Modelling nonlinear thermoacoustic instability in an electrically heated Rijke tube
Modelling nonlinear thermoacoustic instability in an electrically heated Rijke tube
复制标题
电加热 Rijke 管中的非线性热声不稳定性建模
DOI：
10.1017/jfm.2011.176
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发表时间：
2011
影响因子：
3.7
通讯作者：
R. Sujith
中科院分区：
文献类型：
--
作者：
S. Mariappan;R. Sujith
对以电阻加热器为热源的水平瑞克管进行了热声不稳定性分析。由于稳定流动马赫数和热源厚度（相对于声波波长）较小，这种流体流动的控制方程变得僵硬，难以用计算流体动力学（CFD）技术求解。因此，在小马赫数和紧凑热源的极限下进行渐近分析，以消除上述刚度问题。将未知变量以马赫数的幂展开。得到了两套控制方程：一套用于声场，另一套用于加热器周围水动力区非定常流场。在此分析中，声场与加热器非定常放热率之间的耦合从渐近分析中显现出来。此外，在流体动力区动量方程中出现了一个非平凡的附加项，即全局加速度项，这对系统的稳定性有严重的影响。这个术语可以解释为从声学区施加到水动力区的压力梯度。利用分岔图给出了系统参数变化时系统的渐近稳定性。采用Galerkin技术对声学区域进行了数值模拟，采用CFD技术对水动力区域进行了数值模拟。结果证实了全局加速项的重要性。有和没有上述项的模拟得到的分岔图是不同的。在极限循环过程中存在声流现象，并讨论了声流对非定常放热率的影响。
An analysis of thermoacoustic instability is performed for a horizontal Rijke tube with an electrical resistance heater as the heat source. The governing equations for this fluid flow become stiff and are difficult to solve by the computational fluid dynamics (CFD) technique, as the Mach number of the steady flow and the thickness of the heat source (compared to the acoustic wavelength) are small. Therefore, an asymptotic analysis is performed in the limit of small Mach number and compact heat source to eliminate the above stiffness problem. The unknown variables are expanded in powers of Mach number. Two systems of governing equations are obtained: one for the acoustic field and the other for the unsteady flow field in the hydrodynamic zone around the heater. In this analysis, the coupling between the acoustic field and the unsteady heat release rate from the heater appears from the asymptotic analysis. Furthermore, a non-trivial additional term, referred to as the global-acceleration term, appears in the momentum equation of the hydrodynamic zone, which has serious consequences for the stability of the system. This term can be interpreted as a pressure gradient applied from the acoustic onto the hydrodynamic zone. The asymptotic stability of the system with the variation of system parameters is presented using the bifurcation diagram. Numerical simulations are performed using the Galerkin technique for the acoustic zone and CFD techniques for the hydrodynamic zone. The results confirm the importance of the global-acceleration term. Bifurcation diagrams obtained from the simulations with and without the above term are different. Acoustic streaming is shown to occur during the limit cycle and its effect on the unsteady heat release rate is discussed.
焓变影响下预混燃烧大活化能理论
影响因子：
3.7
作者：
WU X
通讯作者：
WU X