Lecture #06 Hotwire anemometry: Fundamentals and ...huhui/teaching/2014Fx/class...Technical...
Transcript of Lecture #06 Hotwire anemometry: Fundamentals and ...huhui/teaching/2014Fx/class...Technical...
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Dr. Hui Hu
Department of Aerospace EngineeringIowa State University
Ames, Iowa 50011, U.S.A
Lecture #06 Hotwire anemometry: Fundamentals and instrumentation
AerE 344 Lecture Notes
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Technical Fundamentals -1
• Thermal anemometers:• Measure the local flow velocity through its relationship to the convective cooling of electrically
heated metallic sensors.
• Hot wire anemometers: • for clean air or other gas flows
• Hot film anemometers:• for liquid or some gas flows
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How a Hot wire Sensor Works
Electric current, i, through wire
The electric current (i) flowing through the wire generates heat (i2Rw)
In equilibrium, this must be balanced by heat lost (primarily convective) to the surroundings.
Flow FieldV
![Page 4: Lecture #06 Hotwire anemometry: Fundamentals and ...huhui/teaching/2014Fx/class...Technical Fundamentals) , 0.02 Re 44 2 1 0.48Re )(1) , 44 Re 140 2 1 (0.24 0.56Re )(1 510. 17 450.](https://reader030.fdocuments.in/reader030/viewer/2022041014/5ec51e8c848dae130f3872a2/html5/thumbnails/4.jpg)
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Technical Fundamentals
• Heat transfer characteristics:• Convection (nature convection, forced convection
or mixed convection depending on Richardson numbers)
• Conduction to the supporting prong• Radiation: <0.1%, is negligible.
TTw
TV ,
wT
prongs
Hot wire
Fluid flow
),/,,,,Pr,(Re,)(
dlaKnMGrNuTTlk
qNu
T
w
TTTa
Mccd
Kn
cVMdTTgGr
Ud
wT
vp
w
Re/
21
;)(
Pr;Re
2
3
![Page 5: Lecture #06 Hotwire anemometry: Fundamentals and ...huhui/teaching/2014Fx/class...Technical Fundamentals) , 0.02 Re 44 2 1 0.48Re )(1) , 44 Re 140 2 1 (0.24 0.56Re )(1 510. 17 450.](https://reader030.fdocuments.in/reader030/viewer/2022041014/5ec51e8c848dae130f3872a2/html5/thumbnails/5.jpg)
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Technical Fundamentals
44Re02.0,)211)(Re48.0
140Re44,)211)(Re56.024.0(
17.051.0
17.045.0
foraNu
foraNu
T
T
n
w
BVATT
E
)](1[ TTaRR wrrw
According to Collis and Willams (1959):
For a given sensor and fixed overheat ratio, The above equation can transfer as the relationship between the voltage output, E, of the hot-wire operation circuit and the flow velocity
Following King’s Law (1915),m
Tn aBANu )
211)(Re(
Wire temperature cannot be measured directly, but can be estimated from its relationship to the wire resistance, Rw, directly measured by the operating bridge.For metallic wires:
temepaturereferenceTtcoefficienyresistivitthermala
r
r
::
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Technical Fundamentals
Flow Field
Current flow through wire
The rate of which heat is removed from the sensor is directly related to the velocity of the fluid flowing over the sensor
The hot wire is electrically heated.
If velocity changes for a unsteady flow, convective heat transfer changes, wire temperature will change and eventually reach a new equilibrium.V
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Technical Fundamentals
• For a sensor placed in a unsteady flow, the unsteady energy equation will become:
),(2ww
w TVqRidt
dTmc
),(:::
wTVqqfluxheatconvectiveqsensortheofheatspecifichc
sensortheofmassthem
The above equation has three unknowns: i, Tw (or Rw) and V
To render this equation solvable, one must keep with the electric current, i, or the sensor temperature (Tw) constant, which can be achieved with the use of suitable electric circuits.
