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This paper presents the preliminary wind tunnel characterization of a microelectromechanical systems (MEMS)-based capacitive floating element shear stress sensor. The floating element structure incorporates interdigitated comb fingers forming differential capacitors, which provide electrical output proportional to the floating element deflection. A compact sensor package combined with a synchronous modulation/demodulation system facilitates mounting in a flat plate model located in an open-loop low-speed wind tunnel. Particle image velocimetry is used to measure the boundary layer velocity profiles for laminar, transitional and turbulent flows. The mean wall shear stress estimated from profile curve fits is in agreement with MEMS sensor output.

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... The experimentally verified capacitance of the sensor electrodes is O(10 pF). Historically, a single-ended configuration has been used in capacitive wall shear stress sensors [6,10,11]. For a dual-axis sensor in this configuration, the fixed electrode pairs (E 1+ , E 1− and E 2+ , E 2− in Fig. 1) are excited by a pair of differential bias voltage signals at two different carrier frequencies, and the common floating element electrode (E 3 in Fig. 1) provides a single output signal which is then buffered for transmission back to the SCU. ...

... As a capacitive sensor with the intention of measuring both mean and dynamic inputs, a standard dc biasing scheme is unsuitable [10]. Because an ideal capacitor has an infinite impedance at dc, a sinusoidal biasing scheme is utilized instead. ...

... MEMS skin friction sensors are considered promising sensors in hypersonic wind tunnel experiments owing to their miniature size, high sensitivity, and stability. In recent years, several researchers have developed MEMS sensors to measure skin friction, including the capacitance-type and comb differential capacitance-type [1][2][3][4][5], piezoresistive-type [6][7][8], and piezoelectric-type [9]. For example, Mills et al. [5] reported a fully differential capacitive wall shear stress sensor for low-speed wind tunnels with the high sensitivity of 196 mV/Pa and a minimum detection limit of 12 mPa at 1000 Hz in a range from 0-10 Pa; Von, P. et al. [8] reported a wall shear stress sensor using four piezoresistors in the cantilever, and the resolution was 0.01 Pa in the range of 2 Pa; Kim, T. et al. [9] reported a piezoelectric floating element shear stress sensor for the wind tunnel flow measurement with the high sensitivity of 56.5 pc/Pa and with the frequency range of the sensor up to 800 Hz. ...

Micro-electromechanical system (MEMS) skin friction sensors are considered to be promising sensors in hypersonic wind tunnel experiments owing to their miniature size, high sensitivity, and stability. Aiming at the problem of short test duration (a few milliseconds) and heavy load in a shock wind tunnel, the fast readout circuit and the sensor head structures of a MEMS skin friction sensor are presented and optimized in this work. The sensor was fabricated using various micro-mechanical processes and micro-assembly technology based on visual alignment. Meanwhile, the sensor head structure was integrated with the fast readout circuit and tested by using a centrifugal force equivalent method. The calibration results show that this sensor provides good linearity, sensitivity, and stability. The measurement ranges are 0–2000 Pa with good performance. The resolution is better than 10 Pa at 3000 Hz detection frequency of the readout circuit for the sensor in ranges from 0 to 1000 Pa. In addition, the repeatability and linearity of static calibration for sensors are better than 1%.

... The upper surface of test-head is its sensing surface, and will be installed evenly with the measurement wall. [7], adopted four supporting cantilevers and comb capacitance sensing and had a measuring range of 0.1-5.0 Pa, however its floating element and comb capacitances were exposed in the flow field, thus it could be only used in low wind tunnels with pure gases. ...

