validation 3. laminar flow around a circular cylinderkshollen/me554/labs/validation_example.pdf ·...

Validation 3. Laminar Flow Around aCircular Cylinder

3.1 Introduction

Steady and unsteady laminar flow behind a circular cylinder, representing flow aroundbluff bodies, has been subjected to numerous experimental and computational studies.Most of the experimental studies are based on flow visualization and they indicate thatas the Reynolds number Re increases, the flow shows a series of different structures [1].One of the most prominent flow structure changes takes place in the vicinity of Re = 40.Below this Reynolds number, the flow is steady and characterized by the presence of asymmetric pair of closed separation bubbles. Beyond Re = 40, the flow becomes unsteadyand asymmetric, and alternate vortex shedding begins.

3.2 Purpose

The purpose of this test is to validate FLUENTs ability to predict the flow structureas well as the reattachment length and Strouhal number against experimental results.The present calculations were confined to the low-Reynolds-number regime (Re = 20,Re = 40, and Re = 100), which encompasses steady symmetrical separated flow as wellas unsteady asymmetric flow. The results were compared with the flow visualizationspresented in [1] and the experimental data in [2].

3.3 Problem Description

An infinitely long circular cylinder of diameter D = 2.0 m is placed in an otherwiseundisturbed uniform crossflow (U = 1.0 m/s) as shown in Figure 3.3.1. The lateralboundary and the exit boundary in the far wake are placed at 5D and 20D from thecenter of the circular cylinder, respectively.

3.3.1 Fluid Properties

The properties of the fluid are assumed to be constant, as shown in Table 3.3.1.

3.3.2 Flow Physics

The Reynolds number is based on the cylinder diameter and the free stream velocity.Different values of Re (20, 40, 100) in the simulation were obtained by changing theviscosity.

c Fluent Inc. September 13, 2002 3-1

Laminar Flow Around a Circular Cylinder

u=1.0, v=0.0

FlowU = 1.0T = 273 K

D

20D

u=0.0v=0.0T = 373 K

W

10D

Figure 3.3.1: Problem Description

Table 3.3.1: Fluid Properties

Reynolds No., Re 20 40 100Density, 1 kg/m3 1 kg/m3 1 kg/m3

Viscosity, 0.1 Pa-s 0.05 Pa-s 0.02 Pa-s

Re =UD

(3.3-1)

The experimental Strouhal number for the Re = 100 case is 0.165, derived from [2] anddefined as

S =D

U(3.3-2)

where is the period of the vortex shedding.

3.3.3 Boundary Conditions

The no-slip wall condition is applied to the cylinder wall. Uniform free stream conditions(U = 1.0 m/s) are applied at the inlet and lateral boundaries. The flow exit is treatedas a zero-normal-gradient outlet boundary.

3.4 Grid

A 51 51 quadrilateral mesh was used in this validation study, and is shown in Fig-ure 3.4.1.

3-2 c Fluent Inc. September 13, 2002

3.5 Case Setup

velocity-inlet-3

velocity-inlet-3

outflow

velocity-inlet-7

Figure 3.4.1: Grid

3.5 Case Setup

The FLUENT case was set up using constant fluid properties and the boundary conditionsdescribed in Section 3.3. Three runs were made using different values of viscosity to yieldthree different Reynolds numbers (Re = 20, 40, and 100) as shown in Table 3.5.1.

Table 3.5.1: Run Conditions

Run 1 2 3Reynolds Number, Re 20 40 100

3.6 Calculation

The second-order discretization scheme was used throughout this study. The first twocases (Re = 20, 40) were run for steady-state solutions and the third case (Re = 100)was modeled as transient with a time step of 0.2 s.

For velocity-pressure coupling, the SIMPLEC algorithm was used. When the SIMPLECalgorithm is used, the pressure under-relaxation is automatically increased to 1.0. (Thesetting for pressure under-relaxation is 0.3 when the default SIMPLE algorithm is used).Here the momentum under-relaxation has also been increased from 0.7 to 0.9 to yieldbetter convergence.

To break the symmetry of the flow and eventually trigger the vortex shedding, artificialperturbation was applied. The flow was perturbed by patching a uniform x velocity of 1m/s in the upper half of the domain and 0 m/s in the lower half. This is done using acustom field function defined as

u =y + |y|

2y(3.6-1)



where u is the x velocity.

This custom field function is saved in the case file with the name initialvelocity.After initializing the flow, the x velocity of the entire fluid zone must be patched withthis custom field function.

