Experimental Studies on Flow Characteristics around Circular Cylinder in Steady and Unsteady Flow

Yeong-Bin Lee, Joo-Hyun Rho, Su-Hwan Yun, Kyu-Hong Kim and Dong-Ho Lee

School of Mechanical and Aerospace Engineering Seoul National University, Institute of Advanced Aerospace Technology

San 56-1, Shinlim-dong, Gwanak-Gu Seoul, Republic of Korea

aerocfd1@snu.ac.kr, http://hypersonic.snu.ac.kr

Abstract: - This paper describes on the airflow characteristics between steady and unsteady flow around the two dimensional circular cylinder in the range of Reynolds number of about 20,000~200,000. It is carried out wind tunnel testing. In the steady state experiment, it was measured maximum, minimum and mean pressure distribution data for 20 seconds by 100Hz. In the unsteady state, test condition is free stream with acceleration of 3m/s2. When the corresponding Reynolds number was reached to the steady state, pressure data were acquired. From the result of test, unsteady flow has different characteristics of surface pressure distribution. Therefore, an accelerated flow is higher pressure drag than steady flow. Key-Words: - Unsteady Aerodynamics, Wind tunnel test, Accelerated flow, Circular cylinder 1 Introduction In the nature, the flow is closer an unsteady flow than steady flow. For example, the high speed train and mobile are affected intermittent cross wind in a bridge and open land, wind effects at entering or exit a tunnel, a whirlwind around huge buildings. Experimental or numerical researches are difficult to simulate real flow (unsteady flow) clearly. Because of this difficulty, many researchers assumed steady flow to unsteady flow. Recently, the accident problems due to gust, thunderstorm are rising. Therefore, The research to understand about aerodynamic characteristics of unsteady state of natural flow phenomenon had been demanded.[1]

Generally, flow around blunt body has complex flow structure such as Karman vortex. The flow has characteristics both steady state and unsteady state. The circular cylinder and square cylinder model are based on the researches of flow around blunt body. So many researches have been studied fluently. Especially, the flow around a circular cylinder has different aspects by sub-critical, critical, super critical regions. On that count, it is researched about steady and unsteady state flow actively in a realm of fluid mechanics

Presently, the typical experimental studies on flow around a circular cylinder have been performed by V. Karman. V. Karman researched about Vortex Street around a circular cylinder. Fage and Warsap

researched about turbulence of free stream and drag and pressure distributions due to roughness. Wieselseger studied drag coefficient of a circular cylinder by various Reynolds number.[2,3,4] Roshko found that the periodic vortex shedding which had disappeared again in a trans-critical regime.[5,6] Schewe researched the Reynolds number effects in flow around bluff bodies.[7,8] T. Kim and Y.Ku studied on flow separation on a square cylinder in ground using experimental and numerical method.[9,10]

In, addition, unsteady flow research applied to rocket launch, turbo machinery, flutter, dynamic stall and vehicle on ground. Prandtl was first to research about accelerated unsteady flow by visualization of initial vortex formation over a circular cylinder.[11]

Gad-del-Hak researched unsteady separating flow on lifting surface. Freymuth investigated Reynolds number dependence of vortex patterns in accelerated flow around airfoil using visualization.[12] Finaish reported on vortex structures and processes over bluff bodies in impulsive flow.[13,14]

However, researches of recent accelerated unsteady flow are limited flow visualization and separating flow. Therefore, researches of accelerated or decelerated flow are needed more detailed, systematic and quantities approximation.

Therefore, this paper presents comparison and analysis Pressure field variations over a circular about accelerated unsteady flow around a circular cylinder in

