Reduced-order modelling of thermoacoustic instabilities in a two-heater Rijke tube

The topic of thermoacoustic instabilities in combustors is well-investigated, as it is important in the field of combustion, primarily in gas-turbine engines. In recent years, much attention has been focused on monitoring, diagnosis, prognosis, and control of high-amplitude pressure oscillations in confined combustion chambers. The Rijke tube is one of the most simple, yet very commonly used, laboratory apparatuses for emulation of thermoacoustic instabilities, which is also capable of capturing the physics of the thermally driven acoustics. A Rijke tube apparatus can be constructed with an electrical heater acting as the heat source, thus making it more flexible to operate and safer to handle than a fuel-burning Rijke tube or a fuel-fired combustor. Augmentation of the heat source of the Rijke tube with a secondary heater at a downstream location facilitates better control of thermoacoustic instabilities. Along this line, much work has been reported on the investigation of thermoacoustics by using computational fluid dynamics (CFD) modelling as well as reduced-order modelling for both single-heater and two-heater Rijke tube systems. However, since reduced-order models are often designed and built upon certain empirical relations, they may not account for the dynamic behaviour of the heater itself, which is a critical factor in the analysis and synthesis of real-time robust control systems. This issue is addressed in the current paper, where modifications have been made to existing models by incorporating heater dynamics. The model results are systematically validated with experimental data, generated from an in-house (electrically heated) Rijke tube apparatus.     

Influence of stack geometry and resonator length on the performance of thermoacoustic engine

Thermoacoustic engines convert heat energy into high amplitude sound waves, which is used to drive thermoacoustic refrigerator or pulse tube cryocoolers by replacing the mechanical pistons such as compressors. The increasing interest in thermoacoustic technology is of its potentiality of no exotic materials, low cost and high reliability compared to vapor compression refrigeration systems. The experimental setup has been built based on the linear thermoacoustic model and some simple design parameters. The engines produce acoustic energy at the temperature difference of 325–450 K imposed along the stack of the system. This work illustrates the influence of stack parameters such as plate thickness (PT) and plate spacing (PS) with resonator length on the performance of thermoacoustic engine, which are measured in terms of onset temperature difference, resonance frequency and pressure amplitude using air as a working fluid. The results obtained from the experiments are in good agreement with the theoretical results from DeltaEc.     

Rijke管热声振荡的稳定性切换行为研究

采用数值方法模拟了强弱两种阻尼条件下传热迟滞时间对一维Rijke管热声系统稳定性的影响,发现Rijke管系统存在稳定性切换现象.在推导了无量纲形式的管内声波动量方程和能量方程之后,利用Galerkin方法对控制方程进行展开并在时间域内数值求解.分析了强阻尼和弱阻尼条件下,给定热源的Rijke管热声振荡的稳定性与传热迟滞时间的关系.结果显示:在两类阻尼条件下,持续增大传热与速度的迟滞时间,系统均呈现出稳定性切换现象,即系统在稳定和不稳定两个状态间持续转变;但弱阻尼系统的不稳定区域宽于强阻尼系统的不稳定区域,系统最大振幅相对增大,且系统热声振荡的主模态在不同模态之间发生转换.最后,通过求解系统各阶模态极限环幅值随传热迟滞时间的变化,发现Rijke管热声振荡稳定性切换现象与迟滞时间存在近似周期性关系.     

热声热机声场的格子气分析

从格子气自动机演化方程恢复了宏观热声方程,采用D2Q9热格子气模型模拟热声热机系统的压力场、温度场和速度场,获得压力驻波的传播和反射过程。模拟结果显示,在所给模拟条件下压力波具有非线性的特征,变截面附近的流场区域会产生引起非线性耗散的涡流。本文也分析了谐振管几何尺寸及格子气粒子密度对系统频率和压力的影响,验证了热声热机格子气模型的有效性。     

热声谐振管的实验研究

本文主要介绍作者热声谐振管研制方面的工作，作者成功地研制了热声谐振实验装置系统。     

Acoustic streaming in closed thermoacoustic devices.

