The MEMS Handbook MEMS Applications (2nd Ed) - M. Gad el Hak Episode 1 Part 8 docx

constant-If a laminar flow facility is used to calibrate the wall-shear-stress sensor, then Equation 6.43 can be written more conveniently in time-averaged form: re-τ苶w苶1/3 Ae–2 where τ苶

average of Equation 6.50 over a large number of cycles and assuming that the turbulent fluctuations aresmall, a linearized expression for the periodic wall-shear stress is obtained.

To summarize, the classical expression, Equation 6.43, gives a relation between the wall-shear stress andthe heat transfer from the wall This expression assumes steady, laminar, zero-pressure-gradient flow, and isnot valid in a turbulent environment Menendez and Ramaprian (1985) have derived an extended version

of Equation 6.43 valid for a periodically fluctuating freestream velocity, Equation 6.50 However, the ter relation contains some assumptions that are questionable for turbulent flows For instance, in thethermal boundary layer it is assumed that the temperature distribution is self-similar and that the localthickness varies linearly These assumptions are relevant for a streamwise velocity oscillation and a weakfluctuation, but certainly not in a turbulent flow, which is strongly unstable in all directions

lat-6.4.3.3 Calibration

Several methods and formulas are in use for calibrating hot-film shear probes operated in the temperature mode and the choice of method depends on flow conditions and sensor used In this subsub-section, two static calibration methods are discussed Both are based on the theoretical analysis leading tothe relation between rate of heat transfer and wall-shear stress, as discussed in the last subsubsection Thechallenge is of course to be able to use the shear-stress sensor in a turbulent environment

constant-If a laminar flow facility is used to calibrate the wall-shear-stress sensor, then Equation 6.43 can be written more conveniently in time-averaged form:

re-τ苶w苶1/3 Ae–2

where τ苶苶 is the desired mean wall-shear stress, e w –2

is the square of the mean output voltage, and A and B are calibration constants The term B represents the heat loss to the substrate in a quiescent surrounding, and

this procedure is similar to a conventional calibration of a hot-wire [King, 1916] However, a laminar flow isoften difficult to realize in the desired range of turbulence wall-shear stress: it is more practical to calibratewithout moving the sensor between calibration site and measurement site In that case, the calibration ismade in a high-turbulence environment and the high-order moments of the voltage must also be considered.Ramaprian and Tu (1983) proposed an improved calibration method, and the instantaneous version

of Equation 6.54, can be re-written and time averaged to give:

where M is the number of calibration points and N is the order of the polynomial above A system of linear

equations is obtained where the calibration coefficients can be computed by a numerical least-square method.For example, the mean wall-shear stress on the left-hand side of Equation 6.57 can be measured with aPreston tube using the method of Patel (1965) The second calibration technique described here is called

“stochastic” calibration by Breuer (1995), who also demonstrated that the validity of the calibration nomial may extend well beyond the original calibration range, although this requires careful determination

poly-of the higher-order statistics as well as a thorough understanding poly-of the sensor response function.The experiments of Bremhorst and Gilmore (1976) showed that the static and dynamic calibration coef-ficients for hot-wires agree to within a standard error of 3% for the velocity range of 3–32 m/s Thus, they

recommend the continued use of static calibration for dynamic measurements As pointed out in previoussection, this is not true for a wall-mounted hot-film One solution to this problem may be to calibrate the

hot-film in pulsatile laminar flow with a periodic freestream velocity U a (t), and make use of the Menendez

and Ramaprian’s formula, Equation 6.50:

τ苶w 苶  (Ae–2

to obtain the additional calibration constants c1and c2 This step is necessary in order to characterize the

gauge dynamic response at relatively high frequencies The constants A and B are obtained from a

steady-state calibration

A difficulty in performing a dynamic calibration is to generate a known sinusoidal wall-shear stress input.Bellhouse and Rasmussen (1968) and Bellhouse and Schultz (1966) achieved this in two different ways.One method is to mount the hot-film on a plate which can be oscillated at various known frequenciesand amplitudes The main drawback to this arrangement is the limited amplitudes and frequencies thatcan be achieved when attempting to vibrate a relatively heavy structure An alternative strategy is to gen-erate the shear stress variations by superimposing a monochromatic sound field of different frequencies

on a steady, laminar flow field A hot-wire close to the wall can be used as a reference

