Measurement Technologies in Fluid Mechanics

Transcription

1 Chapter 3 Measurement Technologies in Fluid Mechanics There is need to measure a variety of parameters in fluid flows, including: velocity, pressure, temperature, density, scalar concentrations, sediment (or other suspended particulate) load, wall stress, and many others. Recently much attention has focused on acoustic and optical techniques as they can be considered non-intrusive in many cases. We will look at a subset of technologies available to the experimental fluid dynamicist. We will focus on the current state-of-the-art technologies but we will also try to at least introduce many others. 3.1 Pressure Measurement There are several reasons we are interested in measuring pressure - pressure for its own sake, as a route to determining the velocity, as a route to determining particulate concentration and even diameter, and as a method for determining distancetoobjects. The Navier-Stokes equations (the conservation of momentum in a fluid) are stated in four dynamic quantities: three components of the velocity and the pressure. Most of you have 1

2 2 Measurement Technologies in Fluid Mechanics encountered determining the steady-state velocity (usually a mean velocity) through determining the static and stagnation pressures with a Pitot-static tube. (depicted below). AvariantofthePitot-statictubeusefulfordeterminingthewallshearstressisthe Preston tube (Preston, J.H., 1954; Patel, V.C., 1965) which essentially is a Pitot-static system mounted at a wall. The Pitot-static and Preston tubes are examples of the using pressure as a means to determining some other quantity of interest. We are also interested in measuring the pressure directly, either to study the spatial pressure field (reallythepressuregradient field) as a forcing of fluid motion or to look at fluid flow generated forces on objects (e.g., wind-loading on a structure or wave loading on a piling). It turns out in both cases we will rely on the same fundamental methods for measuring the pressure - namely we will use a device that converts the pressure to a voltage which can in turn be sampled by acomputer suchadeviceisknownasapressuretransducer. Let s take a quick look at the three fundamental types of pressure transducers: capacitance type, piezoelectric type, and strain-gauge type pressure transducers (note we will ignore manometers as pressure measurement devices as they generally rely on human inspectionforareading as opposed to being sampled by a computer). Capacitor-Type Pressure Transducers We are all quite familiar with the capacitor-type pressure transducer as the standard microphone falls under this category. Conceptually the capacitor-type pressure transducer

3 Measurement Technologies in Fluid Mechanics 3 is quite simple. A membrane is suspended above a rigid back plate. As the pressure changes on the membrane it deflects changing the distance between the membrane and the back plate and hence the capacitance changes. If a constant bias voltage is applied across the membrane and the back plate a constant charge is maintained on the capacitor. Achangeinpressureinducesachangeincapacitancewhichinturn induces a change in the voltage. This voltage can be amplified and calibrated to convert from volts to units of pressure. Strain Gauge Pressure Transducers Similar to a capacitor-type pressure transducer a strain-gauge type pressure transducer is diaphragm based. A strain gauge, or likely multiple strain gauges, ismountedtothe diaphragm. When the diaphragm deflects the diaphragm undergoes a strain which is converted by the strain gauge to a voltage which can be calibrated to pressure. Strain gauge type pressure transducers are perhaps the most widely used transducers for the measurement of pressure as they balance economy and accuracy. Piezoelectric-Type Pressure Transducers Piezoelectric-type pressure transducers have great advantage for fluid mechanics measurements in that they are reversible (in contrast to the previous two types). This means they can not only respond to pressure fluctuations but generate or transmit them as well. We will see in a moment that this capability is taken advantageoftotransmitandreceive acoustic waves. Piezoelectric materials are crystals that produce an electric field when they experience a force (pressure over their surface). Conversely, if an electric field is applied to a piezoelectric crystal the crystal will deform. Thus a piezoelectric transducer can act both as an acoustic transducer and receiver. Manufacturers of various pressure transducers suitable foravarietyofapplications include Paroscientific, Inc ( and Druck ( Industrial suppliers of pressure transducers include Omega Engineering, Inc. (

