2
117.1
T3
A
B
C
D
E
Average
122.2
121.1
120.2
119.0
–
120.7
115.0
115.1
115.0
114.9
–
115.0
116.4
116.4
116.3
116.2
116.3
116.3
116.8
116.8
116.7
116.6
116.5
116.7
126.9
126.8
126.4
125.6
–
126.4
119.4
119.9
119.9
119.8
119.8
119.8
120.4
118.0
117.2
116.5
116.3
117.7
119.9
119.0
118.6
118.3
118.2
118.8
117.0
117.1
116.9
116.4
116.2
116.7
T1
A
B
C
D
E
F
Average
0.6
2.0
7.4
5.5
–
–
3.5
0.6
0.4
2.1
3.3
–
–
1.6
0.2
0.9
0.9
0.9
0.7
1.0
0.4
1.3
2.4
1.3
1.5
0.4
1.4
0.8
3.0
5.5
6.6
9.0
5.4
–
4.7
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
T2
A
B
C
D
Average
4.6
4.8
2.7
–
4.0
2.7
2.5
2.5
–
2.6
1.4
1.0
0.7
–
0.9
0.0
0.1
0.0
–
0.0
2.6
0.3
0.0
–
1.0
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
T3
A
B
C
D
E
Average
2.9
2.7
2.6
2.1
–
2.6
2.7
2.6
2.4
2.0
–
2.5
0.5
0.8
0.1
0.3
1.0
0.2
0.6
0.1
0.4
0.2
1.0
0.4
2.5
1.6
1.2
1.0
–
1.5
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
compute the hydrodynamics and TDG field. As a first step to estimate fish exposure to TDG concentrations, a particle tracking technique that simulates fish as neutrally buoyant particles neglecting
behavioral responses is included in the model.
2. Wells hydroelectric project
Wells Dam, operated and owned by the Public Utility District
No. 1 of Douglas County (Douglas PUD), is at river mile (RM)
515.6 on the Columbia River, Washington, USA. Instead of having
separate structures for spillways, powerhouse, and fish facilities
the project has only one structure, called a hydrocombine. This
makes its design unique. Fig. 2a shows the hydrocombine structure. Fig. 2b shows details of the spillway. Topspills, in bays 2
and 8, are included to facilitate migration of fish swimming near
the free surface. The model extends approximately 5 km downstream of the dam. Fig. 3 shows the modeled tailrace together with
bathymetric information. The compliance station is located at transect T3. The model includes all spillway bays, draft tubes, riverbed,
topspills and spillway lips.
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M. Politano et al. / Computers & Fluids 68 (2012) 168–185
Two models are used. First, free surface simulations near the
dam are performed to predict the free surface and spillway jet regimes. Then, a rigid-lid model is used to predict the hydrodynamics
and TDG field in the entire tailrace. Having the free surface as a
spatially fixed entity facilitates the implementation of the attenuation of the turbulence at the free surface and improves the performance of the model, as free-surface computations are very
expensive. The drawback of this approach is that the effect of the
dispersed phase on the actual location of the free surface is
neglected. The Hydrologic Engineering Centers River Analysis
Systems software (HEC-RAS) is used to compute the free surface
from the end of the VOF simulations to the end of the domain. A
Manning’s roughness coefficient of 0.035 is used in the HEC-RAS
simulations.
3.1. Free-surface simulations
The free surface immediately downstream of the spillway cannot be assumed flat. The large amount of energy dissipated by
spillway flows generates waves in the tailrace that require the
use of a free-surface tracking algorithm. The Volume of Fluid
(VOF) model is used to obtain the free surface for the first 300 m
downstream of the dam. A k–e model is used for turbulence
closure.
3.2. Rigid-lid simulations
Fig. 8. Velocity vectors for June 5 (a and b) and June 4 (c and d). (a and c) Vectors
predicted with the rigid-lid model. (b and d) Vectors measured in the field.
3. Model description
In the present study, the hydrodynamics and TDG concentration
field are calculated using RANS models. The TDG model is implemented into the CFD software FLUENT.
Simulation of all processes related to TDG dynamics encompass
the computation of all individual bubbles entrained in the spillway.
However, this approach requires grid sizes of the order of bubble
radius, which is well beyond current computing capabilities.
Therefore, entrained bubbles need to be modeled instead of solved.
