ME 322: InstrumentationLecture 32

April 10, 2015Professor Miles Greiner

Announcements/Reminders• HW 10 due Monday

• I’m having trouble getting the date for the sample lab so I will post the new lab instructions (including L10PP), the sample data, and the 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

– 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?

V∞ VelocityProbe

Strouhal Number

• What does the vortex shedding frequency depend on?– Increases with – Decreases with

• Dimensionless Strouhal Number– ;

• For , 0.20 < < 0.21 (~constant)– Frequency increases linearly with speed and flow rate– This phenomena used to measure pipe volume flow rate Q

V∞

D Qf

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.

• 0.20 < < 0.21– For

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 compared to 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– ; M and N are constants

• If we can find sensor temperature TS, then we can find – and

𝑉 ∞

hVO

V∞ T∞

I

VE

I

TS RS

R2

How to find TS?• Wire resistance depends on TS

• Temperature Coefficient of Resistance (material property)• RS0 = RS at T = T0

– , – We can find – So, theoretically we can find TS and so

• and

• Two modes of operation

Constant Current Mode

• Excitation voltage VE = constant, and R2 >> RS • = 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, ~ 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) very quickly

increases VO to increase current to sensor and restore its temperature and resistance (RS = RR)

• The current and power to the sensor adjusts to make its temperature constant• Output is VCTA (voltage across sensor)

V∞

VBridge

VCTA

TS RS

RR

CTA Transfer Function• Convection Heat Transfer from probe to fluid• )

• So – )– )– 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 ,

Constants

Hot Film System Calibration

• The fit equation VCTA2 = aSA

0.5+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– 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

DTube

PP

Static

Total+ -

IP

Variable SpeedBlower Plexiglas

Tube

Pitot-Static Probe VC

3 in WC

BarometerPATM TATM

CTA

myDAQ

Cylinder

VCTA

Before Experiment• Construct VI (formula block)• Measure PATM, TATM, and cylinder D • Find m and r for air

• Air Viscosity from A.J. Wheeler and A. R. Ganji, Introduction to Engineering Experimentation, 2nd Edition, Pearson Prentice Hall, 2004, p. 430.

T D P m r

Kelvin inch kPa N-s/m2 Kg/m3296.2 0.125 88.1 1.8262E-05 1.037

Fig. 2 VI Block Diagram

Spectral Measurements Selected Measurements: Magnitude (RMS) View Phase: Wrapped and in Radians Windowing: Hanning Averaging: None

Formula Formula: ((v**2-b)/a)**2

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 blower

speeds

Calibration Measurements and Calculations

• Average Velocity•

IP VCTA PP VA VA1/2 VCTA

2 di2=(aVA

1/2+b-VCTA2)2

[mA] [V] [Pa] [m/s] [m/s]1/2 [V2] [V4]

Table 2 Calibration Data

• The initial and final no-wind hot film voltages and Pitot transmitter currents are the same.

IP

[mA]VCTA

[V]SA

[m/s]SA

1/2

[m1/2/s1/2]VCTA

2

[V2]4.00 2.140 0 0.00 4.585.70 3.670 12 3.52 13.477.40 3.930 17 4.18 15.449.40 4.070 22 4.70 16.5611.60 4.130 26 5.11 17.0616.80 4.460 34 5.83 19.8914.40 4.340 31 5.53 18.8413.30 4.290 29 5.38 18.4011.00 4.160 25 5.01 17.318.50 4.000 20 4.49 16.006.30 3.820 14 3.79 14.594.00 2.140 0 0.00 4.58

Standard Error of the Estimate

• Find best fit line

• Find Standard Error of the Estimate

• Now measure VCTA to determine

xxxx

x

x

xx

VCTA2 𝑆√𝑉 𝐴

𝑆𝑉𝐶𝑇𝐴2

√𝑉 𝐴

Measure VCTA to determine

• Invert

• Uncertainty

• But we want

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 mphWhat 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