Measurements in Fluid Mechanics

058:180 (ME:5180) Time & Location: 2:30P - 3:20P MWF 3315 SC Office Hours: 4:00P – 5:00P MWF 223B-5 HL

Instructor: Lichuan Gui

[email protected]

Phone: 319-384-0594 (Lab), 319-400-5985 (Cell) http://lcgui.net

Lecture 21. Temperature measurement

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Temperature measurement

Temperature scales

- three temperature scales in use today, Fahrenheit (  F), Celsius (  C) and Kelvin (K) Fahrenheit temperature scale - 32 for the freezing point of water - 212 for the boiling point of water - interval divided into 180 parts Celsius, or centigrade, scale - 0 for the freezing point of water - 100 for the boiling point of water - conversion formula: F = 9/5C + 32 Kelvin temperature scale - base unit in International System (SI) of measurement - zero point at absolute zero - difference between the freezing and boiling points of water is 100 degrees - conversion formula: K = C + 273 3

Temperature measurement

Thermometers

Thermal expansion thermometers - liquid-in-glass thermometers - bimetallic thermometers Thermocouples - based on the thermoelectric effect Resistance thermometers - based on the relationship between temperature and electric resistance - include metallic resistance sensors (RTDs), and semiconductor resistance sensors

Coil elements

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Temperature measurement

Liquid-in-glass thermometers

- a bulb, a reservoir in which the working liquid can expand or contract in volume - a stem, a glass tube containing a tiny capillary connected to the bulb and enlarged at the bottom into a bulb that is partially filled with a working liquid. The tube's bore is extremely small - less than 0.5 mm in diameter - a temperature scale is fixed or engraved on the stem supporting the capillary tube to indicate the range and the value of the temperature. The liquid-in-glass thermometers is usually calibrated against a standard thermometer and at the melting point of water - a reference point, a calibration point, the most common being the ice point - a working liquid, usually mercury or alcohol - an inert gas is used for mercury intended to high temperature. The thermometer is filled with an inert gas such as argon or nitrogen above the mercury to reduce its volatilization.

constriction may be used to measure maximal or minimal temperature 5

Temperature measurement

Liquid-in-glass thermometers

- Typical resolution: 0.05-1 K - Immersion types: partial Immersion (inserted in fluid up to marked line) total immersion (inserted in fluid up to liquid column) complete immersion (entirely immersed in fluid) - total immersion required to avoid errors due to temperature difference between immersed and non-immersed sections 𝑻 𝒏𝒐𝒏−𝒊𝒎𝒎 𝑵 𝑻 𝒊𝒎𝒎 - stem correction necessary with partial immersion thermometers e.g. for mercury-in-glass thermometers: ∆𝑇 = 0.00016𝑁 𝑇 𝑖𝑚𝑚 − 𝑇 𝑛𝑜𝑛−𝑖𝑚𝑚 𝑁 - number of degrees (K) of the non-immersed portion 𝑇 𝑖𝑚𝑚 - temperature of the immersed portion 𝑇 𝑛𝑜𝑛−𝑖𝑚𝑚 - temperature of the non-immersed portion - disadvantage: poor spatial and temporal resolutions - advantage: excellent laboratory standards for calibration of other instruments 6

Temperature measurement

Bimetallic thermometers

- two thin plates of different materials - vastly different thermal expansion coefficient - bonded together tightly with one end fixed & another free - curvature of the assembly changed due to temperature variation - helically or spiral coiled assembly used to amplify motion resulting from temperature change Bimetallic thermometer (flat, spiral strip) - bimetallic assemblies also used in thermostatic controls - typical resolution about 1% of full scale, and maximal operation temperature around 500  C 7

Temperature measurement

Thermocouples

Seebeck effect - Any electrical conductor will develop a potential difference (thermoelectric voltage) between two of its points that have a temperature difference.

Thermocouple configuration - two dissimilar metallic wires (e.g. A and B) joined firmly at two junctions - one junction exposed to the temperature of interest (e.g. T 1 ) - the other one (reference junction) kept at known constant temperature (e.g. T 2 ) - reference junction conventionally immersed in an ice bath for reference temperature of 0  C - constant reference temperature also provided with an electronically controlled heated block - common types of thermocouples and their properties - typical resolution in the order of 1  C - highest temperature of 2930  C by tungsten-rhenium type 8

Temperature measurement

Thermocouples

Sensor & measuring circuit 9

Temperature measurement

Resistance thermometers

Resistance temperature detectors (RTDs) - pure metal thermometers of platinum (most popular and accurate), nickel, or copper - typical resolution of 0.1 K, possible high resolution of 0.0001 K - non-linear response fitted with low-order polynomials e.g. resistance R pt of platinum RTD in the range 0f 100-700  C described by Callendar-Van Dusen equation R pt0 – resistance at 0  C Cold-wires - similar construction to HW - high frequency response in temperature measurement Thermistors - semiconductor elements whose resistance is a very strong function of temperature. - extremely high sensitivity to temperature - non-linear response 10

Homework

- Read textbook 12.1-12.2 on page 290 - 296 - Questions and Problems: 6 on page 305 - Due on 10/15

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Learn to write a Matlab program

• to select image samples in a 32×32-pixel window from two images at x=400, y=200

Example of Matlab program:

clear; A1=imread('A001_1.bmp'); A2=imread('A001_2.bmp'); G1=img2xy(A1); G2=img2xy(A2); M=32; N=32; x=400; y=200; g1=sample01(G1,M,N,x,y); g2=sample01(G2,M,N,x,y); g1=g1-mean(mean(g1)); g2=g2-mean(mean(g2)); c=xcorr2(g1,g2); [cm Sx Sy]=peaksearch(c,20) C=xy2img(c); imwrite(C,'C.bmp','bmp'); • • •

http://lcgui.net/ui-lecture2012/hw/00/A001_1.BMP

http://lcgui.net/ui-lecture2012/hw/00/A001_2.BMP

to remove mean gray values of the 2 image samples to determine cross-correlation function to determine particle image displacement 12