Development of an automated calibration system for hotwire anemometers
©2009
Masterarbeit
105 Seiten
Zusammenfassung
Inhaltsangabe:Introduction:
In experimental fluid dynamic measurements hot-wire anemometry is used to record information about flow fields. Furthermore one can obtain the magnitude, the direction and even the time dependant behaviour of the fluid flow, if multiple-wire probes are in operation. The hot-wire measurement technique is based on the convective heat transfer from a heated element to the fluid flow, which is actually proportional to the velocity of the flow. So HWA is an indirect measurement technique. There are miscellaneous sensors which work properly in water or other liquids, air or in gas flows. As an example, Fig. 1.1 shows a cross-wire probe in a fluid flow, which can detect the velocity and its direction in two components, if the main flow direction is in one plane (2D flow).
Predominantly HWA is a research tool for turbulent flow studies, especially transient procedures. Turbulence models have to be built to represent the characteristics of the flow in numerical simulations (CFD). Therefore only detailed experimental measurements lead to reliable information about the local velocity of a turbulent flow. This can be provided by HWA on the basis of its very high spatial and temporal resolution. Although the development of HWA started at the beginning of the 19th century and new techniques like PIV or LDA (direct methods) have been established, it is still a common device in all wind tunnel labs. The analogue output signal can be optimized by filters before signal processing. It can also be deployed to arrange a spectrum analysis, due to the high temporal resolution. Moreover, unlike the digital devices the analogue signal is densely packed. The range of application is large and leads from sub- and supersonic flows, the independency of the medium to high-temperature measurements. HWA is also affordable in contrast to LDA and PIV systems. In spite of these advantages the natural contamination of the hot-wire probe increases by and by, since the particles in the fluid flow mature themselves to the probe and finally isolate it. As this effect of disturbance causes measuring errors, the hot-wire probes have to be calibrated at frequent intervals - best before and after every data acquisition series. However, HWA is an intrusive measurement technique, thus disturbing the flow. Another disadvantage is that it is not applicable in separation and backward flow regions.
The aim of this thesis is to develop an automated calibration system to […]
In experimental fluid dynamic measurements hot-wire anemometry is used to record information about flow fields. Furthermore one can obtain the magnitude, the direction and even the time dependant behaviour of the fluid flow, if multiple-wire probes are in operation. The hot-wire measurement technique is based on the convective heat transfer from a heated element to the fluid flow, which is actually proportional to the velocity of the flow. So HWA is an indirect measurement technique. There are miscellaneous sensors which work properly in water or other liquids, air or in gas flows. As an example, Fig. 1.1 shows a cross-wire probe in a fluid flow, which can detect the velocity and its direction in two components, if the main flow direction is in one plane (2D flow).
Predominantly HWA is a research tool for turbulent flow studies, especially transient procedures. Turbulence models have to be built to represent the characteristics of the flow in numerical simulations (CFD). Therefore only detailed experimental measurements lead to reliable information about the local velocity of a turbulent flow. This can be provided by HWA on the basis of its very high spatial and temporal resolution. Although the development of HWA started at the beginning of the 19th century and new techniques like PIV or LDA (direct methods) have been established, it is still a common device in all wind tunnel labs. The analogue output signal can be optimized by filters before signal processing. It can also be deployed to arrange a spectrum analysis, due to the high temporal resolution. Moreover, unlike the digital devices the analogue signal is densely packed. The range of application is large and leads from sub- and supersonic flows, the independency of the medium to high-temperature measurements. HWA is also affordable in contrast to LDA and PIV systems. In spite of these advantages the natural contamination of the hot-wire probe increases by and by, since the particles in the fluid flow mature themselves to the probe and finally isolate it. As this effect of disturbance causes measuring errors, the hot-wire probes have to be calibrated at frequent intervals - best before and after every data acquisition series. However, HWA is an intrusive measurement technique, thus disturbing the flow. Another disadvantage is that it is not applicable in separation and backward flow regions.
