ME 322: InstrumentationLecture 32
April 10, 2015
Professor Miles Greiner
Announcements/Reminders
•HW 10 due Monday
•I’m having trouble getting the date for the sample lab so I will postthe new lab instructions (including L10PP), the sample data, andthe sample report by the end of today… (sorry for taking so long)
•Marissa Tsugawa will hold a problem review session on Sunday
–Will email time and place
•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 greiner@unr.edu)
–Spring 2016: ME 322 Lab Assistant
Cylinder in Cross Flow (unsteady)
•Speed is reduced in the wake region
•Instability of steady flow causes periodically-shed vortices
•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?
V∞
Velocity
Probe
Strouhal Number
What does the vortex shedding frequency depend on? Increases with 𝑉 ∞ Decreases with 𝐷 𝑓= 𝑉 ∞ 𝐷 𝑆𝑡 𝐷 Dimensionless Strouhal Number 𝑆𝑡 𝐷 = 𝑓𝐷 𝑉 ∞ =𝑓𝑛( 𝑅𝑒 𝐷 ); 𝑅𝑒 𝐷 = 𝑉 ∞ 𝐷 𝜈 = 𝑉 ∞ 𝐷𝜌 𝜇 For 500<𝑅𝑒 𝐷 < 10 5 , 0.20 < 𝑆𝑡 𝐷 < 0.21 (~constant) Frequency increases linearly with speed and flow rate This phenomena used to measure pipe volume flow rate Q
V∞
D
AADUYPR0
Q
f
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. 𝑆𝑡 𝐷 = 𝑓𝐷 𝑉 ∞ 𝑓= 𝑉 ∞ 𝐷 𝑆𝑡 𝐷 0.20 < 𝑆𝑡 𝐷 < 0.21 For 500<𝑅𝑒 𝐷 < 10 5
AADUYPW0
AADUYPV0
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 is attenuated and delayed comparedto probe (2nd order system)
•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 to the surrounding fluid increases with fluid speed
–Two modes:
•Constant Current (film get cooler when speed increases)
•Constant Temperature (more power is required to maintain temperature at high speed)
Hot wire/film circuit Circuit
Probe electrical resistance heating Q = IVO (can be measured) Heat is mostly removed by convection Q = IVO= hA(TS-T∞) Neglecting radiation and conduction Convection Coefficient for small cylinders in cross flow ℎ=𝑁+𝑀 𝑉 ∞ ; M and N are constants If we can find sensor temperature TS, then we can find ℎ= 𝐼 𝑉 𝑂 𝐴( 𝑇 𝑠 − 𝑇 ∞ ) and 𝑉 ∞ = ℎ−𝑁 𝑀 2
𝑉 ∞
ℎ
VO
V∞ T∞
I
VE
I
TS RS
R2
How to find TS?
Wire resistance depends on TS 𝑅 𝑆 = 𝑅 𝑆0 1+𝛼 𝑇 𝑆 − 𝑇 0 = 𝑉 0 𝐼 𝛼= Temperature Coefficient of Resistance (material property) RS0 = RS at T = T0 𝑇 𝑠 = 𝑅 𝑆 𝑅 𝑆0 −1 𝛼 + 𝑇 0 , We can find 𝑅 𝑆 = 𝑉 0 𝐼 So, theoretically we can find TS and so ℎ= 𝐼 𝑉 𝑂 𝐴 𝑇 𝑆 − 𝑇 ∞ and 𝑉 ∞ = ℎ−𝑁 𝑀 2 Two modes of operation
Constant Current Mode
Excitation voltage VE = constant, and R2 >> RS 𝐼= 𝑉 𝐸 𝑅 2 + 𝑅 𝑆 = 𝑉 𝐸 𝑅 2 = constant Probe temperature TS and resistance RS go downs as V∞ goes up Measure V0 = IRS V0 will decrease as V∞ increases Calibrate Problem: Sensor temperature TS must reach equilibrium with its surroundings Takes time, 𝜏= 𝜌𝑐𝑉 ℎ𝐴 ~ 0.01 sec, or frequency 100 Hz Too slow!
VO
V∞ T∞
I
VE
I
TS RS
R2
V0
V∞
Constant Temperature Anemometer (CTA)
•Incorporates hot sensor into a Wheatstone bridge
•If speed V∞ increases, TS and RS “start” to go down
•This decreases VBridge, but Feedback amplifier (op-amp) veryquickly increases VO to increase current to sensor and restore itstemperature and resistance (RS = RR)
•The current and power to the sensor adjusts to make its temperatureconstant
•Output is VCTA (voltage across sensor)
AADUYPY0
V∞
VBridge
VCTA
TS RS
 RR
CTA Transfer Function
Convection Heat Transfer from probe to fluid 𝑄= 𝑉 𝐶𝑇𝐴 2 𝑅 𝑆 =ℎ𝐴 𝑇 𝑆 − 𝑇 ∞ = 𝑀+𝑁 𝑉 ∞ 𝐴( 𝑇 𝑆 − 𝑇 ∞ ) So 𝑉 𝐶𝑇𝐴 2 =𝑎 𝑉 ∞ +𝑏 𝑎=𝑁𝐴( 𝑇 𝑆 − 𝑇 ∞ ) 𝑅 𝑆 𝑏=𝑀𝐴( 𝑇 𝑆 − 𝑇 ∞ ) 𝑅 𝑆 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. Calculate 𝑉 ∞ = 𝑉 𝐶𝑇𝐴 2 −𝑏 𝑎 2 , 𝑤 𝑉 ∞ = ?
