#3.1.1 Targeted operating points

The semiconductor nature of the heating and sensing elements raises a challenge for hot-wire applications, because the TCR varies with the temperature. Figure 2.21 shows the evolution of the central wire’s resistance relative to uniform heating, together with the corresponding TCR. There are four distinct resistance regimes over the investigated temperature span, characterized by alternating positive (metal-like) and negative (semiconductor-like) TCR values. Consequently, unlike metallic wires with TCR, the mean temperature of a semiconductor wire under non-uniform heating—typically Joule heating—cannot be inferred from its mean resistance.

For CTA operation, the relevant quantity is therefore the wire’s resistance variation with respect to Joule heating, as illustrated by the characteristic curve in figure ¿fig:iv_calorimeter?. It shows a decreasing regime followed by an increasing one, where the CTA can operate in a stable manner. In this case, we can consider an equivalent to the TCR called the PCR. Unlike the TCR, the PCR is not an intrinsic property of the material alone but arises from the combined effects of material properties and wire geometry. We therefore propose a PCR curve for each of the three wires relative to the Joule power applied at the central wire. The feedback loops only works for positive PCR values, making the 0 to 5 mW heating range unreachable. Overall, the CTA system achieves optimal sensitivity at the maximum of the heater’s PCR, while the lateral wire measurements are most sensitive when their corresponding PCR reaches peak absolute value.

#3.1.2 Design of the circuit

Due to larger resistance values, SiC wires have to undergo large voltage drops be sufficiently heated,For SiC calorimeters presented above, a … mW heating power generate a 35 V potential on the wires.

meaning that each active component should properly function at these voltages. This forbids the use of commercial CTA circuits, which are designed to work with ~ 1 – 20 \Omega resistances.Typically 4 \Omega for hot wire, 15 \Omega for hot-film probes.

A Perry-type CTA control circuit has been designed to drive high-value SiC resistances, with components able to work up to a 35 V working point, as shown in figure 3.1 (a). This enables the bridge to function at a high enough voltage to properly power the SiC heater. The bridge voltage is mitigated by a 2N2222A BJT driven by the controller output. The main differential amplifier is an ADA4522 which output is amplified by a variable gain INA128 instrumentation amplifier. An offset voltage can be applied independently of the main supply though a second INA128, to conduct square and sine wave tests.

For calorimeter probes, a complementary circuit to use the lateral wires has also been designed, as shown in figure 3.1 (b). A constant current source REF200 drives 100 µA through the lateral wires mounted in series. The wire voltages are measured by two INA128 instrumentation amplifiers.

#3.1.3 Circuit board realization

The PCB was designed with KiCAD

#3.1.4 Frequency response assessment

Determining the true bandwidth of the hot wire in a closed-loop configuration is quite complex: the ideal way is to perform a measure of a direct fluid step, i.e. a sudden velocity change. Because it is very difficult to achieve in practice, a workaround has been found to mimic a flow step as closely as possible. Under steady flow, a voltage step (i.e. a square wave) is sent into the feedback loop to create a sudden unbalance. It has been by shown by Freymuth (1977)¹² that it is equivalent to a flow velocity step, under the assumption that the wire-controller behaves like a third-order system. Although this assumption is not trivial to assess in reality, the CTA has been tested with a SiC calorimeter in a turbulent boundary layer, and a square-wave test has been performed which results are shown in section 3.2.6.

The indirect nature of the thermal skin friction measurement means a calibration curve has to be determined in order to link the sensor output to actual skin friction. The ONERA Lille has a turbulent boundary layer wind tunnel which profile has been mapped.