A derivation of acoustic streaming in a steady-state thermoacoustic device is presented in the case of zero second-order time-averaged mass flux across the resonator section (nonlooped device). This yields analytical expressions for the time-independent second-order velocity, pressure gradient, and time-averaged mass flux in a fluid supporting a temperature gradient and confined between widely to closely separated solid boundaries, both in the parallel plate and in the cylindrical tube geometries (two-dimensional problem). From this, streaming can be evaluated in a thermoacoustic stack, regenerator, pulse tube, main resonator of a thermoacoustic device, or in any closed tube that supports a mean temperature gradient, providing only that the acoustic pressure, the longitudinal derivative of the pressure, and the mean temperature variation are known.     

Rijke管自激热声振荡的数值模拟

为了对热声不稳定的发生及控制机理进行研究,对Rijke管内的自激热声振荡现象进行了数值模拟。采用具有低频散低耗散特点的计算气动声学方法,对带有非线性热源项的声波方程进行数值求解,并比较了不同的热源模型及边界条件对非线性效应的影响。结果表明,计算气动声学方法可以成功捕捉到Rijke管内压力的起振过程,而且在速度扰动达到平均流速度的1/3时,振荡会由线性增长转为非线性增长,最终达到有限幅值极限循环。相比热源项,考虑管口辐射耗散的非线性边界条件在振荡幅值和频谱方面对结果的影响都比较小。数值模拟得到的结果与实验符合较好,表明计算气动声学方法适合于热声振荡问题的研究。      

热声发动机的格子气模拟

在传统的9-bit格子气模型中引入了温度区的概念,并应用于热声发动机的模拟研究.利用改进后的格子气模型,模拟了热声谐振管中的自激振荡和二维温度场的分布及温度随时间的演化过程,同时,对热声板叠的长度和在声场中的位置对声幅的影响也进行了数值研究,所得结果对板叠的优化设计是有价值的.通过对模拟和实验结果的比较,验证了热声机格子气模型的有效性,表明格子气方法适用于热声模拟.     

A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine

Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy.     

容腔调相的单级行波热声发动机起振特性

将容腔结构引入单级环路行波热声发动机系统中进行相位调节,分析了不同容腔位置、容腔内径和容腔长度时系统的起振特性。基于线性热声理论,采用网格传输矩阵数值方法求解系统的起振频率和起振温差;此外,将计算结果与实验结果进行了对比,验证了计算方法的合理性。结果表明:容腔结构可以明显改善系统的起振特性,系统起振温差大幅下降;不同容腔位置处,热机起振特性差异明显;存在最优的容腔内径和容腔长度组合,使得起振温差最低,而容腔尺寸对热机起振频率的影响较小。      

热声热机热声核内传热与流动特性实验研究

本文通过搭建扬声器驱动的热声热机可视化实验台,利用粒子成像测速仪(PIV)和红外热像仪得到冷、热端换热器间速度及温度场分布,对有无声场两种情况下热声核中速度及温度场的变化进行了实验研究。实验结果表明,外加声场改变了热声核中热对流的基本模式,增强了冷热端换热器间的换热能力,对热声核中的温度分布有着显著的影响。揭示了热声核中的流动与换热规律。     

基于热声相控阵列的声聚焦效应

研究基于热声相控阵列的宽频带声聚焦效应.设计新型热声相位控制单元,通过改变单元的空气温度控制声波波速,实现声波透射与反射相位延迟覆盖2π区间.设计四种不同类型的热声相控阵列聚焦透镜,采用8种或2种热声相位控制单元分别实现了透射与反射声聚焦效应.与其他类型的声聚焦透镜相比,热声相控阵列聚焦透镜具有宽频带、高聚焦性能、设计方案简单等优点.     

A passive network model for large diameter thermoacoustic tube systems and its experimental verification

Linear thermoacoustic theory is currently well accepted for simulating thermoacoustic systems, and correction is used to reduce the discrepancy between calculations and experimental results for turbulent flow. In order to calculate passive tube systems and make linear thermoacoustic theory coincide closely with experiments, a passive network model based on fluid network theory is derived. An amendment method is proposed to further correct for turbulence by amending thermal and viscous penetration depths when the ratio of the tube radius to the viscous penetration depth R/δ_v is large. The experiments have been done to verify the model in the acoustic amplifier, Helmholtz resonator, and inertance tube. In addition, the mechanisms of such tubes are further analyzed based on the model.     

