Hot Wire Laboratory

There are many advantages and disadvantages of using a hotwire to measure flow velocities, one of the main advantages is the hotwire produces a continuous analogue output of the velocity at a particular point, and hence information about the velocity can be obtained for any specific time. Another advantage of using a hotwire anemometer is the ability to follow fluctuating velocities to a high accuracy. Also another advantage of using a hotwire anemometer is the sensor is able to relate the voltage and the velocity using hotwire theory. However even though hotwire anemometer is an adequate tool to obtain data it has its drawbacks.
One disadvantage of using a hotwire is that it has to be calibrated due to the theory not coinciding with actual data and the hotwire can only obtain the magnitude of the flow and not the direction. Another disadvantage of using a hotwire is the unsystematic effects that occur such as contamination and probe vibration. Some systematic effects that affect the data are the ambient temperatures and eddy shedding from the wire. One of the main disadvantages of using a hotwire is the output depends on both velocity and temperature, so when the temperature of a fluid increases the measured velocity obtained are too low and adjustment is required. ) Why is setting the correct sampling rate important in digital data acquisition? What experimental parameters or requirements can be used to establish the optimum sampling rate? What may happen if the wrong sampling rate is used? Using the correct sampling rate is important because if the incorrect sampling rate is used some aliasing effects may occur, presenting insufficient data where important data is ignored if the sampling rate is below the optimum, and if the sampling rate is above the optimum more accurate data is obtained which carries the same trend as the optimum with few distortion which are not required.

This can cause inadequacy of the data, where recording is not frequent enough or too frequent. The optimum sampling rate can be established using the Nyquist theory which states that the maximum measures frequency is half the sampling frequency, however the bandwidth of the signal needs to considered, the rule for obtaining the sampling frequency of any probe must be at least 2. 5 times greater than the maximum frequency present. 3) Show how the sampling rate was determined for this experiment.
What was the sampling rate? For a flow around a cylinder an empirical relation between the vortex shedding frequency and Reynolds number (Re) is used to find the sampling rate. The relationship below is used to find the frequency in the flow where the Strouhal number is 0. 2, diameter (d) is 15mm and the free stream velocity (U0) is 10m/s. St=fdU0=0. 1981-19. 7Re? 0. 2 Then by simple algebraic rearranging the frequency is found to be 133. 3Hz. Therefore the maximum frequency experienced is 2f = 2*133. 3 = 266. 6Hz.
To obtain the optimum sampling frequency we simply by using Nyquist theory multiply the maximum frequency by 2. 5 providing an optimum sampling rate of 666. 5Hz. The values for the sampling rate were taken as 330Hz, 660Hz and 1320Hz for experimental purposes to study the over and under sampling of data. 4) In the experiment the hotwire was calibrated in terms of velocity vs (E-E0)2. Plot out the calibrations for U = B((E-E0)2)n and the various polynomials. Compare the different lines. Which is the best to use? Figure [ 1 ] Figure [ 2 ] Figure [ 3 ]
Figure [ 4 ] From the above graphs is can be seen that the best calibration to use is the cubic calibration (figure 2) as this fits the actual velocity line more accurately. 5) If the velocity higher than the ones calibrated foer was measured, which calibration is likely to give the best extrapolated data? Figure [ 5 ] Figure [ 6 ] Figure [ 7 ] Figure [ 8 ] From the above graphs it can be seen that the worse extrapolated data is found using the quartic calibration and the best extrapolated data can be found using the linear calibration of A([V-Vo]^2)^n.
Also higher order polynomial extrapolation can produce invalid values and as a result the error will magnify as high order of polynomials are used, so therefore the linear relationship is recommended. 6) In a fast Fourier transform (FFT) the data in the time domain is converted to the equivalent data in the frequency domain. The original data can therefore be considered as the sum of a series of sine waves of regularly spaced frequencies, with different magnitudes and phases. How is the frequency interval in the FFT determined? How can the frequency interval in an FFT be reduced?
What impact could this have on an experiment? The frequency interval can be obtained by dividing the sampling rate by the number of samples used. For 660Hz the number of samples is 1024, so therefore the frequency interval is 660/1024 = 0. 6445. The frequency intervals can be reduced by increasing the number of samples used; this is advantageous as it gives a more accurate representation of the original signal. 7) Considering the FFT data, what can be done in an experiment to isolate genuine signals from random fluctuations in the data? Give an example of this in graphical form.
Figure [ 9 ] Figure [ 10 ] From figure 9 it can be seen that the peak is unobtainable as the data is very noisy which could be due to disturbances. However this can be overcome by averaging the FFT which allows us to easily identify peaks which can be seen from figure 10. 8) In this experiment, why are 2 frequency peaks seen on the FFT when the hotwire is near the centre line? 2 frequency peaks can be seen on the FFT at the centreline due to the 2 vortices induced by the cylinder but as you move away from the centre line only one of the vortices is predominant.
The two peaks occur at 129Hz and 250Hz. 9) With increasing distance from the centreline, how does the FFT distribution change? Include graphs to illustrate this for various locations across the wake. From the below figures it can be seen that as you move away from the centre line the peaks in the FFT distribution disappear. Figure [ 11 ] Figure [ 12 ] Figure [ 13 ] Figure [ 14 ] Figure [ 15 ] Figure [ 16 ] 10) Plot the probability distribution histograms of velocity for various positions across the wake.
What does the histogram show and how can the variation in the histograms be explained in terms of the properties of the flow? Figure [ 17 ] Figure [ 18 ] Figure [ 19 ] Figure [ 20 ] Figure [ 21 ] Figure [ 22 ] By comparing the above probability distribution figures it can be seen that with distance away from the centreline the flow velocity develops a more uniform velocity. It can be seen that within the 40mm distance away from the centreline, the probability distribution of the velocity produces wide distribution of velocities; this is due to the various velocities inside the wake and turbulence.
For distance more than 40mm away the probability distribution of velocity becomes more uniform, which implies the vortices play no role in affecting the flow at these distances away from the centreline. It can also be seen that the flow speed at these distances increases as the flow diverges and accelerates around the cylinder. 11) Plot a graph showing the variation of mean velocity, RMS velocity and turbulence intensity with distance across the wake. What physical phenomena in the flow are causing the distribution to be the shape they are?
What do the results say about the size of the wake compared to the size of the cylinder? Figure [ 23 ] Figure [ 24 ] Figure [ 25 ] The vortices in the flow cause turbulence to occur behind the cylinder which causes the distributions to change. It can be seen from figure 23 that the velocity changes instantaneously as you move away from the centreline, it can also be observed that from 45mm away and more the velocity start to become more uniform and fluctuate around the free stream velocity. From figure 25 and 25 from 45mm and onwards the RMS and RTI decrease.
From the above graphs it can be deduced that the size of the wake is 45mm from the centreline or a total width of 90mm, which is 6 times the diameter of the cylinder. 12) What are the major sources of error likely to be in this experiment? Try and give a numerical estimate to the possible error(s) in the data. Some of the likely sources of error that may occur during this experiment are the calibration process as the hotwire was only calibrated at the centreline and as the hotwire was lowered using screw mechanism which it not totally accurate, there was no calibration of the at the new position.
Another source of error can be due to pressure fluctuations, and due to the velocity being measured using the pressure differences, these fluctuation can cause the velocity to vary. Another source of error could be the assumption of the flow being 2-d as turbulence is a 3-d. To calculate the error, I used the measured velocity table and the theoretical linear calibration velocity. Taking the average error, the percentage error in the experimental data was 5. 8%. Within a range Can not measure supersonic velocities

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