A Family of Micromachined Wall Hot-Wire Sensors on ...

AIAA 2006-1244

44th AIAA Aerospace Sciences Meeting and Exhibit 9 - 12 January 2006, Reno, Nevada

A Family of Micromachined Wall Hot-Wire Sensors on Polyimide Foil for Measurement on Aerodynamic Surfaces Ulrich Buder*, Andreas Berns†, Jan-Philipp von Klitzing‡ and Ernst Obermeier§ Berlin University of Technology, Berlin, Germany, D-13355 and Ralf Petz** and Wolfgang Nitsche†† Berlin University of Technology, Berlin, Germany, D-10587

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Micromachined wall hot-wires composed of highly sensitive nickel thin film resistors of different geometries on a mechanically flexible substrate are presented. A sensor design optimized to reduce thermal losses and thus enabling measurement of high frequency fluctuations in fluid flows is the basis for a family of thermal anemometers with hot-wires of different widths (2 µm and 5 µm), length-to-width ratios (200 and 400), and cavity geometries. Employing polyimide foil as carrier material enables experimenters to apply sensors to aerodynamic surfaces like airfoils or turbine blades without distorting the original shape of the object due to mechanical mismatch. MicroElectroMechanicalSystems technology provides a diversity of additive and subtractive processes to realize the sensors. Processes originally designed for the micromachining of silicon were adapted to allow for the structuring of polyimide. Commonly employed in additive processes, the subtractive structuring of polyimide foil to the extent accomplished within this project is new to MEMS processing. Successfully realized sensors featuring different wire widths, lengths, and cavity dimensions were characterized in wind tunnel experiments. Sensor calibration against a wall-shear stress balance, cut-off frequency determination using a sine wave sweep, and recording of angular characteristics were conducted for all MEMS hot-wire sensors introduced. Wall-shear stresses of up to 1 N / m², corresponding to 20 m / s free-stream velocity, were obtained in an open wind tunnel on a flat plate with fully developed turbulent flow. Overheat ratios of 1.8 have been used for hours without thermal failure of sensors, providing a maximum cut-off frequency in still air of 80 kHz and a sensitivity of 0.196 V / (N / m²) without amplification in a wall-shear stress range from 0 to 1 N / m² with a power consumption of less than 30 mW for a sensor of 5 µm wire width and length-to-width ratio of 400.

Nomenclature a P R0 RW U0 U

= = = = = =

Overheat Ratio Electrical Power Electrical Resistance of Hot-Wire at Fluid Temperature Electrical Resistance of Hot-Wire in Operation Anemometer Output Voltage without Flow in Constant Temperature Operation Anemometer Output Voltage with Flow in Constant Temperature Operation

*

Ph.D. Student, Microsensor and Actuator Technology Center, Gustav-Meyer-Allee 25, 13355 Berlin, Germany, AIAA Student Member. † Ph.D. Student, Microsensor and Actuator Technology Center, Gustav-Meyer-Allee 25, 13355 Berlin, Germany. ‡ Graduate Student, Microsensor and Actuator Technology Center, Gustav-Meyer-Allee 25, 13355 Berlin, Germany. § Professor, Microsensor and Actuator Technology Center, Gustav-Meyer-Allee 25, 13355 Berlin, Germany. ** Ph.D. Student, Institute of Aeronautics and Astronautics, Aerodynamics, Marchstr. 12, 10587 Berlin, Germany. †† Professor, Institute of Aeronautics and Astronautics, Aerodynamics, Marchstr. 12, 10587 Berlin, Germany 1 American Institute of Aeronautics and Astronautics Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

I.

