非均匀声介质中的声传播及演化规律研究
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摘要
相对于其它种类的热功转换装置与技术,热声热机是一个新兴的、有待于进一步研究的领域。热声热机的主要优势在于构造相对简单、可靠性高、运行寿命长,环保无污染,可以实现小型轻量化,能利用较低品位的热源。在国内外研究者的共同努力下,几十年来装置的结构型式及性能参数不断得到改进和提高,线性热声学理论研究也日臻完善。然而,在热声学基础研究中仍有一些重要的科学问题没有得到充分的研究,造成对热声起振、模态演化、声流、行波环流、高次谐波等一些存在于实际系统的非线性过程或效应的理解不足;而这种认识上局限性也制约了建造者采取恰当措施进一步提高装置的体积功率密度、工作稳定性及效率。有鉴于此,作者以热声热机为应用背景,围绕“非均匀声介质中声场的传播及演化规律”主题,重点针对如何描述“热声稳定性”及“非均匀介质有限振幅声场”这两个理论问题以及相关的工程问题而展开。
作者遵循一条由简入繁、先线性后非线性、科学探讨与工程思考相结合的技术路线,首先从相关文献中总结、提炼了管内小振幅声场的传播规律以及热声工程中涉及到的多孔介质实验技术(复密度、复压缩率、孔隙率、流阻、特征阻抗与波数测量)。论文给出了推导波动方程的一般方法;阐释了在线性条件下,“热声效应”并未改变复密度及复压缩率的数学形式;分析了粘性弛豫与热弛豫在不同热声组件中所起的不同作用,并指出热弛豫对粘性弛豫的合理修正(实际流体的粘性弛豫是不可避免的)可以增强热声效应;从声传播规律的角度分析了主动控制的技术原理以及它对斯特林装置的实用价值;对复合吸声系统进行了无量纲参数的计算,通过等效网络图阐明了主动控制的工作机制。
为了全面地揭示主导热声“起振”的物理机制,作者原创性的提出了“热声振荡器”频域方法以及解释热声多模态共存及演化现象的动力学时域方法。在频域方法中,给出了热声组件对应的二端口Y参数;采用负阻模型和反馈模型分别描述了驻波和行波热声发动机并给出了对应的二端口网络拓扑;应用Nyquist失稳判据获得了热声振荡器的起振条件;还通过拓扑图论证了驻波热声发动机起振于负阻状态、热声—斯特林发动机存在高频模态。该“频域”方法实现了以解析方式反映发动机运行参数和系统结构对起振模态、起振温度的影响。另一方面,在“声场中各位置处振荡模态的演化特征具有时间上的同步性”这一实验观测的基础上,作者使用分离变量法这一朴素的科学思想将非均匀介质中热声多模态起振问题转化成质点多模态振动的初值问题,由此发展了一种考察热声多模态共存及演化现象的时域理论。从动力学视角明确了热声振荡器中多模态效应(共存、压制、演化等)所对应的动力学分岔类型;结合多尺度扰动方法讨论了“极限环”轨道稳定性的科学内涵;以描述自激振荡过程的Van der Pol方程为基础“猜想”了两模态耦合的动力学方程组并给出了方程系数的量化方法,借助Maccari的工作验证了模型的描述能力。此外,基于热声起振表现出的自激振荡特征,作者预测受迫自激振荡具有的“频率俘获”同步振荡效应将为阵列式的高功率热声振荡器的研发提供理论前提。
此外,作者还从工程应用的角度提出了对“非均匀声介质中有限振幅声场”计算模型的要求,指出基于连续介质假设的常规声学方法在处理有限振幅声场时面临的最大问题是表征非线性声场的两种数学形式(时域量与频域量)之间不存在简单的对应规则,从而造成对控制方程的量纲分析(偏导阶数)无法与傅立叶分析(谐波)相统一。为此作者转换了研究思路,运用基于离散假设的“格子方法”尝试模拟了热声装置(典型的非均匀声介质)。在D2Q9模型中补充定义了多体碰撞规则,模拟了不同温度参数下的热声起振过程并对该模型内在的局限性进行了分析。
本论文在热声学领域的理论前沿取得了一些有意义的结果,在目前工作的基础上,可开展进一步的科学研究、发展相关的工程技术。
Compared with other energy conversion and utilization technology, thermoacoustics is a new field which needs further research. Thermoacoustic device has comparatively simple configuration, high reliability, long duration and is environmentally friendly; it also has the potential to be compacted and lightened and the capacity of utilizing low-grade thermal energy. The device configuration and performance have been advanced and improved in these several decades. Moreover, linear thermoacoustic theory has been well established. However, there still exist some important issues not studied adequately, which leads to the weak understanding about non-linear process or effect in real system, such as onset, mode evolution, acoustic stream, loop flow and harmonics. And this cognitive limitation restricts the constructor to adopt appropriate approaches to increase the specific power density, improve the stability and advance the efficiency. Therefore this thesis focuses on the thermoacoustic stability and finite amplitude acoustic field in non-homogeneous media to reveal the propagation and evolution principles in such media, under which the related engineering application is discussed.