5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 25-27, 2008

ISSN: 1790-5117 Page 65 ISBN: 978-960-6766-30-5

various regions of Reynolds number using wind tunnel testing. From the results of test, pressure distribution has difference between steady state and unsteady state. 2 Description of the Experiment 2.1 Experimental Apparatus The experiments were conducted in a closed-type low turbulence wind tunnel in Seoul National University. The dimension of the closed test section is 1m (height) ×1.5m (width) ×2.5m (length) and the maximum wind speed is about 75m/s with a turbulence intensity being less than 0.3%. The test section with a cylinder model is presented in Fig. 1 The free stream velocity was in the range of 5~75m/s (Re=4.22×104~2.05×105). The experiments were carried out with the circular cylinder. The model was made of PVC having a diameter of 0.06m. Pressure taps for measuring the surface pressure distributions were mounted linearly with 22.5° to the center line in order to eliminate the interaction between pressure taps. Each pressure taps were connected to the pressure transducer (Netscanner of Pressure Systems Company) through the 16 channels. Each channel was connected DH200 transducers. These transducers are available with full scale pressure ranges from 10H20 to 0.72psi. There are capable of accuracies up to ±0.05%. Measuring frequency of data is 100Hz. The pressure transducer for measuring velocity of free stream was MKS Bararon Model 220. The variable capacitance differential model has an accuracy of 0.15% in full scale (100torr).

Used softwares for measuring were LABView and Netscnner. Data acquisition boards are E-6110 and E-6024 of National Instruments Company.

Fig. 1 Test section of wind tunnel with model

2.2 Experimental Conditions

In steady flow experiments, the surface pressure distribution data were acquired at specific Reynolds number (2.05×104, 4.11×104, 8.22×104, 1.23×105, 1.64×105 2.05×105) during 20 seconds by 100Hz.

In unsteady flow experiments, using controlling fan of wind tunnel for acceleration of 3m/s2, the accelerated flow was applied to the experimental model. When corresponding Reynolds number is reached to steady state, velocity and pressure distribution over a circular cylinder were measured. From a preliminary test, turbulent intensities of free stream are in 0.3% between steady and unsteady state.

This figure 2 represents the condition of accelerated unsteady flow.

Acceleration

05

101520

0 50000 100000 150000 200000Reynolds number

Time[s

ec.]

a=3m/s2

Acceleration

05

101520

0 50000 100000 150000 200000Reynolds number

Time[s

ec.]

a=3m/s2

Fig. 2 Accelerated unsteady flow

3 Results and Discussions Generally, the flow is explained three governing equation; continuity, momentum, energy. Steady and unsteady flow is a short time for a variation in accordance with distinction. In case of unsteady flow, continuity equation and energy equation are same equations of steady flow. But, momentum equation is added unsteady term for two dimensional flows as euations (1), (2), (3).

0=∂∂

+∂∂

yv

xu

(1)

⎥⎦

⎤⎢⎣

⎡∂∂

+∂∂

+∂∂

−=∂∂

+∂∂

+∂∂

2

2

2

21yu

xu

xp

yuv

xuu

tu ν

ρ (2)

⎥⎦

⎤⎢⎣

⎡∂∂

+∂∂

+∂∂

−=∂∂

+∂∂

+∂∂

2

2

2

21yv

xv

yp

yvv

xvu

tv ν

ρ (3)

Unsteady term is consisted of viscous and inertial term. Momentum equation is normalized by characteristic length, characteristic velocity, and characteristic time. Strouhal number ( UTL / ) influence unsteady terms like the equation (4).[15, 16, 17]

5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 25-27, 2008

ISSN: 1790-5117 Page 66 ISBN: 978-960-6766-30-5

⎥⎦

⎤⎢⎣

⎡∂∂

+∂∂

+∂∂

=∂∂

+∂∂

+∂∂

*

**

*

**

*

*2

yuv

xuu

tu

UTL

LU

yuv

xuu

tu (4)

The unsteady term is disregarded in less then

Strouhal number 1. The problem of steady boundary layer is assumed to time change of flow. This problem is solved by quasi-steady state. However, it has difference between steady state and quasi-steady state if Strouhal number is high.

The flow with acceleration is unsteady flow. Initial flow far away the model is irrotational potential flow. If flow comes in the model, the velocity of flow is similar to velocity of model. Therefore, velocity gradients on the model are occurred highly. At this moment, the vorticity is proportioned to velocity gradient distributes on the surface of model. Distributed vortices diffuse by viscous after time pasts. When the velocity of flow is increasing, convection effects by relative flow that was regarded in start-up from the rest are important. The inertial term is larger than viscous term relatively. The vorticity of viscous diffusion and convection of low are equilibrium. The boundary layer of vorticity is formed. Because of this, the effects are rising, flow separates at surface of model has adverse pressure gradient and this separation point is moved by variations of velocity. Therefore, another flow pattern is created.