Introduction

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P

RECISE characterization of the state of wall-bound flows occurring on the surfaces of a multitude of technical objects used in aerospace transportation (e.g. airplane airfoils, fuselages), earth bound transportation of passengers (e.g. car bodies) and goods (e.g. pipe flows) or power generation (e.g. turbine blades), relies on knowledge of temporal and spatial distributions of wall shear stress and its fluctuations1. Based on such information, not only the prediction of important flow phenomena like transition or separation is possible, but also systems for active flow control can be developed and employed. Active control of transition, separation, noise, and skin friction drag will contribute to air travel safety, environmental compatibility, and airplane efficiency2. Investigating the effect of drag reduction through active control of wall-bound flows on airplanes alone, annual cost reductions of billions of dollars in fuel are estimated3. Sensors detecting wall shear stress either are direct measurement based devices using floating elements or make use of indirect measurement principles relying on heat transfer phenomena4 or momentum balance. Production of the former is usually complex and thus expensive, sensor dimensions are large and miniaturization usually reduces sensor durability. Indirectly measuring sensors, predominantly hot-wires and hot-films, are comparatively easy to manufacture and can be miniaturized without necessarily affecting durability. For measurement of wall shear stress in turbulent flows, sensor miniaturization is highly important as flow features as small as 100 µm within time scales of 2 ms or less can easily occur in low-speed turbulent boundary layers5. To reduce overall sensor size beyond dimensions realizable with conventional machining technology or precision engineering, to lower production costs, and to simplify production processes, MEMS (Micro Electro Mechanical Systems) technology presently is widely used in manufacturing miniature flow sensors for research applications. A variety of MEMS flow sensors employing direct or indirect measuring principles exists6, some of which allow for measurement of turbulent fluctuations up to 20 kHz7 and beyond. While the temporal resolution of selected MEMS and conventional wall shear stress sensors is sufficient for monitoring of fluctuations in wall bound flows, the problem of providing both a high spatial and a high temporal resolution in one shear stress sensor system has received only little attention. Such systems would be well suited to detect the occurrence and amplification of Tollmien-Schlichting instabilities prior to transition8. In combination with miniature actuators closed loop control to eliminate or reduce such instabilities by destructive interference becomes possible. Almost all MEMS sensors used for wall-shear stress measurement today are silicon based due to the predominant role of the material in semiconductor and MEMS processing9. Arrays of micromachined thermal wall shear stress sensors on a rigid silicon substrate have enabled researchers to conduct measurements on flat plates10. The use of such silicon based sensors or sensor arrays on curved surfaces automatically results in boundary layer disturbances caused by the thickness of the silicon sensors and the distortion of the original surface contour. Efforts to reduce this distortion make use of small rigid silicon chips embedded into a mechanically flexible polyimide layer11 to provide semi-flexible wall-shear stress sensor arrays12. Thus a reduction of the mismatch in curvature is possible. Still both bending radius and reproducibility of the original surface shape are limited by the size of the silicon islands (Fig. 1).

Figure 1. Geometrical mismatch of a silicon based semi-flexible sensor array on a typical aerodynamic surface. Both thickness and lateral size of silicon sensors can cause mismatch of measurement surface and sensor and thus introduce errors to flow measurement. 2 American Institute of Aeronautics and Astronautics

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Wall hot-films and hot-wires measure wall shear stress indirectly. The simplest operating principle for such a sensor is the feeding of a constant electrical current into the wire or film, which exhibits an electrical resistance to the current. By Joule Heating electrical energy is converted into heat energy within the wire, thus increasing the wire temperature. Wire temperature and wire resistance are coupled through the temperature coefficient of resistance (TCR). In constant current mode the wire is heated to an equilibrium temperature. Imposing a fluid flow on the heated wire disturbs this equilibrium state as the flow transports heat energy away from the wire by forced convection. A new equilibrium featuring a different wire temperature and thus a changed wire resistance is established. Therefore in constant current operation the wire or film resistance is a measure for the wall shear stress. In constant current mode as well as the more advanced constant temperature operation, in which a feedback amplifier is used to keep the wire temperature constant, the magnitude of the TCR dominates the sensitivity of the sensor at a fixed overheat ratio a. The overheat ratio is defined as a = RW / R0. Due to direct coupling of electrical resistance of the wire and wire temperature, the overheat ratio is an indicator for the operating temperature of the hot-wire. Power consumption and temporal behavior of hot-wires is heavily dependent on thermal losses of the wire to its surroundings. Materials with low thermal conductivity and heat capacity allow for low power consumption and small time constants for heating and cooling of the wire. It is remarkable that all MEMS wall hot-wires presented in literature make use of structures directly coupled to the wire over its full length. Structures like membranes, beams, or bridges13,14 (depicted in Fig. 2 a, b, and c) are most commonly used to provide mechanical support for the wire or to ease production processes. They also influence the thermal equilibrium of the wire and thus have direct influence on power consumption and temporal behavior of the wire. The family of sensors introduced herein is the building block for a sensor system that allows for monitoring of wall shear stress and its spatial and temporal fluctuations. All sensors feature a fully flexible substrate material to avoid mechanical mismatch of sensor and measurement surface as well as small size metallic hot-wires with very high TCR. Power consumption and temporal behavior of the sensors have been optimized through thermal simulation, careful material selection, omitting of supporting structures for the hot-wires, and the introduction of an air filled cavity underneath the wire.

