#1.2.2.1 Working principle

A hot-wire anemometer uses a fine wire which is electrically heated to some overheat point (figure 1.3). Its average temperature settles down to an equilibrium depending on three power contributions:Radiative effects are negligible, as they make for a 10^–4 fraction of the power budget at ambient pressure conditions (Comte-Bellot 1976)⁸.

1. Joule heating power,
2. end conduction thermal losses (undesirable because not velocity-dependent),
3. thermal losses to the fluid: conduction (not velocity-dependent) and forced convection (dependent on the flow velocity).

End conduction losses depend solely on the conductor’s thermal conductivity, and are unwanted because they undermine the device’s sensitivity. The thermal losses to the fluid split into two terms, conduction and forced convection. The ratio between total heat transfer and conductive heat transfer is expressed by the Nusselt number \text{Nu} = \frac{hd}{k}, where k is the thermal conductivity of the fluid, h the convection coefficient and d the characteristic dimension, here the diameter of the wire. Nu gives an image of the efficiency of forced convection, which is desired to be high. King (1914)⁹ empirically expressed the Nusselt number dependence to the Reynolds with calibration constants A and B \text{Nu} = A + B\sqrt{\text{Re}}, meaning that the convective part of heat transfer to the flow varies with the square root of the velocity. Considering an infinitely long cylinder (neglecting the end conduction effects), the power equilibrium over a segment length \ell of resistance R_\text w heated by a current I can be expresssed: R_\text w I^2 = \pi d h \ell \Delta T = \text{Nu} \cdot \pi \ell k \Delta T. For all metals, electrical resistivity depends on the temperature with the relationship R_\text w - R_0 = R_0 \cdot \text{TCR} (T - T_0), defining the TCR expressed in [K^-1] as a constant property of the material, and key contributor to the device’s sensitivity. Usually, hot wires are chosen with high TCR metals, like tungsten or platinum.Platinum has a TCR of 3800 ppm/K while tungsten has a TCR of 3600 ppm/K (Bruun 1996)¹⁰. While being a little less sensitive, tungsten’s high melting point makes it an ideal material for hot wires.


As a consequence, at constant current, there is a dependence of the voltage readout E_\text w at the wire terminals with the flow velocity U: \frac{E_\text w^2}{R_\text w} = \left(A + B \sqrt{U}\right)(T - T_0).

The exact occurrence of the first hot wire remains uncertain, but they were extensively used in research since the 1910s, in order to obtain finer velocity measurements than Pitot tubes. After the Second World War, the eletronics department of the Danish company DISA launched Dantec Dynamics, which quickly became the industry leader in thermal anemometry. Their 55A series probes and controllers were extensively used in both academic research and engineering, accompanying aerospace innovations during the Cold War. Currently, they dominate the market and offer a wide range of probes and controllers and have diversified to other flow measurement techniques.

#1.2.2.2 Constant temperature anemometry

Early hot wires were operated in CC mode, the most common configuration being the hot wire incorporated into a Wheatstone bridge. The bridge voltage sets the overheat value while the arm imbalance reacts proportionally to the probe resistance. While CC anemometers worked well to measure mean flow velocities, the need to also catch fast fluctuations quickly emerged. However, engineers faced a prominent “lag” effect (Dryden & Kuethe 1930)¹¹, due to the thermal time constant of the wire itself, which prohibited any high-frequency content to be caught.

