velocity distribution in diverging channel

1. VELOCITY DISTRIBUTION IN TRANSITION IN
DIVERGING CHANNEL

2. 1. INTRODUCTION
• During floods, water in river enters it flood plains. Due to effects of gravity and momentum it floods over its
flood plain and starts diverging over the area.
• Two stage channels has interaction mechanism between main channel and flood plains which make flow
analysis complex.
• Natural channels have more rougher flood plains than main channel bed. Which makes low velocity flow on
flood plain. In main channel velocity of flow is high. Due to this kinetics effect, flow on main channel is
restricted by flow on flood plains, due to which momentum transfer mechanism takes place.
• Flow analysis consists of evaluating flow parameters such as Distribution of velocity, boundary shear stress,
analysis of flow behavior at junction of main channel and flood plain.
• In literature, Shiono-Knight Model (SKM) etc. are used for mathematical 2D modelling of flow in prismatic
channels. In diverging compound channels, non-prismatic geometry is a main difficulty to evaluate flow
parameters. So numerical modelling is chosen over Analytical modelling.
• Software's such as ANSYS, Open FOAM, etc. has capability of simulating flow by solving Navier-Stokes
equations in 3D flow domain.

3. 1.1 ROUGHNESS AND ITS RESISTANCE
• In this study, A diverging compound channel is simulated for two roughness conditions.
a) Smooth bed case. Channel having smooth bed through out. Glass surface represents flow in smooth bed.
b) Gravel bed case. Gravel bed is used to represent natural rough bed flows.
• In river engineering, Manning’s equation is usually used to represent channel resistance. The main difficulty in using
Manning’s equation is at a given cross-section, the Manning’s n varies with depth. Therefore, the Darcy friction factor (f)
may be preferred to Manning coefficient (n) in defining the roughness of channel surfaces.
• Colebrook & White (1937) clarified how f varies in smooth and rough pipes, conduits running part full and open
channels:
1
𝑓
= −2 log
𝐾𝑠
14.8𝑅
+
2.51
𝑅𝑒 𝑓
𝐸𝑞. (1)
• On the other hand, as Re → ∞, Eq.1 becomes the rough law, in which f is independent of Re and depends only on the
ratio of surface roughness (Ks) to hydraulic radius (R), giving
1
𝑓
= −2 log
𝐾𝑠
14.8𝑅
𝐸𝑞. (2)

4. • Based on Eq.1, the roughness of any surface can be characterized by 𝐾𝑠, the so-called Nikuradse
equivalent sand roughness size, which is defined as a measure of the size of roughness on a flat surface
that would yield the same resistance as that in a circular pipe roughened with uniform grains of sand.
• As channel is diverging, wetted perimeter also increases, also flow area increases which results in uniform
value of Hydraulic radius over small lengths. So uniform value of Hydraulic radius is submitted in Eq. (1).
From That 𝐾𝑠 value is obtained.
• As gravel particles are not in uniform size, sieve analysis was conducted to conclude mean size of particle.
In NHR cases simulation, 𝐷50 size of particle is taken as equivalent sand grain roughness (𝐾𝑠). That is given
as input in Fluent software.

5. • From graph, 𝐷50 size is computed as 10.5mm and standard deviation is computed as 1.37mm. So, 𝐷50 size is opted for
simulations.

6. 2. LITERATURE REVIEW
 Non – Prismatic Channels :
• Bousmar (2002) conducted experiments on FCF channels with Prismatic and Non-Prismatic Floodplains and concluded that
momentum exchange will occur between main channel and flood plain due to kinetics effect.
• Proust (2006) conducted experiments on compound channels with contracting flood plains and concluded the effect of
contraction on distribution of velocity and head loss during flow. Later he developed another method for estimating energy
losses in compound open channels by using First law of Thermodynamics.
• Rezai (2009) Also performed experiments on FCF Channels with over bank flow on prismatic and non – prismatic flood
plains and reported the presence of shear layer between main channel and flood plains. He developed model for computing
momentum exchange by Exchange Discharge Method (EDM). Later he developed model for predicting water surface profile
for non – prismatic flows.
• Bhabani Shankar Das (2019) Performed Experiments on Three Diverging angle channels (5.33, 9.83, 14.54) and five
relative depth flows (0.2-0.5) and concluded that for same discharge, flow velocity is inversely proportional to diverging
angle and Relative depth.
• B. S. Das, K. K. Khatua, K Devi (2019) tested non-prismatic channel data with SKM Model (LDM) and it badly predicted
the velocity distribution as it is developed for prismatic channels, later they used Energy slope instead of bed slope (MLDM)
and concluded that MLDM predicts better than LDM for non-prismatic channels. Later in 2019, They also developed a model
to compute flow resistance in converging and diverging compound channels.
• B Naik, K K Khatua, N G Wright, A Sleigh (2017) developed MVLR Model for prediction of Stage – Discharge curve in
non-prismatic channels and applied it on natural rivers and successfully predicted the discharge with least error.