In this study, an ensemble average model, the algebraic slip mixture model that considers the change of the effective buoyancy
and viscosity caused by the presence of the bubbles and the forces
on the liquid phase due to the non-zero relative bubble–liquid slip
velocity, is used [12]. A Reynolds Stress Model (RSM) is used to
capture the anisotropic behavior of the turbulence.
Kinematic and dynamic boundary conditions and attenuation of
normal components of Reynolds stresses are programmed at the rigid non-flat surface [22].
Details of the TDG model can be found in Politano et al. [19].
Bubble dissolution is included as source/sink in the gas volume
Fig. 9. TDG field for June 4, 2006. Labels display TDG values.
M. Politano et al. / Computers & Fluids 68 (2012) 168–185
175
Fig. 10. TDG field for June 5, 2006. Labels display TDG values.
fraction and TDG equations. It is assumed that air behaves as a
single ‘‘pseudo-component’’ with averaged properties. An overall
mass transfer coefficient describes the migration of mass between
phases. The density of the gas phase is calculated using the ideal
gas law. The bubble velocity is programmed in Fluent assuming
that inertia and viscous shear stresses are negligible compared
to pressure, buoyancy, drag, and turbulent dispersion forces. A
scalar transport equation in the air phase is used to predict the
transport of the bubble number density. Bubble size is computed
using the gas volume fraction and bubble number density at each
point. The volume of bubbles can change for compression and
dissolution. Elevated pressure at the bottom of the tailrace increases the gas density reducing the bubble size. In addition, if
water is undersaturated at local conditions, gas is transferred
from bubbles to the liquid reducing the bubble size. On the other
side, if water is supersaturated at local conditions, a usual condition near the free surface, gas from the liquid is transferred to the
bubbles increasing bubble size. It is assumed that, for the region
downstream of the plunging jet, bubble size changes mainly due
to mass transfer and pressure variations, and therefore bubble
breakup and coalescence processes can be neglected [18].
In this study, the temperature dependency of the Henry’s law
coefficient is modeled using the van’t Hoff equation:
1 1
HeðTÞ ¼ HeðT o Þ exp C T
T To
ð1Þ
where He(T) is the Henry’s law coefficient and T temperature. A constant CT = 1388 K is obtained using molar average of CT values for
gases constituents of air [2].
3.3. Lagrangian model
As a first step to assess the impact of TDG distribution on fish, a
simplified Lagrangian approach is used. The fish are assumed to be
passive neutrally buoyant spherical particles with no behavioral
responses.
Fig. 11. TDG field for May 14, 2006. Labels display TDG values.
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M. Politano et al. / Computers & Fluids 68 (2012) 168–185
Fig. 12. TDG field for May 17, 2006. Labels display TDG values.
The prediction of the particles’ trajectories is achieved by integrating the force balance on each particle:
d~
up
¼ FD
dt
ð2Þ
FD is the drag force per unit mass. The subindex p stands for particle
and ~
u is the velocity. For a spherical particle the equation for the
drag force per unit mass reads:
FD ¼ 3 ql CD ~
ul j~
ul j
up ~
up ~
8 qp
ð3Þ
where q stands for density and the subindex l for liquid phase. The
drag coefficient CD depends on the flow regime. For a spherical particle it is given by:
8
24
>
< Re
a2
a3
C D ¼ a1 þ Re
þ Re
2
>
:
0:4
Re < 0:1
0:1 < Re < 10; 000
Re > 10; 000
ð4Þ
q d j~
u ~
uj
where Re ¼ l p lp l dp , is the particle diameter, l the dynamic visl
cosity, and the constants a1, a2, and a3 depend on the Reynolds
number [14].
The dispersion of particles due to turbulence is accounted for
through a stochastic tracking model, the Random Walk Model
(RWM). Turbulent dispersion is taken into account using the
instantaneous fluid velocity ui þ u0i ðtÞ as opposed to only ui when
integrating the trajectory equations. u0i ðtÞ represents the fluctuating velocity components. The RWM assumes that u0i ðtÞ conforms
to a Gaussian probability distribution. Values for u0i ðtÞ are obtained
from:
qffiffiffiffiffiffiffiffi
u0i ðtÞ ¼ n u0i u0i
ð5Þ
where n is a random number. Values of the fluctuating velocity are
maintained constant throughout a succession of turbulent eddies.
The time spent in turbulent motion (integral time) is approximated
as T L ¼ 0:3 ke. The particle dispersion rate is proportional to TL. Large
Fig. 13. TDG field for June 17, 2006. Labels display TDG values.