4 4 Measurement Technologies in Fluid Mechanics 3.2 Acoustic Doppler Velocimetry - ADV We will start our look at specific instrumentation with acoustic Doppler velocimeters as they offer the fluid measurement community a superb balance of robust technology at modest cost. Acoustic Doppler velocimetry (ADV) technology existsforbothairand water. Examples of an air system include Doppler anemometers (e.g., also known as ultrasonic anemometers (e.g., We will restrict our conversation to water based systems but the arguments are easily generalized to other fluids. If a piezoelectric transducer is mounted in a housing such that it is in contact with water and is free to translate or vibrate in response to an acousticpressurefieldit can be used to ping or send out a sound wave and then listen for any of the acoustic energy to return. Of course if the acoustic ping bounces of asolidfixedsurfaceand reflects back to the transducer the signal will have the identical frequency as the original ping. The elapsed time from ping creation to ping return can be measuredandassuming the water is constant density and the reflecting surface is rigid the distance of the surface from the transducer can be determined based on the speed of sound through water. Now, if there are scatterers in the water small particles either intentionally seeded into the flow or naturally occurring (e.g., sediment, bubbles, phytoplankton) then they too will scatter acoustic energy back toward the transducer. However, if the particles are moving relative to the transducer - particle path line, the particles will impose a Doppler shift on the acoustic wave. This Doppler shift is linearly proportional to the velocity of the particle with respect to the transducer - particle path line. Thus if the Doppler shift can be determined the particle velocity can be calculated. For now we will assume that particles are passive tracers that is we will assume that their trajectories accurately reflect the local fluid velocity. For the types of particles used in laboratory acoustic applications, nearly neutrally buoyant particles with diameters in the 10 µmrange,thisisaverygoodassumption. Wewilldiscussparticles in more detail later in the course and include the potential for particles to haveaslipvelocity thatis for particles to no longer passively follow the flow.

5 Measurement Technologies in Fluid Mechanics 5 When working with acoustic systems there are two fundamental modesofoperation, monostatic and bistatic. Monostatic systems use a single transducer to ping and to listen for acoustic returns. This is possible due to the time lag expected between the ping and the time window when listening will be required. Fromahardwarepointof view this is attractive as the transducer is optimally oriented to listen for an acoustic return and there are no alignment issues. Depending on your point of view the monostatic systems have an advantage or limitation in that they listen over the entire acoustic path. That is if particles occur anywhere over the acoustic path they will scatter acoustic energy back at the transducer. This allows either an integral pictureofthevelocity along the path (an estimate of the mean velocity) or, if only discrete windows in time are sampled during the listening portion then just the portion of the acoustic path that is located one-half the time lag from ping to listen window times the speed of sound is sampled. This is known as range gating and is the mode of operation in an acoustic Doppler current profilers (ADCP). The disadvantage of monostatic systems is that even with range gating the smallest region in space that can be sampled is relatively large and hence the measured velocities have been averaged over some non-trivial length scale making it impossible to obtain small scale (high frequency) measurements. This limit renders such technology challenging to use for the study of turbulence. That said there are clever statistical approaches that can be used to extract someinformationonthe turbulence from such instrumentation. As an example, Stacey etal. (1999)developed avariancebasedapproachtogainstochasticinsightintothevariancestructureofthe velocities (turbulence intensities and Reynolds Stresses) measuredusingacousticdoppler current profilers see Stacey, M.T.; Monismith, S.G.; Burau, J.R.(1999) Measurements of Reynolds stress profiles in unstratified tidal flow J. Geophys. Res. Oceans 104(C5), The bistatic mode of operation requires two transducers, a transmitter and a receiver. This is somewhat more challenging to implement in hardware as thereceivermustbe aligned properly (focused in an analogy to optics) with respect to the transmitter. The advantage is that for two narrow-banded acoustic transducers a fairly small region in

6 6 Measurement Technologies in Fluid Mechanics space can be sampled for Doppler shifted frequencies and hence a point measurement of the velocity can be measured. The acoustic Doppler velocimeter (ADV) is an example of a bistatic acoustic device. Let s look more closely at a typical ADV. Consider a single bistatic system with a bistatic axis - defined as the straight line bisecting the line between the transmitter and the intersection of the transmitter acoustic path and the receiver acoustic path and the line between the receiver and the intersection of the transmitter acoustic path and the receiver acoustic path. The figures below (taken from the - Sontek is one of several commercial ADVmanufacturers and the manufacturer of one of the ADVs you will have access to in this class, Nortek ( is the manufacturer of the other ADVs to whichyouwillhave access) illustrates the bistatic axis and the transmit, scatter, and receive portions of the acoustic signal propagation. The transmitter and receiver are narrow band acoustic transducers. This essentially means that they can transmit and receive acoustic energy in a region defined by a narrow cone emanating from the transducer. The intersection of these two cones defines the sample volume. The transmitter is controlled to generate a short acoustic pulse at a known frequency. The pulse travels through the water at the speed of sound arriving at

