MECH 391 Instrumentation Unsteady Velocity in a Karman Vortex Street Performed: 04/12/06 Pablo Araya: I believe, I performed 50% of the work. N.R.Chalasani: I believe, I performed 50% of the work. ABSTRACT • The objective of this lab was to calibrate a hot film anemometer using a Pitot probe and use it to measure the unsteady speed in a Karman vortex street. • The dominant frequency in the unsteady wake was measured for a range of wind speeds. • The Stroughal number (dimensionless frequency) was consistently one half the predicted value for the full Reynolds number range investigated. Fig. 1 VI Front Panel Fig. 2 VI Block Diagram Convert from Dynamic Data Convert from Dynamic Data Converts the dynamic data type to numeric, Boolean, waveform, and array data types for use with other VIs and functions. Formula Formula Uses a calculator interface to create mathematical formulas. You can use this Express VI to perform most math functions that a basic scientific calculator can compute. -------------------This Express VI is configured as follows: Formula: ((v**2-b)/a)**2 Spectral Measurements Spectral Measurements Performs spectral measurements, such as peak spectrum and auto-power spectrum, on a signal. -------------------This Express VI is configured as follows: Selected Measurements: Magnitude (RMS) View Phase: Wrapped and in Radians Windowing: Hanning Averaging: None Convert from Dynamic Data2 Convert from Dynamic Data Converts the dynamic data type to numeric, Boolean, waveform, and array data types for use with other VIs and functions. Table 1 Air Properties and Cylinder Diameter T °C 300 Patm mbar 860 D inch 0.125 m N-s/m2 1.82E-05 • Air Viscosity from A.J. Wheeler and A. R. Ganji, Introduction to Engineering Experimentation, 2nd Edition, Pearson Prentice Hall, 2004, p. 430. Table 2 Calibration Data IG IP VCTA PG PP PABS mA 4.00 4.20 4.39 4.59 4.69 4.83 4.99 4.87 4.65 4.49 4.30 4.00 mA 4.00 5.93 7.98 10.01 11.17 12.35 14.02 12.72 10.42 8.91 6.95 4.00 volt 1.493 2.675 2.852 2.968 3.022 3.070 3.133 3.091 2.989 2.900 2.776 1.494 Pa 0 125 243 367 430 517 616 542 405 305 187 0 Pa 0 90 186 281 335 390 468 407 300 229 138 0 kPa 86.0 211.7 330.0 454.5 516.7 603.9 703.5 628.8 491.8 392.2 274.0 87.2 r kg/m3 1.01 1.01 1.01 1.01 1.02 1.02 1.02 1.02 1.02 1.01 1.01 1.01 SA m/s 0.00 13.35 19.15 23.52 25.68 27.69 30.32 28.30 24.30 21.26 16.49 0.00 • The initial and final no-wind hot film voltage readings are close but not the same. Figure 3 Hot Film System Calibration 12 3.5 VCTA2 = 1.366SA1/2 + 2.2057 3.0 2.5 VCTA [volt] 2 6 VCTA [volt ] 8 2 10 4 2.0 1.5 1.0 2 0.5 0 0.0 0 1 2 3 SA 0.5 4 0.5 [m/s] 5 6 0 10 20 30 SA [m/s] • The fit equation VCTA2 = aSA0.5+b appears to be appropriate for these data. • The dimensional parameters are a = 1.366 volts2s1/2/m1/2 and b = 2.2057 volts2 40 Fig. 4 Measured Speed vs. Time for Highest Wind Speed 50 45 40 SA [m/s] 35 30 25 20 15 10 5 0 0.5000 0.5005 0.5010 0.5015 0.5020 0.5025 t [sec] • 5 large peaks in 0.00025 seconds corresponds to frequency 1780 hz. Fig. 5 Spectral Content in Wake for Highest Wind Speed 0.45 0.4 SA,RMS [m/s] 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 500 1000 1500 2000 2500 1500 2000 2500 f [hz] 0.25 SA,RMS [m/s] 0.2 0.15 0.1 0.05 0 0 500 1000 f [hz] • Largest spectral content is at 1780 hz. Table 3 Karmon Frequency and Incoming Wind Speed f hz 1780 1340 1280 1060 1536 613 SA m/s 31.06 24.2 22.06 18.33 26.66 11.4 Re [1] 5473 4264 3887 3230 4697 2009 St [1] 0.1820 0.1758 0.1842 0.1836 0.1829 0.1707 Fig. 4 Stroughal versus Reynolds 0.25 Reference Value St = 0.2 to 0.21 St [1] 0.20 0.15 0.10 0.05 0.00 0 1000 2000 3000 4000 5000 6000 Re [1] • Measured Stroughal number is roughly 15% below the expected value. • The reference value is from A.J. Wheeler and A.R. Ganji, Introduction to Engineering Experimentation, 2nd Edition, Pearson Prentice Hall, 2004, p. 337 • Noise in the hot film signal may cause this difference.