ISBN 978-81-934174-2-3

6th International Conference on Urban Design, Transportation, Architectural and Environmental

Engineering (UTAEE-17)
Istanbul (Turkey) Sept. 8-10, 2017

Numerical Investigation of the Recirculation Zone Length

Upstream of the Round-Nosed Broad Crested Weir
Mehmet Anıl Kızılaslan1, Ender Demirel2
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Department of Civil Engineering, Eskisehir Osmangazi Univesity, 26480 Eskisehir, Turkey

Abstract: Broad crested weirs (BCW) are widely used hydraulic structures in streams and irrigation channels
to control the flow and to measure the discharge due to the advantage of having simple geometry. Interaction of
the turbulent flow with the structure generates vortices and recirculation zone upstream of the weir, which may
cause significant morphological changes on the stream bed. In this study, flow structure upstream of the round-
nosed BCW is investigated based on two-dimensional Unsteady Reynolds-Averaged Navier-Stokes Simulations
(URANS). Numerical simulations are conducted using OpenFOAM for different flow rates and rounding
parameters of the weir. The Shear Stress Transport (SST) k-ω turbulence model is employed in order to calculate
the adverse pressure gradients and separation effects accurately on the channel bottom and weir crest.
Numerical results are reported and interpreted with focus on the effect of rounding on the length of the
recirculation zone.
Keywords: Broad crested weir, recirculation zone length, OpenFOAM, turbulence, free-surface.

1. Introduction
Round-nosed BCWs can be used in field and laboratory channels for flow measurement because of their
good range of discharge and high modular limit (Ramamurthy et. Al., 1988). The flow pattern over BCW is still
up to date due to the existence of complex flow structure near the weir. Sarker and Rhodes (2004) carried out
numerical and experimental studies for the investigation of flow structure upstream and downstream of a
rectangular BCW. Free-surface profiles were measured by using pointer-gauge in their experimental study.They
used Fluent software for the simulation of turbulent flow based on Reynolds Average Navier Stokes (RANS)
equations and Volume of Fluid (VOF) method was used to capture the position of the free-surface. Gonzales and
Chanson (2007) used four different BCW geometries to determine the velocity and pressure profiles
experimentally. They observed an effective recirculation zone upstream of the weir which is associated with the
turbulent boundary layer. Zachoval and Rousar (2015) investigatedthe flow structure upstream of a BCW
experimentally using Ultrasonic Velocity Profile (UVP) and Particle Image Velocimetry (PIV) to determine the
flow pattern. Hargreaves et. al. (2007) used different turbulence models to investigate the free-surface profile
over a BCW. They compared numerical results with the experimental results available in the literature showing
that the separation zone could becalculated accurately by the k-ε turbulence model. Modammadpour et. al. (2013)
carried out numerical simulations on a gabion type porous weir to investigate the flow pattern. Kirkgoz et. al.
(2008) conducted numerical and experimental studies to determine the flow pattern upstream of broad crested
and v-notch weirs. Numerical simulations were carried out by using a ANSYS (2009) based on the standard k-ε
and k-ω turbulence closure models. Haun et. al. (2014) simulated flow over a BCW with two different numerical
solvers, namelyFLOW 3D and SSIM 2 and they compared the numerical results consistently. Gogus et. al. (2006)
carried out experimental studies for the effect of threshold height on the approach velocity coefficient, modular
limit and discharge coefficient for BCW. Ramamurthy et. al. (1988) conducted experimental studies to propose a
discharge coefficient as a function of nose radius, weir height and water depth for bothfree and submerged flow
conditions. Felder and Chanson (2012) carried out experimental studies to measurethe free-surface, pressure and

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velocity profiles on a round-nosedBCW. They observed a recirculation zone at the end of the weir. Zachoval et.
al. (2012) investigated the flow separation on the upstream corner of a rectangular BCW.
Aforementioned studiesgenerally focused on discharge coefficient, flow pattern and free-surface profiles.
Complex flow structure near the weir forms recirculation zones at both upstream and downstream of the weir,
which can be responsible for the morphological changes on the river bed. In this study,the length of the
recirculation zone examined numerically for distinct dimensionless rounding parameters of R/P and flow rates.
Numerical simulations are conducted using OpenFOAM and the SST k-ω turbulence closure model is employed
in order to calculate the adverse pressure gradients and separation effects on the walls accurately.

