ME 322: Instrumentation
Lecture 26
March 18, 2016
Professor Miles Greiner
Radiation temperature errors, Lab 9.1 Sensor demo and
instructions
Announcements/Reminders
• After Spring Break
– HW 9 due Monday
• Joseph will give a tutorial the Sunday before (check email)
– Midterm II, Wednesday, March 30, 2016
• Review Monday before midterm
• Joseph will give a review tutorial Tuesday before midterm
– Lab 9 Transient Temperature Response
• Extra-Credit Opportunity
– Week of April 4, 2016
– Open ended Lab 9.1 (described in this lecture)
– 1%-of-grade extra-credit for active participation
Radiation Error: High Temperature (combustion) Gas
Measurements
QConv=Ah(Tgas– TS)
Sensor
h, TS, A, e
Tgas
TS
TW
QRad=Ase(TS4 -TW4)
• 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
– DTRad = Tgas – TS = (se/h)(TS4 -TW4)
– Uncertainty:
𝑤∆𝑇
∆𝑇
Rad
Rad
2
=
𝑤𝜀
𝜀
2
+ −
𝑤ℎ
ℎ
2
+
2
3 2
4𝑤𝑇𝑠 𝑇𝑠3 + 4𝑤𝑇𝑤 𝑇𝑤
4 2
𝑇𝑠4 −𝑇𝑤
2
Conduction through Support (Fin Configuration)
TS
T∞
h
x
L
A, P, k
T0
• Sensor temperature TS is 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):
–
𝑇(𝑥)−𝑇∞
𝑇0 −𝑇∞
=
cosh[𝑚𝐿 1−𝑥/𝐿 ]
cosh 𝑚𝐿
• cosh 𝑎 =
𝑚𝐿 =
ℎ𝑃
𝐿
𝑘𝐴
(dimensionless length)
𝑒 𝑎 +𝑒 −𝑎
2
• Dimensionless Tip Temperature Error from conduction
– 𝐸=
𝑇(𝑥=𝐿)−𝑇∞
𝑇0 −𝑇∞
=
𝑇𝑆 −𝑇∞
𝑇0 −𝑇∞
=
1
,
cosh 𝑚𝐿
(want this to be small, 𝑇𝑆 ≈ 𝑇∞ )
– Decreases as 𝑚𝐿 increases, which happens as
• L, h and P increase,
• k and A decrease
Example
• A 1-cm-long, 1-mm-diameter thermocouple (whose
conductivity is k = 20 W/mK, stainless steel) is
mounted inside a pipe whose temperature is 350°C.
The heat transfer coefficient between gas in the pipe
and the support is 100 W/m2K, and a sensor at the
end of the support reads 500°C. What is the gas
temperature? Assume esensor = 0
• Steady or unsteady
• Radiation or Conduction error
Solution
• Sensor temperature:
•
𝑚𝐿 =
𝑇𝑆 −𝑇∞
𝑇0 −𝑇∞
=
1
cosh 𝑚𝐿
=𝐸
ℎ𝑃
𝐿
𝑘𝐴
• What is given and what must be found?
• To find 𝑇∞ ,
–
–
𝑇𝑆 −𝑇∞
𝐸=
; 𝐸(𝑇0 − 𝑇∞ ) = 𝑇𝑆 − 𝑇∞ ; 𝑇∞
𝑇0 −𝑇∞
𝑇 −𝐸𝑇
1
𝑇∞ = 𝑆 0 , where 𝐸 =
1−𝐸
cosh 𝑚𝐿
• What if esensor = 0.2?
1 − 𝐸 = 𝑇𝑆 − 𝐸𝑇0
Extra Credit Lab 9.1
• 1% of grade, April 4-8, 2016
– Not Required
• Use a low-cost chip to make a measurement
– Open Ended
– Turn in a one paragraph proposal summarizing your test
plan, and the supplies you need by Friday, April 1, 2016
• Some Possibilities
– Get a sample from www.ti.com or Radio Shack
– Available in lab (See Lab 9.1 website)
• Photo Diode, Hall Effect (magnetic field) Chip, Accelerometer
Chip, LM35 temperature sensor chip
• http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Labs/
Lab%2009.1%20Extra%20Credit/Lab9.1%20Index.htm
LM35 precision temperature chip
+5
AI0+
200 Ω
AI0-
myDAQ
GND
Needs 200Ω Resistor across output. VS & Vout use the same ground.
LM35 Data Sheet
•
•
•
•
•
•
•
•
•
•
•
Calibrated directly in °Celsius (Centigrade)
Linear + 10.0 mV/˚C scale factor
0.5˚C accuracy guaranteeable (at +25˚C)
Rated for full −55˚ to +150°C range
Suitable for remote applications
Low cost due to wafer-level trimming
Operates from 4 to 30 volts
Less than 60 µA current drain
Low self-heating, 0.08°C in still air
Nonlinearity only ± 1⁄4°C typical
Low impedance output, 0.1 Ω for 1 mA load
1.5V
-55 C
150 C
-0.55V
Possibilities
• Measure boiling water temperature using an LM35
• Photo diode output voltage versus distance from a light
source (florescent or incandescent)
• Hall effect chip output voltage versus distance and
direction from a magnet
• Vibration of a weighted, cantilevered steel or aluminum
beam
• There are putting “Lab-in-a-Box” setups for check out
from the DeLaMare (Engineering) Library basement,
which can be used at home if you like.
– Measure outdoor light and temperature levels during a 24
hour period
– Dominant car frequency on a bumpy road
– Kitchen oven temperature stability using a thermocouple
(chip temperature limited to 150°C (311°F))
End 2016
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/m2-C.
• ID: Steady or Unsteady?
• What if there is uncertainty in emissivity?
LM 35
Power 4 – 10 watts VS & GND
Output Sensitivity