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THE UNIVERSITY OF LEEDS
School of Civil Engineering
DISSERTATION
Submitted for the degree of
Masters of Science
In
Environmental Engineering
And Project Management
A Computational Fluid Dynamic validation study for the prediction and analysis of free surface flow over a Broad
crested weir
Prepared by
Adeolu Oluwatosin Adegbulugbe
August 2010
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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Abstract
This study described an investigation into the computational fluid dynamic capabilities of the
ANSYS FLUENT and Blender in numerically simulating and modeling free surface flows over a
broad crested weir in a rectangular open channel, for the purpose of validating these
applications. The predicted CFD results from a series of simulations are compared against an
existing experimental data. In FLUENT, by fixing the upstream and downstream heads,
pressure, velocity, downstream discharge and surfaces profiles are all predicted. The analysis
in fluent adopted the Volume of fluid (VOF) model while the investigations were conducted
varying the turbulence model, solution methods, boundary conditions and pressure heads at
upstream. In Blender, by replicating the computational domain and visually observing the flow
characteristics within the rectangular channel, the comparison with experimental results and
real time flow has been documented.
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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Table of Contents
Abstract ................................................................................................................................. ii
Table of Contents.................................................................................................................. iii
List of Tables ......................................................................................................................... vi
List of Figures ....................................................................................................................... vii
List of Abbreviations .............................................................................................................. x
List of Symbols ...................................................................................................................... xi
Acknowledgment ................................................................................................................. xii
1. INTRODUCTION ............................................................................................................. 1
1.1. The Theory of Fluid Simulation ............................................................................................... 1
1.2. The Navier-Stokes Equations .................................................................................................. 2
1.2.1. External Forces ................................................................................................................ 2
1.2.2. Advection......................................................................................................................... 3
1.2.3. Diffusion .......................................................................................................................... 3
1.2.4. Pressure ........................................................................................................................... 4
1.2.5. Incompressibility ............................................................................................................. 4
1.3. Weir applications in Hydraulic Structures ............................................................................... 4
1.4. Flow over a Broad Crested Weir ............................................................................................. 6
1.5. Free Surface Flow idealisation ................................................................................................ 7
1.6. Numerical method for modelling free surfaces ...................................................................... 8
1.6.1. The Lagrangian grid method ........................................................................................... 8
1.6.2. The Marker-and-Cell (MAC) method............................................................................... 9
1.6.3. The Volume of Fluid Method .......................................................................................... 9
1.7. The Problem Statement ........................................................................................................ 11
1.8. Project Scope ......................................................................................................................... 12
1.9. Aims and Objectives .............................................................................................................. 12
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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2. LITERATURE REVIEW ................................................................................................... 14
2.1. Computational fluid Dynamics .............................................................................................. 14
2.2. CFD Analysis with ANSYS FLUENT ......................................................................................... 16
2.3. CFD Analysis with Blender 2.49 ............................................................................................. 17
2.3.1. Lattice Boltzmann Numerical Method .......................................................................... 18
2.3.2. Smooth Particle Hydrodynamic Numerical method ..................................................... 20
2.4. Multiphase Flow .................................................................................................................... 21
2.4.1. Real-time Multiphase Flows .......................................................................................... 21
2.4.2. Multiphase flow models ................................................................................................ 22
2.5. Methodology of the VOF Method ......................................................................................... 23
2.5.1. The Basic Theory ........................................................................................................... 24
2.5.2. The VOF Concept ........................................................................................................... 25
2.5.3. Details of the VOF Technique ........................................................................................ 26
2.5.4. Illustration of Free-Surface Tracking by VOF Technique ............................................... 28
2.6. Review of Relevant Papers .................................................................................................... 29
2.6.1. Hager and Schwalt’s Experimental study of flow over weir ......................................... 29
2.6.2. CFD Validation of the Hager and Schwalt’s Experiment ............................................... 30
2.6.3. Prototype CFD Simulation of Flow over a drop............................................................. 31
3. TEST CASE METHODOLOGY ......................................................................................... 34
3.1. Computational Domain ......................................................................................................... 35
3.2. Methodology for ANSYS FLUENT Simulations ....................................................................... 37
3.2.1. Domain Adjustments and Mesh Refinements in Gambit ............................................. 37
3.2.1.1. Specifying Continuum ................................................................................................... 38
3.2.1.2. Mesh Adaptation ........................................................................................................... 39
3.2.2. Grid Independency Test ................................................................................................ 43
3.2.3. Summary of Simulations Conducted ............................................................................. 45
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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3.3. Simulation Methodology in Blender ..................................................................................... 48
3.3.1. Lights and Camera ......................................................................................................... 48
3.3.2. Geometry modelling in Blender .................................................................................... 49
3.3.3. Geometric Refinements to Computational Domain ..................................................... 52
3.3.3.1. Setting transparency ..................................................................................................... 52
3.3.3.2. Light Refraction (IOR) .................................................................................................... 53
3.3.4. Summary of methodology in Blender ........................................................................... 53
4. RESULTS PRESENTATION AND DISCUSSION .................................................................. 55
4.1. ANSYS FLUENT Results .......................................................................................................... 55
4.1.1. Effect of Turbulence Model ........................................................................................... 56
4.1.2. Effects of Specifying Zones of Continuum .................................................................... 60
4.1.3. Varying Mesh topology (Structured or Unstructured) .................................................. 60
4.1.4. Effect of mesh adaptation and Grid independence results .......................................... 61
4.1.5. Velocity Inlet Simulation ............................................................................................... 62
4.1.6. Pressure Inlet Simulation .............................................................................................. 63
4.1.7. Flow Characteristics downstream ................................................................................. 63
4.1.8. Velocity Predictions. ...................................................................................................... 64
4.1.9. Pressure Predictions ...................................................................................................... 67
4.1.10. Pressure Predictions ...................................................................................................... 68
4.2. Blender Results ...................................................................................................................... 70
4.3. Result discussion ................................................................................................................... 71
5. SUMMARY AND CONCLUSION ..................................................................................... 75
6. RECOMMENDATIONS .................................................................................................. 77
7. REFERENCES ................................................................................................................ 78
APPENDIX ............................................................................................................................ 81
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List of Tables
Table 2.1: Results from the H&S Experiments and D.M. Hargreaves et al. CFD Simulations .....31
Table 2.2: Comparisons between experiment and simulation ...................................................33
Table 3.1: Summary show characteristic parameters of all simulations ....................................41
Table 3.2: Varying Mesh Sizes for Grid Dependency Test (a) 15 Size Mesh (b) 25 Sized Mesh (c)
40 Sized Mesh (d) 50 Sized Mesh Spacing ...................................................................................44
Table 4.1: Initial simulation to investigate appropriate solution methods ................................56
Table 4.2: Results from the study of the effect of turbulence model. .........................................57
Table 4.3: Results from test on the effects of mesh topology ....................................................61
Table 4.4: Results from the grid independence test ...................................................................61
Table 4.5: Result summary of simulations showing Contour Profiles at Drop (weir fall) ...........69
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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List of Figures
Figure 1.1: Three Broad Crested Weir Setup at the Bedford Ouse Watercourse (EA, 2008) ........5
Figure 1.2: Measuring Flows with Weir (Source: Michigan State University Archives) ................6
Figure 2.1: Fundamental Steps of CFD Analysis ..........................................................................14
Figure 2.2: The Blender working environment ............................................................................18
Figure 2.3: A Typical Lattice structure in (a) 2D and (b) 3D ........................................................19
Figure 2.4: Surface in 2d Grid of Elements. .................................................................................26
Figure 2.5: Fluid Fraction Values in Elements, Showing Sharpness of Surface Definition. .........28
Figure 2.6: Close Up Of Fluid Fraction Values Where The Overflow Hits Bottom. ......................28
Figure 2.7: Simulation of Flow over a .........................................................................................32
Figure 3.1:Schematics of the broad crested weir and notations ................................................35
Figure 3.2: Computational Domain (a) With Dimensions (b) With Boundary conditions ..........36
Figure 3.3: Computational Domain Showing Boundary Conditions ...........................................37
Figure 3.4: Computational Domain Showing Boundary Conditions With Assigned Faces .........38
Figure 3.5: Three Computational model types tested (a) with no assigned zone (b) with two
zones separated by but no defined interface (c) with three defined zones and two interfaces. 39
Figure 3.6: Illustrating the H-refinement sub-division ................................................................40
Figure 3.7: Illustrating the hanging node ...................................................................................40
Figure 3.8: Mesh region showing non conformal meshes at the interface ................................42
Figure 3.9: Mesh region shown structured meshes across the domain ......................................42
Figure 3.10: The geometric model as assembled in Blender ......................................................49
Figure 3.11: Presets for Inflow and outflow definitions (Source: Blender.org) ...........................50
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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Figure 3.12: The different volumes initialize types. (a) Volume Initialize (b) Shell Initialize (c)
Initialize both shell and volume (Source: Blender.org) ................................................................51
Figure 3.13: Presets for Domain definition (Source: Blender.org) .............................................52
Figure 3.14: (a) Wire frame view of the computational domain as modeled in Blender.(b)
Camera view of the rendered domain in Blender........................................................................54
Figure 4.1: Plots of the velocity magnitude for a standard К-Ƹ run ............................................57
Figure 4.2: Contours of velocity vector depicting velocity magnitude (a) RNG К-Ƹ model,
Implicit scheme (b) RNG К-Ƹ model Explicit scheme, (c) Standard К-Ƹ model (d) RSM model ...58
Figure 4.3: Contour plots showing the separation curve (drops).(a) with a RNG к-ƹ (b) with a
standard к-ƹ ................................................................................................................................59
Figure 4.4: Plot of velocity magnitude for a RNG К-Ƹ run. ..........................................................59
Figure 4.5: The Computational Domain (Type B) Showing the Velocity inlet Boundary
Condition assigned to the lower third of the Upstream ........62
Figure 4.6: Sequence of flow in the velocity inlet upstream boundary condition .......................63
Figure 4.7: Series of short wave formation as then ....................................................................64
Figure 4.8: Plot of mass flow rate versus successive ..................................................................64
Figure 4.9: Non-dimensional horizontal component of ..............................................................66
Figure 4.10: Non dimensionalised Horizontal component of the velocity at x/Ho .....................66
Figure 4.11: Non-dimensionalised (a) Horizontal component of the .........................................67
Figure 4.12: Contour plots of Computational Domain type 2 with the lower position pressure
inlet at the upstream region........................................................................................................68
Figure 4.13: Render images (a) flow over submerged weir (b) unrealistic propagation of fluid
flow towards downstream of channel.........................................................................................70
Figure 4.14 (a) Rendered view showing flow towards outlet (b) Rendered image of the flow as
seen through channel set to transparent ....................................................................................71
Figure 4.15: Views of the wireframe of the computational Domain ..........................................71
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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Figure 4.16: Rendered View (a) Time = 5secs, Velocity = 10m/s, Real well size 0.030secs, with
bake resolution of 50 (b) Time = 5secs, Velocity = 10m/s with bake resolution of 50, Real well
size 0.030secs, .............................................................................................................................72
Figure 4.17: Rendered Images obtained from animation of flow over.......................................73
Figure 4.18: Rendered image at stream wise velocity of -0.5 and real world size of 0.030 .......74
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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List of Abbreviations
ALE Arbitrary-Lagrangian-Eulerian
CFD Computational Fluid Dynamics
CSOs Combined sewer overflow systems
CSs Combined sewers
FSH Free Surface Height
FSI Fluid-structure interaction
FSM Fractional Step
H&S Hager & Schwalts
H, W&M D. M. Hargreaves, N. G. Wright and H. P. Morvan
LBM Lattice Boltzmann Method
MAC Marker-and-Cell
NITA Non-Iterative Time Advancement option
NS Navier-Stokes
PDEs Partial Differential Equations
SPH Smoothed Particle Hydrodynamics
TH Total Height
UIDs Unsatisfactory intermittent discharges
UWWTD Urban Wastewater Treatment Directive
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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List of Symbols
b channel width
τ stress tensor
C discharge coefficient
g gravitational acceleration
Ho upstream energy head
ho upstream water level
ht tailwater height
hw weir height
k turbulence kinetic energy
l distance around the weir
w l weir length
p pressure
p0 total pressure
Q discharge
t time
u horizontal component of velocity
v velocity
V upstream stream wise velocity
y height above datum
0 y datum height
αa volume fraction of air
α i volume fraction of the i th phase
α w volume fraction of water
ε turbulence dissipation rate
ζ w relative weir length
ρ density
ρ air density
ρw water density
τ stress tensor
μ dynamic viscosity
К-Ƹ K-epsilon
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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Acknowledgment
To God my creator, my advocate and ever present help, for being a still small voice.
To my father, for from him I learnt the values of responsibility to self, family and society.
To my mother, from whom I learnt the virtues of perseverance, patience and Godliness.
1. INTRODUCTION
The design of hydraulic structures has reached such a level of sophistication that details
of the flow through the components can be predicted with reasonable accuracy. In the
past, such information depended largely upon experimental work, with designs relying
heavily on empirically based methods. Advances in computer technology have provided
high speed computing tools for solving approximations to the Navier Stokes equations.
This has resulted in the emergence of the new technology, computational fluid dynamics
(CFD) as a complementary tool to earlier design methods. This technology now enables
designers to carry out a large numbers of computations in a shorter time thus providing
more reliable designs. In the past, the design verification required extensive testing of
model hardware. With the CFD technology, almost all the testing can be performed
numerically. Thus, the costly and time consuming exercise of building and testing the
hardware can largely be avoided. Before I progress into this research work, it is important
that the characteristics of fluids be explained with a short introduction of why the
prediction of its motion is important to Engineering.
1.1. The Theory of Fluid Simulation
A much more technical understanding of the term fluid is required for a better
understanding and appreciation of computational fluid dynamics. Fluid is more of an
effect than a substance. It is a motion that behaves different in many substances and
ranges from small scale effects such as smoke rising from a cigarette to large scale effects
such as waterfalls and ocean waves. The engineering challenge is to understand the
physical behaviours of this fluid motion and therefore be able to predict the outcomes of
its interactions within several engineering context. For example, it would be a
phenomenal achievement to be able to predict the small scale fluid motions like water
coffee in cup or water in a bathtub to much complex motions like underground water
movement or cosmic explosions. Hence the engineering challenge is to simulate, in order
words, predict the dynamic behaviour of this fluids through mathematical and analytical
methods. This is the whole idea behind computational fluid dynamics. There are several
methods through which this is achieved and usually involves solving the Navier-Stokes
equations with various algorithms. The implemented approach all depends on the specific
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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application, the idea is to achieve fluid-like effects in real-time. Hence the understanding
of the Navier-Stokes equations is the first step in the grasp of CFD.