In the first part of this thesis, the propagation principles of small amplitude sound in tube and experimental technology related to thermoacoustic engineering have been refined and concluded. Specifically, the derived method of the wave equation is proposed and the mathematical forms of complex density and compressibility keeping unchangeable under the present thermoacoustic condition are demonstrated. The influence of viscosity and thermal release on various thermoacoustic elements is analyzed. Also the proper combination of thermal release with viscosity release can reinforce the thermoacoustic effect. Active control principle in acoustics is analyzed and its potential contribution to Stirling device is predicted, then, the performance parameters of the combined noise absorption system have been calculated in nondimensional way. The working mechanism of such system is demonstrated by equivalent network topology.
In order to reveal the predominant physical mechanism of onset process, the frequency-domain method, the thermoacoustic oscillator, and time-field dynamic method describing the evolution and the coexistence of modes are originally proposed. In frequency-domain method, thermoacoustic engines are regarded as thermoacoustic oscillators consisting of the active network and the passive network. Accordingly, the two-port Y-parameter for relevant component is derived, and standing wave and traveling wave thermoacoustic engine are described by the negative-resistance and feedback model, respectively. The relevant two-port network topology is given as well. The startup criteria for thermoacoustic oscillators are obtained using Nyquist instability criterion. Moreover, by topological graphs it is verified that standing wave engines would start up in a negative-resistance state and there would exist high frequency modes in thermoacoustic-Stirling engines. By investigating into the frequency response of thermoacoustic system, this method proposed can achieve such an objective that these effects of operating and structural parameters of engine on startup modes and startup temperature can be revealed in an analytical way. On the other hand, based on the mode synchronization of different locations in acoustic field during the evolution process, the multimode oscillation in nonhomogenous media reduced to multimode vibration of particles and then the initial-boundary value problem reduced to initial value problem by the method of separation of variables. From dynamic viewpoint, the relevant bifurcation types of some multimode effects (such as coexistence, oppression, evolution and so on) are identified. The orbit stability of the "limit cycle" and its scientific implication are analyzed by using the method of multiple scales. The dynamic equations of two coupled modes are brought forth based on the Van der Pol equation which was used to describe the self-excited vibration. Also the quantification method for such equation parameters is given. And then the capacity of the equations is demonstrated with the help of the Maccari's work. In addition, on the basis of the self excitation shown by thermoacoustic onset, the feature of forced self-excited oscillation system, frequency capture, can be utilized to guide the construction of high-level power thermoacoustic-oscillator array.
