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ME 322: Instrumentation Lecture 24 March 23, 2015 Professor Miles Greiner Lab 9 calculations

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Announcements/Reminders This week: Lab 8 Discretely Sampled Signals – Next Week: Transient Temperature Measurements HW 9 is due Monday Midterm II, Wednesday, April 1, 2015 – Review Monday Trying to arrange for Extra Credit Opportunity – Introduction to LabVIEW and Computer-Based Measurements Hands-On Seminar NI field engineer will walk through the LabVIEW development environment Potentially 1% of grade extra credit for actively attending Time, place and sign-up “soon”

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

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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 (all in ~8 seconds) 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 )

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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 t = t 0

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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 However, slope does not exhibit a step change in each environment –Temperature of TC center does not response immediately Transient time for TC center to start to respond: t T ~ D 2 c/k TC (order of magnitude) Lab 9 Measured Thermocouple Temperature versus Time

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Type J Thermocouple Properties Not a sphere

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TC Wire Properties (App. B)

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Dimensionless Temperature Error

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Data Transformation (trick)

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To find decay constant b using Excel

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

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Lab 9 Sample Data

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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.

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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.

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Lab 9 Results

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Air and Water Thermal Conductivities Appendix B k Air (T Room ) k water (T Room, T Boiling )

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Lab 9 Extra Credit

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Measurement Results Choice of t D is a compromise between eliminating noise and retaining responsiveness

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What Do We Expect? Expected for Uniform Temperature TC Measured t0t0 T F = T B T i = T R

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What do we measure? titi Expected for uniform temperature TC Measured Q t tTtT

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Sinusoidally-Varying Environment Temperature For example, a TC in a car cylinder or 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, and there will be a phase lag. T ENV T TC

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Heat Transfer from Fluid to TC Q =hA(T – T) Fluid Temp T F (t) T D=2r

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Solution

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Particular Solution =0

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Result

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Compare to Environment Temperature T tDtD

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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 A TC = 0.5 A ENV ? If the combustion gases may be assumed to have the properties of air at 600C, what is the required Nusselt number?

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VI

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