ME 322: Instrumentation Lecture 20 March 6, 2015 Professor Miles Greiner myDAQ A/D converter, temperature uncertainty, First-order, centered numerical differentiation and random errors

Announcements/Reminders HW 7 due now – Did the computers and software in the ECC work the way they are supposed to? HW 8 Due next Friday – Then Spring Break! Please complete the Lab Preparation Problems and fully participate in each lab – For the final you will repeat one of the last three labs, including performing the measurements, and writing Excel, LabVIEW and PowerPoint, solo.

A/D Converter Characteristics Full-scale range V RL ≤ V ≤ V RU – FS = V RU - V RL – For myDAQ the user can chose between two ranges ±10 V, ±2 V (FS = 4 or 20 V) Number of Bits N – Resolves full-scale range into 2 N sub-ranges – Smallest voltage change a conditioner can detect:  V = FS/2 N – For myDAQ, N = 16, 2 16 = 65,536 ±10 V scale:  V = 0.000,310 V = mV = 305  V ±2 V scale:  V = 0.000,061 V = mV = 61  V Sampling Rate f S = 1/T S – For myDAQ, (f S ) MAX = 200,000 Hz, T S = 5  sec

Example A/D Converter Transfer Function

Input Resolution Error

Summary of myDAQ Uncertainties What are these? – AA: Maximum error of the voltage measurement reported by the manufacturer for all voltage levels At different temperatures – MSVE: Maximum error measured at V = 0V for one device – IRE: Random error due to digitization process Which best characterizes voltage uncertainty?

Lab 7 Boiling Water Temperature in Reno

A/D Converters can be used to measure a long series of very rapidly changing voltage Great for measuring a voltage signal – How voltage or measurand changes with time – Would be very difficult using a regular voltmeter Allows determination of – Rates of Change and – Spectral (Frequency) Content The voltage and time associated with each measurement has some error – It is associated with the centers of the voltage sub-range and sampling time. – Additional systematic and random errors as well What can go wrong?

Example T(t) TiTi TBTB

1 st Law of Thermodynamics U

Sample Data Lab 9 Transient Thermocouple Measurements – Download sample data – abs/Lab%2009%20TransientTCResponse/LabIndex.htm abs/Lab%2009%20TransientTCResponse/LabIndex.htm Plot T vs t for t < 2 sec Show how to evaluate and plot first-order centered derivatives with different differentiation time steps – Plot dT/dt vs t for m = 1, 10, 50 Slow T vs t – for 0.95s < t < 1.05s and 25 ° C < T < 45 ° C – How do random errors affect “local” and “time- averaged” slopes?

Effect of Random Noise on Differentiation

Common Temperature Measurement Errors Even for steady temperatures Lead wires act like a fin, cooling a hot the surface compared to the case when the sensor is not there The temperature of a sensor on a post will be between the fluid and duct surface temperature

High Temperature (combustion) Gas Measurements Radiation heat transfer is important and can cause errors Convection heat transfer to the sensor equals radiation heat transfer from the sensor – Q = Ah(T gas – T S ) = A  (T S 4 -T W 4 )  = Stefan-Boltzmann constant = 5.67x10 -8 W/m 2 K 4  Sensor emissivity (surface property ≤ 1) T[K] = T[C] Measurement Error = T gas – T S = (  /h)(T S 4 -T W 4 ) Q Conv =Ah(T gas – T S ) TSTS Q Rad =A  (T S 4 -T W 4 ) T gas TWTW Sensor h, T S, A, 

Problem 9.39 (p. 335) Calculate the actual temperature of exhaust gas from a diesel engine in a pipe, if the measuring thermocouple reads 500 ° C and the exhaust pipe is 350 ° C. The emissivity of the thermocouple is 0.7 and the convection heat-transfer coefficient of the flow over the thermocouple is 200W/m 2 -C. ID: Steady or Unsteady? What if there is uncertainty in emissivity?

Conduction through Support (Fin Configuration) T∞T∞ h x L A, P, k T0T0 TSTS

Example A 1-cm-long, 1-mm-diameter stainless steel support (k = 20 W/mK) is mounted inside a pipe whose temperature is 200 ° C. The heat transfer coefficient between gas in the pipe and the support is 100 W/m 2 K, and a sensor at the end of the support reads 350 ° C. What is the gas temperature? Assume  sensor = 0 Steady or unsteady Radiation or Conduction errors

Solution

t = 0t T TiTi TBTB

Example