By assuming a stepwise temperature variation and introducing the average heat flux q苶 W苶 over the heated

area which is assumed to have a streamwise length L, the desired relation reads:

where Nu — is the Nusselt number averaged over the heated area, Lis the streamwise length of the heated area

normalized with the viscous length-scale v/uτ, and h cis the convective heat transfer coefficient This tion has been derived for flows with pressure gradient by Brown (1967) The dimensionless sensor length

equa-Lis a crucial parameter when examining the assumptions made

The lower limit on Lis imposed by the boundary-layer approximation since there is an abrupt change oftemperature close to the leading and trailing edge zones of the heated strip where the neglected diffusiveterms in Equation 6.45 become significant Tardu et al (1991) have conducted a numerical simulation ofthe heat transfer from a hot-film, and found a peak of the local heat transfer at the leading and trailingedges They conclude that if the hot-film is too narrow, the heat transfer would be completely dominated

by these edge effects Ling (1963) has studied the same problem in a numerical investigation, and concludesthat the diffusion in the streamwise direction can be neglected if the Péclet number is larger than 5000.(The Péclet number here is defined as the ratio of heat transported by convection and by molecular diffusion,

Pe  PrL2, [Brodkey, 1967]) Pedley (1972) concludes that, provided 0.5 Pe0.5 x/L  (1  0.7Pe0.5),there exists a central part of the hot-film where the boundary-layer solution predicts the heat transfer within5%.Figure 6.20 shows the relation proposed by Pedley (1972); it can be seen that the heat transfer is cor-rectly described over a large part of the hot-film area, but as the Péclet number decreases, the influence

from the diffusive terms must be considered For Péclet numbers larger than 40, the heat transfer is correctlydescribed by more than 80% of the heated area.

The upper limit of Lis crucial since there the hot-film thermal boundary layer may not be entirely merged in the viscous sublayer Equation 6.58 has been included in Figure 6.20, and it can be seen thatPéclet numbers larger than 40 correspond approximately to τ苶w苶1/3
0.95 A relatively simple calculation

sub-of the upper limit sub-of L can then be made by assuming that the viscous sublayer is about five viscous

units, which yields an upper limit of Lwhich for air can be estimated to be approximately 47

It can be concluded that the streamwise extent of the hot-film cannot be too small, otherwise the boundary-layer approximations made are not applicable On the other hand, a sensor that is too large willcause the thermal boundary layer to grow beyond the viscous region Additionally, the spatial resolutionwill be adversely affected if the sensor is too large, since the smallest eddies imposed by the flow struc-tures above the wall will then be integrated along the sensor length

6.4.3.5 Temporal Resolution

The temporal resolution of the thermal probe is affected by the different time-constants of the hot-film andthe substrate The hot-film usually has a much shorter time-constant than the substrate The higher the per-centage of the total heat that leaks into the substrate, the lower is the sensitivity of the device to shear-stressfluctuations; this changes the sensor characteristics sufficiently to invalidate the static calibration An exam-ple of this phenomenon is given by Haritonidis (1989), who showed that a hot-film sensor in a fluctuatingwall-shear stress environment will respond quickly to the instantaneous shear stress, while the substratewill react slowly due to its much larger thermal inertia Haritonidis (1989) also showed that the ratio of

the fluctuating sensitivity, S f , to the average sensitivity, S a, can be related to the ratio of the effectivelengths under dynamic and static conditions:

冢 冣2/3

where L a is the average effective length during static calibration and L f is the effective length duringdynamic calibration Due to this, the hot-film becomes less sensitive to shear-stress fluctuations at higherfrequencies and the static calibration in a laminar flow will not give a correct result These length-scalescan be considerably larger than the probe true extent For example, Brown (1967) reported that the effec-tive length-scale from a static calibration was about twice the physical length

0.6 0.8 1 1.2 1.4

FIGURE 6.20 Pedley’s (1972) relation showing the region of validity of the boundary-layer solution as a function

of Péclet number In the area in between the two continuous curves, the boundary-layer approximation predicts the heat transfer accurately to within 5% of the correct value.

Both the substrate material and the amount of heat that is lost to the substrate are crucial when mining the temporal or frequency response of the hot-film sensor At low frequencies, the thermal wavesthrough the substrate and into the fluid are quasi-static, which means that the fluctuating sensitivity of thehot-film is determined by the first derivative of the static calibration curve In this range, on the order of

deter-a couple of cycles per second, the hedeter-at trdeter-ansfer through the substrdeter-ate responds without time ldeter-ag to wdeter-all-shedeter-arstress fluctuations Basically, this frequency range does not cause any major problems

For the high-frequency range at the other end of the spectrum, it is possible to estimate the substraterole by considering the propagation of heat waves through a semi-infinite solid slab subjected to periodictemperature fluctuations at one end This has been reported by Blackwelder (1981), who compared the wave-length of the heat wave to the hot-film length He showed that the amplitude of the thermal wave wouldattenuate to a fraction of a percent over a distance equal to its wavelength A relevant quantity to consider

in this context turned out to be the ratio of the wavelength to the length of the substrate since this is anindication of the extent to which the substrate will partly absorb heat from the heated surface and partlyreturn it to the flow Haritonidis (1989) computed this ratio for a number of fluids and films and con-cluded that at high frequencies the substrate would not participate in the heat transfer process However,this conclusion should be viewed with some caution because the frequencies studied were the highest thatcould be expected in a wall flow