The aim of this thesis is to develop an automated calibration system to […]
Leseprobe
Inhaltsverzeichnis
Constantin Schosser
Development of an automated calibration system for hotwire anemometers
ISBN: 978-3-8366-3960-6
Herstellung: Diplomica® Verlag GmbH, Hamburg, 2010
Zugl. Fachhochschule Regensburg, Regensburg, Deutschland, MA-Thesis / Master, 2009
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Abstract
The main objective of this master's thesis is the development of an automated calibration
system for hot-wire measurements. The earlier generation DANTEC calibration system
was substantially extended, a new calibration unit was designed. A LabVIEW-based con-
trol and measurement program was written, allowing manual and automatic calibration
of one- and two-wire probes. With this newly developed system it is possible to calibrate
up to two component hot-wire probes. Single-wire probes can be calibrated against flow
velocity. Cross-wire probes offer the possibility to accomplish velocity and directional
measurements in 2D flows. Before running the experiment the user can choose steady
state as well as transient flow. The main aim was to implement a new directional cal-
ibration and measurement method - the so called Look-up matrix method. The new
calibration device in combination with the new method improve the accuracy of the ex-
isting hot-wire system. Prior to applying the Look-up matrix method, a simpler method
for DANTEC calibrators was used. These two methods are compared here. The differ-
ent calibration methods have been validated and successfully been used for completing
measurements. The Look-up matrix method provides significantly better results in test
calibrations. In the future this system will be integrated into the new traverse system
in the wind tunnel of the Department of Fluid Mechanics at the Budapest University of
Technology and Economics (BME). The design of the calibration device as well as the
LabVIEW program is kept flexible in order to expand the setup for prospective multi-wire
probe measurements.
Keywords: CTA, hot-wire, Look-up matrix, DANTEC, flow measurement techniques,
aerodynamics, LabVIEW
3
Acknowledgement
My stay in Budapest between November 2008 and April 2009, was enabled by the ad-
visor of my master's thesis. Therefore my ultimate gratitude goes to Dipl.-Ing. M´
arton
Balcz´
o. He offered me the possibility to join the Department of Fluid Mechanics at the
Budapest University of Technology & Economics (BME). Even more I have to thank him
for attending to find an accommodation for me. During the whole period of six month
he offered me an outstanding support to close my project with success.
My thanks and appreciation go to my advisor from the University of Applied Sciences
Regensburg Prof. Dr.-Ing. Stephan L¨
ammlein for his expertise and experience in fluid
mechanics and measurement technologies. His advice and suggestions helped me during
the whole project.
Tam´
as R´
egert, Ph.D. has to be mentioned particularly for his introduction to hot-wire
anemometry and his offer to write a scientific paper with him. I would not have per-
formed this work without Istv´
an Jezs´
o and G´
abor Kalm´
ar, who were constantly helping
me to finish the mechanical part of the project. In addition to that I want to thank
my colleagues and Ph.D. students Mikl´
os Balogh, P´
eter T´
oth, Csaba Horv´
ath, Eszter
Luk´
acs and P´
eter Norbert for a working atmosphere of great significance, I never saw
before. Besides they always had time for answering all of my questions.
Furthermore I want to thank the institution ERASMUS for financial support during
the studies in Budapest.