a)

b)

c)

Figure 2. Structures directly coupled to hot-wires in current silicon-based MEMS wall hot-wire sensors. Sketch a) depicts a membrane supporting the hot-wire, sketch b) and c) show a hot-wire on a beam and on a bridge structure, respectively.

II.

Sensor Design, Optimization and Fabrication

As design and thermal simulation of one of the sensors presented herein (type A) have been discussed in detail in an earlier publication15, this section only provides a brief summary necessary for a thorough understanding. A. Basic Sensor Setup A three-dimensional schematic of the basic set-up of the MEMS hot-wire sensors is given in Figure 3. Unlike the sensors depicted in Figure 2 no mechanical structure is directly coupled to the hot-wire. An air filled cavity thermally insulates the wire and allows the flow to fully surround the wire. At the cavity edges the 2 µm thick and 2 µm or 5 µm wide hot-wire merges with 50 µm wide conducting paths. As Joule heat generation is negligible the conducting paths, unwanted heat losses only occur through heat conduction from the hot-wire over the conducting paths into the substrate.

3 American Institute of Aeronautics and Astronautics

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Figure 3. 3D schematic of half a hot-wire sensor on polyimide foil. B. Material Selection To allow for application of the sensor to aerodynamic surfaces, a flexible substrate material is needed. Polyimide foil, available from different suppliers, has proven compatible with microelectronic processing and, at present, is the most important substrate material for flexible printed circuit boards16. Polyimide is very resistant to chemical attack and, in the group of polymers, has a very high maximum operating temperature of almost 400 °C. Its thermal conductivity is very low (0.147 W·m-1·K-1)17 if compared to the average conductivity of silicon (156 W·m-1·K-1 at 300 K)18 or thin film silicon nitride (4.5 W·m-1·K-1)19, used as membrane material in MEMS wall hot-wires on a supporting membrane over a sealed low-pressure cavity10,20. For the realization of a cavity underneath the hot-wire, structuring of the material using MEMS processes is necessary. A specific polyimide enabling structuring by Reactive Ion Etching (RIE) at sufficiently high etch rates21 was identified. Careful selection of the hot-wire material is necessary as, at given overheat ratio a, the TCR of the material dominates the sensitivity of the sensor to wall shear stress fluctuations. Doped polysilicon, as used in many silicon based micromachined wall hot-wires, exhibits TCRs in the range from 0.0008 K-1 to 0.003 K-1,22 but, dependent on doping concentration exhibits a substantial piezoresistive effect when subjected to mechanical stresses (e.g. membrane bending due to pressure differences). Metals can exhibit even higher TCRs than doped polysilicon with nickel featuring one of the highest known bulk TCR of 0.0068 K-1 of a metal23 that can be deposited by MEMS processes. Thin film metals usually have lower TCRs than bulk metals, however, a TCR for thin film nickel of 0.0055 K-1 has been reported24. Therefore nickel has been selected as wire material.

C. Thermal Optimization Thermal simulations using a 2D cross-sectional model of such sensor featuring a hot-wire of 2 µm x 2 µm crosssection (Fig. 4 left) have shown that energy losses of the hot-wire through heat conduction can be halved by placing a cavity of at least 90 µm depth underneath the wire (Fig. 4 right). Close coupling of the heated resistor and any material with high thermal conductivity (the thermal conductivity of polyimide is approx. five times higher than that of air), as discussed earlier, inevitably increases thermal losses (Fig. 5).

