INTRODUCTION fluid dynamics (CFD) techniques, although not yet to

 

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.

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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

 

 

 

 

 

REFERENCES

 

Bruno, L. and Khris, S. (2003). The
validity of 2D numerical simulations of vortical structures around a bridge
deck. Mathematical and Computer Modelling, 37(7-8), pp.795-828.

 

Brusiani, F., de Miranda, S.,
Patruno, L., Ubertini, F. and Vaona, P. (2013). On the evaluation of bridge
deck flutter derivatives using RANS turbulence models. Journal of Wind
Engineering and Industrial Aerodynamics, 119, pp.39-47.

 

Fransos, D. and
Bruno, L. (2010). Edge degree-of-sharpness and free-stream turbulence scale
effects on the aerodynamics of a bridge deck. Journal of Wind Engineering and
Industrial Aerodynamics, 98(10-11), pp.661-671

 

Hansen, S.O., Srouji,
R.G., Isaksen, B., Berntsen, K., 2015. Vortex-induced vibrations of streamlined
single box girder bridge decks. In: Proc. of 9th National Symposium on Wind
Engineering, ICWE14, Jun 21-26, Porto Alegre, Brazil.

 

Haque, M., Katsuchi,
H., Yamada, H. and Nishio, M. (2015). Flow field analysis of a
pentagonal-shaped bridge deck by unsteady RANS. Engineering Applications of Computational
Fluid Mechanics, 10(1), pp.1-16.

 

Haque, M., Katsuchi,
H., Yamada, H. and Nishio, M. (2016). Investigation of edge fairing shaping
effects on aerodynamic response of long-span bridge deck by unsteady RANS.
Archives of Civil and Mechanical Engineering, 16(4), pp.888-900.

 

Laima, S., Jiang, C.,
Li, H., Chen, W. and Ou, J. (2017). A numerical investigation of Reynolds
number sensitivity of flow characteristics around a twin-box girder. Journal of
Wind Engineering and Industrial Aerodynamics, 172, pp.298-316.

 

Larsen, A. and Walther, J. (1998).
Discrete vortex simulation of flow around five generic bridge deck
sections. Journal of Wind
Engineering and Industrial Aerodynamics,
77-78, pp.591-602.

 

Li, H., Laima, S. and
Jing, H. (2014). Reynolds number effects on aerodynamic characteristics and
vortex-induced vibration of a twin-box girder. Journal of Fluids and
Structures, 50, pp.358-375.

 

Mannini, C., Šoda,
A., Voß, R. and Schewe, G. (2010). Unsteady RANS simulations of flow around a
bridge section. Journal of Wind Engineering and Industrial Aerodynamics,
98(12), pp.742-753.

Mannini, C., Šoda, A. and Schewe, G.
(2010). Unsteady RANS modelling of flow past a rectangular cylinder:
Investigation of Reynolds number effects. Computers & Fluids, 39(9), pp.1609-1624.

 

P.J. Roache,
Verification and Validations in Computational Science and Engineering, Hermosa
Publishers, Albuquerque, New Mexico, 1998

 

Rahman, M.M., Karim,
M.M., Alim, M.A., (2008). Numerical investigation of unsteady flow past a
circular cylinder using 2-d finite volume method. J. Nav. Archit. Mar. Eng., 4.
Ocean Eng. 38, 719–731.?

Schewe, G. and Larsen, A. (1998).
Reynolds number effects in the flow around a bluff bridge deck cross
section. Journal of Wind
Engineering and Industrial Aerodynamics,
74-76, pp.829-838.

Schewe, G. (2001). Reynolds-number
effects in flow around more-or-less bluff bodies. Journal of Wind Engineering
and Industrial Aerodynamics, 89(14-15), pp.1267-1289.

Stringer, R., Zang, J. and Hillis, A.
(2014). Unsteady RANS computations of flow around a circular cylinder for a
wide range of Reynolds numbers. Ocean Engineering, 87, pp.1-9.

Wilcox, D.C., 1998. Turbulence
Modelling for CFD. DCW Industries Inc., La Canada, CA, USA.

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