hot wire anemometry and fluid flow measurement
TRANSCRIPT
8/13/2019 Hot Wire Anemometry and Fluid Flow Measurement
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By Mehak ChopraIndian Institute of Technology Delhi
Guide: Dr B. Uensal
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Characteristics of an ideal instrument Hot Wire Anemometry
Advantages and Drawbacks of Hot Wire Anemometry Principle of Operation Basic Construction of Hot Wire Probe Modes of Operation of Hot Wire Anemometers Governing Equation and Model of HWA Calibration Directional Sensitivity Turbulence Measurement using HWA
Hot Wire Anemometry and Fluid Flow Measurement
Outline
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Fluid Flow
Fluid flow is ubiquitous ! e.g processes in our body, Flow
around airplanes etc ‐ it is essential to measure fluid
flow. Most practical flows are turbulent. Hence it is equally important to measure Turbulent Fluctuations.
Pitot tube – low frequency response Many Methods to measure velocity – discussed earlier
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Characteristics of an ideal
Instrument to measure Velocity Fluctuations Good Signal Sensitivity : Measurable change in output for small changes in velocity
High Frequency Response: to accurately follow transients without any time lag
Wide velocity range Create minimal flow disturbance Good Spatial Resolution
Low in cost High Accuracy Measure velocity component and Detect flow reversal
Easy to useHot Wire Anemometry and Fluid Flow Measurement
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In making measurements, it is not a question of the best instrument but rather which instrument will perform best for the specific application.
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Hot Wire Anemometry Intrusive Technique Measurement of instantaneous velocities and
temperature at a point in a flow.
Hot wire anemometry is an ideal tool for measurement of velocity fluctuations in time domain in turbulent flows Principal tool for basic studies of physics of turbulent
flows. Development of realistic turbulence models, HWA
necessary to carry out fundamental turbulence studies
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Advantages of HWA Good Frequency response: Measurements to several
hundred kHz possible, 1 MHz also feasible Velocity Measurement: measures magnitude and
direction of velocity and velocity fluctuations, Wide
velocity range Temperature Measurements
Two Phase Flow: Measurements in flows containing continuous turbulent phase and distributed bubbles.
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Advantages of HWA Signal to noise ratio : have low noise levels. Resolution of 1 part in 10000 is accomplished
Signal Analysis: Output is continuous analogue signal, both time domain and frequency domain analysis can be
carried out. Output can also be processed by digital
systems.
Measurement of turbulent quantities like vorticity, dissipation rate etc.
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Drawbacks Intrusive Technique : modification of local flow field High Turbulence ‐Intensity Flows :
Errors due to neglecting higher order terms Rectification Error – insensitive to reversal of flow direction.
Contamination : Deposition
of
impurities
in
flow
on
sensor
alter the calibration characteristics and reduce frequency response.
Probe breakage and burn out
Unable to fully map velocity fields that depend strongly on space coordinates and simultaneously on time.
Spatial array of many probes would be required. Fails in hostile environment like combustion
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Principle of Operation Based on convective heat transfer from a heated sensing
element, possessing temperature coefficient of resistance .
Flow Rate
varies
Convective heat
transfer
coefficient (h)
varies
Heat transfer
from filament
varies
Hot Wire Anemometry and Fluid Flow MeasurementOperation of Hot Wire Sensor
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Hot Wire Probe
Hot Wire Anemometry and Fluid Flow MeasurementStructure of hot wire probe
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Characteristics of material used for making sensor
High Temperature Coefficient of resistance High Specific Resistance High Mechanical Strength Good Oxidation Resistance
Low Thermal Conductivity Availability in small diameters
Tungsten : good strength, poor oxidation resistancePlatinum : good oxidation resistance, weakTungsten with thin platinum coating is generally used.At high temperatures – Platinum‐iridium alloys, Platinum ‐
rhodium alloys are used.Hot Wire Anemometry and Fluid Flow Measurement
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Wire Dimensions Large aspect ratios – i.e l/d where l is the wire length and
d is the wire diameter, to minimize conduction losses to
supports and have uniform temperature distribution Small diameter are preferred even though they have less
strength as: maximizes time response due to low thermal inertia
maximize spatial resolution improves signal to noise ratio at high frequencies eliminates output noise
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Classification of Hot Wire ProbesOn the basis of number of sensors:
Single Sensor Probe Dual Sensor Probe Triple Sensor Probe
Information about magnitude and direction of velocity canbe obtained with probes having 2 or more sensors
( X probes,Split Fibre probes)
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Modes of Operation of Hot Wire
Anemometers
Constant Current Constant Temperature Current in the wire is kept
constant
Variations in wire resistancecaused by the flow are measured
by monitoring the voltage drop
variations across the filament.
