Water Management

Proceedings of the Institution of Civil Engineers

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

http://dx.doi.org/10.1680/wama.15.00011
Paper 1500011
Received 20/01/2015
Accepted 06/05/2015
Keywords: dams, barrages & reservoirs/hydraulics andhydrodynamics/mathematical modelling
ICE Publishing: All rights reserved

Three-dimensional numericalmodelling of flow field inshallow reservoirs
1&
Taymaz Esmaeili MSc

4&
Stefan Haun PhD

PhD Student, Department of Urban Management, Graduate School ofEngineering, Kyoto University, Kyoto, Japan
2&
Tetsuya Sumi PhD

Scientific Assistant, Institute for Modelling Hydraulic andEnvironmental Systems, University of Stuttgart, Stuttgart, Germany
5&
Nils Rüther PhD

Professor, Disaster Prevention Research Institute (DPRI), Kyoto
University, Kyoto, Japan

Associate Professor, Department of Hydraulic and Environmental
Engineering, Norwegian University of Science and Technology,
Trondheim, Norway

3&
Sameh A Kantoush PhD

Associate Professor, Disaster Prevention Research Institute (DPRI),
Kyoto University, Kyoto, Japan

1

2

3

4

5

Shallow flows can play a significant role in sediment management for dam reservoirs (e.g. sedimentation inshallow reservoirs and free-flow flushing operation). When shallow flow emerges with symmetric or asymmetricpatterns, the flow domain exhibits complex three-dimensional (3D) features (e.g. helical flows). This study focuseson the numerical modelling of the velocity field in shallow reservoirs with varying geometries and also varying
bed conditions (i.e. flat and misshaped beds). A fully 3D numerical model using the finite-volume method was
utilised to reproduce the 3D flow velocity field. The experimentally measured surface velocity in all cases and velocity
profiles in one case were used to validate the model. The numerical results showed that a slight disturbance in the
inflow boundary condition results in a steady asymmetric flow pattern in reservoirs with a higher defined shapefactor, but does not affect the flow pattern in reservoirs with a lower defined shape factor. Nonetheless, thesimulated and measured flow velocity fields are reasonably consistent in all cases. These results can be used to
optimise the design of sand traps or water storage facilities, and also to optimise sediment management in existing
reservoirs.

Notation
B
b
g
h
i
k
ks
L
P
Pk
Q
t
u
u*

reservoir width
inlet channel width
acceleration of gravity
flow depth
index for three spatial directions
turbulence kinetic energy
equivalent bed roughness
reservoir lengthpressure
production of turbulent kinetic energy
flow discharge
time
velocity fluctuations
shear velocity

Ui
V0
Vin
x
xi
y
z
α
δij
ε
ν
νt
ρ

averaged flow velocity in i directionreference streamwise velocity at the inlet
actual streamwise velocity at the inlet, which isaffected by a slight disturbancecoordinate in longitudinal direction
spatial geometric scale
coordinate in transversal direction
coordinate in vertical direction
magnitude of linear variation of streamwise velocity
along the inlet channel width
Kronecker deltadissipation of k
viscosity of water
eddy viscosity
density of water1

Water Management

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

1.

reservoirs. Their studies revealed that 2D depth-averaged
numerical models can reasonably reproduce the flow velocity
pattern in shallow rectangular reservoirs. As long as secondary
current effects and velocity variations over the flow depth are
not significant, 2D models can be utilised. Compared to 3Dmodels that need a careful setting, 2D models benefit from a
simpler setting. However, the geometry condition may be more
complex in practical cases, and a complex 3D flow pattern
can emerge. The 2D numerical models cannot simulate the secondary current effects directly, particularly velocity variations
over the flow depth on misshaped beds of shallow reservoirs.
Stansby (2006) concluded that 2D depth-averaged models
could not consider the flow curvature over the bed frictionthat emerged because of the vertical mixing, which is inducedby horizontal strain rates. This inability may lead into a significant underestimation of the bed friction in some cases. The
complexity of 3D flow patterns is further magnified over the
existing bed forms, on the misshaped bed, that is obtained
after flushing and lowering the water level. Because completely
different flow patterns may appear over the flow depth, knowledge about the vertical distribution of the streamwise andlateral velocity, which is reproduced using 3D numerical simulations, can provide a more precise evaluation of morphological processes in shallow reservoirs. Nonetheless, 3D numericalmodelling of the symmetric and asymmetric turbulent flow
fields in shallow reservoirs with varying geometries is scarce(Esmaeili et al., 2014a).

Introduction

Shallow flows are described as a flow condition in which
the vertical dimension of the fluid domain is noticeably
smaller than its horizontal dimensions (Yuce and Chen, 2003).
Flows in wide rivers, lakes, coastal lagoons, estuaries and large
reservoirs are examples of shallow waters in the prototype
scale. A flow pattern in wide and shallow reservoirs with asudden expansion of the inlet section may become unstable,
which produces large-scale transversal motions and recirculation zones. This phenomenon can be attributed to thehigh sensitivity of the flow pattern to the initial boundary
condition at the inlet section (e.g. small transverse
disturbance) (Dewals et al., 2008). When large-scale transverse motions and turbulent coherent structures develop in ashallow reservoir, the sediment transportation pattern (i.e.
erosion and deposition) is significantly affected by the velocity
field.
Shallow flows are predominant in nature and also emerge
in many engineering applications such as sudden expansions(Shapira et al., 1990), compound channels (Chu et al., 1991;
Ghidaoui and Kolyshkin, 1999), storage chambers (Adamson
et al., 2003; Stovin and Saul, 1996), settling tanks (Frey et al.,1993), shallow reservoirs sedimentation (Camnasio et al., 2013;
Dufresne et al., 2012; Kantoush et al., 2008a, 2010) and sediment flushing (Esmaeili et al., 2014b; Kantoush and Schleiss,2009).
The effect of geometric and hydraulic boundary conditions on
the flow pattern of shallow reservoirs was clarified in the experimental tests of Dufresne et al. (2011) and Kantoush (2008).
Kantoush (2008) presented a comprehensive review of experimental tests in a series of shallow reservoirs with transverse
flow motions in the symmetric channel expansions. His study
revealed three-dimensional (3D) features of the flow structure
in shallow reservoirs (i.e. secondary flows and 3D stretchingvortices). In addition, the experimental tests show that an
asymmetric flow pattern emerges under a certain geometricand hydraulic condition despite the perfect symmetric geometry and hydraulic condition. Similar results were obtained byAdamson et al. (2003) and Stovin and Saul (1996) regarding
storage chambers and storage tank sedimentation, respectively.
Kolyshkin and Ghidaoui (2003) came to a similar conclusion
about the development of an asymmetric flow pattern in thewake flows, and Mariotti et al. (2013) also presented the analysis of flow instabilities in the river mouth zone with a small
width-to-depth ratio. Recently, Peltier et al. (2014a) presented
a review of the experiments regarding shallow reservoirs, andsuggested the domains for existence of varying flow patterns,
including meandering flows, in shallow reservoirs (Peltier
et al., 2014b).
Dewals et al. (2008), Dufresne et al. (2011) and recently Peltier
et al. (2014c) used two-dimensional (2D) numerical models toinvestigate the turbulent flow patterns in rectangular shallow
2

