This document summarizes a study that used computational fluid dynamics (CFD) to simulate flow patterns around six types of triangular porous weirs with various upstream and downstream slopes. The study examined flow depth, discharge through the porous media, and velocity fields. Key findings include: - Weirs with steeper upstream slopes produced lower upstream water levels and higher ratios of flow passing through the weir. - The weir with a 30° downstream slope produced the highest upstream head and lowest discharge coefficient. - Flow through the porous weirs reduced upstream water levels and vortex areas compared to solid weirs.

1. Mohammad Tavakol- Sadrabadi- M.Sc. Student, Faculty of water Sciences Engineering, Shahid Chamran University of Ahvaz.
Prof .Manoochehr Fathi-moghaddam- Faculty of water Sciences Engineering, Shahid Chamran University of Ahvaz.
References
Introduction
.
through and overflow discharge:
velocity distribution and stream
lines:
Fig4. Relation between (
𝑸 𝒊𝒏
𝑸 𝒕𝒐𝒕𝒂𝒍
) and h/p
.
In upstream and close to solid weirs, the approach flow is separated in vertical plan and an adverse pressure gradient develops on front
face of the weir which makes an eddy in front of the solid weir. In the porous weir, a portion of upstream streamlines can pass through
the weir then pressure gradient is disappeared after weir.(Mohammadpour, Ghani et al. 2013)
Fig6. 2d velocity (left side) and stream wise velocity vectors (right side) around a&d) UsS30. b&e) UsS45. C&f) UsS60
Also results indicate that the flow inside porous domain is quite uniform and changes in velocity magnitude are small and negligible
mostly in weirs with downstream side slope.
In the present study, the flow pattern around rectangular porous weirs with various upstream and downstream slopes was simulated, using
a 3D numerical method. The VOF method and the (K-ε) Renormalized group (RNG) turbulence model was used to simulate fully three
dimensional flows. Results indicate that the DsS30° provides most upstream head and least to downstream. Also the ratio of through to
total flow discharge for constant h/p occurs in DsS30° is the lowest among investigated weirs and the reverse results occur in UsS60°.
The flow crosses through the weirs, weakens the vortex areas so more through discharge, causes smaller and weaker vortices around
weirs. Due to high through discharge, recirculation areas around DsS60° are completely disappeared. It should be noted that vortex areas
appeared only at downstream side of weirs with downstream side slope.
Governing Equations
Abstract
Gabion porous weirs are of environment friendly structures that are made from local materials and have least negative impact
on rivers. In this study a 3D-CFD code was utilized to simulate flow patterns about 6 types of Triangular porous weirs with
various upstream-downstream slopes in 6 discharges run the gamut from 3 to 30 liters per second. The porosity of all weirs was
constant and equal to 50% and also assumed to be made of spherical particles. Simulation results comprise flow surface profile;
velocity distribution around weirs, the ratio of through to overall flow discharge and vortex areas is presented. Results indicate
that the weir with upstream slope of 60° (UsS60°) provides least upstream water level and downstream speed and most ratio of
through to total flow for a constant discharge, and the reverse goes to the weir with downstream slope of 30° ( DsS30°).
Keywords: porous weir- CFD-velocity distribution- through flow discharge
A conventional weir typically consists of an impermeable body constructed of concrete, metal, rubber, etc., since its primary functions
are to collect water and efficiently regulate river flow. However, an impermeable body prevents the longitudinal movement of aquatic
life and transportation of physical and chemical substances in water, eventually having a negative impact on the river
environment.(Haneda 2005) The main characteristic of the materials used in ecological engineering methods is porosity. From the
viewpoint of water quality, physical and chemical substances such as sediments and suspended organic matter can pass downstream
through the permeable body. This eventually minimizes sedimentation and eutrophication in an impoundment. Between the stones,
bacteria inhabiting the granular surface may decompose organic matter. This biochemical reaction contributes to the purification of
river or canal water as it flows through the stones, just like in water purification and sewage water plants.(Mohamed 2010)
The objective of the present study is to investigate the effect of upstream and downstream slope of Triangular porous weirs on flow
depth, flow discharge in porous media and velocity fields in the vicinity of these weirs. Simulations were performed with a general-
purpose computational fluid dynamics (CFD) software, Flow-3D, which solves Reynolds’s average Navier- Stokes (RANS) equations.
The porosity of a porous medium is defined as the open volume divided by the total volume. By constructing a continuum model of the
porous material and applying averaging to each control volume, the usual conservation equations are obtained. Conservation of mass is
expressed as follows:
𝑉 𝑓
𝜕𝜌 𝑓
𝜕𝑡
+ ∇. 𝜌 𝑓
𝑈 = 0 (1)
This equation under assumption of incompressible flow can be expressed as:
𝜕𝑢
𝜕𝑥
+
𝜕𝑣
𝜕𝑦
+
𝜕𝑤
𝜕𝑧
= 0 (2)
Where U is the macroscopic flow velocity.