In the last part, the engineering requirements for the computational mode of the finite amplitude acoustic field in non-homogeneous media are specified. And the disadvantage of the traditional acoustic method dealing with finite amplitude problem is pointed out, which lies in the mismatch of the perturbation expansion series and harmonic expansion series. Then this mismatch leads to the failure of the consistency between dimensional analysis and Fourier analysis. Thus an alternative approach, Lattice Gas Automaton, is applied to simulate the thermoacoustic device which is a typical non-homogeneous media. In the simulation, the collision rules of multi-body are defined; the thermoacoustic onsets under different temperature parameters are shown; the interior limitation of the mode is also mentioned.
In the thesis, the author explores some fundamental and important scientific problem in thermoacoustics and proposed some original ideas, models and predictions. More in-depth research and relevant engineering applications can be fulfilled based on the present work.
作者遵循一条由简入繁、先线性后非线性、科学探讨与工程思考相结合的技术路线,首先从相关文献中总结、提炼了管内小振幅声场的传播规律以及热声工程中涉及到的多孔介质实验技术(复密度、复压缩率、孔隙率、流阻、特征阻抗与波数测量)。论文给出了推导波动方程的一般方法;阐释了在线性条件下,“热声效应”并未改变复密度及复压缩率的数学形式;分析了粘性弛豫与热弛豫在不同热声组件中所起的不同作用,并指出热弛豫对粘性弛豫的合理修正(实际流体的粘性弛豫是不可避免的)可以增强热声效应;从声传播规律的角度分析了主动控制的技术原理以及它对斯特林装置的实用价值;对复合吸声系统进行了无量纲参数的计算,通过等效网络图阐明了主动控制的工作机制。
为了全面地揭示主导热声“起振”的物理机制,作者原创性的提出了“热声振荡器”频域方法以及解释热声多模态共存及演化现象的动力学时域方法。在频域方法中,给出了热声组件对应的二端口Y参数;采用负阻模型和反馈模型分别描述了驻波和行波热声发动机并给出了对应的二端口网络拓扑;应用Nyquist失稳判据获得了热声振荡器的起振条件;还通过拓扑图论证了驻波热声发动机起振于负阻状态、热声—斯特林发动机存在高频模态。该“频域”方法实现了以解析方式反映发动机运行参数和系统结构对起振模态、起振温度的影响。另一方面,在“声场中各位置处振荡模态的演化特征具有时间上的同步性”这一实验观测的基础上,作者使用分离变量法这一朴素的科学思想将非均匀介质中热声多模态起振问题转化成质点多模态振动的初值问题,由此发展了一种考察热声多模态共存及演化现象的时域理论。从动力学视角明确了热声振荡器中多模态效应(共存、压制、演化等)所对应的动力学分岔类型;结合多尺度扰动方法讨论了“极限环”轨道稳定性的科学内涵;以描述自激振荡过程的Van der Pol方程为基础“猜想”了两模态耦合的动力学方程组并给出了方程系数的量化方法,借助Maccari的工作验证了模型的描述能力。此外,基于热声起振表现出的自激振荡特征,作者预测受迫自激振荡具有的“频率俘获”同步振荡效应将为阵列式的高功率热声振荡器的研发提供理论前提。
此外,作者还从工程应用的角度提出了对“非均匀声介质中有限振幅声场”计算模型的要求,指出基于连续介质假设的常规声学方法在处理有限振幅声场时面临的最大问题是表征非线性声场的两种数学形式(时域量与频域量)之间不存在简单的对应规则,从而造成对控制方程的量纲分析(偏导阶数)无法与傅立叶分析(谐波)相统一。为此作者转换了研究思路,运用基于离散假设的“格子方法”尝试模拟了热声装置(典型的非均匀声介质)。在D2Q9模型中补充定义了多体碰撞规则,模拟了不同温度参数下的热声起振过程并对该模型内在的局限性进行了分析。
本论文在热声学领域的理论前沿取得了一些有意义的结果,在目前工作的基础上,可开展进一步的科学研究、发展相关的工程技术。
Compared with other energy conversion and utilization technology, thermoacoustics is a new field which needs further research. Thermoacoustic device has comparatively simple configuration, high reliability, long duration and is environmentally friendly; it also has the potential to be compacted and lightened and the capacity of utilizing low-grade thermal energy. The device configuration and performance have been advanced and improved in these several decades. Moreover, linear thermoacoustic theory has been well established. However, there still exist some important issues not studied adequately, which leads to the weak understanding about non-linear process or effect in real system, such as onset, mode evolution, acoustic stream, loop flow and harmonics. And this cognitive limitation restricts the constructor to adopt appropriate approaches to increase the specific power density, improve the stability and advance the efficiency. Therefore this thesis focuses on the thermoacoustic stability and finite amplitude acoustic field in non-homogeneous media to reveal the propagation and evolution principles in such media, under which the related engineering application is discussed.