A computational fluid dynamic (CFD) code called SSIIM(simulation of sediment movements in water intakes withmultiblock option) was used in this study to simulate the 3D
flow velocity field. The SSIIM program, which was developed
at the Norwegian University of Science and Technology(NTNU), implements a 3D numerical model of flow field bysolving the mass and momentum conservation equation inthree dimensions using various turbulence closure approaches.
Further modifications are also possible in several parts of thesource code (Olsen, 2013). SSIIM was successfully applied tomodel the 3D flow field in open channels with large roughness
elements (Fischer-Antze et al., 2001), compound channels(Wilson et al., 2003) and meandering channels (Stoesser et al.,2010). SSIIM was also used for the coupled computation offlow and sediment fields in the physical model and prototype
scale studies (e.g. Dehghani et al., 2012; Esmaeili et al., 2013;
Fischer-Antze et al., 2008; Olsen and Kjellesvig, 1999;
Ruether et al., 2005). Recently, this CFD code with enhanced
features of grid generation was used to simulate sedimentationand flushing channel evolution in shallow reservoirs (e.g.
Esmaeili et al., 2014b; Harb et al., 2014; Haun and Olsen,
2012a, 2012b).
The assessment of the flow field is necessary to characterise
the domain of the main jet flow, reverse flow and eddies in ashallow reservoir. Knowledge about shallow flows leads toa more appropriate design of storage facilities (e.g. storageWater Management

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

tanks; sewer detention tanks) and more efficient sedimentmanagement strategies in reservoirs and settling basins(Kantoush et al., 2011a, 2011b). Moreover, in a shallow reservoir with misshaped bed, the variation in flow velocity overthe flow depth is noticeable due to the existing friction of
the bed forms. However, a few studies have considered theeffect of various geometric and hydraulic parameters on theflow pattern of shallow reservoirs. Consequently, 3D modellingof the velocity field on flat and misshaped beds of shallow
reservoirs, without a sediment transport condition, was performed in this study and compared with the experimental
measurements.

The large-scale particle image velocimetry (LSPIV) technique
was used to measure the surface velocity field, and ultrasonicvelocity profiler (UVP) devices were used to provide the 3D
flow velocity measurements (Kantoush et al., 2008b). EachUVP device can instantaneously measure 1D velocity profile
over the flow depth. A set of three UVP probes, which wereinclined at 20° to the vertical axis and installed on the movable
frame, allowed measurement of the 3D flow field. The firstvalid UVP measurements were located 12·5 cm away from theside walls and 2·5 cm from the free water surface. Additionally,in the framework of the experimental study, the surface velocity was measured after sediment flushing from the shallow
reservoirs. Plastic particles with a density of 960 kg/m³ andan average diameter of 3·4 mm were used as seed for LSPIV
measurements (Kantoush et al., 2008b). Non-uniform crushed
walnut shells were used as fluid tracers to provide ultrasoundreflection for UVP devices and were also used as suspended
material for modelling sediment deposition. The mediansize of this non-cohesive lightweight and homogenous grainmaterial was 50 μm with a density of 1500 kg/m³. The flow
discharge rate (Q) and water depth (h) were fixed for all
experiments as 0·007 m³/s and 0·2 m respectively, except forthe cases with a misshaped bed. Thus, in all examined configurations with a flat bed, the measured Froude number
was as small as Fr = 0·1 and Reynolds number was as high as
14 000 ≤ Re ≤ 28 000 to ensure that a turbulent flow was developed. For the flow field measurements on misshaped beds
after flushing, the water level and discharge were 0·1 m and
0·007 m3/s respectively.

2.

Physical model set-up and study cases

The experimental tests were performed at the Laboratoryof Hydraulic Constructions of the Swiss Federal Instituteof Technology (EPFL) in a rectangular reservoir with amaximum inner length (L) of 6 m and width (B) of 4 m(Kantoush, 2007). The inlet and outlet rectangular channel
width (b) and length (l ) were 0·25 m and 1 m respectively.
Both channels were located at the centre of the upstream anddownstream side walls of the reservoir. Various shallow reservoir geometries could be achieved by adjusting a moveable
polyvinyl chloride (PVC) plate wall. The reservoir depth was
0·3 m, and both side walls and the bottom floor were hydraulically smooth and flat. The water level in the reservoir was controlled using a 0·25 m wide and 0·3 m high flap gate at theend of the outlet channel. A movable frame of 4 m length was
mounted on the side walls of the reservoir to install themeasurement devices. Table 1 shows the geometrical attributesof five reservoirs used in the present study and also corresponding shape factors (i.e. SF) described by Dufresne et al.
(2011). According to Dufresne et al. (2011), the flow pattern
was symmetric (i.e. S0) when SF was approximately lower than
6·2 and the flow pattern was asymmetric (i.e. A1) when SF
was approximately bigger than 6·8. Thus, in the applied geometries, T11 and T13 have S0 flow pattern whereas T7, T8
and T9 have A1 flow pattern.