4 American Institute of Aeronautics and Astronautics

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Figure 4. A simulated temperature distribution within a 2D model of a wall hot-wire with cavity is shown on the left. On the right an excerpt of results obtained through FEM simulations of thermal conduction within a sensor featuring a hot-wire over an air-filled cavity is depicted. Changes of power consumption against changes of cavity geometry are depicted for the sensor being glued to a aluminum carrier.

a)

b)

Figure 5. Energy balance of wall hot-wire sensor with cavity (a) and wall hot-wire without cavity (b). Without cavity, heat losses into the substrate are substantial and thus heat transfer due to convection is small. A sensor featuring a cavity loses less energy into the substrate. The size of the arrows corresponds to the amount of energy transferred. D. Fabrication and Sensor Types Individual manufacturing steps to realize the sensors described have been published previously15. Process steps and tools developed especially for the realization of the sensors include a carrier for foil handling in equipment designed for wafer handling, a sputtering process to improve film adhesion of metals on polyimide and a reactive ion etching process providing both high etch rate and low surface roughness21. Based on material selection, thermal simulation, and optimization, a multitude of different sensor geometries is imaginable. The list of possible sensor geometries was reduced to six different setups considering effects on sensor sensitivity, mechanical stability and power consumption of the hot-wires, hot-wire end losses, and angular sensitivity. Small wire cross-sections contribute to a high sensitivity and cut-off frequency but reduce the mechanical stability of the wire. Thus wires with 2 µm width (sensor types A, C, E, F) as well as wires with 5 µm width (sensor types B, D, G) were selected for fabrication. As long hot-wires according to literature are less sensitive to variations in flow direction but more likely to fail mechanically, wire length-to-width ratios of 200 (sensor types C, D) and 400 (sensor types A, B, E, F, G) have been realized. To verify the simulation-based conclusion that cavity width has a very small influence on sensor power consumption at sufficiently large cavity depths (compare Fig. 4), sensors with a cavity width of 400 µm (sensor types A, B, C, D, F, G) as well as 1000 µm (sensor type E) have been manufactured. The influence of a tapered hot-wire (2 µm on the cavity edges, 6 µm in the 5 American Institute of Aeronautics and Astronautics

middle of the wire) on the temperature profile and end losses of the sensor is investigated using sensor type F. Figure 6 depicts a successfully realized sensor of type F. Table 1 lists the different sensor types manufactured and their individual geometry.

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Figure 6. MEMS wall hot-wire sensor on polyimide foil.

Table 1. Different wire and cavity geometries based on an optimized basic sensor setup. Wire and conductor dimensions are ten times magnified relative to depicted cavity dimensions. Dimensions in all sketches are comparable.

min. wire width [µm]

length-towidth ratio

cavity width [µm]

A

2

400

400

B

5

400

400

C

2

200

400

D

5

200

400

E

2

400

1000

F

2/4/6

400

400

geometry

sketch of cavity and wire geometry

type

6 American Institute of Aeronautics and Astronautics

III.

Experimental Setup

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A. Temperature Coefficient of Resistance As an experimental determination of hot-wire temperature when heated by electrical power is very difficult, a temperature test cabinet is used to impose known temperatures onto the nickel thin film hot-wires to evaluate their TCR. Four point probe measurement is used to precisely determine hot-wire resistance at various temperatures, as described in Ref. 20. B. Static Calibration, Power Consumption, and Angular Measurement Calibration and angular measurements were conducted in constant-temperature mode using an IFA 100 Anemometry System (TSI). No subsequent amplifying of the signal was conducted. Three single sensors glued onto a cylindrical adapter (Figure 7) inserted flush with the surface of a flat plate were mounted in an open low-speed wind tunnel and evaluated simultaneously. Electrical contact was established using thin insulated wires soldered to the bond-pads of the hot wires and led to the backside of the adapters through holes to the left and right of the individual sensor. Free stream velocities from 0 m / s to 20 m / s were used for static calibration of the sensors. A conventional wall shear stress balance mounted at the same distance from the leading edge of the flat plate as the sensors provided a reference wall shear stress signal. Resulting wall shear stresses ranged from 0 N / m2 to approx. 1 N / m². Calibrations at overheat ratios of 1.2, 1.5, and 1.8 were conducted in enforced turbulent flow. Anemometer output voltage as well as the voltage drop over the hot-wire were recorded using a 16bit analog-digital-converter with a sampling rate of 15 kHz. Sampling time for all measurements was 3 s, anemometer and hot-wire signals provided are averaged over that time period. Hot-wire voltage signals were used to determine the power consumption of the sensors. Sensors featuring the wire geometry of a sensor of type A without cavity were mounted on two of the three cylindrical adapters to obtain reference measurements for calibration and angular sensitivity. Determination of the angular behavior of the hot-wires was conducted by rotating the cylindrical adapter in the plane of the flat plate in steps of 15°. Thus unfortunately the soldering areas are rotated into the flow upstream of the wires and are expected to be a source of flow disturbance at high rotational angles around +/- 90°.

