lecture hot wires
TRANSCRIPT
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Hot-Wire Anemometry
•Purpose:
to measure mean and fluctuating velocities in fluid flows
http://www.dantecmt.com/ www.tsi.com/
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
• Consider a thin wire mounted to supports and exposed to a velocity U.
When a current is passed through wire, heat is generated (I2Rw). In equilibrium, this must be balanced by heat loss (primarily convective) to the surroundings.
Principles of operation
• If velocity changes, convective heat transfer coefficient will change, wire temperature will change and eventually reach a new equilibrium. Velocity U
Current I
Sensor (th in w ire)
Sensor d im ensions:length ~1 m mdiam eter ~5 m icrom eter
W ire supports (St.S t. needles)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Governing equation I
• Governing Equation:
E = thermal energy stored in wire
E = CwTs
Cw = heat capacity of wire
W = power generated by Joule heating
W = I2 Rw
recall Rw = Rw(Tw)
H = heat transferred to surroundings
dEdt W H
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Governing equation II
• Heat transferred to surroundings
( convection to fluid
+ conduction to supports
+ radiation to surroundings)
Convection Qc = Nu · A · (Tw -Ta)
Nu = h ·d/kf = f (Re, Pr, M, Gr,),
Re = U/
Conduction f(Tw , lw , kw, Tsupports)
Radiation f(Tw4 - Tf
4)
H
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Simplified static analysis I
• For equilibrium conditions the heat storage is zero:
and the Joule heating W equals the convective heat transfer H
• Assumptions
- Radiation losses small- Conduction to wire supports small- Tw uniform over length of sensor- Velocity impinges normally on wire, and is uniform over its entire
length, and also small compared to sonic speed.- Fluid temperature and density constant
dE
dtO W H
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Simplified static analysis II
Static heat transfer:
W = H I2Rw = hA(Tw -Ta) I2Rw = Nukf/dA(Tw -Ta)
h = film coefficient of heat transferA = heat transfer aread = wire diameterkf = heat conductivity of fluidNu = dimensionless heat transfer coefficient
Forced convection regime, i.e. Re >Gr1/3 (0.02 in air) and Re<140
Nu = A1 + B1 · Ren = A2+ B2 · Un
I2Rw2 = E2 = (Tw -Ta)(A + B · Un) “King’s law”
The voltage drop is used as a measure of velocity.
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Hot-wire static transfer function
• Velocity sensitivity (King’s law coeff. A = 1.51, B = 0.811, n = 0.43)
2
3
4
5
5 10 15 20 25 30 35 40
U m/s
dU
/dE
/U v
olt
s^-1
1,6
1,8
2
2,2
2,4
5 10 15 20 25 30 35 40
U m/s
E v
olt
s
Output voltage as fct. of velocity Voltage derivative as fct. of velocity
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Directional response I
Velocity vector U is decomposed into normal Ux, tangential Uy and binormal Uz components.
Probe coordinate system
U
U z
U x
U yx
y
z
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Directional response II
• Finite wire (l/d~200) response includes yaw and pitch sensitivity:
U2eff(a) = U2(cos2a + k2sin2a) = 0
U2eff() = U2(cos2+h2sin2) = 0
where:
k , h = yaw and pitch factors
, = angle between wire normal/wire-prong plane, respectively, and velocity vector
• General response in 3D flows:
U2eff = Ux2 + k2Uy2 + h2Uz2
Ueff is the effective cooling velocity sensed by the wire and deducted from the calibration expression, while U is the velocity component normal to the wire
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Directional response III
• Typical directional response for hot-wire probe
(From DISA 1971)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Directional response IV
• Yaw and pitch factors k1 and k2 (or k and h) depend on velocity and flow angle
(From Joergensen 1971)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Probe types I
• Miniature Wire ProbesPlatinum-plated tungsten, 5 m diameter, 1.2 mm length
• Gold-Plated Probes 3 mm total wire length,
1.25 mm active sensor copper ends, gold-plated
Advantages:- accurately defined sensing length
- reduced heat dissipation by the prongs- more uniform temperature distribution
along wire- less probe interference to the flow field
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Probe types II
For optimal frequency response, the probe should have as small a thermal inertia as possible.
