Final-Thesis-present.pptx

MOTIVATION OF PRESENT WORK
 Overloading of pollutants in water bodies particularly in river systems is
one of the major environmental issues worldwide.
 Particularly, in developing countries like ours, where river systems are
being overloaded with pollutants due to rapid land use changes in their
respective catchments. And, anthropogenic activities are responsible
quite a lot for this.
 Natural river systems have their capacity to transport pollutants in their
flows.
 Prediction of hydraulic characteristics in natural river systems is
required in assessment of their pollutant transport capacity along the
flow.
10:31 AM 2

10:31 AM 3
BRIEF LITERATURE REVIEW
Numerous works on straight compound channels in investigation of flow
characteristics and mechanism of lateral momentum transfer from main
channel to floodplains have been reported in recent past using
 Analytical methods (Tang and Knight, 2008; Yang et al., 2013)
 Laboratory experimental works (Rajaratnam and Ahmadi 1981; Knight and
Hamed 1984; Shiono and Knight, 1989; Tominaga and Nezu 1991;
Ackers, 1993; Shiono and Feng, 2003; Fraselle et al., 2008; Fernandes et
al., 2014); SERC FCF at Wallingford, UK.
 Numerical model simulations (Naot et al., 1993; Thomas and Williams,
1995; Sofialidis and Prinos, 1998; Shiono et al., 2003; Nugroho and Ikeda,
2007; Joung and Choi, 2008; Cater and Williams, 2008; Kara et al., 2012;
Xie et al., 2013).
 With the advent of high-speed computers, the study on two and three-
dimensional flows in compound open-channel hydraulics had experienced
surge of interest in recent years, mainly based on Reynolds-averaged
Navier-Stokes (RANS) equations.
.

10:31 AM 4
BRIEF LITERATURE REVIEW…
 Tominaga and Nezu (1991) carried out experimental studies to investigate
secondary current patterns, turbulent structure of flows such as turbulent
intensities and Reynolds stresses under various relative water depth
ratios, and reported a 3-D data set using Fiber-optic Laser Doppler
anemometer (FLDA).
 Naot et al. (1993), Pezzinga (1994), and Sofialidis and Prinos (1998, 1999)
solved 3-D equations and showed that their models are capable of
predicting the time-averaged primary flow including bed shear stress
distributions, secondary currents, turbulent structures for different
compound open-channel geometries.
 Thomas and Williams (1995) were the first to employ LES in three-
dimensional flow to study the flow and turbulence characteristics in a
compound open-channel.
 Cater and Williams (2008) and Kara et al. (2012) also successfully
applied the LES using three-dimensional equations in the simulation of
compound open-channel flows.
 Xie et al. (2013) employed LES approach with dynamic SGS model using
partial cell treatment technique in investigating turbulent structure and
secondary flows in asymmetric compound channel. They compared the
model results with experimental data of Tominaga and Nezu (1991).

10:31 AM 5
BRIEF LITERATURE REVIEW…
 Lin and Shiono (1995) developed 3-D model by solving Navier-Stokes
equations in conjunction with linear and nonlinear k-ε turbulent schemes
to investigate transport processes of solute in compound open channels.
 Chatila and Townsend (1998) presented 2-D FDM in conjunction with
advection-diffusion equation and constant eddy-viscosity model to
simulate inert pollutant transport in compound open channels.
 Shiono et al. (2003) developed 3-D model using two turbulence closure
schemes, viz. k-ε model and algebraic stress model for prediction of
solute transport injected near the water surface for deep flows depth in a
narrow asymmetric compound open channel and compared the simulated
results with experimental work of Shiono and Feng (2003). Common salt
was used as tracer material.
 Laboratory experiments for solute transport in a wide symmetric compound
open-channel were undertaken by Fraselle et al. (2008). Later on,
Fraselle et al. (2010) developed numerical models of Telemac-2D
software using two turbulence schemes, i.e., k-ε and Elder schemes and
compared their model results with the experimental works. Diluted
common salt (NaCl) was used as solute material.