Case

b: m

L: m

B: m

ΔBa

SFb

T7
T8
T9
T11
T13

0·25
0·25
0·25
0·25
0·25

6
6
6
5
3

3
2
1
4
4

1·375
0·875
0·375
1·875
1·875

8·63
11·32
18·82
5·97
3·58

a

ΔB is equal to (B − b)/2
SF is the shape factor introduced by Dufresne et al. (2011),
which is defined as L/ΔB 0·6 b 0·4

bTable 1. Geometrical attributes of experimental cases employedby Kantoush (2008)

Five different reservoir geometries with various lengthto-width (aspect) ratios and reservoir width to inlet channel
width (expansion) ratios used in the experimental study of
Kantoush (2007) were considered to numerically model thedifferent flow patterns encountered. The hydrodynamic boundary utilised in the experimental work was also employed. The
flat bed and misshaped bed, which were obtained after flushingand lowering the water head, were introduced to the SSIIM
program as the initial bed condition. The numerical results
were compared and validated with a 2D systematic measured
surface velocity, which was provided using the LSPIV technique for all cases. Additionally, simulated 3D velocity components were compared with the measured values, which wereobtained using UVP devices in one case.

3.

Numerical model

The fully 3D numerical model SSIIM used in this study
solves the continuity equation together with Reynolds-averaged
Navier–Stokes equations in a 3D grid to compute the water
motion for turbulent flows (Olsen, 2013)
1:

@Ui
¼0
@xi

3

Water Management

2:

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

@Ui@Ui 1 @¼
ðPδij  ρui uj Þ
þ Uj
ρ @xj
@t
@xj

where i = 1, 2, 3 is representative of three directions; where
Uj is the averaged flow velocity, xi is the spatial geometricalscale, ρ is the water density, P is the Reynolds-averaged pressure, δij is the Kronecker delta, and ρui uj is the Reynolds
stress term. The unknown pressure field in the Reynoldsaveraged Navier–Stokes equations is calculated employing thesemi-implicit method for pressure-linked equations (i.e. Simple
method) (Patankar, 1980). The finite-volume approach isapplied as a discretisation method to transform the partial
equations into algebraic equations. The convection term in
the Navier–Stokes equation is solved using the second-order
upwind scheme. The Reynolds stress term is modelled using
the standard k − ε turbulence model with constant empiricalvalues (Launder and Spalding, 1972)
3:

 ui uj ¼ νt

4:

νt ¼

@Ui @Uj
þ
@xj
@xi



2
 kδij3cμ k 2εwhere νt is the turbulent eddy-viscosity, k is the turbulent
kinetic energy and ε is the dissipation rate of k. The equationsfor k and ε are as follows
5:

6:

Dk @k
@k
@
¼
þ Uj
¼
Dt
@t
@xj @xj




νt @k
þ Pk  ενþσ k @xjDε @ε@ε¼ þ Uj
Dt @t
@xj



@
νt @ε
ε
ε2
þ c1ε Pk  c2ε
¼
νþ
@xj
k
σ ε @xjkwhere cμ, c1ε, c2ε, σk and σε are the constant empirical values
and Pk denotes the production of kinetic energy

7:

Pk ¼ ν t@Ui @Uj @Uiþ@xj @xi@xj

The change in water levels was based on the calculatedpressure field using the Simple method. The pressure was
extrapolated to the water surface, and the pressure difference
between a surface node and a downstream node was used toestimate the water elevation difference (Olsen, 2013). This
4

iterative approach is stable and has been used successfully for
simulating a complex flow pattern in a number of cases suchas the Danube river (Tritthart and Gutknecht, 2007). The gridis adaptive and moves with the changes of the bed and waterlevels.
The Dirichlet boundary condition for the water inflow(logarithmic velocity distribution) was used, whereas the zerogradient boundary condition was specified for the water outflow. For rough boundaries of the side walls and the bed,
where there is no water flux, the empirical wall laws introducedby Schlichting (1979) were utilised. For smooth boundaries,
other wall law functions were used (Olsen, 2013).
Based on the grid that was used for experimental measurements, the computational mesh for all reservoir geometries was
made. The mesh cell size for the cases T7, T8, T9, T11
and T13 in the X and Y directions was 5 cm  2·5 cm, 5 cm 
2·5 cm, 5 cm  2·5 cm, 5 cm  2 cm and 2·5 cm  1 cm, respectively. Considering 11 cells for the vertical grid distribution,
the total number of cells over the main reservoir geometry
was 158 400, 107 360, 52 800, 220 000 and 528 000. Dueto the sensitivity of the flow pattern in case T13, a meshwith a higher resolution was used, which was equal to
2·5 cm  1 cm.

4.

Simulation results and discussions

4.1

Surface velocity field on flat beds

Kantoush (2008) observed that in case T7 the issuing flow jet
deviated to the right-hand side and developed an A1 flow
pattern. The main eddy rotated anticlockwise in the centre partof the reservoir, and two smaller eddies rotated clockwise in
the upstream corners. Additionally, a S0 flow pattern with one
main jet trajectory in the centreline and two circulation zones
on each side was developed for case T13. Kantoush (2007)
concluded that the deviation to the right-hand side occurredbecause of random disturbance of the initial flow boundary
condition, and a symmetric situation would be easily established by slightly disturbing the initial boundary condition.
The flow deflection to one side of the reservoir can be attributed to the difference in flow velocity along one side of themain jet compared with the other side, and the consequential
pressure difference. The local pressure difference deviates theflow towards one side of the reservoir and is called the Coanda
effect (Chiang et al., 2000).
In the numerical simulation, the time step was set as 2 s forruns T8 and T9, whereas it was 0·5 s for T7, T11 and T13.
Smaller time steps contributed to faster and more stable convergence of the computations in wider reservoirs. Simulations
were performed using geometry and inflow/outflow boundary
conditions that were similar to the physical model. The k − εturbulence model was used, and simulations were conducteduntil a steady-state flow condition was obtained. The

Water Management

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

simulations show that the model cannot reproduce an A1 flow
pattern when the geometry configuration and hydraulic boundary condition are perfectly symmetric because the appliedmathematical algorithms were not intended to reproduce thistype of artificial asymmetric numerical result when the input
boundary condition is symmetric.

