Chapter 1

CHAPTER 1: Introduction:

Flow measurement is an important field in fluid mechanics and modern industries, such as petrol measurements, as well as food industries, where everything must be counted in a suitable manner, to achieve the required product with the accepted conditions and specifications.

in the other hand to measure the flow, there are many types of devices which are used to do so, the variation in the device depends on the flow state, such as if it is isothermal, viscous flow, liquid or gas, and for gas measurement, we have to take gas compressibility in to our calculation.

Such a device is called (Flow Measurement devices) as examples of these devices:

1- Thermal anemometer.2- Ultrasound.3- Pressure transducers.4- Turbine flow measurement.

A thermal anemometer, controlled at a fixed temperature above the ambient, responds to convective heat transfer. With forced convective heat transfer, the output is proportional to the sensor’s Reynolds number (Re). Looking at the Reynolds number terms we can see how it measures mass rate per unit area. It does NOT measure volumetric flow rate but a density weighted version know as standard flow rate. The thermal anemometer automatically compensates for density because it responds to the Reynolds number.

CHAPTER 2: THERMAL ANEMOMETER

2.1 Definition:

A thermal anemometer uses a heated probe element that is inserted into an airstream. Air speed can then be inferred from the heating power necessary to maintain the probe at a temperature elevation. This power should be some way proportional to air speed.

In this device an electrically heated wire is placed in the gas pathway, which is cooled by the gas flow (Figure 5). The degree of cooling depends on the gas flow rate, which can thus be calculated. A modification of this device uses a heated screen or film instead of a wire.

The hot wire (usually platinum) has an operating temperature as high as 400°C, and is incorporated into a balanced Wheatstone bridge circuit. Cooling the wire changes its resistance and unbalances the bridge. Most designs work on the constant temperature system, whereby a correcting current is applied through the hot wire to compensate for the cooling effect of the gas, maintaining a constant

wire temperature and thus restoring the balance in the Wheatstone bridge. This current is measured and from it the gas flow rate is determined. To compensate for changes in the gas temperature, a second wire is usually incorporated, which is maintained at ambient temperature. Minor corrections are also made according to the gas composition, to accommodate the variation in specific heat capacity, but hot wire anemometry is generally extremely accurate.

This cooling effect occurs with flow in either direction, and so to measure exhaled tidal volume the hot wire anemometer is placed in the expiratory limb of the circuit. It can be modified to provide information about the direction of flow by using an additional heated wire placed just downstream from a small bar, as shown in Figure 5b. This bar shelters the wire from the full cooling effects of flow in one direction but not the other, and thus inspiratory and expiratory flows can be calculated separately. For this purpose the sensor must be placed in the Y-piece of the circuit. This technique is particularly useful for neonatal ventilation.

2.2 Fundamental Concepts:

Thermal anemometer (hot wire anemometer) is a device for measuring the mass flow rate with the help of heat and mass transfer concepts.

The thermal anemometer measure the mass unit area flow rate, so it measures the true velocity of the fluid, but the process must be done at fixed temperature above the ambient temperature, so it will respond to the convective heat transfer, so by the forced convection, the output will be proportional to sensors Reynolds number, and because Reynolds number measures the density, not the volumetric flow rate, which is known as (standard flow rate).

2.2.1 Reynolds Number

Reynolds Number Is a dimensionless number which gives the ration

between the inertial forces (ρ V2L2) to the viscous forces (μVL).

Re = ρVD

μ = VDν ……………………………………………………………Eqn (2.1)

Where:ρ = Actual Density of the flow.

V = Actual Velocity.

D = Sensor Diameter.μ = Viscosity.ν = Kinematic Viscosity.The density times the velocity (ρ V) which makes the thermal anemometer mass flow rate device.

2.2. Standard velocity:

it is the multiplication of ρV normalized to a standard density (ρ s).

Standard Velocity = ρV/ρ s………………Eqn(2.2)Where ρs is the standard gas density (for air at 25℃ and 760 mm Hg is 1.184 Kg/m3).2.2.3 Standard Volumetric flow rate:It the product of the velocity times density time the area normalized to standard density.Standard volumetric flow rate = Area * Standard Velocity= A* ρV/ ρs..........Eqn(2.3)

Mass flow rate can be easily calculated by multiplying standard volumetric flow rate by the standard density.

