INTRODUCTION

The increasing demand

on building long-span cable bridges to connect people, places and the

transportation of goods such as Humber bridge, have always proved to be a complex

challenge for engineers. This is especially

difficult because cable bridges are found to be extremely sensitive to wind

effects which causes the bridge to exhibit a vortex-induced vibration at a

relatively low range wind speeds. As a

consequence, this vibration can not only affect the simple durability and

serviceability of the bridge but also dangerously provoke a phenomena called

resonance. Resonance occurs when the frequency

of the vortex shedding matches the natural frequency of the structure. If this phenomenon occurs, it may lead to

disastrous consequences such as the failure of Tacoma Narrows Suspension Bridge in 1940 when shedding frequency

caused resonance with torsional natural frequency.

Traditionally, the

study of aerodynamic responses of a bridge are obtained from wind tunnel tests,

but it can prove to be substantially expensive and time consuming. Therefore, the current state of the art

computation fluid dynamics (CFD) techniques, although not yet to substitute

wind-tunnel test, play an important role on identifying and studying the

complex phenomena of the unsteady flow around a bridge deck.

The aim of this

project is to select the most suitable turbulence model utilizing the 2D-

Reynolds-averaged Navier-Stokes (URANS) Turbulence model approach, capable of

efficiently compute the complex features of the flow such as the separation of

the flow, vortex shedding, transition to turbulence. The effects of the lift

and drag coefficient is investigated when the bridge deck subjected to

different flow regimes, Reynolds number 103 to 106 . The bridge selected

for this investigation is the Humber bridge, located in the Northeast of

England, UK. The Humber bridge deck has

a streamlined bridge deck geometry.

The simulations start

by employing the Shear Stress Turbulence model (SST) and the k-w model to

investigate the flow around a circular cylinder. The numerical results for the

round cylinder simulations are compared to existing experimental data. Based on the Turbulence model and numerical

scheme that produced the most reliable data, the modelling of turbulence of the

flow around Humber bridge deck geometry can be investigated. The purpose of

this study is to understand the effects of drag and lift on the bridge deck at

different Reynolds numbers and effectively propose a bridge deck geometry

optimization.

1. LITERATURE REVIEW

1.1 Turbulence Models

The numerical

modelling of the flow around bluff bodies and bridge decks by using the

computational approach based on 2-D unsteady Reynolds-averaged

Navier-Stokes(URANS) equations can be employed to reasonably predict the

aerodynamic loads and other features of the flow Mannini et al., (2010). The author compares two Turbulence models, the

one-equation SAE eddy-viscosity model and the two-equation EARSM-LEA k-w model.

The first model is unable to detect the unsteadiness of the flow and streamline

curvature, the second one successfully predicts the flow field features and

also gives results which are very close to the experimental data, respectively.

Mannini et all.,

(2010) concludes that the 2-D URANS-LEA approach is capable to capture complex

Reynolds number effects but it is crucial it employs fine grid refinement such

a meshes with high resolution near the wall.

The authors also highlight the importance of small details such the

degree of corner sharpness as this can dramatically change the flow field

around the bridge.

Although results can

be extremely accurate when solved by the use of more advanced approaches such

as 3-D detached-eddy simulations (DES) or large-eddy simulation (LES), these

have a significant higher cost and are also substantially time and CPU

demanding Mannini et al., (2010).

The complex physical

phenomena of the vortex shedding, flow separation and reattachment, laminar to

turbulent transition and alternating large and small eddies can also be

investigated by analysing the flow through simple geometries bodies such as a

circular cylinder or a rectangular cylinder.

Stringer et all., (2014)

were able to study the flow around a circular cylinder for wide range of

reynolds number by using the a 2D Unsteady Reynolds-Averaged Navier-Stokes (URAS)

approach, SST turbulence model and are able show great agreement with previous

experimental results date up to Reynolds number 105. Mannini, Šoda and Schewe, (2010) study the

flow past a rectangular cylinder with chord-to thickness ratio of 5.0. The author shows that it is possible to

achieve reasonable predictions of the main aerodynamics quantities with the 2-D

URANS approach when these are coupled with advanced turbulence models such as

the EARSM-LEA.

