Adeolu's Dissertation

97
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

Transcript of Adeolu's Dissertation

Page 1: Adeolu's Dissertation

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

Page 2: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

ii

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.

Page 3: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

iii

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

Page 4: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

iv

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

Page 5: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

v

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

Page 6: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

vi

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

Page 7: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

vii

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

Page 8: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

viii

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

Page 9: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

ix

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

Page 10: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

x

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

Page 11: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

xi

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

Page 12: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

xii

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.

Page 13: Adeolu's Dissertation

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

Page 14: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

2

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.

Page 15: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

3

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.

Page 16: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

4

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

Page 17: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

5

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

Page 18: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

6

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.

Page 19: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

7

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

Page 20: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

8

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)

Page 21: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

9

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.

Page 22: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

10

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).

Page 23: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

11

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.

Page 24: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

12

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;

Page 25: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

13

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.

Page 26: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

14

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

Page 27: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

15

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.

Page 28: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

16

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

Page 29: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

17

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.

Page 30: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

18

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.

Page 31: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

19

(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

Page 32: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

20

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.

Page 33: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

21

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,

Page 34: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

22

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.

Page 35: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

23

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.

Page 36: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

24

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

Page 37: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

25

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).

Page 38: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

26

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).

Page 39: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

27

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.

Page 40: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

28

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).

Page 41: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

29

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

Page 42: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

30

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

Page 43: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

31

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.

Page 44: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

32

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

Page 45: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

33

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).

Page 46: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

34

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.

Page 47: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

35

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.

Page 48: Adeolu's Dissertation

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

Page 49: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

37

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

Page 50: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

38

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

Page 51: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

39

(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.

Page 52: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

40

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.

Page 53: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

41

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

Page 54: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

42

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

Page 55: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

43

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)

Page 56: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

44

(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

Page 57: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

45

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-

Page 58: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

46

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

Page 59: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

47

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

Page 60: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

48

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

Page 61: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

49

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;

Page 62: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

50

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

Page 63: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

51

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.

Page 64: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

52

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

Page 65: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

53

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.

Page 66: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

54

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.

Page 67: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

55

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.

Page 68: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

56

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

Page 69: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

57

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

Page 70: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

58

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

Page 71: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

59

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

Page 72: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

60

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.

Page 73: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

61

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

Page 74: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

62

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

Page 75: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

63

(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).

Page 76: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

64

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

Page 77: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

65

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.

Page 78: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

66

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

Page 79: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

67

(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

Page 80: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

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.

Page 81: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

69

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

Page 82: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

70

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.

Page 83: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

71

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

Page 84: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

72

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

Page 85: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

73

(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

Page 86: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

74

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.

Page 87: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

75

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

Page 88: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

76

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.

Page 89: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

77

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.

Page 90: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

78

7. REFERENCES

Acheson, D.J. (1990). Elementary Fluid Dynamics. Oxford: Oxford University Press.

Aliabadi S . et. al, (2003). Parallel finite element simulation of mooring forces on floating

objects. International Journal of Numerical Methods in Fluids 41 809–822. Available at

http://onlinelibrary.wiley.com/doi/10.1002/fld.459/pdf (accessed on 1 August 2010)

Blender.org (2010). Fluid simulation tutorial. Available at

http://wiki.blender.org/index.php/Doc:Tutorials/Physics/BSoD/Fluid (accessed on 1 July

2010)

Boiten W. (2002). Flow measurement structures. Flow Measurement and

Instrumentation 13 (5-6) pp.203–207. Available at

http://www.sciencedirect.com/science?_ob=ArticleURL (accessed on 12 June2010)

Brennen, C. E. (2005). Fundamentals o f Multiphase Flows. New York: Cambridge

University Press. Available at

http://assets.cambridge.org/97805218/48046/excerpt/9780521848046_excerpt.pdf

(accessed on 24 June 2010)

Chirila, D. B. (2010). Introduction to Lattice Boltzmann Methods. Available at

http://www.awi.de/fileadmin/user_upload/Research/Research_Divisions/Climate_Scien

ces/Paleoclimate_Dynamics/Modelling/Lessons/Einf_Ozeanographie/lecture_19_Jan_2

010.pdf (accessed on 5 July 2010).

Chung, T.J. (2002). Computational Fluid Dynamics. UK: Cambridge University Press.

Crabbe, A.D. (1974), Some Hydraulic Features of Square-Edged Broad- Crested Weir.

Water and Water Engineering 78 (10), PP. 354–358.

Fach S. et. al, (2009). Determining the spill flow discharge of combined sewer overflows

using rating curves based on computational fluid dynamics instead of the standard weir

equation. Water Science Technology 60 (12), 3035–43. Available at:

http://www.ncbi.nlm.nih.gov/pubmed/19955626 (accessed on 13 July 2010).

Ferziger J. and Peric .M, (1997). Computational Methods for Fluid Dynamics. Springer,

Verlag, Berlin.

Flow science Inc. (2005). CFD-101: The basics of computational fluid dynamics (CFD): Modeling simulating fluid flows with free Surfaces. . Available at: http://www.flow3d.com/cfd-101/cfd-101-free-surface-fluid-flow.html (accessed on 5 June 2010).