7 Measurement Technologies in Fluid Mechanics 7 the sample volume some fixed time later. In the sample volume the small particles scatter some portion of the acoustic energy in all directions. A small portion of this energy is scattered back along the receiver axis where the receiver detects the acoustic energy. The frequency of the acoustic pulse arriving at the receiver has been Doppler shifted by the particles motion relative to the bistatic axis. The receiver records a voltage signal which contains the Doppler shift frequency. This voltage is sampled and the Doppler shift frequency, f d,canbedeterminedinanumberofwaysincludingensemblespectral techniques. The velocity along the bistatic axis, u bs,canthenbefoundfrom u bs = C w 2 f d f t (3.1) where C w is the speed of sound in water and f t is the frequency of the transmit pulse. Note that the bistatic axis is positive going towards the intersection of the transmitter and receiver axis. By using multiple bistatic axes the components of velocity ina2-dplaneorin full3-dcan be determined. An example of a 3-D probe (again from is shown on the following page. The system is composed of a single transmitter and three receivers. Each of the three bistatic axis resolves a component of the velocity along the transmitter axis

8 8 Measurement Technologies in Fluid Mechanics and a component of the velocity in the plane of the receivers (along the axes between the transmitter and the receivers). Thus the component along thetransmitteraxisis measured at three locations and portions of the orthogonal in-receiver-plane components are sampled at two or three locations depending on how the axis aredefined ADV Geometry We may work with either a Sontek 10 MHz Lab ADV or a 10 MHz Nortek Vectrino + probe (actually a 4-receiver version of an ADV). The Sontek probe has its sampling volume located approximately 5 cm from the sampling head and the receivers bounded within a circle of diameter 7.7 cm. Thusthebistatic

9 Measurement Technologies in Fluid Mechanics 9 axis is inclined relative to the transmitter axis by tan 1 (1.7/5) 20 where I have assumed that the center of the receiver lies on a circle with approximately 7 cm diameter (recall that the bistatic axis is located halfway along the radius hence at one-quarter the diameter, or 1.7 cm). Sontek defines one of the three receivers as the x coordinate (marked by a red tip) and the z coordinate is defined along the transmitter axis (perpendicular to the plane of the receivers) with the positive direction into the transmitter (up the probe shaft). The y coordinate is found by the right-hand-rule and clearly lies twothirds the way between the two remaining (e.g., not x-defined) receivers. If we look at the trigonometric conversion of the bistatic velocity components to Cartesian velocity components we find [ u = ξ 1 ξ 2 + ξ 3 cos π ] sin θ (3.2) 2 3 [ ξ2 ξ 3 v = sin π ] sin θ (3.3) 2 3 [ ] ξ1 + ξ 2 + ξ 3 w = cos θ (3.4) 3 where ξ 1 is the bistatic velocity (velocity along the bistatic axis, commonly referred to as teh beam velocity) withapurex-component in the x y plane, ξ 2, ξ 3 are the right-handrule sequentially encountered bistatic or beam velocities, θ is the 20 angle subtended by the z axis and the three bistatic axes, and the π/3 anglearisesfromthegeometryof the three receivers which are all 120 apart in the x y plane. Now, looking at u and arbitrary setting the beam velocity strengths to a magnitude of 100 we see that ξ 1 contributes sin(π/9) 100 = 34 of the signal and ξ 2 and ξ 3 each contribute cos(π/3) sin(π/9) 100 = 17 for a total signal content of 68. Looking at v we see that ξ 2 and ξ 3 each contribute sin(π/3) sin(π/9) 100 = 30 for a total signal content of 59. Finally, looking at z we see that each beam contributes cos(π/9) 100 = 94 for a total signal content of 282. Normalizing by the w component signal content we see that the u component has only about 24% of the signal content of w and the v component has only about 21% of the signal component of w. Thus if you are interested in accuracy in the instantaneous