Haque et al., (2015)

and Haque et al., (2016) both studies adopt the unsteady RANS simulation with

the k-w SST Turbulence model and the standard methodology

by Roache (1998) to the check the convergence of the grid system as this is a

crucial source of error.

Haque et al., (2015) investigates

through unsteady RANS simulations the flow features around a pentagonal bridge

deck by varying Reynolds number 2×104 to 20×104. The author uses k – SST Turbulence model as

it is believed to the superior to both the k – epsilon (k – e) and k- omega (k – w) models turbulence models. The SST model uses k – w model to estimate

turbulence near the wall and k- outside the boundary layer Stringer et al,. (2014). Although Haque et al., (2015) noticed some

discrepancies where large flow separations occur the unsteady RANS simulation

capture the velocity field and flow pattern very accurately.

The selection of an

appropriate Turbulence model is crucial. The

URANS 2D Turbulence model was identified as the best compromise between

accuracy and computational cost. Sun et al., (2009); Wilcox, (1998;) and many authors such as,

Mannini et al., (2010), and Brusiani

et al., (2013) all have used the Reynolds-averaged Navier-Stokes (URAS)

approach coupled with the k- wTurbulence models for their numerical simulations with

successful predictions of the flow features.

However, SST Turbulence is still

considered to be superior as this model combines both the k- epsilon and k-w turbulence models.

1.2 Reynolds Number Sensitivity

When the wind flows

through a body such a bridge box girder it has a tendency to separate at the

sharp corners and form wake and vortex regions around the surface of the bluff

body where the flow is more or less coherent. The impact of these regions on

the structure depends on the Reynolds number Hansen et al., (2015).

Many studies have

been carried out to investigate the effects of the Reynolds number on simple

geometries bodies such as a circular and rectangular cylinder. These studies have served a bench mark for

then further investigate aerodynamic characteristics of more complicated

structures such a bridge deck.

One of the first and

most famous investigation is the flow around a circular cylinder. Zdravkocich (1990) refined the flow regime

around a circular cylinder in 15 distinct ranges) Table 1.

Table 1

Re Range

Flow Regime

Re < 1 Creeping Flow 5 < 40 Steady Separation (Foppl vortices) 40 < Re < 300 Laminar periodic shedding 200 < Re < 1.4x10^5 Subcritical 1.4x10^5 < Re < 1x10^6 Critical 1x10^6 < Re < 5x10^6 Supercritical 5x10^6 < Re < 8x10^6 Transcritical Re>8x 10^6

Postcritical

When Re < 40, the
fluid is smooth and moves in the streamlines, however when Re > 40, there is

separation of the boundary layer over the cylinder due to an adverse pressure

gradient, causing the formation of shear layers (Hansen et al.,2015).

When it comes to

Reynolds number sensitivity in sharp edged bodies, Schewe, (2001) investigates a wide

range of the Reynolds number effects on three main bodies: a circular cylinder,

a trapezoidal-shaped bridge and a thick airfoil. During all three cases Scheme, (2001) was

able to verify that the Reynolds number has a dramatic effect on force

coefficient and St number. Both authors, Mannini, et al., (2010) and Schewe et al, (1998) were also able

to observe that although sharp-edged bluff bodies are believed to be insensitive to the

variation of Reynolds number due to the flow separation location be known, the

value of Reynolds number has a great influence on the flow reattachment and

also on the laminar-to turbulent transition.

Author Laima et al., (2017) investigates the

Reynolds number effects on the flow characteristics over a twin box girder

using the LES Smagorinsky-Lilly model with Reynolds ranging from 102

to 107, also concluding that flow around the twin-box girder has a

very high sensitivity to Reynolds number.

1.3 Flow characteristics around a

bridge deck

Regarding the flow behaviour around

the bridge deck Haque et al., (2015), observe a trend on the flow pattern that

when Reynolds number is increased to up to 13x 104 the flow

separations on the bottom-deck leading edge side also increases, however the

top deck leading-edge side and bottom-deck trailing-edge side the flow

separations decreases.

With the prospects of Sharp edges

bodies such a bridge decks also having sensitivity to Reynolds number authors

such a Schewe, (2001) and Larsen, (1998) and Schewe, (2001) investigates

further and found that this dependency is mainly due to topological structures changes

of the separated flow and the wake.