The most difficult problem occurs for frequencies in the intermediate range, resulting in a clear strate influence and an associated deviation from the static calibration Hanratty and Campbell (1996)showed that damping by the thermal boundary layer for pipe flow turbulence is important when:

For Pr  0.72, this requires the dimensionless length in the streamwise direction, L, to be less than 90 Forturbulence applications, this is most disturbing since it is in this frequency range where the most ener-getic eddies are situated The primary conclusion from this discussion is that all wall-shear stress mea-surements in turbulent flows require dynamical calibration of the hot-film sensor

6.4.3.6 MEMS Thermal Sensors

Kälvesten (1996) and Kälvesten et al (1996b) have developed a MEMS-based, flush-mounted wall-shearstress sensor that relies on the same principle of operation as the micro-velocity sensor presented by Löfdahl

et al (1992) The shear sensor is based on the cooling of a thermally insulated, electrically heated part of

a chip As depicted in Figure 6.21, the heated portion of the chip is relatively small, 300 60 30 µm3, and

is thermally insulated by polyimide-filled, KOH-etched trenches The rectangular top area, with a length to side-length ratio of 5:1, yields a directional sensitivity for the measurements of the two perpen-dicular in-plane components of the fluctuating wall-shear stress Due to the etch properties of KOH, the

side-30 µm-deep, thermally-insulating trenches have sloped walls with a bottom and top width of about side-30 µm.The sensitive part of the chip is electrically heated by a polysilicon piezoresistor and its temperature ismeasured by an integrated diode For the ambient temperature, a reference diode is integrated on the sub-strate chip, far away from the heated portion of the chip (Note that for backup, two hot diodes and twocold diodes are fabricated on the same chip.)

Kälvesten (1996) performed a static wall-shear stress calibration in the boundary layer of a flat plate

A Pitot tube and a Clauser plot were used to determine the time-averaged wall-shear stress The power sumed to maintain the hot part of the sensor at a constant temperature was measured and Figure 6.22 showsthe data for two different probe orientations For a step-wise increase of electrical power, the response timewas about 6 ms, which is double the calculated value This response was considerably shortened to 25 µswhen the sensor was operated in a constant-temperature mode using feedback electronics.Table 6.2 listssome calculated and measured characteristics of the Kälvesten MEMS-based wall-shear stress sensor.Jiang et al (1994; 1996) have developed an array of wall-shear stress sensors based on the thermal princi-ple The primary objective of their experiment was to map and control the low-speed streaks in the wall region

con-of a turbulent channel flow To properly capture the streaks, each sensor was made smaller than a typical streakwidth For a Reynolds number based on the channel half-width and centerline velocity of 104, the streaks areestimated to be about 1 mm in width, so each sensor was designed to have a length less than 300 µm

Figure 6.23 shows a schematic of one of Jiang et al.’s sensors It consists of a diaphragm with a thickness

of 1.2 µm and a side-length of 200 µm The polysilicon resistor wire is located on the diaphragm and is 3 µmwide and 150 µm long Below the diaphragm there is a 2 µm-deep vacuum cavity so that the device willhave a minimal heat conduction loss to the substrate When the wire is heated electrically, heat is trans-ferred to the flow by heat convection resulting in an electrically measurable power change which is a function

of the wall-shear stress.Figure 6.24 shows a photograph of a portion of the 2.85 1.00 cm2streak-imagingchip containing just one probe The sensors were calibrated in a fully-developed channel flow with knownaverage wall-shear stress values.Figure 6.25 depicts the calibration results for 10 sensors in a row The out-put of these sensors is sensitive to the fluid temperature, and the measured data must be compensated forthis effect Measurements of the fluctuating wall-shear stress using the sensor of Jiang et al (1997) havebeen reported by Österlund (1999) and Lindgren et al (2000)

6.4.3.7 Floating-Element Sensors

The floating-element technique is a direct method for sensing skin friction, which means a direct surement of the tangential force exerted by the fluid on a specific portion of the wall The advantage of thismethod is that the wall-shear stress is determined without having to make any assumptions about eitherthe flow field above the device or the transfer function between the wall-shear stress and the measuredquantity The sensing wall-element is connected to a balance which determines the magnitude of the appliedforce Basically two arrangements are distinguished to accomplish this: displacement balance, which is

mea- sensitive diode

Temperature-Electrically heated chip

Aluminum Buried silicon dioxide

Polyimide-filled, KOH-etched trench

Flat plate

Temperature reference diode

Heating resistor

sensitive diode

Temperature-Aluminum (a)

