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ME 322: Instrumentation Lecture 27 Midterm Review

ME 322: Instrumentation Lecture 27 Midterm Review. March 1, 2014 Professor Miles Greiner. Announcements/Reminders. This week: Lab 9 Transient Temperature Response HW 9 is due now Midterm II, Wednesday, April 2, 2014 Josh McGuire will hold review sessions:

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ME 322: Instrumentation Lecture 27 Midterm Review

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  1. ME 322: InstrumentationLecture 27Midterm Review March 1, 2014 Professor Miles Greiner

  2. Announcements/Reminders • This week: Lab 9 Transient Temperature Response • HW 9 is due now • Midterm II, Wednesday, April 2, 2014 • Josh McGuire will hold review sessions: • Today, 5-6 PM PE 215, Tuesday 7-8 PM, DMS Rm? • He will e-mail specifics • Two Extra-Credit Opportunities • Both 1%-of-grade extra-credit for active participation • LabVIEW Computer-Based Measurements Hands-On Seminar • Friday, April 18, 2014, 2-4 PM, Place TBA • Open ended Lab 9.1 • Proposal this Friday, 4/4/14

  3. Midterm II • Handout last year’s exam • Neither Josh nor I will work those problems • These specific problems will not be on this year’s exam • Open book + bookmarks + 1 pages of notes • ~4 problems, with parts • Focus on materials not covers on Midterm I • Study • HW, Lab Calculations, Notes, Text reading • If you missed a lecture you may want to talk to student’s who attended, since some information is not on the lecture slides • Units, significant figures • Especially on statistical-analysis and propagation-of-uncertainty problems • Know how to used your calculator • Special needs: see me today (confirm)

  4. Fluid Speed and Uncertainty PT > PS PT > PS PS PS • Pitot and Pitot-Static Probes • (power product?) • C accounts for viscous effects, which are small • Assume C = 1 unless told otherwise • Need to determine pressure difference and fluid density V

  5. Fluid Density and Uncertainty • Ideal Gases • (power product?) • R = Gas Constant = RU/MM, • Ru = Universal Gas Constant = 8.314 kJ/kmol K • MM = Molar Mass of the gas • RAir = 0.2870 kPa-m3/kg-K • T[K] = T[°C] + 273.15,Gas Absolute Temperature, • P, Gas staticpressure • Can incorporate into speed calculation • (power product?) • Liquids • (Tables)

  6. Water Properties • Be careful reading headings and units

  7. Pressure Transmitter Measurement • = 998.7 kg/m3, g = 9.81 m/s2 • FS = (3 or 40 inch) • Manufacturer stated uncertainty: 0.25% of Full Scale • Certainty level = ? (need to be told on test) • For FS = 3 inch WC • PFS = rWghFS= (998.7 kg/m3)(9.81 m/s2) (3 inch) = 746.6 Pa • wP = 0.0025 PFS = 1.9 Pa • For FS = 40 inch WC • PFS = rWghFS= (998.7 kg/m3)(9.81 m/s2) (40 inch) = 9954 Pa • wP = 0.0025 PFS = 25 Pa

  8. Static Pressure • PStat = PATM – PG(power product or linear sum?) • Uncertainty: • For general linear sums

  9. Volume FlowRate • Variable Area Meter (venturi): • Need , (throat), , (iterate) • This expression needs pipe and throat dimensions • Presso Formulation: • = • : Given by manufacturer • Don’t need A2 or b

  10. Discharge Coefficient Data from Text • Nozzle: page 344, Eqn. 10.10 • C = 0.9975 – 0.00653 (see restrictions in Text) • Orifice: page 349, Eqn. 10.13 • C = 0.5959 + 0.0312b2.1 - 0.184b8+ (0.3 < b < 0.7)

  11. Centerline-Speed/Volume-Flow-Rate Consistency • Estimated centerline-speeds for a given volume flow rate Q • Slug Flow: VS = Q/A • Parabolic Speed Profile: VP = 2VS

  12. Temperature Measurements TT TS TT • Thermocouple, metal pair AB • from page 300 (bookmark) • Standard Uncertainty, certainty level = ? (need to be told) • 2.2°C for T < 293°C • 0.7% of reading for T > 293°C

  13. Not quite linear • Different sensitivities (slopes)

  14. Transfer Function (Type-J-TC/DRE–TC-J TC) ? Out of range Transfer Function 10 • For TS < 400C • (linear) • ; = 500 • Inverted transfer function: TS = (40°C/V)*VSC • Conditioner Provides • Reference Junction Compensation (not sensitive to TT) • Amplification (Allows normal DVM or computer acquisition to be used) • Low Pass Filtration (Rejects high frequency RF noise) • Linearization (Easy to convert voltage to temperature) • Galvanic Isolation (TC can be used in water environments) Reading VSC [V] 0 400 Measurand, T [°C] 0