1.2. The Navier-Stokes Equations
The Navier-Stokes differential equations are a set of partial differential equations (PDEs)
that illustrate the motion of viscous incompressible fluids. Thus the first assumption in
this theory is that fluids are indeed a collection of particles. Therefore the Navier-Stokes
principle describes the properties of fluid exclusively by its viscosity and density. The
terms describe the forces acting on a particle, derived by observing the behavior in a unit
cube around the particle. This is done under the assumption that the fluid inside this unit
cube behave uniformly. The Navier-Stokes equations were derived from Newton’s second
law of motion, which states that
Force = mass x acceleration
They describe the changes in a velocity vector, i.e. the acceleration of the fluid, as a sum
of the forces acting on the fluid including forces introduced by the fluids own movement.
In a compact vector notation the Navier-Stokes equations are presented as:
1.2.1. External Forces
Navier-Stokes’ first equation represents external forces and is given by the following
expression:
Where the force field , is the addition of all external forces . ρ is the
density of the fluid, which describes the mass of a unit cube of fluid. ū is a vector quantity.
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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There are four equations and four unknowns: u, v, w, p. the four terms on the right-hand
side of Equation (1) represent accelerations. (Jiyuan, T. et al., 2008)
1.2.2. Advection
The second term in the Navier-Stokes equations represents advection. This describes the
force of the fluid motion working on itself or in simple term the interaction between
molecules of fluid bouncing into each other and distributing inertia on collision with other
particles. The contribution of advection is described by:
A test of Advection is an effective way of verifying and validating fluid simulation,
particularly with high graphically displayed simulations, and as will be introduced latter
should be a convenient validation test for Blender’s CFD capabilities.
1.2.3. Diffusion
Diffusion occurs when part of the fluid passes by an obstacle, or another part of the fluid
with a different velocity. The fluid is slowed down and vortices appear. The contribution
of diffusion is described by the term:
v is the kinematic viscosity of the fluid, simply describes how thick the fluid is, because
this affect the easy of fluidity of the fluid. This resistance, results in the diffusion of the
momentum (and therefore velocity), and hence the term diffusion.
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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1.2.4. Pressure
Fluid moving in and out of the observed unit cube causes the pressure to change.
Differences in pressure between the unit cube and its surroundings affect the velocity as
described given by
Where is the density of the fluid and p is the pressure. Because the molecules of a fluid
have freedom of interaction with their environment and each other, they tend to Squish
and Slosh. So any applied force to a fluid does not instantly propagate through the entire
volume. Instead, the molecular particles in close proximity to the force push on those
farther away, building up pressure with the fluid. This is immediately visible as the fluid
accelerates obviously from the inverse proportional relationship between pressure and
area. A phenomenon explained in Newton’s second law.
1.2.5. Incompressibility
To ensure that the volume of the fluid is kept constant, the net flow of the unit cube
should be zero, indicating that the amounts of fluid entering and leaving the cube should
be equal. This is described by the incompressibility constraint:
What is most important in when simulation fluids is to correctly determine the current
velocity field at each step in time. Therefore solving the Navier-Stokes equations for
incompressible flow acquires the velocity field that can be utilized to move fluids, objects
and other quantities through space and time.
1.3. Weir applications in Hydraulic Structures
Weirs have found several applications in many hydraulic structures main for flow
measuring purposes or as overflow structures. Sewer overflow systems are a typical
example of the latter and are a design necessity in many combined sewer systems to
ensure that any excess flow which is typical in combined sewer systems is discharged in a
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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controlled way and at specified and managed locations. Combined sewers (CS’s) are
responsive to rainfall. The heavier the rain, the greater the flow the sewer has to carry
therefore wet weather or intense storms persisting over a long period of time makes the
combined sewers particularly vulnerable because combined sewers are known to carry
municipal wastewater and rainfall in the same pipes prior to discharge. It is inevitable in
heavy rainfall or equivalent weather events that some of these sewers will be
overwhelmed.
The overloading, if not relieved by combined sewer overflow systems (CSOs), would lead
to storm sewage flooding homes, gardens, streets, highways, open spaces and surface
waters at discharge locations. CSOs are therefore essential structures in many combined
sewer systems. When the system is full, they act as release valves designed to carry any
excess flow by underground pipes to an outfall point, often a local watercourse. The
discharge from the sewer is substantially diluted by rainwater and joins a watercourse
swollen by rainfall. In July 2009 the UK recorded the heaviest rainfalls since 1888 in
England and Wales hence the concern for the improvements in the design of CSOs (B.
Thompson, 2006). In the UK the development of sewerage systems has been based on
the conveyance of domestic and industrial effluents and the surface runoff from
catchment surfaces in underground conduits.
Figure 1.1: Three Broad Crested Weir Setup at the Bedford Ouse Watercourse (EA, 2008)
Three types of system are used:
1. Combined systems, where foul and surface waters are conveyed in the same conduit
2. Separate systems, where foul and surface waters are conveyed in different conduits
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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3. Partially separate systems, which are a combination of the combined and separate
systems.
Figure 1.2: Measuring Flows with Weir (Source: Michigan State University Archives)
However, the most common type of sewerage system utilised in the UK is the combined
system. Combined sewerage systems incorporate combined sewer overflow systems
(CSOs) to divert excess flows received during storm events into discharge surface waters,
thus relieving other hydraulic structures within the system and reducing the risk of
flooding in urban areas. Discharges from CSOs, known as intermittent discharges, contain
both foul sewage and storm water and therefore contain large amounts of pollutants,
including gross solids and finely suspended solids in solution. THE UK Environment Agency
also identified a total of over 4,500 unsatisfactory intermittent discharges (UID) which
required improvement and it is anticipated that approximately 2000 more will require
attention over the next five years (Thompson, 2006).
1.4. Flow over a Broad Crested Weir
Flow over weir systems are used to obtain spill flow data that is essential in the
calibration and design optimisation of sewer overflow systems. Hence, by using standard
weir equations, flow parameters can be measure and the derived data obtained help to
enhanced design and optimize the eventual performance of the CSOs. Since the
determination of spill flow discharge data is paramount in the design of effective sewer
overflow systems, the adoption of CFD simulations can proof a useful tool in predicting
discharges and other flow parameters.
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Thus, the developments of CFD applications have made immense contributions to solving
a vast range of engineering challenges. Once the results obtained can be validated, (i.e. a
test of whether the backend equations used give a solution that is a true representation
of the physical situation), its use can be relied on to give accurate interpretations of true
behaviours (Fach et al., 2009).
1.5. Free Surface Flow idealisation
Numerical solutions of the free surfaces in both two dimensional and three dimensional
Navier-Stokes models may be complicated, depending on the hydraulic conditions of the
problem at hand. What exactly is the problem with free surface modelling and
idealisation? To effectively answer this, let’s consider exactly what the term free surfaces
are. The reason for the free designation arises from the large difference in the densities of
the gas and liquid (e.g., the ratio of density for water to air is 998.9). A low gas density
means that its inertia can generally be ignored compared to that of the liquid. In this
sense the liquid moves independently, or freely, with respect to the gas. The only
influence of the gas is the pressure it exerts on the liquid surface. In other words, the gas-
liquid surface is not constrained, but free. In heat-transfer texts the term Stephen
Problem is often used to describe free boundary problems. It should be obvious that the
presence of a free or moving boundary introduces serious complications for any type of
analysis. For all but the simplest of problems, it is necessary to resort to numerical
solutions. Even then, free surfaces require the introduction of special methods to define
their location, their movement, and their influence on a flow (Flow science Inc. 2005).
A majority of fluid flow in real time often involve free surfaces in difficult geometries and
in most cases are very unsteady. Hydraulics structures for example in which free surface
flows are frequent include spillways, around bridge pilings, flood overflows, flows in
sluices, locks, and a host of other structures including natural and man-made rivers. The
ability to numerically model free surface flows is quite tedious but reward provided this
computations are done accurately and with reasonable computational resources. There is
absolutely not worth in attempting a simulation if the cost of building and testing a
replica physical model is cheaper (Flow science Inc. 2005). Many programs were adapted
to solving the partial differential equations describing the dynamics of fluids however, not
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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many programs are able to accurately solve equations involving free surfaces in their
simulations. The challenge is a traditional numerical one often referred to as the free-
boundary problem. A free boundary poses the difficulty that on the one hand the solution
region changes when its surface moves, and on the other hand, the motion of the surface
is in turn determined by the solution. Changes in the solution region include not only
changes in size and shape, but in some cases, may also include the coalescence and break
up of regions (Hou, 1995). This VOF method is especially applicable to flows having free
surfaces and in this review, I will attempt to illustrate the logic behind the VOF method.
1.6. Numerical method for modelling free surfaces
Let’s briefly introduce some numerical techniques and approaches that have been used to
model free surfaces, indicating the advantages and disadvantages of each method. It is
however essential to mention at this point that no matter the method employed; three
essential features are required to effectively model free surfaces:
1. A scheme is needed to describe the shape and location of a surface.
2. An algorithm is required to evolve the shape and location with time.
3. Free-surface boundary conditions must be applied at the surface.
1.6.1. The Lagrangian grid method
The Lagrangian grid method is conceptually the simplest means of defining and tracking a
free surface is to construct a Lagrangian grid that is imbedded in and moves with the
fluid. Many finite-element methods use this approach. Because the grid and fluid move
together, the grid automatically tracks free surfaces. At a surface it is necessary to modify
the approximating equations to include the proper boundary conditions and to account
for the fact that fluid exists only on one side of the boundary. If this is not done,
asymmetries develop that eventually destroy the accuracy of a simulation. The principal
limitation of Lagrangian methods is that they cannot track surfaces that break apart or
intersect. Even large amplitude surface motions can be difficult to track without
introducing re-gridding techniques such as the Arbitrary-Lagrangian-Eulerian (ALE)
method (Hirt et al., 1970)
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1.6.2. The Marker-and-Cell (MAC) method
The earliest numerical method devised for time-dependent, free-surface, and flow
problems was the Marker-and-Cell (MAC) method. This scheme is based on a fixed,
Eulerian grid of control volumes. The location of fluid within the grid is determined by a
set of marker particles that move with the fluid, but otherwise have no volume, mass or
other properties. This has been used primarily for two-dimensional simulations because it
requires considerable memory and CPU time to accommodate the necessary number of
marker particles. Typically, an average of about 16 markers in each grid cell is needed to
ensure an accurate tracking of surfaces undergoing large deformations. The disadvantage
of the MAC method is in its utilization of marker particles. Particles utilized in the MAC
method do not follow flow processes in regions involving converging/diverging flows.
Markers are usually interpreted as tracking the centroids of small fluid elements.
However, when those fluid elements get pulled into long convoluted strands, the markers
may no longer be good indicators of the fluid configuration (Harlow and Welch, 1965).
Aliabadi et al. (2003) reviewed methods used to address the free-surface issue in
multidimensional modelling. The choice of technique depends on the complexity of the
expected free-surface shape. A common question is whether small water-surface
displacement is expected, or whether breaking waves and hydraulic jumps are expected.
1.6.3. The Volume of Fluid Method
One of the advantages of the VOF method is that the water surface need not be smooth
or even single-valued. Since this method will be utilized in this report to model free
surfaces is mandatory that this be introduced extensively. The volume of fluid method is
based on the concept of a fluid volume fraction. The idea for this approach originated as a
way to have the powerful volume tracking feature of the MAC method without its large
memory and CPU costs. Within each grid cell (control volume) it is customary to retain
only one value for each flow quantity (e.g. pressure, velocity, temperature,) For this
reason it makes little sense to retain more information for locating a free surface.
Following this reasoning, the use of a single quantity, the fluid volume fraction in each
grid cell, is consistent with the resolution of the other flow quantities.
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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If we know the amount of fluid in each cell it is possible to locate surfaces, as well as
determine surface slopes and surface curvatures. Surfaces are easy to locate because
they lie in cells partially filled with fluid or between cells full of fluid and cells that have no
fluid. Slopes and curvatures are computed by using the fluid volume fractions in
neighboring cells. It is essential to remember that the volume fraction should be a step
function, i.e., having a value of either one or zero. Knowing this, the volume fractions in
neighboring cells can then be used to locate the position of fluid (and its slope and
curvature) within a particular cell (Hirt and Nichols, 1998).
Free-surface boundary conditions must be applied as in the MAC method, i.e., assigning
the proper gas pressure (plus equivalent surface tension pressure) as well as determining
what velocity components outside the surface should be used to satisfy a zero shear-
stress condition at the surface. In practice, it is sometimes simpler to assign velocity
gradients instead of velocity components at surfaces. Finally, to compute the time
evolution of surfaces, a technique is needed to move volume fractions through a grid in
such a way that the step-function nature of the distribution is retained. The basic
kinematic equation for fluid fractions is similar to that for the height-function method,
where F is the fraction of fluid function:
A straightforward numerical approximation cannot be used to model this equation
because numerical diffusion and dispersion errors destroy the sharp, step-function nature
of the F distribution. It is easy to accurately model the solution to this equation in one
dimension such that the F distribution retains its zero or one values. Imagine fluid is filling
a column of cells from bottom to top. At some instant the fluid interface is in the middle
region of a cell whose neighbor below is filled and whose neighbour above is empty. The
fluid orientation in the neighbouring cells means the interface must be located above the
bottom of the cell by an amount equal to the fluid fraction in the cell. Then the
computation of how much fluid to move into the empty cell above can be modified to
first allow the empty region of the surface-containing cell to fill before transmitting fluid
on to the next cell (Hirt and Nichols, 1981).
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In two or three dimensions a similar procedure of using information from neighboring
cells can be used, but it is not possible to be as accurate as in the one-dimensional case.
The problem with more than one dimension is that an exact determination of the shape
and location of the surface cannot be made. Nevertheless, this technique can be made to
work well as evidenced by the large number of successful applications that have been
completed using the VOF method.
The VOF method has lived up to its goal of providing a method that is as powerful as the
MAC method without the overhead of that method. Its use of volume tracking as
opposed to surface-tracking function means that it is robust enough to handle the
breakup and coalescence of fluid masses. Further, because it uses a continuous function it
does not suffer from the lack of divisibility that discrete particles exhibit (Nichols and Hirt,
1980).
1.7. The Problem Statement
As a result, a significant amount of research into optimizing the design of hydraulic
structures related issues has taken place in recent years, one of which looks into ways of
optimizing the design of CSOs. FLUENT has been successfully utilized in the analysis of
CFD models and have achieved a reasonable degree of validation. However, it is not short
of certain drawbacks, one of which is the accurate definition of free surfaces (the
interface between gas and liquid). The difficulty is a classical mathematical one often
referred to as the free-boundary problem. A free boundary poses the difficulty that on
the one hand the solution region changes when its surface moves, and on the other hand,
the motion of the surface is in turn determined by the solution.
Fluid-structure interaction (FSI) is another important and interesting phenomenon, but it
is a difficult challenge for numerical modeling. However there are several cases in which
the interaction between the fluid and adjoining structure governs the physical behaviour
of the system. Although FLUENT is constantly modified to conveniently idealise and solve
fluid structure interactions, other applications have achieved significant progress in
idealising and represent this phenomena. A recent example is an open source application,
Blender 2.49, originally a 3D animation package that was development with backend fluid
dynamic equations and thus capable of carrying out computational fluid simulation.
