3.3.1. Direct Absorption and Dilution Method

The dilution measurements consist of a repeated laser wavelength scan (without the sinusoidal modulation) across the selected C2H2 absorption line. Each scan is acquired as a set of 20,000 points for each channel, in 1 ms. A binning over 100 points reduces the points per ramp to 200. Binning, and average of the scans, are performed by the FPGA, producing a spectrum every 28 ms. These spectra are saved in the computer. The final waveform is fitted by using the theoretical Voigt absorption profile. According to the procedure described in [18], the mixing ratio can be inferred by the fitting parameters, provided that temperature, pressure, molecular linestrength and path-length are known. Pressure and temperature are measured by sensors included in the Pitot probe (accuracy 0.05% and 0.3%, respectively), the linestrength is reported in HITRAN molecular database [10] with accuracy 1% and the pathlength was measured to be 580 ± 1.5 mm.

In order to verify the quality of our data, and to decide the best integration time for our measurements, we performed the Allan-Werle Variance [19,20] on mixing ratio measurements. Figure 6 shows the results obtained for two different speeds of the fan (expressed as % of the maximum speed). The best integration time results to be 8 s, corresponding to an Allan-Werle Variance *σAWV* of 1.5 ppm at 30% and 0.9 at 75%. The slight difference can be due to the different measurement conditions. It is worth noting that this is the Allan-Werle test of the whole system, formed by the fan, the mass-flow meter and our optical apparatus. Dilution measurements are stationary, so, according to the Allan–Werle analysis, we can further average over 285 scans, for 8 s total measurement time. Figure 7 shows the averaged absorption profile, with the fit curve and the residual.

**Figure 6.** Allan-Werle test of the system at two different fan speeds, with respect to maximum.

The calculation of the flow speed is performed by measuring the steady-state concentration of the tracer, when the amount of injected tracer per unit time and the transverse section of the duct are known, according to the formula:

$$V = \frac{T}{CS} \tag{3}$$

where *V* is the velocity (m/s), *T* is the flow (m3/s) of the injected tracer, *C* is the mixing ratio measured downstream, and *S* (m2) is the transverse area of the duct.

**Figure 7.** Plot of a direct absorption acquisition and its analysis.

3.3.2. Wavelength Modulation Spectroscopy and TT Method

To perform Second Derivative WMS, the fast modulation (1 MHz) is added to the laser sweep (1 kHz) and the acquired signal is deconvolved at 2 MHz. An example of WMS signals from the reference cell and from one measuring point along the stack is shown in Figure 8, where the different shapes of the two waveforms are due to the different pressures inside the cell and the stack. The peak values of the profiles in Figure 8 are proportional to the concentration. In the TT method, the time profile of the peak heights is acquired at two different measuring points (reference is only used to check that the laser wavelength is not drifting), when a concentration burst of the tracer is inserted inside the stack. In order to have the maximum acquisition rate, the laser wavelength sweep is stopped and the laser is set at the peak of the absorption. In principle, it would be possible to implement an active stabilization routine, based on an odd derivative (demodulation at an odd multiple of the modulation frequency). As a matter of fact, due to the stability of the laser driver, active stabilization was not necessary, and emission stability was maintained for a time larger than the 10 s of the measurement duration. With this procedure, the acquisition rate is 1 kHz, sufficient to follow the time profile of C2H2 inside the stack.

To obtain the concentration burst, the tracer gas line was closed and opened with a delay as short as possible. An example of the TT measurements, at two different points of the stack, at three different flow speeds, is reported in Figure 9. The velocity can be obtained by calculating the time delay between two corresponding timestamps of the red and blue curves of Figure 9. The selection of the timestamps is not a minor issue and it will be analyzed in the next section. The geometrical distance between the two measuring planes (3.54 m) divided by the delay yields the average gas velocity.

**Figure 8.** Wavelength Modulation Spectroscopy (WMS) signals from the reference cell (blue) and one of the measurement points along the stack (red).

**Figure 9.** Set of Transit Time (TT) measurements at three different flow speeds, at the lower (blue) and upper (red) measurement points.