Hager, W.H. and Schwalt, M. (1994). Broad Crested Weir. Journal of Irrigation and

Drainage Engineering ASCE 120 (1), pp. 13–26. Available at:

Page 91: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

79

http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JIDEDH0001200

00001000013000001&idtype=cvips&prog=normal (accessed on 15 June 2010)

Hargreaves, D. M. et al, (2007). Validation of the volume of fluid method for free surface

calculation: The broad crested weir. Engineering Applications of Computational Fluid

Mechanics 1 (2), pp. 136–146

Harlow F.H and J.E Welch, (1965). Numerical calculation of time-dependent viscous

incompressible flow. Journal of Computational Physics 3 (1), 80-93.

Hirt C.W. and Nichols B.D. (1998). Methods for Calculating Multidimensional, Transient

Free Surface Flows Past Bodies, Journal of Computational Physics 141 (2), 112–152.

Hirt C.W. et al. (1970). A Lagrangian method for calculating the dynamics of an

incompressible fluid with free surface. Journal of Computational Physics 5 (1) 103–124.

Hirt, C.W. and Nichols, B.D. (1981). Volume of fluid (VOF) method for the dynamics of

free boundaries. Journal of Computational Physics 39, pp. 201–225.

Hirt, C.W. and Nichols, B.D. (1981). Volume of fluid method for the dynamics of free

boundaries. Journal of Computational Physics 39 201–225.

Hou Y. (1995). Numerical solutions to free boundary problems. Acta Numerica 4 (1),

336–415.

Howcast Media, (2009). How to make your first movie – Phase 5 Lights. Available at:

http://www.howcast.com/videos/62602-How-To-Make-Your-First-Movie-Phase-5-

Lighting (accessed on 5 July 2010).

Ibrahim R. A. (2005). Liquid sloshing dynamics: theory and applications. UK: Cambridge

University Press. Available at:

http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521838856&ss=exc

(Accessed on 13 July 2010)

Jiyuan, T. et al., (2008) Computational fluid dynamics: A practical approach. USA:

Elsevier Inc.

Kantor, M. (2007). Project No. 1M0579: Computational fluid dynamics – A useful tool in

the Research of hydraulic structures. Prague: Author.

Monaghan J. J, (2005). Smoothed particle hydrodynamics. Available at:

http://iopscience.iop.org/0034-4885/68/8/R01/pdf/rpp5_8_R01.pdf (accessed on 5 July

2010).

Page 92: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

80

Moss, W.D. (1972). Flow Separation at the Upstream of a Square-Edged Broad-Crested

Weir, Journal of Fluid Mechanics 52 (2), pp.307–320.

Murat, U. and Wright S.J. (2003). Influence of downstream control and limited depth on

flow hydrodynamics of impinging buoyant jets. Environmental Fluid Mechanics 3: 85–

107. Available at: http://www.springerlink.com/content/v170322h5l454437/fulltext.pdf

(accessed on 25 August 2010).

Paterson, A.R. (1997). First course in fluid dynamics. Cambridge: Cambridge University

Press.

Petrila, T. and Trif, D. (2005). Basics of fluid mechanics and introduction to

computational fluid dynamics. United States: Springer business media, inc.

Ramamurthy et al. (1988). Characteristics of Square-Edged and Round-Nosed Broad-

Crested Weir. Journal of Irrigation and Drainage Engineering. 114 (1). PP. 61-73.

Rao, S.S. and Shukla, M.K. (1971). Characteristics of Flow over Weirs of Finite Crest

Width. Journal of Hydraulic Division ASCE. 97 (11), PP.1807–1816. Available at:

http://alrafidain.engineering-coll-mosul.com/files/no2/E/EF-2-A-2009.pdf (accessed on

2 August 2010)

Sarker M.A. and Rhodes D.G. (2004). Calculation of Free-Surface Profile over a

Rectangular Broad-Crested Weir. Flow Measurement and Instrumentation 15 (4),

pp.215–219

Thompson B.T. (2006). Combined sewer overflows, Stockton on Tees-UK: ThompsonRPM

Tracy, H.J. (1957). Discharge Characteristics of Broad-Crested Weirs. U.S Geological

Survey Circular 397 pp. 1–15.

Versteeg, H.K. and Malalasekera, W. (2007). An introduction to computational fluid

dynamics: The finite volume approach. London: Pearson Education Limited.

Yakhot V. and Orsag S. (1986). Renomalisation group analysis of turbulence. Journal of

Science and Computing 1 (1), 7–51. Available at:

http://www.springerlink.com/content/t265g570w4737g23/fulltext.pdf (accessed on 25

August 2010).

Page 93: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

81

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.

Page 94: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

82

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

Page 95: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

83

Figure A. 3: X-Y plot of strain rate for a typical RNG run

Page 96: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

84

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)

Page 97: Adeolu's Dissertation

A CFD validation Study for the Prediction of Free Surface Flows – Adeolu Adegbulugbe

85

(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