It should be noted that the use of artificial perturbation is not mandatory. It was appliedhere to expedite the symmetry breaking and subsequent vortex shedding.

3.7 Results

3.7.1 Re = 20 and Re = 40

The near-wake contours of stream function and the velocity vectors for the Re = 20 andRe = 40 cases are shown in Figures 3.7.13.7.4. The flows are seen to be practicallysymmetric.

The reattachment length is measured from the downstream side of the cylinder to thepoint where the x velocity changes sign from negative to positive. In this FLUENT model,a line named centerline and aligned with the x axis was created. XY plots of x velocityalong the centerline are shown in Figures 3.7.5 and 3.7.6. The reattachment lengths,normalized by the cylinder radius (R = 1 m), are shown in Table 3.7.1.

Figure 3.7.7, which was taken from [2], shows the time evolution of the reattachmentlength collected from various sources. The present results are seen to agree fairly wellwith the data from [2].

Table 3.7.1: FLUENT Dimensionless Reattachment Lengths (LA)

Re = 20 Re = 40LA 1.85 4.27

3.7.2 Re = 100

Figures 3.7.83.7.17 show the instantaneous velocity vector field and the correspondingstreamlines at the five phases during one cycle of the vortex shedding. The alternateformation, convection, and diffusion of the vortices are clearly seen. To quantify theperiodicity of the flow, the time history of the y velocity at a point situated 1 m behindthe cylinder in the near wake (x, y) = (2, 0) was recorded and is shown in Figure 3.7.18.The average period was found to be = 12.1 s, which is equivalent to a Strouhal numberof 0.165. Figure 3.7.19, taken from [2], shows a collection of data from many sources onthe Strouhal number vs. Reynolds number relationship. The FLUENT result agrees wellwith an average of the data shown in the figure.


3.7 Results

Contours of Stream Function (kg/s)Laminar Flow Over a Cylinder ( Re=20)

FLUENT 6.0 (2d, segregated, lam)Feb 05, 2002

1.01e+01

1.00e+01

1.00e+01

1.00e+01

1.00e+01

1.00e+01

1.00e+01

1.00e+01

1.00e+01

9.99e+00

9.98e+00

9.98e+00

9.97e+00

9.96e+00

9.96e+00

9.95e+00

Figure 3.7.1: Stream Function Contours in the Wake (Re = 20)

Contours of Stream Function (kg/s)Laminar Flow Over a Cylinder ( Re=40)


1.01e+01

1.00e+01

1.00e+01

1.00e+01

1.00e+01

1.00e+01

1.00e+01

1.00e+01

1.00e+01

9.99e+00

9.98e+00

9.98e+00

9.97e+00

9.96e+00

9.96e+00

9.95e+00

Figure 3.7.2: Stream Function Contours in the Wake (Re = 40)



Velocity Vectors Colored By Velocity Magnitude (m/s)Laminar Flow Over a Cylinder ( Re=20)


6.00e-01

5.60e-01

5.20e-01

4.80e-01

4.40e-01

4.00e-01

3.61e-01

3.21e-01

2.81e-01

2.41e-01

2.01e-01

1.61e-01

1.21e-01

8.11e-02

4.12e-02

1.30e-03

Figure 3.7.3: Velocity Vectors in the Wake (Re = 20)

Velocity Vectors Colored By Velocity Magnitude (m/s)Laminar Flow Over a Cylinder ( Re=40)


7.85e-01

7.33e-01

6.81e-01

6.28e-01

5.76e-01

5.24e-01

4.72e-01

4.20e-01

3.67e-01

3.15e-01

2.63e-01

2.11e-01

1.59e-01

1.06e-01

5.43e-02

2.09e-03

Figure 3.7.4: Velocity Vectors in the Wake (Re = 40)


3.7 Results

X VelocityLaminar Flow Over a Cylinder ( Re=20)


Position (m)

(m/s)Velocity

X

32.521.510.50

5.00e-03

0.00e+00

-5.00e-03

-1.00e-02

-1.50e-02

-2.00e-02

-2.50e-02

-3.00e-02

-3.50e-02

-4.00e-02

centerline

Figure 3.7.5: x Velocity Along the Centerline (Re = 20)

X VelocityLaminar Flow Over a Cylinder ( Re=40)


Position (m)

(m/s)Velocity

X

6543210

4.00e-02

2.00e-02

0.00e+00

-2.00e-02

-4.00e-02

-6.00e-02

-8.00e-02

-1.00e-01

-1.20e-01

centerline

Figure 3.7.6: x Velocity Along the Centerline (Re = 40)



