Experimental approach of Fluid mechanics

A study of flow past cylinders at low Reynolds numbers

By

Kamal Bow SelvamAlexandre paes de carvalhoAnuj SachdevaAnanthakrishnan

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ContentsObjectives...............................................................................................................................................3

Vortex Shedding.....................................................................................................................................3

Equipments............................................................................................................................................4

Methodology..........................................................................................................................................4

Wind tunnel........................................................................................................................................5

Selection of pressure/velocity sensor.................................................................................................5

Wind tunnel calibration......................................................................................................................5

Hot wire calibration............................................................................................................................5

Error Estimation.....................................................................................................................................5

Repeatability error.............................................................................................................................5

Hysteresis error..................................................................................................................................5

Position of pressure taps/Hotwire......................................................................................................6

Frequency measurement...................................................................................................................6

Experimental data..................................................................................................................................7

1. Strouhal number Vs Reynolds number...........................................................................................7

2. Effect of surface Roughness............................................................................................................7

3. Comparison of hotwire and pressure taps.....................................................................................8

Conclusion..............................................................................................................................................9

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Objectives

The experiment was conducted to study the behavior of vortex shedding frequency with respect to different variables. The objectives of this experimental campaign were to test cylinders with different sections to find the vortex shedding frequencies and calculating the strouhal numbers. The values were measured using pressure and velocity sensors.

Vortex Shedding

One interesting phenomenon on fluid mechanics is the vortex shedding in the wake of a cylinder. This shedding happens after the flow passes by a blunt body like a cylinder and some alternating low pressure vortices are created downstream of the body. This phenomenon is important to be studied because when the vortex shedding frequency matches the resonance frequency of a structure, the structure starts to resonate.

The frequency at which vortex shedding takes place for a cylinder is related to the Strouhal number by the following equation:

Where is the Strouhal number, is the vortex shedding frequency, is the diameter of the cylinder, and is the flow velocity. The Strouhal number depends on the body shape and on the Reynolds number.

For a large range of Reynolds numbers of the flow, this shedding occurs with a constant Strouhal number of about 0,2. But for low values of Reynolds (Re<1000), the value of Strouhal for the vortex shedding decreases as can be seen on the graphic below.

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Equipments

The equipments used on these experiments were:

Wind tunnel number 3 on Ensica’s Fluid Mechanics Department Cylinders with diameters 50, 12 and 1 mm. Dantec’s hot wire sensor. Pressure Sensors made by Delta Ohm. Oscilloscope Tektronix TDS2004B

All the manufacturer information’s for the sensors were available on the test bench.

MethodologyDuring the tests, measures have been taken varying some parameters of the

experiment: flow velocity and the diameter of the cylinder. So, different measures were taken from different cylinders. The sensors generate a time dependent signal and the oscilloscope translated it, via Fast Fourier Transform, into a frequency domain response. Within this response, we were able to search for peaks corresponding to the vortex shedding frequencies.

These measurements were repeated with the pressure sensors and repeated again with the hot wire sensor for confirmation of the obtained information.

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Wind tunnel:

The experiment is to be conducted in the bandwidth of 5m/s to 22m/s which is the available bandwidth of the wind tunnel.

Selection of pressure/velocity sensor:

The frequency of vortex shedding is measured from the pressure and velocity fluctuations. To have the best sensor, we need to know the bandwidth of frequencies which are possible. It was calculated using the Strouhal number of 0,2.

Lowest frequency = 0.2 * Lowest velocity / Biggest diameter = 20Hz

Highest frequency = 0.2 * highest velocity / Lowest diameter = 4400Hz

Either pressure taps or hot wire anemometer could be used to the measurements because both are capable for the possible frequency range of the experiment.