Figure 7. MEMS wall hot-wire sensors of different geometries on a cylindrical carrier to be inserted into a wind tunnel wall.

C. Cut-off Frequency Measurement In accordance with the measurement method proposed by Freymuth25, an electrical sine sweep is fed into the hot-wire input circuit and compared to the response of the anemometer system. The generation of the sine sweep signal and the signal comparison is conducted using a signal generator and analyzer, the output of the analyzer is post-processed on a conventional personal computer.

7 American Institute of Aeronautics and Astronautics

IV.

Results and Discussion

A. Temperature Coefficient of Resistance The average TCR in a temperature range of 20 °C to 150 °C of the nickel thin film hot-wires manufactured is 0.0054 K-1 and thus not substantially smaller than the one of a nickel reference resistance defined in DIN 43760 for nickel temperature measuring resistors of 0.006 K-1. The resistance-temperature behaviors of both hot-wire and reference resistor with a resistance of 10.8 Ohms at 20 °C is depicted in Figure 8.

Electrical Resistance,

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20 18 16 14 12 Resistance Hot-Wire Reference Resistance DIN 43760

10 20

40

60

80

100

120

140

160

Temperature, °C Figure 8. Resistance-temperature behavior of micromachined nickel thin film hot-wire and reference resistance according to DIN 43760. B. Static Calibration, Power Consumption and Angular Measurement Free stream velocities of 30 m / s resulting in a wall-shear stress of 2 N / m² (as measured with a conventional wall-shear stress balance) caused none of the hot-wires to fail mechanically at overheat ratios of up to 1.8. It is expected that even substantially higher wall-shear stresses will not induce mechanical failure of the sensors. Sensor calibration against the signal of a wall-shear stress balance was conducted for all sensor geometries listed in Table 1. Figure 9 shows calibration curves of sensor types B, C, D, E, F, and of a reference sensor without cavity in a wall shear stress range from 0 to almost 1 N / m² at an overheat ratio of 1.2 (left) and 1.8 (right). Data of sensor A were omitted in the graphs for improved clarity, as calibration curves of sensors of type A and type E have a maximum deviation of 5 %. The reference sensor without cavity features the lowest average wall shear stress sensitivity in the given measurement range of 0.027 V / (N / m²) and 0.047 V / (N / m²) for overheat ratios of 1.2 and 1.8, respectively. Of all sensor types with cavity, the sensor of type B, having the largest wire dimensions (2000 µm x 5 µm x 2 µm), shows the highest wall shear stress sensitivity of 0.095 V / (N / m²) and 0.196 V / (N / m²) at a = 1.2 and a = 1.8, respectively. Regardless of overheat ratio, comparing sensor types featuring hot-wires of equal width reveals that hot-wires with a length-to-width ratio of 400 provide larger wall shear stress sensitivities than sensor types with a length-to-width ratio of 200. Within a group of hot-wires with the same length-to-width ratio, the sensors featuring wider wires exhibit larger voltage differences. This advantage in wall shear stress sensitivity, however, is connected to a higher power consumption of sensors with wider wires and larger length-to-width ratios (Fig. 10). Only sensor type F featuring a hot-wire with tapered cross section does not seem to fit into the observed correlation. Even though the sensor has a high power consumption, the voltage difference obtained in flow is the smallest of all sensor types with cavity. The average wire width of a hot-wire of type F is 3.75 µm, consequently the power consumption is higher as that of a 2 µm wide hot-wire. Based on this average wire width, sensor type F features an unfavorable length-to-width ratio of 213, which, as described above, goes along with a reduced sensitivity. Normalizing the anemometer output voltage difference by the power consumption of the sensor, a relative sensitivity can be established which is depicted in Figure 11. 8 American Institute of Aeronautics and Astronautics