MEMS-based skin friction sensors are used to measure and validate skin friction and its distribution, and their advantages of small volume, high reliability, and low cost make them very important for vehicle design. Aiming at addressing the accuracy problem of skin friction measurements induced by existing errors of sensor fabrication and assembly, a novel fabrication technology based on visual alignment is presented. Sensor optimization, precise fabrication of key parts, micro-assembly based on visual alignment, prototype fabrication, static calibration and validation in a hypersonic wind tunnel are implemented. The fabrication and assembly precision of the sensor prototypes achieve the desired effect. The results indicate that the sensor prototypes have the characteristics of fast response, good stability and zero-return; the measurement ranges are 0–100 Pa, the resolution is 0.1 Pa, the repeatability accuracy and linearity are better than 1%, the repeatability accuracy in laminar flow conditions is better than 2% and it is almost 3% in turbulent flow conditions. The deviations between the measured skin friction coefficients and numerical solutions are almost 10% under turbulent flow conditions; whereas the deviations between the measured skin friction coefficients and the analytical values are large (even more than 100%) under laminar flow conditions. The error resources of direct skin friction measurement and their influence rules are systematically analyzed.

In this study, the optical flow method for the skin-friction-stress estimation from the unsteady oil film distribution was reformulated based on the variational method, and the validity of the proposed method was verified in comparison with the conventional method. The regularization is proposed to be added directly to the skin-friction-stress field in the proposed method while the regularization is added to the amount of oil movement in the conventional method. As a result, the smoothness of the skin-friction-stress field can be controlled by adjusting the regularization parameter in the proposed method whereas it was difficult in the conventional method. The performance of the proposed method was evaluated to be superior to the previous method through the numerical and experimental data.

This paper describes the development and experimental characterization of a temperature-compensated wall shear stress sensor system designed to reduce temperature sensitivity and be non-invasive to low-speed aerodynamic flows. The differential capacitive microelectromechanical systems (MEMS) sensor is fabricated using a novel, low-cost approach to creating backside electrical contacts, creating a hydraulically smooth surface without the use of through-silicon vias. Temperature compensation in the form of a thermistor provides a greater than 10x reduction in temperature sensitivity, thus increasing the accuracy of mean shear stress measurements in flow environments where the temperature is not held constant. Characterization of a 5 kHz bandwidth, 300 Pa temperature-compensated shear stress sensor system yields a sensitivity of 35.3 mV/Pa at 1 kHz, minimum detectable signal of 0.13 mPa/rtHz, and a temperature sensitivity of 77 mPa/degC, a ~32x reduction compared to previous-generation devices.

This article presents correlations for indirect measurement of skin friction inside a laminar separation bubble induced by hypersonic shock-boundary layer interaction (SBLI) on a flat plate. The correlations, based on parameters that are known to influence the SBLI region, were developed using exhaustive numerical and analytical studies. Experiments were conducted in a hypersonic shock tunnel at Mach 8.6 (±0.22) to measure surface heat-flux and pressure in the zone of SBLI on a flat plate, which were then used to supplement and validate the correlations. The data predicted by the correlations agreed reasonably well with that of exact solutions. The case studies contained non-reacting air, behaving as a perfect gas on a flat surface.

The phase-averaged skin-friction analysis based on global luminescent oil film (GLOF) was conducted for periodically fluctuating unsteady phenomena at the frequency of approximately 150 Hz which is estimated based on Karman vortex shedding. An unsteady pressure transducer and a camera were synchronized, and the time-averaged and phase-averaged skin-friction fields were investigated. The time-series image pair data obtained by the camera were decomposed into eight intervals of a phase angle of π/4 with synchronizing the signal of the unsteady pressure. The phase-averaged result shows the periodical pattern corresponding to the vortices structure generated from the edge of the test model which was not resolved by the time-averaged result. The phase-averaged processing was successfully applied to the GLOF measurement, and the results showed the detail information of skin friction at each phase.

