Fourier-bessel Series On The Theory And Application Of Coupled Multiphysics In Wave Propagation

Wave propagation along a moving pipeline flow is of wide prospect in aerospace and aeronautical applications. Due to the high response, non-invasion and no-moving component construction, ultrasonic flow meter can promote the propellant on-orbit management and provide a reliable real-time monitor for space operation such as on-orbit refueling. Furthermore, predicting and damping pipeline noise can enhance the aeronautical engine and then decrease operation risk. This thesis addresses the coupled dynamics of acoustics, fluid flow and temperature in pipeline wave propagation. Particular consideration is given to the modeling of the coupled multi-physical dynamics and to the introduction of a novel calculation method based on Fourier-Bessel series. In the application of propellant measurement, a continuous ultrasonic flow measurement methodology based on multi-tone wide laning strategy is proposed and then measurement performance in water is theoretically analyzed. In the application of aeronautical noise prediction and reduction, noise propagation in engine pipeline is comprehensively addressed based on theoretical study.The theoretical research part is organized as follows:Firstly, a novel mathematical method based on Fourier-Bessel series is proposed to solve the governing equations of coupled multiphysical dynamics in wave propagation. As the fluid particle’s disturbance from wave propagation is finite and integrable, it can be expressed in terms of Fourier-Bessel series, which are orthogonal and complete in Lebesgue space. With the properties of Bessel functions, the governing equations can be transformed from complicated differential equations to homogeneous algebraic linear equations. Based on the matrix theory, the wave number representing phase velocity and attenuation coefficient can be iteratively solved by the existence criterion of a non-trivial solution to the deduced homogeneous linear equations. The proposed method imposes no constraints, thus can theoretically handle more complicated wave propagation problem compared with the existing methods. Using the method, the problem of wave propagation in an inviscid fluid with a complex pipeline flow is solved. Meanwhile the phase velocity is parametrically analyzed.Secondly, isentropic flow acoustics in a homogeneous viscous compressible fluid with a moving pipeline flow is investigated. Such configuration is widely accepted in liquid applications. From the continuity equations of mass and momentum, the governing equation of linear acoustic velocity is deduced, leading to two coupled second-order differential equations. The equations incorporate the interactions between acoustic field and flow field. With the proposed method, the axial wave number can be iteratively solved. After numerically verifying the method’s convergence, the phase velocity and wave attenuation in different pipeline radii, acoustic frequencies, fluid viscosities, wall impedances are parametrically analyzed; meanwhile comparisons between different flow profiles are demonstrated comprehensively. It should be noticed that the cut-off frequency of isentropic flow acoustics under the effect of fluid viscosity can be expressed in an analytical equation.Thirdly, acoustic wave in a thermoviscous fluid with a moving pipeline flow is researched, which governs the coupled dynamics of acoustic field, flow field and temperature field. Wave propagation in liquids can be assumed isentropic, but non-isentropic wave propagation in gases should be considered as the effect of thermal conductivity is significant. Furthermore, in the presence of an axial temperature gradient, the non-isentropic process of wave propagation is prevalent. Theoretically, the non-isentropic assumption includes both the fluid viscosity and thermal conductivity, leading to a more realistic description of wave propagation. Starting from the conservations of continuity, momentum and energy, mathematical formulations of linear wave propagation governing the interactions of acoustics, fluid flow and temperature dynamics are given, resulting in three coupled second-order differential equations with respect to acoustic velocity and temperature. Furthermore, comparisons of the wave propagation in different water models(viscous and thermoviscous water) are comprehensively addressed, showing that viscous water is acceptable in the case of low Mach flow. At last, the effects of the axial temperature gradient on phase velocity and wave attenuation are compared. Unlike cut-off frequency in a viscous fluid, the inclusions of fluid viscosity and thermal conductivity make impossible the attempt of finding a simple mathematical expression to regulate the cut-off frequency in a thermoviscous fluid. Fortunately, this thesis gives a reasonable way to predict the number of wave modes in a specific configuration.The application research is as follows:Firstly, a novel design methodology of continuous ultrasonic flow measurement based on multi-tone wide laning strategy is proposed. Such method can be used to gauge the liquid propellant in aerospace applications. In the traditional pulse transit time method, the inconsistency of ultrasonic transducers results in measurement error. As the traditional method neglects the fluid viscosity and thermal conductivity and takes the plane wave assumption as the basis, the high-order wave modes in pipeline propagation is ignored. Based on the theoretical research of wave propagation, a new method of continuous ultrasonic flow measurement is proposed. Specifically, a multi-tone wide laning strategy is introduced to solve the integral ambiguity; meanwhile the fractional phase shift is tracked by a phase-lock loop with a high accuracy, promising a good measurement precision.Secondly, theoretical prediction of ultrasonic flow measurement in pure water is investigated. The performance of ultrasonic flow meter is affected by many factors: fluid viscosity and thermal conductivity, flow profile, axial temperature gradient, acoustic frequency, wall impedance, pipeline radii, to mention a few. Based on the theoretical research, the measurement performances of the first four wave modes are comprehensively discussed. Specifically, measurement performances among different fluid models in three different flow profiles are compared in details. Parametric analysis of pipeline radius, acoustic frequency and fluid viscosity is given; meanwhile comparison between rigid wall and lined wall are investigated. The effect of axial temperature gradient is also addressed. As the flow Mach number increases, the tendency of the measurement performance becomes complicated especially in laminar and turbulent flows where the shear affects are present. Also, the shear affect alters the actions of wall impedance on measurement performance. Acoustic frequency and pipeline radius amplify the influence of the shear mechanics. The increase of convective flow enlarges the measurement error in a predicable way.Thirdly, aeroacoustic propagation is analyzed using the proposed method based on the theory of viscothermal wave propagation. Specially, the effect of pipeline radii on phase velocity and attenuation coefficient is investigated. Comparisons of wave propagation in different flow profile are addressed. Phase velocity and wave attenuation as functions of acoustic frequency are illustrated in different flow profiles through an engine pipeline. The cut-off frequency of wave mode is comprehensively rechecked and new insight is given. Present contributions have been used in the analysis of noise prediction and damping in aeronautical engine.To sum up, in an attempt of demonstrating the characteristics of wave propagation in a moving pipeline flow, present thesis mathematically deduces the coupled multiphysical dynamics including acoustic, flow and temperature fields. Meanwhile, a general solution based on the Fourier-Bessel series is proposed to calculate the proposed differential equations. Theoretically results are applied to the research of liquid propellant measurement in spacecraft and noise prediction and damping in aeronautical engine. Furthermore, the contributions have wide engineering prospects, such as pipeline monitor in industrial production, exhaust process in transport tools and blood flow in life science.