7.  Channel Transitions & Rough Bed Flows :
Channel transitions are of classified as Horizontal transitions (expansion/contraction in width), Vertical Transitions
(Modifying Bed height), Combined Transition (Both Hump and Expansion/contraction). As depth of flow increases with
increase in width of channel and providing Sump in flow direction, so Increase of flow depth from 8cm to 18cm is done.
• W A A K Alawaadi (2019) conducted experiments on simple and compound rectangular channel flows for both smooth
and rough conditions.
• Nandana Vittal and V V Chiranjeevi (1998) explains methods available for design of open channel transitions.
• Abdullarahman (2008) presented direct solutions to channel transition problems such as horizontal transition (change in
width), vertical transition (change in bed height) and combined transitions (change in width and hump). Iterative process
used by K Subramanya, is also compared and direct formulations gives good results and reduces computational resources.
• Rashmi Rekha Das (2015) carried out flow analysis in trapezoidal channel with non-homogeneous roughness and found
the variation of pattern of velocity with change in differential roughness. Experiments are conducted with materials like
concrete, sand, gravel for variation of roughness along width of channel.
• Nirjharini Sahoo (2012) in her thesis Effect of differential roughness on flow characteristics in compound channel
carried out Experiments using plastic mat and wire mesh for varying roughness on flood plain for different cases and
concluded the effect of differential roughness on flow parameters such as velocity distribution, boundary shear stress.
• S K Banerjee (2016) carried out experimental study on gravel bed channels in trapezoidal channels. Two conditions
namely Constant bed load and transport of bed load is considered. Gravel of size 13.5mm and 6.5mm are used for
experimentation.

8.  Computational Fluid Dynamics :
• D W Knight, N G Wright (2005) prepared a detailed report on guidelines for CFD Simulations for Free surface flows.
• Shyaama Al Hashimi (2018) carried out numerical modelling for turbulent open channel expansion using k-ꞷ model for
simulation.
• Khazee and M Mohammadiun (2012) performed 3D simulations using VOF model and LES Turbulence model and
seven sub grid scales are used for seven aspect ratio’s, bed slopes, convergent and divergent conditions.
• Ramamurthy et al (2013) performed 3D simulation for right angle bend in open channel flows using K – ε, K-ꞷ & RSM
and concluded that RSM predicts flow pattern better than other two models.
• Iehisa Nezu (2005) carried out a detailed review on Open channel flow turbulence and it’s research prospect in the 21st
century.
• Rameshwaran and Naden (2003) performed 3D simulation of compound channel flows.
• B Naik, K K Khatua, Nigel Wright, A Sleigh, P K Singh (2017) conducted numerical simulation on converging
compound channel using k- ꞷ model.
• Abinash Mohanta, K C Patra (2018) performed a detailed analysis on numerical simulations using LES Model.
• D Sofialidis, P Prinos (1998) performed 3D numerical simulation for low relative depth turbulent flows with K-ε model
with low Reynolds number formulations.

11. EXPERIMENTAL VALIDATION WITH ANSYS
• Considering all conditions mentioned, ANSYS Simulation results are compared with experimental cases for
validation and ANSYS gives identical pattern and near results to experimental values.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
VELOCITY
(M/S)
WIDTH (M)
GRAVEL BED CASE
Experimental ANSYS
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
VELOCITY
(M/S)
WIDTH (M)
SMOOTH BED FLOW
Experimental ANSYS

12. • Impact of Horizontal Transition (Diverging Angle) On Flow Velocity:
• Horizontal transition is indicated by increase in diverging angle. It is observed that flow separation varies with increase
in flow length and cross section area.
• In 2m Diverging length channel flow separation happens out side diverging part and by increase in diverging length
point of flow separation becomes closer to diverging part of channel.

14. 0
0.05
0.1
0.15
0.2
0.25
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
VELOCITY
(M/S)
WIDTH (M)
DAV BEFORE HUMP
H_Exp H_min H_Max
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
VELOCITY
(M/S)
WIDTH (M)
DAV AFTER HUMP
H_Exp H_Min H_Max

15. REFERENCES
1. Bousmar, D., 2002. Flow modelling in compound channels. Momentum transfer between main channel and prismatic or non-prismatic floodplains. Unité de
Génie Civil et Environnemental, 12, p.326.
2. Vaghefi, M., Akbari, M. and Fiouz, A.R., 2016. An experimental study of mean and turbulent flow in a 180 degree sharp open channel bend: Secondary flow
and bed shear stress. KSCE Journal of Civil Engineering, 20(4), pp.1582-1593.
3. Singh, P.K., Banerjee, S., Naik, B., Kumar, A. and Khatua, K.K., 2018. Lateral distribution of depth average velocity & boundary shear stress in a gravel bed
open channel flow. ISH Journal of Hydraulic Engineering, pp.1-15.
4. B. Naik, K. K. Khatua, Nigel Wright, A. Sleigh & P. Singh (2018) Numerical modeling of converging compound channel flow, ISH Journal of Hydraulic
Engineering, 24:3, 285-297, DOI: 10.1080/09715010.2017.1369180
5. Alawadi, W.A.A.K., 2019. Velocity distribution prediction in rectangular and compound channels under smooth and rough flow conditions (Doctoral
dissertation, University of Salford).
6. Fluent, A.N.S.Y.S., 2011. Ansys fluent theory guide. ANSYS Inc., USA, 15317, pp.724-746.
7. Guide, A.F.U., 2011. Release 14.0, ANSYS. Inc., USA, November.
8. Wikipedia contributors (2020). Reynolds stress equation model [online]. Available at: Reynolds stress equation model – Wikipedia.
9. Mohanta, A. and Patra, K.C., 2018. LES modeling with experimental validation of a compound channel having converging floodplain. Journal of The
Institution of Engineers (India): Series A, 99(3), pp.519-537.
10. Knight, D.W., Wright, N.G. and Morvan, H.P., 2005. Guidelines for applying commercial CFD software to open channel flow. Report based on research
work conducted under EPSRC Grants GR, 43716, p.31.
11. Khatua, K.K. and Patra, K.C., 2007. Boundary shear stress distribution in compound open channel flow. ISH Journal of Hydraulic Engineering, 13(3), pp.39-
54.

16. THANK YOU