ME 322: Instrumentation Lecture 24

1. ME 322: InstrumentationLecture 24 March 24, 2014 Professor Miles Greiner

2. Announcements/Reminders • This week: Lab 8 Discretely Sampled Signals • Next Week: Transient Temperature Measurements • HW 9 is due Monday • Midterm II, Wednesday, April 2, 2014 • Review Monday • Extra Credit Opportunity, Friday, April 18, 2014 • Introduction to LabVIEW and Computer-Based Measurements Hands-On Seminar • NI field engineer Glenn Manlongatwill walk through the LabVIEW development environment • 1% of grade extra credit for actively attending • Time, place and sign-up “soon”

3. Transient Thermocouple Measurements • Can a the temperature of a thermocouple (or other temperature measurement device) accurately follow the temperature of a rapidly changing environment?

4. 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, hBoiling, hAir, and hRTWater • Compare each h to the thermal conductivity of those environments (kAir or kWater)

5. Dimensionless Temperature Error T Environment Temperature TF Initial Error EI = TF – TI Error = E = TF – T ≠ 0 TI TI t t = t0 • At time t = t0 a thermocouple at temperature TIis put into a fluid at temperature TF. • Error: E = TF – T • Theory for a lumped (uniform temperature) TC predicts: • Dimensionless Error: • (spherical thermocouple) TF T(t)

6. Lab 9 Measured Thermocouple Temperature versus Time • From this chart, find • Times when TC is placed in Boiling Water, Air and RT Air (tB,tA,tR) • Temperatures of Boiling water (maximum) and Room (minimum) (TB, TR) • Thermocouple temperature responds more quickly in water than in air • However, slope does not exhibit a step change in each environment • Temperature of TC center does not response immediately • Transient time for TC center: tT ~ D2rc/kTC

7. Type J Thermocouple Properties • State estimated diameter uncertainty, 10% or 20% of D • Thermocouple material properties (next slide) • Citation: A.J. Wheeler and A.R. Gangi, Introduction to Engineering Experimentation, 2nd Ed., Pearson Education Inc., 2004, page 431. • Best estimate: • Uncertainty: • tT ~ D2rc/kTC; = ?

8. TC Wire Properties (App. B)

9. Dimensionless Temperature Error • For boiling water environment, TF = TBoil, TI = TRoom • During what time range t1<t<t2does decay exponentially with time? • Once we find that, how do we find t?

10. Data Transformation (trick) • Where , and b = -1/t are constants • Take natural log of both sides • Instead of plotting versus t, plot ln() versus t • Or, use log-scale on y-axis • During the time period when decays exponentially, this transformed data will look like a straight line

11. To find decay constant b using Excel • Use curser to find beginning and end times for straight-line period • Add a new data set using those data • Use Excel to fit a y = Aebx to the selected data • This will give b = -1/t • Since t, • Calculate (power product?), ? • Assume uncertainty in b is small compared to other components • What does convection heat transfer coefficient depend on?

12. Thermal Boundary Layer for Warm Sphere in Cool Fluid Thermal Boundary Layer • h increases as k increase and object sized decreases • = Dimensionless Nusselt Number TF T r D Conduction in Fluid

13. Lab 9 Sample Data • http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Labs/Lab%2009%20TransientTCResponse/LabIndex.htm • Plot T vs t • Find TBand TR • Calculate q and plot vs time on log scale • In Boiling Water, TI = TR, TF = TB • In Room Temperature air and water, TI = TB, TF = TR • Select regions that exhibit exponential decay • Find decay constant for those regions • Calculate h and wh for each environment • For each environment calculate • NuD • BiD

14. Fig. 4 Dimensionless Temperature Error versus Time in Boiling Water • The dimensionless temperature error decreases with time and exhibits random variation when it is less than q < 0.05 • The q versus t curve is nearly straight on a log-linear scale during time t = 1.14 to 1.27 s. • The exponential decay constant during that time is b = -13.65 1/s.

15. Fig. 5 Dimensionless Temperature Error versus Time t for Room Temperature Air and Water • The dimensionless temperature error decays exponentially during two time periods: • In air: t = 3.83 to 5.74 s with decay constant b = -0.3697 1/s, and • In room temperature water: t = 5.86 to 6.00s with decay constant b = -7.856 1/s.

16. Lab 9 Results • Heat Transfer Coefficients vary by orders of magnitude • Water environments have much higher h than air • Similar to kFluid • Nusselt numbers are more dependent on flow conditions (steady versus moving) than environment composition

17. Air and Water Thermal ConductivitiesAppendix B • kAir (TRoom) • kwater(TRoom, TBoiling)

18. Lab 9 Extra Credit • Measure time-dependent heat transfer rate Q(t) to/from the TC (when TC is placed into boiling water) • 1st Law • Differentiation time step • Sampling time step • Integer m • What is the best value of m?

19. Measurement Results • Choice of DtDis a compromise between eliminating noise and responsiveness

20. What Do We Expect? Expected for Uniform Temperature TC TF = TB Ti = TR Measured t0

21. What do we measure? Expected for uniform temperature TC Q Measured tT t ti

22. Sinusoidally-Varying Environment Temperature • For example, a TC in a car exhaust line • Eventually the TC will have • The same average temperature and unsteady frequency as the environment temperature • However, its unsteady amplitude will be less than the environment temperature’s. TTC TENV

23. Heat Transfer from Fluid to TC Fluid Temp TF(t) Q =hA(T – T) • Environment Temperature: TE = M + Asin(wt) • Divided by hA and • Let the TC time constant be (for sphere) • 1st order, linear differential equation, non-homogeneous T D=2r

24. Solution • Solution has two parts • Homogeneous and non-homogeneous (particular): • T = TH+TP • Homogeneous solution • Solution: • Decays with time, not important as t∞ • Particular Solution to whole equation • Assume ) • ) • Plug into non-homogeneous differential equation to find constants C, D and E

25. Particular Solution • Plug in assumed solution form: • Collect terms: • + • Find C, D and E in terms of A and M • C = M =0 =0 =0

26. Result • ) • where

27. Compare to Environment Temperature tD • Same mean value • If 1 >> = • Then • Minimal attenuation and phase lag • Otherwise • ( T

28. Example • A car engine runs at f = 1000 rpm. A type J thermocouple with D = 0.1 mm is placed in one of its cylinders. How high must the convection coefficient be so that ATC = 0.5 AENV? • If the combustion gases may be assumed to have the properties of air at 600C, what is the required Nusselt number?

30. Can we measure time-dependent heat transfer rate, Q vs. t, to/from the TC?1st Law Differential time step

31. Measurement Results • Choice of dtD is a compromise between eliminating noise and responsiveness

32. Lab 9 Transient Thermocouple Response T Environment Temperature TF Faster Slower TC Initial Error EI = TF – TI Error = E = TF – T ≠ 0 TI TI t t = t0 • At time t = t0 a small thermocouple at initial temperature TI is put into boiling water at temperature TF. • How fast can the TC respond to this step change in its environment temperature? • What causes the TC temperature to change? • What affects the time it takes to reach TF? TF T(t)

33. VI

34. Lab 9

35. Initial Transient Time

36. Transform Trick Small Same for air & water

37. Lab 9 Find h in: Boiling Water Room Temper Air and water Why does h vary so much in different environments? Water, Air What does h depend on? T TF T r D NuD≡ Nusselt number