4
Contents
Declaration
2
Abstract
3
Acknowledgement
4
Abbreviations
8
1
Introduction
9
2
Theory of hot-wire-anemometry
11
2.1
Hot-wire probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1
Measuring chain . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2
Probe selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.3
Coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2
Heat transfer of HWA . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1
Ohmic resistance of a hot-wire
. . . . . . . . . . . . . . . . . . 15
2.2.2
Thermal balance . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3
Influences on the sensor signal . . . . . . . . . . . . . . . . . . . 18
2.3
Electrical circuit of HWA
. . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1
CCA mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.2
CTA mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.3
Ohmic and complex resistance of a hot-wire
. . . . . . . . . . . 20
2.4
Anemometer setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.1
Overheat adjustment . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.2
Square wave test . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.3
Low-pass filtering
. . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5
Reference velocity for hot-wire calibrations . . . . . . . . . . . . . . . . 22
2.5.1
Calculation of the fluid velocity . . . . . . . . . . . . . . . . . . 23
2.5.2
Adjusting a defined mass flow in the calibrator . . . . . . . . . . 24
2.6
Calibration methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6.1
Velocity calibration . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6.2
Calibration of cross-wire sensors according to the DANTEC method 27
5
Contents
6
2.6.3
Look-up matrix method . . . . . . . . . . . . . . . . . . . . . . 30
2.6.4
Temperature correction . . . . . . . . . . . . . . . . . . . . . . 32
2.7
Spatial resolution errors . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3
Design of the automated calibration facility
34
3.1
Initial requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2
Dimensioning of the mechanical components . . . . . . . . . . . . . . . 34
3.3
Design of the calibration device . . . . . . . . . . . . . . . . . . . . . . 37
3.4
Important components of the measuring system
. . . . . . . . . . . . . 40
3.5
Positioning accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4
Experimental approach during calibration and measurement
42
4.1
Measurement devices
. . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.1
Measuring chain . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.2
Arrangement of the measuring system . . . . . . . . . . . . . . . 44
4.1.3
Controller card ISEL IT 116 . . . . . . . . . . . . . . . . . . . . 45
4.1.4
Pressure transducer SETRA 239 . . . . . . . . . . . . . . . . . . 45
4.1.5
Hot-wire sensors . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.1.6
CTA unit DISA Type 55M01/55M10 . . . . . . . . . . . . . . . 47
4.1.7
Analogue-to-digital converter . . . . . . . . . . . . . . . . . . . 48
4.2
Calibration equipment DISA Type 55D90 . . . . . . . . . . . . . . . . . 50
4.3
Description of the settings . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.1
Overheat setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.2
Dynamic bridge balancing . . . . . . . . . . . . . . . . . . . . . 53
4.3.3
Precise positioning of the hot-wire probe . . . . . . . . . . . . . 54
4.3.4
Calibration of the pressure transducer . . . . . . . . . . . . . . . 54
4.4
LabView programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4.1
Calibration program . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4.2
Measurement program . . . . . . . . . . . . . . . . . . . . . . . 64
4.4.3
step motor control . . . . . . . . . . . . . . . . . . . . . . . . . 66
5
Measurement results
67
5.1
Hot-wire calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.1.1
Single-wire probe (steady flow) . . . . . . . . . . . . . . . . . . 67
5.1.2
Single-wire probe (transient flow) . . . . . . . . . . . . . . . . . 68
5.1.3
Cross-wire probe (steady flow) . . . . . . . . . . . . . . . . . . . 69
5.1.4
Cross-wire probe (transient flow) . . . . . . . . . . . . . . . . . 71
5.2
Hot-wire validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2.1
Single-wire probe (steady state flow) . . . . . . . . . . . . . . . 73
5.2.2
Single-wire probe (transient flow) . . . . . . . . . . . . . . . . . 74
Contents
7
5.2.3
Cross-wire probe (steady state and transient flow) . . . . . . . . 75
5.3
Summary of validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.4
Discussion and limitations . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.4.1
Single-wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.4.2
Cross-wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6
Perspective
82
Bibliography
85
List of symbols
86
Figures and Pictures
93
A Appendix: About hot-wire measurements
94
A.1 Spatial resolution error - turbulent velocity distribution . . . . . . . . . . 94
A.2 Table for quick selection of HW probes . . . . . . . . . . . . . . . . . . 96
B Appendix: Datasheets
98
B.1 Hot-wire probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