Important considerations:
• Wire length should be as short as possible (spatial resolution; want probe length << eddy size)
• Aspect ratio (l/d) should be high (to minimise effects of end losses)
• Wire should resist oxidation until high temperatures (want to operate wire at high T to get good sensitivity, high signal to noise ratio)
• Temperature coefficient of resistance should be high (for high sensitivity, signal to noise ratio and frequency response)
• Wires of less than 5 µm diameter cannot be drawn with reliable diameters
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Probe types III
• Film Probes
Thin metal film (nickel) deposited on quartz body. Thin quartz layer protects metal film against corrosion, wear, physical damage, electrical action
• Fiber-Film Probes
“Hybrid” - film deposited on a thin wire-like quartz rod (fiber) “split fiber-film probes.”
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Probe types IV
• X-probes for 2D flows2 sensors perpendicular to each other. Measures within ±45o.
• Split-fiber probes for 2D flows2 film sensors opposite each other on a quartz cylinder. Measures within ±90o.
• Tri-axial probes for 3D flows3 sensors in an orthogonal system. Measures within 70o cone.
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Hints to select the right probe
• Use wire probes whenever possible
relatively inexpensive better frequency response can be repaired
• Use film probes for rough environments
more rugged worse frequency response cannot be repaired electrically insulated protected against mechanical and
chemical action
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Modes of anemometer operation
Constant Current (CCA)
Constant Temperature (CTA)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Constant current anemometer CCA
• Principle:Current through sensor is kept constant
• Advantages:- High frequency
response
• Disadvantages:- Difficult to use- Output decreases with velocity- Risk of probe burnout
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Constant Temperature Anemometer CTA I
• Principle:Sensor resistance
is kept constant by servo amplifier
• Advantages:- Easy to use- High frequency
response- Low noise- Accepted standard
• Disadvantages:- More complex circuit
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Constant temperature anemometer CTA II
• 3-channel StreamLine with Tri-axial wire probe 55P91
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Modes of operation, CTA I
• Wire resistance can be written as:
Rw = Ro(1+
Rw = wire hot resistanceRo = wire resistance at To = temp.coeff. of resistanceTw = wire temperatureTo = reference temperature
• Define: “OVERHEAT RATIO” as:
a = (Rw-Ro)/Ro =
• Set “DECADE” overheat resistor as: RD = (1+a)Rw
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Modes of operation, CTA II
• The voltage across wire is given by:
E2 = I2Rw2 = Rw(Rw - Ra)(A1 + B1Un)
or as Rw is kept constant by the servoloop:
E2 = A + BUn
• Note following commentsto CTA and to CCA:
- Response is non-linear: - CCA output decreases
- CTA output increases
- Sensitivity decreases with increasing U
1,6
1,8
2
2,2
2,4
5 10 15 20 25 30 35 40
U m/s
E v
olt
sCTA output as fct. of U
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Dynamic response, CCA I
Hot-wire Probes:
• For analysis of wire dynamic response, governing equation includes the term due to thermal energy storage within the wire:
W = H + dE/dt
The equation then becomes a differential equation:
I2Rw = (Rw-Ra)(A+BUn) + Cw(dTw/dt)
or expressing Tw in terms of Rw:
I2Rw = (Rw-Ra)(A+BUn) + Cw/
Cw = heat capacity of the wire = temperature coeff. of resistance of the wire
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Dynamic response, CCA II
Hot-wire Probes:
The first-order differential equation is characterised by a single time constant :
= Cw/(n)
The normalised transfer function can be expressed as:
Hwire(f) = 1/(1+jf/fcp)
Where fcp is the frequency at which the amplitude damping is 3dB (50% amplitude reduction) and the phase lag is 45o.
Frequency limit can be calculated from the time constant:
fcp = 1/2
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Dynamic response, CCA III
• Hot-wire Probes:
Frequency response of film-probes is mainly determined by the thermal properties of the backing material (substrate).