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Blender’s accurate definition of free surfaces makes it effective in potentially idealising
both free surfaces and fluid structure interactions and thus a greater advantage over
FLUENT. However, since initially not developed to carryout computational fluid
simulations, this project is aimed at verifying and validating its effectiveness as a CFD
package using flow over a broad crested weir. It is expected that results and finding from
this dissertation will aid in optimising the design of combined sewer overflow systems.
1.8. Project Scope
A validated flow over a broad crested weir will be simulated using the volume over fluid
method to idealise flow in free surfaces. Using the blended application, a replicate flow
over a broad crested weir will also be simulated and a comparison of results obtained
between the two applications will be studied to verify and validate the effectiveness of
the Blender applications as an efficient CFD application. The project will also examine the
accuracy of Blender in idealising free surface flows in comparison to the VOF method
applicable in the FLUENT application.
1.9. Aims and Objectives
As computational fluid dynamics finds applications in a number of increasing industrial
and professional disciplines, the accuracy of their various CFD predictions becomes a
problem because of the simplified mathematical nature of the equations, solved
inevitably incorporating terms which generate falsely idealised physical theories.
Therefore, whereas accurate predictions are required to produce reliable designs and
optimise system performances, most professional and industrial users simply assume the
validation of these applications. This lack of validation creates knowledge gaps in areas
new to CFD.
Thus it is therefore the aim of this report to provide a proof of verification (i.e. to test
whether the numerical solution is an accurate solution of the equations set up to
represent the physical situation) and validation (i.e. a test of whether the equations used
give a solution that is representative of the physical situation) for the Blender application.
The objectives will however include the following;
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To investigate the capabilities of the FLUENT application in accurately predicting and
providing the true physical representation of the free surface flow phenomena using
the volume of fluid method.
To investigate the capabilities of the Blender application in accurately predicting and
providing the true physical representation of the free surface flow phenomena.
To compare and evaluate the performances of both applications in idealising the free
surface flow phenomena.
To validate the effectiveness of the Blender applications as an efficient CFD
application.
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2. LITERATURE REVIEW
2.1. Computational fluid Dynamics
The CFD (Computational Fluid Dynamics) is a powerful tool in the field of fluid flows. This
is a mathematical approach using numerical methods to solve partial differential
equations. These equations describe in a mathematical way the flow of fluid and all
connected phenomena. The fundamental steps of a complete CFD solution procedure are
in Figure 1. The first step is a theoretical analysis of the problem. The next step is a
solution pre-processing consisting of the preparation and schematization of the
computational domain, generation of a mesh for discretization, selection of a suitable
mathematical solution model and an effective numerical solver. It is followed by a
computational stage and the selection of suitable checkpoints to monitor the
convergences of the solution. An important part of the whole stage is the review and
verification of the results. It is a great advantage if the results can be compared with the
measured data in a model or a prototype structure. If any discrepancies or major
differences are reported, revisions in some steps of the solution procedure are necessary,
i.e. changing the computational mesh, changing the settings of the solver at its start or
choosing a more appropriate built-in model and repeating the computation (Kantor,
2007).
Figure 2.1: Fundamental Steps of CFD Analysis
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The advantages of CFD are:
It supplements results obtained from physical modeling and gives results above
the limits of the experimental stage.
It provides data which cannot be achieved in the experimental stage.
It is less expensive than the laborious experimental stage with many repetitions.
It shortens the time of innovative development of a new product or water
industry technology.
It is more flexible to implement any changes and bring new options and strategies
of solutions.
It explains reasons not effects.
Some notable disadvantages of CFD are:
It requires a CFD specialist and expert in fluid problems as well.
As computations are intensive the computer performance required must be very
high.
It is generally known that the dynamics of a simple fluid is described in the most general
form, by the Navier-Stokes equations (Chirila, 2010)
Where:
Is the fluid velocity
Is the density of the fluid
Is the pressure
Is the kinematic viscosity of the fluid and
Is the acceleration due to external forces acting upon the fluid element
After writing down the initial equations, we may employ a series of order-of-magnitude
estimates and manipulations to simplify the equations for the particular system (e.g.
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ocean, atmosphere, industrial flow problem and several others. In most practical
situations, the system is too complex to be reduced to a system of equations which are
analytically tractable, especially if we are asking detailed questions (e.g. will it be a sunny
day tomorrow in Leeds?) instead of more general questions (e.g. what is the average
humidity of the earth’s atmosphere?). One way of making further progress in such
complex situations is to integrate the model equations numerically. This approach is not
devoid of dangers (as additional issues like accuracy of the computer’s floating-point
representations come into play). However, it is, quite often, the best we can do. Perhaps
one of the first properties of numerical models that the beginner may realize is their
diversity (D. B. Chirila, 2010).
Essential to every such approach is the way physical space is discretized or, more exactly,
none which kind of space sub-division is the numerical integration performed. Our exact
partial differential equations are then ultimately translated to algebraic difference
equations, which are then solved locally at each space sub-division. The specific solution
algorithms are also themselves adapted to the type of space sub-division (also known as
mesh types), so one generally assigns a name to the pairs of mesh and algorithm (Chirila,
2010).
2.2. CFD Analysis with ANSYS FLUENT
The FLUENT application has been around for close to 5 decades and was first introduced
in the late 70’s. This ANSYS fluid dynamics software offers unparalleled breadth and
depth in the modeling of fluid flow related physics phenomena. Viscous and turbulent,
internal and external flows and a broader list of physical phenomena such as modeling
multiphase flows, chemical reaction, and combustion can be calculated with ease. A
variety of solver methods and numerical schemes are available. This includes finite-
volume solvers using both coupled and segregated methods for general fluid flow
modeling, and a finite-element solver for viscous flows of complex fluids. Fully
unstructured grids can be used with all common cell-types, including polyhedral meshes.
ANSYS FLUENT software contains the broad physical modeling capabilities needed to
model flow, turbulence, heat transfer, and reactions for industrial applications ranging
from air flow over an aircraft wing to combustion in a furnace, from bubble columns to oil
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platforms, from blood flow to semiconductor manufacturing, and from clean room design
to wastewater treatment plants. Special models that give the software the ability to
model in-cylinder combustion, aero-acoustics, turbo-machinery, and multiphase systems
have served to broaden its reach. Perhaps the most intriguing capability is the
applications interactive solver set-up, solution, and post-processing capabilities which
make it easy to pause a calculation, examine results with integrated post-processing,
change any setting, and then continue the calculation within a single application.
2.3. CFD Analysis with Blender 2.49
Blender is a 3D graphics application used predominantly for animation and movie making.
It has a convincing 3 dimensional modeling prowess that has amazed CFD experts and
defiles most present technology with regards to computing accuracy and capabilities of
today’s computers. An open source application, Blender has been able to product
simulations that compete with most present day industrial and academic CFD
applications. This modeling and animation program also competes with much more
expensive commercial products such as Autodesk Maya, yet, unlike other free and low-
cost alternatives, Blender runs fast, never crashed, and offers a wealth of deep features.
Blender was developed as an in-house application by the Dutch animation studio Neo-
Geo and Not a Number Technologies. It was primarily authored by Ton Roosendaal.
Thuerey (2007) developed a fluid simulation capability for it, called El'Beem, from his
work in modeling metal foams using the Lattice Boltzmann Method (LBM) for fluid flow.
Blender Fluid Simulation is meant primarily for animation graphics and is not physically
rigorous. However, it contains gravity, mass, inertia, and viscosity and has often been said
to have surface tension capabilities as well. Viscosity choices are listed in the program for
water, honey, oil and "manual". According to Thuerey (2007), the "realworld-size"
variable, which is listed as the longest dimension of the solution domain in meters, is
primarily used to adjust the visual viscosity of the fluid. So all one can say is that when it is
set to water, it models a fluid that behaves similarly to water in a domain of loosely know
scale. In some cases, It looks exactly and even better than water.
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Figure 2.2: The Blender working environment
The algorithm used for Blender’s fluid simulation is the Lattice Boltzmann Method (LBM);
other fluid algorithms include Navier-Stokes (NS) solvers and the Smoothed Particle
Hydrodynamics (SPH) methods. Therefore, a review of this computational method is
necessary.
2.3.1. Lattice Boltzmann Numerical Method
There are some additional non traditional methods such as the Lattice Boltzmann Models,
which was adopted by the developers of the Blender application. LBM is advantageous as
a numerical method because of its simplicity of coding but also has several disadvantages,
the most serious being the relative stiffness of the approach relative to the equations it
eventually integrates. In simple terms this disadvantage requires that some extra effort is
required for solving anything different from the Navier-Stokes equations. Lattice
Boltzmann Methods evolved out of Lattice-Gas Cellular Automata (LGCA), statistical toy-
models (inspired by the kinetic theory of gases, to which Ludwig Boltzmann brought
significant contributions, which simulated a gas through particles at discrete points in
space represented by Boolean variables. This means that the mass of a particle is fixed to
1.
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(a) (b)
Figure 2.3: A Typical Lattice structure in (a) 2D and (b) 3D (Source: D. B. Chirila, 2010).
LGCA and LBM are both sub-classes of Cellular Automata. Common characteristics for all
of these models include:
Set of connected sites (the lattice)
Some state-variables defined at each site (several Boolean variables for LGCA or
several real variables for LBM, as will be explained in next section)
An update rule, based on local and neighbour information (for LGCA and LBM, we have
a composite update rule, namely collision and streaming)
Perhaps the most important characteristic of the models was the discretization of velocity
space, which means that particle velocities were restricted to a finite set of orientations.
Denote by the discretized probability distribution functions , thereby eliminating the
need for ensemble averaging (D. B. Chirila, 2010). At each time-step, the particles move
along their corresponding directions, approaching the next lattice point. If more than one
of these Boolean particles arrive simultaneously at the same lattice point, a collision rule
is applied, which re-distributes the particles such that the conservation laws (for mass and
momentum) are satisfied. The lattice Boltzmann method is a powerful technique for the
computational modeling of a wide variety of complex fluid flow problems including single
and multiphase flow in complex geometries. It is a discrete computational method based
upon the Boltzmann equation (D. B. Chirila, 2010). It considers a typical volume element
of fluid to be composed of a collection of particles that are represented by a particle
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velocity distribution function for each fluid component at each grid point. The time is
counted in discrete time steps and the fluid particles can collide with each other as they
move, possibly under applied forces. The rules governing the collisions are designed such
that the time-average motion of the particles is consistent with the Navier-Stokes
equation (D. B. Chirila, 2010).
2.3.2. Smooth Particle Hydrodynamic Numerical method
The smoothed particle hydrodynamics (SPH) can simply be described as a method that
obtains an approximate numerical solution to fluid dynamics equations by replacing the
fluid with a set of particles. From the mathematician point of view, the particles are just
interpolation points from which properties of the fluid can be calculated. Physicists on the
other hand, consider the SPH particles to be material particles and therefore can be
treated like any other particle system. Without going into the entire numerical solution,
the SPH method provides the following advantages (Monaghan, 2005)
Pure advection is treated exactly. For example, if the particles are given a colour, and
the velocity is specified, the transport of colour by the particle system is exact.
Modern finite difference methods give reasonable results for advection but the
algorithms are not Galilean invariant so that, when a large constant velocity is
superposed, the results can be badly corrupted.
In the case of multiply materials each described by its own set of particles, interface
problems are often trivial for SPH but difficult for finite difference schemes.
The introduction of particles, bridge the gap between the continuum and
fragmentation in a natural way. Consequently, the best current method for the study
of brittle fracture and subsequent fragmentation in damaged solids is the SPH method.
Resolution can be adjusted to depend on position and time, which makes the method
very attractive for most astrophysical and geophysical problems.
This method holds a computational advantage, particularly in problems involving
fragments, drops or stars that focus the computation only where the matter resides.
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Finally, because of the SPH method has large similarities with molecular dynamics,
complex physical theories can easily be included
However, one often reoccurring argument regarding this method is the uncertainty and
prior identification of which particles during interactions would reproduce the equations
of fluid dynamics or continuum mechanics. (Monaghan, 2005)
2.4. Multiphase Flow
The term multiphase flow refers to any fluid flow consisting of more than one phase or
component, which are show some level of phase separation at a scale well above the
molecular level. Examples include gas/solids flows, or liquid/solids flows or gas/particle
flows just to mention a few (Brennen, 2005). Flows of this nature often pose differs
challenges with regards to solving flow equations, however virtually every processing
technology must deal with multiphase flows. In turbines for example, several multiphase
flows are typical industrial experiences. Multiphase flow phenomena are frequent in
electro photographic processes to papermaking, to the pellet form of almost all raw
plastics. The amount of granular material that is transported every year is enormous and,
at many stages, that material is required to flow.
2.4.1. Real-time Multiphase Flows
Clearly the ability to predict the fluid flow behaviour of these processes is central to the
efficiency and effectiveness of those processes. For example, the effective flow of toner is
a major factor in the quality and speed of electro photographic printers. Multiphase flows
are also a ubiquitous feature of our environment whether one considers rain, snow, fog,
avalanches, mud slides, sediment transport, debris flows, and countless other natural
phenomena to say nothing of what happens beyond our planet.
Very critical biological and medical flows are also multiphase, from blood flow to semen
to the bends to lithotripsy to laser surgery cavitations and so on. No single list can
adequately illustrate the diversity and ubiquity; consequently any attempt at a
comprehensive treatment of multiphase flows is flawed unless it focuses on common
phenomenological themes and avoids the temptation to digress into lists of observations.
Two general topologies of multiphase flow can be usefully identified at the outset,
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namely disperse flows and separated flows. By disperse flows we mean those consisting
of finite particles, drops or bubbles (the disperse phase) distributed in a connected
volume of the continuous phase. On the other hand separated flows consist of two or
more continuous streams of different fluids separated by interfaces (Brennen, 2005).
2.4.2. Multiphase flow models
A persistent theme throughout the study of multiphase flows is the need to model and
predict the detailed behavior of those flows and the phenomena that they manifest.
There are three ways in which such models are explored (Brennen, 2005):
Experimentally, through laboratory-sized models equipped with appropriate
instrumentation,
Theoretically, using mathematical equations and models for the flow, and
Computationally, using the power and size of modern computers to address the
complexity of the flow.
Clearly there are some applications in which full-scale laboratory models are possible.
But, in many instances, the laboratory model must have a very different scale than the
prototype and then a reliable theoretical or computational model is essential for
confident extrapolation to the scale of the prototype. There are also cases in which a
laboratory model is impossible for a wide variety of reasons. Consequently, the predictive
capability and physical understanding must rely heavily on theoretical and/or
computational models and here the complexity of most multiphase flows presents a
major hurdle. It may be possible at some distant time in the future to code the Navier-
Stokes equations for each of the phases or components and to compute every detail of a
multi-phase flow, the motion of all the fluid around and inside every particle or drop, the
position of every interface. But the computer power and speed required to do this is far
beyond present capability for most of the flows that are commonly experienced. When
one or both of the phases becomes turbulent (as often happens) the magnitude of the
challenge becomes truly astronomical. Therefore, simplifications are essential in realistic
models of most multiphase flows.