B.1.1
Single-wire probe DISA type 55P11 . . . . . . . . . . . . . . . . 98
B.1.2
Cross-wire probe DANTEC type 9055P0511
. . . . . . . . . . . 98
B.1.3
Specifications
. . . . . . . . . . . . . . . . . . . . . . . . . . . 99
B.1.4
ISEL IT 116 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
B.2 NI 6036E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
B.3 SETRA 239
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Abbreviations
Abbreviation
Description
1D
One-dimensional
2D
Two-dimensional
ADC
Analogue digital converter
BNC
Bayonet nut connector
CAD
Computer aided design
CCA
Constant current anemometry
CFD
Computational fluid dynamics
CSV
Comma separated value
CTA
Constant temperature anemometry
DAQ
Data acquisition
GPIB
General purpose instrumentation bus
HWA
Hot-wire anemometry
HW
Hot-wire
LDA
Laser doppler anemometry
NI
National Instruments
PIV
Particle image velocimetry
PT
Pressure transducer
RAM
Random access memory (of a computer)
RMS
Root mean square
RS232
Serial port
subVI
Subroutine of a Virtual Instrument
VI
Virtual Instrument
X
Cross
8
1 Introduction
In experimental fluid dynamic measurements hot-wire anemometry is used to record
information about flow fields. Furthermore one can obtain the magnitude, the direction
and even the time dependant behaviour of the fluid flow, if multiple-wire probes are in
operation. The hot-wire measurement technique is based on the convective heat transfer
from a heated element to the fluid flow, which is actually proportional to the velocity
of the flow. So HWA is an indirect measurement technique. There are miscellaneous
sensors which work properly in water or other liquids, air or in gas flows. As an example,
Fig. 1.1 shows a cross-wire probe in a fluid flow, which can detect the velocity and its
direction in two components, if the main flow direction is in one plane (2D flow).
Figure 1.1: Cross-wire probe in a two-dimensional fluid flow [FJ]
Predominantly HWA is a research tool for turbulent flow studies, especially transient
procedures. Turbulence models have to be built to represent the characteristics of the
flow in numerical simulations (CFD). Therefore only detailed experimental measurements
lead to reliable information about the local velocity of a turbulent flow. This can be
provided by HWA on the basis of its very high spatial and temporal resolution. Although
the development of HWA started at the beginning of the 19th century and new techniques
like PIV or LDA (direct methods) have been established, it is still a common device in
all wind tunnel labs. The analogue output signal can be optimized by filters before
signal processing. It can also be deployed to arrange a spectrum analysis, due to the
high temporal resolution. Moreover, unlike the digital devices the analogue signal is
densely packed. The range of application is large and leads from sub- and supersonic
flows, the independency of the medium to high-temperature measurements. HWA is also
affordable in contrast to LDA and PIV systems. In spite of these advantages the natural
contamination of the hot-wire probe increases by and by, since the particles in the fluid
9
Chapter 1. Introduction
10
flow mature themselves to the probe and finally isolate it. As this effect of disturbance
causes measuring errors, the hot-wire probes have to be calibrated at frequent intervals
- best before and after every data acquisition series. However, HWA is an intrusive
measurement technique, thus disturbing the flow. Another disadvantage is that it is not
applicable in separation and backward flow regions.
The aim of this thesis is to develop an automated calibration system to implement an
in situ calibration. A traverse system will move the hot-wire probe to the calibrator.
Immediately after accomplishing the calibration, the traverse will adjust the probes po-
sition directly in the wind tunnel to fulfil the measuring task. Reasons for applying the
in situ calibration are to minimize mistakes and to accelerate this time-consuming pro-
cedure. The disturbance of the flow, caused by the probe and its fixation is the same
during calibration and experiment. Disconnecting cables between calibration and mea-
surement, which avoids additional errors, is not necessary anymore. Furthermore it is
not needed to move the computer system and the pressure supply. This thesis consists
of the mechanical design of the calibration facility, of the composition of the computer
programs needed and of an experimental validation. All parts of the calibration and of
the measurement program are generated in LabVIEW 8.5 - a development environment
for a visual programming language by National Instruments [FD], [HD].
2 Theory of hot-wire-anemometry
The following paragraph is meant to give the reader a detailed description about the
theory and operation of hot-wire anemometry. The calibrator's flow behaviour, the probe
selection, the electrical part and the critical points of the technique and the calibration
procedure are also discussed.
2.1 Hot-wire probes
2.1.1 Measuring chain
The hot-wire sensor with its probe support is connected to the hot-wire unit with
a screened cable using a BNC connector.