In hypersonic flight, drag is composed of two main components besides abduction drag: wave drag, which is caused by shock waves, and skin friction drag, which is caused by friction. Wave drag is correlated to the Mach number, and skin friction drag is related to the flow state of the surface in the flight. The flow state corresponds to the Reynolds number, the rough degree of the surface, and the flight vehicle’s angle of attack. In hypervelocity, the skin friction is proportional to the product of the gas density multiplied by the square of the flight velocity. Related research results [1] show that the skin friction drag accounts for almost 50 % of the total drag in hypersonic vehicles with scramjet. In high lift-to-drag ratio vehicles, such as wave riders, the ratio is the same. Research on the skin friction balance measurement in shock tunnels is useful to vehicle layout research, drag reduction, and structure optimization, as well as the design of the engine shape, inlet, and insulate section of vehicles.

A large scale spatio-temporally periodic disturbance was excited in a turbulent boundary layer via a wall-actuated dynamic roughness. Streamwise velocity, wall pressure, and direct wall shear stress measurements were made with a hot wire, pressure microphone, and a micro-scale differential capacitive sensor, respectively. Phase-averaged fields for the three quantities were calculated and analyzed. A phase calibration between the various sensors was performed with an acoustic plane wave tube over a range of operating conditions to validate a direct phase comparison between the respective quantities. Results suggest encouraging agreement between the phase of the wall shear stress and velocity near the wall; however, more refined velocity measurements are needed to make quantitative comparisons to the wall pressure. Overall, this work highlights the potential for wall-based control with applications towards reducing turbulent drag.

In this paper, we carried out numerical experiments to study the effect of the shear stress and the wall pressure on the optical mode shift of two embedded cylindrical microlasers. The optical cavities (laser) are encapsulated in a slab that is clamped at the bottom surface while the other sides of the slab are free-stress boundaries. When a uniform shear stress and pressure is applied on the top surfaces of the slab, the morphology of the optical resonators are perturbed. This leads to a shift in the optical modes [commonly referred to as the whispering gallery mode (WGM)] of the resonators. The effect of the geometry (size and position of the optical cavities) and materials properties on the optical mode shift are studied. The results show a linear dependency of the WGM shift on the applied external pressure. In addition, the optical mode shift is slightly dependent on the geometry and the material properties. The effect of the shear stress on the WGM shift shows a quadratic dependency and this nonlinearity is strongly dependent on the position of the resonators within the slab. The studies also show that the proposed configuration could be used as a sensor for simultaneous measurements of wall pressure and shear stress.

The design and implementation of a novel dynamic calibration technique for shear-stress sensors is presented. This technique uses the oscillating wall shear stress generated by a traveling acoustic wave as a known input to the shear-stress sensor. A silicon-micromachined, floating-element shear-stress sensor has been dynamically calibrated up to 4 kHz using this method. These data represent the first broadband, experimental verification of the dynamic response of a shear-stress sensor.

The theoretical bases and implementation of state-of-the-art measurement
techniques for wall shear stress are reviewed and illustrated with
graphs and diagrams. The general structure of a turbulent boundary layer
is described, and sections are devoted to local and global correlation
methods (Clauser plots, Preston tubes, Stanton tubes, and heat-transfer
methods), momentum-balance methods (pressure gradients and momentum
thickness gradients), and direct methods (conventional and micromachined
floating elements). The importance of accurate instrument calibration is
stressed, and comparisons with theoretical predictions and near-wall
velocity measurements are recommended when feasible.

This paper presents the development of a floating-element shear stress sensor that permits the direct measurement of skin friction based on geometric Moiré interferometry. The sensor was fabricated using an aligned waferbond/thin-back process producing optical gratings on the backside of a floating element and on the top surface of the support wafer. Experimental characterization indicates a static sensitivity of 0.26 μm/Pa, a resonant frequency of 1.7 kHz, and a noise floor of 6.2 mPa/√Hz.