0,10

Type B Type E Type D Type C Type F A w/o Cavity

U - U0, V

0,06

Type B Type E Type D Type F Type C A w/o Cavity

0,18 0,16 0,14 0,12

U - U0, V

0,08

0,20

0,04 0,02

0,10 0,08 0,06 0,04 0,02

0,00

0,00 -0,02

0,0

0,2

0,4

0,6

0,8

0,0

1,0

0,4

0,6

0,8

1,0

Wall Shear Stress, N / m²

Figure 9. Static Calibration of MEMS wall hot-wire sensors of types B, C, D, E, and F. A reference sensor without cavity was also calibrated. The left graph shows calibration data for sensors operated at an overheat ratio of 1.2, the right graph provides data obtained at an overheat ratio of 1.8. 0,024

0,07

0,020

0,06

Power Consumption, W

Power Consumption, W

A w/o Cavity Type B Type F Type E Type D Type C

0,016 0,012 0,008 0,004 0,000 0,0

0,2

0,4

0,6

0,8

A w/o Cavity Type B Type F Type D Type E Type C

0,05 0,04 0,03 0,02 0,01 0,00

1,0

0,0

Wall Shear Stress, N / m²

0,2

0,4

0,6

0,8

1,0

Wall Shear Stress, N / m²

Figure 10. Power Consumption of MEMS wall hot-wire sensors of types B, C, D, E, and F dependent on wall shear stress. A reference sensor without cavity is also investigated. The left graph shows data for sensors operated at an overheat ratio of 1.2, the right graph provides data obtained at an overheat ratio of 1.8.

0,0

0,2

Type C Type E Type D Type B Type F A w/o Cavity

(U - U0) / P, V / W

Type E Type C Type D Type B Type F A w/o Cavity

(U - U0) / P, V / W

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Wall Shear Stress, N / m²

0,2

0,4

0,6

0,8

Wall Shear Stress, N / m²

1,0

0,0

0,2

0,4

0,6

0,8

1,0

Wall Shear Stress, N / m²

Figure 11. Anemometer output voltage difference normalized by power consumption of MEMS wall hotwire sensors of types B, C, D, E, and F dependent on wall shear stress. A reference sensor without cavity is also investigated. The left graph shows data for sensors operated at an overheat ratio of 1.2, the right graph provides data obtained at an overheat ratio of 1.8. 9 American Institute of Aeronautics and Astronautics

Power normalized sensitivity, which is especially important when operating a multitude of sensors in an array setup, is highest for sensor types featuring 2 µm wide hot-wires. Differences in length-to-width ratio of the hot-wires seem to have no pronounced influence on relative sensitivity in the experiments conducted. As expected, the relative sensitivity of sensor type F and the reference sensor without cavity are low. The normalized angular behavior of a hot wire of type B for a full rotation of the cylindrical sensor carrier at an overheat ratio of 1.8 and a free stream flow velocity of 20 m / s is depicted in Figure 12. Fluid flow normal to the wire length is defined as 0°, positive angles describe rotation in negative mathematical direction. As expected, the flow is disturbed at angles of –90°, 90°, and 270° due to upstream soldering areas and thus locally does not follow the cosine law (red line in Figure 12).