The time constant for film-probes becomes:
= (R/R0)2F2sCsks/(A+BUn)2
s = substrate densityCs = substrate heat capacityks = substrate heat conductivity
and the normalised transfer function becomes:
Hfilm(f) = 1/(1+(jf/fcp)0.5)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Dynamic response, CCA IV
• Dynamic characteristic may be described by the response to
- Step change in velocity or
- Sinusoidal velocity variation
Amplitude response and phase lag
Upper frequency lim it f = ½ Frequency
6 dB/octave
3 dB 30°
Ve locity
Resistance
Time
Time
U2
R1
U1
R2
0.63 (R1-R )
2
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Dynamic response, CCA V
• The hot-wire response characteristic is specified by:
For a 5 µm wire probe in CCA mode~ 0.005s, typically.(Frequency response can be improved by compensation circuit)
(From P.E. Nielsen and C.G. Rasmussen, 1966)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Dynamic response, CTA I
• CTA keeps the wire at constant temperature, hence the effect of thermal inertia is greatly reduced:
Time constant is reduced to
CTA = CCA/(2aSRw)
where
a = overheat ratio S = amplifier gainRw = wire hot resistance
• Frequency limit:
fc defined as -3dB amplitude damping
(From Blackwelder 1981)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Dynamic response, CTA II
• Typical frequency response of 5 mm wire probe (Amplitude damping and Phase lag):
Phase lag is reduced by frequency dependent gain (-1.2 dB/octave)
(From Dantec MT)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Velocity calibration (Static cal.)
• Despite extensive work, no universal expression to describe heat transfer from hot wires and films exist.
• For all actual measurements, direct calibration of the anemometer is necessary.
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Velocity calibration (Static cal.) II
• Calibration in gases (example low turbulent free jet):
Velocity is determined from isentropic expansion:
Po/P = (1+(2)
a0 = (0 )0.5
a = ao/(1+(2)0.5
U = Ma
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Velocity calibration (Static cal.) III
• Film probes in water
- Using a free jet of liquid issuing from the bottom of a container
- Towing the probe at a known velocity in still liquid
- Using a submerged jet
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Typical calibration curve
• Wire probe calibration with curve fit errors
Curve fit (velocity U as function of output voltage E):
U = C0 + C1E + C2E2 + C3E3 + C4E4
(Obtained with Dantec 90H01/02)Calibrator)
4.0761.731
11.12 18.17
U velocity
25.22 32.27 39.32
1.853
1.975
2.096
2.218
2.340
E 1 (v)
E 1 v.U
4.076-0.500
11.12 18.17
U velocity
25.22 32.27 39.32
-0.300
-0.100
0.100
0.300
0.500
E rror (% )
E rror (% )
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Dynamic calibration/tuning I
• Direct method
Need a flow in which sinusoidal velocity variations of known amplitude are superimposed on a constant mean velocity
- Microwave simulation of turbulence (<500 Hz)- Sound field simulation of turbulence (>500 Hz)- Vibrating the probe in a laminar flow (<1000Hz)
All methods are difficult and are restricted to low frequencies.
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Dynamic calibration/tuning II
• Indirect method, “SINUS TEST”
Subject the sensor to an electric sine wave which simulates an instantaneous change in velocity and analyse the amplitude response.
103
102
102
103
104
105
106
10
101
Frequency (Hz)
-3 dB
Am
plit
ude
(m
V r
ms)
1
103
102
102
103
104
105
106
10
10
Frequency (Hz)
-3 dB
Am
plit
ude
(m
V r
ms)
1
Typical Wire probe response Typical Fiber probe response
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Dynamic calibration/tuning III
• Indirect method “SQUARE WAVE TEST”
Subject the sensor to an electric sine wave which simulates an instantaneous change in velocity and analyse the shape of the anemometer output
(From Bruun 1995)
h0.97 h
0.15 ht
fc
=1.3
w
w
1
For a wire probe (1-order probe response):
Frequency limit (- 3dB damping): fc = 1/1.3
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Dynamic calibration
Conclusion:
• Indirect methods are the only ones applicable in practice.
