Accurate measurement of flue gas velocity is crucial for safe production, energy saving and emission reduction in power plants. In this paper, a real-time flue gas audio-range velocimeter was developed using a novel sonic driving mode, quadratic-convex frequency sweeping. Both numerical analysis and in situ experiments were conducted which had validated the developed velocimeter. The accuracy and robustness of the developed velocimeter was quantitatively assessed by root mean square error (RMSE) and standard deviation (SD) from the tests data. The test data was intentionally contaminated with varied levels of noises, forming sets of measurement data with varied signal-to-noise ratios (SNRs). The simulation results show that within the variation of SNR from 0 dB to −18 dB, the averaged relative RMSE obtained using this proposed quadratic-convex driving mode is 1.2 dB and 2.3 dB lower than those obtained using linear and quadratic-concave driving modes, respectively. The experiment results indicate that the RMSE and SD values based on the quadratic-convex driving mode are less than 0.1 for each given SNR. Compared with the traditionally adopted method of linear frequency sweeping, the proposed sonic driving scheme can significantly improve the accuracy and robustness of flue gas velocity measurement.

Accurate ranging and real-time temperature monitoring are essential for metrology and safety in electrical conduit applications. This paper proposes an acoustic time-of-flight (TOF) estimation method based on the digital lock-in filtering (DLF) technique for conduit ranging and thermometry. The method establishes the relationship between the frequency and the time domain by applying a linear frequency modulated Chirp signal as the sound source and using the DLF technique to extract the first harmonic of the characteristic frequencies of the transmitted and received signals. Acoustic TOF estimation in the conduit is then achieved by calculating the mathematical expectation of the time difference between each characteristic frequency in the time-frequency relationship of the two signals. The experimental results with enhanced noise interference on different conduit lengths and various temperature conditions, proved that the proposed DLF method can establish a robust linear time-frequency relationship according to the characteristics of the Chirp signal, and the measurement accuracy of TOF has also been confirmed. Compared to the conventional method, the DLF method provides the lowest absolute error and standard deviation for both distance and temperature measurements with an enhanced robustness.

A simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening is presented. The proposed approximation scheme is highly accurate and provides an accuracy better than 10⁻¹⁷ for arbitrary α_L/α_G ratios. In particular, the accuracy reaches an astonishing 10⁻³⁴ (quadruple precision) in the domain 0 ≤ α_L/α_G ≤ 0.2371 ∪ α_L/α_G ≥ 33.8786.

Real-time and accurate flue gas temperature and velocity measurement is crucial for the safety, efficiency, and low emission of a power plant operation. This article describes a new technique for measuring flue gas temperature and velocity based on acoustic frequency division multiplexing (FDM) in a simultaneous way. The FDM method provides a technique that allows the simultaneous utilization of multiple acoustic signals that leads to a greatly reduced measurement cycle time required; therefore, the measurement system’s temporal resolution is significantly improved. With this new FDM method, the composite signal formed of two channels’ is decomposed by using a Butterworth filter for the extraction of the amplitude and phase information of signals passing each of the individual channels. From the derived frequency signals, the time of flight (TOF) on each acoustic path can be obtained. Demonstrated through both a theoretical analysis and experimental results, by applying the new technique, the measurement period can be reduced to 0.083 times (or say less than 10%) of that by using a traditional method. At the same time, the experimental results indicate that the new technique also improves the accuracy of the measurements. The sensitivity of the FDM method is 3.3, and 2.6 times higher than that of the HWA and traditional methods for velocity, and 1.6 and 1.4 times higher for temperature measurement. Moreover, its optimal robustness and precision are verified by several combined experiments with and without wind with background noise.