The present paper describes an experimental investigation of closed-loop separation control using plasma actuators. The post-stall-separated
flow over a NACA 0015 airfoil is controlled using a single dielectric barrier discharge actuator located at the leading edge.
Open-loop measurements are first performed to highlight the effects of the voltage amplitude on the control authority for
freestream velocities of 10–30m/s (chord Re=1.3×105 to 4×105). The results indicate that partial or full reattachment can be achieved and motivate the choice of the slope seeking approach
as the control algorithm. A single-input/single-output algorithm is used to autonomously seek the optimal voltage required
to achieve the control objective (full flow reattachment associated with maximum lift). The paper briefly introduces the concept
of slope seeking, and a detailed parameterization of the controller is considered. Static (fixed speed) closed-loop experiments
are then discussed, which demonstrate the capability of the algorithm. In each case, the flow can be reattached in an autonomous
fashion. The last part of the paper demonstrates the robustness of the gradient-based, model-free scheme for dynamic freestream
conditions. This paper highlights the capability of slope seeking to autonomously achieve high lift when used to drive the
voltage of a plasma actuator. It also describes the advantages and drawbacks of such a closed-loop approach.

A statistical-based approach to detect outliers in fluid-based velocity measurements is proposed. Outliers are effectively
detected from experimental unimodal distributions with the application of an existing multivariate outlier detection algorithm
for asymmetric distributions (Hubert and Van der Veeken, J Chemom 22:235–246, 2008). This approach is an extension of previous methods that only apply to symmetric distributions. For fluid velocity measurements,
rejection of statistical outliers, meaning erroneous as well as low probability data, via multivariate outlier rejection is
compared to a traditional method based on univariate statistics. For particle image velocimetry data, both tests are conducted
after application of the current de facto standard spatial filter, the universal outlier detection test (Westerweel and Scarano,
Exp Fluids 39:1096–1100, 2005). By doing so, the utility of statistical outlier detection in addition to spatial filters is demonstrated, and further,
the differences between multivariate and univariate outlier detection are discussed. Since the proposed technique for outlier
detection is an independent process, statistical outlier detection is complementary to spatial outlier detection and can be
used as an additional validation tool.

This paper reports a novel optical fiber-based micro-shear stress sensor utilizing a flexible membrane and double SU-8 resist structures as a moving micro-mirror, together with an optical fiber as a micro-Fabry-Perot interferometer. This sensor can be employed in air or liquid environments with high sensitivity because of its waterproof design. Through UV lithography processes on thick SU-8 resist, the roughness of the reflection surface has approached 7 nm (Ra value), suitable for optical applications. A single-mode optical fiber is employed for detecting the displacement of the floating element induced by shear stress. Tests have been carried out successfully and a detection possibility of 10 nm-displacement of the floating element and a displacement sensitivity of 0.128 nm/nm (spectrum shift/floating element displacement) has been demonstrated. The temperature coefficient of this fiber-optic sensor has been characterized to be 3.4 nm/K linearly from 25 to 48°C. Fluid tests have also been performed by placing the sensor inside the inner wall of a precisely machined rectangular channel and the result shows a sensitivity of 0.4 nm/ml/min (spectrum shift/flow rate), corresponding to a shear stress resolution of 0.65 Pa/nm (shear stress/spectrum shift). The minimum detectable shear stress is thereby estimated as 0.065 Pa from the reading resolution of the spectrometer of 0.1 nm, comparable to its counterparts with resolutions from 0.1-1 Pa.

An integral method is presented for calculating two-dimensional incompressible turbulent separated boundary layers. The procedure is based upon the inner variable theory developed by Das and White (1986), who originally formulated the problem via a direct boundary layer scheme. This scheme required several modifications, including reformulation of the method into the inverse mode. In this paper the inverse theory is described which utilizes the displacement thickness distribution as input. This theory also incorporates an improved pressure gradient-wake correlation, and eliminates the need for the second derivative distribution of the velocity, which has always been a source of uncertainty in previous inner-variable approaches. The theory has been verified by comparing its prediction against several separated flow experiments. The results show good agreement with experimental data.