M. Politano et al. / Computers & Fluids 68 (2012) 168–185
177
Fig. 14. Isosurfaces of TDG source for two simulations with different values of forebay TDG.
TL values indicate greater turbulent motions in the flow and greater
particle turbulent dispersion.
Compensated TDG, TDGC, is calculated as:
C
TDGC ¼ P ð6Þ
He
where C is the concentration of dissolved gases in water, and P is the
total pressure. According to Eq. (6), approximately 10% of TDG is
compensated by 1 m of depth.
3.4. Computational mesh
Grid sizes are determined based on the study by Turan et al.
[22] on water entrainment due to spillway surface jets. Hexahedral
multiblock structured grids with about 7 105 elements are created in Gridgen V15 for the VOF simulations. The grids are refined
near the free surface and solid walls. The main features of a typical
mesh used for the VOF simulations are depicted in Fig. 2. Note the
grid refinement near the expected free surface in Fig. 2b. Fig. 2c
shows the mesh at the river bed used for the entire VOF model.
The rigid lid grids are created using Gridgen and Gambit with
approximately 9 105 elements. They have an unstructured region, from 500 m to 100 m downstream of the dam, created with
a paving technique available in Gambit to reduce grid size. Fig. 4
shows overall views of grids used for the rigid lid simulations.
Fig. 4a and b display details of the grid at the free surface near
the spillway for two different spill configurations, spread and concentrated spill configurations, respectively. Fig. 4c shows a detail of
the unstructured mesh connecting structured blocks.
Fig. 15. Slice through bay 7. Labels display TDG values and white dotted lines zero TDG source.
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M. Politano et al. / Computers & Fluids 68 (2012) 168–185
3.5. Boundary conditions
3.5.1. Walls and riverbed
Dam walls and the riverbed are modeled using no-slip walls
with zero TDG and gas fluxes. Previous numerical and reducedscale models suggest little effect of riverbed roughness on the three
dimensional characteristics of the flow field in hydropower tailraces [8,11]; hence no special treatment is used for the riverbed
roughness in this study.
3.5.2. Top surface
In the VOF simulations, a pressure outlet boundary condition
with atmospheric pressure is applied at the top of the VOF grids
to allow free air flow and avoid unrealistic pressures.
The free surface in the rigid-lid simulations is modeled and programmed in Fluent as presented in Turan et al. [22]. Kinematic and
dynamic conditions at the free surface are used for the liquid velocity. Conditions enforcing zero normal fluctuations at the free surface are used to represent the attenuation of turbulence at the
Fig. 16. Streamlines colored by TDG for the 7Q10 simulations. Numbers next to the spillway bays show discharge in m3/s.
M. Politano et al. / Computers & Fluids 68 (2012) 168–185
179
Fig. 17. Predicted TDG concentration at sensor location for the 7Q10 and compliance simulations.
free surface. The gas phase is allowed to leave the simulation
domain through the free surface. For the TDG concentration, a Neumann boundary condition is used as used by Politano et al. [19].
3.5.3. Downstream end
A hydrostatic pressure profile is imposed at the downstream
end of the VOF simulations. The TWE is obtained using the Wells
Dam tailwater curve.
In the rigid lid simulations, an outflow boundary condition is
used. A zero TDG gradient condition is programmed at the outlet
of the rigid lid simulations.
3.6. Model parameters
Grid sizes prevent the computation of the entrained air. To the
best knowledge of the authors, air entrainment in a prototype scale
spillway has never been measured. In this study, the entrained
bubbles are model parameters. Bubble size and gas volume fraction at the spillway gates (boundary conditions) are selected during the calibration process following a trial-and-error procedure
to match TDG field data. The same bubble diameter and gas volume fraction obtained during calibration are used for all the
simulations.
3.7. Numerical method
3.5.4. Spillway bays and powerhouse units
A constant mass flow rate, assuming a uniform velocity distribution, is assigned at the spillways and at the powerhouse units.
The gate opening of each of the bays was determined using the
spillway gate rating curves. It is assumed that air is not entrained
with the turbine inflow.
For the rigid-lid simulations, the TDG concentration measured
in the forebay is used with spillway and powerhouse releases.
The model equations are solved sequentially using the unsteady
FLUENT solver. The pressure at the faces is obtained using a body
force weighted scheme. The continuity equation is enforced using
a Semi-Implicit Method for Pressure-Linked (SIMPLE) algorithm.
