Transcript Lecture Slides

ME 322: Instrumentation
Lecture 32
April 8, 2016
Professor Miles Greiner
Kaman Vortex Street, Unsteady fluid speed
measurements, Hot film probe, Constant temperature
Anemometer, Calibration, Lab 11
Announcements/Reminders
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HW 10 due now
HW 11 due Friday, April 15, 2016
Next week: Lab 10 Vibrating Beam
Did you know?
– HW solutions are posted on WebCampus
– Exam solution posted outside PE 213 (my office)
• Help wanted (see me [email protected])
– Are you interested in being an ME 322 Lab Assistant in
spring 2017 (and possibly Fall 2016)?
• If you have a Laptop, you may want to load LabVIEW
and bring it to class to follow along
• Lab-in-a-Box
– All the equipment for Lab 10 (and 12) is in DeLaMare library
basement. LabVIEW also in Library.
Announcements/Reminders
• ME Dept. Graduate/Undergraduate Poster Session
– Today, 3 PM, HREL 109
• Elective Courses for Fall
– MSE 465 Fundamentals of Nuclear Power
• Go to LMR 474 to get a prerequisite override form
– ME 493-1003 Energy Engineering
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Economics of the power generation
CO2 reduction potential.
steam cycles (Rankine) and combined cycles
Combustion and flue gas analysis
Equipment used in power plants.
data on nuclear, hydroelectric, energy storage, solar, and wind
energy, power plants
• Student competition covering small energy generation system
production with a minimum cost maximum efficiency.
Cylinder in Cross Flow (unsteady)
V∞
Velocity
Probe
• Speed is reduced in the wake region
• Instability of steady flow causes periodically-shed vortices
– Karman Vortex Street
• Figure shows unsteady speed measured by a probe in wake
– Fairly regular oscillations, period P ~ 0.01/6 = 0.0017 sec
– Peak oscillatory frequency of f = 1/P ~ 600 Hz
• Broad spectrum of frequencies
– Can a Pitot probe measure oscillations at these high frequencies?
• How to measure rapidly changing speeds?
Strouhal Number
U∞
f
D
Q
Q
• What does the vortex shedding frequency depend on?
– Increases with 𝑈∞
– Decreases with 𝐷
𝑉∞
𝑆𝑡𝐷
𝐷
• 𝑓=
• Dimensionless Strouhal Number
– 𝑆𝑡𝐷 =
𝑓𝐷
𝑈∞
= 𝑓𝑛(𝑅𝑒𝐷 ); 𝑅𝑒𝐷 =
𝑈∞ 𝐷
𝜈
=
𝑈∞ 𝐷𝜌
𝜇
• From Data: or 500 < 𝑅𝑒𝐷 < 105 , 0.20 < 𝑆𝑡𝐷 < 0.21
– Frequency increases linearly with speed and flow rate
– This phenomena used to measure pipe volume flow rate Q
Example
• A car in Reno is moving at 60 miles/hour and has a
¼-inch diameter antenna. At what frequency will
vortices be shed from it? The air temperature is
27°C and the atmospheric pressure is 86 kPa.
• 𝑆𝑡𝐷 =
• 𝑓=
𝑓𝐷
𝑈∞
𝑈∞
𝑆𝑡𝐷
𝐷
• 0.20 < 𝑆𝑡𝐷 < 0.21
– For 500 < 𝑅𝑒𝐷 < 105
• http://plasticity.szynalski.com/tone-generator.htm
How to measure Rapidly Varying Speed?
• Pressure Method
– Pitot probes transmit pressure to transducers using tubes
– This is ok for slowly varying speeds
– At high frequencies, pressure response at transducer (at the other ends of tubes) is
attenuated and delayed compared to the probe (2nd order system, like accelerometer)
• Heat Transfer Method
– Hot Wire or Hot Film probe
• Very small wire or metal-plated quartz on a support fork
– Electrically heated surface
– Heat transfer from the wire to the surrounding fluid increases with fluid speed
– Two modes:
• Constant Current (film get cooler when speed increases)
• Constant Temperature (more power to film to maintain temperature at high speed, involves control)
Hot wire/film circuit
U∞ T∞
R2
I
I
T S RS
VO
VE
• Probe electrical resistance heating
ℎ
𝑈∞
– Q = IVO (can measure both I and VO)
• Most of the heat is removed by convection
– Q = IVO= hA(TS-T∞)
• Neglecting radiation and conduction
• Convection Coefficient for small cylinders in cross flow
– ℎ = 𝑁 + 𝑀 𝑈∞ ; M and N are constants (based on data)
• If we can find sensor temperature TS, then we can find
–ℎ=
𝐼𝑉𝑂
𝐴(𝑇𝑠 −𝑇∞ )
and 𝑈∞ =
ℎ−𝑁 2
𝑀
How Ito find
T
?
