A method of measuring the mean flow velocity in pipe is proposed. The method basically utilizes the change of wavenumber due to internal flow in pipe. An array sensor such as accelerometer or microphone is used to measure the change of wavenumber in pipe.
To get formula of the mean flow velocity, pipes are modeled as rigid duct, simple beam, or cylindrical shell according to the instrumentation types and modeled shapes of pipes. The formula of the mean flow velocity is derived in terms of the wavenumber change for each pipe model. The correlation between signals measured at equally spaced sensors is derived. The wavenumber change is estimated based on the correlation matrix.
Some considerations are presented necessary to measure actual flow velocity more precisely. Selection guideline of pipe model is provided to choose appropriate pipe model. Effective measurement range of the mean flow velocity is established based on the assumption related to the formula of the mean flow velocity. Effect of the ratio of signal to noise is evaluated to reduce measurement errors caused by the noise. Proper number of sensors in measurement is suggested to use sensors effectively.
The method proposed in this study is effective under the condition that only one-dimensional waves are propagated in the pipe. The upper and lower limits of frequency range, in which only one-dimensional waves are propagated, are suggested. When the distance between sensors is the multiple of the half-wavelength of interest, there exists a singular condition under which the estimated flow velocity becomes inaccurate. The frequency range, in which there exists the singular condition, is provided.
Two possible errors can be considered in the measurement when more than one sensor are used. One is the random noise in each sensor and the other is the phase and magnitude mismatches between sensors. Thus, the success of the proposed method greatly depends on how well we can reduce effects of the errors. The method of reducing the effects of the errors is proposed.
Numerical simulation was performed to confirm the adequacy of the proposed method. The simulation results reveal that the error caused by the sensor mismatch has great effect on measurement of the flow velocity. The signal calibration related to the sensor mismatch is found to be necessary for accurate flow velocity estimation.
Experiment for each pipe model was conducted to verify the proposed method. The experiment results show that the flow velocity by the proposed method can be measured with 4% error, which is more accurate than our previous method of 10% error.