The hot-wire box applies the constant-
temperature operation mode, thus also called CTA anemometer. It includes the electrical
circuit and the amplifier (section 2.3). The analogue output signal is proportional to the
fluid velocity and provides continuous velocity time series. It is digitised in the ADC.
Then the signal is in the RAM of the computer and can be linearised and processed.
Output quantities can be the amplitude, the mean velocity, the RMS velocity, turbulence
intensity, moments, power spectra, etc [DA]. Fig. 2.1 illustrates the CTA measuring
chain.
Figure 2.1: Measuring chain of CTA HWA [DA]
11
Chapter 2. Theory of hot-wire-anemometry
12
2.1.2 Probe selection
Basically one can distinguish between hot-wire and hot-film probes. The sensor consists
of a wire or a film and two pins for support. Hot-film sensors (Fig. 2.2) consist of a
thin metal film on a quartz substrate. Nickel is often used for this purpose. To prevent
the film from corrosion another isolating coat can be applied. Generally the hot-film's
electrical inertia is higher and its frequency response is inferior in comparison to a hot-
wire. It is more robust and can chemically be protected. If it is broken, it cannot be
repaired [CT].
Figure 2.2: One-dimensional hot-film probe [DA]
Hot-wire sensors (Fig. 2.3) are affordable, they have a very low thermal capacity and
a good frequency response. They can be repaired, if damaged. The most often used
materials are nickel, platinum or tungsten [CT]. For measuring the velocity in one-
dimensional flows, only one wire is needed (1D probe). DANTEC applies wire coatings
at the two sides of the wire to improve the spatial resolution of the probe.
Figure 2.3: Variety of one-dimensional sensors [DA]
The developed calibration system is able to calibrate probes with two wires (Fig. 2.4).
With these, one can obtain both velocity components in a 2D flow. All directional
dependent sensors have a certain angular limit of application. E.g. a (two-dimensional)
cross-wire is defined between = ±45
.
Chapter 2. Theory of hot-wire-anemometry
13
Figure 2.4: Variety of two-dimensional sensors [DA]
In general it is also possible to attach up to three wires in one sensor (see Fig. 2.5).
In this case the fluctuations in three dimensions can be recorded. Spatial oscillations of
the velocity, e.g. in a boundary layer, can be recorded using arrays of probes.
Figure 2.5: Three-dimensional sensor [DA]
Choosing a certain probe depends on several considerations. The probe's electrical inertia
shall be minimal. In order to allocate a good spatial resolution, the length of the wire
should be as short as possible (length - vortex size). The ratio wire length to diameter
should be as high as practicable, so as not to disturb the behaviour of the flow. A high
sensitivity and a good signal-noise ratio can be obtained, if the temperature of the wire
is high. Thus the oxidation temperature shall be high [CT]. In appendix A.2 a short
guide for a quick selection of probes can be found.
2.1.3 Coordinate system
The direction of the recorded velocity vectors have to be transformed from the probe
fixed coordinate system to the wind tunnel system, which is dependent on the measuring
task. Fig. 2.6 to 2.8 show the coordinate systems which are used.
Chapter 2. Theory of hot-wire-anemometry
14
Figure 2.6: 1D probe in a 1D flow u >> v, w
Figure 2.7: Wire fixed coordinate system of the x-probe
Figure 2.8: X-probe in a 2D flow u, w >> v
Chapter 2. Theory of hot-wire-anemometry
15
2.2 Heat transfer of HWA
2.2.1 Ohmic resistance of a hot-wire
As considered in section 1, the heat transfer from the heated wire to the moving fluid
is mainly induced by the relative velocity of the flow. A measurement of the relative
velocity is possible, if all other influence values are minimized. The amount of heat
supply to the wire can be easily measured with the electronical equipment.