The idea to broaden the bandwidth by operating hot wires at a constant resistance (i.e. temperature) was first introduced by Ziegler (1934)¹², and laid the groundwork for substantial improvements in the frequency response. The first commercial CTA system was launched in 1958 by DISA. In the late 60’s, the emergence of low-cost high-performance IC amplifiers enabled quick developments in control theory to improve the frequency response to 16 kHz (Freymuth 1967)¹³, then 25 kHz (Freymuth 1977)¹⁴. Ultimately, careful component selection and precise fine-tuning of the control loop time constants enabled Watmuff (1994)¹⁵ to develop a research-grade 250-kHz anemometer which is still in use at Princeton and Melbourne universities. Currently, Dantec advertises a 450-kHz bandwidth for their latest system. To illustrate the benefits of closed-loop control, Ghouila-Houri et al. (2017)¹⁶ showed the open-loop time constant of the HTGS (which is presented in detail in section 1.2.3.4) heating element to be around one millisecond, limiting the bandwidth to the kilohertz. By using a CTA controller, the HTGS response time has been improved more than ten-fold, enabling to get energy spectra up to 13 kHz (Ghouila-Houri et al. 2021)¹⁷.

The core block diagram of a CTA has been established by Perry & Morrison (1971)¹⁸ (figure 1.5). The hot wire is placed into a Wheatstone bridge regulated with a feedback loop. At equilibrium, the bridge’s arm resistances are equal, i.e. the hot wire Z_\text{HW} matches the potentiometer Z_\text{OH}, assuming a bridge ratio of 1. The error voltage E_\text{i} equals zero, and a DC voltage E_\text{o} is fed at the top of the bridge. Resistance fluctuations in the hot wire will unbalance the bridge and creating a small error voltage E_\text{i}. The differential amplifier compensates to equalize both of its inputs, bringing back the bridge at equilibrium. The fluctuating bridge voltage serves as the controller’s output, giving an image of the power compensation needed to maintain constant temperature. The hot wire overheat (OH, temperature increase from ambient) can be tuned with the Z_\text{OH} potentiometer. Assuming square-root resistance dependence to flow velocity, the power compensation image E_\text O^2 of the controller also scales with the square root of the flow velocity: E_\text O^2 = A + B\sqrt U.

#1.2.2.3 Micro- and nanoscale hot wires

While temporal resolution was greatly improved by refining control electronics, spatial resolution still matters in order to fully capture fine details of the turbulence. Commercially available hot-wire probes are made with 1 mm long wires with typical diameters of 5 µm. In this context, advances in microfabrication for solid-state electronics led to the emergence of the MEMS field, opening the way to miniaturized flow sensors. Jiang & Ho (1994)¹⁹ at UCLA/CalTech first reported the successful fabrication of a 160 × 1 × 0.5 µm hot wire out of polysilicon, in order to address both spatial resolution and individual by-hand manufacturing issues. During the nineties, their team extensively refined and characterized iterations of this design to improve the sensitivity and thermal bandwidth (Mischler et al. 1995)²⁰.

In the early 2010s, a team at Princeton University developed an out-of-plane nanoscale hot wire (Bailey et al. 2010)²¹, which launched the NSTAP sensor series. The sensing wire was shrunk down to 100 × 60 × 2 nm, in order to capture the very smallest turbulent eddies at high-Reynolds, and enabled to overcome the spatial filtering effect. More recently, they introduced an ultrafast temperature probe (cold wire) (Arwatz et al. 2015)²², and a X-shape probe to measure two components of the velocity vector (Fu et al. 2019)²³. The thesis work of Samie (2018)²⁴ reported extensive modelling and in-flow characterizations of NSTAP, using Jonathan Watmuff’s optimized CTA controllers in high-Reynolds flows, and showed exceptional agreement to analytical and numerical models.

Simultaneously, our research team at IEMN developed a similar design, with nanocrystalline diamond prongs for mechanical robustness and end thermal conduction minimizing (Talbi et al. 2015)²⁵. The sensing wire was made of a stress-compensated Ni/W multi-layer and the device characterized in steady flows up to 30 m/s. More recently, a Montpellier University team reported the fabrication of the µTA, a similar microscale thermal anemometer, with a 60 × 1.5 × 0.2 µm platinum heater supported by silicon prongs (Baradel et al. 2021)²⁶. It successfully characterized a turbulent boundary layer with a 25 m/s freestream velocity.