(b)

FIGURE 6.21 Flush-mounted wall-shear stress sensor (a) Top-view; (b) schematic cross-section (Reprinted with permission from Kälvesten, E [1996] “Pressure and Wall Shear Stress Sensors for Turbulence Measurements,” Royal Institute of Technology, TRITA-ILA-9601, Stockholm Sweden.)

w (Pa) 42

43 44 45 46

TABLE 6.2 Some Calculated and Measured Characteristics of the MEMS-based Wall-Shear Stress Sensors Fabricated by Kälvesten et al (1994)

Heated chip top-area, A  w ᐉ (µm2 ) 300 60 1200 600 300 60 1200 600

Thermal conduction conductance, G c(µW/K) 372 510 426 532

Thermal convection conductance, G f(µW/K)

Perpendicular Configuration at 50 m/s 6,7 207 21.0 231

a direct measurement of the distance the wall-element is moved by the wall-shear stress; or null balancewhich is the measurement of the force required to maintain the wall-element at its original position whenactuated on by the wall-shear stress.

The principle of a floating-element balance is shown in Figure 6.26 In spite of the fact that the forcemeasurement is simple, the floating-element principle is afflicted with some severe drawbacks which stronglylimit its use as has been summarized by Winter (1977) It is difficult to choose the relevant size of thewall-element in particular when measuring small forces and in turbulence applications Misalignmentsand the gaps around the element, especially when measuring small forces, are constant sources of uncertaintyand error Effects of pressure gradients, heat transfer, and suction or blowing cause large uncertainties inthe measurements as well If the measurements are conducted in a moving frame of reference, effects of

Diaphragm

Polysilicon thermistor wire

FIGURE 6.24 SEM photo of a single wall-shear stress sensor (Reprinted with permission from Jiang, F., Tai, Y-C, Walsh, K., Tsao, T., Lee, G.B., and Ho, C.-H [1997] “A Flexible MEMS technology and Its First Application to Shear Stress

Skin,” in Proc IEEE MEMS Workshop (MEMS ’97), pp 465–470.)

2.2 2 1.8 1.6 1.4

Mean output voltage (V) 1.2

gravity, acceleration, and large transients can also severely influence the results Haritonidis (1989) cussed the mounting of floating-element balances and errors associated with the gaps and misalignments.

dis-In addition, floating-element balances fabricated with conventional techniques have in general poor quency response and are not suited for measurements of fluctuating wall-shear stress To summarize, theidea of direct force measurements by a floating-element balance is excellent in principle, but all the draw-backs taken together make them difficult and cumbersome to work with in practice It was not until theintroduction of microfabrication in the late 1980s that floating-element force sensors achieved a revital-ized interest in particular for turbulence studies and reactive flow control

fre-6.4.3.8 MEMS Floating-Element Sensors

Schmidt et al (1988) were the first to present a MEMS-based floating-element balance for operation inlow-speed turbulent boundary layers A schematic of their sensor is shown in Figure 6.27 A differentialcapacitive sensing scheme was used to detect the floating element movements The area of the floatingelement used was 500 500 µm2, and it was suspended by four tethers, which acted both as supports andrestoring springs The floating element had a thickness of 30 µm, and was suspended 3 µm above the sil-icon substrate on which it was fabricated The gap on either side of the tethers and between the elementand surrounding surface was 10 µm, while the element top was flush with the surrounding surface within

1 µm The element and its tethers were made of polyimide, and the sensor was designed to have a width of 20 kHz A static calibration of this force gauge indicated linear characteristics, and the sensor wasable to measure a shear stress as low as 1 Pa However, the sensor showed sensitivity to electromagneticinterference due to the high-impedance capacitance used, and drift problems attributed to water-vaporabsorption by the polyimide were observed No measurements of fluctuating wall-shear stress were madebecause the signal amplitude available from the device itself was too low in spite of the fact that the first-stage amplification was fabricated directly on the chip

band-Since the introduction of Schmidt et al.’s sensor, other floating-element sensors based on transduction,capacitive, and piezoresistive principles have been developed [Ng et al., 1991; Goldberg et al., 1994; Pan et al.,1995] Ng et al.’s sensor was small and had a floating element with a size of 120 40 µm2 It operated on

a transduction scheme and was basically designed for polymer-extrusion applications so it operated in theshear stress range of 1–100 kPa Goldberg et al.’s sensor had a larger floating element size, 500 500 µm2