10 10 Measurement Technologies in Fluid Mechanics measurements in a particular direction the goal is to use the ADV defined z coordinate in that direction. Thedilemma,however,isthatiftheflowisinthez direction the probe is then in its most intrusive position as the flow will have either just impacted the probe head or be about to impact the probe head. Hence, it is not common to mount an ADV with z in the dominant flow direction, even if this velocity is the principal velocity of interest. The above description of estimating the velocity is actually adescriptionofincoherent processing, inwhichasinglepingisusedtoestimatethevelocityandthese pings can be fired at essentially arbitrary time separation. It turns out that this is not actually how the ADV estimates the velocity, but it is one of the modes of operation of ADCPs, also referred to as acoustic Doppler profilers (ADPs), as mentioned above, these are range gated instruments that can calculate the velocity along a beam. Instead ADVs use a more accurate technique known as pulse-coherent processing which involves sending two pings, separated by a short lag in time, and determining the change in position (phase) of the ensemble of particles in the measurement volume between the two pings (problem set #1, problem 3 is exactly analogous). This is a more accurate (less noisy) measurement of the velocity than single-ping incoherent analysis. To further reduce the noise levels the ADV ensemble averages individual measurements and reports this ensemble average at ausersetrate.therateatwhichitcansampleisdeterminedbythelengthoftheping. Note that the travel time for a ping, the time it takes a ping to travel to the sampling volume and be scattered back (after scattering) to a receiver adistanceofjustover10 cm in the case of a 5 cm probe is set by the speed of sound through water. Forfresh water the speed of sound is approximately 1480 m/s at 20 C. Thus for a 5 cm probe there is a travel time of only about 70 µs. The length of the ping is determined by the design of the probe. The tradeoffs are shorter pings will have lower signal to noise ratio while longer pings will mean that fewer pings can be ensembled toreducethenoiseto an equivalent level. The Sontek ADV 10 Mhz probe is set up to ping times per second. This is fixed. The maximum recommended sampling rate is 25 Hz. Hence the probe hardware ensemble averages the results of all pings arriving over a 40 ms window in

11 Measurement Technologies in Fluid Mechanics 11 time and reports the mean as the instantaneous velocity at this time. If the user chooses to slow the sampling rate down the reported velocities will be basedonalargerensemble and hence the result will have reduced noise levels. The Sontek recommendation for 25 Hz maximum sample rates is based on an accuracy of 1% of the velocity range at 25 Hz. Let s now contrast the Sontek probe (which is one of the original generation of ADVs) with the more recently released Nortek Vectrino + probe. Like the Sontek the Nortek has its sampling volume located approximately 5 cm from the sampling head but the Nortek uses 4 receivers mounted in two orthogonal pairs (see web page for a link to the Nortek Vectrino Manual) each at an angle of 30 to the probe axis hence the bistatic axis is inclined about 15 from this axis. Nortek defines one of the four receivers as the x coordinate (marked by a red tip) and the z coordinate is defined along the transmitter axis (perpendicular to the plane of the receivers) with the positive direction into the transmitter (up the probe shaft). The y coordinate is found by the right-hand-rule and lies in the direction of the probe arm to the left of the x probe looking down the probe shaft. If we look at the trigonometric conversion of the bistatic velocity components to Cartesian velocity components we find [ ] ξ1 ξ 3 u = sin θ (3.5) 2 [ ] ξ2 ξ 4 v = sin θ (3.6) 2 [ ] ξ1 + ξ 3 w 1 = cos θ (3.7) 2 [ ] ξ2 + ξ 4 w 2 = cos θ (3.8) 2 where ξ 1 is the bistatic velocity (beam velocity) which is in the +x-direction, ξ 2 is the bistatic velocity in the +y-direction, ξ 3 is the bistatic velocity in the x-direction, and ξ 4 is the bistatic velocity in the y-direction. Note the direction of encounter of each beam follows the right-hand-rule from the +x axis. θ is the 15 angle subtended by the z axis and the four bistatic axes, and the denominators of 2 arise from the averaging of the 2 measurements in each of the beam pairs. The Vectrino is reallytwoorthogonal 2-D measurement systems that each measure the vertical velocity and one orthogonal