Momentum equations are as follows:
𝑢
𝜕𝑢
𝜕𝑥
+ 𝑣
𝜕𝑢
𝜕𝑦
+ 𝑤
𝜕𝑢
𝜕𝑧
= −
1
𝜌
𝜕𝑝
𝜕𝑥
+ 𝜗
𝜕2
𝑢
𝜕𝑥2 +
𝜕2
𝑢
𝜕𝑦2 +
𝜕2
𝑢
𝜕𝑧2 + 𝐺 𝑥 + 𝑓 𝑥
− 𝑏 𝑥 (3)
𝑢
𝜕𝑣
𝜕𝑥
+ 𝑣
𝜕𝑣
𝜕𝑦
+ 𝑤
𝜕𝑣
𝜕𝑧
= −
1
𝜌
𝜕𝑝
𝜕𝑦
+ 𝜗
𝜕2
𝑣
𝜕𝑥2 +
𝜕2
𝑣
𝜕𝑦2 +
𝜕2
𝑣
𝜕𝑧2 + 𝐺 𝑦 + 𝑓 𝑦
− 𝑏 𝑦 (4)
𝑢
𝜕𝑤
𝜕𝑥
+ 𝑣
𝜕𝑤
𝜕𝑦
+ 𝑤
𝜕𝑤
𝜕𝑧
= −
1
𝜌
𝜕𝑝
𝜕𝑧
+ 𝜗
𝜕2
𝑤
𝜕𝑥2 +
𝜕2
𝑤
𝜕𝑦2 +
𝜕2
𝑤
𝜕𝑧2 + 𝐺 𝑧 + 𝑓 𝑧
− 𝑏 𝑧 (5)
Where 𝜗 is the fluid kinematic viscosity; (u, v, w) are velocity components in three dimensions, ρ is the fluid density, (𝐺 𝑥,𝐺 𝑦,𝐺 𝑧) are
body accelerations, (fx, fy, fz) are viscous accelerations, (bx, by, bz) are flow losses in porous media.
Turbulence model:
The turbulence model used in this study is K-ε (RNG) method. The K-ε model is a sophisticated and widely used–model consists of two
transport equations for the turbulent kinetic energy 𝑘 𝑇 and its dissipation (𝜀 𝛵), the so-called k-ε model.(Harlow and Nakayama 1967)
Numerical modeling:
A steady state, incompressible and viscous flow was considered in this study with 6 discharges varying from 3 to 30 l/s. A first order
approximation of momentum equation and Power-Law scheme and the generalized minimum residual method (GMRES) was employed
to solve the computational domain. Fig.1 shows a sample of 3d mesh generation used to solve the computational domain.
Fig1-orthographic view of mesh quality and computational domain
6 types of weirs were investigated in total; 3 with upstream slope and 3 with downstream slopes of 30°, 45° and 60° with a constant
height of 16 cm. Porosity of all weirs is equal to 50% and is assumed to be formed of spherical particles of 32 mm diameter.
(K-ε) Renormalized group turbulence model was utilized to predict water surface profile and velocity distribution in the vicinity of
weirs.
Simulation Results and Analysis:
Water surface:
Water surface profile of flow over weirs with various upstream slopes in discharge of 3 l/s is presented in fig2. Based on simulation
results, the upstream head decreases by increasing in upstream/downstream slope. Also in all cases, the weirs with upstream slope
caused less upstream flow depth in comparison with the equal slope of downstream. The affiliation of upstream depth with minimum
downstream depth in all considered discharges for all investigated weirs is shown in fig 3.
Fig2. Water surface profile over porous weirs with various upstream/downstream slopes in discharge of 3 l/s
Results and Analysis
10th International River
Engineering Conference,19-21
Jan 2016, Ahvaz, Shahid
Chamran University.
Numerical Simulation of flow patterns around
Triangular porous weirs
irec10-03490305
0.00
0.05
0.10
0.15
0.20
0.25
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
upstreamdepthofflow(m)
Downstream depth (m)
UsS 60° UsS 30° UsS 45°
DsS 60° DsS 30° DsS 45°
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Flowdepth(m)
Distance from weir's endpoint (m)
DsS 30 ° DsS 60 °
UsS 45° UsS60°
DsS45° UsS 30°
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-0.1 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5
Q(in)/Q(Total)
h/Lw
DsS 30 DsS 45
DsS 60 UsS 30
UsS 45 UsS 60
According to results, the weir with downstream slope of 30° (DsS30°)
produces maximum upstream head in all discharges. This means that
the (DsS30°) owns the least discharge coefficient (𝐶 𝑑).
The essence of flow about the gabion weirs is quite different from that of solid weirs. fraction of flow which crosses through the weir,
causes this discrepancy. This through discharge, results lower upstream level and its interaction with overflow causes more energy
dissipation. The definition of through and overflow discharges are of favorite topics for researchers. Fig 4. shows the dimensionless
graph of the ratio of through discharge to total discharge for various h/p conditions for each weir.
velocity distribution around porous weirs
with upstream and downstream slopes is
presented in fig.5. Simulation results
show that flow patterns and the velocity
vector around weirs are a function of
weir up/ downstream slope. Maximum
downstream X velocity at Q= 30 L/s
occurs on downstream slope of DsS30;
where the U component is about 1.5.
Also minimum U belongs to UsS 60;
which means this could be more effective
when the canal bed is susceptible to
erosion
Fig3. Relationship of Upstream-downstream
depth of flow over weirs in discharges of 3 to
30 l/s
Fig4. Relation between (
Qin
Qtotal
) and h/p
In the present study, recirculation areas around weirs are very
small to none because of high porosity ratio (50%) of
materials. To determine the probable circulations, a
comparison between 2d- velocity vectors and streamwise
velocity distribution around downsream slope weirs is
presented in fig 6. Based on simulation results, recirculation
flow, occurs at end of downstream slope of DsS30° and
DsS45°. The discharge crosses through the weirs, weakens the
vortex areas, so more through discharge causes less vorticity
and its shown in Fig7(c,f) where more through flow discharge
and velocity in DsS60 in comparison wih others, causes the
vortex to disappear.
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Fig5. Velocity distribution at upstream and downstream face of weirs with a) upstream slope and
Q=3l/s b) downstream slope Q= 3 l/s c) upstream slope at Q=30 l/s d) downstream slope at Q= 30
l/s
Conclusion