Improvement of wind speed measurement in mine roadway by transit-time difference method: correction of error caused by nonlinear trajectory of ultrasonic in turbulent flow

Abstract The difference between the assumed conditions and the actual engineering scenario results in a systematic theoretical error when applying the transit-time difference method to measure flow rate in turbulent fields. This paper examines the theoretical error in turbulence at a geometric scale such as that of a coal mine roadway. A three-dimensional coupled simulation model of ultrasonic propagation integrating pressure acoustics, computational fluid dynamics and ray acoustics was developed. Numerous simulation cases were designed, and the influencing factors of theoretical error were quantified using statistical analysis methods. The results indicate that the theoretical error is positively correlated with flow rate and wall roughness, while negatively correlated with the equivalent diameter of the roadway section. In comparison to the theoretically assumed uniform flow field, the propagation time of ultrasonic waves in the turbulent flow field is shorter in the downstream direction and longer in the upstream direction. The relative value of the theoretical error is approximately 2%, and the absolute value is characterized by the multiple regression prediction model. The high degree of fit of the model suggests that 96.9% of the variation in absolute error can be reliably explained, which enhances the accuracy and engineering applicability of the transit-time difference method.