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In disperse flows, two types of models are prevalent, trajectory models and two-fluid
models. In trajectory models, the motion of the disperse phase is assessed by following
either the motion of the actual particles or the motion of larger, representative particles.
The details of the flow around each of the particles are subsumed into assumed drag, lift
and moment forces acting on and altering the trajectory of those particles. The thermal
history of the particles can also be tracked if it is appropriate to do so. Trajectory models
have been very useful in studies of the rheology of granular flows primarily because the
effects of the interstitial fluid are small. In the alternative approach, two-fluid models, the
disperse phase is treated as a second continuous phase intermingled and interacting with
the continuous phase.
Effective conservation equations (of mass, momentum and energy) are developed for the
two fluid flows; these included interaction terms modeling the exchange of mass,
momentum and energy between the two flows. These equations are then solved either
theoretically or computationally. Thus, the two-fluid models neglect the discrete nature
of the disperse phase and approximate its effects upon the continuous phase. Inherent in
this approach, are averaging processes necessary to characterize the properties of the
disperse phase; these involve significant difficulties. The boundary conditions appropriate
in two-fluid models also pose difficult modeling issues. In contrast, separated flows
present many fewer issues. In theory one must solve the single phase fluid flow equations
in the two streams, coupling them through appropriate kinematic and dynamic conditions
at the interface.
2.5. Methodology of the VOF Method
Critical emphasis is placed on the VOF method in this research and as enumerated in the
research objective and would be the numerical computational method utilised to validate
the applications. The VOF method has been known for several decades and gone through
several process of improvement. Their use and effectiveness are widespread, for several
reasons:
1. They preserve mass in a natural way, as a direct consequence of the development of
an advection algorithm based on a discrete representation of the conservation law.
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2. No special provision is necessary to perform reconnection or breakup of the interface
and in this sense the change of topology is implicit in the algorithm.
3. They can be relatively simply extended from two-dimensional to three dimensional
domains.
2.5.1. The Basic Theory
The goal of this discussion is to show why the VOF approach offers a natural way to
capture free surfaces and their evolution with great efficiency. There are a few general
concepts about computational methods and the VOF technique in particular that can be
used to gain an understanding of how and why VOF works so efficiently. All numerical
methods must use some simplification to reduce a fluid flow problem to a finite set of
numerical values that can then be manipulated using elementary arithmetical operations.
A typical procedure for approximating a continuous fluid by a discrete set of numerical
values is to subdivide the space occupied by the fluid into a grid consisting of a set of
small, often rectangular “bricks.” Within each element an averaging process is applied to
obtain representative element values for the fluid’s pressure, density, velocity and
temperature.
Simple equations can be devised to approximate how each element’s values interact with
neighbouring elements over time. The density for example of an element can only change
when there is a net flow of mass exchanged between an element and its neighbours (i.e.,
conservation of mass). The material velocity that carries mass between elements is
computed from the conservation of momentum principal, usually expressed in the form
of the Navier-Stokes equations, which uses the pressures acting between neighbouring
elements to approximate the changing fluid velocities in the elements.
This idea of an element interacting with its neighbours is essentially what is meant by a
partial differential equation; that is, evaluating the effects of small changes caused by the
variation in quantities nearby (Flow science Inc., 2005). Partial differential equations are
typically derived in engineering text books as the limit of approximations made with small
control volumes whose sizes are then reduced to infinitesimal values. In a numerical
simulation the same thing is done except that the control volume sizes cannot be taken to
the limit because that would require too many elements to keep track of. In practice, the
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goal is to use enough elements to resolve the phenomena of interest, and no more, so
that computing times are kept to a minimum.
Arithmetical operations associated with an element generally involve only simple
addition, subtraction, multiplication and division. For instance, the change of mass in an
element involves the addition and subtraction of mass entering and leaving through the
faces of the element over a fixed interval of time. A simulation requires that these
operations be done for thousands or even millions of elements as well as repeated for
many small time intervals. Computers are ideal for performing these types of repetitive
operations very rapidly. Simulating fluid motion with free surfaces introduces the
complexity of having to deal with solution regions whose shapes are changing. A
convenient way to deal with this is to use the Volume of Fluid (VOF) technique described
next (Flow science Inc., 2005)
2.5.2. The VOF Concept
The VOF technique is based on the idea of recording in each grid cell the fractional
portion of the cell volume that is occupied by liquid. Typically the fractional volume is
represented by the quantity F. Because it is a fractional volume, F must have a value
between 0.0 and 1.0. In interior regions of liquid the value of F would be 1.0, while
outside of the liquid, in regions of gas (air for example), the value of F is zero. The location
of a free surface is where F changes from 0.0 to 1.0. Thus, any element having an F value
lying between 0.0 and 1.0 must contain a surface. It is important to emphasize that the
VOF technique does not directly define a free surface, but rather defines the location of
bulk fluid. It is for this reason that fluid regions can coalesce or break up without causing
computational difficulties. Free surfaces are simply a consequence of where the fluid
volume fraction passes from 1.0 to 0.0. This is a very desirable feature that makes the
VOF technique applicable to just about any kind of free surface problem (Flow science Inc.
2005).
Another important feature of the VOF technique is that it records the location of fluid by
assigning a single numerical value (F) to each grid element. This is completely consistent
with the recording of all other fluid properties in an element such as pressure and velocity
components by their average values (Flow science Inc., 2005).
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2.5.3. Details of the VOF Technique
For accuracy purposes it is desirable to have a way to locate a free surface within an
element. Considering the F values in neighbouring elements can easily do this. For
example, imagine a one-dimensional column of elements in which a portion of the
column is filled with liquid, Fig. 3. The liquid surface is in an element in the central region
of the column, which will be referred to as the surface element. Because we assume the
values of F must be either 0.0 or 1.0, except in the surface element, we can use this to
locate the exact position of the surface. First a test is made to see if the surface is a top or
bottom surface. If the element above the surface element is empty of liquid, the surface
must be a top surface. It the element above is full of liquid then, of course, the surface is
a bottom surface. For a top surface we compute its exact location as lying above the
bottom edge of the surface element by a distance equal to F times the vertical size of the
element. A bottom surface is similarly located a distance equal to F times the vertical size
of the element below the top edge of the surface element. Locating the surface within an
element in this way follows from the definition of F as a fractional volume of liquid in the
element (Flow science Inc. 2005)
Calculating surface locations in one-dimensional columns is simple, accurate and requires
very little arithmetic. In two and three dimensional situations, however, computing a
location is a little more complicated because there is a continuous range of surface
orientations possible within a surface cell. Nevertheless, dealing with this is not difficult. A
two-dimensional example, Fig. 2.4, will illustrate a simple way to not only compute the
location of the surface, but also to get a good idea of its slope and curvature (Flow science
Inc. 2005)
Figure 2.4: Surface in 2d Grid of Elements.
(Source: Flow science Inc. 2005).
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As in the one-dimensional case, it is first necessary to find the approximate orientation of
the surface by testing the neighbouring elements. In Fig. 2.4 the outward normal would
be closest to the upward direction because the difference in neighbouring values in that
direction is larger than in any other direction. Next, local heights of the surface are
computed in element columns that lie in the approximate normal direction. For the two-
dimensional case in Fig. 2.4 these heights are indicated by arrows. Finally, the height in
the column containing the surface element gives the location of the surface in that
element, while the other two heights can be used to compute the local surface slope and
surface curvature.
In three-dimensions the same procedure is used although column heights must be
evaluated for nine columns around the surface element. Although a little more
computation is needed, it consists primarily of simple summations in the columns and
then sums and differences of column heights for evaluating the slope and curvature.
Based on this discussion, the reader should now see how the fractional fluid volume can
be used to quickly and easily evaluate all the information needed to define free surfaces.
The region occupied by fluid in the flow over a step problem is much less than half of the
open region in the computational grid. If it were necessary to also solve for the flow of
gas surrounding the liquid, then considerably more computational time would be
required. In order to perform solutions only in the liquid, however, it is necessary to
specify boundary conditions at free surfaces. These conditions are the vanishing of the
tangential stress and application of a normal pressure at the surface that equals the
pressure of the gas.
It is important to note that movement and deformation of a free surface must be
computed by solving for the fraction of fluid variable, F, as it moves with the fluid.
Because the variable F is discontinuous (i.e., primarily 0.0 or 1.0) some care must be taken
to maintain this discontinuity as it moves through a computational grid. In the VOF
method, special advection algorithms are used for this purpose.
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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2.5.4. Illustration of Free-Surface Tracking by VOF Technique
Fluid volume fraction is coloured uniformly in each grid element to represent its value in
that element. The free surface is sharply defined nearly everywhere. Only in the lowest
and narrowest part of the nappe is there any noticeable loss of a sharp fluid fraction
distribution, for computational purposes this doesn’t really matter because the simulation
method treats elements interior to the liquid as though they are pure liquid elements. It
should also be pointed out that turbulence and air entrainment are observed in actual
experiments. Thus, the appearance of fluid fraction values a little less than unity is
somewhat realistic. This is not erroneous because the intersection of jet of liquid with a
pool, which is responsible for turbulence and air entrainment, is also responsible for the
entrainment of fluid fraction values into the interior of the liquid (Flow science Inc. 2005).
Figure 2.5: Fluid Fraction Values in Elements, Showing Sharpness of
Surface Definition. (Source: Flow science Inc. 2005).
Figure 2.6: Close Up Of Fluid Fraction Values Where The Overflow Hits Bottom.(Source: Flow science Inc. 2005).
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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2.6. Review of Relevant Papers
Three papers which show close similarities either in terms of VOF application to an
idealised free surface flow regime or study of the characteristics of flow over a broad
crested weir are review in the research paper. Brief details have been documented
because they have shown close similarities to one or more aspects of this study. As a
basis for CFD validation of modelling free surfaces flows over common hydraulic
structures, our simulations will be compared against existing sets of experimental and
computational data available in existing literatures. In particular, one of the earliest
experimental studies of free surface flows was conducted by W.H Hager and Markus
Schwalt. Though an experiment study, their data for free surface flows over a broad
crested weir is adopted for validation purposes and would represent our basis of
comparison with experimental physical finding.
It is also necessary to review research works carried out by D.M. Hargreaves, N.G Wrights
and H.P Morvan on the validation of the VOF method for free surface calculation. Since
this research study provides the mean for comparing computational results of a similar
case scenario. In this paper, a series of CFD simulations are compared against an existing
set of experimental data for the free surface flow over a broad crested weir. The
experimental data was obtained from the Hager and Schwalt’s experiment of 1994.
A general search for non published findings or independent attempts to simulate free
surface flows also revealed a prototype simulation of the flow over a drop by the flow 3D
development team headed by C.W Hirt. This independent work attempted the CFD
validation of the energy loss at drop experiment by N. Rajaratnam and M.R. Chamani. A
review of the flow 3D team findings has been comprehensively documented because it
illustrates the accuracy of the VOF method.
2.6.1. Hager and Schwalt’s Experimental study of flow over weir
For the purpose of validation with an existing experimental data, this paper has utilized
one of the earliest research paper illustrating flow features of a free surface flow
situation. An experimental attempt by Hager and Schwalt in 1994 to study the flow
features over a broad crested weir. Their comprehensive experiment utilized a broad
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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crested weir of height 401mm and length 500mm placed in a horizontal rectangular
channel which was 499mm wide and 700mm high. Although their experiment was
basically to proposed the use of broad crested weirs as an additional standard structure
for hydraulic measurements and overflow structures against the general conception at
the time suggesting them to be poor overflow structures and not accurate in discharge
measurements. Hager and Schwalt, in their experiment were able to proffer conditions in
which if followed would render the broad crested weir efficient as a measuring structure
and an overflow structure. These conditions were documented as follows;
I. Sharp-crested upstream weir corner.
II. Vertical upstream face.
III. Smooth and horizontal weir surface.
IV. Weir length Lw such that 0.1 < ~ < 0.4.
V. Minimum overflow depth ho = 50 mm.
VI. Rectangular and straight approach and tail water channels.
2.6.2. CFD Validation of the Hager and Schwalt’s Experiment
For the purpose of validation with an existing CFD computational data, this paper has
adopted data from D.M. Hargreaves, N.G Wrights and H.P Morvan’s paper on the
validation of Computational fluid Dynamics for modeling free surface flows. In their
research work, Hargreaves et. al endeavoured the validation of the VOF method for free
surface calculations by attempting to CFD model of the Hager and schwalt’s experimental
research work, by conducting simulations of a broad crested weir of 400mm high and
500mm wide within a rectangular channel of 800mm high and 3500mm in length. Few
alterations were made to the CFD model, however the following summaries the CFD
model setup for the Hargreaves et al. validation study simulation.
Transient state was used as against the steady state solution method adopted in the
Hager and Schwalts experiment.
A geometric reconstruction surface tracking algorithm was used hence the need for
transient state.
The RNG К-Ƹ turbulence model was used.
The use of the Body forced-weight pressure discretization scheme
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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The use of second-order discretization scheme for the momentum, turbulence kinetic
energy and dissipation equations.
The use of the PISO pressure velocity coupling algorithm
A time step of 2.0 x 10-4 was used throughout to keep the simulation stable owning to
the demands of the VOF model
To successfully reach steady state, the team conducted close to two hundred and seventy
thousand time steps to arrive at a solution. The results revealed a slightly lowering of the
free surface upstream of the weir relative to the experimental results in the Hager and
Schwalts experiment. From this research D.M. Hargreaves et al. successfully validated
CFD applications in the modeling of free surface flows over hydraulic structures
Table 2.1: Results from the H&S Experiments and D.M. Hargreaves et al. CFD Simulations
Run
Notes Ho
(mm)
Q2(m3 s-1 x 10-3)
H&S CFD
1 2D, RNG 50.9 8.25 8.27
6 2D, RNG 60.7 10.90 10.84
7 2D, RNG 84.4 17.81 17.65
8 2D, RNG 108.4 25.98 25.74
9 2D, RNG 139.2 37.59 37.49
10 2D, RNG 178.0 54.83 54.42
11 2D, RNG 204.7 68.07
67.38
11b 2D, Standard К-Ƹ 69.38
11c 2D, RSM 66.96
11d 3D, RNG 68.37
2.6.3. Prototype CFD Simulation of Flow over a drop
Vast work had been done on the energy loss at a drop by numerous researchers, notably
White (1943), Gill (1979) and by N. Rajaratnam and M.R. Chamani (1995). However the
flow 3D team endeavour to carry out a CFD validation of the energy loss at a drop using
the VOF method. All of the geometric and material properties used in the N. Rajaratnam
and M.R. Chamani experiments of 1995 were used in the simulation.