These changes on the topological structure of the separated flow are

caused by the laminar/turbulent transition and its location Schewe, (2001). Schewe, (2001) also showed that the flow

around slender two-dimensional cross section structures may be highly three

dimensional. Schewe, (2001) explains

that the reason why flow separation is often Reynolds number dependent is

because the boundary layer has a global influence on the flow around the body

such as the location of the laminar/turbulent transition point or the separated

shear layer, both of which are responsible for the formation of separation

bubbles or the topological structure of the flow. The author highlights the main features of

the three bodies: At subcritical flow

the transition occurs in the wake which in response turns wide. This means high

drag and low value of St.

At supercritical flow, separation

bubbles occur and the boundary layer is now turbulent, the separation is forced

into a longer path length which in result produces a narrower wake and minimum

value of drag coefficient and a maximum of St number Schewe, (2001). At transcritical state transition occurs

before separation, however this has no significant effect on the size of the

wake or values of drag coefficient and strauhal number.

Another

characteristic trend observed by different authors is that the flow

reattachment moves upstream as Re number is increased. Mannini, Šoda and Schewe, (2010) observed

through the LEA model that the location of the reattachment point on the lower

side of the cylinder moves upstream as the RE in increased, which explain the

Re-dependency of the lift coefficient.

This Re-dependency

has also been confirmed by Laima

et al., (2017). The author investigates

the Reynolds number sensitivity of flow past a twin-box girder with Reynolds numbers

ranging from 102 ? Re ? 107. At the Leading

edge his finding demonstrates that at Reynolds number range 1.6 x 103 to

5x 103 the laminar separation of the flow occurs in corner of the

deck and reattaches on the surface, the separation bubble length increase with

the increase of Reynolds number. As Reynolds

number increases, 6 x 103 to 8 x 104, the transition from

shear layer to turbulence and reattachment points gradually move back upstream,

resulting into the bubble shrinkage with increase of Reynolds number. Finally, at relatively high Reynolds number

higher then 8×104, there is almost no variance on boundary layer

transition to turbulence or turbulent separation-reattachment Laima et al., (2017) and Li, Laima

and Jing, (2014).

Laima et al., (2017) carry on by

observing the flow in the trailing edge and finds the following pattern: At first a Karman vortex appears then a transition

of shear layer to turbulence develops, generating separation bubbles on the upper

and lower trailing edges. As the the

Reynolds number increases to 2×104 the separation bubble at the

lower side shrinks to zero and only at Reynolds number 107 the

separation bubble at the upper size finally shrinks to zero. This happens because the uppers side trailing

edge is blunter then the lower edge, which also means it has much wider

Reynolds number sensitivity.

The same pattern was

also observed by Li,

Laima and Jing, (2014), who investigates the Reynolds number effects on

aerodynamic characteristics and the vortex-induced vibrations of a twin-box

girder. Li et al., (2014) uses Reynolds numbers in the range of 5.85 x 103

to 1.12 x 105 for the simulations. He was able to detect that with

the increase of the Reynolds number the transition point from laminar flow to

turbulence flow and reattachment point of the separated shear layer moves

upstream gradually and the bubble sizes shrinks which indicates that the shear

layer and leading separation bubble are very dependent on the Reynolds number

and the Strouhal number increases with the increase o Reynolds number.

Concluding, although

some may think that sharp edged bodies are insensitive to the Reynolds number,

authors such as Schewe,

(2001); Mannini, et al.,

(2010) proved otherwise. This

Re-sensitivity is mainly due to topological structure changes, flow separations

and vortex shedding. These typical flow

feature can be observed and investigated by deploying the 2D URANS turbulence

model, which according to many author including Mannini et all., (2010) and

Haque et al., (2015), it is an efficient model that provides a good trade-off between computacional cost

and accuracy.

However, it is crucial to select a suitable Turbulence model and to ensure that

a grid-independent solution exists, which means the solution does not change

when the mesh is refined. It has also

been recognised that when Reynolds number values are increased so does the lift

coefficients and Strouhal numbers (St).

Conversely, drag coefficient decreases. However, at sufficiently high

Reynolds number, the drag coefficient may become independent of Reynolds

number.

OBJECTIVES

·

Selection of the most efficient Turbulence model

that is capable to model the flow around a bridge deck.

