UNIVERISTY OF MANCHESTER
SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL ENGINEERING
INSTRUMENTATION AND MEASUREMENT
VORTEX SHEDDING FROM A CYLINDER & DATA ACQUISITION
COURSE:MEng MECHANICAL ENGINEERING
DUE DATE:27TH NOVEMBER 2012
1) What are the main advantages and disadvantages of using a hotwire to measure flow velocities? 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. 2) 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...