Typically, two to three nonlinear iterations are needed within each
time step to converge all variables to a L2 norm of the error <103.
For the free surface computations, a modified High Resolution
Interface Capturing (HRIC) scheme is used to solve the water vol-
Fig. 18. TDG source isolines for the 7Q10 simulations at a slice located 50 m downstream of the dam. Numbers show discharge in m3/s.
TDG source per unit length ( kg-air /m s )
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M. Politano et al. / Computers & Fluids 68 (2012) 168–185
4.1. Calibration and validation
0.3
ume fraction. Solutions are obtained using variable time-step between 0.001 and 0.004 s.
A fixed time-step of 10 s is used for the rigid-lid model simulations. In order to improve convergence, the model is first run
assuming single-phase flow and then bubbles are injected into
the domain. All simulations are run on a dual Intel Xeon 5150
2.66 GHz processors (total of 4 cores) with 8 GB of RAM.
A field study was performed between May 14 and June 28, 2006
by EES et al. [5] to study TDG production dynamics at the dam.
Acoustic Doppler Current Profiler (ADCP) data were collected on
June 4 and 5 along three transects, as indicated in Fig. 8. Data were
collected at depth increments of approximately 2.0 m. The average
sampling time was 10 min at each station, which resulted in
approximately 600 data points per station. A qualitative comparison between depth averaged measured and predicted velocity vectors is performed to evaluate the model capability to capture the
general tailrace flow pattern.
TDG sensors were deployed in three transects, T1, T2 and T3,
placed at 360, 1041, and 4742 m downstream of the dam, respectively. Symbols in Fig. 3 show the location of the TDG sensors. TDG
data collected on June 4, June 5, May 14, May 17, and June 17 were
selected to calibrate and validate the model presented in this
paper.
On June 4, the dam operated in a spread pattern with near uniformly spill across bays 2 through 10. On June 5, May 14, and May
17, the bulk of the spill discharge was concentrated through bay 7.
On June 17, the spillway flow was concentrated across bays 7, 8,
and 9 in a configuration called a crown operation.
Three gas volume fractions a = 0.02, 0.03 and 0.04 and singlesized bubble diameters of 0.005 and 0.008 m are numerically
evaluated.
4. Simulation conditions
4.2. TDG forebay simulations
Results of ten simulations are presented in this paper. The purpose of the first five simulations are to calibrate and validate the
model. Two additional simulations are performed to study the effect of the TDG concentration in the forebay on the TDG field in
the tailrace. The preferred dam operation, when the plant is operating at the 7Q10 discharge, that results in minimum TDG at the
compliance station, is studied performing three extra simulations.
Finally, an additional simulation is carried out to investigate compliance with water quality standards. Table 1 shows spillway and
powerhouse operating conditions as well as forebay TDG and forebay and tailwater levels used for the simulations.
The forebay simulations (FBSs) use forebay TDG values of 110%
and 115% with a concentrated spill configuration.
0.2
0.1
7Q10-A
7Q10-B
7Q10-C
0.0
-0.1
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
Depth (m)
Fig. 19. TDG source per unit length for the 7Q10 simulations at a slice located 50 m
downstream of the dam.
4.3. 7Q10 flow simulations
4.3.1. Forebay and temperature conditions
Forebay TDG, forebay elevation, and water temperature are selected using historical data for daily average flows in a 10-year period 1999–2008. 43,200 hourly records of data are filtered to
include values in which outflow is equal to or greater than
5663.4 m3/s. Temporal distribution of hourly values (by week of
Fig. 20. Slice through the bay that concentrates the bulk of the spilled flow for the 7Q10 simulations. Labels display TDG values and white dotted lines zero TDG source.
M. Politano et al. / Computers & Fluids 68 (2012) 168–185
181
Fig. 21. TDG, gas volume fraction and bubble diameter isosurfaces for the compliance simulation.
the year) range from early April to early September, with the middle quartiles (25–75%) occurring between weeks of June 4 and June
25. Median values of the distribution occur at the week of June 11.
Hourly flow measurements averaged 6258.0 m3/s (±509.7 m3/s
SD). During these ‘high flow’ events, 50% of flows are lower than
6088.1 m3/s and only 12% of values exceed 6954.6 m3/s. Water
temperatures during these occurrences range from 4.1 to 19.7 °C,
with a median temperature of 13.0 °C. Forebay TDG during these
occurrences ranges from 99.9% to 120.1% with a median TDG of
112.5%. Average daily forebay elevations are also collected from
Data Access in Real Time throughout the same period. Forebay elevation ranges from 236.2 to 238.0 m, with a median elevation of
237.6 m. Since the distributions of the variables have a slightly
negative skew, the median values, rounded to the nearest whole
number or percent, are used to best represent conditions to be
used in the simulations under high-flow events.