·

Investigation of drag and lift coefficients, as

well as Strauhal number, pressure and velocity distribution around the bridge

deck when subjected to different Reynolds numbers.

·

Bridge deck optimization: The study of the effects

of the bridge geometry on the velocity and pressure distribution around the

deck.

METHODOLOGY

This project starts

by correctly and efficiently selecting the best and most suitable Turbulence model

for the Humber bridge computational flow simulation. In order to validate the correct Turbulence

model, the flow around a circular cylinder, known to be sensitive to Reynolds

number changes will be studied and numerical results compared to experimental

results.

Initially the flow

around the circular cylinder will be modelled at a subcritical regime flow. The simulations start by subjecting the

bridge to a low Reynolds number Re=103 and a two-equation turbulence

model, Shear Stress Transport model (SST) used. Shear Stress Transport (SST) Turbulence model

is famously recognized to produce numerical results in good agreement with

experimental results, Rahman et al. (2008).

Also, by using a low Reynolds number the vortex shedding, velocity and

pressure distribution can also be easily observed.

Subsequently, the

flow is then modelled at a high Reynolds number, Re= 106. This will ensure that the Turbulence model

selected is able to capture the flow characteristics with accuracy at a low and

high Reynolds number. The Shear Stress Transport

model still applies.

In order to ensure

that the solution is grid-independent as well as converges, a test with different

mesh sizes is applied. The first

simulation starts with a mesh size (Ds) = 0.01, followed

by (Ds) = 0.005, (Ds) = 0.0025 and

finally (Ds)= 0.00125. Once the solution obtained does not

change with further mesh refined, the correct mesh size is then selected. For validation of the model employed on this

simulation, results for drag and lift coefficient is compared to previous

experimental data.

Next, a comparison

between Turbulence models results can be performed. The chosen model for this comparison is the k

– w Turbulence model, as this model can

successfully estimate turbulence in the near wall region. Again, results can be compared with previous

experimental data.

Based on the findings

of the flow around a circular cylinder the numerical modelling techniques and

the Turbulence model of the simulation is then applied to the the flow around a

bridge deck. A geometrically similar

model of Humber bridge is simulated and the characteristics of the wind flow

such force coefficients, velocity and pressure distributions around the bridge

can finally be evaluated. The flow

modelling starts with a low Reynolds number, Re = 103, increasing to

104, 105 and 106. The effects on drag, lift coefficient and

Strauhal number can be investigated when the bridge deck is subjected to

different Reynolds number.

Finally, a bridge

optimization study can be conducted by small changes being applied to the

original Humber bridge geometry. The

results of this changes can be compared to the original geometry results and

therefore a final conclusion can be drawn.

WORK PLAN & TIMETABLE

1st Phase-

Turbulence model validation (Flow around a circular cylinder)

Case

Re

V(m/s)

D(m)

r

m

Ds

Dt

t

Model

V.1

103

1

0.2

1000

0.2

0.01

0.005

30

SST

V.2

106

1

0.2

1000

0.002

0.01

0.005

30

SST

V.2.1

106

1

0.2

1000

0.002

0.0005

0.0025

30

SST

V.2.2

106

1

0.2

1000

0.002

0.00025

0.00125

30

SST

V.2.2.1

106

1

0.2

1000

0.002

0.00025

0.00125

30

K-w

2nd Phase

– Flow around the Humber bridge deck

Case

Re

V(m/s)

D(m)

r

m

Ds

Dt

t

Model

C-1

103

1

28.5

1000

0.002

0.00025

0.00125

30

SST

C-2

104

1

28.5

1000

0.002

0.00025

0.00125

30

SST

C-3

105

1

28.5

1000

0.002

0.00025

0.00125

30

SST

C-4

106

1

28.5

1000

0.002

0.00025

0.00125

30

SST

3rd Bridge

Optimization

Case

Re

V(m/s)

D(m)

r

m

Ds

Dt

t

Model

C-2.1

104

1

28.5

1000

0.002

0.00025

0.00125

30

SST

C-2.2

104

1

28.5

1000

0.002

0.00025

0.00125

30

SST

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validity of 2D numerical simulations of vortical structures around a bridge

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Patruno, L., Ubertini, F. and Vaona, P. (2013). On the evaluation of bridge

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