-> conclusion fils chauds

#1.2.3.1 The boundary layer

Close to a solid surface in contact with a fluid, a no-slip condition is forced on the fluid due to its viscosity. This results in a velocity gradient ranging from u = 0 at y = 0 on the wall surface, to u = u_\infty infinitely far away (figure 1.7). The profile of this gradient widely depends on the Reynolds number, wall roughness, geometry and pressure distribution. The boundary layer is defined as the zone between the wall and the point where flow velocity reaches 99 % of the freestream velocity. Consequently, a WSS \tau_\text w develops at the wall-fluid interface, depending solely on the fluid’s dynamic viscosity \mu = \rho\nu and the velocity gradient on the wall: \tau_\text w = \mu \left. \frac{\partial u}{\partial y} \right|_{y=0}

This WSS (or skin friction), is one of the main contributors to the aerodynamic drag force, the other being the pressure drop created by flow separation of the back-facing surfaces. While measuring WSS value is of great interest for optimizing surfaces and geometries for drag reduction, it also gives information about freestream velocity and boundary layer vorticity content. Figure 1.8 shows a classification of the existing WSS measurement techniques. It is possible to infer the WSS value with boundary layer profiling, i.e. measuring the u(y) velocity profile by multiple hot-wire measurements. However, this is valid only for stationary, well developed flows because of the time needed to perform the series of measurements. However, this indirect inference of the wall shear stress needs backup from a direct measurement such as the oil film technique. An oil droplet is deposited on the wall, which will be spread out by the wall shear force. Knowing the viscosity and optical index of the oil, an interferometric measurement of its thickness gives a direct measure of the WSS. The focus of this work is mainly on sensors, therefore sensor-based methods are developed in the following paragraphs. In particular, emphasis is brought on those compatible with microfabrication processes: obstacles, balances and thermal sensors. Additionally, there is much more literature on balances and thermal sensors than on obstacle-based methods, because they offer higher sensitivity and spatial resolution, and are non-intrusive since they do not require any protruding structures.

#1.2.3.2 Obstacles

In a similar manner to Pitot tubes, obstacles can be used to measure WSS by obstructing the flow at wall proximity. Because the large space-averaging due to their size, they are limited to flows with thick boundary layers. Concerning fences and pillars nonetheless, there have been miniaturization efforts, with piezoresistive or optical transduction methods replacing the pressure intakes. Ernst Obermeier’s team at TU Berlin, while reporting proficient developments in thermal flow sensors (developed below), also developed a 5000 × 315 × 10 µm MEMS fence sensor, with piezoresistors placed at the stress concentration zones (von Papen et al. 2004)²⁸. Over the late 2000s and early 2010s, they refined the design and conducted static and dynamic characterizations in a vortex rig flow (Savelsberg et al. 2012)²⁹. However, the authors noted that the natural resonance frequency of the structure, around 2 kHz, was a limiting factor to dynamically characterize the turbulent boundary layer.

Pillars, while presenting the same mechanical filtering effect as fences, can be placed in arrays in order to 2D map the two components of the wall shear force. The concept has first been implemented by Große et al. (2006)³¹ at Aachen University, with 200 to 300-µm-high polymer pillars with a reflective tip for optical characterizations. They have been characterized in a deionized water flow, in order to obtain high shear rates at low Reynolds (\leq 1). They successfully demonstrated 2D mapping of WSS with a spatial resolution of 125 µm in both water and air (Gnanamanickam et al. 2013)³².

However, the limitations inherent to obstacle-based methods, even at MEMS scales, hindered further development, and little to no follow-up research appears to have been reported in the 2010s and 2020s. In contrast, other approaches to WSS measurement have continued to evolve and have demonstrated significant progress, namely direct and thermal methods.