Constants
Hot Film System Calibration
•The fit equation VCTA2 = aSA0.5+b appears to be appropriatefor these data.
•The dimensional parameters are
–a = 1.366 volts2s1/2/m1/2 and
–b = 2.2057 volts2
Lab 11 UnsteadySpeed in a KarmanVortex 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
–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
Setup
Add CTA and cylinder in cross flow Do not use Venturi tube or Gage Pressure Transducer Assume Pstat = PATM (Pgage = 0) Tunnel Air Density 𝜌= 𝑃 𝐴𝑇𝑀 𝑅 𝐴𝑖𝑟 𝑇 𝐴𝑇𝑀
DTube
PP
Static
Total
+
-
IP
Variable Speed
Blower
Plexiglas
Tube
Pitot-StaticProbe VC
3 in WC
Barometer
PATM
TATM
CTA
myDAQ
Cylinder
VCTA
Before Experiment
•Construct VI (formula block)
•Measure PATM, TATM, and cylinder D
•Find  and  for air
•Air Viscosity from A.J. Wheeler and A. R. Ganji, Introduction toEngineering Experimentation, 2nd Edition, Pearson Prentice Hall,2004, p. 430.
Fig. 2 VI Block Diagram
Fig. 1 VI Front Panel
Calibrate CTA using Pitot Probe
•Remove Cylinder
•Align hot film and Pitot probes (carefully)
–4 probes cost $600
•Measure VCTA,AVG and IPitot for different blowerspeeds
Calibration Measurements and Calculations
Average Velocity 𝑉 𝐴 =𝐶 2 𝑃 𝑃 𝜌 𝐴𝑖𝑟 = 2 𝜌 𝑊 𝑔𝐹𝑆 𝐼 𝑃 −4𝑚𝐴 16𝑚𝐴 𝜌 𝐴𝑖𝑟 𝜌 𝐴𝑖𝑟 = 𝑃 𝐴𝑇𝑀 𝑅 𝐴𝑖𝑟 𝑇 𝐴𝑇𝑀 𝐹𝑆=(3 𝑖𝑛𝑐ℎ 𝑊𝐶) 2.54 𝑐𝑚 𝑖𝑛𝑐ℎ 1 𝑚 100 𝑐𝑚 𝜌 𝑊 =998.7 𝑘𝑔 𝑚 3
Table 2 Calibration Data
•The initial and final no-wind hot film voltages and Pitottransmitter currents are the same.
Standard Error of the Estimate
Find best fit line 𝑉 𝐶𝑇𝐴,𝑓𝑖𝑡 2 =𝑎 𝑉 𝐴 +𝑏 Find Standard Error of the Estimate 𝑠 𝑦,𝑥 = 𝑠 𝑉 𝐶𝑇𝐴 2 , 𝑉 𝐴 = 𝑎 𝑉 𝐴 𝑖 +𝑏 − 𝑉 𝐶𝑇𝐴 2 𝑖 2 𝑛−2 Now measure VCTA to determine 𝑉 𝐴
x
x
x
x
x
x
x
x
VCTA2
𝑆 𝑉 𝐴
𝑆 𝑉 𝐶𝑇𝐴 2
𝑉 𝐴
Measure VCTA to determine 𝑉 𝐴
Invert 𝑉 𝐶𝑇𝐴,𝑓𝑖𝑡 2 =𝑎 𝑉 𝐴 +𝑏 𝑉 𝐴 = 𝑉 𝐶𝑇𝐴 2 −𝑏 𝑎 2 Uncertainty 𝑠 𝑉 𝐴 , 𝑉 𝐶𝑇𝐴 2 = 𝑠 𝑉 𝐶𝑇𝐴 2 , 𝑉 𝐴 𝑎 = 𝑠 𝑉 𝐴 But we want 𝑠 𝑉 𝐴 𝑉 𝐴 = 𝑉 𝐴 2
Cylinder in cross flow
Wake: region of reduced speed
Frequency
Strughold #:
For
 
 Constant
Page 360 to 361
Measure flow rate in a pipe
Example
A car antenna D = 0.25 in and car s=60 mph
What will the frequency of the shed vortices be?
 
Before we used: Pressure Method
Pito-probe/pressure transmitter  (too slow)
Heat transfer method:
-hot film or hot wire probe
-small electrically heated surface
Probe:
Acid etched wire (hot wire)
-small but brittle
Metal plated quartz cylinder (hot film).
Probe electrical resistance heating
 → Can measure I, V0  Q [watts]
Heat is mostly dissipated by convection
For small cylinders in cross flow
How to find TS:
Wire resistance changes with its temperature TS:
α ≡ material property
So theoretically by measuring: A, I, V0, & known α.
Tow modes of operation:
1)  Constant current
     VE ≡ constant & R2 >> RS
As U↑,  h↑, TS↓, RS↓
Problem:
TS must reach equilibrium with surroundings.
Takes time
Max frequency Response
2) Constant Temp Anemometer (CTA)
•Uses electronic feedback (op-amp) to very VE so TS (and RS)
 stay constant.
Wheat stone bridge circuit