2. Numerical Modelling
In Computational Fluid Dynamics (CFD), the k-ω turbulence model is a common two-equation
turbulencemodel, that is used as a closure for the Reynolds-Averaged-Navier-Stokes (RANS) equations. In this
study, Wilcox’s (2006) version of k-ω model equations were used, which are defined as the following governing
equations(OpenFOAM, 2015):

̅ [ ] (1)

̅ [( ) ] (2)
where;

̅̅̅
(3)

(4)

̅̅̅ ̅̅̅
(5)

(6)

Where, is eddy viscosity, is turbulent dissipation rate, is the turbulent energy, is turbulent
Reynolds stress tensor, and are turbulence modelling constants, mean rate of deformation components.
Details of the numerical model can be found in (Wilcox, 2006).

2.1 Numerical Setup

OpenFOAM is an open source CFD toolbox that enables to modify the standard solvers and developnovel
boundary conditions. A custom boundary condition was implementedat the inlet to reduce the length of the
computational domain and time. The following parabolic velocity distribution is applied at the inlet of the
computational domain (Cassan and Belaud, 2012):

( ) (7)

Where is shape factor which is set to 0.1 in this study, is the area averaged horizontal velocity
component at the inlet, which can be calculated from the flow rate and water depth .
Geometry and computational mesh were generated using blockMesh utility which is available in
OpenFOAM. Computational mesh is clustered in the vicinity of the bottom of the channel, rounded upstream
corner, top of the weir and free-surface in order to capture severe variations in flow quantities accurately. As
shown in Fig.1, non-orthogonality of the mesh increases near the rounded nose to fit the mesh to the circular

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wall. Thus, non-orthogonal correction needs to be applied during numerical solution in order to obtain
converged results in both velocity and pressure fields accurately.

Fig. 1: Different views of non-orthogonal vairable mesh.

In this study, four different rounding parameters were selected as shown in Table 1,in order to investigate
the effect of rounding on the recirculation zone length. Numerical simulations were performed for different flow
rates of Q=15, 45, 85 and 125 lt/s over a broad-crested weir with dimensions of P=37.5 cm, L=80 cmas shown in
Fig. 2.Thus, effects of rounding and flow discharge on the development of recirculation zone will be examined
based on the numerical simulation results for steady state flow field.

TABLE I:Rounding parameters in numerical simulations.

Case R/P
Case1 0.02
Case2 0.0094
Case3 0.1876
Case4 0.25

g
H

h0
Q
x Outlet
R
P
Q
L

Fig. 2: Schematic view of the BCW.

Numerical simulations were performed during 100 seconds in each computational run in order to avoid the
effects of initial conditions and to obtain time-averaged flow data. It should be noted that adequate data needs to
be collected during the simulations to obtain time-averaged flow field which is required to plot the streamlines at
the post-processing step. Preliminary numerical simulation results showed that free-surface height and velocity

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remained unchanged after 100 seconds even though the flow discharge exceeds the maximum value of 125 lt/s,
which is acceptable for the present problem.
The Reynolds number for the present problem isdefined in Equation (8) and calculated Reynolds numbers
are listed in Table 1 for each case. Corresponding Reynolds numbers show that the flow is fully turbulent.

√
(8)

in whichRe is the Reynolds number of the flow, ν is the kinematic viscosity of the fluid, H is the energy head
over the weir. Boundary conditions for the turbulence are calculated and applied at the inlet of the channel based
on the %5 intensity of the turbulence as shown in Table II, which is common for fully developed open channel
flows.
TABLE II: Numerical parameters for Case1
Q (lt/s) Re k ω Number of mesh
15 106397 2.39E-5 5.43 317496
45 308214 1.34E-4 6.62 317496
85 580484 3.4E-4 7.04 317496
125 730319 6.3E-4 7.59 317496

3. Results and Discussion

In this study, flow structure upstream of the round-nosed BCW is investigated based on two-dimensional
Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations.Numerical simulations are conducted using
OpenFOAM. The Shear Stress Transport (SST) k-ω turbulence model is employed in order to calculate the
adverse pressure gradients and separation effects on the walls accurately.Numerical simulations were performed
on a rectangular channel with having 2.2 m upstream length . The length of the recirculation zone is determined
based on the horizontal velocity profiles and streamline patterns at the post-processing step. Horizontal velocity
profiles at different locations are plotted in Fig. 3 for R/P=0.02 and R/P=0.25. The velocity of the fluid is
significantly affected by the radius of the nose as shown in Fig. 3b.

Fig. 3. Horizontal velocity profiles for R/P=0.02 and R/P=0.25.

