omae2013-10454: experimental study on flow around circular cylinders with low aspect ratio

Nantes| France | June | 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering 1

EXPERIMENTAL STUDY ON FLOW AROUND CIRCULAR CYLINDERS WITH LOW ASPECT RATIO

June | 2013

Rodolfo T. Gonçalves

Guilherme F. Rosetti

Guilherme R. Franzini

André L. C. Fujarra

TPN – Numerical Offshore Tank

Department of Naval Architecture and Ocean

Engineering

Escola Politécnica – University of São Paulo

São Paulo, SP, Brazil


Outline

• Introduction

• Objectives

• Experimental Setup

• Results

– Force measurements

– PIV

• Conclusions


Introduction

• The flow field around stationary low aspect ratio cylinders, 𝐿/𝐷 < 6, is much less understood than the classical case of infinite length cylinder;

• VIM in the offshore scenario: – Spars (1.5 < L/D < 6);

– Monocolumns (0.2 < L/D < 0.5);

– SS columns (0.4 < L/D < 3).

Models of the flow around low aspect ratio

circular cylinder. Source: Kawamura et al.

(1984)


Objectives

• Understand the aspect ratio influence in the forces around the cylinder (streamwise, x, and transverse, y, directions) and vortex shedding frequency: through force measurements.

• Visualize the flow around the free end and immediately behind the cylinder where the flow recirculates: using PIV technique.

• Very low aspect ratio cylinders:

0.1 ≤ 𝐿 𝐷 ≤ 2


Experimental Setup

• All the experiments were carried out in a recirculating water channel at the NDF – Fluid & Dynamics Research Group Laboratory facility of USP – University of São Paulo, Brazil.

• The dimension of the test section is 7500x700x700mm and the flow has low levels of turbulence (less than 2%).

• The model was made of PVC - polyvinyl chloride with external diameter 𝐷=125mm and was placed at the centerline of the channel.


Experimental Setup

Force Measurements • A 6-DOF load cell was used to acquire the

hydrodynamic forces.

• Eight different aspect ratios were tested, namely 𝐿/𝐷 = 0.1, 0.2, 0.3, 0.5, 0.75, 1.0, 1.5 and 2.0;

• The range of Reynolds number covers 10,000 < Re < 50,000;

• 40 different velocities to each aspect ratio;

• The changes in the aspect ratio were made changing the water level, 𝐻, of the water channel.

z

x

L

U

h

H Free end

Free surface

D

y

xW

Water channel bottom

U

Water channel lateral

TOP VIEW

SIDE VIEW

Load cell

x

z

x y

z


Experimental Setup

PIV Measurements

• Two different planes were chosen to be measured:

– horizontal mid-span plane at 𝑧/𝐿 = −0.5, and;

– vertical centre plane at 𝑦/𝐷 = 0.

• PIV measurements were performed in some aspect ratio cases, namely 0.3, 0.5, 1.0 and 2.0;

• Reynolds number equal to 43,000.

zy

xFree-surface

plane

PIV horizontalplane

z y

xFree-surface

plane

PIV verticalplane


Experimental Results Force Measurements

• The non-dimensional forces were evaluated for each Reynolds condition (180s tested):

– 𝐶𝑥 (𝑡) =2𝐹𝑥(𝑡)

𝜌𝐿𝐷𝑈2

– 𝐶𝑦(𝑡) =2𝐹𝑦(𝑡)

𝜌𝐿𝐷𝑈2

• The vortex shedding frequency, 𝑓𝑠, was inferred from the frequency related to the largest peak energy in the of the 𝐶𝑦(𝑡):

– 𝑆𝑡 =𝑓𝑠𝐷

𝑈

0 20 40 60 80 100 120 140 160 1800.5

1

1.5

Cx

Time [s]

Re = 43 000

Original Signal

Filtered Signal 0,05Hz<f<1,00Hz

0 20 40 60 80 100 120 140 160 180-0.4

-0.2

0

0.2

0.4

Time [s]

Cy

Re = 43 000

Original Signal

Filtered Signal 0,05Hz<f<1,00Hz

• Time history of force coefficients for cylinder with 𝐿/𝐷 = 2.0 and Re = 43,000: (a) streamwise and (b) transverse direction.



Mean force, 𝐶𝑥, in the streamwise direction

• The values of 𝐶𝑥 decrease with decreasing aspect ratio, except for 𝐿/𝐷 = 0.1;

• The standard deviations are largest for the lowest aspect ratios;

• 𝐹𝑟𝐿 = 𝑈/ 𝑔𝐿 in lowest

aspect ratio conditions are high, 𝐹𝑟𝐿 > 0.5;

00.511.522.530

0.2

0.4

0.6

0.8

1

L / D

Cx

0 1 2 3 4 5

x 104

0

0.2

0.4

0.6

0.8

1

Reynolds Number (Re)

Cx

L / D = 2.00

L / D = 1.50

L / D = 1.00

L / D = 0.75

L / D = 0.50

L / D = 0.30

L / D = 0.20

L / D = 0.10



Fluctuation force, 𝐶𝑥 𝑟𝑚𝑠, in the streamwise direction

• The values of non-dimensional streamwise force fluctuation 𝐶𝑥 𝑟𝑚𝑠 is practically constant, 𝐶𝑥 𝑟𝑚𝑠~0.1 for cylinders with 2 ≤ 𝐿/𝐷 ≤ 0.75, but with a decrease for 𝐿/𝐷 < 0.5;

Fluctuation force, 𝐶𝑦 𝑟𝑚𝑠, in the transverse direction

• The values of non-dimensional transverse force fluctuation 𝐶𝑦 𝑟𝑚𝑠

is practically constant, 𝐶𝑦 𝑟𝑚𝑠~0.06 ± 0.01 for cylinders

with 2 ≤ 𝐿/𝐷 ≤ 0.75, but with a decrease for 𝐿/𝐷 < 0.5.