A step height of 62cm
Water is the fluid in question with a know density and viscousity
Depth of water at inlet was set at 15.5cm and was given a velocity of 123.0cm/s.
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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Acceleration due to gravity = 9.81.
Figure 2.7: Simulation of Flow over a Step Showing Pressure Contours (Source: Flow
science, 2005)
Because some turbulence was expected to develop in the pool to the left of the overflow,
a turbulence model (the Renormalization Group or RNG model) was used in the
simulation. Subsequent simulations without a turbulence model produced very similar
results, which is not too surprising since most of the important elements of the flow are
smooth (i.e., non-turbulent) inflow, overflow and outflow streams.
To summaries a description of the CDF modeling, the left boundary was a specified
velocity boundary (also with a specified fluid height). The right boundary was an outflow
boundary where all flow quantities have a zero gradient normal to the boundary to
encourage a uniform outflow. The top and bottom boundaries are rigid walls, while in the
third direction the boundaries were treated as planes of symmetry (i.e., walls with zero
viscous drag). The surface of the step was also treated as a free-slip boundary. Initial
conditions could have been set to roughly approximate the expected flow arrangement.
Because a transient flow simulator was used, a simple initial condition was defined that
consisted of just a block of fluid on top of the step, Fig. 6 with the same horizontal
velocity and height assigned to the left boundary.
The overflow (sheet of liquid or nappe) leaving the top of the step has both an upper and
lower free surface. At the bottom of the overflow a pool has formed between the
overflow and the face of the step, while downstream, liquid is flowing to the right with a
flat, steady surface. Strictly speaking, the flow conditions in the pool region are not steady
because turbulent mixing is generated in the pool by the impinging fluid. There is,
however, an average configuration and that is what is reported in the experiments. As
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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expect with VOF iterations, considerable amount of computational time was required to
achieve such accuracy. The Flow 3D team stated a total CPU time on a desktop Pentium 4,
3.20GHz computer was 88s.
Table 2.2: Comparisons between experiment and simulation
Comparison Table Experimental Results Simulation Results
Outflow Height/Step Height 0.094 0.094
Pool Height/Step Height 0.41 0.41
Angle of Nappe at Bottom 57° 59°
Energy Loss/Initial Energy 0.29 0.296
(Source: Flow science Inc. 2005).
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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3. TEST CASE METHODOLOGY
Before the methodology for this research work is explained, I will provide a brief
introduction into the problems this research is aimed at addressing. ANSYS FLUENT as
discussed in the literature review is capable of carrying out free surface simulations, a
point well illustrated and experiment by a few researcher using more conventional
numerical simulation methods. However, this research study is aimed at validating ANSYS
FLUENT’s VOF method and therefore answers the question ‘How effective is FLUENT’s
VOF method in achieving results similar to a true physical free surface flow phenomenon’.
Likewise, simulations in Blender have shown impressive visual representations of complex
fluid flows but how realistic from an Engineering point of view are these simulations in
comparison with the physical free surface flow phenomena. Therefore, the methods
adopted enable the collection of data which can be compared with experimental results
typically the Hager and Schwalts 1994 experiment.
It becomes apparent at this juncture, that the starting point for comparison will be the
use of similar or identical domains in both applications. These pose a slight problem for
this study and it paramount that these be enumerated. Firstly, although Blender allows
the modeling of a geometrical domain, the unit less nature of the application only allows
scaling the geometries to its inbuilt grid system. In other words, while units of millimeter,
meters, inches and more can be specified in FLUENT, Blender is void of this. Secondly,
ANSYS FLUENT allows the extraction of data. A range of resulting data ranging from
pressure, turbulence, velocity, density and including custom field options for customizing
specific data at virtually every point in the domain. In Blender however, this will be a little
more challenging because the application was written for screen play and animation, this
capability was not designed within the application. To extract computed numerical data,
additional scripts would be required to convert embedded strings to readable
interpolative form. Without writing this script, Blender can only be compared and
validated by visually investigation. Having enumerated these challenges, the research
study proceeded to model and simulates free surface flow over a broad crested weir
setup in both applications.
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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3.1. Computational Domain
The simulations described here are run using ANSYS FLUENT. For the selection of weir
geometry, the following are thoroughly considered;
Figure 3.1: Schematics of the broad crested weir and notations (Hargreaves et al., 2007)
It is important to note that in the hydraulics of a broad crested weir the discharge
coefficient is related to the approach energy head and not to the approach flow depth.
Thus, the effect of velocity of approach is completely contained since the discharge
coefficient is related to the approach energy head and not to the approach flow depth.
In summary, the effect of velocity of approach is a function of the approach flow depth
and the weir height.
The weir configuration at the upstream should have a domain which extends as least
thrice the energy head (Ho) a requirement stated as a requirement by Boiten (2002) in
his study of weir discharge measurement.
For water, the typical limit head is some 30-50 mm. A distinct feature of the broad-
crested weir is the corner separation, which was analyzed by Moss (1972). Its length
was found to be 0.77ho, and its maximum height is 0.15ho. Tracy (1957) was able to
generalize the surface profile using ho as normalizing parameter, provided 0.1
0.4. Further, a number of limits concerning the approach flow depth, channel width,
weir height, and crest length were specified.
Crabbe (1974) expanded the application limits as proposed by Singer (1964) in terms of
weir length and weir height, and Sreetharan came up with limits as wide as 0.08 < <
5.6 and 0.006 < Ho/w < 4.
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
36
For large values of aeration of the lower nappe is essential.
According to Ramamurthy et al. (1987) the upstream corner of a broad crested weir
may be considered sharp provided the radius of curvature is smaller than R < 0.094w.
Thus, extreme sharpness of corner radius on the flow is not necessary.
For the validation study, a vertical slice 2D model was used. The use of a 2D model can be
justified on the grounds that Hager and Schwalts indicated their experiments were
essentially 2D in nature and only took measurements on the centerline in the channel.
With a 2D model it is possible to produce a grid that resolves the vertical and stream wise
directions with sufficient accuracy. Adding a third dimension severely limits the accuracy
of the simulations because of the necessarily reduced refinements in the 3 coordinate
directions. Flow features over a broad crested weir are to be investigated in a modeled
horizontal rectangular channel 500mm wide, 3500mm total length and 800mm high. A
broad crested weir of height 400mm and length 500mm is placed in the channel. Figure
3.1a shows the dimensions of the domain used in the modeling.
(a)
(b)
Figure 3.2: Computational Domain (a) With Dimensions (b) With Boundary conditions
Symmetry
Nappe
Pre
ssu
re In
let
Pre
ssu
re O
utle
t
3500mm
80
0m
m
1000mm 2500mm
40
0m
m
500mm
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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3.2. Methodology for ANSYS FLUENT Simulations
Like most CFD applications ANSYS FLUENT requires the subdivision of the computational
domain into a number of smaller mesh or grid cells overlaying the whole domain
geometry. It is therefore generally expected that the discretized domain needs to
adequately resolve the important physics and capture the geometrical details of the
domain within the flow region. The quest to yield a well-constructed mesh deserves as
much attention as prescribing the necessary physics to the flow problem. The 2D
geometry was modeled and discretised in Gambit, appropriate boundary conditions was
assigned to the computational domain. A structured mesh is used to ensure that proper
mesh quality is achieved before computation and the research experimented on the
effects of varying the modeling techniques and mesh topology on the final computational
results. In addition, this research will vary the solution methods and iteration parameters
to investigate and prescribe best practice simulation methodology for the Volume of fluid
method for flow over a broad crested weir simulation.
3.2.1. Domain Adjustments and Mesh Refinements in Gambit
Although other geometry formation applications can be used for the setup considered,
Gambit was employed because of its simplicity and immaculate exporting preferences to
the ANSYS FLUENT application. Gambit allows the geometry formation, meshing
(discretization) and boundary conditions to be assigned before final exportation and
computational analysis in ANSYS FLUENT. In addition, zone specifications can be assigned
as well as specific continuum types to regions of critical observation. Boundary conditions
and model meshing carried out in Gambit are vital to the entire performance during
simulation. While the precision of results obtained are a function of the mesh sizes as
much as also the solution methods adopted in FLUENT.
Symmetry
Nappe
Pressure Inlet
Pressure O
utlet
Interface
Interface
Figure 3.3: Computational Domain Showing Boundary Conditions
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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Symmetry
Nappe
Pre
ssu
re In
let
Pre
ssu
re O
utle
t
Interface
Interface
Face 1
Face 2
Face
3
Figure 3.4: Computational Domain Showing Boundary Conditions With Assigned Faces
3.2.1.1. Specifying Continuum
A zone-type specification defines the physical and operational characteristics of the
model at its boundaries and within specific regions of its domain. Continuum-type
specifications, such as FLUID or SOLID, define the characteristics of the model within
specified regions of its domain. The importance of specifying zones in the computational
domain was highlighted in the various investigated simulations. The research study tried
out a number of different modeling adjustments to the domain such as adopting all three
differently modified computational domains in figure 3.4 and observing the accuracy of
the results obtained. Fig.3.4 shows the various computational domains iterated. Fig.3.4a
represents a computational domain with no assigned zone continuum type while Fig. 3.4c
shows the preferred (zoned and with interfaces defined) computational domain used for
final validation and comparison with experiment and previously simulated data. SIM A to
D was run using the domain in fig 3.4a while the domain in fig 10b was used for SIM’s 1
and 2.
Symmetry
Nappe
Pre
ssu
re In
let
Pre
ssu
re O
utle
t
Face 1
(a)
Symmetry
Nappe
Pre
ssure
Inle
t
Pre
ssure
Ou
tlet
Face 1
Face 2
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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(b)
Symmetry
Nappe
Pre
ssu
re In
let
Pre
ssu
re O
utle
t
Interface
Interface
Face 1
Face 2
Face
3
(c)
Figure 3.5: Three Computational model types tested (a) with no assigned zone (b) with two zones separated by but no defined interface (c) with three defined zones and two
interfaces.
3.2.1.2. Mesh Adaptation
Mesh adaptation, also known as Adaptive Mesh Refinement (AMR), refers to the
modification of an existing mesh so as to accurately capture flow features. Generally, the
goal of these modifications is to improve resolution of flow features without excessive
increase in computational effort. There are three main mesh adaptation strategies and
combinations of these three have lead to other new strategies in recent times. These
main three include R-refinement, H-refinement, or P-refinement. In this study however,
the H-refinement strategy was adopted. H-refinement is the modification of mesh
resolution by changing the mesh connectivity. Depending upon the technique used, this
may not result in a change in the overall number of grid cells or grid points. The simplest
strategy for this type of refinement subdivides cells, while more complex procedures may
insert or remove nodes (or cells) to change the overall mesh topology. In the subdivision
case, every "parent cell" is divided into child cells. For every parent cell, a node is added
on each face. For 2D quadrilaterals, a node is added at the cell centre also. If these nodes
are joined, we get 4 new "child cells" from the parent cells. Therefore, every quadrilateral
parent cell will give rise to four new child cells. The advantage of such a procedure is that
the overall mesh topology remains the same with the child cells taking the place of the
parent cell in the connectivity arrangement. The subdivision process is similar for a
triangular parent cell, as shown below. It is easy to see that the subdivision process
increases both the number of points and the number of cells.
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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Figure 3.6: Illustrating the H-refinement sub-division
The H-refinement mesh adaptation often leads to the development of hanging nodes. The
hanging node occurs in 2D when one of the cells sharing a face is divided and the other is
not, as shown below. For two quad cells, one cell is divided into four quads and other
remains as it is. The highlighted node is the hanging node.
Figure 3.7: Illustrating the hanging node
This leads to a node on the face between the two cells which do not belong to both of the
parent cells. The node "hangs" on the face, and one of the cells becomes an arbitrary
polyhedron. In the above case, the topology seemingly remains same, but the right
(undivided) cell actually has five faces.
The simplest refinement anyone can think of is to divide all cells in the domain. This is
referred to as "Uniform Refinement". Although it does improve the solution vastly, it is
easy to realise that we are going for a huge unwanted effort in doing so. Therefore, to
achieve the goal of mesh adaptation, the refinement is done at "selected" regions alone
based on certain criterion. This is referred to popularly as AMR or Adaptive Mesh
Refinement.
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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The geometry formation in Gambit were refined and redefined on a number of occasions
during the analysis. FLUENT provides additional refinement one of which is the smooth
and swap tool. During the course of the study Initial geometries produced were void of
zones or continuum type specifications however having understood the effects of
specifying zones within a domain to the accuracy of predictions, they were subsequently
included. To further ensure realization of a replicate physical phenomena, mesh
refinements in form of assigning boundary layers to walls is utilized. This is a local
refinement technique that is widely used in many CFD applications and it involves the
concept of a stretched grid in the near vicinity of domain walls. In a real physical flow,
there will be a developing boundary layer that will grow in thickness as the fluid enters
the left boundary and migrates downstream along the bottom wall of the domain. In
contrast, the coarse stretched grid at the very least catches some of the essential features
of the actual physical boundary layer. It is therefore not surprising that the accuracy of
the computational solution is greatly influenced by the grid distribution inside the
boundary layer region.
For the modeled geometry in this report, Gambit allows for this refinement by allowing
near wall mesh refinements in form of assigning boundary layers. In simple terms, a
boundary layer is that layer of fluid in the immediate vicinity of a bounding surface.
Because the shear stress is maximum in the boundary layer, there is need to use a much
smaller mesh size in this region. This is to reduce the numerical errors resulting from the
discretisation of the governing equations in this region. At this point, it becomes
expedient to list a summary of the simulations conducted. Hence tables 3.1 give a
summary of the mesh topology and other simulation parameters used for the conducted
simulations.
Table 3.1: Summary show characteristic parameters of all simulations
SIMULATIONS No.
Mesh Type NOTES Ho (mm)
1 Structured 2D - RNG 50.90
2 Non conformal 2D - RNG 60.70
3 Structured 2D - RNG 84.40
4 Non conformal 2D - RNG 108.40
5 Structured 2D - RNG 139.20
6 Structured 2D - RNG 178.00
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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7 Structured 2D - RNG 204.70
8 Structured 2D - RNG 50.90
9 Non conformal 2D - RNG 60.70
10 Structured 2D - RNG 84.40
11 Non conformal 2D - RNG 108.40
12 Non conformal 2D - RNG 139.20
13 Non conformal 2D - RNG 178.00
14 Structured 2D - RNG 204.70
A Structured 2D - RNG 50.90
B Structured 2D - RNG 60.70
C Structured 2D - RNG 84.40
D Structured 2D - RNG 108.40
Generating a good mesh is a large part of the CFD problem and a good quality mesh is
usually the first step in achieving good results. What is a satisfactory mesh for a problem
will not automatically be so when another model option is enabled and the real effect of
the mesh type is further researched in this study. Hargreaves, Morvan and Wright in the
paper, the Validation of the volume of free method for free surface calculations, utilised
non conformal meshes resulting in a reduction of overall cell count. In this study, both
structured meshes and non conformal meshes are adopted in the investigation.