It had the same application and the same principle of operation as the Ng et al.’s balance Neither of thesetwo sensors is of interest in turbulence and flow control applications since their sensitivity is far too low.The capacitive floating-element sensor of Pan et al (1995) is a force-rebalance device designed for wind-tunnel measurements, and is fabricated using a surface micromachining process Unfortunately, this particu-lar fabrication technique can lead to non-planar floating-element structures The sensor has only beentested in laminar flow and no dynamic response of this device has been reported

Recently, Padmanabhan (1997) has presented a floating-element wall-shear stress sensor based on opticaldetection of instantaneous element displacement The probe is designed specifically for turbulent boundary

layer research and has a measured resolution of 0.003 Pa and a dynamic response of 10 kHz A schematicillustrating the sensing principle is shown in Figure 6.28 The sensor is comprised of a floating elementwhich is suspended by four support tethers The element moves in the plane of the chip under the action

of wall-shear stress Two photodiodes are placed symmetrically underneath the floating element at the ing and trailing edges, and a displacement of the element causes a “shuttering” of the photodiodes Underuniform illumination from above, the differential current from the photodiodes is directly proportional

lead-to the magnitude and sign of shear stress Analytical expressions were used lead-to predict the static and dynamicresponse of the sensor; based on the analysis, two different floating-element sizes were fabricated, 120

120 7 µm3and 500 500 7 µm3 The device has been calibrated statically in a laminar flow over a stressrange of four orders of magnitude, 0.003–10 Pa The gauge response was linear over the entire range ofwall-shear stress The sensor also showed good repeatability and minimal drift

A unique feature of the shear sensor just described is that its dynamic response has been tally determined to 10 kHz Padmanabhan (1997) described how oscillating wall-shear stress of a knownmagnitude and frequency can be generated using an acoustic plane-wave tube A schematic of the cali-bration experiment is shown in Figure 6.29 The set-up is comprised of an acrylic tube with a speaker-compression driver at one end and a wedge-shaped termination at the other end The latter is designed

experimen-to minimize reflections of sound waves from the tube end and thereby set up a purely travelling wave inthe tube A signal generator and an amplifier drive the speaker to radiate sound at different intensities andfrequencies At some distance downstream, the waves become plane; at this location a condenser micro-phone (which measures the fluctuating pressure) and the shear-stress sensor are mounted The flow fieldinside the plane-wave tube is very similar to a classical fluid dynamics problem — the Stokes secondproblem The only difference is that instead of an oscillating wall with a semi-infinite stationary fluid, theplane-wave tube has a stationary wall and oscillating fluid particles far away from the wall Solutions tothe Stokes problem can be found in many textbooks [Brodkey, 1967; Sherman, 1990; and White, 1991].Padmanabhan (1997) converted the boundary conditions and derived corresponding analytical expres-sion for the plane-wave tube The analytical solution of the fluctuating wall-shear stress was compared

to the measured output of the shear-stress sensor as a function of frequency and a transfer function of

Embedded conductor Floating-element

Silicon

Passive electrodes

Vd

On chip Off chip

the sensor was determined As expected, the measured shear stress showed a square-root dependence onfrequency.

6.4.3.9 Outlook for Shear-Stress Sensors

Since coherent structures play a significant role in the dynamics of turbulent shear flows, the ability to trol these structures will have important technological benefits such as drag reduction, transition control,mixing enhancement, and separation delay In particular, the instantaneous wall-shear stress is of interest forreactive control of wall-bounded flows to accomplish any of those goals An anticipated scenario to realizethis vision would be to cover a fairly large portion of a surface, for instance parts of an aircraft wing or fuse-lage, with sensors and actuators Spanwise arrays of actuators would be coupled with arrays of wall-shearstress sensors to provide a locally controlled region The basic idea is that sensors upstream of the actuatorsdetect the passing coherent structures, and sensors downstream of the actuators provide a performance mea-sure of the control Fast, small, and inexpensive wall-shear stress sensors like the microfabricated thermal orfloating-element sensors discussed in this section would be a necessity in accomplishing this kind of futuris-tic control system Control theory, control algorithms, and the use of microsensors and microactuators forreactive flow control are among the topics discussed in several chapters within this handbook

As mentioned in the introduction, the fluctuating wall-shear stress is an indicator of the turbulenceactivity of the flow In the ongoing development of existing turbulence models for application in high-Reynolds-number flows, absolute values of the fluctuating wall-shear stress are of significant interest Toaccomplish this kind of measurements, reliable methods for conducting dynamical calibration of wall-shear stress sensors are needed and must be developed The recent calibration method of Padmanabhan(1997) is of interest and other strategies are likely to develop in the future Another intriguing possibilitythat would be challenging is to design a microsensor where the dynamic effects of the gauge could be con-trolled in such a way that only a static calibration of the sensor would be adequate.