#1.2.3.3 Direct methods

Mechanical systems can perform a direct measurement of the WSS value without needing a protruding obstacle. A floating mass-spring system flush-mounted to a wall will undergo a displacement \delta, which can be measured by several transduction methods (figure 1.10). Consequently, the sensitivity depends solely on the spring’s elastic modulus k and wet area A of the mass. This results in accurate and calibration-free WSS measurement: \tau_\text w = k\delta/A. As a downside, these designs are more complex to microfabricate than fences or pillars. In order to convert the displacement to a readout value, several transduction principles can be employed: combed capacitances, strain gauges, piezoelectric crystals and optical interferometry. Froude (1872)³⁴ did pioneer direct WSS measurement in water flow, by flush-mounting a floating plate to a ship hull. During the 50s and 60s, the developments of electric transduction methods enabled sensitivity and temporal resolution improvements, and WSS balances were extensively used on wind tunnels, experimental aircrafts and rockets.

The first microfabricated WSS balance was developed during the PhD thesis of Schmidt (1988)³⁵ at MIT, out of polyimide deposited on an oxidized silicon wafer. This laid the groundwork for the most common direct shear sensor architecture, consisting of a floating element supported by a parallel linkage spring array, and using capacitive transducers to convert displacement into a readout voltage. A similar design was introduced with piezoresistive transducers for use in liquid environments (Shajii et al. 1992)³⁶, enabled by wafer bonding to have the floating mass made of silicon and have the strain gauges electrically insulated. Over the 1990s, MIT research teams further refined this design by introducing optical transducing to improve the sensor resolution in low-speed configurations (in the mPa range), also enabling dynamic measurements up to 10 kHz (Padmanabhan et al. 1997)³⁷.

Mark Sheplak, who did postdoctoral work at MIT between 1995 and 1998, brought WSS balance knowledge to University of Florida and reported continuous iterative developments on the design up to this day (as of 2025). One of the main challenges in flow measurement in general, is to accurately generate fully characterized flow configurations, in order to calibrate the sensors. This is particularly true for dynamic calibrations, as it is complex to generate a physical flow step input or sinusoidal sweep. Answering this challenge, Sheplak’s research group developed a novel calibration method for wall shear stress sensors, based on standing acoustic waves in a tube (Sheplak et al. 1998)³⁸, generating a sinusoidal velocity field. Chandrasekaran et al. (2005)³⁹ reported dynamic calibration of WSS balances with optical transduction up to 20 kHz using this apparatus. Chandrasekharan et al. (2011)⁴⁰ reported an iteration of the design with capacitive transduction, with an improvement on dynamic range of one order of magnitude. Mills et al. (2015)⁴¹ achieved hydraulic smoothness by managing to route the electrical contacts to the wafer’s backside, which resulted in a high TRL, packaged sensor system. The company IC2 was created in 2001 in order to generate the intellectual property related to direct WSS sensors. Eventually, he outcome of these two decades of iterations led to commercialization of these sensors in the DirectShear series. In 2025, IC2 partnered with Dantec Dynamics in order to broaden their reach. Currently, they sell the complete system compatible with the National Instruments PXI platform.

#1.2.3.4 Thermal wall shear stress sensors

While thermal WSS sensors operate similarly to out-of-plane hot wires, their heating element is flush-mounted on the wall surface (figure 1.12). This configuration makes the forced convection losses linked to the WSS instead of the velocity. These sensors are an extension of classic hot wires, and are called “hot films” because the heating element, usually nickel, is deposited onto a flexible polyimide, which can be glued to a wall. Because of their similarities to hot wires, hot films can be operated with the same CC and CTA control circuits. Dantec Dynamics commercializes the 55R glue-on probe series for use in air or water. The robustness and ease of integration of these sensors is mitigated by the consequent conduction losses to the substrate, which, unlike hot wires, occur on the entire length of the heating element. As a consequence, glue-on hot films are much less sensitive than their prong-mounted counterparts.