This paper studied comparison and analysis about pressure distribution between steady state and accelerated unsteady state.

Figure 3 represents separation occur over 70degrees and suction peak is appeared in steady state experiment.[18] In addition when Reynolds number is increased, the energy exchange increase. So, the rear of the cylinder pressure can be seen that the value is slowly recovering.

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135 180 225 270 315 360

Angle[deg.]Cp

4.11E+04 8.22E+041.23E+05 1.64E+052.05E+05 Reference[18]

Fig. 3 Cp in steady flow

Figure 4 shows pressure distribution of accelerated

unsteady flow in specific Reynolds number. From the result of test, steady and accelerated unsteady flow has differences of aerodynamic characteristics. That is, it is known from surface pressure distribution over a circular cylinder to drag and lift components of pressure distribution. Drag and lift components of pressure distribution have difference between steady and accelerated unsteady flow clearly. Effects of Viscous term and Strouhal number increase in initial flow starts up from the rest. Then vortex formation and shedding over a circular cylinder makes unstable flow. Maximum and minimum values of pressure distribution are larger. But When Reynolds number is increased, inertial term is getting higher than viscous term, Strouhal number is getting lower. Therefore flow is getting more stable. Surface pressure distributions lower than pressure distributions of steady state up to 1.0×105. That is, flow velocity increase due to acceleration. Momentum is supplied to flow under flow is unstable. For that reason, Reynolds number on a circular cylinder seems to be larger. Figure 5 shows drag and lift component of Cp.

Figure 6 shows summation of drag component to know detailed about variation of pressure distribution. According to comparisons of drag component, the flow characteristics fluctuate in low Reynolds number. When Reynolds number is increasing, the variations of drag component are small. In the regions of low Reynolds number, the effects of viscous term are higher than effects of inertial term in unsteady term and the flow is more complex due to vortex formation by Strouhal number. But, when Reynolds number is increasing, the effects of inertial term are getting higher than effects of viscous term. Strouhal number is getting smaller too. Therefore the flow is getting stable. According to figure 6, drag component is higher than drag component of mean steady state up to about 1.0×105.

Maximum variations of drag component are about 7~10% up to 1.64×105 (15seconds later) In the regions of high Reynolds number, unsteady flow with acceleration has much momentum than steady flow, and effects of inertial term are larger. Then Vortex on a circular cylinder is getting larger. At the regions of accelerating flow around a circular cylinder after a start from rest, pressure distribution is lower than mean value of steady state.

5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 25-27, 2008

ISSN: 1790-5117 Page 67 ISBN: 978-960-6766-30-5

Re=4.11e+04

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135 180 225 270 315 360

Angle[degree]

Cp

Steady Unsteady

Re=8.22e+04

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135 180 225 270 315 360

Angle[degree]

Cp

Re=1.23e+05

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135 180 225 270 315 360

Angle[degree]

Cp

Re=1.64e+05

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135 180 225 270 315 360Angle[degree]

Cp

Re=2.05e+05

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135 180 225 270 315 360

Angle[degree]

Cp

Fig. 4 Cp in unsteady flow

Re=4.11e+04

-1

-0.5

0

0.5

1

1.5

0 45 90 135 180

Angle[degree]

Cp

cosθ

Re=4.11e+04

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135 180

Angle[degree]

Cp

sinθ

Re=8.22e+04

-1

-0.5

0

0.5

1

1.5

0 45 90 135 180Angle[degree]

Cp

cosθ

Re=8.22e+04

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135 180

Angle[degree]

Cp

sinθ

Re=1.23+05

-1

-0.5

0

0.5

1

1.5

0 45 90 135 180

Angle[degree]

Cp

cosθ

Re=1.23e+05

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135 180

Angle[degree]

Cp

sinθ

Re=1.64+05

-1

-0.5

0

0.5

1

1.5

0 45 90 135 180

Angle[degree]

Cp

cosθ

Re=1.64e+05

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135 180

Angle[degree]

