1. ME 322: Instrumentation Lecture 23 March 13, 2015 Professor Miles Greiner Transient TC response, Modeling, Expected and observed behaviors, Lab 9, Plot transformation, Heat Transfer Measurement

2. Announcements/Reminders HW 8 is due now – How did plotting and LabVIEW programing go? Midterm II, April 1, 2015 – Next week is Spring Break!

3. So far in this course… Quad Area Measurement – Multiple, independent measurements of the same quantity don’t give the same results (random and systematic errors; mean, standard deviation) Steady Measurements – Pressure Transducer Static Calibration – Metal Elastic Modulus – Fluid Speed and Volume Flow Rate – Boiling Water Temperature Discrete sampling of time varying signals using computer data acquisition (DAQ) systems – Allows us to acquire unsteady outputs versus time

4. Transient Instrument Response Can measurement devices follow rapidly changing measurands? – temperature – pressure – speed

5. Lab 9 Transient Thermocouple Response At time t = t 0 a small thermocouple at initial temperature T I is dropped into boiling water at temperature T F. 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 the TC to reach T F ? T t t = t 0 TITI TFTF Faster Slower TC Error = E = T F – T ≠ 0 T(t) TITI TFTF Environment Temperature Initial Error E I = T F – T I

6. Heat Transfer from Water to TC Q [J/s = W] Fluid (water) Temp T F T(t,r) Surface Temp T S (t) D=2r

7. Energy Balance (1 st law)

8. For a Uniform Temperature TC

9. Solution

10. 0.37 0.14 0.05 0.011 Dimensionless Temperature Error

11. Prediction versus Measurement tItI TITI TFTF

12. Semi-Infinite Body Transient Conduction  TiTi  t = 0 ∞  x

13. After t > t t, is TC temperature uniform?  T CONV  T TC T r  T CONV  T TC T r

14. Lab 9 Transient TC Response in Water and Air Start with TC in air Measure its 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 the environment (k Air or k Water )

15. Thermocouple temperature responds much more quickly in water than in air How to determine h all three environments? Measured Thermocouple Temperature versus Time

16. Dimensionless Temperature Error

17. Data Transformation (trick)

18. TC Wire Properties (App. B)

19. Have a good spring break!

20. The diameter uncertainty is estimated to be 10% of its value. Thermocouple material properties values are the average of Iron and Constantan values. The uncertainty is half the difference between these values. The values were taken from [A.J. Wheeler and A.R. Gangi, Introduction to Engineering Experimentation, 2nd Ed., Pearson Education Inc., 2004, page 431] The time for the effect of a temperature change at the thermocouple surface to cause a significant change at its center is t T = D 2  c/k TC. Its likely uncertainty is calculated from the uncertainty in the input values. Table 1 Thermocouple Properties

21. Lab 9 Sample Data

22. Lab 9 Place TC in (1) Boiling water T B, Room temperature air T A, and Room temperature water T W Plot Temperature versus time Why doesn’t TC temperature versus time slope exhibit a sudden change when it is placed in different environments?

23. 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  < 0.05 The  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.

24. 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.

25. Table 2 Effective Mean Heat Transfer Coefficients The effective heat transfer coefficient is h = -  cDb/6. Its uncertainty is 22% of its value, and is determined assuming the uncertainty in b is very small. The dimensional heat transfer coefficients are orders of magnitude higher in water than air due to water’s higher thermal conductivity The Nusselt numbers Nu D (dimensionless heat transfer coefficient) in the three different environments are more nearly equal than the dimensional heat transfer coefficients, h. The Biot Bi number indicates the thermocouple does not have a uniform temperature in the water environments

26. 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 D T r TFTF Nu D ≡ Nusselt number

27. Lab 9 Expect h to increase as k increases and D decreases. k in appendix: k Air pg 454 → T Room k water pg 453 → T Room, T Boiling

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

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

30. Measurement Results Choice of dt D is a compromise between eliminating noise and responsiveness

32. So far in this course… Quad Area Measurement – Multiple, independent measurements of the same quantity don’t give the same results (random and systematic errors, mean, standard deviation) Steady Measurements – Pressure Transducer Static Calibration Transfer Functions, Linear regression, Standard Error of the Estimate – Metal Elastic Modulus Strain Gage/Wheatstone Bridge, Propagation of Uncertainty – Fluid Speed and Volume Flow Rate Pitot-Static Probes, Venturi Tubes – Boiling Water Temperature Thermocouples Discrete sampling of time varying signals using computer data acquisition (DAQ) systems – Allows us to acquire unsteady outputs versus time – LabVIEW, derivatives, spectral analysis