Temperature hence Resistanceof the wire is kept constant by
using a servo amplifier The measurable signal when a
change in flow velocity occurs is
the change in current to be fed to
the sensor.
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Basic Circuitry of Constant Current Anemometer
Hot Wire Anemometry and Fluid Flow MeasurementCircuit Diagram of Constant Current Anemometer
f
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Basic Circuitry of Constant
Temperature AnemometerVelocity
VariesError Voltage
(e2 – e1) variesInput Voltage to
amplifier varies
Change in current i
through the sensor
Restores the
resistance of sensor
to original value
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CCA vs CTA Compensation of Thermal inertia of the filament is
automatically adjusted in CTA as the flow conditions vary.
CTA is
used
the
same
way
as
it
is
calibrated.
Calibration
is
dynamic in this case, while in CCA instrument is
calibrated at constant temperature and used in a
constant current mode. In constant current mode, wire can be destroyed by
burning out if velocity is very small. There is no such
danger in CTA In CTA there is no thermal cycling hence long life of probe.
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CTA Measuring Chain
Hot Wire Anemometry and Fluid Flow MeasurementBasic CTA Measuring Chain
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General Hot Wire Equation
Where:W – power generated by joule heating given
by I2Rw where Rw = Rw (T w )Q – heat transfer rate to surrounding
Q i – thermal energy stored in the wire (C w T w ) Cw – Heat capacity of wireTw – Temperature of wire
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Q = Q fc + Q nc + Q r + Q cForced convection term given
by
h*A*(T w – T A )
natural convection term
Radiation to
surrounding given by
A*σ *ε *(T 4w – T 4 A )
Conductionto prongs
given by
‐
(k*A*dT/dx) where A is the area of the wireT A is the temperature of the fluid h is the heat transfer coefficientσ is the Stefan ‐Boltzmann constant ε is the emissivityk is the thermal conductivity
Hot Wire Anemometry and Fluid Flow Measurement
H t T f d t
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Heat Transfer due to radiation
Performing an energy balance on this differential element,
neglecting radiation and self convection we get:
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Natural Convection : is effective at very low velocities. It depends on the value of Grashof number Gr ( )
According to Collis and Williams (1959), It can be neglected
for hot wire probes with large values of aspect ratio, if
Radiation: in most hot wire anemometer applications this
term is very small and can be neglected
Re>Gr1/3
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Forced Convection: plays the main role in heat
transferred to the surrounding. It depends upon Nusselt number
Where
Re = Reynolds number Pr = Prandtl number which accounts for fluid properties. (generally constant)
α 1= angle between free stream flow direction and flow normal to the cylinder Gr = Grashof number which accounts for free convection (buoyancy) effectsMa = Mach number which accounts for compressibility effects
γ = C p / C v
a t = overheat ratio or temperature loading (T w – T a )/ T a2l/d = accounts for sensors dimension
kf /k w = ratio
of
thermal
conductivity
of
fluid
to
sensor
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Simple Model for Hot Wire Anemometer Considering only forced convection as the mode of heat
exchange and not considering heat storage term:
Where Tw= Temperature of wireTa = Temperature of fluid
As , hence
Resistance is a function of temperature:
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Simple Model for Hot Wire
Anemometer Thus putting the value of Nu (by Kings Law) and
expressing resistance as a function of temperature,
Hence for finite length hot wire anemometer,
In terms of voltage Ew, For CTA, as temperature and resistance are constant,
Hot Wire Anemometry and Fluid Flow Measurement
)
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Dynamic Characteristics Wire not respond instantaneously due to its thermal
inertia.
Dampen the variation in wire resistance Rw and result in
flow fluctuation measured smaller than they are.
Heat Storage term needs to be accounted in heat balance equation
Hot Wire Anemometry and Fluid Flow MeasurementCw = thermal capacity
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Dynamic Characteristics The above differential equation has time constant τ given
by
Frequency limit is given by
Hot Wire Anemometry and Fluid Flow Measurement
Exponential change in resistance of wire with instantaneous rise in
velocity
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Frequency Response of CTA The servo ‐loop amplifier reduces the time constant and
increases the wire frequency limit.
where τw = wire time constant alone and =
a = overheat ratioRw = wire resistanceS = amplifier gain
Amplitude transfer function for
velocity fluctuation
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Methods to Determine Dynamic Response of CTA
A small electronic square wave signal is injected into the
bridge and response of anemometer voltage E is observed.
Output voltage response to this current signal has the same
time constant as the response to the flow velocity signal
Square wave test response of CTA
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Calibration Probe is exposed to a set
of known velocities and
output voltage E is recorded.