The corresponding methods are known as: (1). Constant-current anemometry(2). Constant-temperature anemometry
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The unsteady energy equation is highly-nonlinear. When linearized in the vicinity of an operation point, namely at a particular flow speed, Vop, and sensor temperature, Twop , it leads to the following first-order differential equation:
Constant-current anemometry
sR
)()( opopw VVKEEdtdE
:w TKa time constant, which is proportional to the overheat ratio, and a static sensitivity,
.)()( opTwopw
ww VVKTT
dtdT
ws RR
constRERREi
so
wso
/)/(
wRiE The voltage output will be
Since voltage, E, is proportional to, Rw , which, in turn, is linearly related to Tw, the linearized E-V relationship will be:
:w is usually ~ 1ms for thin hot-wire and ~ 10 ms for slim cylindrical hot-film.
For flow with variable velocity or temperature, overheat ratio will vary as well.Flow low speed flow, it may result in “burnout”, for high-speed flow, sensitivity is low
wREo
E Ec
R’c
Rc
C
Compensation circuit
Voltage follower
sensor
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The unsteady energy equation is highly-nonlinear. When linearized in the vicinity of an operation point, namely at a particular flow speed, Vop, and sensor temperature, Twop , it leads to the following first-order differential equation:
Constant-current anemometry
sR
)()( opopw VVKEEdtdE
:w TKa time constant, which is proportional to the overheat ratio, and a static sensitivity,
.)()( opTwopw
ww VVKTT
dtdT
ws RR
constRERREi
so
wso
/)/(
wRiE The voltage output will be
Since voltage, E, is proportional to, Rw , which, in turn, is linearly related to Tw, the linearized E-V relationship will be:
:w is usually ~ 1ms for thin hot-wire and ~ 10 ms for slim cylindrical hot-film.
For flow with variable velocity or temperature, overheat ratio will vary as well.Flow low speed flow, it may result in “burnout”, for high-speed flow, sensitivity is low
wREo
E Ec
R’c
Rc
C
Compensation circuit
Voltage follower
sensor
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• Electric current through the sensor is adjustable continuously through an electric feedback system, and in response to the changes in convective cooling, to make the temperature of the hot wire keep in constant.
• The unsteady energy equation becomes steady equation
• Dynamic response of the anemometer is the same as its static response with a wide frequency range.
Constant-temperature anemometry (CTA) - 1
.
0)(),( 22 VqRiTVqRidt
dTmc wwww
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Constant-temperature anemometry (CTA)-2
2R
dR wR
EB
R2
ERsw
sensor
Ew
EoffsetEsw
-
+Differential amplifier
R1
Constant temperature circuit
• Sensor, Rw, comprises one leg of the Wheatstone bridge. • An adjustable decade resistor array, Rd, compress opposite leg of the bridge.• The bridge ratio R2/R1 is fixed, and R2/R110~20 to make sure to supply most of the available power
to the sensor.• The two midpoints of the bridge are connected the input of a high-gain, low noise differential
amplifier, whose out put is fed back to the top of the bridge.• If R2/Rd= R1/Rw, then EB-Ew=0, the amplifier output will be zero.• If Rd is increased to a value R’d, the resulting bridge imbalance will generate an input imbalance to
the amplifier. • The amplifier will create some current through both legs of the bridge. The additional current
through the hot wire will create additional joule heating, which tend to increase its temperature and thus its resistance, until the resistance increasing sufficiently to balance the bridge once more.
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Various effects and error source
• Velocity orientation effects:– Effective cooling velocity
Veff = V cos .– In reality, flow velocity
tangential to the sensor would result in cooling.
– Veff = V (cos2 + k2 sin2 )1/2
– Typical values of K2 are 0.05 and 0.20.
TTw
TV ,
wT
prongs
Hot wire
Fluid flow
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Various effects and error source
• Prong interference effects:– Interference of the prongs and the probe
body may produce additional complications of the heat transfer characteristics.
– For example a stream in binormal direction will produce higher cooling than a stream with the same velocity magnitude but in the normal direction.
