ME 322: Instrumentation Lecture 40 April 29, 2015 Professor Miles Greiner Review Labs 10 and 11

Announcements/Reminders This week: Lab 12 Feedback Control Working with TSI to get the Lab 11 CTA to work Remember you are not graded on how well the CTA’s work HW 13 due now HW 14 due Monday (may drop) Review Labs 10, 11, and 12; Today and Friday Supervised Open-Lab Periods Saturday and Sunday Drop Extra-Credit Lab 12.1 and LabVIEW Workshop 6 points will be added to everyone’s Midterm II score Lab Practicum Finals (May 6-14) – Guidelines, Schedule

College of Engineering Innovation Day: Friday, May 1, events/innovation-day events/innovation-day

Lab 10 Vibration of a Weighted Cantilever Beam W L T M T T LBLB LELE Accelerometer Clamp MWMW E (given)

Table 1 Measured and Calculated Beam Properties Use the units you are given, or the ones you used to measure W L T M T T LBLB LELE Accelerometer Clamp MWMW E (given)

Figure 2 VI Block Diagram

Figure 1 VI Front Panel

Use f S ~600 Hz > 2f M to capture the peaks When plotting a versus t, use time increment  t = 1/f S The oscillatory frequency is clearly higher for the shorter L B. Looks like ()=sin(2+) –Measure f from spectral analysis ( f M ) –Find b from exponential fit to acceleration peaks Disturb beam and measure a(t) for two L B ’s

Warning: Be careful to check (view) you’re a(t) data before processing For example, see oscillations between 2 and 4 seconds

Figure 4 Oscillatory Amplitude Versus Frequency The sampling time and frequency were T 1 = 10 sec and f S = 600 Hz, so the system is capable of detecting frequencies between 0.1 and 300 Hz, with a resolution of 0.1 Hz. –To plot a RMS vs t, use frequency increment  f = 1/T 1 For beam lengths of L B = 13 and 7 inches, the peak frequencies are, respectively, f M = 7.50 ± 0.1 and ± 0.1 Hz. –These frequencies are easily detected from this plot. Can we predict these measured oscillatory frequency from length, mass and elastic modulus measurements?

Fig. 5 Peak Acceleration versus Time The average exponential decay constants for the beam lengths of L B = 13 and 7 inches, are b = and , respectively The magnitude of these “constants” (slope of the curves) decreased slightly with time.

Equivalent Endpoint Mass M EQ Beam Mass M B L T M T LBLB LELE Clamp MWMW

Beam Equivalent Spring Constant, K EQ F  LBLB

Predicted Frequencies

Table 2 Calculated Values and Uncertainties The intermediate mass is small compared to the equivalent mass. For both beam lengths, the damping is sufficiently low so that the predicted undamped and damped frequencies, f OP and f P, are nearly the same The predicted damped frequencies are roughly 12 to 17% higher than the measured values, and their confidence intervals do not overlap.

Time and Frequency Dependent Data

Lab 11 Unsteady Speed in a Karman Vortex Street Nomenclature – U = air speed – V CTA = Constant temperature anemometer voltage Two steps – Statically-calibrate hot film CTA using a Pitot probe (this part worked) – Find frequency, f P with largest U RMS downstream from a cylinder of diameter D for a range of air speeds U (working on this part) Compare to expectations (St D = Df P /U = )

Setup D Tube P Static Total + - IPIP Variable Speed Blower Plexiglas Tube Pitot-Static Probe 3 in WC Barometer P ATM T ATM CTA myDAQ Cylinder V CTA Hot Film Probe

Calibration Calculations

Hot Film System Calibration The fit equation V CTA 2 = aU 0.5 +b appears to be appropriate for these data.