  15. A/D Converter Characteristics • Sampling Rate fS[samples/second] • Sampling time DtS= 1/fS[seconds/sample] • Full-scale range VRL ≤ V ≤ VRU • FS = VRU- VRL • Number of Bits N • Converter resolves full-scale range into 2N sub-ranges • Smallest voltage change that can be detected: FS/2N • Input Resolution Error, IRS • Random error due to digitization process • Inside full-scale range: • Outside range: ∞ • Absolute Voltage Accuracy, AVA • Larger than IRS, Includes calibration and other errors

  16. Numerical Differentiation of Discretely Sampled Signals • First-order Centered Differencing • is the differentiation time step [sec] • , • is the samplingtime • m = integer (1, 2, or ?) • What is the best value for m (1, 10, 20, ?) • Compromise between responsiveness and sensitivity to random errors

  17. Fourier Transform of Discretely Sampled Signal V 0 t T1 • Any function V(t), over interval 0 < t < T1, may be decomposed into an infinite sum of sine and cosine waves • , • Discrete frequencies: , n = 0, 1, 2, … ∞ (integers) (not continuous) • Only admits modes for which an integer number of oscillations span the total sampling time T1. • The root-mean-square (RMS) coefficient for each mode quantifies its total energy content for a given frequency (from sine and cosine waves) • LabVIEW find versus numerically • When processing, need to add: 0, , , n = 2 n = 1 n = 0 sine cosine

  18. Examples (ME 322r Labs) Frequency Domain Time Domain Function Generator 100 Hz sine wave • Converts signals from time-domain to frequency-domain (spectral energy content) Damped Vibrating Cantilever Beam Unsteady Speed Air Downstream from a Cylinder in Cross Flow

  19. Upper, Lower, and Resolution Frequencies • If a signal is sampled at a rate of fS for a total time of T1 , the highest and lowest finite frequencies that can be accurately detected are: • (f1= 1/T1) < f < (fN = fS/2) • The frequency resolution • Smallest frequency change that can be detected • f1= 1/T1 (same as minimum frequency) • To reduce lowest frequency (and increase frequency resolution), increase total sampling time T1 • To observe higher frequencies, increase the sampling rate fS.

  20. How to predict indicated (or Alias) Frequency? • fa = fmif fs > 2fm • Otherwise using folding chart on page 106 • Let fN = fs/2 be the maximum frequency that can be accurately observed using sampling frequency fs. Maximum frequency that can be accurately measured using sampling frequency fS .

  21. TC Response to Temperature Step Change 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 thermocouple at TI is put into a fluid at TF. • Error: E = TF – T • Theory for a lumped (uniform temperature) TC predicts: • Dimensionless Error: • (spherical thermocouple) TF T(t)

  22. To find heat transfer coeff. h from T vs t Data • If given T versus t data in the exponential decay period • Calculate and for each time • Find the least-squares coefficients a and b of • Calculate (power product?), ? • Assume uncertainty in b is small compared to other components • Find and for TC from appendix

  23. TC Response to Sinusoidally-Varying Temp tD • Environment Temp: • TC Temp: • TC has same mean temperature and frequency () • TC temperature has attenuated amplitude and is delayed • Minimal if , where , otherwise: T

  24. High Temperature (combustion) Gas Measurements QConv=Ah(Tgas– TS) Sensor h, TS, A, e Tgas • Radiation heat transfer is important and can cause errors • Convection heat transfer to the sensor equals radiation heat transfer from the sensor • Q = Ah(Tgas – TS) = Ase(TS4 -TW4) • s = Stefan-Boltzmann constant = 5.67x10-8W/m2K4 • e = Sensor emissivity (surface property ≤ 1) • T[K] = T[C] + 273.15 • Measurement Error = Tgas– TS= (se/h)(TS4-TW4) • How does uncertainty in s and h affect this? TS TW QRad=Ase(TS4 -TW4)

  25. Conduction through Support (Fin Configuration) TS T∞ • Sensor temperature TS will be between those of the fluid T∞ and duct surface T0 • Support: cross sectional area A, parameter length P, conductivity k • Convection heat transfer coefficient between gas and support h • Fin Temperature Profile (from conduction heat transfer analysis): • (dimensionless length) • Dimensionless Tip Temperature Error from conduction • , (want this to be small) • Decreases as • L, h and P increase • k and A decrease h x L A, P, k T0

  26. TC Signal Conditioners

  27. Input Resolution Error (IRE) Random error Absolute Voltage Accuracy (AVA) AVA > IRE Temperature Resolution Error

  28. Sampling Sampling Rate Frequency fs Sampling time ts Total Sampling time Ti Number of samples

  29. Frequency Sampling Rate fs Total time If Vs(t) contains frequencies higher than Then analysis will give false (alias) frequencies. See page 106 (bookmark)

  30. TC time constant Dimensionless Temp Error

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