6.4.4 Pressure Sensors

6.4.4.1 Background

In turbulence modeling, flow control, and aeroacoustics, the fluctuating pressure beneath a bounded flow is a crucial parameter By measuring this random quantity much information can be gleanedabout the boundary layer itself without disturbing the interior of the flow The fluctuating wall-pressure iscoupled via a complex interaction to gradients of both mean-shear and velocity fluctuations as described

wall-by the transport equations for Reynolds stresses [Tennekes and Lumley, 1972; Hinze, 1975; Pope, 2000].The characteristics of the fluctuating wall-pressure field beneath a turbulent boundary layer have beenextensively studied in both experimental and theoretical investigations, and reviews of earlier work may befound in Blake (1986), Eckelmann (1990), and Keith et al (1992) However, from the experimental per-spective, knowledge of pressure fluctuations is far from being as comprehensive as that of velocity fluc-tuations, since there is a lack of a generally applicable pressure-measuring instrument that can be used in

Speaker B&K microphone

Propagating plane wave Shear-stress sensor end-terminationWedge-shaped

A/D data acquisition

Amplifier

Function generator

(a)

(b)

Particle velocity

Tube wall

Shear-stress sensor

Frequency-dependent boundary layer thickness, ()

() = 6.5 /

2 acrylic tube

FIGURE 6.29 An acoustic plane-wave tube for the calibration of a floating-element shear sensor (a) Overall iment set-up; (b) probe region (Reprinted with permission from Padmanabhan, A [1997] Silicon Micromachined Sensors and Sensor Arrays for Shear-Stress Measurements in Aerodynamic Flows, Ph.D Thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts.)

exper-the same wide variety of circumstances as exper-the hot-wire anemometer In spite of this, some general factshave been established for wall-pressure fluctuations For example, the order of magnitude of the root-mean-square (rms) value, the general shape of the power spectra, and the space-time correlation characteristics[Harrison, 1958; Willmarth and Wooldridge, 1962; Bull, 1967; Bull and Thomas, 1976; Schewe, 1983; Blake,1986; Lauchle and Daniels, 1984; Farabee and Casarella, 1991].

A clear shortcoming in many of the experiments designed to measure pressure fluctuations is the ity of the data In the low-frequency range, the data may be contaminated by facility-related noise, while

qual-in the high-frequency range the spatial resolution of the transducers limits the accuracy The former ficulty is usually circumvented by noise cancellation techniques [Lauchle and Daniels, 1984] or by using

dif-a free-flight glider dif-as dif-an experimentdif-al pldif-atform This problem mdif-ay not be considered dif-as dif-a mdif-ajor obstdif-acletoday At the other end of the spectrum, the spatial-resolution problem is more difficult to handle Themain criticism raised is that in many experiments the size of the pressure transducer used has been fartoo large in relation to the thickness of the boundary layer in context, let alone in relation to the characteris-tic small-scale The ultimate solution is of course to use small sensors, but testing in tunnels containingfluids with high viscosity — to increase the viscous length-scale in the flow — has also been tried Usinghighly viscous fluids creates its own set of problems Very specialized facilities and instrumentation areneeded when oil or glycerin, for example, are used as the working fluid An oil tunnel is expensive to buildand to operate Moreover, the Reynolds numbers achieved are generally low, and it is not clear how to extrap-olate the results to higher-Reynolds-number flows [Gad-el-Hak and Bandyopadhyay, 1994]

Pinhole microphones have also been utilized in an attempt to improve the sensor's spatial resolution.Unfortunately, results from this type of arrangement are questionable, and to this end the use of pinholemicrophones must be considered as an open question Bull and Thomas (1976) concluded that the use ofpinhole sensors in air may lead to severe errors in the measured spectra, while Farabee (1986), Gedney andLeehey (1989), and Farabee and Casarella (1991) all claimed that the pinhole sensors are most effectivefor wall-pressure measurements

Based on the above arguments, it seems then that the only realistic solution to improve measurements

of fluctuating wall-pressure is to use small sensors For this reason microfabrication offers a unique tunity for reducing the diaphragm size by at least one order of magnitude MEMS also provides an oppor-tunity to fabricate inexpensive, dense arrays of pressure sensors for correlation measurements and studies

oppor-of coherent structures in turbulent boundary layers In this subsection, we describe the basic principles usedfor MEMS-based pressure sensors/transducers/microphones We look specifically at the design of pressuresensors utilizing the piezoresistive principle, which is particularly suited for measurements of wall-pressure fluctuations in turbulent flows The section contains also a summary of measurements conductedwith MEMS pressure sensors and when possible a comparison to conventional data Finally, we provide

an outlook for the use of MEMS-based pressure sensors for turbulence measurements and flow control