2.2.4 Standard Density:

Different gases have different standard densities. This is often described using the gas’s molecular weight (molar fraction or volumetric % sum of all elements).

ρs = ρ air (MW/MWair)……………..Eqn(2.4)

then

mass flow = A(ρV/ ρs) * ρ air (MW/MWair)………….Eqn(2.5)

2.3 Conversion between Actual and Standard Flow:

Conversion between the actual and standard flow can be done by scaling gas density by using ideal gas law.

Va= Vs (Ps/Pa)*(Ta/Ts) ……………….Eqn(2.6)

or

Qa= Qs (Ps/Pa)*(Ta/Ts)……………….Eqn(2.7)

WhereVa is actual velocity, Vs is standard velocity.Qa is actual volumetric flow.Qs is standard volumetric flow.Ps is the standard pressure in absolute units.Pa is the actual pressure in absolute units.Ta is the actual temperature in absolute units (Kelvin or Rankin).Ts is the standard temperature in absolute units (Kelvin or Rankin).* °K = °C + 273.16, °R = °F + 459.67.

And for more accurate conversion, compressibility (Z) can take place in the above equation to be:

Va= Vs (Ps/Pa)*(Ta/Ts)*(Za/Zs) …………..Eqn(2.8)

2.4 Dynamic Theory of the Anemometer:

An anemometer is an instrument for measurement of the velocity of a fluid or gas. Here the gas is common air. The instrument is fast and sensitive when used in the right way. (John P. Bentley: Principles of measurement systems. Longman, London and New York (1983) pp. 307-323).Principle of operation: A thin tungsten wire heated by an electrical current is cooled by air. The temperature of the wire may be calculated from the resistance. Therefore the velocity of the air may be calculated from the resistance R of the wire and the electrical current I through the wire.

By measuring R & I we calculate the air velocity.

In practice the resistance R is made constant by using a Wheatsone bridge in which the error voltage E is automatically controlled to zero. The control system is changing the supply voltage Y of the bridge until E is zero. In this way Y is proportional to the current I through the wire.

The wire can be assumed as first order system, so small change in the input power will cause a temperature change of the wire. So by increasing the input voltage Y of the bridge will increase the resistance R therefore the Voltage error E will decrease.

CHAPTER 3: Error Sources for Hot Wire Anemometer

Error Sources can be summarized as:

1- Gas property induced errors.2- Flow Profile.3- Acoustic noise sources.4- Gas Species Decomposition.

3.1 Gas Property Induced Errors:

1- Pressure Changes: Pressure changes effects the calibration of some gases, like N2 has 2.5% for each 100 Psi shift in its viscosity, which directly affect the mass flow readings, on the other hand He can be approximated to have no change with the pressure. Also the compressibility Z can be factor for some gases, e.g. CH4:

20 °C, 101.3 KPa, Z= 0.9975 20 °C, 800 KPa or 7.9 bar, Z= 0.9875 or 1% deviation.

2- Temperature Changes: Temperature changes will affect the gas thermal conductivity and viscosity so the calibration will drift. This is typically 2.5% /100 °C. The minimum drift occurs near 3000 SFPM (Standard feet per minute) where the dynamic temperature compensation is performed. The use of velocity temperature mapping (VTM) or multiple calibration curves for different gas temperatures largely eliminates this source of error.

3-Temperature Profile: Temperature Profile in the pipe will produce flow errors. This is caused by using non insulated pipe upstream of the sensor where the gas is above or below the ambient temperature.4- Low flow free convective: Low flow free convective heat transfer forces compete with forced convective and conductive heat transfer forces for power. This causes measurable errors (depending on gas type, temperature, pressure, and orientation of sensor to both flow and gravity) starting at about 300 SFPM and becomes significant down at about 100 SFPM.