12 12 Measurement Technologies in Fluid Mechanics horizontal component. Thus the Vectrino independently measures the vertical velocity twice (reported above as w 1 and w 2 and in the Vectrino software as Z1 andz2) as well as independently measuring the two horizontal components. Again arbitrarily setting the bistatic velocities to 100, looking at the horizontal plane we see that we have 2 measurements that contain a signal of strength sin θ 100 = 26 whereas the vertical component contains 4 measurements of strength cos θ 100 = 97. Thus the vertical component has 2 97/(2 26) = 3.7 timesasmuchinformationasthehorizontal components. Hence, as we found with the Sontek, if you are interested in accuracy in the instantaneous measurements in a particular direction thegoalistousetheadv defined z coordinate in that direction. NotablytheNortekhaslesssignalcontentthen the Sontek in the horizontal plane (due to the more acute bistatic angle) while having more signal content in the vertical. Also, we have a second measurement of the vertical velocity. More on the use of this second velocity shortly. The Nortek Vectrino with the + software option samples at 200-5,000Hzandthen reports an average at a maximum of 200 Hz. The user can customize the sampling rate as the software just bins the internally sampled data and, as with the Sontek, slower sampling rates will yield lower noise as more pings are used in theensemblethatis reported as the instantaneous velocity; this of course also smooths out high frequency details of the flow which may be of interest Signal-to-Noise (SNR) Ratio An important parameter when working with ADVs is the signal strength. The signal strength is reported as a signal-to-noise ratio (SNR) and is defined as the ratio of the scattered acoustic energy to the electronic noise level of the instrument (e.g., the acoustic energy registered by the ADV when no ping is present at the receiver). The SNR is reported generally in decibels (db), and is defined as: SNR = 20 log 10 amplitude signal+noise amplitude noise (3.9)

13 Measurement Technologies in Fluid Mechanics 13 To obtain reasonable estimates of mean velocity (say at leasta10saverage)ansnr of 5 db is the minimum recommended by Sontek and if one is to have confidenceinthe individually reported velocities (recall that they are the ensemble average of a number of pings), and hence turbulence quantities, an SNR of 15 db is the minimumrecommended by Sontek. To get a better feel for SNR let s look at two plots of thesignalstrength recorded at the receivers by the Sontek ADV we have in the lab. Signal strength (counts*0.45 = db) Beam 1 Beam 2 Beam Time/Distance The first figure is the signal strength received in relatively clean water - e.g., no scatterers. The second figure is the signal strength received in the presence of scatterers. The ADV processing algorithm takes advantage of a bit of user supplied knowledge about the flow under study to improve the noise level of the measurement. The user is required to input a velocity range to operate the instrument. This determines the exact shape of apingaswellasparametersinthesignalprocessingusedtoextract the Doppler shift. The noise level is tied to the overall velocity range and increases with velocity range. Hence, in general, measurements made at the same velocity at ahighervelocityrange will be nosier than measurements made at lower velocity ranges. Thus the goal is to make the measurement with the minimum required velocity range to achieve minimum

14 14 Measurement Technologies in Fluid Mechanics Signal strength (counts*0.45 = db) Beam 1 Beam 2 Beam Time/Distance measurement noise. Note that the indicated ranges in software are approximate (they are roughly the maximum bistatic velocity ranges) as the maximum velocity magnitude in the z direction is approximately four times smaller than the maximum in the x y plane (again, due to the geometry). For example, selecting a range of ±10 cm/s results in a maximum velocity in the z direction of ±15 cm/s while the maximum velocity in the x y plane is ±60 cm/s. For the Nortek the relationship is a bit more complex, apparently, but the good news is Nortek software reports the actual maximum horizontal and vertical velocities for a given nominal velocity range in the software Velocity Range and Pulse-Coherent Processing When selecting a velocity range you are really selecting a time lag between the two coherent pulses. Lower velocity ranges have longer time lagstoallowtheparticlesto move the same fixed distance (some fraction of the measurement volumesize,discussed