4.3.2. Dam configuration
The total powerhouse capacity of the Wells Dam is 6229.7 m3/s.
Taking a conservative approach, nine out of ten turbines are assumed to be operating at 91% of their full capacity.
During Juvenile Bypass operations, spillway bays 2 and 10 are
topspills with a flowrate of 48.1 m3/s and bays 4, 6 and 8 need to
spill a minimum of 48.1 m3/s.
All 7Q10 simulations concentrate the spill in a few gates. In simulation 7Q10-A, the spill flow is concentrated in bays 6, 7 and 8.
Gate 7 is operating at full capacity and gates 6 and 8 distribute
the remaining flow. With this configuration, 66.6% of the spilled
flow goes through bay 7 and 12.4% through the adjacent bays. In
simulations 7Q10-B and 7Q10-C, the effect of operating with a central, fully open gate and another, eastern or western gate is studied.
Simulation 7Q10-B concentrates 66.2% in bay 7 and 18.4% in bay 3,
while 7Q10-C has 66.2% and 18.5% of the spill flowing through bays
5 and 9, respectively.
4.4. Standard compliance simulation
The standard compliance simulation (CS) has settings similar to
those used on other projects for evaluation of compliance with regard to forebay TDG and powerhouse configuration. Nine out of ten
turbines are working at full capacity, the forebay TDG is 115%, and
the water temperature is 15.5 °C. Based on the results of the 7Q10
simulations, the spill is concentrated in bay 7.
After reaching a steady condition, the exposure of particles to
TDG is calculated, injecting particles in spillway bays 4, 6, 7, and
8 and turbines 2, 5, and 9. Approximately 1000 particles are released from each of the turbines and spillway bays 4, 6, and 8. At
the beginning of the simulation, evenly spaced particles are placed
Fig. 22. Percent of time particles are exposed to TDG without considering
hydrostatic compensation.
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M. Politano et al. / Computers & Fluids 68 (2012) 168–185
on two lines, in the span-wise direction, along the inlets. The lines
are at one third and two thirds of the total height of the surface.
Due to the greater discharge in bay 7, around 5000 particles are injected in this bay. The particles are evenly distributed on six lines
equally spaced across the height of the bay.
5. Numerical results
5.1. Calibration and validation
TDG concentrations using a constant gas volume fraction of 0.03
and a bubble diameter of 0.5 mm at the spillway gates brackets the
field data with the smallest error. Bigger volume fraction and smaller bubble size overpredicts TDG while smaller volume fraction
underpredits TDG. The selected parameters are used for each spillway at the inlet of the model for all simulations.
The convergence parameters of the VOF simulations are the
flow rate and TWE at the downstream end of the VOF model. These
simulations reach a statistically steady state after approximately
20–30 min, which take about 30–45 days of computing time.
Fig. 5 displays the evolution of the convergence parameters for
the May 14 simulation. Dotted lines represent the target values.
Velocity vectors and free surface location obtained with the VOF
model for May 14 and June 4 are shown in Figs. 6 and 7, respectively. Vectors are interpolated in a coarser grid to help visualization. The spillway flow on May 14 is concentrated in bay 7 and
the powerhouse unit underneath this bay is not operating. Fig. 6a
shows the predicted water attraction towards the surface jet generated in the full open bay 7. In Fig. 6b, the gray line represents the
location of the free surface. Although May 14 has the lowest TWE
and the powerhouse unit beneath the open spillbay is not operating, the jet predicted by the VOF model does not tend to plunge.
This result suggests that, at the simulated TWE, hydrocombine
geometry prevents the formation of plunging jets, minimizing
the possible transport of bubbles to depth. On June 4, a submerged
hydraulic jump is formed in bay 7. This flow regime has the potential to aerate the water leading to higher TDG production. Powerhouse units beneath the spillway bays help to keep the jet
tangent to the free surface.