5-Wet VS Dry Flow Rates: The thermal anemometer responds to all gas molecules which hit it. In the case of water vapor (H20) dissolved in Air, it reads what is known as wet standard volumetric flow or WSCFM. For intake combustion processes you want to know the dry standard volumetric flow or DSCFM which is 21% O2 so your fuel air ratio can be properly computed. Knowing the specific humidity ratio ω you can use the following equation up to 5% ω and get results within 1%:

DSCFM = WSCFM x 0.622/ (0.622 + ω) Where DSCFM = Dry Standard Cubic Feet per Minute.WSCFM = Wet Standard Cubic Feet per Minute.

3.2 Flow Profile & Correction Factor:

At low velocity, a laminar velocity profile develops across the pipe cross section as shown in the figure. Note that the peak velocity is about 30% higher than the velocity average (V average). At higher flow rates, a flatter velocity profile develops where the peak velocity is closer to the average. So depending on where the sensor is located, it will read a different fraction of the average velocity. It is the average velocity multiplied by the cross sectional area that will obtain the total flow.

The use of a velocity dependent correction factor can convert the local velocity measurement to average velocity.

Flow = Vlocal*Area*C.F(Vlocal)

The correction factor curve was measured from a 4" ID pipe with a 2" welded support, triple sting CD sensor. For other sized ducts, the data can be scaled by the Reynolds Number.

3.3 Acoustic, sound or pulsing pressure induced errors:

It is not verified yet in the laboratory, Pneumatic control valves, reciprocating pumps, sonic nozzles, pressure regulators etc. all tend to induced pressure pulsations in to the piping or ducting. At high enough amplitude, the instantaneous gas velocity will reverse direction when compared to the average flow. This causes a thermal sensor to lose heat to this gas on both the forward and reverse flow rate. The heat loss to the fluid is then higher than it was when calibrated on a gas moving in one direction at the same net flow rate. So the sensor will read higher flow than is actually flowing. The source of this pressure wave can be upstream or downstream of the sensor. In some plumbing configurations the pulsations will be sympathetic with the standing wave sound reflections in the pipes which will allow the amplitude to grow very high. Starting at the fundamental and all the harmonics of the standing

wave pattern these phenomena can aggravate a flow measurement with a thermal anemometer.

3.3.1 Mitigation of acoustic induced errors:

To prevent a standing wave of sound in the piping, we simply need to introduce enough sound absorption to prevent the buildup of a large sound wave with each reflection from each end of the piping section where the flow meter is in. Elimination of these acoustic induced errors can be controlled using expansion tanks, mufflers etc. to attenuate the sound waves and return the piping/duct to a smooth one-way flow field so the thermal sensor does not produce false high readings. Inserting a tank between the noise source and sensor is often all that is required to correct this error source. Even a branching tee with a short stub to a tank will attenuate the sound enough to correct most applications which suffer from high acoustic noise. In some applications, a control valve and shut off valve can be swapped so the control valve is not in the same sound-resonator as the sensor.

3.4 Gas species decomposition from the velocity sensor heat:

Some gas species, like ozone (O3) can be induced to decompose from the heated velocity sensor. As it requires heat to split up a molecule, the thermal sensor will read high under this condition. The heat of recombination, O combines with O to make O2 occurs downstream of the sensor and is not detected. So while the net chemical reaction from O3 to O2 is exothermic giving off heat, the first step is endothermic. In this case, the only mitigation is to reduce the application temperature or the sensor overheats to below the activation energy needed to initiate this decomposition. In the case of O3, this is 80 to 100 °C. The opposite issue where the sensor surface could at as a catalyst for a recombination and the sensor picks up too much heat, so it reads low, has not been observed but is possible. Higher temperature applications are more likely to observe catalytic heat absorption.

CHAPTER 4: INSTLATION & CALIBRATION:

4.1 CIRCUITS AND SENSORS:

For installing hot wire or hot film anemometer there are many ways to connect them, such as:

1- Internally heated transistor.2- Externally heated Diode Bridge.3- Internally heated NTC Resistor Bridge.4- Externally heated NTC

Resistor Bridge.5- Hot wire, internally

heated.