Figure 1 shows the jet evolution pattern of case T7 after a jet
was issued into the stagnant shallow water, which eventually
established a steady asymmetric flow condition. First, whenthe main jet flow attaches to the downstream wall at t = 240 s,
it returns backwards, which causes energy dissipation andvelocity reduction as shown in Figure 1(a). Because of the
non-uniform velocity distribution and the consequential
pressure difference (Coanda effect), the flow field is transversally unstable, and the main jet flow slightly deviates to the left
side. In the subsequent stage of t = 240–480 s, a transitional

8:

3

2
Y: m

Because the S0 flow pattern was not observed in the physicalmodel experiments for special geometries, Dewals et al. (2008)
introduced a slight disturbance in the initial boundary condition for 2D numerical simulations. They used a non-uniform
cross-sectional discharge in the inlet boundary to examine thestability of the numerical model outputs. The identical conceptof slight disturbance in the inflow boundary condition was
implemented here for all runs, and the non-uniform crosssectional velocity distribution was used in the inflow boundary
condition:hyiVin ðxÞ ¼ V0 1  α 0  5 þ
b

1

0

0

1

2

3
X: m
(a)

4

5

6

0

1

2

3
X: m
(b)

4

5

6

0

1

2

3
X: m
(c)

4

5

6

3

Y: m

2

1

0

3

Y: m

where Vin is the actual streamwise velocity value, which is
specified as the inflow boundary condition, V0 is the reference
value (i.e. total discharge divided by inlet cross section area), αmeasures the magnitude of the linear variation, b denotes theinlet channel breadth and y is the coordinate along the transversal direction, which changes between –b/2 and b/2 (i.e. theright and left sides of the inlet channel respectively). Assumingthat α = 2·5% for numerical modelling, the initial velocity magnitude differs by 2·5% at one side of the inlet channel compared to the other side. This type of disturbance is inevitablein the experimental set-up. Nonetheless, a notably small perturbation of the inflow condition will significantly affect theA1 flow pattern in the numerical results. Changing α between
1 and 4% shows a notably close flow field to that observed in
the physical model except for case T7, in which there is a
threshold value for α. For this case, the smallest value of α toreproduce the A1 flow pattern is 2·5%, and this value is also
used for other cases with A1 flow patterns. This type of result
reveals the unstable nature of symmetric flows in such geometries, and consequently the high sensitivity of the flow field
to the inflow boundary condition. Depending on which side of
the inlet has the higher velocity, the jet deflection to each sideof the reservoir (i.e. right or left) can be obtained. A limited
number of runs also showed the contribution of the bed andside-wall roughness in the development of the A1 flow pattern
in case T7 even with α of 1% when the roughness increases. A
higher roughness can affect the initial flow condition, which isconsistent with the findings of Chu et al. (1991) about theeffect of friction on the velocity profile and consequently theflow pattern. However, an intensive numerical study should be
performed in the future, with a physical model study on theinteraction between slight disturbances in the inflow boundary
condition and the side and bed roughness and their effect on
the flow pattern.

2

1

0

Figure 1. Various stages of asymmetric flow pattern development
in shallow reservoirs with flat beds: (a) attachment of main jet
flow to the downstream wall (t = 240 s); (b) deviation of main jet
flow from centreline to the right-hand side during the transitional
stage (t = 480 s) and (c) attachment of main jet flow to the rightside wall (t = 1800 s)

5

Water Management

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

Surface velocity: m/s
0Surface velocity: m/s

0·02 0·04 0·06 0·08 0·10 0·12 0·14 0·16 0·18

0 0·02 0·04 0·06 0·08 0·10 0·12 0·14 0·16 0·18

3

2

2
Y: m

Y: m

3

1

1

0

0

1

2

3
X: m
(a1)

4

5

0
0

6

Y: m

Y: m
1

2

3
X: m
(b1)

4

5

0

1

2

3
X: m
(b2)

0
0

1

2

3
X: m
(c2)

6

5

6

4

5

6

1·0
Y: m

Y: m

0·5
0

1

2

3
X: m
(c1)

4

5

0·5

6

4

4

3

3

Y: m

Y: m

4

1

0
0

1·0

2

4

5

6

2

1

1

0

0
1

2

3
X: m

4

5

(d1)

Figure 2. Left: the measured surface velocity field with velocity
vectors over flat bed for case: (a1) T7; (b1) T8; (c1) T9; (d1) T11;(e1) T13, respectively and right: corresponding simulated velocity
field for each case (continued on next page)

6

3

2

1

0

2

X: m
(a2)

2

0

1

0

1

2

3
X: m
(d2)

4

5

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

4

4

3

3

Y: m

Y: m

Water Management

2

1

1

0

2

0
0

1

2

3

0

1

2

X: m

X: m

(e1)

(e2)

3

Fig. 2. Continued

phase occurs, where the jet gradually deviates from the left
side to the right side as shown in Figure 1(b). Similar to thefirst stage, the locally reduced pressure because of the higher
velocity on one side than the other side tends to amplify
the jet deflection. Meanwhile, upstream corner vortices areformed and their size increases, which controls the centre
anti-clockwise vortex. Afterwards, the main jet flow reattaches
to the right side wall, and a steady A1 flow pattern finally
emerges over the shallow reservoir as illustrated in Figure 1(c).
The simulated jet evolution pattern was consistent with theexperimental observations. Furthermore, an identical jet evolution pattern was obtained for cases T8 and T9.
Figure 2 illustrates the measured and simulated surface velocity
magnitudes and flow distribution patterns for five selected
experiments. As shown in Figure 2, an A1 flow pattern develops in cases T7, T8 and T9, whereas an almost S0 flow patterndevelops in cases T11 and T13. The model can simulate asurface flow velocity pattern that is similar to the measured
pattern by reproducing the dominant aspects of the flow field,
such as the main flow jet trajectory, location of the reverse
flow, main vortices and corner gyres. Nevertheless, the numerical model results show a straighter and longer reverse flow
trajectory than the observations, and a concentrated main jet
flow for all cases. Consequently, the upstream corner gyres in
the numerical outputs have a smaller size than those of theexperimental measurements. This situation is predominant forT11 (Figures 2(d1) and 2(d2)).

