Transcript Hot-Wire Anemometry • Purpose: to measure mean and fluctuating velocities in

AAE 520 Experimental Aerodynamics
Hot-Wire Anemometry
•Purpose:
to measure mean and fluctuating velocities in
fluid flows
http://www.dantecmt.com/
www.tsi.com/
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
Principles of operation
•
•
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.
If velocity changes,
convective heat
transfer coefficient
will change, wire
temperature will
change and
eventually reach a
new equilibrium.
Current I
Sensor dimensions:
length ~1 mm
diameter ~5 micrometer
Wire supports
(St.St. needles)
Velocity U
Sensor (thin wire)
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AAE 520 Experimental Aerodynamics
Governing equation I
•
Governing Equation:
dE
W  H
dt
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
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AAE 520 Experimental Aerodynamics
Governing equation II
•
Heat transferred to surroundings
H
( convection to fluid
+ conduction to supports
+ radiation to surroundings)
Convection

Conduction

f(Tw , lw , kw, Tsupports)
Radiation

f(Tw4 - Tf4)
Qc = Nu · A · (Tw -Ta)
Nu = h ·d/kf = f (Re, Pr, M, Gr,a ),
Re = r U/m
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AAE 520 Experimental Aerodynamics
Simplified static analysis I
•
For equilibrium conditions the heat storage is zero:
dE
 O W  H
dt
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
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AAE 520 Experimental Aerodynamics
Simplified static analysis II
Static heat transfer:
W =H
h
A
d
kf
Nu
=
=
=
=
=

I2Rw = hA(Tw -Ta)

I2Rw = Nukf/dA(Tw -Ta)
film coefficient of heat transfer
heat transfer area
wire diameter
heat conductivity of fluid
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.
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AAE 520 Experimental Aerodynamics
Hot-wire static transfer function
•
Velocity sensitivity (King’s law coeff. A = 1.51, B = 0.811, n = 0.43)
2,4
dU/dE/U volts^-1
5
E volts
2,2
2
1,8
4
3
2
1,6
5
10
15
20
25
30
35
40
U m /s
Output voltage as fct. of velocity
5
10
15
20
25
30
35
40
U m /s
Voltage derivative as fct. of velocity
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AAE 520 Experimental Aerodynamics
Directional response I
Probe coordinate system
y
U
a