10:31 AM 6
 Based on their experimental observations, Sanjou et al. (2010) concluded
that two layer model can be very useful to understand the spanwise flow
features and interaction between upper and lower layers in compound
open channel.
 Earlier, Knight and Demetriou (1983) experimentally showed variation
of apparent shear forces at horizontal interface of the channel for different
discharges in compound channels.
 Chau and Jin (1995) suggested for use of sophisticated turbulence
model to capture the interaction between turbulence and mixing across the
interface.
 Also, they suggested incorporation of transport equations in their two layered
model as future scope of work.
Problem of hydrodynamics and solute transport
in compound open channels using two layer 2-D model
with LES as turbulent closure scheme
RESEARCH GAP

Ref.: Khatua et al., 2009
10:31 AM 7
Ref.: Joung & Choi, 2008
RESEARCH GAP…

COMPOUND OPEN-CHANNEL: A TWO LAYER SYSTEM
bl
hl
bfp bfp
hu
Lower Layer
Upper Layer
10:31 AM 8
Zb
hl
datum
Transverse Section
surface layer
bottom layer
datum
hu
hl
Longitudinal Profile
surface layer
bottom layer
hu
Zb

Following are the research objectives of present study:
 Development of two layer 2-D hydrodynamic numerical model for
compound open-channel using LES approach
 Validation of hydrodynamic model using past experimental data on
symmetric and asymmetric compound channels
 Development of two layer 2-D solute transport model for compound
open-channel using LES approach
 Validation of solute transport model using past experimental data on
symmetric and asymmetric compound channels
OBJECTIVE OF PRESENT WORK
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GOVERNING EQUATION: ASSUMPTIONS
 By integrating 3-D N-S equations vertically from bottom to top face of each
layer with consideration of mass and momentum exchange between the layers.
 A hydrostatic pressure distribution is assumed on each layer, i.e., convection and
friction terms in momentum equation in vertical direction are much smaller than
pressure gradient and gravitation.
 Density in each layer is same and constant, i.e., variation in density between
the layers is neglected.
 Coriolis force is negligible.
Zb
hl
datum
Transverse Section
surface layer
bottom layer
datum
hu
hl
Longitudinal Profile
surface layer
bottom layer
10:31 AM 10

GOVERNING EQUATION: HYDRODYNAMIC
Upper Layer:
10:31 AM 11
h
hu
hl
bu
bl
vu
uu
w0
v0
u0
vl
ul
LOWER LAYER
H. INTERFACE

Lower Layer:
10:31 AM 12
Subscripts ‘u’ and ‘l’ designate the variables corresponding to upper and lower layers.
Symbols appearing as ‘o’, ‘s’ and ‘b’ denote the position at interface, surface and bed.
hk, uk and vk represent filtered water depth, streamwise and spanwise layered average
velocity, respectively in kth layer;
is layered average filtered turbulent stress at ith face in jth direction in kth layer.
are filtered shear stresses in ith direction at surface, interface and bed.
uo, vo and wo are filtered velocity at interface in streamwise, spanwise and vertical
directions
= mass density of water; so= channel bed slope in streamwise direction.
g = gravitational acceleration.


Bed Shear Stress terms
*
u Friction Velocity
f
c Coefficient of Bed Resistance
n Manning’s Roughness coefficient
m
u m
v Layer Averaged Velocities
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Shear Stress at horizontal Interface between Upper and Lower Layers
 Mixing Layer Thickness at the interface
Velocities at horizontal Interface
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ck concentration in layers (kg/m3), k= u, l
vtk SGS eddy diffusivity (m2/s) in ith direction of kth layer
sk quantity of inert solute (kg/m2/s) in kth layer
Ke rate of exchange of solute concentration from one layer to other (per sec)
GOVERNING EQUATION: SOLUTE TRANSPORT
Upper Layer:
Lower Layer:
10:31 AM 15

U : State vector,
E and G : Vectors representing flux terms
S : Vector representing source term
GOVERNING EQUATION: DIVERGENCE FORM
10:31 AM 16

GOVERNING EQUATION: DIVERGENCE FORM
10:31 AM 17

Application of Gauss divergence theorem yields
governing equation in integral form
METHOD OF SOLUTION: FINITE VOLUME METHOD
Assuming vector U and S to be uniform over
grid cell – 2-D case
Surface integral approximated by
sum over four walls of grid cell
F.n = E.nx + G.ny
10:31 AM 18
Method of lines and Cell-centre approach are adopted for approximation of
various terms of numerical flux

METHOD OF SOLUTION: CONVECTIVE FLUX TERM
For fixed grid cell, time derivative of variable
Evaluation of numerical flux at a face of grid cell (i,j)
L R
L
R
i,j i+1,j
i,j+1 i+1,j+1
Face of grid cell
X
Y
UR and UL obtained using MUSCL
(Monotone Upwind Scheme for
Conservation Laws) approach
10:31 AM 19

Slope limiter ‘minmod’ used to suppress non-physical oscillation of
solution
minmod (a,b) = a, if |a| < |b| and a.b > 0
b, if |a| > |b| and a.b > 0
0, if a.b < = 0
Determination of positive coefficient α from max of
METHOD OF SOLUTION: CONVECTIVE FLUX TERM
10:31 AM 20