Figure 3 quantitatively demonstrates the simulated streamwise
and transversal surface velocity distribution against themeasured one at the middle cross-section of the reservoirs forcases T8 and T13. The numerical model results are consistent
with the measurements in case T8, which has an A1 flow
pattern as shown in Figure 3(a). Figure 3(b) shows that in caseT13 there is a slight discrepancy between the simulated andmeasured surface velocity fields, particularly along the centreline and side walls of the reservoir. The reason could be theconcentrated simulated flow pattern, with a lower diffusionof the main jet and reverse jet flows compared to the measurements. Furthermore, Figure 4 shows similar outputs in both the
upstream and downstream areas of case T7. The overall trend of
surface velocity variations was reproduced using the numericalmodel. To provide a higher resolution longitudinal distributionof the surface velocity, the simulated streamwise velocity along
the reservoir length (i.e. beside the right wall, along the centreline and beside the left wall) was plotted against the measured velocity for case T8 and for the right half of case T13 in Figure 5.
As shown in Figure 5(a), regarding case T8, apart from the area
near the inlet and outlet, the numerical model results are reasonably consistent with the measurements. An identical condition
was found for the other cases with A1 flow pattern (e.g. cases T7
and T9). The longitudinal velocity distribution for the left halfof case T13, as depicted in Figure 5(b), is notably close to thatof the right half. Figures 3–5 show that numerical results areglobally consistent with the measured surface velocity components for varying geometries with varying flow patterns.
7Water Management

Surface velocity: m/s

0·2

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

X = 3 m simulated streamwise velocity
X = 3 m measured streamwise velocity
X = 3 m simulated transversal velocity
X = 3 m measured transversal velocity

0·1

0

–0·1
0

0·5
1·0
1·5
Y (coordinate across the reservoir): m

2·0

(a)

Surface velocity: m/s

0·3

X = 1·5 m simulated streamwise velocity
X = 1·5 m measured streamwise velocity
X = 1·5 m simulated transversal velocity
X = 1·5 m measured transversal velocity

0·2

0·1

0

–0·1
0

0·5

1·0
1·5
2·0
2·5
3·0
3·5
Y (coordinate across the reservoir): m
(b)

4·0

Figure 3. The measured streamwise and transversal surface
velocity against the simulated velocity at the middle of thereservoirs’ length with the flat bed condition for case: (a) T8;(b) T13; the view direction is upstream

It should be noted that there may be more than one solution
for initiating the A1 flow pattern. Thus, other types of slight
disturbances of the inlet boundary condition can produce theA1 flow pattern in relevant cases (e.g. slight deflection of theinlet channel or a combination of inlet channel deflection andnon-uniform cross-sectional velocity).

4.2

Surface velocity field on misshaped beds

The measured bed morphology for cases T8, T11 and T13
after sediment flushing and lowering the water head is shownin Figure 6. The bed morphology was introduced tothe model as the initial boundary condition for each caseto simulate the 3D flow field. In addition, a slight disturbanceof the inflow boundary condition was not considered. Because
8of the shallower flow condition, with higher velocity components on the existing friction of various bed forms, the flow
field simulation on misshaped beds is more complex than thaton flat beds. For all three cases, the bed roughness was considered as 0·00015 m, which is three times the median grain
size.
The measured surface velocity after flushing using the LSPIV
technique and the simulated surface velocity using the
3D model are shown in Figure 7. For case T8, Figures 7(a1)and 7(a2) show that the simulated hydraulic and geometric features of the main jet flow and reverse flow trajectory areslightly different from the measured ones. Here, the developed
flushing channel attracts the jet flow and stabilises the flow
pattern. Similarly to the surface velocity pattern on flat
beds, the reverse flow trajectory is longer and straighter, andthe upstream vortices have smaller longitudinal size thanthe observed ones. The differences between the measured andsimulated surface velocity patterns and sizes of the upstream
vortices are more prominent in cases T11 and T13.
Figures 7(b1) and 7(b2) show that the upstream corner vortices
cannot be reproduced by the numerical model for case T11,
while their sizes are underestimated in case T13, as shown in
Figures 7(c1) and 7(c2). Compared to the flow patterns inshallow reservoirs with flat beds, there is more discrepancy
between the simulation results and the measurements. One
possible reason for this discrepancy is the presence of various
types of bed forms with different roughness values at different
places on the bed floor. Another reason is the k − ε turbulencemodel, which represents a lower diffusion in simulation of theflow field in shallow reservoirs (Dewals et al., 2008).
The simulated streamwise and transversal surface velocities at
the middle of the channel length were plotted against themeasured velocities in Figure 8. Similar to the surface velocity
field on flat beds, the numerical outputs are quantitatively
in reasonable agreement with the measurements. Figure 9 also
shows the simulated surface velocity against the measured
velocity in the upstream and downstream zones of case T11.
This figure shows a small deviation of the main jet flow fromthe centreline of the reservoir, which first goes to the rightside (Figure 9(a)) and subsequently to the left-hand side
(Figure 9(b)). This deviation implies a non-straightforward
flow motion along the centreline when the reservoir is wide.