• Sinus test necessary for determination of frequency limit for fiber and film probes.
• Square wave test determines frequency limits for wire probes. Time taken by the anemometer to rebalance itself is used as a measure of its frequency response.
• Square wave test is primarily used for checking dynamic stability of CTA at high velocities.
• Indirect methods cannot simulate effect of thermal boundary layers around sensor (which reduces the frequency response).
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Disturbing effects (problem sources)
• Anemometer system makes use of heat transfer from the probe
Qc = Nu · A · (Tw -Ta)Nu = h · d/kf = f (Re, Pr, M, Gr,
• Anything which changes this heat transfer (other than the flow variable being measured) is a “PROBLEM SOURCE!”
• Unsystematic effects (contamination, air bubbles in water, probe vibrations, etc.)
• Systematic effects (ambient temperature changes, solid wall proximity, eddy shedding from cylindrical sensors etc.)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem sourcesProbe contamination I
• Most common sources:- dust particles- dirt- oil vapours- chemicals
• Effects:- Change flow sensitivity of sensor
(DC drift of calibration curve)- Reduce frequency response
• Cure:- Clean the sensor- Recalibrate
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem SourcesProbe contamination II
• Drift due to particle contamination in air
5 m Wire, 70 m Fiber and 1.2 mm SteelClad Probes
-20
-10
0
10
20
0 10 20 30 40 50
U (m/s)
(Um
-Uac
t)/U
act*
100%
w ire
fiber
steel-clad
Poly. (steel-clad)Poly. (f iber)
(From Jorgensen, 1977)
Wire and fiber exposed to unfiltered air at 40 m/s in 40 hours
Steel Clad probe exposed to outdoor conditions 3 months during winter conditions
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem SourcesProbe contamination IV
• Low Velocity- slight effect of dirt on heat transfer- heat transfer may even increase!- effect of increased surface vs. insulating effect
• High Velocity- more contact with particles- bigger problem in laminar flow- turbulent flow has “cleaning effect”
• Influence of dirt INCREASES as wire diameter DECREASES
• Deposition of chemicals INCREASES as wire temperature INCREASES
* FILTER THE FLOW, CLEAN SENSOR AND RECALIBRATE!
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem SourcesProbe contamination III
• Drift due to particle contamination in waterOutput voltage decreases with increasing dirt deposit
0,1
1
10
0,001 0,01 0,1 1
Dirt thicknes versus sensor diameter, e/D
% v
olt
age
red
uct
ion
theory
fiber
w edge
(From Morrow and Kline 1971)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem SourcesBubbles in Liquids I
• Drift due to bubbles in water
In liquids, dissolved gases form bubbles on sensor, resulting in:
- reduced heat transfer- downward calibration drift
(From C.G.Rasmussen 1967)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem SourcesBubbles in Liquids II
• Effect of bubbling onportion of typicalcalibration curve
• Bubble size depends on- surface tension- overheat ratio- velocity
• Precautions- Use low overheat!- Let liquid stand before use! - Don’t allow liquid to cascade in air! - Clean sensor!
(From C.G.Rasmussen 1967)
155
e
175 195 cm/sec
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem Sources (solved) Stability in Liquid Measurements
• Fiber probe operated stable in water
- De-ionised water (reduces algae growth)- Filtration (better than 2 m)- Keeping water temperature constant (within 0.1oC)
(From Bruun 1996)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem sourcesEddy shedding I
• Eddy shedding from cylindrical sensorsOccurs at Re ~50
Select small sensor diameters/ Low pass filter the signal
(Fro
m E
ckel
man
n 1
975)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem SourcesEddy shedding II
• Vibrations from prongs and probe supports:
- Probe prongs may vibrate due to eddy shedding from them or due induced vibrations from the surroundings via the probe support.
- Prongs have natural frequencies from 8 to 20 kHz
Always use stiff and rigid probe mounts.
