One-dimensional refraction properties of compression shocks in non-ideal gases
One-dimensional refraction properties of compression shocks in non-ideal gases
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DOI：
10.1017/jfm.2017.10
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发表时间：
2017-03-10
影响因子：
3.7
通讯作者：
Touber, Emile
中科院分区：
文献类型：
--
作者：
Alferez, Nicolas;Touber, Emile
非理想气体是指可变形的物质，其中声速可以在等熵压缩后降低。由于长程分子相互作用，这可能发生在相变附近，例如液-汽临界点。等熵体可以在压力/比容相图中局部凹陷（例如Bethe-Zel'dovich-Thompson（BZT）气体）。继贝特（Bethe）的开创性工作之后，Rep. 545，Office of Scientific Research and Development，1942）关于非理想气体中激波的研究，本文探讨了具有正等压体积膨胀率的非反应但任意物质中稳定压缩激波的折射性质。进行了小扰动分析，以获得垂直于激波阵面的折射场的热声特性的解析表达式。发现了三种新的机制：（i）广泛但有选择性的（上游马赫数）熵模式的放大（比相应的理想气体大几百倍）;（ii）不连续（上游马赫数）激波管非容许部分出现后的折射特性（iii）所产生的声学模式出现相移，因此存在扰动激波不产生任何声场的条件（即，“安静”冲击，以与2D或3D中预期的自发D 'yakov-Kontorovich声发射形成对比）。在多维流动，特别是可压缩湍流的背景下，这些结果表明，通过各种途径，所提供的能量（以熵，涡或声学模式的形式）可以以其他熵，声学和涡模式的形式重新分配，在理想气体中根本无法实现。这些发现与接近液-汽临界点运行的涡轮机和压缩机（如有机朗肯循环膨胀机、超临界CO2压缩机）、具有奇异状态方程（如早期宇宙）的连续介质模拟的天体物理流动或具有小但有限温度效应的玻色-爱因斯坦凝聚有关。
Non-ideal gases refer to deformable substances in which the speed of sound can decrease following an isentropic compression. This may occur near a phase transition such as the liquid-vapour critical point due to long-range molecular interactions. Isentropes can then become locally concave in the pressure/specific-volume phase diagram (e.g. Bethe-Zel'dovich-Thompson (BZT) gases). Following the pioneering work of Bethe (Tech. Rep. 545, Office of Scientific Research and Development, 1942) on shocks in non-ideal gases, this paper explores the refraction properties of stable compression shocks in non-reacting but arbitrary substances featuring a positive isobaric volume expansivity. A small-perturbation analysis is carried out to obtain analytical expressions for the thermo-acoustic properties of the refracted field normal to the shock front. Three new regimes are discovered: (i) an extensive but selective (in upstream Mach numbers) amplification of the entropy mode (hundreds of times larger than those of a corresponding ideal gas); (ii) discontinuous (in upstream Mach numbers) refraction properties following the appearance of non-admissible portions of the shock adiabats; (iii) the emergence of a phase shift for the generated acoustic modes and therefore the existence of conditions for which the perturbed shock does not produce any acoustic field (i.e. 'quiet' shocks, to contrast with the spontaneous D'yakov-Kontorovich acoustic emission expected in 2D or 3D). In the context of multidimensional flows, and compressible turbulence in particular, these results demonstrate a variety of pathways by which a supplied amount of energy (in the form of an entropy, vortical or acoustic mode) can be redistributed in the form of other entropy, acoustic and vortical modes in a manner that is simply not achievable in ideal gases. These findings are relevant for turbines and compressors operating close to the liquid-vapour critical point (e.g. organic Rankine cycle expanders, supercritical CO2 compressors), astrophysical flows modelled as continuum media with exotic equations of state (e.g. the early Universe) or Bose-Einstein condensates with small but finite temperature effects.