# Simulation of Fluid Dynamics Monitoring Using Ultrasonic Measurements
## 5 Temporal Temperature Fluctuation Measurement by Ultrasound
Using the finer sampling, the peak of the experimental PSD curve is confirmed at 3 Hz for each position. Using data with a coarser time step gives merely the same results for the central point, as the peak frequency at 3 Hz is clearly visible. From these comparisons, we thus verify that the peak frequency of the temperature fluctuation is possibly detected. In the next step, the idea is to search for this flow indicator using ultrasonic measurements. The ultrasonic parameters which are selected are the maximum amplitude of the wave at one point and the corresponding time of flight (TOF). Two examples are shown in Figure 9. The two points have the same altitude: one point is close to the jet, and the second one is after the three jets (from the emitter position). The position \(x\) = 0.035 m is close to the jets, and the temperature behavior exhibits clear periodic fluctuation. The position \(x\) = 0.105 m is far from the jets, and the temperature remains constant over the 10 s of the  
Figure 8: Temperature PSD curves calculated from the CFD data at three different \(x\) positions (\(y\) = 0.09 m; \(z\) = 0.1 m), with two sampling rates. CFD simulation, so the corresponding PSD curve gives no frequency information. At the position \(x=0.035\,\mathrm{m}\), among the two PSD calculated with ultrasonic parameters, only those calculated with the time of flight exhibit a clear \(3\,\mathrm{Hz}\) peak as for the temperature PSD. At the position \(x=0.105\,\mathrm{m}\), the same observation is performed: the time-of-flight PSD exhibits a clear \(3\,\mathrm{Hz}\) peak as for the temperature PSD. This result is very interesting, as it demonstrates that the history of temperature fluctuations is transported by the ultrasonic wave and a receiver positioned after the jets is able to analyze the temperature fluctuation. The idea is further deepened using measurements of time-of-flight PSDs at various positions along the x-axis. These curves are compared with PSD curves calculated on CFD data. The resulting curves are presented in Figure 10.  
The calculation of the PSDs with the low sampling CFD data (sampling frequency of \(10\,\mathrm{Hz}\)) shows that only the PSDs on the positions \(x=-0.035\,\mathrm{m}\) and \(0.035\,\mathrm{m}\) exhibit a frequency peak at \(3\,\mathrm{Hz}\). On the other hand, as expected, following the hypothesis of the transport of the fluctuation information by the ultrasonic wave, for positions beyond \(x=-0.035\,\mathrm{m}\), all the time-of-flight PSDs contain this information. We also cumulated (added) all the PSDs calculated at the different points, the PSD curve being defined as a cumulated temperature PSD curve in Figure 10. The \(3\,\mathrm{Hz}\) peak emerges clearly with a secondary peak at \(1\,\mathrm{Hz}\). The comparison with the PSD of the TOF at \(x=0.105\,\mathrm{m}\) shows that the ultrasonic measurement clearly indicates this peak but does not find the secondary peak. There is therefore a limit in the sensitivity of the detection of these fluctuations by an ultrasonic measurement technique, but simulations and results demonstrate that a pair of transducers positioned in a through-transmission setup would allow the temperature fluctuation frequency to be registered. Figure 9: History and PSD analysis for temperature, time of flight and wave amplitude.