Figure 3.8: Mesh region showing non conformal meshes at the interface
Figure 3.9: Mesh region shown structured meshes across the domain
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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The Topology of a structured mesh is rectangular and this means that the mesh volume is
a quadrilateral in 2d or a hexahedron in 3d. Each mesh volume is linked only to its
immediate neighbours but the edges can be mapped around curves. In addition, mesh
volumes may not be the same size. The use of a structured mesh often reduces storage
and CPU requirements. Unstructured grid or non conformal grid on the other hand can
have their mesh volumes linked to any other volume in the domain and can be any shape.
There is less computationally efficient than a structured grid but can still read a structured
grid topology. Non conformal grids introduce flexibility but this flexibility creates
problems with computation such as numerical diffusion and skewness and therefore they
are regarded as inefficient. It is often known that because the faces are not automatically
aligned with the flow you can get false diffusion. The general perception is that
quadrilateral mesh often give better results when utilised in a simulation, therefore part
of the investigations conducted in this research is to study the effect of the use of
structured and unstructured mesh in a CFD computation. To investigate this, simulations
SIM 1, 2, 3, 4, 5, 6, 9 and 11 were conducted alternating between structured and non
conformal mesh respectively. Table 11 shows the results of the simulations.
3.2.2. Grid Independency Test
Grid convergence is the term used to describe the improvement of results by using
successively smaller cell sizes for the calculations. A calculation should approach the
correct answer as the mesh becomes finer, hence the term grid convergence.
(a)
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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(b)
(c)
(d)
Table 3.2: Varying Mesh Sizes for Grid Dependency Test (a) 15 Size Mesh (b) 25 Sized Mesh (c) 40 Sized Mesh (d) 50 Sized Mesh Spacing
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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The examination of the spatial convergence of a simulation is a straight-forward method
for determining the ordered discretization error in a CFD simulation. The method involves
performing the simulation on two or more successively finer grids. For the computational
domain in this study, we are bound to determine the error band for the engineering
quantities obtained from the finest grid solution and likewise, to determine the error on
the much coarser grids.
Grid independence test conducted were on energy pressure heads 50.9, 60.7 and 84.4
where grid sizes 15, 25, 40 and 50 were iterated and results described in SIM 14, 15, 16
and 17. Table 12 shows the results for these simulations.
3.2.3. Summary of Simulations Conducted
The simulations described here are run using ANSYS FLUENT version 12.1 (2009). A
number of different solutions methods were iterated to obtain the most explicit
simulation of the VOF method’s representation of free surface flow over the broad
crested weir setup. For the purpose of documentation, the simulations conducted can be
grouped under the following iterations,
1. Varying Mesh topology (Structured or Unstructured)
2. Varying Solution Methods
3. With and Without Zone Interfaces
4. Changing the Boundary conditions
Over the past few decade as CFD has evolved, better algorithms and more computational
power has become available to CFD analysts, resulting in diverse solver techniques. One
of the direct results of this development has been the expansion of available mesh
elements and mesh connectivity also referred to as the mesh topology (how cells are
connected to one another). The easiest classifications of meshes are based upon the
connectivity of a mesh or on the type of elements present and in this research the effects
of the mesh topology was investigated alongside the other objectives of the study.
Varying the solution method was intended to study the effect of pressure-velocity
coupling methods on the VOF scheme. FLUENT provides four segregated types of
algorithms: SIMPLE, SIMPLEC, PISO, and (for time-dependant flows using the Non-
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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Iterative Time Advancement option (NITA)) Fractional Step (FSM). These schemes are
referred to as the pressure-based segregated algorithm. Spatial discretization
specifications of momentum, pressure, turbulent Kinetic energy and turbulent dissipation
rate were all ran initially in first order upwind with the implicit formulation scheme. This
was until simulations showed some semblance of stability (refrained from diverging)
subsequently, the second order upwind solver was adopted.
The model geometry has a profound impact on the accuracy of the simulation and
therefore a number of modifications to the geometry were made to study its impact on
the simulation. The general dimension of the geometry was maintained however, the
impact of zone specification was investigated alongside the effects of using specifying and
meshing interfaces. Gambit provides the options of introducing zones in the domain
continuum, however FLUENT requires that in the case where two or more zones are
specified in the under the continuum type, interfaces must introduced and meshed. At
the unset of this research, no continuum type specification was made and the need to
introduce zones was later discovered as the owning to a series of failed simulations.
Geometry adjustments were made to the domain and at the onset two zones continuum
types were assigned. The continuum types, water and air were then separated by
duplicating the interface edge and assigning the interface boundary condition.
Subsequently when this is exported to FLUENT, new mesh interfaces must be specified
and their zones defined. Simulations conducted using this zoned and interface models are
displayed in figure 9 (Appendix A).
An additional simulation was performed by changing the inlet geometry and boundary
condition. The effect of a slice gate was replicated by assigning a velocity inlet to the third
of the inlet as shown in figure 10 (Appendix A). The results of this simulation are
discussed in the following chapter. The numerical model used was transient owing to the
use of the geometric reconstruction surface tracking algorithm. The re-normalised group
theory (RNG) К-Ƹ Turbulence model of Yakhot and Orsag (1986) was used with standard
wall functions. This is one of the ranges of turbulence models classes as Reynolds-Average
Navier-Stokes (RANS) model as defined by Ferziger and Peric (1997). They are timed
average approximations that are widely used in industrial applications. The RNG К-Ƹ has
known advantages when there are strong curvatures in the streamlines as is the case with
A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe
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the acceleration flowing over the weir. The standard К-Ƹ model is known to be of limited
accuracy when used to model flow bluff bodies such as weir. The sensitivity of the results
to the turbulence model was tested in the present work, by using the standard К-Ƹ model
and the Reynolds stress model (RSM) of launder et. al (2005) in addition to the RNG К-Ƹ
model. For the purpose of comparison with the Blender simulation the generalized
description of the CFD modeling setup can be described as follows;
The pressure discretisation scheme was force-weighted because of the presence
of gravity.
Second-order discretization scheme was used for the momentum, turbulence
kinetic energy and dissipation equations.
The PISO pressure velocity coupling algorithm was use, purely because it is
designed specifically for transient simulations.
A time step of 2.0x10-4 was used throughout to keep the simulation stable
because of the demand of the VOF model.
The domain extends as least 3HO upstream of the weir which was stated as a
requirement by Boiten (2002).
The types and position of the boundary conditions used are shown in figure 7(b). Pressure
inlets was assigned to the upstream boundary however the free surface heights, total
heights and bottom levels are specified under the flow specific methods. The values used
are dependent on the geometry build up in Gambit. The intensity and hydraulic diameters
are also specified for momentum. With these specified, FLUENT internally calculates the
volume fraction and static pressure at the inlet based on the position of the face, relative
to the free surface position. The energy head, HO, is also required in order to take into
account the dynamic pressure of the flow.
Subsequently FLUENT applies the appropriate static pressure outlet, only the free surface
height (or tail water) height was required. A tail water level of 0.1m was adopted
representing 25% of the weir height. This ensures subcritical flow at the outlet of the
domain for the various cases simulated. The important of maintain subcritical flow study
show that in the absence of any topographic downstream control, the horizontally
moving radial flow (after impingement) attains a critical the total rate entrainment into
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the near field mixing zone of an impinging, buoyant jet is strongly influenced by the
presence of a downstream control. In the absence of any downstream control, the flow
attains a critical flow state of maximum entraining type. This condition can be expressed
as the sum of the upper and lower densi-metric Froude Numbers being approximately
equal to one (Ulasir and Wright, 2003).
The upper boundary above air phase was specified as a symmetry condition, which
enforces a zero normal velocity and a zero shear stress. Use of a symmetry boundary
condition in this way is a standard practice for such distant, open boundaries. All other
unmarked boundaries are set as walls. On the walls, the no-slip condition was applied and
the walls were assumed to be smooth.
Fig. 3(b) also shows a small pressure outlet. This is to allow air into the model so that the
nappe can separate from the weir and allow the weir to function correctly, rather than
having the flow dribble down the face of the weir. Finally after several iterative
simulations, the best solutions for displaying the VOF method, SIM’s A, B, C, and D were
run to compute flow characteristics. These results are displayed in table 4.1.
3.3. Simulation Methodology in Blender
A three dimensional model of the geometry setup was replicated in Blender. Unlike
FLUENT Blender allows geometry modelling within the application and without the use of
any third party application like Gambit. Because the geometry is an important aspect of
the final result, Blender modelling capability is well designed to allow virtually any
material geometric shape and virtually any domain to be produced. Perhaps one of the
drawbacks of the blended application is the absence of a dimensioning capability.
Nevertheless Blender allows a vast range of visually enabled iterations with the capability
of remodelling to suit the preferred output. In Blender the scene setup is crucial to the
final simulation display and appropriately positioning lights and camera is the first task to
be prioritised.
3.3.1. Lights and Camera
The concept of lights and camera as adopted in film making was adopted in the geometry
setup. The film maker’s principle focuses on an accurate positioning of the lights in the
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room to accentuate the character and place character in the centre of the picture. For a
good multipurpose setup, three lights in a classic arrangement know as “three point
lighting” is employed as follows. (Howcast Media, 2009)
One light in front of and slightly above the subject at a 45-degree angle. This is the key
light.
A second light behind and above the subject. This is the backlight, and it helps
separate the subject from the background.
A third light on the opposite side of the key light. This is the fill light. The light from
this source should be indirect or diffuse, so consider reflecting it, or shining it off a
wall or at the ceiling
3.3.2. Geometry modelling in Blender
Modelling in Blender is done in scenes and each scene would contain the selected
animation. For the purpose of the study, a simple three dimensional model of the domain
was done to a proportionate scale before simulations are performed. Simulations in
Blender are in actual sense animations of the modelled setup in real time.
DOMAIN INFLOW BOUNDARY
INLET WEIR CHANNEL OUTLET BOUNDARY
Figure 3.10: The geometric model as assembled in Blender
There are six geometry objects that need to be assembled in Blender to represent the
computational domain;
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1. The main structure the rectangular channel built to hold as a single entity the broad
crested weir.
2. The Broad crested weir, through which fluid flow is to be observed.
3. The inflow water source that allows for the specification of flow direction and
velocity. The need to assign inflow rather than a volume specification is inherent in
the fact that for setup constant flow of water over the weir is the desired output.
4. A domain and a source of fluid. Blender requires the computational domain to be
embedded in virtual domain (being the rectangular mesh structure) that defines the
limits of the simulation. The domain will act as an invisible wall for the fluid.
5. The outflow required to take fluid out the domain.
Once the geometry is setup the tasks of assigning a fluid simulation follows subsequently.
This defines the behavioural characteristic of each geometric element. It simply tells each
geometric element how to behave during simulation. The inflow is enabled and set to
initialization volume as shown below. Inflows will inject water inside the domain. Extreme
care is taken not to fill up the entire domain, or the calculations will be severely
downgraded. The difference between inflow and volume specifications in Blender is that
the volume specification defines a fixed amount of water. A volume of water can move
around but has a contact quantity that remains the same. An inflow, on the other hand, is
a never ending source of fluid. It will begin with that volume of fluid, but will keep
pumping out more. In the inflow's options, Inflow velocity magnitude needs to be
predetermined iteratively. The velocity direction is also required to set the inflowing fluid
in its path. (Blender.org 2010)
Figure 3.11: Presets for Inflow and outflow definitions (Source: Blender.org)
The outflow is assigned and enabled to control the fluid exiting the domain. The amount
of water put inside the domain is defined by both the area of the cross section
perpendicular to the flow and the velocity set. Volume Initialize will instruct the
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simulation to initialize the inner part of the object as fluid and this is preferred for this
setup. Figure shows all three optional volume initialize types. Init Shell if assigned will
only initialize a thin layer for all faces of the mesh, this also works for non closed meshes.
Init both if assigned, combines volume and shell, this requires that the mesh be closed.
The open channel and the solid weir are specified as obstacles. As the name implies, is an
object that is placed in the fluid simulation to obstruct the flow.
(a) (b) (c)
Figure 3.12: The different volumes initialize types. (a) Volume Initialize (b) Shell Initialize
(c) Initialize both shell and volume (Source: Blender.org)
Blender requires a domain for the simulation to be done, this is not to be mistaken as the
computational domain explained above. The domain of the simulation is a box where the
fluid calculation will be done. The dialogue boxes below illustrate the required elements
to be specified. The resolution specified is essential to the simulation and this is a very
important property to be selected. It will determine the extent of graphical detail the
rendered results will show. A resolution of 50 was initially set and as a better
understanding of this parameter was finally understood, the resolution was subsequently
increased to 250. The higher the resolution, the better the graphic detail but also the
more memory is used (both RAM and HD) and baking time.
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Figure 3.13: Presets for Domain definition (Source: Blender.org)
Figure 3.7(b) below show the render image of the modelled computational domain. To
ultimately study the flow feature as generated in Blender, this study made a few
adjustments to the model.
3.3.3. Geometric Refinements to Computational Domain
Blender, like most 3D animation applications produces images and animations in real
time. Therefore solid objects will appear as it would in a real world environment and all
images render will possess the physical characteristics it originally would possess in the
real-time environment. Consider the flow of water in a three dimensional rectangular
channel, to observe the profile of the flow over the weir, a section across the channel
would be required. However, taking a section would limit the window of observation and
therefore hinder the complete observation of the flow. Two ways the methodology
adopted overcomes this limitation to adopting Blender’s transparency and Light
refraction setup.
3.3.3.1. Setting transparency
In Blender, the base colour of an object can be defined within the Diffuse panel tab
similar to picking colours off a palette. By setting the alpha parameter between a range of
0 (object totally invisible) to 1 (object totally visible). Although the application allows
three different methods for defining transparency, this study utilised the Z-Depth based
and Raytraced transparency. Raytraced transparency
When looking through a glass bottle, the background environment is deformed by the
thickness and the curves of the object. This phenomenon is called refraction, and
simulating it would add a lot of realism to the render. It currently can only be done using
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raytracing. Ray tracing involves sending a ray of light from the camera and when it
reaches a transparent surface, instead of showing what is exactly behind it on the same
trajectory, the ray will be deflected by the curves of the transparent surface according to
its density, thereby showing a slightly different part of the environment. Z depth
transparency on the other hand allows the glass object to show the objects standing
behind it, and not anymore the background set in the World menu. The density values of
the material needs to be specified to accurately achieve transparency.
3.3.3.2. Light Refraction (IOR)
Observing the images through a drinking glass, it is typical to notice a distortion of the
objects located in its background. Transparent objects like glass often distort the path of
light from linear to deflect according to the curvature of the object and its density. This
phenomenon is called light refraction and can be reproduced by activating
the Raytrace option in the transparency panel.