It can be seen in Fig.3 that the backward effects upstream of the weir increase as the radius of the weir
increases. The rounding of the upstream nose strongly affects the flow field near the weir. Streamline patterns

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are given in Fig. 4 for the flow rates Q=15 and 125 lt/s and roundingR/P=0.02 and 0.25. The length of the
recirculation is obtained from Fig.4 by digitizing the flow data. Length of the recirculation zone is determined as
57.5 cm for Q=15 lt/s. It is clearly seen from the figure that the length of the recirculation zone decreases when
the R/P increases due to fact that separation effects on the rounded nose decreases when the rounding increases.
Recirculation zones are calculated for each case and listed in Table III.

Fig. 4. Streamlines for Q=15 and 125 lt/s.

The following conclusions can be drawn based on the results listed in Table III:

1. The length of the recirculation zone decreases as the rounding of the nose increases for a fixed flow rate
which may be associated with the separation effects on the bed. The separation on the channel bottom
decreases when the rounding of the nose increases since the flow discharge capacity of the weir has
increased. This observation points out that morphological changes associated with the recirculation
effects may be critical for the weirs having square edged upstream corner.
2. Flow rate is not as much effective as the rounding on the development of the recirculation zone. If we
consider the case having minimum rounding, the length of the recirculation zone decreases when the
flow rate increases. However, the length of the recirculation zone starts to increasing surprisingly when
the flow rate becomes 125 lt/s. This may be due to that the effect of separation on the bed becomes
significant after a certain value of Reynolds number.
3. Separation of the flow on the crest produces an additional dead zone for small values of rounding as
seen in Fig.4. Moreover, the length of the recirculation zone on the crest increases as the flow rate
increases. This proves that the flow discharge capacity of the weir reduces when the rounding of the
nose decreases.
4. A sudden drop is observed at the entrance of the crest and it vanishes as the rounding of the weir
increases.

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 TABLE III: Recirculation zone lengths
Q (lt/s) Case Nose Rounding (cm) Recirculation zone length (m)
Case1 0.75 0.575
Case2 3.525 0.5125
15
Case3 7.035 0.4923
Case4 9.375 0.3856
Case1 0.75 0.5436
Case2 3.525 0.45
45
Case3 7.035 0.3874
Case4 9.375 0.346
Case1 0.75 0.5086
Case2 3.525 0.4857
85
Case3 7.035 0.3446
Case4 9.375 0.31
Case1 0.75 0.5462
Case2 3.525 0.493
125
Case3 7.035 0.378
Case4 9.375 0.341

4. References
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Hydraulic Engineering, 138, 367-373., 2012.
[3] Göğüş, M., Defne, Z., Özkandemir, V., “Broad-Crested Weirs with Rectangular Compound Cross Sections”, Journal of
Irrigation and Drainage Engineering, 132(3), 272-280, 2006.
[4] Hargreaves, D. M., Morvan, H.P., Wright, N.G. “Validation of the Volume of Fluid Method for Free Surface
Calculation: The Broad Crested Weir”, Engineering Applications of Computational Fluid Mechanics, 1(2), 136-
146,2007.
[5] Haun, S., Olsen, N.R.B., Feurich, R. “Numerical Modeling of Flow Over Trapezoidal Broad-Crested Weir”,
Engineering Applications of Computational Fluid Mechanics, 5(3), 397-405,2011.
[6] Kirkgoz, M.S., Akoz, M.S., Oner, A.A. “Experimental and Theoretical Analyses of Two-Dimensional Flows Upstream
of Broad-Crested Weirs”, Canadian Journal of Civil Engineering, 35, 975-986, 2008.
[7] Mohammadpour, R., Ghani, A.A., Azamathulla, H.M. “Numerical Modeling of 3-D Flow Porous Broad Crested Weirs”
Applied Mathematical Modelling, 37, 9324-9337, 2013.
[8] OpenFOAM, The OpenFOAM Foundation; OpenCFD Ltd.:Bracknell, UK, 2015.
[9] Ramamurthy, A.S., Tim, U.S., Rao, M.V.J. “Characteristics of Square-Edged and Round-Nosed Broad-Crested Weirs”,
Journal of Irrigation and Drainage Engineering, 114, 61-73, 1988.
[10] Sarker, M.A., Rhodes, D.G. “Calculation of Free-Surface Profile Over a Rectangular Broad-Crested Weir”, Flow
Measurement and Instrumentation, 15, 215-219, 2004.
[11] Zachoval, Z., Roušar, L. “Flow Structure in front of the Broad-Crested Weir”, EPJ Web of Conferences, 92,
02117.2015.