ME 322: InstrumentationLecture 33

April 13, 2015Professor Miles Greiner

Lab 11 calculations

Announcements/Reminders• HW 10 due now

• On Friday I announced the delay

• HW 11 due Friday• This week: Lab 10 Vibrating Beam

• Sign up for 1.5-hour Lab 11 periods with your partner in lab• This is one of the labs that you could be asked to repeat on the

final

• Help wanted– Spring 2016: ME 322 Lab Assistant– see me greiner@unr.edu

Lab 11 Unsteady Speed in a Karman

Vortex Street

• Nomenclature– U = air speed (instead of V)– VCTA = Voltage output of constant temperature anemometer (CTA)

• Two steps– Statically calibrate hot film CTA using a Pitot probe – Find frequency, fP with largest URMS downstream from a cylinder of diameter D for a range

of air speeds U (Measured with no rod, Why?)• Compare to expectations (StD = DfP /U = 0.2-0.21)

Setup

• Same as Lab 6 but add CTA and cylinder, and do not use Venturi tube or Gage Pressure Transducer

• Tunnel Air Density

DTube

PP

Static

Total+ -

IP

Variable SpeedBlower Plexiglas

Tube

Pitot-Static Probe VC

3 in WC

BarometerPATM TATM

CTA

myDAQ

Cylinder

VCTA

Before Experiment• Construct VI (formula block)• Measure PATM, TATM, and cylinder D • Find m and r for air

• Air Viscosity from A.J. Wheeler and A. R. Ganji, Introduction to Engineering Experimentation, 2nd Edition, Pearson Prentice Hall, 2004, p. 430.

T D P m r

Kelvin inch kPa N-s/m2 Kg/m3296.2 0.125 88.1 1.8262E-05 1.037

Fig. 2 VI Block Diagram

Spectral Measurements Selected Measurements: Magnitude (RMS) View Phase: Wrapped and in Radians Windowing: Hanning Averaging: None

Formula Formula: ((v**2-b)/a)**2

Fig. 1 VI Front Panel

Calibrate CTA using Pitot Probe

• Remove Cylinder– So air speed is relatively steady

• Align hot film and Pitot probes – So both are exposed to same air speed– Careful, hot film probes cost $150 each

• Based on physical analysis (last lecture) we expect

• For different blower speeds (and outlet covering) measure – VCTA (use myDAQ, average voltage using fS ~ 48,000 Hz, tS ~ 1 sec)– IP (Pitot probe, DMM, “eyeball” average)– In Lab 11 use 8-12 wind speed

• including blower off• In Final used fewer if time is an issue

Cylinder

Hot FilmProbe

PitotProbe

Calibration Calculations

–

IP

[mA]VCTA

[V]UA

[m/s]UA

1/2

[m1/2/s1/2]VCTA

2

[V2]

Hot Film System Calibration

• The fit equation VCTA2 = aU1/2 +b appears to be appropriate for these data.

• Using least squares the best values for the dimensional parameters are – a = 2.643 volts2s1/2/m1/2 – b = 4.5742 volts2

IP

[mA]VCTA

[V]UA

[m/s]UA

1/2

[m1/2/s1/2]VCTA

2

[V2]4.00 2.140 0.0 0.00 4.585.70 3.670 12.4 3.52 13.477.40 3.930 17.5 4.18 15.449.40 4.070 22.0 4.70 16.56

11.60 4.130 26.2 5.11 17.0616.80 4.460 33.9 5.83 19.8914.40 4.340 30.6 5.53 18.8413.30 4.290 28.9 5.38 18.4011.00 4.160 25.1 5.01 17.318.50 4.000 20.1 4.49 16.006.30 3.820 14.4 3.79 14.594.00 2.140 0.0 0.00 4.58

Standard Error of the Estimate

• Find coefficients of best fit line, a and b

• Find Standard Error of the Estimate

xxxx

x

x

xx

VCTA2

𝑆√𝑉 𝐴 ,𝑉𝐶𝑇𝐴2

𝑆𝑉𝐶𝑇𝐴2 , √𝑉 𝐴

√𝑈

UA1/2

[m1/2/s1/2]VCTA

2

[V2]di

2=(aVA1/2+b-VCTA

2)2

[V4]0.00 4.58 0.003.52 13.47 0.014.18 15.44 0.024.70 16.56 0.005.11 17.06 0.395.83 19.89 0.155.53 18.84 0.015.38 18.40 0.005.01 17.31 0.014.49 16.00 0.013.79 14.59 0.090.00 4.58 0.00

0.260.10

Measure VCTA to determine and • Invert transfer function

– (use this function in VI)• Uncertainty

– (68%) • uncertainty in is independent of U

• But we want the uncertainty in U, (not uncertainty in )– Power Product?

– But (68%)– (68%)– (68%)

• uncertainty in U increases with U

Unsteady Speed Downstream from a Cylinder

• Enter values of a and b in VI• For each measurement use fS ~ 48,000 Hz, sampling time tT ~ 1 sec• For each blower speed

– Remove cylinder to measure average speed approaching cylinder UA – Return cylinder and measure unsteady speed

• Determine frequency fP with highest URMS

– Eyeball– Uncertainty in fP is larger of

» Frequency resolution: ½(1/tT) ~ 1/2 Hz, or» Eyeball range

• Repeat for ~5 different blower speeds

UA

Hot Film

0

1

2

3

4

5

6

0 0.002 0.004 0.006 0.008 0.01

time, t [sec]

Spee

d, s

[m/s

]

With Cylinder

Without Cylinder

Fig. 2 VI Block Diagram

Spectral Measurements Selected Measurements: Magnitude (RMS) View Phase: Wrapped and in Radians Windowing: Hanning Averaging: None

Formula Formula: ((v**2-b)/a)**2

0

0.1

0.2

0.3

0.4

0 500 1000 1500 2000 2500 3000

f [Hz]

S rm

s [m

/s]

Fig. 4 Spectral Content in Wake for Highest and Lowest Wind Speed

• The sampling frequency and period are fS = 48,000 Hz and tT = 1 sec.• The minimum and maximum detectable finite frequencies are 1 and 24,000 Hz.• The frequency resolution is ½ (1/tT) = ½ hz• However, the shape of the peaks are somewhat broad, leading to

(a) Lowest Speed

(b) Highest Speed

0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000 2500 3000f [Hz]

S rm

s [m

/s]

fp = 2600 Hz

fp = 751 Hz

Dimensionless Frequency and Uncertainty

• UA from LabVIEW VI

• fP from LabVIEW VI plot• ½(1/tT) or eyeball uncertainty • Re = UADr/m (power product)

• StD = DfP/UA (power product)

UA [m/s] WUa [m/s] fP [Hz] wfp [Hz] Re WRe St WSt

37.8 1.3 2600 50 7084 236 0.218 0.00834.1 1.2 2427 50 6385 224 0.226 0.00927.3 1.1 1892 50 5121 201 0.220 0.01023.0 1.0 1596 50 4312 184 0.220 0.01216.5 0.8 1218 50 3081 156 0.235 0.01511.8 0.7 751 50 2214 132 0.202 0.018

Comparison with Expectations

• Are the values you get for St within the expected range?

Demo

• Construct VI– Formula Block– Convert to Dynamic Data

• Perform calculations using sample data from Lab 11 webpage– http://

wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Labs/Lab%2011%20Karmon%20Vortex/Lab%20Index.htm