Wind tunnel calibration:

Before starting the wind tunnel Dynamic pressure monitor of the wind tunnel is calibrated using an external calibrated velocity meter. The dynamic pressure is to be deduced from the velocity meter before comparison. Error 1= 2.5%

Hot wire calibration:

The hot wire was not required to be calibrated as we did not require the absolute values of velocity. Only the fluctuations were required.

Error EstimationRepeatability error:

To quantify the precision error, a sample of 5 measurements of frequency is taken repeatedly. The standard deviation of the measured values is obtained as 0.13(= Error 2)

Hysteresis error:

To determine the repeatability of the instrument in both the directions the hysteresis error was calculated to be close to zero.

Total error = 0.15 HzActual measurement = Mean of measure quantities+/- 0.15 Hz

Position of pressure taps/Hotwire:

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The best radial position of pressure taps with maximum intensity is found by trial and error method so as to have sharp cut off from the noise. It was found to be 125Degrees. This can be seen in the image.

The best position of the hot wire anemometer is selected by trial and error method to avoid resonance of hot wire anemometer with the vortex shedding frequency

Fig 1.1. Figure showing the position of pressure tap to have maximum intensity and the peak on the oscilloscope

Fig 1.2 Figure showing the position of hot wire to reduce resonance of the instrument with vortex shedding

frequency

Frequency measurementThe frequency corresponding to vortex shedding is maintained 10 divisions away

from noise. This is maintained throughout the experiment to have accurate uniform reading. It can be seen in the image.

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Experimental data

The experiment was conducted with the above setting for the following data acquisition.

1. Strouhal number Vs Reynolds number

This is done to study the effects of frequency with change in Reynolds number. The obtained results are found to be line with general notion.

200 400 600 800 10000.155

0.160.165

0.170.175

0.180.185

0.190.195

0.20.205

St for D = 0.05m

Frequency

Stro

uhal

Num

ber

Fig 2.1 obtained Strouhal number as a Fig 2.2 Theoretical resultfunction of the Reynolds number

The strouhal number becomes constant after a Reynolds number of 1000 irrespective of cylinder diameter.

2. Effect of surface Roughness

The behavior of vortex shedding is studied in relation to the surface roughness. It was found that the vortex shedding frequency can be controlled by increasing the surface roughness which reduces the frequency. This changing on the behavior is due to the transition of the flow from laminar to turbulent. Using a hot wire anemometer at the turbulence region produced noise in the FFT which made difficult to find the peaks. The drag measurement technique can be used to calculate the frequency with roughness. Since Time was constrained we were not able to do that.

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10 12 14 16 18 203035404550556065707580

vortex freq by hot wire

Theoritical

Frequencywith roughness strip

Mean Freauecy of 5 trials without rough-ness strip

velocity m/sec

vort

ex sh

eddi

ng fr

quen

cy H

z

The above results shows that the frequency is reduced .

3. Comparison of hotwire and pressure taps

The hot wire and pressure tap allowed us to study the vortex shedding with very high and very low vortex shedding frequency.

10 12 14 16 18 200

102030405060708090

vortex freq by pressure taps

frequency

velocity m/s

vort

ex s

hedd

ing

freq

uenc

y

10 12 14 16 18 2030

40

50

60

70

80vortex freq by hot wire

Fre-quency

velocity m/s

vort

ex s

hedd

ing

freq

uenc

y

Fig 3.1 showing the low frequencies measured by pressure tap and hot wire anemometer. Experimental set up was not available to measure very high frequencies of order 4000Hz using pressure taps.

Anyway, although both were able to capture the phenomena and its characteristic frequency, using the hot wire sensor made easier to obtain the peaks on the oscilloscope.

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ConclusionThe experiment designed by the team was successful as it was possible to capture well enough the studied phenomena. Vortex shedding frequency (or the strouhal number) was plotted as a variable dependent on Reynolds number (or velocity) and surface roughness. A comparison between measuring capability of pressure taps and hot wire anemometer was also found out. Error estimation of measurement was also found out to be +-0.15 Hz

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