4-1-1 INTERNALLY HEATED TRANSISTOR - 'TRANEMOMETER'

The temperature sensing elements are the base-emitter junctions of two probe transistors Q1, Q2. The base-emitter junction voltage is typically 0.7 Volts with a temperature coefficient near -2 mV per deg C. The lower transistor Q2 has its collector wired to its base. This one acts as a passive diode, only there to sense ambient temperature. These transistors form the left side of a bridge,

the right side is resistors R1, R2, and the trimmer R3. Amplifier A1 senses the balance of the bridge. If the voltage over the Q1 junction is too high, then A1 will drive the Q1 base up. More current will pass through both transistors but Q2 is fully conducting and does not change its temperature appreciably with change in current. Having a high collector voltage, Q1 will be heated while Q2 remains essentially at ambient temperature. That heating lowers the Q1 base-emitter voltage until balance is restored. The heater and the temperature detection are inherent in the transistor itself. So A1 keeps Q1 a certain number of degrees hotter than Q2. How many depends on the trimmer setting, with this circuit typically around 5 degrees centigrade. Resistor R4 senses how much current is flowing

through Q1-Q2. The (small) voltage developed over R4 by this current is amplified by A2 into the output pin 7. A2 has an offset input but otherwise simply translates the additional current needed to maintain the temperature difference between the two B-E junctions. The more current, the more heat is being removed from hot Q2. Actually A2 is not simple at all. If R9 and R10 are trimmers, you can go nuts trying to adjust them. The reason is that “input offset” in the front. As the bias changes, the gain is affected.

The original article mentions a problem with this circuit. The sensor transistors may latch up in a current rush mode, with the top Q1 fully on and current limited essentially only by the small sensing resistor R4. Then Q1 can no more hold its temperature and the bridge balancing fails. This mode is easily evoked by a minimal disturbance, e.g. like putting a scope probe in contact with the circuit. The remedy is the threshold feedback from A2 via two diodes (a transistor in the original article). If the output at A2 goes too high, essentially over some half the supply, then the feedback diodes open and A1 is quenched such that probe current is cut off again. While this safety device is in operation, the output of the circuit is in error (output no longer goes up with airspeed). Without it, however, it goes up and stays up until you turn off the circuit.  The capacitor C1 is not commented in the original article, but apparently slows operations to be in the tens of milliseconds range, preventing oscillation. Still this is much faster than the thermal time constants in Q1-Q2.

Power is supplied from a single 9V battery. The power-on indicator LED is used to offset the nominal ground and form a negative supply for the op-amps. Otherwise their inputs come too close to the negative supply, such that they do not operate.

It is hard to understand the talk about linearity in the original article until you realize it is stated for a rather small range, up to 250 ft/min, 1.27 m/s. I find from my calibrations in the 1 to 10 m/s range that the device is close to logarithmic, as seen here in the calibration for a probe with TO-18 case transistors. Its output voltage increases about equally much for each doubling of the air speed. And this is also the kind of behavior one would like to have, this largely obviates need for a range switch.

There is some freedom in dimensioning, on one hand the current sensing R4, on the other the divider R11-R9, these together define the probe 'rest' (still air) current. Additionally the A2 gain controlling R10 implies a limit on max. Air speed when the feedback diodes open to cut out Q1 heating.

When switched on, the meter goes beyond full scale since Q1-Q2 is initially the same temperature. Then output creeps down as Q1 heats, takes time. For the balance trimmer R3 I use a multiturn pot, this is a very sensitive one to set. I prefer to zero the meter output at about 0.25 m/s air speed. Rather than in still air which is somewhat indeterminate because of whatever thermal convection then goes past Q1, also taking maximal time to reach equilibrium. To get readings at low air speed like 1 m/s is a matter of tens of seconds.

There remain problems with this circuit. This is the reason I have gone through all the following variant schemes. The worst objection is the setting of the balancing R3 trimmer that is extremely sensitive - when you touch it the reading moves very far out before returning to near where it was, and this takes a lot of time. Also I blame this for poor stability in calibration, several times it has differed as much as a factor of two in air speed, taking the instrument out from store. It can be questioned also on more theoretical grounds. The 'cold' transistor Q2 is also heated to a variable degree because it conducts the governed current. These current times the 0.7 volt Q2 voltage is no negligible power. Also the Q1 base-emitter voltage depends not only on temperature but also on the controlling base current injected by A1 via R5. This gives a spurious extra voltage right at the most sensitive spot where bridge balance is sensed; actually causing a positive feedback that may harm stability.