S
R
U∞ T∞
2
I
T S RS
VE
VO
• Wire resistance depends on TS
– 𝑅𝑆 = 𝑅𝑆0 1 + 𝛼 𝑇𝑆 − 𝑇0
=
𝑉0
𝐼
(can be measured)
• 𝛼 = Temperature Coefficient of Resistance (material property)
• RS0 = RS at T = T0
– 𝑇𝑠 =
𝑅𝑆 𝑅𝑆0 −1
𝛼
+ 𝑇0 ,
𝑉0
𝐼
– We can find 𝑅𝑆 =
– So, theoretically we can find TS, so we can find both
• ℎ=
𝐼𝑉𝑂
𝐴 𝑇𝑆 −𝑇∞
and 𝑈∞ =
ℎ−𝑁 2
𝑀
• Two modes of operation
Constant Current Mode
U∞ T∞
R2
I
I
TS RS
VO
VE
V0
U∞
• Excitation voltage VE = constant, and R2 >> RS
• 𝐼=
𝑉𝐸
𝑅2 +𝑅𝑆
=
𝑉𝐸
𝑅2
= constant
• Probe temperature TS and resistance RS go downs as U∞ goes up
• Measure V0 = IRS
– V0 will decrease as U∞ increases
– Calibrate
• Problem: Sensor temperature TS must reach equilibrium with its
surroundings
– Takes time, 𝜏 =
• Too slow!
𝜌𝑐𝑉
ℎ𝐴
~ 0.01 sec, or frequency 100 Hz
Constant Temperature Anemometer (CTA)
R2=50 Ω
Rcontro~ 50Ω
VCTA
S∞
R3=10 Ω
TS RS
VBridge
• Incorporate sensor into a “balanced” Wheatstone bridge (Vbridge =0)
• If speed U∞ increases, TS and RS “start” to go down (Vbridge <0)
• Feedback amplifier (op-amp) very quickly increases VO to increase
current to sensor, restore its temperature and resistance (RS = R3/5)
• The current and power to the sensor adjusts to make its temperature
constant
• Output is VCTA (voltage across sensor)
CTA Transfer Function
• Convection Heat Transfer from probe to fluid
• 𝑄=
2
𝑉𝐶𝑇𝐴
𝑅𝑆
= ℎ𝐴 𝑇𝑆 − 𝑇∞ = 𝑀 + 𝑁 𝑈∞ 𝐴(𝑇𝑆 − 𝑇∞ )
Constants
2
• So expect 𝑉𝐶𝑇𝐴
= 𝑎 𝑈∞ + 𝑏
– 𝑎 = 𝑁𝐴(𝑇𝑆 − 𝑇∞ )𝑅𝑆
– 𝑏 = 𝑀𝐴(𝑇𝑆 − 𝑇∞ )𝑅𝑆
– Or find constants a and b by calibration
• Feedback amplifiers respond very quickly
– Accurate for up to f = 400,000 Hz
– Requires feedback control (Lab 12)
• To use CTA, measure VCTA, and invert transfer function
– Calculate 𝑈∞ =
2
𝑉𝐶𝑇𝐴
−𝑏
𝑎
2
, 𝑤𝑈∞ = ?
Hot Film System Calibration
• The fit equation VCTA2 = aUA0.5+b appears to be appropriate
for these data.
• The dimensional parameters are
– a = 1.366 volts2s1/2/m1/2 and
– b = 2.2057 volts2
Lab 11 Unsteady
Speed in a Karman
Vortex Street
• Use the same wind tunnels as Lab 6
– Sign up for 1.5 hour periods with your partner in lab next week
• Two steps
1.
2.
Statically calibrate hot film CTA using a Pitot probe
Measure unsteady speed downstream from a cylinder of diameter D
• Perform spectral analysis and find frequency with peak amplitude, fP
• Measure “steady” speed without cylinder V
• Calculate StD = DfP /V and compare to expectations
End 2016
Before Experiment
• Construct VI (formula block)
• Measure PATM, TATM, and cylinder D
• Find m and r for air
T
D
P
m
r
N-s/m2 Kg/m3
Kelvin inch kPa
296.2 0.125 88.1 1.8262E-05 1.037
• Air Viscosity from A.J. Wheeler and A. R. Ganji, Introduction to
Engineering Experimentation, 2nd Edition, Pearson Prentice Hall,
2004, p. 430.
Fig. 2 VI Block Diagram
Spectral Measurements
Selected Measurements: Magnitude (RMS)
View Phase: Wrapped and in Radians
Windowing: Hanning
Averaging: None
Formula
Starting point VI
Formula: ((v**2-b)/a)**2
Fig. 1 VI Front Panel