Uy
x
Uz
Ux
z
Velocity vector U is decomposed into normal Ux, tangential
Uy and binormal Uz components.
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AAE 520 Experimental Aerodynamics
Directional response II
•
Finite wire (l/d~200) response includes yaw and pitch sensitivity:
U2eff(a) = U2(cos2a + k2sin2a)
 =0
U2eff( ) = U2(cos2 +h2sin2 )
a =0
where:
k , h = yaw and pitch factors
a ,  = 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
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AAE 520 Experimental Aerodynamics
Directional response III
•
Typical directional response for hot-wire probe
(From DISA 1971)
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AAE 520 Experimental Aerodynamics
Directional response IV
•
Yaw and pitch factors k1 and k2 (or k and h) depend on
velocity and flow angle
(From Joergensen 1971)
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AAE 520 Experimental Aerodynamics
Probe types I
•
Miniature Wire Probes
Platinum-plated tungsten,
5 mm 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
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AAE 520 Experimental Aerodynamics
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
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AAE 520 Experimental Aerodynamics
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.”
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
Probe types IV
•
X-probes for 2D flows
2 sensors perpendicular to each other.
Measures within ±45o.
•
Split-fiber probes for 2D flows
2 film sensors opposite each other on a quartz
cylinder. Measures within ±90o.
•
Tri-axial probes for 3D flows
3 sensors in an orthogonal system. Measures
within 70o cone.
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AAE 520 Experimental Aerodynamics
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
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AAE 520 Experimental Aerodynamics
Modes of anemometer operation
Constant Current (CCA)
Constant Temperature (CTA)
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AAE 520 Experimental Aerodynamics
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
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AAE 520 Experimental Aerodynamics
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
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AAE 520 Experimental Aerodynamics
Constant temperature anemometer CTA II
• 3-channel StreamLine with
Tri-axial wire probe 55P91
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
Modes of operation, CTA I
•
Wire resistance can be
written as:
Rw = Ro(1+a o(TwTo))
Rw = wire hot resistance
Ro = wire resistance at To
a o = temp.coeff. of resistance
Tw = wire temperature
To = reference temperature
•
Define: “OVERHEAT RATIO” as:
a = (Rw-Ro)/Ro = a o(TwT0)
•
Set “DECADE” overheat resistor as: RD = (1+a)Rw
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AAE 520 Experimental Aerodynamics
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
2,4
Note following comments
to CTA and to CCA:
- Response is non-linear:
- CCA output decreases
- CTA output increases
- Sensitivity decreases
with increasing U
2,2
E volts
•
2
1,8
1,6
5
10
15
20
25
30
35
U m /s
CTA output as fct. of U
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40
AAE 520 Experimental Aerodynamics
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/a oRo(dRw/dt)
Cw = heat capacity of the wire
ao = temperature coeff. of resistance of the wire
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
Dynamic response, CCA II
Hot-wire Probes:
The first-order differential equation is characterised by a single time
constant t :
t = Cw/(aoRo(A+BU 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 = 1/2pt
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AAE 520 Experimental Aerodynamics
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:
t = (R/R0)2F2rsCsks/(A+BUn)2
rs = substrate density
Cs = substrate heat capacity
ks = substrate heat conductivity
and the normalised transfer function becomes:
Hfilm(f) = 1/(1+(jf/fcp)0.5)
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AAE 520 Experimental Aerodynamics
Dynamic response, CCA IV
Velocity
Amplitude response and phase lag
U
2
3 dB
30°
6 dB/octave
U
1
Time
Resistance
R
1
0.63 (R -R )
1
R
2
Upper frequency limit f = ½
pt
Frequency
2
Time
t
•
Dynamic characteristic may be described by the response to
- Step change in velocity
or
- Sinusoidal velocity variation
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AAE 520 Experimental Aerodynamics
Dynamic response, CCA V
•
The hot-wire response characteristic is specified by:
(From P.E. Nielsen
and C.G. Rasmussen,
1966)
For a 5 µm wire probe in CCA mode t ~ 0.005s, typically.
(Frequency response can be improved by compensation circuit)
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
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
t CTA = t CCA/(2aSRw)
where
a = overheat ratio
S = amplifier gain
Rw = wire hot resistance
•
Frequency limit:
fc defined as -3dB amplitude
damping
(From Blackwelder 1981)
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AAE 520 Experimental Aerodynamics