METHOD OF SOLUTION: VISCOUS FLUX TERM
Derivative in X-direction
Auxiliary grid cell to determine
First order derivative in X & Y-directions
10:31 AM 21

METHOD OF SOLUTION: TURBULENCE TERM
In Hydrodynamic Equations
In Solute Transport Equations
10:31 AM 22
is Schmidt number (0.5 to 1.0)
(Boussinesq approximation)

METHOD OF SOLUTION: TURBULENCE CLOSURE SCHEME
Standard Smagorinsky Model (SS Model)
Smagorinsky coefficient, C a calibration parameter varies between
0.02 to 0.25 depending upon various factors including type of flow
10:31 AM 23
: SGS shear stresses
: SGS eddy viscosity
Sij : Strain rate
: Grid volume

Dynamic Subgrid Scale Model (DSGS Model)
METHOD OF SOLUTION: TURBULENCE CLOSURE SCHEME
SGS stress at each test filter level is related by Germano identity
Lij the resolved turbulent stress for each layer
Using least square minimization approach
< - > represents spatial averaging in homogenous directions so as to
stabilize the computations following summation convention of repeated
indices.
10:31 AM 24
(Over-determined term)

METHOD OF SOLUTION: BOUNDARY CONDITIONS
Upstream boundary
 Known quantities such as Discharge, flow velocities prescribed
(Dirichlet condition)
 Water depth or Flow velocity is extrapolated from the inner
grids in such a way that flow should remain in subcritical state.
 Discharge in transverse direction is zero to ensure
spanwise flow normal to boundary
 Convective fluxes are calculated based on known quantities.
 Derivative of diffusive fluxes are calculated based on interpolation
technique
 Inlet values of respective terms are adjusted for various turbulence
schemes
10:31 AM 25

Downstream boundary
 Downstream boundaries are chosen far away from the region
of measurement
 Zero gradients for dependent variables along the grid lines
(Neumann condition)
 Convective and diffusive fluxes are calculated in terms of
variable at inner nodes.
 Derivative of diffusive flux equal to zero as flow is assumed to be
perpendicular to the boundary grid
 Values of various terms of model turbulence schemes are set
10:31 AM 26

Side wall boundary
 Normal gradients of flow variables are extremely large.
 Fine grid mesh required to resolve these gradients.
 Turbulent fluctuations are suppressed and viscous effects
become important in viscous sub-layer region
 Standard turbulence models not valid near the wall.
 Special wall modelling procedure required.
 Standard wall functions are based on the assumption that the
first grid point is located in logarithmic region and universal wall
law is valid
 Reflection technique adopted at solid walls boundary conditions
 Cell width near wall is chosen as y+
≥30.
 Boundary conditions for solute transport model,
10:31 AM 27

Model grid along with ghost cells
Partial slip condition : A wall function is applied to avoid the
necessity of using extremely small grids
near solid wall
where up = tangential velocity component along the wall boundary
Side Wall Boundary …
10:31 AM 28

Wall shear velocity,   2
/
1
* /
)
( 

 w
w
sign
u 
Side Wall Boundary …
where τw is the wall shear stress
p
p
u
u



Using Similarity rule near the wall
0
t
p
u u v
y y x

 

 
  
  
 
  
 
2
b p p
y u
u u
y
 
 
   

 
Slip velocity ub at the wall boundary
Velocity gradient at ∆y/2 away from the wall is
10:31 AM 29

Predictor part
Corrector part
METHOD OF SOLUTION: PREDICTOR-CORRECTOR SCHEME
10:31 AM 30
The explicit scheme is 2nd order accurate in both space and time. More
Efficient, robust and easy of implementation.

METHOD OF SOLUTION: STABILITY CONDITION
Courant-Friedrichs-Lewy (CFL) condition
10:31 AM 31

10:31 AM 34
PERFORMANCE ASSESSMENT
OF
HYDRODYNAMIC MODEL
&
SOLUTE TRANSPORT MODEL

SYMMETRIC AND ASYMMETRIC
COMPOUND OPEN CHANNEL
MODEL SIMULATION: EXPERIMENTAL DATA
bu
bl
hl
hu
Y
U P P E R L A Y E R
LOWER LAYER
Horizontal Interface
X
h
10:31 AM 35
(Tominaga and Nezu, 1991; Shiono and Feng, 2003; Fraselle et al., 2008)
h
hu
hl
bu
bl