4.3

Velocity distribution over the flow depth

The velocity field distribution over the flow depth is important for analysing sediment transportation in reservoirs.
The numerically simulated 3D flow velocity field in the reservoirs with flat beds was therefore compared with the measured
3D velocity components that were provided using the UVP
measurements. Figure 10(a) shows the measured streamwise
velocity distribution over the flow depth in upstream, middle,
and downstream areas of case T8. Figure 10(b) corresponds
to the simulated streamwise velocity for this case.

Water Management

X = 1 m simulated streamwise velocity
X = 1 m measured streamwise velocity
X = 1 m simulated transversal velocity
X = 1 m measured transversal velocity

X = 2 m simulated streamwise velocity
X = 2 m measured streamwise velocity
X = 2 m simulated transversal velocity
X = 2 m measured transversal velocity

0·2

Surface velocity: m/s

0·2

Surface velocity: m/s

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

0·1

0

–0·1

0·1

0

–0·1
0

0·5
1·0
1·5
2·0
2·5
Y (coordinate across the reservoir): m

3·0

0

(a)

0·2

Surface velocity: m/s

Surface velocity: m/s

3·0

(b)

X = 4 m simulated streamwise velocity
X = 4 m measured streamwise velocity
X = 4 m simulated transversal velocity
X = 4 m measured transversal velocity

0·2

0·5
1·0
1·5
2·0
2·5
Y (coordinate across the reservoir): m

0·1

0

–0·1

X = 5 m simulated streamwise velocity
X = 5 m measured streamwise velocity
X = 5 m simulated transversal velocity
X = 5 m measured transversal velocity

0·1

0

–0·1
0

0·5
1·0
1·5
2·0
2·5
Y (coordinate across the reservoir): m

3·0

(c)

0

0·5
1·0
1·5
2·0
2·5
Y (coordinate across the reservoir): m

3·0

(d)

Figure 4. The measured streamwise and transversal surface
velocity against the simulated one for case T7 at: (a) x = 1 m;(b) x = 2 m; (c) x = 4 m; (d) x = 5 m; the view direction is upstream

Regarding the cases with misshaped beds, the simulated lateralflow velocity contours over the depth and the secondary flow
velocity vectors at the middle of the reservoir length are illustrated in Figures 10(c) and 10(d) for case T8 and the right halfof case T13 respectively. Numerical outputs in Figure 10(b)reveal that higher longitudinal velocity is deflected towards theright bank side, and the reverse flow is reproduced near theleft bank side. This change in flow direction across the reservoir is also qualitatively consistent with the experimental
observations in Figure 10(a). The measurements also showthat the vertical velocity magnitudes over the flow depth arenotably small compared to the other velocity components (i.e.
streamwise and lateral) when the reservoir bed is flat and horizontal. The discrepancy between the calculated and measured
outputs can be attributed to the existing roughness of the sidewalls, which affects the flow field and was neglected in thecomputations. On the other hand, Figures 10(c) and 10(d)show the complexity of the 3D flow field development on existing bed friction in shallow reservoirs with misshaped beds,
where the velocity magnitude and direction can vary over theflow depth, and circulation zones in the vertical direction may
emerge. This type of output is beneficial for a precise analysis
of flow characteristics (e.g. water levels) and potential erosionand deposition zones during anticipated floods, when the bed
has been disturbed and complex bed geometry has been developed because of the sediment flushing process.
To more comprehensively assess the numerical model results,
the velocity field in the streamwise and lateral directions (i.e.
U, V, respectively) at two different vertical levels from the bed(i.e. z = 0·045 m, 0·155 m), in three longitudinal sections forcases T8, is shown in Figure 11. This figure shows that9

Water Management

Simulated streamwise velocity y = 0·5 m
Measured streamwise velocity y = 0·5 m
Simulated streamwise velocity y = 1 m
Measured streamwise velocity y = 1 m
Simulated streamwise velocity y = 1·5 m
Measured streamwise velocity y = 1·5 m

0·25
0·20
0·15

Bed level: m
00·005 0·010 0·015 0·020 0·025 0·030 0·035 0·040 0·045 0·050

2

Y: m

Surface velocity: m/s

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

0·10

1

0·05
0

0

0

1

2

3
X: m

–0·05

5

6

(a)

–0·10

Bed level: m

0 0·5 1·0 1·5 2·0 2·5 3·0 3·5 4·0 4·5 5·0 5·5 6·0
X (coordinate along the reservoir): m
0

(a)

0·25
0·20

3
Y: m

0·30

0·005 0·010 0·015 0·020 0·025 0·030 0·035 0·040 0·045 0·050

4Simulated streamwise velocity y = 0·5 m
Measured streamwise velocity y = 0·5 m
Simulated streamwise velocity y = 1 m
Measured streamwise velocity y = 1 m
Simulated streamwise velocity y = 1·5 m
Measured streamwise velocity y = 1·5 m
Simulated streamwise velocity y = 2 m
Measured streamwise velocity y = 2 m

0·35

Surface velocity: m/s

4

2

0·15
0·10
1

0·05
0

0

–0·05
0

0·5

1·0

1·5

2·0

2·5

3·0

0

1

2

4

3

5

X: m

X (coordinate along the reservoir): m

(b)

(b)
4

Figure 5. Longitudinal distribution of surface streamwise velocity
over the flat bed reservoirs for: (a) case T8; (b) the right half ofcase T13

Bed level: m
0·050
0·045
0·040
0·035
0·030
0·025
0·020
0·015
0·010
0·005
0

streamwise velocity magnitudes are different from the measured ones near the inlet, particularly at the level near thesurface (i.e. z = 0·155 m). This difference is considerable forthe longitudinal section adjacent to the left side wall (i.e.
y = 1·625 m), because a complex combined vortex is formed at
the upstream left zone of the reservoir consisting of two
smaller sub-vortices with different rotation directions. It should
be noted that the numerical model mainly reproduces one
vortex system in this area. The simulated streamwise velocities
are generally consistent with the UVP measurements in otherparts of the reservoir, although some fluctuations are foundin the measurements. Regarding the transversal velocities, thenumerical model outputs are reasonably consistent with themeasurements except in the aforementioned upstream zone.
The numerical model outputs represent the negative transversal
10

