Hot Wire Anemometry and Fluid Flow Measurement

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



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



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




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



In making measurements, it is not a question of the best instrument but rather which instrument will perform best for the specific application.




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




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.




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.




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




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



Hot Wire Probe

Hot Wire Anemometry and Fluid Flow MeasurementStructure of hot wire probe



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



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




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)




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.




Basic Circuitry of Constant Current Anemometer

Hot Wire Anemometry and Fluid Flow MeasurementCircuit Diagram of Constant Current Anemometer

f



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



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.




CTA Measuring Chain

Hot Wire Anemometry and Fluid Flow MeasurementBasic CTA Measuring Chain



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




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


H t T f d t



Heat Transfer due to radiation

Performing an energy balance on this differential element,

neglecting radiation and self convection we get:




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






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






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:




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,


)



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



Dynamic Characteristics The above differential equation has time constant τ given

by

Frequency limit is given by


Exponential change in resistance of wire with instantaneous rise in

velocity



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




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




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.


Calibration of hot wire sensor

using pitot tube



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


Di i l S i i i f H i



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:




Directional Sensitivity of Hot wire probes

E2 = A + B(Ueff )n




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






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 =




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




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.








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






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)




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




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


Meas rement of Integral



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.


Diagram of Pitot Tube



Methods To Measure Turbulence Fluctuations

Hot Wire Anemometry Laser Doppler Anemometry Particle Imaging Velocimetry

Flow Visualization Acoustic Anemometry Thermal Markers Discharge Anemometry




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

Documents

Hot Wire Anemometry and Fluid Flow Measurement