For routine calculations of the properties of the incompressible turbulent boundary layer with arbitrary pressure gradient, the presently accepted method is the Karman integral technique, which consists of three simultaneous equations, the three unknowns being the momentum thickness, the skin friction, and the shape factor. Considerable empiricism is contained in the Karman method, so that the reliability is only fair. The present paper derives an entirely new method, based upon a suggestion of R. Brand and L. Persen. The new approach results in a single equation for the skin friction coefficient, with the only parameter being the nominal Reynolds number and the only empiricism being a single assumption about the effect of pressure gradient. No other variables, such as shape factor or momentum thickness, are needed, although they can of course be calculated as byproducts of the analysis. The new method also contains a built-in separation criterion, which was the most glaring omission of the Karman technique. Agreement with experiment is as good or better than the most reliable Karman methods in use today.

This paper presents the development of a microelectromechanical systems (MEMS)-based piezoresistive shear stress sensor for the direct, quantitative measurement of time-resolved, fluctuating skin friction. The sensor structure integrates laterally-implanted diffused piezoresistors into the sidewall of the sensor tethers for detecting the floating element deflection via a strain-induced resistance change. The sensor was optimally designed using a nonlinear electromechanical model. Preliminary experimental characterization indicates a sensitivity of 4.24 μV Pa and a noise floor of 11.4 mPa/√Hz (for a 1 Hz bin centered at 1 kHz ) for a bias voltage of 1.5 V . The tested device is linear up to the maximum testing range of 2 Pa and possesses a flat dynamic response up to the frequency testing limit of 6.7 kHz .

An iterative procedure, based on the proper orthogonal decomposition (POD), first proposed by Everson and Sirovich (J Opt Soc Am A 12(8):1657-1664, 1995) is applied to marred particle image velocimetry (PIV) data of shallow rectangular cavity flow at Mach 0.19, 0.28, 0.38, and 0.55. The procedure estimates the POD modes while simultaneously estimating the missing vectors in the PIV data. The results demonstrate that the absolute difference between the repaired vectors and the original PIV data approaches the experimental uncertainty as the number of included POD modes is increased. The estimation of the dominant POD modes is also shown to converge by examining the subspace spanned by the POD eigenfunctions.

Three designs of surface-micromachined shear stress sensors have been tested and calibrated in a continuum how channel, The first design, for moderate shear stress conditions, is composed of passive sensors with optically determined sensitivities of 9 and 5.5 Pa/mu m of Boating-element deflection for two variants. The second-generation design features Boating elements integrated with on-chip electronics. The deflection is thus measured with a voltage output that displays significant nonlinearities due to the limitations of drive electronics. Complete calibration of the third design was performed, as these sensors were integrated with complex active element control circuitry. These devices demonstrated a device sensitivity of 1.02 V/Pa +/- 5% over a sensor range of 0.5-3.7 V.

The design and fabrication of shear stress sensors based on the floating-element method and polysilicon-surface-micromachining technology is reported. Three designs have been developed for microfabrication, two including monolithic integration of mechanical sensor elements with on-chip circuitry. The first design is a four-mask standard polysilicon-surface-micromachining process to develop passive floating-element sensors with optically determined deflection sensitivity. The second-generation devices are fabricated in a six-mask modified N-channel metal-oxide-semiconductor process, where sensor elements and signal conditioning circuitry have been integrated on the sensor die for amplified voltage output. The third design modifies the commercially available micromachined by replacing the accelerometer element with a shear-stress-sensitive floating element, enabling active sensing for Linear response and self-test features.

The principle techniques for measuring skin friction in turbulent
boundary layers in external flow situations are examined with regard to
the equipment they use, the methods of evaluating the data, and their
limits of application. Techniques covered include force-measurement
balances; velocity profile and pressure measurements by surface pitot
tubes or about obstacles; and the use of analogies with heat transfer,
mass transfer, or surface oil flow.