3.3.4. Summary of methodology in Blender
The computational domain is modeled as described and shown below. The use of lights
was effectively used to capture the simulation since a greater part of our comparison is
based on visual study. In addition, the material property of the rectangular channel was
changed to give a transparent view through the channel. This enables a visual inspection
of the flow characteristic within the channel. The physical properties of water have been
reproduced to enhance the visual appreciation of the fluid motion. It is however
important to point out that as mentioned earlier, Blender 2.49 gives limitations of scalar
dimensioning.
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Figure 3.14: (a) Wire frame view of the computational domain as modeled in Blender.(b) Camera view of the rendered domain in Blender.
Firstly, in creating and assigning the domain (rectangular channel) care is taken to ensure
it encompasses the entire setup. All other element of the scene must lie within the
specified domain. We want the domain to be just small enough to contain only what is
necessary, but not smaller than the walls. The weir is assigned as an obstacle within the
fluid simulation this allows the water to flow around the walls and over the weir. Setting
the obstacle to Init Shell instructs Blender to consider the outer surfaces. In other words,
the water is outside the object and stays out. In this case water is enabled to flow over
the weir and not through the weir.
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4. RESULTS PRESENTATION AND DISCUSSION
Results obtained from both applications are presented in a systematic order starting with
data presentation for simulations in ANSYS FLUENT. It is important to state at this point
that several experimental simulations where conducted but have not been presented as
relevant to the scope of this study. However, a conscious effort has been made to discuss
those results that have provided answers to the initial problem statements discussed in
the introduction. It is also important to mention the use of third party applications such
as MATLAB and Excel spread sheets for post processing purposes and presentation of
data collected. To keep this study within the defined scope, the functionalities and
methodologies utilised within these applications have not been concisely discussed,
however short references have been made to these applications whilst presenting the
data obtained.
4.1. ANSYS FLUENT Results
A comprehensive study and meticulous data extraction was carried out in ANSYS FLUENT.
A total of 23 simulations were performed to investigate the effectiveness of the volume
of fluid methods in ANSYS FLUENT for the determination of the characteristics of free
surface flows. To achieve this, the methodology adopted investigated the following and
their effects in the overall and final results obtained.
Determining the effect of the Mesh topology (Structured or Unstructured) on the
computational results.
The sensitivity of the result to the turbulence model adopted.
Varying the appropriate Solution Methods within ANSYS FLUENT for the computational
prediction of the multiphase characteristics of a free surface flow.
Determining the effect of mesh adaptation procedures such as defining zones of
continuums and grid independence.
Lastly, comparing the flow characteristics (in terms of flow mass, flow rate, ease of
convergence, pressure and velocity data) with physical experimental data and
similar CFD validation results.
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Since the upstream and downstream total energy head are fixed during simulation, the
main measures of accuracy are the predicted discharge and the free surface profile.
Therefore a greater part of the results obtained compared discharge values and free
surface profiles with experimental results obtained in the Hager and Schwalts research. At
the onset of the study, several simulations where performed to pre-determine the most
appropriate (closely matching experimental) turbulence model, initializations solutions,
iteration parameters that best yield the comparable results to physical flow patterns
expected for flow over a broad crested weir. Table 4.1 gives a summary of a few
experimental simulations conducted and results obtained.
Table 4.1: Initial simulation to investigate appropriate solution methods
SIM No. SUMMARY SOLUTION METHODS ho(mm)
Ho
(mm) *Discharge (Q)
(X103m/s-1)
T1 Explicit, RNG, 2nd Order, Geo-Reconstruct 50.7 50.9 12.718
T2 Explicit, RNG, 2nd Order, Geo-Reconstruct 50.7 50.9 9.743
T3 2D, Implicit, 1st Order Momentum and Turbulence & Volume Fractions 60.5 60.7 16.217
T4 Explicit, RNG, 2nd Order, Geo-Reconstruct 84.1 84.4 23.076
T5 2D, Explicit, Standard К-Ƹ, 1ST Order Momentum and Turbulence, Geo-Reconstruct
84.1 84.4 17.819
T6 2D, Explicit, RNG, 2nd Order Momentum and Turbulence Geo-Reconstruct 84.1 84.4 18.960
T7 Explicit, RNG, 2nd Order, Geo-Reconstruct 138.4 139.2 31.842
Comparing these results to the Hager and Schwalts experimental results show large
variations in particular with the implicitly run simulations. The standard К-Ƹ solver gave
much closer values. In addition, simulations T1, T2 and T3 show huge variations in
discharge reading with the experimental values from H&S experiments shown in the table
1.2.
4.1.1. Effect of Turbulence Model
As mentioned earlier, the predicted discharges at the downstream end of the channel
was a main determinant of result accuracy. This discharge values were also compared
when varying the turbulence model and table 4.2 shows the results as obtained from the
study. As explained in the methodology three turbulence models were use to simulate
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the flows of the same upstream and downstream pressure head conditions. By keeping
the pressure heads at 138.4mm above the datum (weir crest) and 100mm above the base
of the channel at the downstream region, the sensitivity of the RNG К-Ƹ, RSM and
Standard К-Ƹ turbulence models well all investigated.
Table 4.2: Results from the study of the effect of turbulence model.
SIM No.
TURBULENCE MODEL AND MODEL SOLVERS ho(mm) Ho (mm)
*Discharge (Q) (X103m/s-1)
1
2D, Explicit, Standard К-Ƹ, 1ST Order Momentum and Turbulence, Geo-Reconstruct 138.1 139.20 40.457
2 2D, Explicit, RNG, 2nd Order Momentum and Turbulence Geo-Reconstruct 138.1 139.20 38.260
3 2D,RSM Explicit, 1st Order Momentum and Turbulence & Volume Fractions 138.1 139.20 32.540
Results from the H&S experiment revealed a physical discharge of 37.59m3s-1 and from
the table above, the RNG К-Ƹ turbulence gave the closest results. To further understand
the discrepancies in the results, the velocity vectors as generated for the turbulence
model was investigated as well as the velocity magnitude plots.
Figure 4.1: Plots of the velocity magnitude for a standard К-Ƹ run
The velocity magnitude plot for the standard К-Ƹ initialized solution depicts a drop in the
velocity after peak values of 0.5 was attained (as shown in fig 4.2), the RNG run revealed a
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fairly constant velocity value after peak values at a distance of 0.5m. No subsequent
drops after peak values. (see figure 4.4).
(a) (b)
(c) (d)
Figure 4.2: Contours of velocity vector depicting velocity magnitude (a) RNG К-Ƹ model, Implicit scheme (b) RNG К-Ƹ model Explicit scheme, (c) Standard К-Ƹ model (d) RSM model
The RNG approach, attempts to account for the different scales of motion through
changes to the production term. The RNG model was developed using Re-Normalisation
Group (RNG) methods by Yakhot et al to renormalize the Navier-Stokes equations and
account for the effects of smaller scales of motion. Fig 4.2 and 4.4 show the different
vector flow at the drop for both the К-Ƹ RNG and Standard turbulence models. In the
standard k-epsilon model, the eddy viscosity is determined from a single turbulence
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length scale, so the calculated turbulent diffusion is that which occurs only at the
specified scale, whereas in reality all scales of motion will contribute to the turbulent
diffusion.
(a) (b)
Figure 4.3: Contour plots showing the separation curve (drops).(a) with a RNG к-ƹ (b) with a standard к-ƹ
It is quite interesting to note the predicted separation curve from tests of varying the
turbulence models. The standard К-Ƹ model in 4.3b shows almost no existing separation
curve. This corroborate results from the H,W&M validation study in which the drawbacks
of the К-Ƹ model in predicting separation was highlighted. The closest to experimental
results of separation curve produced by any of the turbulence models simulated was the
RNG К-Ƹ model. This, along with closeness of discharge values to experimental (discussed
earlier) resulted in the adoption of the RNG К-Ƹ model chiefly in the course of this study.
Figure 4.4: Plot of velocity magnitude for a RNG К-Ƹ run.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8
Velocity Magnitude
(m/s)
Position
RNG K-E RUN
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For the RNG turbulence model the prediction of constant velocity magnitude are slightly
closed to existing experimental values than the standard К-Ƹ (K-epsilon) turbulence
model. It is often documented that the RNG k - epsilon model offers a significant
improvement on the standard k - epsilon model, this is verified with respect to the case
study and subsequently, the study adopted the explicitly solved, RNG К-Ƹ model, 2nd
Order, Geo-Reconstruct as best practice for simulations adopting the volume of fluid
method.
4.1.2. Effects of Specifying Zones of Continuum
In addition, defining zones and the use of zone separation with interfaces as illustrated in
fig. 3.4c was observed to possess the following advantages.
1. At initialization, defining zones allow the gradual study of flow within the channel.
This is possible because setting a volume fraction of 1, fluent fills the zone
continuum with the specified fluid and subsequently flow from the inlet boundary
conditions adds to this liquid fraction.
2. The definition of zone allow fluent to apply the equations for the specified fluid
within the specified zone.
3. The development of free surfaces is noticed from the onset of the simulations when
zones of continuum are applied to the geometry. Although not realistic at the on-set
of the simulations, the true free surface condition gradually develops.
4.1.3. Varying Mesh topology (Structured or Unstructured)
Utilizing the same energy pressure heads at the upstream end of the domain for alternate
simulations while varying the mesh topology between a structured type and non
structured type (non-conformal mesh) as shown in fig. 3.7and 3.8. These simulations are
run explicitly with identical parameters across each simulation. Very little differences
were observed in simulations run by alternating between the use of structure and the
non structural mesh. SIM’s 2, 4, 9 and 11 required more time step to attain convergence,
this is expected as this their computational domain contained unstructured meshes.
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Table 4.3: Results from test on the effects of mesh topology
SIMULATIONS No.
Mesh Type NOTES Ho
(mm)
Discharge (Q) (m3 s-1 x 10-3)
CFD *H,M&W
1 Structured 2D - RNG 84.40 18.12 17.65
2 Non conformal 2D - RNG 84.40 18.05
3 Structured 2D - RNG 60.70 9.45 10.84
11 Non conformal 2D - RNG 60.70 11.03
4 Non conformal 2D - RNG 50.90 8.99 8.27
6 Structured 2D - RNG 50.90 9.17
5 Structured 2D - RNG 108.40 29.91 25.74
9 Non conformal 2D - RNG 108.40 25.33
These extra calculations lead to run time of approximately 2 to 2.5 times that of the
structured mesh. In all results however non conformal (non-structurally) meshed domains
recorded results closest to results obtained from the H,W&M validation study. This is
important to note since structured meshes are often considered to give more accurate
final results. Table 4.1 show results from the analysis.
4.1.4. Effect of mesh adaptation and Grid independence results
Mesh adaptation procedure investigated the effect adaptive processes such as geometric
progression, grid convergence and wall boundary layers have on the results. While very
minimal differences occur with the use of boundary layers, significant differences were
observed with domains meshed with 40mm and 50 mm mesh spacing. Table 4.4 gives a
summary of the results obtained from the grid independence test.
Table 4.4: Results from the grid independence test
SIM No.
Ho
(mm)
MESH SIZES
SPACINGS
TOTAL QUADRILATERAL
CELLS Discharge (Q)
(X103)
14 50.90 10 26919 9.17
15 50.90 15 12170 10.4
16 50.90 25 5970 12.25
17 50.90 40 1718 3.33
18 50.90 50 1040 3.58
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4.1.5. Velocity Inlet Simulation
An additional run was conducted to study the effect of replacing the pressure inlet
boundary condition with a velocity inlet boundary condition. The lower phase of the
upstream inlet wall (200mm from channel base) is assigned a velocity inlet boundary
condition. All other boundary conditions remain as previously assigned (see figure 4.4
below). A velocity magnitude of 1m/s is assigned and figures 4.5 below show the
simulation results progressively.
Figure 4.5: The Computational Domain (Type B) Showing the Velocity inlet Boundary Condition assigned to the lower third of the Upstream
The RNG k - epsilon model is used at a time step size of 0.0002sec, the solution is control
by setting the non-iterative solver relaxation factors for pressure and momentum to 0.3
and 0.7 respectively. Since volume fractions are set and patched at the onset, the lower
zone of continuum at initialization is filled. As the simulation progresses in channel
turbulence is observed as shown in fig 4.5(c)
(a)Time =2.46sec
(b)Time=4.14secs
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(c)Time=5.59secs
(d)Time= 9.07secs (solution Diverges)
Figure 4.6: Sequence of flow in the velocity inlet upstream boundary condition
4.1.6. Pressure Inlet Simulation
Changing the velocity inlet boundary condition as used in the computational domain
(Type B) to pressure inlet was experiment to study the effect of the buildup of fluid
behind the weir wall. As document in several literatures, an impulsive acceleration to a
liquid can result in impact hydrodynamic pressure on the free surface of the channel walls
(Ibrahim, 2005).
4.1.7. Flow Characteristics downstream
Flux results at the downstream end of the channel show varying resulting signifying the
occurrences of wave and the transition from super critical flow to subcritical flow at this
region. Figure (4.7) show an illustration of these short wave developments. The flux
values at the downstream end of the channel also corroborate this finding. When plots of
the mass flow rate after successively readings of time step are plotted, the results show
an unsteady and undulating flow pattern. (See figure 4.6 below).
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Figure 4.7: Series of short wave formation as then flow moves towards outlet.
Figure 4.8: Plot of mass flow rate versus successive increase in time step
4.1.8. Velocity Predictions.
Hager and schwalts, with the aid of a propeller meter measured the stream-wise velocity
using a number of rakes positioned at -0.5, 0, 0.5, 1.0, and 2.0 from the corner of the
upstream weir wall. With these rakes the non dimensionless velocity and its trends could
be plotted. The non-dimensionless velocity for a channel flow can be defined as
-40
-30
-20
-10
0
10
20
30
0 2000 4000 6000 8000 10000 12000
Mas
s fl
or
rate
(kg
/s)
No. of Time Steps
Mass Flow Rate
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Where is the local velocity and is the friction velocity at the closest wall (in this
case being the weir wall at the upstream end of the weir) and being the
dimensionless velocity, this is commonly used in boundary layer theory. The Local velocity
can be obtained from FLUENT and is denoted as Vx under the velocity plots. The
frictional velocity at the closest wall, for the domain consider, is a function of the
upstream pressure head and can thus be computed as (2gHo) 1/2.
FLUENT allows the creation of virtual lines and rakes and as such the non dimensionless
velocity can be plotted as well. Fig. 4.8 below shows these plots for simulations 10 and 11.
It is interesting to note that while the trends in non dimensional velocities are similar,
their magnitudes differ. This is however expected since the upstream pressure head for
SIM 10 is much greater than for SIM 11 and these pressure heads are inversely
proportional to the dimensionless velocities. The results are as expected with the H&S
experimental results but vary slightly in magnitude. Fig. 4.9 shows the results for rakes
drawn at -0.5m and 0m from the face of the upstream weir wall.