00.511.522.530

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

L / D

Cy rm

s

00.511.522.530

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

L / D

Cx rm

s



PSD for force in the transverse direction

• It is possible to determine a dominant frequency for a cylinder with 𝐿/𝐷 = 2;

• The value of 𝑆𝑡 is pratically constant with Reynolds number for cylinder with 𝐿/𝐷 = 2;

• The value of 𝑆𝑡 deacreses with increasing Reynolds number for cylinder with 𝐿/𝐷 = 0.3;



St values • The values of 𝑆𝑡 showed a marked

decrease with decreasing aspect ratio; • Same behavior reported by other

authors (Sakamoto & Arie (1983), Fox & West (1993), Park & Lee (2000), Sumner et al. (2004) and Iungo et al. (2012);

• It is interesting to note that for 𝐿/𝐷 < 0.5, it was not possible to define a unique dominant frequency constant with Reynolds.

• This fact is due to the three-dimensional structures formed downstream the cylinder for these aspect ratio conditions, but it is possible to note that these structures have lower shedding frequency.

00.511.522.530

0.05

0.1

0.15

0.2

0.25

L / D

Str

ou

ha

l N

um

be

r (S

t)


Experimental Results PIV Measurements

PIV horizontal plane at 𝑧/𝐿 = −0.5

• Contours of the mean streamwise velocity 𝑈𝑥/𝑈 together with streamlines;

• The streamlines for 𝐿/𝐷 = 2.0 show the typical picture of the flow around a circular cylinder;

• The bubble length at mid span length reduces significantly with the decreasing aspect ratio;

• The effects of the free end are clearly present already and they are much stronger for the lowest aspect ratio cylinder, in which the free-end effects on the longitudinal recirculation region distort the bubble in the horizontal plane. For 𝐿/𝐷 = 0.3, it is difficult to find the bubbles in the horizontal plane.

L/D = 2.0 L/D = 1.0

L/D = 0.3 L/D = 0.5



PIV vertical plane at 𝑦/𝐷 = 0

• Contours of the mean streamwise velocity 𝑈𝑥/𝑈 together with streamlines;

• The incident flow moves below the free-end cylinder, separating at the leading edge;

• Behind the cylinder, a large longitudinal recirculation region is observed for both cases;

L/D = 2.0 L/D = 1.0

L/D = 0.3 L/D = 0.5



Mean vorticity at horizontal plane

• In general, the flow field in the horizontal plane, consists of two symmetric vortices with positive or negative values with respect to the wake center plane, 𝑦/𝐷 = 0.

• The vertical vorticity, 𝜔𝑧𝐷/𝑈, decreases with decreasing aspect ratio, this fact corroborates that the vortex shedding diminishes in the horizontal plane for decreasing aspect ratio.

L/D = 2.0 L/D = 1.0

L/D = 0.3 L/D = 0.5



Mean vorticity at vertical plane

• Looking at the transverse vorticity, 𝜔𝑦𝐷/𝑈, the shear layer below the free-end cylinder is visible.

• This remains fairly steady for approximately 0.2𝐷 below and 0.5𝐷 behind and above the free end for all aspect ratios.

• The results showed that for 𝐿/𝐷 ≤ 0.5, the entire wake is contaminated with three-dimensional effects due to the free end.

L/D = 2.0 L/D = 1.0

L/D = 0.3 L/D = 0.5


General Conclusion Force Measurements

• The forces in the streamwise direction, x, decrease with decreasing aspect ratio, from 𝐶𝑥~1 for 𝐿/𝐷 = 2 to 𝐶𝑥~0.7 for 𝐿/𝐷 = 0.3.

• The forces in the transverse direction are practically constant, 𝐶𝑦 𝑟𝑚𝑠~0.06 ± 0.01, for cylinders with 2 ≤ 𝐿/𝐷 ≤ 0.75.

• The higher three-dimensional behavior of the wake is also responsible for the decrease in the Strouhal number, from 𝑆𝑡~0.15 for 𝐿/𝐷 = 2 to 𝑆𝑡~0.05 for 𝐿/𝐷 = 0.5.


General Conclusions PIV Measurements

• The visualizations showed two recirculation regions: the first one below the free-end cylinder, and the second one behind the cylinder characterizing a recirculation bubble;

• PIV measurements in the vertical xy plane must be performed. Results obtained by Rosetti et al. (2013) – OMAE2013-10963, confirm the existence of vortex with main vorticity in the streamwise direction, that can be the source of alternating forces for low aspect ratio cylinders when the Von Kármán does not exist;


Think about...

Illustration of vortex tubes associated to the flow around a semi-sphere body (Re>2,000). Source: Tamai et al. (1987).


Acknowledgments

• The authors thank Eng. Dr. Ivan Korkischko and Eng. César M. Freire for their help in performing the tests.

• The authors thank Prof. Dr. Julio R. Meneghini for his help in the discussions, and to support the tests.

• The authors would also like to acknowledge CNPq and CAPES for the financial support, and also PNV-USP.


THANKS

[email protected]

omae2013-10454: experimental study on flow around circular cylinders with low aspect ratio

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