This paper reviews three relatively modern categories of skin-friction measurement techniques that are broadly classified as microelectromechanical systems (MEMS)-based sensors, oil-film interferometry, and liquid crystal coatings. The theory, development, limitations, uncertainties, and misconceptions of each of these techniques are presented. Current and future uses of the techniques are also discussed. From this review, it is evident that MEMS-based techniques possess great promise, but require further development to become reliable measurement tools. Oil-film techniques have enhanced capabilities and greater accuracy compared to conventional shear-stress measurement techniques (i.e., Preston tube, Clauser plot, etc.) and, as a result, are being employed with increasing frequency. Liquid crystal coatings are capable of making measurements of mean shear-stress vector distributions over a region of a model, but complex calibration and testing requirements limit their usefulness.

The paper considers a problem which was first treated mathematically by Lighthill in a different physical context. Solutions are provided for the limiting case of forced convection across a turbulent boundary layer when Pr→∞, i.e. when the thermal boundary layer is wholly confined within the laminar sublayer whose velocity profile is linear. The case of a flat plate with a uniform temperature or with one step in temperature is treated in great detail, and a convenient tabulation of formulae for a number of cases is provided. The case of a variable wall temperature is solved in two ways. First, the temperature distribution is replaced by a sequence of steps and superposition is used. Secondly, an exact analytic solution is given for the case when the temperature function consists of a step followed by a distribution given analytically. In the latter ease, closed-form equations are given for a polynomial temperature variation of which a linear temperature variation is a special case.

Uncertainty estimation is an important part of any measurement but is often neglected for complex valued or multivariate data (e.g., vectors). This paper presents a methodology for estimating the uncertainty in multivariate experimental data and applies it to the measurement of the frequency response function obtained when using a periodic random input signal. This multivariate uncertainty method is an extension of classical uncertainty methods used for scalar variables and tracks the correlation between all variates along with the sample variance instead of just tracking the standard uncertainty. The method is used in this paper to propagate the sample covariance matrix from spectral density estimates to the uncertainty in the frequency response function estimate for two different system models. In the first model the case when only the output signal is corrupted by noise is considered, while in the second model both the input and output signals are corrupted by uncorrelated noise sources. The results for the single-noise model are verified by comparing them to published expressions in the literature, while the results for the two-noise model are verified by using a direct computation of the statistics. Finally, the method is applied to experimental data from two microphone measurements within an acoustic waveguide. The random uncertainty estimates in the frequency response function from the multivariate method agree well with the results from a direct computation of the statistics.

It is shown how the cubic law for the variation in eddy kinematic
viscosity very near a smooth wall can be combined with the linear law in
the logarithmic region by the use of a simple interpolation formula.
This formula leads to an explicit closed-form expression for the
velocity distribution over a smooth wall in a turbulent boundary layer
which should prove useful in studies of heat and mass transfer and
turbulent boundary layer procedures.

Shear stress at the fluid–wall interface is one of the most frequently studied parameters in fluid dynamics. It is also a parameter of very small magnitude and calls for high resolution force sensors. Macroscopic sensors compromise dynamic bandwidth for the required high resolution and therefore cannot resolve shear stress data in space and/or time, which is very important for fundamental understanding in non-laminar fluid dynamics. We exploit the linear reduction in stiffness accompanied by cubic reduction in mass by miniaturization to design and fabricate a novel micro-electro-mechanical sensor (MEMS) for direct measurement of shear stress along and across the direction of fluid flow, with 0.01 Pa resolution and 50 kHz bandwidth along the flow. The mechanical component of the sensor is a floating beam element and capacitive comb drives supported by an in-plane torsional spring. A resonant RLC circuit, capable of sub-femtofarad capacitive sensing, is used to sense the displacement in the floating beam under shear. Fabrication of the sensor is demonstrated using silicon-on wafer (SOI) technology. The small overall size of the sensor, wide range of measurement, large bandwidth and high spatial and temporal resolution will make it useful in a wide variety of civil and military applications such as aerospace, automotive, marine and biomedical.

