Thermal-Mechanical Wave Propagation in Inviscid Non-Uniform Flow Confined by Heating Pipeline and Implications for Transit-Time Flow Meter

Thermal-mechanical wave propagation (phase velocity, distributions of acoustic pressure and temperature) in inviscid non-uniform flow confined by heating circular pipeline is mathematically formulated from conservations of continuity, momentum, and energy. A novel solution in the form of zeroth-order Bessel series, which are complete and orthogonal in Lebesgue Space, is proposed to regulate the high-order differential equations to algebraic linear equations. As a result, the problem is solved by non-trivial solution of homogeneous linear equations. Based on the proposed method, phase velocity, and pressure and temperature distribution in the presence of axial temperature gradient are comprehensively analyzed in both laminar and turbulent flow. Furthermore, measurement performance of ultrasonic transit-time flow meter is investigated in both laminar and turbulent flow with variations of ultrasound frequency, pipeline radii, and axial temperature gradient. It is shown that temperature gradient imposes outstanding influence on phase velocity and measurement performance. Another point is that decreasing the cylinder radius and ultrasound frequency are effective ways to diminish the influence of temperature gradient for laminar flow, however, in turbulent flow, measurement accuracy with lower frequency is worse than higher frequency.