The electrically applied power Q
el
to heat the wire or film, can be calculated as
Q
el
= I · E [W ]
(2.1)
Due to the Ohm's law of the wire's resistance R
w
, Eq. 2.1 can be written as
Q
el
= I
2
· R
w
=
E
2
R
w
(2.2)
It is important to know how the resistance R
w
is dependent on the temperature. The
resistance of the wire can be approximated as a non-linear n-power Taylor series
R
w
(T ) = R(T
0
) · [1 +
1
(T
w
- T
0
) +
2
(T
w
- T
0
)
2
+ · · · +
n
(T
w
- T
0
)
n
]
(2.3)
For gauging with hot-wires it is advantageous to receive a linear behaviour of the resis-
tance R
w
. In this case the materials used should have a high value of
1
and a small
value of
2
. Table 2.1 shows common materials and their temperature coefficients
1,2
for HWA [HB], [TA].
Material
1
[
C
-1
]
2
[
C
-2
]
Nickel
6, 0 · 10
-3
6, 5 · 10
-6
Tungsten
3, 6 · 10
-3
7, 0 · 10
-7
Platinum
3, 8 · 10
-3
5, 5 · 10
-7
Table 2.1: Temperature coefficients
1,2
[FB], [HB]
2.2.2 Thermal balance
In order to describe the principle of the hot-wire's heat transfer more precisely, an analytic
solution for the relation between the sensor signal and the velocity of the fluid flow
should be given in this paragraph. The heat flux is dependent on all mechanisms of heat
transport (Fig. 2.9).
Chapter 2. Theory of hot-wire-anemometry
16
· Natural convection
Q
nc
· Forced convection
Q
f c
· Thermal conductance
Q
co
· Thermal radiation
Q
ra
Figure 2.9: Heat balance of a hot-wire [FD]
All heat fluxes mentioned above, can be combined in one equation:
Q
el
=
Q
nc
0
+
Q
f c
+
Q
co
(0)
+
Q
ra
0
= I
2
· R
w
(2.4)
The natural convection described by the Grashof number Gr
Gr =
g · · T · d
3
w
2
(2.5)
must not be neglected, if the relevance of the forced convection is small in contrast
to the natural convection, which actually means at low velocities of the fluid flow
U
< 0, 1
m
s
. It can also be said
Re > Gr
1
3
.
(2.6)
The dominating heat dissipation is caused by the forced convection. The heat flux of
this heat transfer mechanism can be described with Eq. 2.7.
Q
f c
= h · · l
w
· d
w
A
w
· (T
w
- T
f
)
(2.7)
With the Nusselt number N u
N u =
h · d
w
k
f
,
(2.8)
the heat flux can be given as
Q
f c
= N u · · l
w
· k
f
· (T
w
- T
f
) .
(2.9)
Chapter 2. Theory of hot-wire-anemometry
17
The heat flux of the thermal conductance from the warm wire to the cold pins is ap-
proximately 10 - 20% of the whole heat flux. For both pins it is given by
Q
co
= 2 · k
w
dT
dx
·
d
2
w
4
end of pin
.
(2.10)
To solve Eq. 2.10, the temperature gradient at the end of the sensor has to be known.
The temperature distribution along the wire is an implicit function of the sensor's Nus-
selt number N u and the surrounding fluid. For long hot-wires
d
w
l
w
> 200 the thermal
conductance can be neglected [FD].
Thermal radiation, which is given by
Q
ra
=
· · A
w
· T
4
w
- T
4
f
(2.11)
can be neglected at normal wire temperature of about
T
w
= 300
C
Q
ra
0, 001 ·
Q
co
.
(2.12)
The energy equation (Eq. 2.4) can now be rephrased as
E
2
R
w
= 2 k
w
d
2
w
4
dT
dx
end of sensor
+ N u l
w
k
f
(T - T
f
) .
(2.13)
For an analytical solution, the Nusselt number has to be determined. If the Gr-,
M a- and Kn - number and relationship
l
w
d
w
are neglected, the Nusselt number can be
described as
N u = N u (Re, P r, T, . . .) .
(2.14)
With the Nusselt number introduced by McAdams, an example for the fundamental
relationship between U
and E can be given by
E
2
R
w
= k
w
·
d
2
w
2
dT
dx
+ 0.32 l
w
k
f
T + 0.43 l
w
k
f
T ·
d
w
0.52
· U
0.52
Re
0.52
. (2.15)
The determination of the geometrical dimensions of a sensor is not accurate enough.