4.1.1.2. Internally heated transistor - alternate layout

The base potentials of the cold reference Q2 and the hot Q1 are directly compared by the differential amplifier. Q2 is fed with a largely constant current determined by R1. The amplifier gain is basically R6/R5 resulting from its negative feedback. The problematic thing is that the servo action to maintain a temperature difference also implements a positive feedback via R4 and the base-emitter resistance inherent in Q1. This latter depends rather unpredictably on the Q1 properties. The original #1 circuit has the same problem, but with the present circuit it is easier to see this is the case. If the

positive feedback is too large, then the circuit will go unstable or latch up, but this can be cured by increasing R4 or decreasing R6.

4.1.2 EXTERNALLY HEATED DIODE BRIDGE

This circuit remains with the principle of diode forward voltage temperature dependence, but now the hot diode is externally heated by a resistor. This diode was clamped to the heater with a tiny strip of brass sheet and also sealed to it with a drop of cyanoacrylate glue. The photo shows the probe tip cold and heated diodes. They are mounted on a flexible multiple conductor strip, retrieved from a head arm of a junked hard disk drive. The glass encapsulated 1N4448 diodes seem to have a fairly low thermal resistance; the data sheet says 0.24 K/mW including 10 mm leads.The small voltage developed over R3 purports to govern the forward drop difference, and hence the temperature difference between the diodes. The gain of the balance sensing amplifier is by necessity moderated by the R5/R4 feedback network, together with a big slowing down capacitor C1.  There is a delay of heat transfer from the heater to the heated diode. If the servo loop gain is too high, this will make the circuit oscillate between fully on and off. The R6 heater resistor

consumes more power than the bare amplifier can deliver, so an intermediate emitter follower transistor is added. The rather low input voltage bias to the amplifier from the sensing diodes necessitates D3 to increase the margin of amplifier negative supply.

The calibration appears to be better reproducible and have a larger air speed range than circuit #1. Also, the characteristic of voltage U vs. air speed is attractive. But response is very slow, and possibly somewhat oscillating.

4.1.3 INTERNALLY HEATED NTC RESISTOR BRIDGE

The resistance of an NTC (Negative Temperature Coefficient) resistor, often called thermistor, typically decreases to about half at a 25 degree centigrade temperature rise. This makes it a very sensitive component, much used in electronic thermometers. I used Mitsubishi type RH 16 in a common miniature form, a little bead at the end of two thin connecting leads. In the diagram the left arm of the bridge is high impedance while the right arm is low impedance. The balance sensing amplifier provides the bridge feed voltage via a buffer emitter follower to boost power. When the bridge feed voltage U goes up, then only the low

impedance arm of the bridge is appreciably heated - the high impedance arm holds another thermistor and is for compensation against ambient temperature change.

This circuit is simple, reliable, and sensitive. But one slight difficulty may be to find a sufficiently low resistance thermistor such that it can be driven enough hot at high speed, given the rather low supply voltage. The alternative with R1=10k is for a very moderate temperature rise, some 5K.

Amazingly, the output sometimes oscillates a trifle with a period of a few seconds, motivating C1 to quench that. I guess this may be because the NTC chip is heated unevenly throughout its volume, and that the oscillation period relates to the time it takes for local heat to even out within the chip.

4.1.4

EXTERNALLY HEATED NTC RESISTOR BRIDGE

Also an externally heated version was tried. The photo shows the probe with the hot NTC Resistor lashed with thin copper wire to the heater resistor. The original heater resistor leads are cut off and replaced by 0.24mm wire wrap leads to reduce uncontrolled thermal leakage. The hot array is isolated from the cold reference

NTC resistor by a lashing of sewing thread.This circuit performs well, except for its inherent thermal delay between heater and sensor. This necessitates the slowing down feedback capacitor. Without it the circuit will oscillate between on and off, with it the final reading is reached after a prolonged delay, to the order of 30 seconds.