Y: m

3

2

1

0
0

1

2

3

X: m
(c)

Figure 6. The misshaped bed obtained after sediment flushingwith lowering the water level for case: (a) T8; (b) T11; (c) T13

Water Management

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

Surface velocity: m/s
0Surface velocity: m/s

0·02 0·04 0·06 0·08 0·10 0·12 0·14 0·16 0·18 0·20 0·22 0·24 0·26 0·28 0·30

00·02 0·04 0·06 0·08 0·10 0·12 0·14 0·16 0·18 0·20 0·22 0·24 0·26 0·28 0·30

2

Y: m

Y: m

2

1

1

0

0
0

1

2

3
X: m

4

5

6

0

1

2

3
X: m

(a1)

0·02 0·04 0·06 0·08 0·10 0·12 0·14 0·16 0·18 0·20 0·22 0·24 0·26 0·28

00·02 0·04 0·06 0·08 0·10 0·12 0·14 0·16 0·18 0·20 0·22 0·24 0·26 0·28

4

3

Y: m

Y: m

3

2

2

1

1

0

0
0

1

2

3

5

4

0

1

2

Surface velocity: m/s

3

Y: m

5

2

1

3

X: m
(c1)

Surface velocity: m/s

4

0·28
0·26
0·24
0·22
0·20
0·18
0·16
0·14
0·12
0·10
0·08
0·06
0·04
0·02
0

3

Y: m

0·28
0·26
0·24
0·22
0·20
0·18
0·16
0·14
0·12
0·10
0·08
0·06
0·04
0·02
0
2

4

(b2)

(b1)
4

1

3
X: m

X: m

0

6

Velocity magnitudes: m/s

4

0

5

(a2)

Velocity magnitudes: m/s
0

4

2

1

0

0

1

2

3

X: m
(c2)

Figure 7. Left: the measured surface velocity field with vectors
over misshaped bed after flushing for case: (a1) T8; (b1) T11; (c1)
T13, respectively and right: corresponding simulated velocity field
for each case11

Water Management

X = 3 m simulated streamwise velocity
X = 3 m measured streamwise velocity
X = 3 m simulated transversal velocity
X = 3 m measured transversal velocity

0·35

0·25

0·15

0·05

–0·05

0

0·5
1·0
1·5
Y (coordinate across the reservoir): m
(a)

0

0·25

0·15

0·05

–0·05

0·5 1·0 1·5 2·0 2·5 3·0 3·5
Y (coordinate across the reservoir): m
(a)

4·0

X = 4 m simulated streamwise velocity
X = 4 m measured streamwise velocity
X = 4 m simulated transversal velocity
X = 4 m measured transversal velocity

0·35

Surface velocity: m/s

Surface velocity: m/s

0·25

0·15

0·05

–0·05

–0·15

–0·15
0

0·5

1·0

1·5

2·0

2·5

3·0

3·5

4·0

Y (coordinate across the reservoir): m(b)

Figure 8. The measured streamwise and transversal surface
velocity against the simulated one at the middle of the reservoirs’length with misshaped bed condition for case: (a) T8; (b) T13; theview direction is upstream

velocities, whereas the measured velocities show positive values
because of the existing complex combined vortex.

Conclusions

In the present study, the SSIIM program was used to reproduce
the 3D velocity field on flat and misshaped beds of rectangularshallow reservoirs with varying geometries. The surface
velocity was measured using the LSPIV technique to validate
the model. In addition, 3D velocity components over the flow
depth, which were provided by the UVP, were compared with
the numerical results. The following results were obtained fromthe present work.

12

0·05

–0·15

2·0

X = 1·5 m simulated streamwise velocity
X = 1·5 m measured streamwise velocity
X = 1·5 m simulated transversal velocity
X = 1·5 m measured transversal velocity

0·35

&

0·15

–0·05

–0·15

5.

X = 2 m simulated streamwise velocity
X = 2 m measured streamwise velocity
X = 2 m simulated transversal velocity
X = 2 m measured transversal velocity

0·35

Surface velocity: m/s

0·25
Surface velocity: m/s

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

Various aspects and hydrodynamic characteristics ofshallow waters in varying reservoir geometries such as0

0·5 1·0 1·5 2·0 2·5 3·0 3·5
Y (coordinate across the reservoir): m

4·0

(b)

Figure 9. The measured and simulated surface velocity over the
misshaped bed of case T11 at (a) x = 2 m; (b) x = 4 m; the view
direction is upstream

jet trajectory, recirculation zones, eddies and flow
distribution pattern, can be represented by the numericalmodel on both flat and misshaped beds. Two sets ofhydraulic parameters (e.g. water depth, Froude number,roughness) corresponding to each bed type (i.e. flat or
misshaped) were used in the simulations. Similarly to theobservations, the model reproduces both symmetric (S0)and asymmetric (A1) flow patterns in the symmetricgeometry set-up of the reservoirs after introducing aslight disturbance in the inflow boundary condition (i.e.
perturbation) for all cases with a flat bed. The numericalresults show that the flow pattern is insensitive to thesmall disturbance in the inflow boundary condition of
the geometries with lower shape factors (i.e. cases T11
and T13). In this condition, the numerical model
converges to a steady S0 flow pattern. However, theWater Management

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

z

z
Y

X

2
4

0·5
Y: 1·0
m

1·5

X:
m

3

5
2·0 6

0
1
2
3
4

0·5
1·0
Y: m

1·5

5
2·0 6

(a)

(b)

Velocity magnitude: m/s

Velocity magnitude: m/s–0·010–0·008 –0·006–0·004–0·002

00·002 0·004 0·006 0·008

0·15

m

0

–0·010–0·008 –0·006–0·004–0·002

00·002 0·004 0·006 0·008

CL

Z: m
0
0

0·5

1·0
Y: m
(c)