Furthermore, effects of contamination, material fatigue and corrosion cannot be consid-
ered. Due to these facts a direct calibration of the hot-wire combined with King's law
or a polynomial curve fit is used in practice [LK]. This analytical solution is helps to
understand the heat transfer mechanisms of hot-wire probes [FD], [TA].
Chapter 2. Theory of hot-wire-anemometry
18
2.2.3 Influences on the sensor signal
Fig. 2.10 shows a schematic diagram of a calibration curve of a hot-wire. The non-linear
behaviour between the gauged voltage E and the velocity U
of the fluid flow is caused
by influences of the heat transfer.
Figure 2.10: Influences in the calibration curve [FD]
With the increase of the Ma-number the probe reaches its maximum of cooling among
the items M - N - O. In this range the sensor signal is not unique. Between K and
L the influence of the natural convection dominates, due to the coeval decrease of flow
velocity and the absence of the forced convection. The part L - M can be approximated
with the power law, respectively King's law (Eq. 2.16). A polynomial or spline fit can
raise the accuracy [FD], [TA].
E
2
= A + B · U
n
(2.16)
2.3 Electrical circuit of HWA
Due to Eq. 2.2 two different ways of handling the electrical circuit have been developed.
Either the wire current I or the wire temperature and thus, the wire resistance R
w
is
kept constant.
2.3.1 CCA mode
The CCA method (see Fig. 2.11) keeps I constant and is the most simple circuit for
HWA. In this case the heat flux is a function of the voltage E.
Q = f (E)
(2.17)
Chapter 2. Theory of hot-wire-anemometry
19
A Wheatstone bridge is used to improve the sensitivity of the sensor. At first the overheat
ratio
R
h
R
0
shall be set, by adjusting R
c
using the relationship
R
h
R
2
=
R
c
R
1
(2.18)
The overheat ratio a is the relation between the hot-wire's resistance at the working
and at the ambient temperature. For every velocity ¯
U , the Wheatstone bridge has to
be balanced, by decreasing R
b
. The recorded voltage E corresponds to a certain flow
velocity U
[HB], [TA].
f
c
1
2
b
Figure 2.11: Circuit of constant current anemometry (CCA)
Handicaps of CCA mode [TA]:
· Small bandwidth, due to the thermal inertia of the wire
· No overheat protection for the HW (U
0 I = const. HW f using)
· Unsuitable for measurements of oscillating flow
· No possibility to compensate frequency response (non-linear behaviour)
Advantages of CCA mode [TA]:
· Ratio of signal and noise better than in CTA mode
· Temperature measurements are precise
· Simple circuit
· No problems with different probes and its cables
Chapter 2. Theory of hot-wire-anemometry
20
2.3.2 CTA mode
The outstanding advantage of the CTA mode is the constant working temperature of
the hot-wire and the resulting constant hot resistance. Hence the thermal inertia of
the sensor is automatically adapted, when velocity of the fluid flow alter quickly. As a
consequence, a feedback control system needed to put this in action is more complex
than the electric circuit of the CCA mode. [HB] An operational amplifier with a fast
response keeps the constant temperature of the probe (constant resistance). The hot-
wire is placed in a Wheatstone bridge as well. If the flow conditions vary, the value
change of the wire's resistance is detected by the voltage E at the input of the op-
amp. The bridge current is its output and represents the actuating variable (see Fig.
2.12).
c
1
2
k
Figure 2.12: Circuit of constant temperature anemometry (CTA)
Actually only CTA circuits are commercially available today. Nevertheless, some CTA
circuits have the possibility to switch into CCA mode.
2.3.3 Ohmic and complex resistance of a hot-wire
The Wheatstone bridge has to be adapted to the resistance of the hot-wire and its
connector cables (using R
c
). But its resistance is complex (Fig. 2.13). A simple ohmic
adjustment leads to unstable behaviour of the amp. Thus a compensator network R
k
has to be trimmed as well (Fig. 2.12).