 This particular probe design is perhaps not optimal. The red markings show readings when the probe was rotated in 45 degree increments relative to the airflow direction. When the 'cold' reference thermistor is located downstream the of the hot one, then readings go much too high. It might have been better when the cold reference thermistor had protruded beyond the heated one.

I believe this is a similar principle as used for a hot ball anemometer in The Amateur Scientist, Sci. Am., and Nov. 1995. I have not been able to retrieve that article right now, but ISTR that they used thermocouples rather than thermistors. However, the fairly big balls used there must make it extremely slow, maybe adequate for measuring average wind speed in meteorology.

4.1.5 HOT WIRE, INTERNALLY HEATED:

The hot wire anemometer is a classical type and appears to be the one predominantly used for professional work. An orthodox such probe is made from Wollaston wire, a thin silver wire with a platinum core (priced like US$ 500 for 8 inches of it). After soldering it to its posts under a microscope you etch away the silver to leave a sub micrometer diameter platinum wire. An exercise well beyond most amateurs.

I found a workaround to this by breaking the glass bulb off a small incandescent lamp, the type shown beside. After soldering its external connecting leads and lashing

the assembly to a slender wood stick I filed a tiny notch at the bottom of the bulb (at the mark in the photo). The assembly was cautiously held in a vise and the bulb broken off, using a loose fitting tube for a lever. It was then mounted in a protective holder, fabricated from 0.2 mm brass plate.It must be noted that without its bulb and inert atmosphere the filament cannot withstand anywhere near the original lamp specification before being burned out. Be aware the lamp cold resistance is 10-20 times lower than what is given by nominal voltage and power. This particular lamp happens to have 20 ohms cold resistance. For tungsten the resistive temp coefficient is 0.0045 /K such that the bridge balances value of 22 ohms is reached at about 22 degrees centigrade temperature elevation. This is a very moderate rise, such that correction will be necessary if ambient temperature deviates appreciably from normal. Tweaking the fixed resistor values in the bridge allows for some other temperature level. On one hand R2 should be large enough to ensure the filament is never burnt out. On the other hand R2 and supply voltage limit heating current such that there is a definite maximum measurable speed.

Few lamps are constructed such that you can break off the bulb, leaving the filament intact. Another one I found is a 24 V lamp for decoration candlesticks. A 12V 5W halogen lamp was marginally successful, but since that one has a cold resistance below 1 ohm it draws considerable current and needs an additional power transistor to drive it.

Having broken the barrier of fabricating a probe, this is my favorite anemometer beyond all competition. The circuit is simple and stable and measurement time is milliseconds, shorter than any of the other alternatives by several orders of magnitude. But indeed this can make it difficult to calibrate, since it follows the rapid speed variations from any turbulence in the air stream.

One must remember that this poor man's version of a hot wire anemometer has its limitations. It still does not obey King's law, probably because the lamp filament is helically coiled, making for an outer diameter vastly larger than that of an orthodox hot wire. Also the contact between the filament and its post may be questionable with the low voltage used in this application. At one instance I have repaired a faulty probe by carefully pinching such a joint with pliers.

4.2 CALIBRATION:

4.2.1 AIR SPEED

To get an air stream of known speed I used a vacuum cleaner, fed from a variable transformer. That way the fan speed could be set arbitrarily over some range. The cleaner hose was connected to a Venturi tube to measure flow rate and the device ended with a nozzle where the probe under test was placed centrally. To extend the measurement range I could alternate between 22, 46 and 86 mm diameter nozzles. Knowing its diameter and assuming a uniform air speed over its intake area A (m2) it is elementary to convert from flow Q (m3/s) into speed V (m/s): V = Q/A. After running for a while the fan will heat the air passing it. To avoid spurious effects from that, air was sucked from the room rather than blown out from the nozzle.The flow meter Venturi tube has two probe holes to measure the pressure drop from input to constriction. By virtue of the Bernoulli law this drop is proportional to the square of the flow rate and was taken with a water U manometer, later with a differential pressure transducer. The tube was calibrated by measuring the time elapsed to fill a plastic bag of known volume. The Venturi expands gradually after the constriction such that pressure is partially regained. This has nothing to do with the flow measurement as such, but it reduces the throttling effect of the meter.