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem SourcesTemperature Variations I
• Fluctuating fluid temperatureHeat transfer from the probe is proportional to the temperature
difference between fluid and sensor.
E2 = (Tw-Ta)(A + B·Un)As Ta varies:- heat transfer changes- fluid properties change
Air measurements:- limited effect at high overheat ratio- changes in fluid properties are small
Liquid measurements effected more, because of:- lower overheats- stronger effects of T change on fluid properties
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem SourcesTemperature Variations II
• Anemometer output depends on both velocity and temperature
When ambient temperature increases the velocity is measured too low, if not corrected for.
Hot-wire calibrations at diff. temperatures
1,51,61,71,81,92,02,12,22,32,4
5 10 15 20 25 30 35 40
T=20
T=25
T=30
T=35
T=40
Relative velocity error for 1C temp. increase
-2,7
-2,5
-2,3
-2,1
-1,9
-1,7
-1,5
0 10 20 30 40
Tdiff=10 C
(Fro
m J
oer
gen
sen
an
d M
oro
t199
8)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem Sources Temperature Variations III
Film probe calibrated at different temperatures
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Problem Sources Temperature Variations IV
• To deal with temperature variations:
- Keep the wire temperature fixed (no overheat adjustment), measure the temperature along and correct anemometer voltage prior to conversion
- Keep the overheat constant either manually, or automatically using a second compensating sensor.
- Calibrate over the range of expected temperature and monitor simultaneously velocity and temperature fluctuations.
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Measurements in 2D Flows I
X-ARRAY PROBES (measures within ±45o with respect to probe axis):
• Velocity decomposition into the (U,V) probe coordinate system
where U1 and U2 in wire coordinate system are found by solving:
U = U1·cos1 + U2·cos
2
V = U1·sin1 - U2·sin
2
Ucal12·(1+k1
2)·(cos(90 - 1))
2 = k1
2U1
2 + U22
Ucal22·(1+k2
2)·(cos(90 - 2))
2 = U1
2 + k22U2
2
U = U1·cos1 + U2·cos
2
V = U1·sin1 - U2·sin
2
Ucal12·(1+k1
2)·(cos(90 - 1))
2 = k1
2U1
2 + U22
Ucal22·(1+k2
2)·(cos(90 - 2))
2 = U1
2 + k22U2
2
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Measurements in 2D Flows II
• Directional calibration provides yaw coefficients k1 and k2
(Obtained with Dantec 55P51 X-probe and 55H01/H02 Calibrator)
-40.00
34.68
29.14
23.59
18.04
12.49
6.945-24.00 -8.000 8.000
Angle (deg)
Uc1,Uc2 vs. Angle
Uc1,Uc2
24.00 40.00 -40.00
3.000
0.600
0.200
-0.200
-0.600
-1.000-24.00 -8.000 8.000
Angle (deg)
K1,K2 vs. Angle
K1,K2
24.00 40.00
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Measurements in 3D Flows I
TRIAXIAL PROBES (measures within 70o cone around probe axis):
P robe stem
45°
55°
35°
3
1
z
x
35°
2
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Measurements in 3D Flows II
• Velocity decomposition into the (U,V,W) probe coordinate system
where U1 , U2 and U3 in wire coordinate system are found by solving:
left hand sides are effective cooling velocities. Yaw and pitch coefficients are determined by directional calibration.
U = U1·cos54.74 + U2·cos54. 74 + U3·cos54.74
V = -U1·cos45 - U2·cos135 + U3·cos90
W = -U1·cos114.09 - U2·cos114.09 - U3·cos35.26
U1cal2·(1+k1
2+h1
2) ·cos
235.264 = k1
2·U1
2+ U2
2+ h1
2·U3
2
U2cal2·(1+k2
2+h2
2)·cos
235.264 = h2
2·U1
2+ k2
2·U2
2+ U3
2
U3cal2·(1+k3
2+h3
2)·cos
235.264 = U1
2+ h3
2·U2
2+ k3
2·U3
2
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Measurements in 3D Flows III
• U, V and W measured by Triaxial probe, when rotated around its axis. Inclination between flow and probe axis is 20o.