The rigid-lid model is able to reproduce the general flow pattern
of the Wells tailrace. Depth-averaged predicted and measured
velocity vectors on June 4 and 5 are shown in Fig. 8. Vectors are
scaled differently in each transect for easy visualization. Since
the total flow on June 5 is 30% greater than on June 4, larger veloc-
Fig. 23. Percent of time particles are exposed TDG considering hydrostatic
compensation.
ity vectors are observed and predicted in this day. The best agreement is obtained at the most downstream transect, approximately
2 km downstream of the dam, when the flow becomes more stable.
The model is able to capture the recirculation zone on the east side
created by the sudden expansion of the river cross section downstream of the dam creates.
Table 2 summarizes the TDG average values measured and predicted at transects T1, T2, and T3 and the TDG percentage difference between predictions and measurements. The model
performs best for May 14 and May 17, where the transect average
errors are below 1%. For June 4 and June 17, the model overpredicts
TDG values, whereas the June 5 simulation underpredicts TDG values. At transect T3, where the compliance sensor is located, the
transect average error is within ±3% for all the simulations. On June
17, the percentage of spill was the lowest. However, in this day the
TDG production was the maximum. The model is able to predict
this tendency. However, numerical results overpredict TDG for this
operation. The maximum transect average error, 4.6%, is found at
transect T1 for June 17. According to the model, the crowned spill
configuration results in more flow and air entrained to depth. Note
that, on this day, all turbine units that prevent plunging flows were
operating. However, elevated TDG values are observed near the
bottom downstream of the bays operating at high flowrates.
Comparison between TDG measured and predicted is shown in
Figs. 9–13, for June 4, June 5, May 14, May 17, and June 17, respectively. Slices show the vertical TDG distribution at the transects
used during the field study. The model captures the TDG gradients
in the flow direction. Higher TDG is predicted near the dam as a result of maximum TDG production caused by the dissolution of entrained bubbles. Downstream of the aeration zone, TDG
concentration changes primarily by mixing and degasification at
the free surface. Higher TDG values are observed in the west shore.
Some of the water is transported back to the dam in the recirculation observed in the east region, but most of the supersaturated
water moves longitudinally along the main river channel. If spill
flows are concentrated in the central dam region, a second eddy
is formed in the west region and the highest TDG values are observed in the central region of T1, decreasing the TDG lateral gradient. When a turbine is operating, TDG values near the bottom
are those corresponding to the forebay. On May 14 and May 17,
units below operating spillways are closed and supersaturated
water is transported to depth.
Analysis of TDG field data obtained during the entire study
demonstrates that, most of the time and for similar values of spill
and TWE, a spillway configuration that concentrates the spillway
flow through one bay results in lower net TDG production [5]. Con-
Fig. 24. Percent of particles in the simulated domain at different simulation times.
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M. Politano et al. / Computers & Fluids 68 (2012) 168–185
sistent with the observations, the model predicts lower values of
net TDG production for the full gate spillway configuration. Note
that, however, in the particular spread flow selected for calibration,
TDG values are of the same order than those obtained for full open
gate. According to the model, a full open gate operation results in
skimming surface jets with lower TDG production and elevated
degasification. Submerged jumps observed in the spread operation
entrain more bubbles to high pressure, favoring dissolution.
5.2. TDG forebay effect
The production of TDG is proportional to the difference between
TDG concentration at equilibrium, which depends on pressure and
temperature, and local TDG. Thus for higher local TDG, originated
by higher forebay TDG, the production of TDG is smaller. The degasification also depends on the local TDG. The mass transfer rate at
the free surface, leading to saturated water, increases with local
TDG. In addition, if water is supersaturated at local conditions,
gas is transferred from the water to the bubbles reducing the
TDG concentration. Fig. 14 shows two isosurfaces of TDG production downstream of bay 7. The isosurface of positive production
of TDG is bigger for smaller forebay TDG. On the other hand, the
isosurface of negative production of TDG (degasification by bubble
exposure to supersaturated water) is smaller for the simulation
with smaller forebay TDG.
Fig. 15 shows a vertical slice through bay 7, colored by TDG concentration. The white line encircles the zone with positive production of TDG. Above this region, there is degasification, and below
that, the mass transfer is zero because bubbles are not present.
At the simulated conditions, though production is bigger and degasification is smaller for forebay TDG 110%, the resulting TDG concentration is smaller than that obtained for forebay TDG 115%.
phenomenon promotes mixing and dilution but also exposes more
water to air, increasing the resulting TDG. This is true as long as the
water is not saturated with air at the local conditions. In simulation
7Q10-B the jet from bay 3 prevents water from being drawn towards the higher aerated region downstream of bay 7. In this simulation, the western eddy traps most of the TDG produced
downstream of bay 3 creating an important TDG lateral gradient.