– In reality,Veff = (VN2+ K2 VT
2 + h2 VB2 )1/2
– VN , VT and VB are the normal tangitail and binormal velocity components.
– Typically, h2=1.1~1.2– To minimize the effect, it usually use
long and thin prongs. Tapered prongs are also recommended.
TTw
TV ,
wT
prongs
Hot wire
Fluid flow
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Various effects and error source
• Heat conduction effects:– Previous analysis is based on 2-D
assumption with l/d = . – In reality, the effect of end conduct may
effect the accuracy of the measurement results
– Cold length, lc = 0.5*d ((Kw2/K)(1+aR)/Nu) 1/2
– Kw is thermal conductivity of the sensor– K is thermal conductivity of the fluid– aR is overheat ratio– Effect of the sensor length l/lc– A recent study has demonstrate that end
conduction effects are expected to decrease significantly as the Reynolds number increasing
TTw
TV ,
wT
prongs
Hot wire
Fluid flow
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Various effects and error source
• Compressibility effects:– The velocity and temperature fields around
the sensor become quite complicated when M>0.6.
TTw
TV ,
wT
prongs
Hot wire
Fluid flow
SSMForSTSSV
V
T
V
2.100
55.0)(2
nVBAE n
Modified King’s law for compressible flow:
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Various effects and error source
• Temperature variation effects:– Calibration at Temperature T1.– Correlation is needed if real measurements
will be conducted at Temperature T2.– When the flow temperature varies from
position to position or contain turbulent fluctuations, corrections is much more complicated.
– It requires simultaneous flow temperature measurements.
– Sv is increasing with overheat ratio aT. – At extremely low aT, a thermal anemometer
is totally insensitive to velocity variations, and becomes a resistance thermometer. The sensor is called cold wire.
TTw
TV ,
wT
prongs
Hot wire
Fluid flow
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Various effects and error source
• Composition effects:– Composition of flow may affect the
convective heat transfer from a thermal anemometer in as much as it affect the heat conductivity of surrounding fluid.
– It requires simultaneous measurements of fluid species concentration.
TTw
TV ,
wT
prongs
Hot wire
Fluid flow
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Various effects and error source
• Reverse flow and high-turbulence effects:
– thermal anemometer could not resolve velocity orientation.
– Forward flow can not be identified from reversing flow
– In highly turbulent flow (turbulent intensity >25%), reverse flow will occurr statistically some time, therefore, using thermal anemometer for the flow velocity measurement may result quite large measurement uncertainty.
– Pulsed Hot –wire concept
TTw
TV ,
wT
prongs
Hot wire
Fluid flow
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Multi-sensor probes
• Cross-wire (X-wire) design:
V2
V1
V2
V1
V2
V1
V
Veff-A
Veff-B
)(22
)(22
21
21
VVV
VVV
Beff
Aeff
)(22
)(22
2
1
BeffAeff
BeffAeff
VVV
VVV
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Multi-sensor probes
• Three sensor design• Four sensor design:
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Diameter of hot wires
• L = 0.8 ~ 1.5 mm• D = ~ 5 m for conventional applications• D = ~ 10 m for high-speed applications• D = ~ 2 m for low speed applications• Prongs: usually tapered to be d 1mm
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Dr. Hui Hu
Department of Aerospace EngineeringIowa State University
Ames, Iowa 50011, U.S.A
Lecture #05 Determination of the Aerodynamic Performance of a Low Speed Airfoil based on Pressure Distribution Measurements
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Aerodynamic Performance of An Airfoil
X/C *100
Y/C
*100
-20 0 20 40 60 80 100 120
-40
-20
0
20
40
60
vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5
shadow region
GA(W)-1 airfoil
25 m/s
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 2 4 6 8 10 12 14 16 18 20
CL=2Experimental data
Angle of Attack (degrees)
Lift
Coe
ffici
ent,
Cl
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0 2 4 6 8 10 12 14 16 18 20