There are alternative ways of calibrating for air speed. The probe could be put on a motor driven trolley, or at the end of a rotating boom. Or you could compare with some calibrated reference anemometer.

4.2.2 TEMPERATURE

One would like to know the temperature of the probe element. For

the thermistor and hot wire this is simple since the bridge balance criterion (same resistance ratio both sides) tells about their hot electrical resistance. For those the temperature can then be computed from their known cold resistance and the temperature coefficient. For a direct measurement I used a small oil filled container, carried on a digital thermometer probe. First the anemometer circuit was left to stabilize in still air and its output voltage was recorded. The container was heated with a soldering iron and was then left to cool down slowly while its temperature was tracked by the thermometer. At intervals the probe hot element was dipped into the oil. At the point where the anemometer output then stayed at its earlier recorded value, the oil temperature equals that of the probe tip. The small paper wing in the photo was to shield the cold reference sensor from hot air rising from the oil bath.

4.3 CALIBRATION OF CYLINDRICAL SENSORS

The physics of fluid flow and convective heat transfer are inextricably linked by relationships of the general form

Nu = ƒ ( Re, Pr, Kn, ...geometrical factors )

Where the Nusselt, Reynolds, Prandtl and Knudsen Numbers are all non-dimensional quantities. In the context of a cylindrical thermal anemometer, the above equation may be expanded to give

…Eqn(4.1)

Where is the fluid density, U is its velocity and its viscosity, d is a typical dimension such as the hot-wire diameter, is the heat loss, L is the wire length, k is the thermal conductivity and the mean-free path of the fluid and T and Ta the temperatures of the wire and fluid respectively. The geometrical factors referred to include not only the length-diameter ratio of the cylinder L/d but also quantities such as the support geometry for the cylinder and the orientation of the sensor with respect to the flow. It can be seen

that the heat loss depends on many parameters.

In 1914, King derived a solution for the heat transfer from an infinite cylinder in an incompressible low Reynolds number flow that may be written as:

Nu = A' + B' Re0.5 …..Eqn(4.2)

where A' and B' are constants so that

……Eqn(4.3)

The rate of heat loss to the fluid is equal to the electrical power delivered to the sensor V2/R where V is the voltage drop across the sensor and R is its electrical resistance. If the fluid properties and wire resistance remain constant this expression reduces to

V2 = A'' + B''U0.5 …..Eqn(4.4)

where A" and B" are constants. When the conductive heat losses to the sensor supports or the substrate do not change with fluid velocity, the constant A may be replaced by the quantity V0

2, where V0 is the voltage across the sensor under zero flow conditions.

In practice, the voltage registered at the anemometer output is not that across the sensor but the e.m.f. E that is applied to the top of the Wheatstone bridge, the two arms of the bridge acting as potential dividers so that the relationship becomes in effect

E2 - A2 = B U0.5 ……..Eqn(4.5)

The constant A may be replaced by the zero-flow voltage E0 when high accuracy is not required. In practice, the value of the exponent changes with sensor and velocity as do the values of A and B and it’s therefore necessary to calibrate each sensor individually and to check this calibration frequently. An exponent of 0.45 is nearer to

that found in practice.

Since no universal calibration is available, the sensors must be calibrated. To do this, a low turbulence flow of known velocity must be used. Ideally, the probe should be placed into it in the same attitude that it will be used.

In use, errors arise due to changes in ambient temperature and other fluid properties and due to the deposition of impurities in the flow on the sensor. Standard procedures are available to correct for the effects of changes in temperature. The time for which a calibration is valid depends on the individual situation. In high speed wind tunnels, large particles can remove a wire with annoying frequency.

If care is taken and calibrations performed at frequent intervals, then an accuracy of better than 1 percent can be achieved for hot-wire velocity measurements in turbo machines.