6.4.4.2 Pressure-Sensor Principles

Many different methods have been advanced for the detection of pressure fluctuations [Sessler, 1991].The principles available are based on detecting the vibrating motion of a diaphragm using piezoelectric,piezoresistive, and capacitive techniques These principles were already known at the beginning of thetwentieth century, but the introduction of photolithographic fabrication methods during the last twodecades has provided strong impetus since this technology offers sensors fabricated to extremely low tol-erance, increased resolution due to a high degree of miniaturization, and low unit-cost This method of fab-rication is also compatible with other IC techniques so electronic circuitry like pre-amplifiers can beintegrated close together with the sensor, an important factor for improving pressure sensor performance.This section will provide a short background of the previously mentioned principles for pressure sensoroperations The word “microphone” will be used for a device whereby sound waves are caused to gener-ate an electric current for the purpose of transmitting or recording sound

A piezoelectric sensor consists of a thin diaphragm, which is either fabricated in a piezoelectric rial or mechanically connected to a cantilever beam consisting of two layers of piezoelectric material withopposite polarization A vertical movement of the diaphragm causes a stress in the piezoelectric material

mate-and generates an electric output voltage Royer et al (1983) presented the first MEMS-based piezoelectricsensor shown in Figure 6.30 This sensor consists of a 30 µm-thick silicon diaphragm with a diameter of

3 mm On top of the diaphragm a layer of 3–5 µm ZnO was deposited, sandwiched between two SiO2layersthat contained the upper and lower aluminum electrodes The sensor can be provided with an integratedpreamplifier, and is basically used for microphone applications A sensitivity of 50–250 µV/Pa, and a fre-quency response in the range of 10 Hz–10 kHz (flat within 5 dB) were recorded Other researchers have pre-sented similar piezoelectric silicon microphones [Kim et al., 1991; Kuhnel, 1991; Schellin and Hess, 1992;Schellin et al., 1995], and the sensitivities of these microphones were in the range of 0.025–1 mV/Pa.However, applications of the piezoelectric microphone to turbulence measurements are strongly limitedbecause of its high noise level, which has been found to be in the range of 50–72 dB(A)SPL These noiselevels are most commonly measured using an A-weighted filter, in dBs relative to 2 105Pa, which isthe lowest sound level detectable by the human ear The A-weighted filter corrects for the frequency char-acteristics of the human ear and provides a measure of the audibility of the noise

A piezoresistive sensor consists of a diaphragm which is usually provided with four piezoresistors in aWheatstone bridge configuration One common arrangement is to locate two of the gauges in the middle,and two at the edge of the diaphragm When the diaphragm deflects, the strains at the middle and at the edge

of the diaphragm would have opposite signs which cause an opposite effect on the piezoresistive gauges.The most important advantage of this detection principle is its low output-impedance and its high sen-sitivity The main drawback is that the piezoresistive material is sensitive to both stress and temperature.Unfortunately, this gives the piezoresistive sensor a strong temperature dependency Schellin and Hess (1992)presented the first MEMS-fabricated piezoresistive sensor, which is shown in Figure 6.31 This particularsensor was used as a microphone and it had a diaphragm made of 1 µm-thick, highly boron-doped sili-con with an area of 1 mm2 The diaphragm was equipped with 250-nm-thick, p-type polysilicon resistors,

which were isolated from the diaphragm by a 60-nm silicon dioxide layer Using a bridge supply voltage of

Al upper electrode

SiO2

Al concentric lower electrodes

SiO2

Si

ZnO

FIGURE 6.30 Cross-sectional view of a piezoelectric silicon microphone (Reprinted with permission from Royer, M.,

Holmen, P., Wurm, M., Aadland, P., and Glenn, M [1983] “ZnO on Si Integrated Acoustic Sensor,” Sensors and Actuators

4, pp 357–362.)

Polysilicon piezoresistor

SiO2

Boron-doped diaphragm

SiO2

Si

Metallization

FIGURE 6.31 Cross-sectional view of a piezoresistive silicon microphone (Reprinted with permission from

Schellin, R., and Hess, G [1992] “A Silicon Microphone Based on Piezoresistive Polysilicon Strain Gauges,” Sensors and

Actuators A 32, pp 555–559.)

6 V, this transducer showed a sensitivity of 25 µV/Pa and a frequency response in the range of 100 Hz–5 kHz(3dB) However, the sensitivity was lower than expected by a factor of 10, which was explained by theinitial static stress in the highly boron-doped silicon diaphragm To improve the sensitivity of the piezor-esistive sensor, different diaphragm materials have been explored such as polysilicon and silicon nitride[Guckel, 1987; Sugiyama et al., 1993].