A statistical model is introduced that describes the occurence of spurious vectors in PIV data. This model is used to investigate the performance of three different post-interrogation procedures: the global-mean, the local-mean and the local-median test. The model is also used to optimize the performance of these procedures. Predicted performances agree very well with those obtained from an artificially generated PIV record. It is demonstrated that the detectability as the conventional measure for the reliability of a measured displacement vector is very inefficient, compared to the three tests described here. The local-median test has the highest efficiency.

Methods for calculating the statistical uncertainty associated with the sampling of random processes such as those which
occur in turbulence research are given. In particular, formulas based on normal distribution assumptions and on any general
distribution shape are given for means, variances, Reynolds stresses, correlation coefficients, homogeneous and mixed turbulent
triple products and fourth order turbulence moments. In addition, two resampling algorithms, the “bootstrap” and “jackknife”,
are presented and compared using actual turbulence data. The availability of these methods will allow turbulence data to be
presented with statistical uncertainty error bars on all turbulence quantities.

The paper presents a direct, capacitive shear stress sensor with performance sufficient for time-resolved turbulence measurements. The device employs a bulk-micromachined, metal-plated, differential capacitive floating-element design. A simple, two-mask fabrication process is used with DRIE on an SOI wafer to form a tethered floating element structure with comb fingers for transduction. Experimental results indicate a linear sensitivity of 7.66 mV/Pa up to the testing limit of 1.9 Pa at a bias voltage of 10 V , and a bandwidth of 6.2 kHz . The sensor possesses a dynamic range Gt 102 dB and a noise floor of 14.9 muPa/radic(Hz) at 1 kHz , outperforming previously reported sensors by nearly two orders of magnitude in MDS.

This paper presents the development of a floating-element-based capacitively sensed direct wall-shear-stress sensor intended for measurements in a turbulent boundary layer. The design principle is presented, followed by details of the fabrication, packaging, and characterization process. The sensor is designed with an asymmetric comb finger structure and metalized electrodes. The fabrication process uses deep reactive ion etching on a silicon-on-insulator wafer, resulting in a simple two-mask fabrication process. The sensor is dynamically characterized with acoustically generated Stokes layer excitation. At a bias voltage of 10 V, the sensor exhibits a linear dynamic sensitivity of 7.66 mV/Pa up to the testing limit of 1.9 Pa, a flat frequency response with resonance at 6.2 kHz, and a pressure rejection of 64 dB. The sensor has a noise floor of 14.9 μPa/√(Hz) at 1 kHz and a dynamic range >;102 dB. The sensor outperforms previous sensors by nearly two orders of magnitude in noise floor and an order of magnitude in dynamic range.

This paper presents the design, fabrication, and characterization of unique piezoresistive microfabricated shear stress sensors for direct measurements of shear stress underwater. Sidewall-implanted piezoresistors measure lateral force (integrated shear stress) and traditional top-implanted piezoresistors detect normal forces. In addition to the oblique-implant technique, the fabrication process includes a hydrogen anneal step to smooth scalloped silicon sidewalls left by the deep reactive ion etch (DRIE) process. This step was found to reduce the 1/f noise level by almost an order of magnitude for the sidewall-implanted piezoresistors. Lateral sensitivity was characterized using a microfabricated silicon cantilever force sensor. Out-of-plane sensitivity was evaluated by laser Doppler vibrometry and resonance of the plate element. In-plane sensitivity and out-of-plane crosstalk were characterized, as well as hysteresis and repeatability of the measurements. TSUPREM-4 simulations were used to investigate the discrepancies between the theoretical and experimental values of sidewall-implanted piezoresistor sensitivity. The sensors are designed to be used underwater for studies of hydrodynamic flows.