Dynamic response, CTA II
•
Typical frequency response of 5 mm wire probe (Amplitude
damping and Phase lag):
(From Dantec MT)
Phase lag is reduced by frequency dependent gain (-1.2 dB/octave)
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AAE 520 Experimental Aerodynamics
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.
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AAE 520 Experimental Aerodynamics
Velocity calibration (Static cal.) II
•
Calibration in gases (example low turbulent free jet):
Velocity is determined from
isentropic expansion:
Po/P = (1+(g 1)/2M 2)g
a0 = (g RT0 )0.5
a = ao/(1+(g 1)/2M 2)0.5
U = Ma
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/(g 1)
AAE 520 Experimental Aerodynamics
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
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AAE 520 Experimental Aerodynamics
Typical calibration curve
•
Wire probe calibration with curve fit errors
E1 v.U
Error (%)
2.340
0.500
2.218
0.300
2.096
0.100
E1 (v)
Error (%)
1.975
-0.100
1.853
-0.300
1.731
4.076
11.12
18.17
25.22
U velocity
32.27
39.32
-0.500
4.076
11.12
18.17
25.22
32.27
U velocity
(Obtained with Dantec 90H01/02)Calibrator)
Curve fit (velocity U as function of output voltage E):
U = C0 + C1E + C2E2 + C3E3 + C4E4
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39.32
AAE 520 Experimental Aerodynamics
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.
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AAE 520 Experimental Aerodynamics
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.
3
3
10
Amplitude (mV rms)
Amplitude (mV rms)
10
2
10
-3 dB
10
1
10
-3 dB
2
10
10
1
2
10
3
10
4
10
5
10
Frequency (Hz)
Typical Wire probe response
6
10
1
10
2
10
3
10
4
10
5
10
Frequency (Hz)
Typical Fiber probe response
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6
10
AAE 520 Experimental Aerodynamics
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
f =
c
0.97 h
h
1
1.3 t
w
t
t
0.15 h
w
(From Bruun 1995)
For a wire probe (1-order probe response):
Frequency limit (- 3dB damping):
fc = 1/1.3 t
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AAE 520 Experimental Aerodynamics
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).
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
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,a ),
•
•
•
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.)
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
Problem sources
Probe 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
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
Problem Sources
Probe contamination II
Drift due to particle
contamination in air
5 mm Wire, 70 mm Fiber and
1.2 mm SteelClad Probes
20
(Um-Uact)/Uact*100%
•
10
0
w ire
fiber
-10
steel-clad
-20
0
10
20
30
40
50
Poly. (steelclad)
Poly. (fiber)
U (m /s)
(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
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AAE 520 Experimental Aerodynamics
Problem Sources
Probe 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!
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AAE 520 Experimental Aerodynamics
Problem Sources
Probe contamination III
Drift due to particle contamination in water
Output voltage decreases with increasing dirt deposit
10
% voltage reduction
•
theory
1
fiber
w edge
0,1
0,001
0,01
0,1
1
Dirt thicknes versus sensor
diam eter, e/D
(From Morrow and Kline 1971)
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AAE 520 Experimental Aerodynamics
Problem Sources
Bubbles in Liquids I
•
Drift due to bubbles in water
(From C.G.Rasmussen 1967)
In liquids, dissolved gases form bubbles on sensor, resulting in:
- reduced heat transfer
- downward calibration drift
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AAE 520 Experimental Aerodynamics
Problem Sources
Bubbles in Liquids II
•
•
e
Effect of bubbling on
portion of typical
calibration curve
Bubble size depends on
- surface tension
- overheat ratio
- velocity
•
Precautions
-
155
Use low overheat!
Let liquid stand before use!
Don’t allow liquid to cascade in air!
Clean sensor!
175
195 cm/sec
(From C.G.Rasmussen 1967)
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AAE 520 Experimental Aerodynamics
Problem Sources (solved)
Stability in Liquid Measurements
•
Fiber probe operated stable in water
(From Bruun 1996)
- De-ionised water (reduces algae growth)
- Filtration (better than 2 mm)
- Keeping water temperature constant (within 0.1oC)
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AAE 520 Experimental Aerodynamics
Problem sources
Eddy shedding I
•
Eddy shedding from cylindrical sensors
(From Eckelmann 1975)
Occurs at Re ~50
Select small sensor diameters/ Low pass filter the signal
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AAE 520 Experimental Aerodynamics
Problem Sources
Eddy 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.
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AAE 520 Experimental Aerodynamics
Problem Sources
Temperature Variations I
•
Fluctuating fluid temperature
Heat 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