PAST EXPERIMENTAL DATA
MODEL SIMULATION: EXPERIMENTAL DATA
10:31 AM 36

HYDRODYNAMIC MODEL SIMULATION: RESULTS
STANDARD SMAGORINSKY MODEL (SS MODEL)
DYNAMIC SUBGRID SCALE MODEL (DSGS MODEL)
10:31 AM 37

10:31 AM 38
Normal Asymmetric Compound Channel
(L/B=31)
SS MODEL
Comparison between
Deep Flows
&
Shallow Flows

SS MODEL: Normal Asymmetric Compound Channel
(Exp.S-2 & S-3:Tominaga and Nezu, 1991)
10:31 AM 39
Deep Flows
Shallow Flows

(Exp.S-2 & S-3:Tominaga and Nezu, 1991)
10:31 AM 40

Grid Dependence Test
(Exp.S-2:Tominaga and Nezu, 1991)
10:31 AM 41

Comparison of Primary
Flow Velocity
(Tominaga and Nezu, 1991)
Deep flows (Exp.S-2)
Shallow flows (Exp.S-3)
10:31 AM 42

% difference between Primary Velocities of Two Layers
w.r.to Bulk Mean Velocity
10:31 AM 43

Comparison of Bed Shear
Stresses
(Tominaga and Nezu, 1991)
10:31 AM 44

Secondary Flow Velocity Profile at Horizontal Interface
10:31 AM 45
Magnitude of maximum secondary current
of the order of 0.12% of Ub
Magnitude of maximum secondary current
of the order of 0.23% of Ub

Shear Stress Profile at
10:31 AM 46

SGS Turbulent Shear Stress
Profile in Upper Layer
10:31 AM 47

Profile in Lower Layer
10:31 AM 48

Wide Symmetric Compound Channel
(L/B=8)
&
Narrow Asymmetric Compound Channel
(L/B=100)
Comparison between
DSGS MODEL
&
SS MODEL
10:31 AM 49

(Fraselle et al., 2008; Fraselle et al., 2010)
(Shiono and Feng, 2003; Shiono et al., 2003)
bu=1.2 m
bl=0.4 m
hl=0.0506 m
hu=0.025 m
Y
U P P E R L A Y E R
LOWER LAYER
X
h=0.0756 m
HYDRODYNAMIC MODEL SIMULATION
10:31 AM 50

10:31 AM 51
HYDRAULIC CHARACTERISTICS OF CHANNELS

10:31 AM 52
HYDRODYNAMIC MODEL SIM.: WIDE SYM. COMP.

Model Grids
(Upper Layer: 500 x 70, Lower Layer: 500 x 26)
A
A
u
p
s
t
r
e
a
m
d
o
w
n
s
t
r
e
a
m
Upper
layer
at
section
AA
sidewall S1
sidewall S3
Upper Layer
10:31 AM 53

Model Grids
(Upper Layer: 500 x 70, Lower Layer: 500 x 26)
A’
A’
upstream
downstream
Lower
Layer
at
section
A’A’
sidewall S1
sidewall S3
Lower Layer
10:31 AM 54

DSGS Model: Variation of SGS Coefficient, C
10:31 AM 55
HYDRODYNAMIC RESULT: WIDE SYM. COMP.

Flow Velocity
(Fraselle et al., 2008 ; Fraselle et al., 2010)
DSGS Model
SS Model
10:31 AM 56

% difference between
Primary Velocities of
Two Layers
w.r.to Bulk Mean
Velocity
DSGS Model
SS Model
10:31 AM 57

Bed Shear Stress Profile
DSGS Model
SS Model
10:31 AM 58

Secondary Velocity Profile
at Horizontal Interface
DSGS Model
SS Model
10:31 AM 59
Magnitude of maximum secondary
current of the order of 1.5% of Ub

Typical Secondary Flow Velocity at Horizontal Interface
Vector plot
10:31 AM 60

DSGS Model
SS Model
10:31 AM 61

DSGS Model
SS Model
10:31 AM 62

DSGS Model
SS Model
10:31 AM 63

Narrow Asymmetric Compound Channel
Comparison between
DSGS MODEL
&
SS MODEL
10:31 AM 64

10:31 AM 65

DSGS Model: Variation of SGS Coefficient, C
10:31 AM 66
HYDRODYNAMIC RESULT: NARROW ASYM. COMP.