The cumulative TDG source per unit length as a function of the
distance from the free surface at 50 m from the dam is presented in
Fig. 19. At approximately 15 m from the surface, the cumulative
TDG source has reached its maximum for each of the simulations
indicating that the TDG production is negligible below this depth.
At about 6 m from the free surface, the TDG source is negative,
indicating net degasification. In this low-pressure region, the excess of gas is transferred from the water to the bubbles. The degasification is similar for all the configurations. However, the
production of TDG is smaller for 7Q10-B. Fig. 20 shows slices with
contours of gas volume fraction and tangent velocity vectors
through bay 7 for simulations 7Q10-A and 7Q10-B and through
bay 5 for simulation 7Q10-C. The white line encircles the zone with
positive TDG source. In the spillway configuration 7Q10-B, bubbles
remain closer to the free surface, decreasing the TDG production.
According to the model, in 7Q10-A and 7Q10-C water attracted
from the west side towards the jet transports bubbles to high-pressure regions, increasing the TDG production. In addition, TDG production is further increased by the increment of interfacial area as
bubbles shrink due to compression and dissolution.
According to the model, concentrating the spilled flow in bay 7,
with minimum discharges in the adjacent bays, is the best configuration to minimize TDG production at the Wells Dam. If additional
water needs to be spilled, discharge through bay 3 is recommended.
5.4. Standard compliance simulation
5.3. 7Q10 flow simulations
The TDG distribution as a function of the west shore at transects
T1, T2 and T3, for the compliance simulation, is presented in
Fig. 17. The x-axis on the top shows the location of the TDG sensors. At transects T2 and T3, the TDG field shows a quasi-uniform
distribution indicating that TDG reached a developed condition upstream of transect T2. The maximum TDG value at the compliance
station on transect T1 is 118% and at the compliance station is
116.7%. According to the model, with the proposed operational
configuration, Wells Dam meets State of Washington TDG water
quality standards for 7Q10 flows.
140
120
100
TDG
The predicted flow pattern and TDG distribution for the 7Q10
simulations are shown in Fig. 16 with streamlines colored by
TDG. A slice at transect T1 shows vertical and lateral TDG distributions. Concentrating an important amount of the spilled flow in
one central spillway bay results in two distinct zones with eddies
close to each river bank. Depending on the spillway operation,
the west bank eddy can influence the flow and TDG field a few meters downstream of the dam. As observed for the other operational
conditions, high TDG is observed downstream of operating bays
due to dissolution of entrained bubbles. Simulation 7Q10A shows
maximum TDG values at the center of the spillway. Concentrating
the flow in central bays results in less lateral TDG gradient in T1. In
7Q10B and 7Q10C, some of the spill is released at the end bays,
resulting in a more noticeable TDG lateral gradient. Though higher
TDG values are observed with these configurations, supersaturated
water quickly loses the TDG excess as moves downstream.
Fig. 17a–c shows the TDG concentration values predicted by the
model as a function of the distance from the west shore at transects T1, T2, and T3, respectively. The TDG mixing with the
7Q10-A operation is higher than the other simulated configurations. However, this configuration produces the highest averaged
downstream TDG values. On the other hand, simulation 7Q10-B,
with the highest TDG lateral gradient in T1, results in the lowest
TDG levels at transect T3.
Contours of TDG source together with tangent velocity vectors
in a vertical slice at 50 m downstream of the dam, for every
7Q10 simulation, are presented in Fig. 18. Negative and positive
values represent degasification and TDG production, respectively.
The white contour line shows zero TDG source. In simulations
7Q10-A and 7Q10-C, water near the west bank is attracted towards
the spillway surface jet originated in bay 7 or 5, respectively. This
80
60
40
20
0
20
40
60
80
100
Time (min)
TDG-A
TDG-B
TDG C-A
TDG C-B
Fig. 25. History of exposure to TDG and TDGC for two particles released from bay 4.
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M. Politano et al. / Computers & Fluids 68 (2012) 168–185
Isosurfaces of TDG, gas volume fraction, and bubble diameter
can be seen in Fig. 21. The zones with high TDG concentrations
are limited to a small region directly downstream of bay 7, which
corresponds with the aerated zone with high gas volume fraction.
Maximum values of TDG near bay 7 are slightly above 125%, but
supersaturated water quickly degases. Bubble size isosurfaces
show the reduction of bubble size at depth due to compression
and dissolution.
