Calibration of the 3C–SiC calorimeter in a turbulent boundary layer · MEMS sensors for flow measurement in harsh environments

#3.2.1 Sensor used

-> représentation brève du calorimètre SiC/Si/verre

#3.2.2 Wind tunnel facility

The flow characterizations were conducted in the ONERA Lille boundary layer wind tunnel facility (figure ¿fig:wt_schematic?). The square test section has a with of 30 cm. A 2 mm-thick rod followed by a 20 mm-long abrasive is installed near the air intake to generate a turbulent boundary layer on the left wall.

Figure 3.3.
Boundary layer wind tunnel facility, ONERA Lille

#3.2.3 Flush-mounting of sensors on the wind tunnel wall

The SiC sensor is flush-mounted on a wall panel, at x = 1.52 m from the rod, as well as a reference Dantec 554R7 hot-film sensor powered by a StreamLine Pro CTA. The boundary layer can be considered two-dimensional, so we assume that the SiC sensor and hot-film respond to the same wall shear stress values. The sensor die was positioned within a milled pocket of a support printed circuit board (PCB), ensuring all surfaces remain flush with the wind tunnel wall (figure ¿fig:wt_plug_photo?). Wire bonding provided electrical connection between the die and the PCB, the latter also serving as mechanical support and a routing medium for electrical contacts. A connector soldered to the backside allowed contacts access and enabled a cable connection between the sensor and the main controller board. The support PCB was glued to a plug that fits tightly within the sensor wall panel, ensuring secure mounting (figure 3.4).

#3.2.4 Measurement setup

-> CTA + dantec minicta + dewesoft

Thirty-second-long acquisitions were carried out at a sampling frequency of 200 kHz for steady freestream velocities ranging from 0 to 40 m/s in order to calibrate the SiC heater/CTA controller for wall-shear stress values. The wind tunnel’s boundary layer was profiled using a motorized hot wire stage for each speed step, and the corresponding wall shear stress was calculated using the Coles-Fernholz method, (Fernholz & Finleyt 1996)¹¹³ yielding values up to 2.5 Pa. In addition, the dynamic response of the CTA was assessed by performing square-wave tests under a freestream velocity of 10 m/s, by injecting a 300 mV peak-to-peak square wave voltage to the offset input of the circuit (offset voltage shown in figure 3.1).

#3.2.5 Wall shear stress calibration

#The Coles-Fernholz method

For each speed step, the Coles-Fernholz indirect wall shear stress assessment technique was used. At sensors position x = 1.52 m, the one-dimensional velocity profile u(y) enable calculation of the boundary layer momentum thickness \theta:

\theta = \int_0^\delta \frac{u(y)}{U_\infty}\left( 1 - \frac{u(y)}{U_\infty}\right)dy,

with \delta the boundary layer thickness. The skin friction coefficient C_\text f is expressed:

C_\text f = 2\left( \frac{1}{k} \ln \left(\frac{ \theta U_\infty}{\nu} \right) + C \right)^{-2}\kern -12pt,

where k = 0.384 and C = 4.127. Ultimately, the wall shear stress \tau is calculated for each speed step following: \tau = \rho C_\text f /2.

The CTA output voltage was time-averaged for thirty seconds and expressed as a variation relative to the no-flow condition (figure 3.5):

\text{CTA response} = \frac{E_\text O (\tau) - E_\text O(\tau = 0)}{E_\text O(\tau = 0)}.

The plotted error margins show the standard deviation of the fluctuation for each recording, which is mainly due to the frequency content of the turbulence. The resulting calibration curve shows good similarity with measurements performed using the Dantec 55R47, as well as with results reported in the literature for comparable surface-mounted hot-wire wall shear stress sensors. (Ghouila-Houri et al. 2017)¹¹⁴, (Chamard et al. 2023)¹¹⁵

#Calorimetric response to wall shear stress

Figure 3.5.
Calibration curve of the SiC heater operated by the in-house CTA

Figure 3.6.
Lateral wire differential measurement versus overheat voltage, at constant 30 m/s freestream velocity and no-flow condition.

-> LW measurement

#3.2.6 Square-wave tests

#Theory and assumptions

#Assessment of the CTA’s dynamic response

While static calibration characterizes steady-state performance, the dynamic response of the CTA system was evaluated using a 100 mV step perturbation under a 10 m/s flow, with the resulting transient output shown in figure 3.7. Following Freymuth (1977)¹² the first zero crossing occurring at t_0 = 113 µS allows an approximate estimate of the cutoff frequency of our in-house CTA: f_\text{c} \approx 1/(1.3t_0) =6.8 kHz.

Figure 3.7.
CTA response for a 300 mV peak-to-peak square wave at 10 m/s freestream velocity.

#3.2 Calibration of the 3C–SiC calorimeter in a turbulent boundary layer