4.4 Probe Response to angle

When a cylindrical sensor is placed so that its axis is not perpendicular to the flow direction, there will be a component of velocity that is parallel to the axis of the sensor. If the sensor has infinite length, then the effective cooling velocity that the sensor experiences is that which is perpendicular to the sensor; the parallel component has no effect. Thus, the effective cooling velocity ueff may be obtained from the expression

u cos = ueff…….Eqn(4.6)

where is the yaw angle between the flow vector and the normal to the axis of the sensor. In the case a wire with a finite length, the temperature is not constant over the length of the wire and aerodynamic perturbations are created by the prongs. These are taken into account by arguing that the component of velocity that is parallel to the axis of the wire now contributes to the cooling effect. A simple probe responds to changes in flow direction in a manner shown in the figure below. The interference of the prongs can be reduced by using prongs that are more widely spaced and

plating the ends of the sensing wire with copper or gold to ensure there is little resistance heating except in the central un-plated portion. In this case variation of pitch angle does not affect the response greatly.

It is important to recognize that cylindrical hot-wire and hot-film sensors are capable only of determining the magnitude of the velocity (or a vector component) since the heat transfer is the same whatever the sign of the vector. As a result, conventional sensors are unsuitable for use when the flow reverses such as happens inside separation bubbles. Under these circumstances, specialized multiple sensor probes capable of determining the magnitude and direction of the flow are required.

Typical hot wire response curve to yaw angle

4.4Velocity and Angle Measurements

Two wires arranged as an X probe can be used to make two-dimensional measurements. In the three-sensor method that is employed when three-dimensional information is required, the three elements of a probe are usually aligned with the axes of a rectangular system of co-ordinates. This probe allows the simultaneous determination of the three velocity components and

six turbulence quantities but the spatial resolution is relatively poor. A reduced spatial resolution implies often restricts the effective frequency response much more than the thermal response of the individual sensors.

The calibration and repair of three sensor probes is very time consuming. An alternative technique to using multi-sensor probes involves the use just one sensor but placing the sensor at a number of orientations to the flow. Strictly, only three orientations are required to find the mean components of velocity but the method can be improved by using the method of least squares.

4.5Turbulence Measurements

The figure below shows a typical measurement situation where U is the mean fluid velocity that is normal to the wire and u, v and w are velocity fluctuations in three perpendicular directions. The axis of the sensor is aligned with the w direction so that the sensor will have a very poor response to the w component providing that the length-diameter ratio of the sensor is large (i.e. L/d>200). Therefore, the sensor sees the effective cooling vector U' which, providing v is not too large, has the same magnitude as (U+u') so that at low turbulence intensities the wire is measuring the magnitude of the velocity in the direction of the mean flow. Thus,

the stream-wise turbulence intensity can be derived by calculating the root-mean-square of the velocity-time history. In isotropic turbulence, this measurement and that of the mean velocity are in error by about 2 percent when the turbulence intensity is about 20 percent.

Mean (U) and Instantaneous (u') flow velocities

To obtain the components of turbulence that are normal to the mean flow vector, a variety of two and three sensor techniques are

used to determine the magnitude and direction of the instantaneous flow vector. From this, the time-mean and turbulent flow properties may be found.

4.6Boundary Layer Measurements

It is an unfortunate consequence of the laws of heat transfer that when a heated element is positioned close to a solid surface, an increase in heat transfer occurs. A correction must therefore be made to the general form of King's law if accurate measurements of the blade surface boundary layers are to be obtained. In the case of a 5 m diameter wire, the effect of wall proximity upon the heat transfer extends to 1-2 mm from the surface so that the effects of wall proximity are present in many measurements.

The still-air correction technique is the most commonly used. It involves the measurement of the heat transfer from the wire to the blade surface in still air at the various locations encountered in the experiment. The heat transfer is proportional to the square of the bridge output voltage, E0

2 in still air. The general form of King's law equation is then modified to give

E2 - A2 - [E02(y) - E0

2()] = B Un……Eqn(4.7)

Where the constants A, k and n have the same values as determined from a free-stream calibration and the term in the square brackets represents the increased heat transfer.