Should be done at low
turbulence intensities and constant temperature
Pitot ‐static tube is
generally used for velocity
measurement.Where h is total pressure
in height of flowing fluid.
Hot Wire Anemometry and Fluid Flow Measurement
Calibration of hot wire sensor
using pitot tube
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Calibration Calibration curve is
plotted between Hot Wire Voltage and Velocity.
Typical Calibration curve is
nonlinear and sensitivity decreases as velocity
increases.
As constants A, B and n can
be determined by
regression analysis
Hot Wire Anemometry and Fluid Flow Measurement
Di i l S i i i f H i
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Directional Sensitivity of Hot wire
probes For an infinitely long sensor , heat transfer varies
with the cosine of angle between the velocity and the
wire normal and Velocity along the sensor has no cooling effect. For a finite length sensor, a directional sensitivity
factor k (yaw factor) is introduced, which describes
prong interference.
For 3
‐dimensional
flows,
pitch
factor
h
is
introduce Effective cooling velocity is given by:
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Directional Sensitivity of Hot wire probes
E2 = A + B(Ueff )n
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Determination of Direction To determine direction using a single wire probe, Rotate
the probe in the flow. The orientation which gives maximum current is the
direction of flow
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Turbulence Measurements However, the second moment of turbulent fluctuations or variance <(u’)2> is not zero and is a
measure of intensity of fluctuations
Standard deviation of velocity (σ ) or urms is square root of variance. Turbulence Intensity =
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Turbulence Measurements
Velocity Sensitivity is given ( )
Thus fluctuating component of velocity is related to
fluctuating voltage e’:e’ = u’
Hence if calibration constants are known, fluctuation in
velocity can be calculated by fluctuation in voltage
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Filtering and Signal Dynamic Range Voltage fluctuations may be very small compared to
mean voltage. Difficult for ADC to measure both average and fluctuating
components. Anemometer output is sent to a high pass filter which
eliminates mean value <E> of voltage
Output of high pass filter is sent to an oscilloscope inorder to observe peak ‐peak fluctuations and set the
amplifier gain.
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References1. Özgür Ertunç and Franz Durst, “On the high contraction ratio
anomaly of
axisymmetric
contraction
of
grid
‐generated
turbulence”, PHYSICS OF FLUIDS 20, 025103 2008
2. Bruun H.H, “Hot Wire Anemometry ‐Principal and Signal Analysis”, Oxford University Press
3. Perry A.E,
“Hot
‐Wire
Anemometry”,
Oxford
Science
Publication4. Smol’yakov A.V. and Tkachenko V.M. ,“ The Measurement of
Turbulent Fluctuations”, Springer‐Verlag Berlin Heidelberg 19835. Goldstein R.J,“Fluid Mechanics Measurement”, Hemisphere
Publishing6. Jorgensen F.E(2002), “ How to measure turbulence with hot wire anemometers – a practical guide”
7. Tropea C et al, “Springer Handbook of Experimental Fluid
Mechanics” SpringerHot Wire Anemometry and Fluid Flow Measurement
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Compressibility Effects For high velocity flows, compressibility effects become
significant. Need to consider Mach number Ma and Cp
Knudsen number
(Kn)
is
important
parameter
for
low
density flows and is given by:
where λ = molecular mean free path In this case Nu = Nu(Re, Kn)
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Hot Film Probes
Platinum or nickel film are deposited on thermally insulating substrate like
quartz. Used in liquid flows and high temperature ultrasonic gas flows due to their
sturdy construction
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Turbulent Flows Most practical flows are turbulent.
Contribute significantly to transport of momentum, heat and mass.
A complex, unpredictable and random process.
Responsible for most fluid friction losses. Rational design of airplanes, ships, turbines etc – have to
consider turbulence.
Hence it is equally important to measure Turbulent Fluctuations
Hot Wire Anemometry and Fluid Flow Measurement
Meas rement of Integral
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Measurement of Integral
Properties Instruments like Pitot tubes,
venturimeters ‐ Only measure integral properties like mean velocity.
Differential pressure meters Low frequency response
Do not respond to fluctuations in velocity, hence unable to
measure turbulence.
Hot Wire Anemometry and Fluid Flow Measurement
Diagram of Pitot Tube
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Methods To Measure Turbulence Fluctuations
Hot Wire Anemometry Laser Doppler Anemometry Particle Imaging Velocimetry
Flow Visualization Acoustic Anemometry Thermal Markers Discharge Anemometry
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Computational Fluid Dynamics Turbulence modeling is an important issue in CFD Measurements are made as a supplement to computer
modeling
These methods
provide
high
quality
experimental
flow
data for validation of existing computer codes containing
turbulence models