稠密可压缩气粒两相流动中的等熵声速计算建模及物理规律

On modeling and physical laws of isentropic speed of sound in dense gas-particle two-phase compressible flows

气体相与颗粒相混合流场的声速研究,由于具有重要的基础理论价值与广泛的工程应用背景,逐渐受到人们重视.针对稠密可压缩气粒两相流动,综合考虑颗粒相所占空间体积以及颗粒间相互作用,推导给出了新的等熵声速计算公式;新公式包含了已有的纯气体、稀疏气粒两相流情形的计算公式作为其特例,一方面验证了公式推导的正确性,另一方面说明新公式更具有通用性;分析了不同颗粒质量分数条件下的声速变化规律,相应结果与普朗特的理论分析符合,特别对于稠密气粒两相流动工况得到了一些新的物理认识;开展了颗粒间相互作用建模参数的物理分析,揭示了其对气粒两相流动声速的影响机理.本文取得的成果为稠密可压缩气粒两相流动研究以及相关工程应用提供理论支撑.

Study of isentropic sound speed of two-phase or multiphase flow has theoretical significance and wide application background.As is well known,the speed of sound in fluid containing particles in suspension differs from that in the pure fluid.In the particular case of bubbly liquids（gas liquid two-phase flow）,the researches find that the differences can be drastic.Up to now,the isentropic speed of sound in the flow field with a small volume fraction of bubbles（less than 1%）,has been investigated fully both experimentally and theoretically.In this paper,we consider another situation,as the case with solid particles in gas,which is the so-called gas particle two-phase flow.Although many results have been obtained in gas liquid two-phase flow,there is still a lot of basic work to do due to the large differences in the flow structure and flow pattern between gas particle two-phase flow and gas liquid two-phase flow.Treating the gas particle suspension as the relaxed equilibrium,thermodynamic arguments are used to obtain the isentropic speed of sound.Unlike the existing work,we are dedicated to developing the computational model under dense condition.The space volume occupied by particle phase and the interaction between particles are overall considered,then a new formula of isentropic sound speed is derived.The new formula includes formulae of the pure gas flow and the already existing dilute gas particle two-phase flow as a special case.On the one hand,the correctness of our formula is verified.On the other hand,the new formula is more general.The variations of sound speed with different mass fractions of particle phase are analyzed.The theoretical calculation results show that the overall physical law of sound speed change is that with the increase of the particle mass fraction,the sound speed first decreases and then increases.The velocity of sound propagation in gas particle two-phase flow is far smaller than in pure gas in a wide range,so it is easy to reach the supersonic condition.When the particle volume fraction is below 10%,the result is consistent with Prandtl theoretical analysis.In this range,the influences of the particle phase pressure modeling parameters can be neglected.When the particle volume fraction is more than 10%,the particle phase pressure modeling parameters produce influences.Furthermore the corresponding physical principles and the mechanisms are discussed and revealed.The new formula and physical understandings obtained in this paper will provide a theoretical support for the researches of dense gas particle two-phase compressible flow and related engineering applications.