Cp

sinθ

Re=2.05+05

-1

-0.5

0

0.5

1

1.5

0 45 90 135 180

Angle[degree]

Cp

cosθ

Re=2.05e+05

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135 180

Angle[degree]

Cp

sinθ

Fig. 5 Drag and Lift component of Cp

5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 25-27, 2008

ISSN: 1790-5117 Page 68 ISBN: 978-960-6766-30-5

0.6

0.7

0.8

0.9

1

1.1

1.2

10000 50000 90000 130000 170000 210000

Reynolds number

ΣC

pcosθ

*(c

/L)

Steady flow

Unsteady flow

Fig. 6 ΣCpcosθ*(c/L) Difference

between steady and unsteady

Therefore, it could show drag and lift is lower over a circular cylinder due to Wagner effect well-known. So accelerated unsteady flow has higher pressure drag than steady state flow.

Consequently, the flow that assumed steady state has difference of aerodynamic characteristics of unsteady flow. When Reynolds number increase, the effects are getting larger. The flow assumed steady state and quasi-steady state are insufficient to predict unsteady flow. 4 Concluding remarks In conclusion, we have investigated pressure distribution over a circular cylinder under steady state and accelerated unsteady state using wind tunnel test. From the results of experiment, pressure distribution has been changed by steady state and accelerated unsteady state.

In the regions of 5seconds during flow is started from the rest, drag and lift components of the flow is lower due to Wagner effect well-known.

But Strouhal number and unsteady term due to momentum supply by acceleration are getting higher than steady state in the range of up to about 1.0×105. Then the pressure distribution of accelerated unsteady flow is higher than steady flow over a circular cylinder. That is, integrals of drag component show the effects clearly. Consequently, pressure drag of accelerated unsteady flow could be higher than steady state flow. Acknowledgement We would like to thank to “Next Generation High Speed Train Project” and “BK21, Flight vehicle research center in Seoul national university”.

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[3] D.J. Tritton, “Experiments on the flow past a circular cylinder at low Reynolds numbers”, Journal of Fluids Mechanics, Vol. 6, pp.547-567, 1959

[4] M. Coutanceau, R. Bouard, “Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation Part 1. Steady flow”, Journal of Fluids Mechanics, Vol. 79, pp. 231-256, 1977

[5] W.C.L. Shih, C. Wang, D. Coles, A. Roshko, “Experiments on flow past Rough circular cylinders at large Reynolds numbers”, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 49, pp.351-368, 1993

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[8] H.J. Niemann, N.Holsher.,”A recview of recent experiments on the flow past circular cylinder”,Journal of Wind Engineering and Industrial Aerodynamics, Vol. 33, pp. 197-209, 1990

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[11] P. Freymuth, W. Bank, and M. Palmer, “Reynolds number dependence of vortex patterns in accelerated flow around airfoils”, Experiments in Fluids, Vol. 3, pp.109-112, 1985

5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 25-27, 2008

ISSN: 1790-5117 Page 69 ISBN: 978-960-6766-30-5

[12] F.Finaish, M. Palmer, and P. Freymuth, “A parametric analysis of vortex patterns visualized over airfoils in accelerating flow”, Experments in Fluids, Vol. 5, pp.284-288, 1987

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[14] A. Golovkin, V.M. Kalyavkinm V.G. Kolkov, “Optical visualization of accelerated and decelerated flow over a circular cylinder”, Fluid Dynamics, Vol. 16, No.2, pp.266-271, 1981

[15] Fey, M. Konigm H. Eckelmann, “A new strouhal reynolds number relationship for the circular cylinder in the range 47<Re<2× 105”, Physics fluids, Vol. 10, pp. 1547-1549, 1998

[16] William Frederick Durand, Aerodynamic Theory, Peter Smith Publisher, 1976

[17] Frank M. White, Viscous Fluid Flow, McGRAW-HILL, 1991

[18] John D. Anderson, Fundamentals of Aerodynamics 2nd edition, McGRAW-HILL, 1991

5th WSEAS International Conference on FLUID MECHANICS (FLUIDS'08) Acapulco, Mexico, January 25-27, 2008

ISSN: 1790-5117 Page 70 ISBN: 978-960-6766-30-5