In the first part of this thesis, the propagation principles of small amplitude sound in tube and experimental technology related to thermoacoustic engineering have been refined and concluded. Specifically, the derived method of the wave equation is proposed and the mathematical forms of complex density and compressibility keeping unchangeable under the present thermoacoustic condition are demonstrated. The influence of viscosity and thermal release on various thermoacoustic elements is analyzed. Also the proper combination of thermal release with viscosity release can reinforce the thermoacoustic effect. Active control principle in acoustics is analyzed and its potential contribution to Stirling device is predicted, then, the performance parameters of the combined noise absorption system have been calculated in nondimensional way. The working mechanism of such system is demonstrated by equivalent network topology.
In order to reveal the predominant physical mechanism of onset process, the frequency-domain method, the thermoacoustic oscillator, and time-field dynamic method describing the evolution and the coexistence of modes are originally proposed. In frequency-domain method, thermoacoustic engines are regarded as thermoacoustic oscillators consisting of the active network and the passive network. Accordingly, the two-port Y-parameter for relevant component is derived, and standing wave and traveling wave thermoacoustic engine are described by the negative-resistance and feedback model, respectively. The relevant two-port network topology is given as well. The startup criteria for thermoacoustic oscillators are obtained using Nyquist instability criterion. Moreover, by topological graphs it is verified that standing wave engines would start up in a negative-resistance state and there would exist high frequency modes in thermoacoustic-Stirling engines. By investigating into the frequency response of thermoacoustic system, this method proposed can achieve such an objective that these effects of operating and structural parameters of engine on startup modes and startup temperature can be revealed in an analytical way. On the other hand, based on the mode synchronization of different locations in acoustic field during the evolution process, the multimode oscillation in nonhomogenous media reduced to multimode vibration of particles and then the initial-boundary value problem reduced to initial value problem by the method of separation of variables. From dynamic viewpoint, the relevant bifurcation types of some multimode effects (such as coexistence, oppression, evolution and so on) are identified. The orbit stability of the "limit cycle" and its scientific implication are analyzed by using the method of multiple scales. The dynamic equations of two coupled modes are brought forth based on the Van der Pol equation which was used to describe the self-excited vibration. Also the quantification method for such equation parameters is given. And then the capacity of the equations is demonstrated with the help of the Maccari's work. In addition, on the basis of the self excitation shown by thermoacoustic onset, the feature of forced self-excited oscillation system, frequency capture, can be utilized to guide the construction of high-level power thermoacoustic-oscillator array.
In the last part, the engineering requirements for the computational mode of the finite amplitude acoustic field in non-homogeneous media are specified. And the disadvantage of the traditional acoustic method dealing with finite amplitude problem is pointed out, which lies in the mismatch of the perturbation expansion series and harmonic expansion series. Then this mismatch leads to the failure of the consistency between dimensional analysis and Fourier analysis. Thus an alternative approach, Lattice Gas Automaton, is applied to simulate the thermoacoustic device which is a typical non-homogeneous media. In the simulation, the collision rules of multi-body are defined; the thermoacoustic onsets under different temperature parameters are shown; the interior limitation of the mode is also mentioned.
In the thesis, the author explores some fundamental and important scientific problem in thermoacoustics and proposed some original ideas, models and predictions. More in-depth research and relevant engineering applications can be fulfilled based on the present work.
引文
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