Experimental data
Angle of Attack (degrees)
Dra
g C
oeffi
cien
t, C
d
X/C *100
Y/C
*100
-40 -20 0 20 40 60 80 100 120 140
-60
-40
-20
0
20
40
60
vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5
shadow region
GA(W)-1 airfoil
25 m/s
Airfoil stall
Airfoil stall
Before stall
After stallcV
DCd2
21
cV
LCl2
21
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Determination of the Aerodynamic Performance of a Low Speed Airfoil based on Pressure Distribution Measurements
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Determination of the Aerodynamic Performance of a Low Speed Airfoil based on Pressure Distribution Measurements
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Determination of the Aerodynamic Performance of a Low Speed Airfoil based on Pressure Distribution Measurements
NACA0012 airfoil with 49 pressure tabs
-3.0-2.5-2.0-1.5-1.0-0.5
00.51.01.52.02.53.0
0 1 2 3 4 5 6 7 8 9 10 11 12
X (inches)
Y (i
nche
s)
1
5 1021
253040
47
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
1.0
1.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
upper surfacelower surface
x / c
Cp
-1.5
-1.0
-0.5
0
0.5
1.0
1.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
upper surfacelower surface
x / c
Cp
Before stall
After stall
2
21
V
PPC p
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Determination of the Aerodynamic Performance of a Low Speed Airfoil based on Pressure Distribution Measurements
What you will have available to you for this portion of the lab:• A Pitot probe already mounted to the floor of the wind tunnel for acquiring dynamic
pressure throughout your tests.• A Setra manometer to be used with the Pitot tube to measure the incoming flow velocity.• A thermometer and barometer for observing ambient lab conditions (for calculating
atmospheric density).• A computer with a data acquisition system capable of measuring the voltage from your
manometer.• The pressure sensor you calibrated last week• A NACA 0012 airfoil that can be mounted at any angle of attack up to 15.0 degrees.• Two 16-channel Scanivalve DSA electronic pressure scanners.
-3 .0-2 .5-2 .0-1 .5-1 .0-0 .5
00.51.01.52.02.53.0
0 1 2 3 4 5 6 7 8 9 10 11 12
X (inches)
Y (in
ches
)
1
5 1222
253040
47
![Page 28: Lecture #06 Hotwire anemometry: Fundamentals and ...huhui/teaching/2014Fx/class...Technical Fundamentals) , 0.02 Re 44 2 1 0.48Re )(1) , 44 Re 140 2 1 (0.24 0.56Re )(1 510. 17 450.](https://reader030.fdocuments.in/reader030/viewer/2022041014/5ec51e8c848dae130f3872a2/html5/thumbnails/28.jpg)
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
• Calculating airfoil lift coefficient and drag coefficient by numerically integrating the surface pressure distribution around the airfoil:
Determination of the Aerodynamic Performance of a Low Speed Airfoil based on Pressure Distribution Measurements
21
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12/1
12/1
ppp
ppp
NN
iii
y ,y ,
1N1
1i1
NNN
iiiii
yyxxxyyxxx
iii xpN 2/1'iii ypA 2/1'
(7) ''
(6) ''
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iii
N
ii
N
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ypAA
xpNN
cos'sin''sin'cos''
ANDANL
![Page 29: Lecture #06 Hotwire anemometry: Fundamentals and ...huhui/teaching/2014Fx/class...Technical Fundamentals) , 0.02 Re 44 2 1 0.48Re )(1) , 44 Re 140 2 1 (0.24 0.56Re )(1 510. 17 450.](https://reader030.fdocuments.in/reader030/viewer/2022041014/5ec51e8c848dae130f3872a2/html5/thumbnails/29.jpg)
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Required Plots for the Lab Report
• You must generate plots of CP for the upper and lower surfaces of the airfoil for the angles of attack that you tested.
• Make comments on the characteristics of the CP distributions.
• Calculate CL and CD by numerical integration CP for the angles of attack assigned to your group.
• You must report the velocity of the test section and the Reynolds number (based on airfoil chord length) for your tests.
• You must provide sample calculations for all the steps leading up to your final answer.
• You should include the first page of the spreadsheet used to make your calculations