Flow Velocity
(Shiono and Feng, 2003 ; Shiono et al., 2003)
10:31 AM 67

% difference between Primary
Velocities of Two Layers
w.r.to Bulk Mean Velocity
DSGS Model
SS Model
10:31 AM 68

Bed Shear Stress Profile
DSGS Model
SS Model
10:31 AM 69

Secondary Flow Velocity Profile at
DSGS Model
SS Model
10:31 AM 70

Vector plot
Typical Secondary Flow Velocity at Horizontal Interface
10:31 AM 71

DSGS Model
SS Model
10:31 AM 72

DSGS Model
SS Model
10:31 AM 73

DSGS Model
SS Model
10:31 AM 74

WIDE SYMMETRIC COMPOUND CHANNEL
&
NARROW ASYMMETRIC COMPOUND CHANNEL
SOLUTE TRANSPORT MODEL SIMULATION: RESULTS
DYNAMIC SUBGRID SCALE MODEL (DSGS MODEL)

SOLUTE TRANSPORT DSGS MODEL: WIDE SYM. COMP.
0.0375 m
0.415 m
0.4 m
Experimental Runs
0.025 m
0.415 m
0.4 m
0.0125 m
Numerical Runs
10:31 AM 76
(Fraselle et al., 2008)
(Present Model)
2m 3m 4m 6m 9m
0m
10m
Solute type
Common salt NaCl

10:31 AM 77
SOLUTE TRANSPORT RESULT: WIDE SYM. COMP. (I1)

UPPER LAYER
LOWER LAYER
10:31 AM 78

10:31 AM 79

UPPER LAYER
LOWER LAYER
10:31 AM 80

SOLUTE TRANSPORT DSGS MODEL: NARROW ASYM. C0MP.
Numerical Runs
0.055 m
0.0275 m
0.055 m
0.05 m
Experimental Runs
10:31 AM 81
(Shiono & Feng, 2003)
(Present Model)
0m 13m 14m
20m
Solute type
Rhodamine 6G

10:31 AM 82
SOLUTE TRANSPORT RESULT: NARROW ASYM. C0MP. (C1)

UPPER LAYER
LOWER LAYER
10:31 AM 83

10:31 AM 84

UPPER LAYER
LOWER LAYER
10:31 AM 85

10:31 AM 86

UPPER LAYER
LOWER LAYER
10:31 AM 87

CONCLUSIONS: HYDRODYNAMIC MODEL
1) The model result on flow parameters like interfacial shear stress
and vertical flow velocity gives insight about the overall momentum
exchange between the main channel and the floodplain of straight
compound open-channel.
2) Based on sensitivity analysis, the average values of model
parameters C and α equals to 0.1 and 0.5 respectively are found
to be adequate for simulation of hydraulic characteristics.
3) Significant difference in layered average primary flow velocities
near the junction of lower and upper layers is of the order of 10-
14% of mean bulk velocity.
4) Analysis of variations of flow variables in compound channels in
terms of bed shear stress distributions and, spanwise and vertical
velocities at the horizontal interface revealed the existence of
horizontal vortices where momentum exchange takes place.
5) Spanwise distribution of shear stresses at interface of compound
channel reveals the dominance of shear stresses at the junction.
10:31 AM 88
The major findings of hydrodynamic model simulations are:

6) The developed model has been able to simulate satisfactorily the
depth averaged primary velocity in compound open channels. The
model is able to reproduce one inflection point in case of shallow
flows in symmetric compound channel while two inflection points in
case of deep flows in asymmetric compound channel.
7) The maximum secondary currents are generated near the junction of
the main channel and floodplain; the direction of the currents
indicates the trend of mass and momentum transfer from lower to
upper layer. Horizontal isolines plots of secondary currents, bed and
interfacial shear stresses indicate the formation of vortices near the
junction of the main channel and floodplains.
8) The variation of depth averaged dynamic model parameter C in
compound channels is in the range of 0.02 to 0.145.
9) The DSGS model has been found to give better results vis-à-vis SS
model in simulating hydraulic characteristics in compound open
channel flows.
CONCLUSIONS: HYDRODYNAMIC MODEL
10:31 AM 89

CONCLUSIONS: SOLUTE TRANSPORT MODEL
1) DSGS model has been able to predict the peak solute
concentrations irrespective of point of injection in the compound
channel cross-section. The spanwise distribution of concentration
across the junction of the main channel and floodplain, depends
upon the magnitude of secondary currents.
2) The developed model has been able to simulate the concentration
of solute in both symmetric (Exps.I-1, I-4) and asymmetric (Exp.C-
1, C-2, C-3) compound open channels with RMSE ranging from
0.01 g/l to 0.05 g/l and 0.73 ppb to 1.19 ppb respectively.
3) The presence of vertical velocity component causes higher rate of
distribution of concentrations vertically vis-à-vis in horizontal
direction.
4) The performance of developed model is better at downstream
locations as compared to upstream locations due to better mixing
of pollutants.
10:31 AM 90
The major findings of transport model simulations are:

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