Most MEMS-fabricated pressure sensors are based on the capacitive detection principle, and a vast ity of these sensors are used as microphones Figure 6.32 shows a cross-sectional view of such condensermicrophone together with the associated electrical circuit The latter must be included in the discussionsince the preamplifier constitutes a vital part in determining the sensitivity of the capacitive probe Basically,

major-a condenser microphone consists of major-a bmajor-ackchmajor-amber (with major-a pressure equmajor-alizing hole), major-a bmajor-ackplmajor-ate (withacoustic holes), a spacer, and a diaphragm covering the air gap created by the spacer located on the back-

plate The condenser, C m , and a DC-voltage source, V b, constitute the sensing part of the microphone.Fluctuations in the flow pressure field above the diaphragm cause it to deflect which in turn changes the

capacitance, C m These changes are amplified in the preamplifier, H o, which acts as an impedance converter

with a bias resistor, R b , and an input capacitance, C i In this figure, C pis a parasitic capacitance which is

of interest when determining the microphone attenuation In discussing the sensitivity of a capacitivesensor, the open-circuit sensitivity is a relevant quantity and is considered to consist of two components,

namely the mechanical sensitivity, S m , and the electrical sensitivity, S e The total sensitivity is a weighted

value of both The former sensitivity, S m , is defined as the increase of the diaphragm deflection dw ing from an increase in the pressure, dp, acting on the microphone:

Pressure equalization hole

Cp Ci

Rb

Ho

− +

Voltage sour ce

Parasitic capacitance Amplifier

Output

−

FIGURE 6.32 Cross-sectional view of a condenser microphone The microphone is connected to an external d.c bias voltage source, and loaded by a parasitic capacitance, bias resistor, and a preamplifier with an input capacitance (Reprinted with permission from Löfdahl, L., Kälvesten, E., and Stemme, G [1996] “Small Silicon Pressure Transducers for Space-

Time Correlation Measurements in a Flat Plate Boundary Layer,” J Fluids Eng 118, pp 457–463.)

FromFigure 6.32we obtain the relation dw  ds a o, where Sa ois the thickness of the air gap betweenthe diaphragm and the backplate The electrical sensitivity of the microphone is given by the change in the

voltage across the air gap dV resulting from a change in the air-gap thickness ds a o Thus:

The quasi-static, open-circuit sensitivity Sopenof a condenser microphone may be defined as Sopen

S m S e The output signal e mcan then be expressed as:

where p is the fluctuating pressure For details of this derivation, see Scheeper et al (1994).

Hohm (1985) presented the first electret microphone based on MEMS technology The backplate,(1 1)-cm2silicon, was provided with one circular acoustic hole with a diameter of 1 mm A 2 µm-thickSiO2layer was used as electret and was charged to about 350 V The diaphragm was a metallized 13 µm-thick foil with a diameter of 8 mm Later polymer foil diaphragms were used in condenser microphones

by Sprenkels (1988) and Murphy et al (1989) In these microphones, the fabrication was made more patible with standard thin-film technology Bergqvist and Rudolf (1991) showed that MEMS-fabricatedmicrophones can achieve a high sensitivity For example, microphones with a (2 2)-cm2diaphragm had

com-an open-circuit sensitivity in the rcom-ange of 1.4–13 mV/Pa In these microphones, diaphragms with ness of 5–8 µm were fabricated using an anisotropic etching in a KOH solution and applying an electro-chemical etch-stop More details on the design and performance of the capacitive pressure sensors can befound in Scheeper et al (1994)

thick-An overview of the most significant dimensions, measured sensitivity, noise level, and high frequencyresponse of first-generation MEMS pressure sensors is provided in Table 6.3

The data from this table indicate that the piezoelectric sensors seem to have the highest noise levels.Although simple in design, they have fairly low sensitivity and relatively large spatial extension of theirdiaphragms The piezoresistive sensors seem to be most flexible since the major advantage of locating

dV



ds a

o

Table 6.3 Summary of Silicon Micromachined Microphones in Chronological Order

Transducer Diaphragm Upper Frequency Sensitivity Equivalent Noise

Voorthuyzen et al (1989) Capacitive 2.45 2.45 15 19 60

Schellin and Hess (1992) Piezoresistive 1 1 10 0.025 at 6 V —

Kuhnel and Hess (1992) Capacitive 0.8 0.8 16 0.4–10 25

Kälvesten (1994) Piezoresistive 0.1 0.1
25 0.0009 at 10 V 90

Kovacs and Stoffel (1995) Capacitive 0.5 0.5 20 0.065 58