An acoustic model of NIST’s long-wavelength acoustic flowmeter for gas flow in large-diameter pipes

NIST is investigating long-wavelength acoustic flowmeter (LWAF) technology to accurately measure gas flow in large-diameter pipes, such as smokestacks used by coal-burning power plants. To aid in the data analysis and development of the method, we constructed a lumped-element acoustic model of the LWAF based on existing theory for sound propagation in circular ducts, modified to include flow. The model calculates the ratio of the acoustic pressure amplitudes and phase differences between two locations in a partial standing wave downstream of a continuous sound source up to the duct’s cut-on frequency. We used the numerical calculations of the reflection coefficient by Munt [J. Sound Vibration 142, 413–436 (1990)] to model the radiation impedance as a function of flow speed. In the absence of flow, the model was used to calibrate the positions of several microphones in the LWAF. In the presence of flow, the model predicts qualitatively the measured amplitude ratios and phase differences as a function of flow rate. Quantitative comparison is limited by the uncertainty of the radiation impedance and its flow dependence. This limitation prompts us to investigate ways to either measure the radiation impedance or eliminate it by using multiple coherent sound sources.