Figure 3.7.7: Reattachment Length vs. Time (from [2])


3.7 Results

Contours of Stream Function (kg/s) (Time=4.2200e+01)Laminar Flow Over a Cylinder ( Re=100)

FLUENT 6.0 (2d, segregated, lam, unsteady)Jun 06, 2002

1.01e+01

1.01e+01

1.01e+01

1.00e+01

1.00e+01

9.98e+00

9.95e+00

9.93e+00

9.90e+00

9.88e+00

9.85e+00

Figure 3.7.8: Stream Function Contours in the Wake (Re = 100, t = 42.2 s)

Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=4.2200e+01)Laminar Flow Over a Cylinder ( Re=100)

FLUENT 6.0 (2d, segregated, lam, unsteady)Feb 05, 2002

8.00e-01

7.47e-01

6.94e-01

6.41e-01

5.88e-01

5.35e-01

4.82e-01

4.28e-01

3.75e-01

3.22e-01

2.69e-01

2.16e-01

1.63e-01

1.10e-01

5.69e-02

3.81e-03

Figure 3.7.9: Velocity Vectors in the Wake (Re = 100, t = 42.2 s)





1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.00e+01

1.00e+01

9.99e+00

9.97e+00

9.95e+00

9.93e+00

9.91e+00

9.89e+00

9.87e+00

9.85e+00




8.00e-01

7.47e-01

6.94e-01

6.41e-01

5.88e-01

5.35e-01

4.82e-01

4.28e-01

3.75e-01

3.22e-01

2.69e-01

2.16e-01

1.63e-01

1.10e-01

5.69e-02

3.81e-03



3.7 Results



1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.00e+01

1.00e+01

9.99e+00

9.97e+00

9.95e+00

9.93e+00

9.91e+00

9.89e+00

9.87e+00

9.85e+00




8.00e-01

7.47e-01

6.94e-01

6.41e-01

5.88e-01

5.35e-01

4.82e-01

4.28e-01

3.75e-01

3.22e-01

2.69e-01

2.16e-01

1.63e-01

1.10e-01

5.69e-02

3.81e-03






1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.00e+01

1.00e+01

9.99e+00

9.97e+00

9.95e+00

9.93e+00

9.91e+00

9.89e+00

9.87e+00

9.85e+00




8.00e-01

7.47e-01

6.94e-01

6.41e-01

5.88e-01

5.35e-01

4.82e-01

4.28e-01

3.75e-01

3.22e-01

2.69e-01

2.16e-01

1.63e-01

1.10e-01

5.69e-02

3.81e-03



3.7 Results



1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.01e+01

1.00e+01

1.00e+01

9.99e+00

9.97e+00

9.95e+00

9.93e+00

9.91e+00

9.89e+00

9.87e+00

9.85e+00




8.00e-01

7.47e-01

6.94e-01

6.41e-01

5.88e-01

5.35e-01

4.82e-01

4.28e-01

3.75e-01

3.22e-01

2.69e-01

2.16e-01

1.63e-01

1.10e-01

5.69e-02

3.81e-03




Velocity Magnitude (Time=4.2200e+01)Laminar Flow Over a Cylinder ( Re=100)


Time (s)

(m/s)Magnitude

Velocity

454035302520151050

7.00e-01

6.00e-01

5.00e-01

4.00e-01

3.00e-01

2.00e-01

1.00e-01

0.00e+00

-1.00e-01

-2.00e-01

-3.00e-01

-4.00e-01

Average Y Velocity

Figure 3.7.18: y Velocity History (Re = 100, t = 42.2 s)


3.8 Conclusion

Figure 3.7.19: Strouhal Number vs. Reynolds Number (from [2])

3.8 Conclusion

FLUENT has been validated for a classical example of external flows around bluff bodies.The results agree fairly well with the data from various sources, in terms of the lengthof the recirculation region in the two steady cases (Re = 20, Re = 40), and the vortexshedding frequency in the unsteady case (Re = 100).

3.9 References

1. Coutanceau, M. and Defaye, J.R., Circular Cylinder Wake Configurations A FlowVisualization Survey, Appl. Mech. Rev., 44(6), June 1991.

2. Braza, M., Chassaing, P., and Minh, H.H., Numerical Study and Physical Analysisof the Pressure and Velocity Fields in the Near Wake of a Circular Cylinder, J.Fluid Mech., 165:79130, 1986.


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