A silicon-based micromachined, floating-element sensor for low-magnitude wall shear-stress measurement has been developed. Sensors over a range of element sizes and sensitivities have been fabricated by thin-wafer bonding and deep-reactive ion-etching techniques. Detailed design, fabrication, and testing issues are described in this paper. Detection of the floating-element motion is accomplished using either direct or differential capacitance measurement. The design objective is to measure the shear-stress distribution at levels of O(0.10 Pa) with a spatial resolution of approximately O(100 μm). It is assumed that the flow direction is known, permitting one to align the sensor appropriately so that a single component shear measurement is a good estimate of the prevalent shear. Using a differential capacitance detection scheme these goals have been achieved. We tested the sensor at shear levels ranging from 0 to 0.20 Pa and found that the lowest detectable shear-stress level that the sensor can measure is 0.04 Pa with an 8% uncertainty on a 200 μm×500 μm floating element plate.

This paper discusses a noninvasive sensing technique for the
direct measurement of low-magnitude shear stresses in laminar and
turbulent air flows. The sensing scheme detects the flow-induced
in-plane displacement of a microfabricated floating-element structure
(500 μm×500 μm×7 μm), using integrated photodiodes.
The wall-mounted floating-element sensors were fabricated using a
wafer-bonding technology. The sensors were calibrated in a
custom-designed laminar flow cell and subsequently shown to be able to
transduce shear stresses of 0.01 Pa during tests in a low-speed wind
tunnel

A microfabricated floating-element (120 μm×140
μm×5 μm) liquid shear stress sensor has been developed using
wafer-bonding technology. The sensor has been designed for high shear
stresses (1-100 kPa) and high-pressure environments (up to 6600 psi) and
utilizes a piezoresistive transduction scheme. Analytical and
finite-element method (FEM) modeling have been performed to predict the
sensor response. The sensor has been tested for both its mechanical
integrity in high-pressure environments and its output response in the
controlled environment of a cone and plate viscometer. The processing
steps in the fabrication of the sensor, the analytical and FEM modeling,
the experimental procedures, and the results of the experiments are
described

A microfabricated floating-element shear-stress sensor for measurements in turbulent boundary-layers is reported. Using surface micromachining of polyimide, a 500- mu m multiplied by 500- mu m probe has been fabricated incorporating a differential-capacitor readout circuit. A model for the sensor response is described and is used for the design of an element to measure shear stresses of 1 Pa in air. The sensor is packaged for calibration in laminar flow, and electrical results obtained match the expected response.

A MEMS shear stress sensor for turbulence measurements Design and characterization of microfabricated piezoresistive floating element-based shear stress sensors

- Y Li
- V Chandrasekharan
- B Bertolucci
- T Nishida
- L Cattafesta
- M Sheplak

19 Li, Y., Chandrasekharan, V., Bertolucci, B., Nishida, T., Cattafesta, L., and Sheplak, M., " A MEMS shear stress sensor for turbulence measurements, " 46th AIAA Aerospace Sciences Meeting and Exhibit, AIAA, Reno, NV, 2008. 20 Barlian, A. A., Park, S. J., Mukundan, V., and Pruitt, B. L., " Design and characterization of microfabricated piezoresistive floating element-based shear stress sensors, " Sensors and Actuators a-Physical, Vol. 134, No. 1, 2007, pp. 77–87.

Viscous Fluid Flow A Numerical Study of Turbulent Separated Flows

- F M D White

White, F. M., Viscous Fluid Flow, McGraw-Hill, New York, 2nd ed., 1991. 32 Das, D., " A Numerical Study of Turbulent Separated Flows, " Amer. Soc. Mech. Engineers Forum on Turbulent Flows, FED, Vol. 51, 1987, pp. 85–90.

A MEMS-based shear stress sensor for high temperature applications

- N Tiliakos
- G Papadopoulos
- A O Grady
- V Modi
- R Larger
- L Frechette