15 Measurement Technologies in Fluid Mechanics 15 shortly) and higher velocity ranges will have shorter time lags to keep the particles within the measurement volume. As we have already seen, a very fast way to estimate how far the particles have moved is to correlate two signals and to cary out the calculation as a periodic correlation based on the FFT. The location of the correlation peak tells us how far the particles have moved. If we think of the correlation as periodicandrangingover [ π, π] thenweseethatthemaximumvelocityisfoundbydeterminingthedisplacement as a phase, applying a calibration to convert from phase to distance, and dividing by the time lag between pulses to get the velocity. This understanding of pulse-coherent processing leads us to twoimportantconclusions: (1) it is possible to get a phase ambiguity and (2) strong local shear(e.g.,turbulence) can lead to a decorrelation hindering our analysis. Exploring the first point further we see that there is a wrap-around effect or ambiguity jump if a velocity within the measurement volume exceeds the maximum determinable velocity of a given velocity range. The velocity is determined as a phase angle between 180 and 180. Thus if a velocity in the measurement volume is outside the velocity range a phase with magnitude greater than 180 will be induced. However, the signal analysis routines will alias this shift into the range. The determined velocity will wrap around the range, much like our previous discussion of aliasing. If the velocity is less than 2 times the maximum measurable velocity based on the velocity range setting (which is usually the case if the range has been set appropriately) then the determined velocity will have opposite sign of its expected value and a very clear discontinuity in velocity will occur (hence the term ambiguity jump). These occurrences can general be removed easily, either byinspectionor asignalprocessingroutine. Athirdpartypost-processingsoftware with this capability is WinADV ( lab/twahl/winadv/), written by Tony L. Wahl of the U.S. Bureau of Reclamation. An example of aliasing (taken from the WinADV manual) is shown onthenextpage. The velocity is seen to rise at t =24sandthenallofasuddenjumptoanegativestrong velocity. Actually the velocity has just increased a little bit further but in phase space it has gone to something like 185 which is aliased to 175.Thevelocityremainsatthis

16 16 Measurement Technologies in Fluid Mechanics value for a while but occasionally drops four times between t =50sandt =60sand we see the four spikes back to positive velocity. This would be easytofixasitisobvious what is happening. Now let s consider the effects of strong local shear on ADV measurements. ADV software typically reports two parameters in real-time to characterize the quality of the acoustic signal of each axis: SNR and Correlation. SNR is the value just describedabove. Correlation is a measure of the strength of the cross-correlation peak used to determine the Doppler shift, reported as a normalized correlation coefficient in percent. A value of 100% (equivalent to ρ ab =1)isanoptimalsignalinthatthereisaperfectcorrelationofthe first acoustic (a) returnwiththesecondacousticreturn(b) meaningthattheparticles are in exactly the same position with respect to each other and thepingsdidnotsuffer any degradation due to encountering other particles along their acoustic path. In general values greater than 70% are considered to indicated good measurement conditions and suitable for making turbulence measurements. Why might the value be below this? The SNR may be low (usually an indication of poor particle seeding), the probe may be out of the water, there may be bubbles or scum on the acoustic transducers, or bubbles or other large scatterers in the measurement volume, etc. So the firststepuponseeinglow correlation is to check the SNR. If it is low, wipe the probe tips of any bubbles (gently!) and ensure that the probe is submerged in the water. If it is still low you likely need to increase the seeding density.

17 Measurement Technologies in Fluid Mechanics 17 ADVs are measurement devices used frequently in the field where naturally occurring seed particles are relied upon. In the lab we generally need to seed thewaterandthisistypically done with neutrally buoyant particles in the 10 µmrange. Anexcellentparticlethat meets these criteria is Sphericel ( manufactured by the PQ Corporation ( These are an industrial grade particle with a price in the $1/pound range. We have recently been using a new industrial particle, Orgasol, manufactured by Arkema ( This is a nylon particle with narrow diameter ranges centered approximatelyaround5, 10, 20, 30, 40, 50, and 60 µm. The cost is about an order of magnitude higher but that is still pretty cheap! We like them when we need larger particles. Now, after doing all of the above frequently we will see the SNR andcorrelationvalue jump up to acceptable ranges. However, we may have an excellent SNR and still low correlation, why? Local shear. Recall that the correlation is perfect if the particles in the measurement volume simply translate to a new position. However, due to mean shear (e.g., in a boundary layer) or turbulence these particles generally move with respect to each other. The further they move with respect to each other theweakertheywill correlate with each other. Consider the following example: Now, both turbulence and shear require time to move the particles with respect to each other hence we can reduce the decorrelation of the signal by shortening the time lag between the coherent pulses (i.e., increase the velocity range). If shear is the cause of poor correlation values this will improve the correlation. As described above this works against the noise character of the instrument, however, shear is a stronger source of noise