Anemometer Output Difference V - V0°

-90

-45

0

45

90

135

180

225

270

Sensor Type B Cosine Function

Figure 12. Angular behavior of a wall hot-wire sensor of type B. The cosine function is given as reference. The sensitivity of different hot-wire geometries to changes in angle for a rotation from –90° to 90° is depicted in Figure 13. Data of all hot-wires exhibit the assembly-related disturbance at angles of -90° and 90° which is also observed in Figure 12. The signal of the reference sensor without cavity shows the lowest dependence on flow

0,00

-0,01

-0,02

U - U0°

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Angle, °

A w/o Cavity Type D Type F Type C Type B Type E

-0,03

-0,04

-0,05 -90

-60

-30

0

30

60

90

Angle, ° Figure 13. Angular behavior of MEMS wall hot-wire sensors of types B, C, D, E, and F at an overheat ratio of 1.2 and a free stream velocity of 20 m / s (corresponding to a wall shear stress of approximately 0.94 N / m²). A reference sensor without cavity is also investigated. 10 American Institute of Aeronautics and Astronautics

C. Cut-off Frequency Measurement The cut-off frequency of a constant-temperature hot-wire anemometer system is a combination of the corresponding frequencies of control electronics and the hot-wire itself. As the experimentally determined cut-off frequencies of the different MEMS wall hot-wires examined only differ negligibly a dominant influence of the control circuit on the cut-off frequencies is assumed. Thus, representatively, the dependency of the cut-off frequency on the overheat ratio for a sensor of type A is depicted in Figure 14.

Cut-Off Frequency [Hz]

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angle, which is caused by the close thermal coupling of wire and substrate. The substrate in proximity of the wire is heated and is cooled more effectively as in a narrow hot-wire. Amongst the different types of wall hot-wire sensors with cavity, the sensor types featuring a length-to-width ratio of 400 exhibit a larger drop of anemometer voltage when angled than hot-wires with smaller length-to-width-ratios. Comparing sensors with equal length-to-widthratios, 5 µm wide hot-wires are less sensitive to rotation than narrower types with an equal length-to-width-ratio. The sensor of type F with an effective wire width of 3.75 µm and an effective length-to-width ratio of 213 thus should show a rotation dependent voltage drop smaller than that of a sensor of type C (2 µm wide hot-wire, lengthto-width-ratio of 200) but larger than that of a sensor of type D (5 µm wide hot-wire, length-to-width-ratio of 200). The experimental data for sensor type F shows a corresponding behavior. The experimentally determined angular behavior of the different sensor types is based on thermal conduction within the wire. Increased thermal conduction within wires with larger cross-section yields temperature profiles along the wire length that feature smaller regions of constant temperature, in which no thermal transfer to the fluid takes place. Comparing hot-wires with equal width a longer hot-wire (larger length-to-width ratio) has a temperature profile with a larger region of constant temperature in which no thermal energy is transferred to the flow.

80000 70000 60000 50000 40000 30000

Cut-Off Frequency 2 at = 0 N/m

20000

1,2 1,3 1,4 1,5 1,6 1,7 1,8

Overheat Ratio Figure 14. Cut-Off Frequency of MEMS wall hot-wire (type A) anemometer in constant-temperature mode at different overheat ratios.

V.

Conclusion

Different MEMS wall hot-wire sensors on a flexible substrate material have been developed. Aerodynamic tests have proven their suitability to accurately measure high frequency fluctuations up to 80 kHz using standard constant-temperature anemometer systems. Based on FEM analysis and first principles, thermal optimization of the sensors has been conducted, the effectiveness of which is well demonstrated by comparing the power consumption of hot-wires with cavity and hot-wires without cavity. Employing a flexible substrate material, a mismatch of measurement surface and sensor surface is avoided. Dependent on the individual application, a specific sensor type should be selected: If large absolute wall shear stress sensitivity is required and low power consumption is not of primary importance, a wire with large cross section and length should be used. In applications requiring high energy efficiency, especially in array setups, sensors with a high power-related sensitivity seem best suited. It was shown experimentally that MEMS wall hot-wires with small cross section provide high power-related wall shear stress 11 American Institute of Aeronautics and Astronautics

sensitivity. Wires with small length-to-width ratio but large cross section should be used in flows with an unknown and unwanted wall shear stress component lateral to the wire, as the flow angle dependent anemometer voltage drop is smallest for such sensors.

Acknowledgments Financial support by the Deutsche Forschungsgemeinschaft (SFB 557, TP C6) is gratefully acknowledged.

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12 American Institute of Aeronautics and Astronautics