These predicted results vary considerable from the H&S experiment however are a
perfect match with the H,W&M predicted results. The result show that velocity increases
steadily towards the upstream weir wall and subsequently increases rapidly away from
the wall as shown in fig 4.9. At the nappe or recirculation zone, although the results
shows similar characteristics as portrayed by the shape of the curve, this predicted
results shows much larger recirculation than both the experimental and H,W&M
predicted results.
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Figure 4.9: Non-dimensional horizontal component of velocity at upstream for SIM 10 & 11
Figure 4.10: Non dimensionalised Horizontal component of the velocity at x/Ho (a) -0.5, (b) 0.0 both for SIM 11
Reasons for this discrepancy is obviously as a result of small upstream pressure head
values (67.38mm) adopted in both studies as against 108.4mm adopted in this
investigation. There is very little expectation of errors in the predicted simulations (apart
from discretized errors or physical approximation errors), however that mention, the use
of physical measuring instruments like the propeller meter adopted in the experimental
study could introduce errors in the experimental data.
0.68
0.7
0.72
0.74
0.76
0.78
0.8
0.82
1.128 1.129 1.13 1.131
Ho
Vx/(2gHo)1/2
SIM 10
0.68
0.7
0.72
0.74
0.76
0.78
0.8
0.82
1.572 1.574 1.576 1.578 1.58
Ho
u/(2gHo)1/2
SIM 11
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0 1 2
Ho
Vx/(2gHo)1/2
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0 0.2 0.4 0.6
Ho
Vx/(2gHo)1/2
x/Ho @ Rake 0.0
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(a) (b)
Figure 4.11: Non-dimensionalised (a) Horizontal component of the velocity at the recirculation zone (b) Pressure Head profile at the interface above the weir.
4.1.9. Pressure Predictions
With the use of pressure taps H&S produced plots of pressure head p/ρgHo against the
ration of Ho, weir to inlet distance. The H,W&M validation study noted a slight deviation
in their results as compared to the the experimental result. They noted the failure of the
predicted CFD results in capturing the drop in pressure immediately downstream of the
weir corner. The results obtained here show, interesting similarities and deviations from
both experimental and H,W&M validation results. On one hand, fig 4.10b show the
attainment of peak pressure values at x/Ho = 1, then captures the expected drop in
pressure at 1.5m (exactly the start of the downstream zone) but also show the
subsequent rise in pressure head at two successive points downstream. This discovery
was initially discarded as erroneous or as a result of iterative convergence errors,
however subsequent plots on SIMs 10 and 12 show similar trends.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-2 -1 0 1 2 3
y/H
o
Vx/(2gHo)1/2
SIM 11
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 0.5 1 1.5 2 2.5 3 3.5
p/ρ
gHo
x/Ho
SIM 11
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68
(a) t=1.01secs (b) t=1.51secs
(c) t=2.01secs (d) t=4.01secs
Figure 4.12: Contour plots of Computational Domain type 2 with the lower position pressure inlet at the upstream region
4.1.10. Pressure Predictions
Unsuccessful attempt were made to extract the free surface profiles in FLUENT and
failure to achieve this led to the compilation of contour plots showing the surface profiles
in Table 4.5 below.
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Table 4.5: Result summary of simulations showing Contour Profiles at Drop (weir fall)
SIMS No.
Mesh Type
NOTES Ho
(mm) Contour Plot
1 Structured
2D – RNG, Explicitly Run, 2nd Order Momentum, TDR &TKE, Volume Fraction (Geo-Reconstruct), k - epsilon model.
50.90
2 Non conformal
2D –RNG, Explicitly Run, 2nd Order Momentum, TDR &TKE, Volume Fraction (Geo-Reconstruct), k - epsilon model.
60.70
3 Structured
2D –Standard k - epsilon model, Explicitly Run, 1st Order Momentum, TDR &TKE, Volume Fraction (Geo-Reconstruct)
84.40
4 Non conformal
2D –Standard k - epsilon model, Explicitly Run, 1st Order Momentum, TDR &TKE, Volume Fraction (Geo-Reconstruct)
108.40
5 Structured
2D – Standard k - epsilon model, Explicitly Run, 1st Order Momentum, TDR &TKE, Volume Fraction (Geo-Reconstruct)
139.20
6 Structured
2D – Standard k - epsilon model, Explicitly Run, 1st Order Momentum, TDR &TKE, Volume Fraction (Geo-Reconstruct)
178.00
9 Non conformal
2D –Standard k - epsilon model, Explicitly Run, 1st Order Momentum, TDR &TKE, Volume Fraction (Geo-Reconstruct)
60.70
D Structured
2D –Standard k - epsilon model, Explicitly Run, 1st Order Momentum, TDR &TKE, Volume Fraction (Geo-Reconstruct)
108.40
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4.2. Blender Results
At the onset of this study, the challenge of obtaining numerical data from blender was
highlighted. It was established however that on the basis of comparison with results in
FLUENT, physical visual data could be utilised to achieve the objectives of validating the
application. Unlike FLUENT, blender’s visual package is quite advance and as was expect
quite impressive. The entire process in blender was more of imagery refinement and
although, actual fluid simulations are performed, it is evident that the adoption of camera
effects, lights and scenes has a major role to play. Figure 4.13 below show renders images
of simulated flows. As can be seen, the visual representation of both the fluid and the
domain require adjustments to observe the characteristics of the flow.
Figure 4.13: Render images (a) flow over submerged weir (b) unrealistic propagation of fluid flow towards downstream of channel.
To improve on this image the study adopted utilised the Raytracing tool in blender to give
the channel a transparent material property, similar to experimental chambers used for
the study of flow characteristics. In addition, blender provide an optional tool known as
onlycast which allow faces of pipes or channels to cast shadows only without being
viewing the rendered image. Applying this allows the flow to be monitored without
visually observing the channel.
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Transparency was then assigned to the channel and the camera angle repositioned as
shown in figure 4.13. The resulting image showed short fluid flow over the weir towards
the downstream region of the channel.
Figure 4.14 (a) Rendered view showing flow towards outlet (b) Rendered image of the flow as seen through channel set to transparent
Figure 4.15: Views of the wireframe of the computational Domain
4.3. Result discussion
Blender is equipped with a vast array of simulation prowess however this study has
uncovered a number of aspects that do not precisely validate Blender as an accurate
commercial or industrial CFD application. I shall start with the modeling aspect and work
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my way down to visually observed results. A bulk of the modeling sequence is filmmaking.
The fact that blender provides a domain that needs to encompass the entire setup is a
source of concern. It appears the domain controls the amount of fluid as again the set
parameters at the inflow. First with respect to realism, this study observed the key
characteristics and flow patterns depicted by Blender in simulating a fluid flow over a
broad crested weir. Fig. (4.15) show simulations set to a real world size 0.030 at a flow
start time of 5 seconds, velocity of 10m/s and a bake resolution of 50, even with all the
cinematographic effects of lights and cameras, blender failed to apply the “real world
size” consistently with regards to fluid simulation and fills the entire channel with the
fluid. It is difficult to associate the scalar values of 1 or lower values of 0.030 to represent
a dimension or scale of reference. There is therefore the need to rectify this flaw in
Blender.
(a) (b)
Figure 4.16: Rendered View (a) Time = 5secs, Velocity = 10m/s, Real well size 0.030secs, with bake resolution of 50 (b) Time = 5secs, Velocity = 10m/s with bake resolution of 50, Real well size 0.030secs,
Apart from the absence of a physical scaling factor of the kind used in hydraulic research
models, the turbulence from this defined inflow looks unrealistic, coarse and violent. In
Fig. 4.16, the inflow mesh was scaled to reduce its turbulence nevertheless; the resulting
horizontal flow produced other noticeable horizontal flows along the edges and less in an
x-directional shape between the corners. Also obvious are visible lumpy triangular air
pockets in between the flow particles irrespective of the shape or size of the inflow object
as seen in Fig. (4.17). The spurts of water leaping up out of the leading edge of high flow
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(in figure 4.17) was initially thought to be a resultant of the velocity value assigned but a
reduction in velocity from 1.2 to 0.5 showed very similar fluid motion. To reduce the
speed of the flow, the directional of flow was changed to the negative z direction giving
the flow a downward fluid path that eventually accumulates and flows over the weir.
Figure 4.17: Rendered Images obtained from animation of flow over
The total absence of air bubbles as should be the case with normal fluid motions is
noticeable in Fig 4.18 below. Note the almost perfect stream line of fluid motion even at
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contact with weir. This property, advection, as explained earlier and describe by
expressions in the Navier-Stokes equations is not particularly visible in this simulation.
While the rendered flow images in Fig 4.17 have a more realistic look, their patterns of
fluid motion are flawed with respect to interactions with objects in its part. The accuracy
of the results for simulating free surface flow however shows certain limitations from a
visual or graphical perspective. The effect of velocity used might be responsible for this
anomalies, however in real time fluid motion show no correlation with the rendered
images shown in Fig 4.18.
Figure 4.18: Rendered image at stream wise velocity of -0.5 and real world size of 0.030
This is not to say that the application is incapable of actual and realistic fluid simulations
but from this investigation, the use of cinematographic effects or in other words
animation and camera effects are obvious to a very large extent. Therefore while
elements of computational fluid dynamics are utilised by blender much of the results are
reflections of camera, lights and animation.
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5. SUMMARY AND CONCLUSION
The importance of weirs in modern day hydraulic structures has been discussed. In
particular, its use as a calibrating or measuring device has drawn concerns commercially
in the design and installation of these hydraulic structures. Therefore, this study
explained the importance of the application of CFD in optimizing design. To then ensure
that predicted results are inconformity with physical real time behaviour of the
interactions of fluid in any environment, it is expedient that the verification and validation
of CFD applications be done before their use as commercial or industrial applications. The
aim of the study was therefore tailored to the verification and validation of two CFD
applications, one already in use commercially and the other a recent addition to
numerical computation. To attempt a verification and validation, flow over a broad
crested weir was successfully simulated in ANSYS FLUENT and Blender, both to varying
degrees of accuracy. This report then critically discussed the accuracy of the results
obtained in both applications. The study started off by explaining the characteristics of
fluids in motion and proceeded to explain with the use of basic mathematical equations
the expected physical representation of fluid motion as stated by Navier-Stokes. The
concept of free surface flow was then highlighted and the challenges and complexities
inherent in the simulation of multiphase flows such as the fluid flow over a broad crested
weir were critically described. Relevant literatures to this study were reviewed and
physical experimental data from the Hager and Schwalts experiment was selected as a
base for comparison. In addition, the validation study by Hargreaves, Wright and Morvan
were frequently used to cross check predictions from this study.
The study proceeded to simulate the flow of water over a broad crested weir and
investigated the simulation capabilities of the both application in representing and
predicting free surface flows. ANSYS FLUENT show remarkable predictions of free surface
flows using the volume of fluid (VOF) method. In the test on the effect of the turbulence
model, the RNG k-epsilon model showed almost perfect similarities with experimental
data obtained in the H&S experimental result with slight differences in pressure and
velocity predictions. Discharge at the downstream of the channel was a source of concern
as values fluctuated rapidly; the study however associated this with formation of waves at
the downstream zone of the channel as evident in the contour plots from selected runs. It
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was thought that if the channel length at this downstream region was extended,
discharge values would ultimately results in non fluctuating values.
While Blender showed more graphical prowess, the results showed flaws in scalar
quantification and realism to some extent. Although the study showed that the
application is capable of performing CFD simulation, it was discovered that much of this
simulations are enhanced by light effects and camera refinements as typical of the
animation industry. In general, filmmaking techniques have been adopted to show a
resemblance of actually performing CFD and as such cannot be validated for used a CFD
application.
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6. RECOMMENDATIONS
The inability to extract raw velocity, pressure and other scalar quantitative data from
Blender has limited the comparison of the capability of the blender application. An
effective comparison can be achieved with this extracted data in hand. To achieve this,
there is the need to develop script capable of identifying first and foremost the relevant
data file and subsequently developing a post processing suite capable of displaying the
data for ease of interpretation. In addition, Blender is without doubt a powerful
application and considering the fact that the developers have incorporated solvers of fluid
dynamic equations says a a lot as to what the future holds for CFD and the industry. If an
industrial variant of the application is develop, one that incorporates the analytical
aspects as expected of any CFD application but in addition, incorporates the visual
prowess of Blender in solving engineering problem. While Blender may be discarded by
the CFD industries and academics, its potentials remain to be tapped and thus opening a
new field to post-processing of CFD data. One would easily agree that basing engineering
design for industrial or commercial purposes on the effectiveness of the interpretation of
numerical data (a bunch of numbers), appears a technological era behind actual visual (in
real-time) representation of data for design purpose.
With regards to fluid dynamics and the weir case study, there is a need to further
investigate the flow characteristics at the downstream region. As well as numerous
validation and verification exercises of the prediction accuracy of CFD application in
general.
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APPENDIX
Table A.1: Main characteristics of simulations
The main flow characteristic where also recorded and compared with those computed in
the Hager and Schwalts experiment. These flow parameters are computed for selected
simulations as listed in Table A.1.
The Froude number Fo is based on the approach velocity Vo given as
The Reynolds number Ro is based on the velocity 1/2. And is computed as
..................................................................... Equation 9
The Froude’s Number is also computed from,
..................................................................... Equation 10
With = 1.15x10-6m2s - 1 as kinematic viscosity for water of 15o temperature.
SIMs No.
Ho
(mm) Ho
(mm) Approach Velocity
(Vo)
*Discharge (Q)
(X103)
Channel Width
(b) (mm)
Weir Height
(w) (mm)
Froude Number
(Fo) Reynolds No. (Ro)
A 50.90 50.90 0.3613 9.27 0.5 0.4 0.016105 9.89E+08
B 60.70 60.70 0.3938 12.03 0.5 0.4 0.016084 1.29E+09
C 84.40 84.40 0.4209 17.85 0.5 0.4 0.014592 2.11E+09
D 108.40 108.40 0.4654 25.32 0.5 0.4 0.014247 3.07E+09
E 139.20 139.20 0.5738 40.05 0.5 0.4 0.015505 4.47E+09
Note: * Values are read off from the mass flow rate and converted to Volumetric flow rates.
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Figure A.1: Contour plot of Volume Fractions (air) at time step size = 0.0002 (RSM turbulence Model)
Figure A.2: Monitor plot showing convergence history of mass flow rate at upstream for a RNG K-epsilon run
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Figure A. 3: X-Y plot of strain rate for a typical RNG run
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Figure A.4: Phase contour plot for a RNG turbulence run, explicit and Geo-reconstruct and all second order, upstream TH:0.48, FSH:0.38, Downstream FSH:0.35, Reference value at
0.45,
(a) (b)
(c) (d)
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(e) (f)
Figure A.5: Pathline plots of particle( water and air) at upstream and downstream
surfaces, showing the surfaces of interaction (a) SIM 1 (b) SIM3 (c) SIM 8 (d) SIM 9 (e) SIM
10 (f) SIM 11
Recommended