18 18 Measurement Technologies in Fluid Mechanics so the rule of thumb is to shorten the lag to get the correlation over70%ifthishelps. Note that the poor correlation induced errors (noise) in the measurements are uniformly randomly distributed across phase and hence they only weakly biasthemeanvelocity (noise has a mean of zero so if your flow has a near zero mean velocity then there is no bias but if it has a non-zero mean flow then the magnitude of the mean is biased low). Thus if your only interest is mean velocities then working at correlation values as low as 30% may produce acceptable results Sampling Volume The sampling volume size in any instrument is important to understand as this sets the spatial region over which the reported value is being averaged over. Hence it is impossible to measure spatial structure at scales smaller than the sampling volume size. ADVs have relatively large sampling volume sizes in comparison with other laboratory state-of-the-art measurement techniques. That said the measurement volume size is still small. The Sontek ADV we work with has a measurement volume size that is about 6.0 mm in diameter (set by the diameter of the transmitter) with a height of 7.2 mm (set based on desired data averaging needs). The result is a volume of0.20cm 3. Note that the height of the measurement volume, measured along the z axis, is set by the need to receive multiple pings to be able to report an average velocity at the requested data rate, insuring 1% accuracy. If the user is willing to forgo this averaging the ping length can be modified to reduce the sample volume height to as little as 1.2 mm with a resultant increase in noise level (adjusted with low-level controls). In fact, the Nortek Vectrino we will work with for Lab #1 allows usercontrolover the vertical extent of the measurement volume. The vertical extent of the measurement volume is set by two parameters: The length of time the instrument listens and the length of the transmitted pulse. The Vectrino allows you to set the length of the transmitted pulse and the total sampling volume (which is actually the length of over which the

19 Measurement Technologies in Fluid Mechanics 19 instrument listens + 2 times the transmitted pulse length). AfinalconsiderationwhenworkingwithADVsistheirabilityto measure near boundaries. If care is taken measurements can be made with the maximum extent of the measurement volume one-half the distance above a boundary (hence order 1 mm for the Nortek Vectrino). Note that if the boundary is a solid smooth surface a thin piece of acoustically damping material may need to be placed on the boundary to absorb some of the energy or the instrument may not function properly. Alternatively, as described below, the energy of the acoustic ping can be reduced) Other Control/Configuration Parameters The Nortek line of instruments allows the user to set the acoustic ping level. In general we will work at the highest ping level (HIGH + in the Vectrino) but in regions with strong scatterers or boundary returns it may be worth going to lowerlevels. Forbattery deployments this saves battery life as well. We will collect our data in traditional Cartesian coordinates but ADVs can generally be configured to store the original bi-statatic axis measurements allowing the user to do the coordinate transform later. This can be valuable if you have reason to believe one of the beams may be affected by the deployment configuration (shape of bottom boundary, instrument frame partially affecting one beam, etc). For more detail on ADVs see the Nortek Vectrino manual on the course website on the /handouts link. You will be given a chance to play with all of these aspects during the first laboratory exercise.

20 20 Measurement Technologies in Fluid Mechanics Acoustic Scattering Acoustic scattering is a function of particle diameter and sound speed. Below is a plot for fresh water at 20C. As you can see, for particles below an optimal size, the scattering efficiency decays as 10 3whileforparticleswithadiameterabovetheoptimalsize, scattering efficiency decays as 10 1, hence it pays to error towards larger particles in general. Optimal scattering occurs at a particle diameter = λ/(2π) whereλ is the acoustic wavelength. For a 10 Mhz sound wave (λ =148micron VectrinoandSontek ADVs) at 20C this yields a particle with diameter of 24 micron. Thuslowerfrequencies are more sensitive to larger particles. Note that acoustic energy at lower frequencies decays more slowly than that at higher frequencies so lower frequency systems are used when interested in making measurements over larger distances Relative Sensitivity khz 1200 khz 6 Mhz 10 Mhz Partilce diameter (mm)