In order to analyze the exposure of fish to TDG, the history of
particles released from different spillway bays and turbines is analyzed. Position, TDG, and TDGC of each particle are recorded every
10 s during 2 h. Figs. 22 and 23 show the percent of time particles
are exposed to a given TDG range. Accounting for the hydrostatic
compensation dramatically changes the TDG particles exposure.
After 2 h, an insignificant difference is found from different releases. According to the simulations, 97.6% of the time, particles
traveling through the tailrace are exposed to TDG values between
115% and 120%. Note that the particles reach that level of exposure
only 8.3% of the time when considering the hydrostatic compensation. When considering hydrostatic compensation, particles are in
undersaturated water approximately 70% of the time.
The percentage of particles within the tailrace for different releases as a function of time is shown in Fig. 24. At 30 min from
the injection, all particles are in the Wells Dam tailrace. After
45 min, 74.7% of the particles released from the turbine 2 are still
in the tailrace because the western eddy has trapped some particles. Particles released from turbine 9 and bay 8 are affected by
the eastern eddy and approximately 40% of them are still in the
tailrace after 45 min. After 75 min, fewer than 20% of the particles
are in the tailrace. The simulations present inert particles without
any fish behavioral rule. Fish tag studies demonstrate that fish
swim following the main river flow and therefore fish residence
time is expected to be smaller than those calculated for inert
particles. An animation of particle exposure to TDG and TDGC of
particles released from the bay 7 is available at TDG-7Q10.avi.
Fig. 25 shows the history of exposure to TDG (line) and TDGC
(symbol) for two individual particles released from the bay 4.
Every time the particle is at the free surface, the TDG and TDGC
are the same and line and symbol intersect. Particle A is trapped
by the western eddy and stays longer in the domain. According
to the model, the particle is exposed to values of TDGC greater
than 100% only 17% of the time. After about 60 min, the particle
leaves the eddy, passing through the zone with high TDG created
by the high discharge at bay 7. Particle B is unaffected by the
western eddy and it is exposed to values of TDGC greater than
100% only 3.1% of the time. This particle leaves the simulated
river reach in less than half the time of the trapped particle.
Although literature reports different values of TDG at which
the effects of GBD can become severe, it is understood that exposure to TDGC levels below 110%, that is valid for 83.9% of the
time, could cause only minor signs of GBD with no obvious indication of debilitating effects on fish. Though differences between
the behavior of passive particles and actual fish are expected, the
modeling presented in this paper shows the importance of evaluating the effect of TDG considering not only TDG values, but also
exposure time and hydrostatic compensation.
6. Conclusions
The application of a 3D two-phase model, capable of predicting
TDG and computing exposure of particles to TDG to 5 km of the
tailrace of the Wells Hydroelectric Project, is presented. The model
accounts for the effect of bubbles on the liquid hydrodynamics and
the turbulence suppression at the free surface. TDG is calculated
considering the dissolution of bubbles of different sizes, convection
and mixing.
The model is calibrated and validated against velocity and TDG
field data collected in 2006. A constant gas volume fraction of 0.03
and a single-sized bubble diameter of 0.5 mm are used as input
data. These values produce values of TDG that compare well
against field data collected. At the compliance transect the average
TDG error is within ±3% for all the simulations.
The model is used to obtain a better understanding of the effect
of the value of forebay TDG on the resulting TDG downstream.
According to the model, higher forebay results in smaller TDG production and higher degasification. Different dam configurations are
numerically evaluated for compliance flows. Analysis of field data
and model results indicate that concentrating the spill flow in
one bay, instead of spreading it across several bays, results in the
lowest TDG concentration. According to the model, minimum
TDG concentrations are obtained when the spill flow is concentrated in bay 7 and the bulk of the remaining spill is flowing
through bay 3. An additional scenario is modeled to demonstrate
that Wells Dam could be operated within State TDG standards.
TDG exposure to inert particles taking into account the effects of
hydrostatic compensation is calculated. Including hydrostatic compensation drastically changes the estimates of particles exposure
to TDG. When accounting for hydrostatic compensation, particles
are in undersaturated water 70% of the time and 83.9% of time they
are exposed to TDG levels below 110%. Future modeling efforts include utilizing behavioral models to better describe trajectories
and the true risks to fish downstream of spillways.
Appendix A. Supplementary material
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.compfluid.2012.
08.003.
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