-2
-1
0
1
2
3
4
5
0 30 60 90 120 150 180 210 240 270 300 330 360
Roll angle.
Vel
oci
ty c
om
po
nen
t, m
/s
Umeas
Vmeas
Wmeas
Res,meas
Uact
Vact
Wact
Res,act
-0,15
-0,10
-0,05
0,00
0,05
0,10
0,15
0 60 120 180 240 300 360
Roll angleM
eas.
- A
ct. v
el.,
m/s
Up-Uact
Vp-Vact
Wp-Wact
(Obtained with Dantec Tri-axial probe 55P91 and 55H01/02 Calibrator)
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Measurement at Varying TemperatureTemperature Correction I
Ecorr = ((Tw- Tref)/(Tw- Tacq))0.5(1±m)
Eacq.
• Recommended temperature correction:
Keep sensor temperature constant, measure temperature and correct voltages or calibration constants.
I) Output Voltage is corrected before conversion into velocity
- This gives under-compensation of approx. 0.4%/C in velocity.
Improved correction:
Selecting proper m (m= 0.2 typically for wire probe at a = 0.8) improves compensation to better than ±0.05%/C.
Ecorr = ((Tw- Tref)/(Tw- Tacq))0.5
Eacq.
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Measurement at Varying Temperature Temperature Correction II
• Temperature correction in liquids may require correction of power law constants A and B:
In this case the voltage is not corrected
Acorr = (((Tw-To)/(Tw-Tacq))(1±m)
·(kf0/kf1)·(Prf0/Prf1)0.2
·A0
Bcorr = ((Tw-To)/(Tw-Tacq))(1±m)
·(kf0/kf1)·(Prf0/Prf1)
0.33·(f1/
f0)n·(f0/
f1)
n·B0
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Data acquisition I
• Data acquisition, conversion and reduction:
Requires digital processing based on
- Selection of proper A/D board
- Signal conditioning
- Proper sampling rate and number of samples
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Data acquisition II
• Resolution: - Min. 12 bit (~1-2 mV depending on range)
• Sampling rate: - Min. 100 kHz (allows 3D probes to be sampled with approx. 30 kHz per sensor)
• Simultaneous sampling:- Recommended (if not sampled simultaneously there will be phase lag between sensors of 2- and 3D probes)
• External triggering:Recommended (allows sampling to be started by external event)
A/D boards convert analogue signals into digital information (numbers)
They have following main characteristics:
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Data acquisition III
Signal Conditioning of anemometer output
• Increases the AC part of the anemometer output and improves resolution:
EG(t) = G(E(t) - Eoff )
• Allows filtering of anemometer - Low pass filtering is recommended- High pass filtering may cause phase distortion of the signal
(From Bruun 1995)
A nem om eter
E (1)E (t)-E off
G (E (t)-E off)
tt
t
E G
O ffse t A m p lifie r
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
Data acquisition IV
Sample rate and number of samples
• Time domain statistics (spectra) require sampling 2 times the highest frequency in the flow
• Amplitude domain statistics (moments) require uncorrelated samples. Sampling interval min. 2 times integral time scale.
• Number of samples shall be sufficient to provide stable statistics (often several thousand samples are required)
Proper choice requires some knowledge about the flow aforehand
It is recommended to try to make autocorrelation and power spectra at first as basis for the choice
AAE 520 Experimental Aerodynamics
Purdue University - School of Aeronautics and Astronautics
CTA AnemometrySteps needed to get good measurements:
• Get an idea of the flow (velocity range, dimensions, frequency)
• Select right probe and anemometer configuration
• Select proper A/D board
• Perform set-up (hardware set-up, velocity calibration, directional calibration)
• Make a first rough verification of the assumptions about the flow
• Define experiment (traverse, sampling frequency and number of samples)
• Perform the experiment
• Reduce the data (moments, spectra, correlations)
• Evaluate results
• Recalibrate to make sure that the anemometer/probe has not drifted