热声系统中回热器特征阻抗与传播常数的研究

针对本实验室一台声驱动热声系统,采用传递函数法研究声驱动系统中回热器的特征阻抗和传播常数.通过调节谐振管长度,改变回热器表面的阻抗,从理论上分析了回热器网络传输方程中的声传播常数、特征阻抗与系统网络元件中的阻抗、导纳和流的关系.并且进一步讨论有无换热器以及不同的加热功率对回热器网络参数的影响.结论有利于进一步量化回热器的网络参数.     

Modular system for studying tonal sound excitation in resonators with heat addition and mean flow

An educational experimental system has been developed for studying tonal sound generation in acoustic resonators. Tones are excited by either heat addition or vortex shedding in the presence of mean flow. The system construction is straightforward and inexpensive. Several test arrangements and experimental data are described in this paper. The experimental setups include a modified Rijke tube, a standing-wave thermoacoustic engine, a baffled tube with mean flow, and an acoustic energy harvester with a piezoelement. Simplified mathematical models for interpreting data are discussed, and references are provided to literature with more advanced analyses. The developed system can assist both graduate and undergraduate students in understanding acoustic instabilities via conducting and analyzing interesting experiments.     

热声发动机的优化计算设计

把改进的12-Bit格子气模型用于复杂边界的热声发动机的模拟研究,成功模拟了带共振腔的驻波管中热声振荡演化过程。对热声板叠的长度、热声板叠在共振管中的位置以及共振腔的几何大小对热声振荡振幅的影响进行了数值计算。计算结果显示,当共振腔与细管的宽度比为2.2,板叠位置相对于细管长为0.34时,驻波管中热声振荡振幅达到最大。共振腔尺寸的研究,对于热声发动机性能的的优化设计有指导意义。     

驻波热声系统的自激振荡机理

热声发动机的起振过程是一个产生并维持自激振荡的过程, 研究热声自激振荡机理有助于进一步了解热声效应的实质. 根据热声网络理论, 建立了驻波热声发动机的整机网络. 将热声网络比拟成电网络, 利用厄米特式计算了输入热声网络的视在功流, 功流平衡对应自激, 在角频率虚部为零的情况下计算了热声发动机的阈值温度和运行频率. 结果表明, 计算值与实验值符合得较好, 充气压力与阈值温度和运行频率的耦合关系大致相同. 所得结论有助于进一步探究热声效应机理以及热声发动机系统的优化设计.     

Open cycle traveling wave thermoacoustics: mean temperature difference at the regenerator interface

In an open cycle traveling wave thermoacoustic engine, the hot heat exchanger is replaced by a steady flow of hot gas into the regenerator to provide the thermal energy input to the engine. The steady-state operation of such a device requires that a potentially large mean temperature difference exist between the incoming gas and the solid material at the regenerator's hot side, due in part to isentropic gas oscillations in the open space adjacent to the regenerator. The magnitude of this temperature difference will have a significant effect on the efficiencies of these open cycle devices. To help assess the feasibility of such thermoacoustic engines, a numerical model is developed that predicts the dependence of the mean temperature difference upon the important design and operating parameters of the open cycle thermoacoustic engine, including the acoustic pressure, mean mass flow rate, acoustic phase angles, and conductive heat loss. Using this model, it is also shown that the temperature difference at the regenerator interface is approximately proportional to the sum of the acoustic power output and the conductive heat loss at this location.     

Thermal modeling and performance analysis of a thermoacoustic refrigerator

A heat-driven thermoacoustic refrigerator has been designed and tested. A detailed thermal model of the device is presented. Energy balances within the system are discussed using external, heat exchanger, and stack control volumes in order to clarify the relationships of work and heat fluxes below and above onset. Thermal modeling is discussed as a tool for performance analysis as well as for determining system heat losses and finding input heat flows required by a thermoacoustic code. A method of using the control volume balance equations to find stack work and device efficiencies is presented. Experimental measurements are compared to DELTAE thermoacoustic modeling predictions. Modeling results show that viscous losses within the system have a significant impact on the device performance as well as on the ability of DELTAE to accurately predict performance. Modeling has led to an understanding of system performance and highlighted loss sources that are areas for improvement in a redesign.