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AAE 520 Experimental Aerodynamics
Problem Sources
Temperature Variations II
• Anemometer output depends on both velocity and
temperature
Hot-wire calibrations at diff. temperatures
-1,5
T=20
-1,7
T=25
-1,9
T=30
-2,1
T=35
-2,3
T=40
-2,5
Tdiff=10 C
-2,7
5
10
15
20
25
30
35
40
0
10
20
30
40
When ambient temperature increases the velocity is measured too
low, if not corrected for.
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(From Joergensen and Morot1998)
2,4
2,3
2,2
2,1
2,0
1,9
1,8
1,7
1,6
1,5
Relative velocity error for 1C temp. increase
AAE 520 Experimental Aerodynamics
Problem Sources
Temperature Variations III
Film probe calibrated at different temperatures
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AAE 520 Experimental Aerodynamics
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.
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AAE 520 Experimental Aerodynamics
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
U = U1·cosa1 + U2·cosa2
U = U1·cosa1 + U2·cosa2
V = U1·sina1 - U2·sina2
V = U1·sina1 - U2·sina2
where U1 and2 U2 in
wire coordinate
system
are found by solving:
2
2
2
2
2
Ucal12 ·(1+k12 )·(cos(90 - a1))2 = k12 U12 + U22
Ucal1 ·(1+k1 )·(cos(90 - a1)) = k1 U1 + U2
Ucal22 ·(1+k22 )·(cos(90 - a2))2 = U12 + k22 U22
Ucal2 ·(1+k2 )·(cos(90 - a2)) = U1 + k2 U2
2
2
2
2
2
2
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AAE 520 Experimental Aerodynamics
Measurements in 2D Flows II
•
Directional calibration provides yaw coefficients k1 and k2
Uc1,Uc2 vs. Angle
K1,K2 vs. Angle
34.68
3.000
29.14
0.600
23.59
0.200
Uc1,Uc2
K1,K2
18.04
-0.200
12.49
-0.600
6.945
-40.00
-24.00
-8.000
8.000
Angle (deg)
24.00
40.00
-1.000
-40.00
-24.00
-8.000
8.000
24.00
40.00
Angle (deg)
(Obtained with Dantec 55P51 X-probe and 55H01/H02 Calibrator)
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AAE 520 Experimental Aerodynamics
Measurements in 3D Flows I
TRIAXIAL PROBES (measures within 70o cone around probe axis):
z
3
35°
x
Probe stem
55°
1
35°
45°
2
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AAE 520 Experimental Aerodynamics
Measurements in 3D Flows II
•
Velocity decomposition into the (U,V,W) probe coordinate system
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
where U1 , U2 and U3 in wire coordinate system are found by solving:
U1cal ·(1+k1 +h1 ) ·cos 35.264= k1 ·U1 + U2 + h1 ·U3
2
2
2
2
2
2
2
2
2
U2cal ·(1+k2 +h2 )·cos 35.264 = h2 ·U1 + k2 ·U2 + U3
2
2
2
2
2
2
2
2
2
U3cal ·(1+k3 +h3 )·cos 35.264 = U1 + h3 ·U2 + k3 ·U3
2
2
2
2
2
2
2
2
2
left hand sides are effective cooling velocities. Yaw and pitch
coefficients are determined by directional calibration.
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
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.
5
Umeas
4
Vmeas
3
Wmeas
2
Res,meas
1
Uact
0
Vact
Meas. - Act. vel., m/s
Velocity component, m/s
•
Wact
-1
0,15
0,10
0,05
Up-Uact
Res,act
-2
0
30 60 90 120 150 180 210 240 270 300 330 360
Roll angle.
0,00
Vp-Vact
-0,05
Wp-Wact
-0,10
-0,15
0
60
120
180
240
300
360
Roll angle
(Obtained with Dantec Tri-axial probe 55P91 and 55H01/02 Calibrator)
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
Measurement at Varying Temperature
Temperature Correction I
•
Recommended temperature correction:
Keep sensor temperature constant, measure temperature and
correct voltages or calibration constants.
I) Output Voltage is corrected before conversion into velocity
Ecorr = ((Tw- Tref )/(Tw- Tacq))
0.5
Eacq.
- This gives under-compensation of approx. 0.4%/C in velocity.
Improved correction:
0.5(1±m)
Ecorr = ((Tw- Tref)/(Tw- Tacq))
Eacq.
Selecting proper m (m= 0.2 typically for wire probe at a = 0.8) improves
compensation to better than ±0.05%/C.
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
Measurement at Varying Temperature
Temperature Correction II
•
Temperature correction in liquids may require correction
of power law constants A and B:
(1±m)
Acorr = (((Tw-To)/(Tw-Tacq))
0.2
·(kf0/kf1)·(Prf0/Prf1) ·A0
(1±m)
Bcorr = ((Tw-To)/(Tw-Tacq))
·
0.33 m m
n
(kf0/kf1)·(Prf0/Prf1) ·( f1/ f0)n·(rf0/rf1) ·B0
In this case the voltage is not corrected
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
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
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
Data acquisition II
A/D boards convert analogue signals into digital information (numbers)
They have following main characteristics:
•
•
•
•
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)
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
Data acquisition III
Signal Conditioning of anemometer output
EG
Anemometer
Offset
Amplifier
G(E(t)-E off)
E(t)-E off
E(1)
t
t
t
(From Bruun 1995)
•
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
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
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
Purdue University - School of Aeronautics and Astronautics
AAE 520 Experimental Aerodynamics
CTA Anemometry
Steps 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
Purdue University - School of Aeronautics and Astronautics