HW
i
Figure 2.13: Equivalent circuit diagram of a hot-wire
Chapter 2. Theory of hot-wire-anemometry
21
2.4 Anemometer setup
2.4.1 Overheat adjustment
To determine the operating temperature of the wires, the overheat adjustment has to
be done. Therefore the decade resistor in the right arm of the Wheatstone bridge has to
be adjusted. The overheat ratio a relates the cold and the warm values of the resistors.
In an air flow, an overheat ratio of a = 0.8 is usually applied.
a =
R
h
- R
0
R
0
(2.19)
The overheat temperature T
ov
= T
h
- T
0
can be estimated by knowing the wires
temperature coefficient
0
.
T
h
- T
0
=
a
0
(2.20)
It is recommended to do the overheat setup before every series of measurements [FJ].
2.4.2 Square wave test
The reasons for the dynamic bridge balancing (or square wave test) are:
· Check, if the servo-loop is stable.
· To optimise the bandwidth.
For this purpose, a square wave signal is applied to the top of the Wheatstone bridge.
CTA units include such a feature. The time it takes to get the bridge into balance again
is related to time constant and also the bandwidth of the system [DA]. The frequency
response can be adjusted, by changing filter and gain of the amplifier (Fig. 2.14). The
hot-wire's temporal resolution is described by the upper frequency limit.
h
o
0.
97 h
o
0.15 h
o
t [s]
E [V]
Figure 2.14: Frequency response of one hot-wire
Chapter 2. Theory of hot-wire-anemometry
22
For hot-wire probes, the bandwidth can be calculated as
f
c
=
1
1.3 ·
.
(2.21)
For fibre-film probes, the bandwidth can be calculated as
f
c
=
1
.
(2.22)
2.4.3 Low-pass filtering
We apply low-pass filters in order to remove noise and the prevent the signal from alias
errors. These errors may occur during the discretization of analogue signals. Reproducing
a signal which is recorded without respect to the Nyquist-Shannon sampling theorem
can lead to wrong peaks in the power spectrum (Fig. 2.15).
Figure 2.15: Analogue signal without and with alias error [AA]
To avoid this phenomenon, a low-pass filter has to be applied, which only lets the lower
frequencies pass. Therefore the highest frequency that occurs has to be determined.
Hence the cut-off frequency f
cu
can be calculated as
f
cu
= 2 · f
max
.
(2.23)
If low-pass filtering is not performed, the amplitude (energy) at frequencies lower than
the cut-off frequency f
cu
is contaminated by higher frequencies [FJ]. If the bridge is
configured to a low upper frequency limit, it can be used as a low-pass filter.
2.5 Reference velocity for hot-wire calibrations
A precise reference velocity is fundamental for hot-wire calibrations. There are different
ways to allocate this reference:
Chapter 2. Theory of hot-wire-anemometry
23
· Calibration unit with pressure supply
· Pitot tube in a wind tunnel
Figure 2.16: Two different velocity references
2.5.1 Calculation of the fluid velocity
In the experiment of this project a calibration unit is used as the reference velocity for
the hot-wire calibration (section 4.2). After the air passing the pressure control unit
DISA Type 55D44, it enters the nozzle unit DISA Type 55D45 with a constant mass
flow rate. The air passes through filters, flow straighteners and finally comes out of the
replaceable nozzle. The fluid velocity U
of the calibrator is the reference velocity for
the hot-wire probes. It corresponds with the measured pressure p
tr
from the difference
pressure transducer (Fig. 2.17).
Figure 2.17: Sketch of the nozzle unit
Details
- Seiten
- Erscheinungsform
- Originalausgabe
- Jahr
- 2009
- ISBN (eBook)
- 9783836639606
- DOI
- 10.3239/9783836639606
- Dateigröße
- 8.5 MB
- Sprache
- Englisch
- Institution / Hochschule
- Fachhochschule Regensburg – Mechanical Engineering
- Erscheinungsdatum
- 2010 (Januar)
- Note
- 1,0
- Schlagworte
- lookup labview flow hotwire