How to Construct VI (Block Diagram) Use for both static-calibration and unsteady measurements Don’t need to store speed vs time

Front Panel

Unsteady Speed Downstream of a Cylinder When the cylinder is removed the speed is relatively constant When the cylinder is installed, downstream of the cylinder – The average speed is lower compared to no cylinder – There are oscillations with a broadband of frequencies

Fig. 4 Spectral Content in Wake for Highest and Lowest Wind Speed The sampling frequency and period are f S = 48,000 Hz and T T = 1 sec. The minimum and maximum detectable finite frequencies are 1 and 24,000 Hz (not all are shown). It is not straightforward to distinguish f P from this data. Its uncertainty is w fp ~ 50 Hz. (a) Lowest Speed (b) Highest Speed f p = 2600 Hz f p = 751 Hz U RMS [m/s] U RMS [m/s]

Dimensionless Frequency and Uncertainty

Fig. 5 Strouhal versus Reynolds The reference value is from A.J. Wheeler and A.R. Ganji, Introduction to Engineering Experimentation, 2 nd Edition, Pearson Prentice Hall, 2004, p Four of the six Strouhal numbers are within the expected range.

Process Sample Data hing/MECH322Instrumentation/Labs/Lab%20 11%20Karmon%20Vortex/Lab%20Index.htm hing/MECH322Instrumentation/Labs/Lab%20 11%20Karmon%20Vortex/Lab%20Index.htm

Lab 9 Transient TC Response in Water and Air Start with TC in room-temperature air Measure its time-dependent temperature when it is plunged into boiling water, then room-temperature air, then room-temperature water Determine the heat transfer coefficients in the three environments, h Boiling, h Air, and h RTWater Compare each h to the thermal conductivity of those environments (k Air or k Water ) Also calculate Biot number (dimensionless thermal size) and delay time for center to respond

LabVIEW VI

Dimensionless Temperature Error T t t = t 0 TITI TFTF Error = E = T F – T ≠ 0 T(t) TITI TFTF Environment Temperature Initial Error E I = T F – T I

From this chart, find –Times when TC is placed in Boiling Water, Air and RT Air (t B, t A, t R ) –Temperatures of Boiling water (maximum) and Room (minimum) (T B, T R ) Thermocouple temperature responds more quickly in water than in air Slope does not exhibit a step change in each environment –Temperature of TC center does not response immediately Transient time for TC center: t T ~ D 2  c/k TC Measured Thermocouple Temperature versus Time

Type J Thermocouple Properties

TC Wire Properties (App. B)

Data Transformation (trick)

Find decay constant b using Excel

Dimensionless Temperature Error versus Time for Room-Temperature Air and Water Decays exponentially during two time periods: –In air: t = 3.83 to 5.74 sec, b = /s –In water: t = 5.86 to 6.00 sec, b = /s.

Lab 9 Results

Air and Water Properties (bookmark)

Lab 9 Sample Data

Thermal Boundary Layer for Warm Sphere in Cool Fluid T D r TFTF Conduction in Fluid Thermal Boundary Layer

Lab 9 Transient TC Response in Air & Water Wire yourself TC → Conditioner (+)TC → White Wire (-)TC → Red Stripe Conditioner to → MyDAQ Com → (-) V out → (+) Write VI Easy Fig 1 & 2 will not be given

Acq uire Data F s = 1000 Hz T­ i = 8 sec At least 2 seconds in each environment. Room temp water Boiling water Room temp air Room temp water Fig 3 Plot T Vs. t ID time t B, t A, t R ID Temp T Room = T min T Boil = T max

Fig 4 For boiling water vs. t Identify: Start & end times of exponential decay period (looks linear) Select exp decay data y Add data to plot Fit to that data  Show results on the plot Find b  Units s -1 Fig 5 Room Temp Air & Water vs. t Find Table 2

Lab 10: Vibrating Beam You will be given beam and its E and W E VI fig 1 &2

Table 2

Undamped Predicted Frequency if b = 0, λ = 0 Measured Damping Coeff If Then W fp ≈ W fop Is