1·5

0
0

2·0

Figure 10. The streamwise velocity distribution over the flow
depth of case T8 with flat bed at x = 1·5 m, 3·5 m and 5·2 m using(a) UVP measurement and (b) 3D numerical model; simulated

&

0·14
0·12
0·10
0·08
0·06 0·18
0·04 0·12
0·02 0·06
0
0
0
–0·02
–0·04
–0·06
–0·08

1

Z: m

0·15

Streamwise velocity: m/s

X:

Streamwise velocity: m/s
0·14
0·12
0·10
0·08
0·06 0·18
0·04 0·12
0·02 0·06
0
0
–0·02
0
–0·04
–0·06
–0·08

Y

X

calculated flow pattern in geometries with higher shapefactors (i.e. cases T7, T8 and T9) converges to a steadyA1 flow pattern. Regardless of the bed condition, thecomputed flow velocity magnitudes are reasonably
consistent with the experimental observations. Some
discrepancy exists between the numerical results and themeasurement in the upstream vortex dimensions and flow
field in this area for both bed types. This discrepancy ismainly due to the simulated longer flow and reverse
flow jet patterns, and also to the simulated concentrated
flow and reverse flow jet patterns with a lower flow
diffusion in the numerical outputs. The lower diffusion
can be attributed to the application of the standard k − εturbulence model. In the case of the misshaped beds, thevarying bed friction over the reservoir geometry may
increase the discrepancy.
Further development of the study with higher Froudenumbers (e.g. greater than 0·2) and a wider range of shapefactors would be useful for practical purposes. The numerical model could then be used for reproducing the complex
flow field during an anticipated flood over the misshaped beds of existing reservoirs (e.g. after the flushing
operation). The results could be sustainable flood risk
management in reservoirs, particularly those near urban
areas, by effectively predicting the water levels and the

0·5

1·0
Y: m
(d)

1·5

2·0

lateral velocity distribution over the flow depth at x = 3 m on
misshaped bed of (c) T8 and (d) right half of T13&

consequential fluvial processes. Moreover, a detailed
sensitivity analysis of flow field to various influential parameters including hydraulic and numerical parameters
could enrich this study field. Specifically, in reservoirs with
an A1 flow pattern and a lower shape factor (SF) suchas T7, the contribution of roughness in addition to the perturbation should be assessed to initiate the A1 flow pattern
in a future study.
3D numerical modelling enables us to simulate the flow
and sedimentation pattern with a resolution over theflow depth. Consequently, the effects of different
measures on the flow pattern can be evaluated to direct
sedimentation into preferential zones. Thus, the results ofthis paper can be applied to optimally design sand trap
facilities or reservoirs for low-head power plants to increaseor decrease the sedimentation. Regarding the prototype
scale reservoirs, the shallow-flow condition emerges
during the sediment flushing operation with fulldrawdown, and plays a significant role in removing
deposited sediment from the reservoir. Different
velocity distribution patterns may lead to different
morphological processes in the reservoir. Therefore, 3D
numerical models can be used to predict and manage
shallow-flow behaviour under different scenarios toincrease flushing efficiency. However, the coupled
13

0·25

Streamwise velocity: m/s

0·20
0·15

Three-dimensional numerical modelling offlow field in shallow reservoirs
Esmaeili, Sumi, Kantoush, Haun and Rüther

Simulated streamwise velocity y = 0·625 m
Measured streamwise velocity y = 0·625 m
Simulated streamwise velocity y = 1·125 m
Measured streamwise velocity y = 1·125 m
Simulated streamwise velocity y = 1·625 m
Measured streamwise velocity y = 1·625 m

0·10
0·05
0

0·15
0·10
Lateral velocity: m/s

Water Management

Simulated lateral velocity y = 0·625 m
Measured lateral velocity y = 0·625 m
Simulated lateral velocity y = 1·125 m
Measured lateral velocity y = 1·125 m
Simulated lateral velocity y = 1·625 m
Measured lateral velocity y = 1·625 m

0·05
0
–0·05

–0·05
–0·10

–0·10

Streamwise velocity: m/s

0·20
0·15

0 0·5 1·0 1·5 2·0 2·5 3·0 3·5 4·0 4·5 5·0 5·5 6·0

X (coordinate along the reservoir): m

X (coordinate along the reservoir): m

(a1)

(a2)

Simulated streamwise velocity y = 0·625 m
Measured streamwise velocity y = 0·625 m
Simulated streamwise velocity y = 1·125 m
Measured streamwise velocity y = 1·125 m
Simulated streamwise velocity y = 1·625 m
Measured streamwise velocity y = 1·625 m

0·10
0·05
0

0·15
0·10
Lateral velocity: m/s

0·25

0 0·5 1·0 1·5 2·0 2·5 3·0 3·5 4·0 4·5 5·0 5·5 6·0

Simulated transversal velocity y = 0·625 m
Measured transversal velocity y = 0·625 m
Simulated transversal velocity y = 1·125 m
Measured transversal velocity y = 1·125 m
Simulated transversal velocity y = 1·625 m
Measured transversal velocity y = 1·625 m

0·05
0
–0·05

–0·05
–0·10

–0·10
0 0·5 1·0 1·5 2·0 2·5 3·0 3·5 4·0 4·5 5·0 5·5 6·0

0 0·5 1·0 1·5 2·0 2·5 3·0 3·5 4·0 4·5 5·0 5·5 6·0

X (coordinate along the reservoir): m

X (coordinate along the reservoir): m

(b1)

(b2)

Figure 11. Left: the measured streamwise velocity over the flow
depth using UVP against the simulated velocity for case T8 withflat bed at (a1) z = 0·045 m; (b1) z = 0·155 m; right: measured

simulation of flow and sediment field that interact with the
movable bed under unsteady flow conditions during adrawdown flushing is challenging; this problem should benumerically investigated using 3D numerical models forboth physical and prototype-scale models. The results
could provide a valuable perspective for upcoming sedimentmanagement measures and plans (e.g. free-flow flushing
operations) in existing reservoirs.
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