MECH 322 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 measure the natural frequency of a Karman vortex street. • A hot film anemometer was calibrated at steady speeds using a Pitot probe in a wind tunnel. It was then used to measure unsteady speeds in the wake behind a cylinder. The dominant frequency was determined for a range of wind speeds using a LabVIEW function. • The Strouhal number (dimensionless frequency) was constant (as expected) but consistently 70% above the predicted value for the investigated Reynolds number range. Fig. 1 VI Front Panel Fig. 2 VI Block Diagram Formula Formula: ((v**2-b)/a)**2 Spectral Measurements This Express VI is configured as follows: Selected Measurements: Magnitude (Peak) View Phase: Wrapped and in Radians Windowing: Hanning Averaging: None Table 1 Air Properties and Cylinder Diameter T K 300 Patm mbar 860 D inch 0.125 m 2 N-s/m 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 [mA] [mA] [V] [Pa] 4 4.00 1.490 0 4.06 4.60 2.425 37 4.11 5.07 2.550 69 4.16 5.60 2.633 100 4.3 7.13 2.790 187 4.52 9.32 2.932 324 4.69 11.00 3.017 430 4.89 13.08 3.102 554 4.6 10.00 2.966 374 4.36 7.52 2.821 224 4.1 4.90 2.505 62 4.01 4.00 1.492 6 PP PABS [Pa] 0 28 50 75 146 249 327 424 280 164 42 0 [kPa] 86.20 86.24 86.27 86.30 86.39 86.52 86.63 86.75 86.57 86.42 86.26 86.21 r [kg/m3] 1.01 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.01 SA [m/s] 0.00 7.43 9.92 12.13 16.96 22.09 25.33 28.82 23.46 17.98 9.10 0.00 • The initial and final no-wind hot film voltage readings are close but not the same. Figure 3 Hot Film System Calibration 3.5 10 3.0 VCTA 8 0.5 2.5 2 = 1.3657SA + 2.1951 VCTA [volts] VCTA0.5 [volts0.5] 12 6 4 2.0 1.5 Extra Credit (not required) 1.0 2 0.5 0 0.0 0 1 2 SA2 3 [m2/s2] 4 5 6 0 5 10 15 20 25 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 = 2.195 volts2 35 Fig. 4 Measured Speed vs. Time for Lowest Wind Speed 6 Without Cylinder Speed, s [m/s] 5 4 3 With Cylinder 2 1 0 0 0.002 0.004 0.006 0.008 0.01 time, t [sec] • • • The sampling rate appears to be sufficiently fast to capture the shape of the unsteady trace. Turbulence or instabilities at the tunnel entrance may cause unsteadiness in the speed even when there is no cylinder in the flow With the cylinder, there are roughly 6 large peaks in 0.01 seconds, corresponds to a frequency 600 Hz. SRMS [m/s] Fig. 5 Spectral Content in Wake for Lowest Wind Speed with and without Cylinder 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 (a) With cylinder 0 200 400 600 800 1000 1200 1400 1600 1800 2000 1400 1600 1800 2000 SRMS [m/s] Frequency, f [hz] 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 (b) Without cylinder 0 200 400 600 800 1000 1200 Frequency, f [hz] • • The cylinder increases the unsteadiness at all frequencies, but most significantly near 516 Hz. This frequency is 14% below the observation in Fig. 4. There is another peak at 268 Hz. Table 3 Karman Frequency and Incoming Wind Speed f [Hz] 3500 3200 2764 2100 1500 516 SA [m/s] 31.49 28.13 23.98 18.89 13.34 4.68 Re [1] 5603 5005 4267 3361 2374 833 St [1] 0.35 0.36 0.37 0.35 0.36 0.35 • The dominant frequency f and centerline speed SA were determined as several wind speeds. • The Reynolds number is ReD = SADr/m • The Strouhal number is StD = fD/SA Fig. 6 Strouhal versus Reynolds 0.40 0.35 St [1] 0.30 0.25 Reference Value St = 0.2 to 0.21 0.20 0.15 0.10 0.05 0.00 0 1000 2000 3000 4000 5000 6000 Re [1] • The reference value is from A.J. Wheeler and A.R. Ganji, Introduction to Engineering Experimentation, 2nd Edition, Pearson Prentice Hall, 2004, p. 337. • Measured Strouhal number is roughly 70% Above the expected value. • There may be an error in the anemometer calibration method. Extra (not part of report) 2006 Summary 1.20 1.00 StD 0.80 0.60 0.40 0.20 0.00 0 2000 4000 6000 ReD 8000 10000 0. 09 0. 11 0. 13 0. 15 0. 17 0. 19 0. 21 0. 23 0. 25 0. 27 0. 29 0. 31 0. 33 0. 35 0. 37 0. 39 0. 41 0. 43 0. 45 0. 47 0. 49 0. 51 0. 53 0. 55 0. 57 0. 59 0. 61 N Histogram 16 14 12 10 8 6 4 2 0 StD