In a similar way than other sensors presented above, thermal WSS sensors have benefitted from technological advances in MEMS for the last thirty years. In addition to reducing the measurement volume and improving the bandwidth, the stake was to thermally insulate the heating element as much as possible to gain sensitivity. One year prior to the first micromachined hot wire anemometer, Ho’s team introduced a microscale thermal WSS sensor made of a polysilicon heater on a silicon nitride diaphragm (Liu et al. 1994)⁴². Various lengths were investigated, ranging from 80 to 200 µm. While the vacuum cavity under the membrane showed to greatly improve the sensitivity, the researchers noted a decrease in the frequency response due to a greater heating volume (Huang et al. 1996)⁴³. Nonetheless, the batch fabrication advantages of MEMS technologies enabled such hot films to be parallel manufactured onto a single imaging chip for distributed WSS measurement. Each sensor is separated by 300 µm. Experiments were conducted to study flow separation in different configurations: fully developed turbulent flow on a flat plane (Jiang et al. 1996)⁴⁴, stalling airfoil (Yoshihiro et al. 1997)⁴⁵ and turbulent channel flow (Miyagi et al. 2000)⁴⁶.

Concurrently with the development of skin friction balances, Mark Sheplak’s team presented a similar membrane WSS sensor, made of a 200 × 4 × 1.5 µm platinum heater on a silicon nitride membrane (Sheplak et al. 2002)⁴⁷. It has been dynamically calibrated up to 7 kHz in a plane wave tube generation setup.

-> Développements sur le fil chaud Sheplak

In Europe, the technological advances in MEMS flow sensors were driven by two main projects: AEROMEMS from 1997 to 2001, and AEROMEMS II from 2002 to 2005. Beyond sensor engineering, they were large scale multi-disciplinary projects aimed at implementing reactive flow separation control using MEMS sensors and actuators (Warsop 1999)⁴⁸, (Warsop 2004)⁴⁹. A year prior to the beginning of AEROMEMS, Ernst Obermeier’s team at TU berlin presented an hybrid structure between the hot wire and hot film, for pipe gas flow sensing applications. A calorimetric structure (central heater flanked by two passive resistors) is deposited on a single supporting bridge, with a backside cavity and flow guide to maximize the thermal transfer through the fluid (Qiu et al. 1996)⁵⁰. In the AEROMEMS framework, they tested their microfence sensor (mentioned above) in a separated flow, which is the specific flow configuration targeted by the project (Schober et al. 2004)⁵¹. One year later, they introduced a hot-wire wall sensor. Like a hot film, it uses a free-standing heating element, here 800 × 2 × 2 µm, which reduces substrate thermal losses even more effectively than a membrane (Buder et al. 2005)⁵². Continuing their developments, they introduced a double-wire wall sensor to detect flow direction, which is useful in determining flow separation bubbles. Eight of these sensors were mounted on the chord of an airfoil to correlate the flow separation to the lift coefficient (Buder et al. 2008)⁵³.

Our research group at IEMN participated in the AEROMEMS II project by investigating an hybrid approach between membrane and hot film sensors. A microbridge-supported heater was patented by Viard et al. (2013)⁵⁴. This presented the advantage of unlocking large aspect ratio (1000 × 3 µm) wires, specifically designed to measure QSV, which are near-surface “eddy rolls”, large in the streamwise direction and narrow cross-stream. The wire could then be flush-mounted parallel to the flow, and detect the cross-stream WSS generated by these structures. This concept was microfabricated during the thesis work of Romain Viard (2010)⁵⁵. Iterating on this work, the HTGS, a calorimetric structure was presented and statically characterized in a turbulent boundary layer by Ghouila-Houri et al. (2016)⁵⁶. The resistance increase inherent to the miniaturization process made the use of commercial CTAs impossible, without shorting the sensor with a parallel resistance, hindering its sensitivity. Using a dedicated control circuit, (Ghouila-Houri et al. 2019)⁵⁷ demonstrated a 13 kHz dynamic response in a turbulent boundary layer, beyond the bandwidth of Dantec’s glue-on hot films. Further developments were focused on improving the TRL of these micro-bridge supported structures. Backside electrical connections were achieved by using TSV, and flight tests were conducted to monitor aerodynamic parameters on a microlight aircraft (Ghouila-Houri et al. 2023)⁵⁸.