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arXiv 2211.04516physics.flu-dyn
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流体-颗粒流中turbulence调制的广义k-ε模型

A generalized k-epsilon model for turbulence modulation in fluid-particle flows

Roar Skartlien, Teresa Lynne Palmer, Olaf Skjæraasen

摘要:

大量的文献资料表明,直径大于湍流积分长度尺度10%的颗粒($D/l >0.1$)倾向于将载流流体的湍流动能增加到高于单相值,本文提出了一个修正的$k-ε$型唯象模型,该模型具有小颗粒无湍流调制的正确渐近极限,颗粒,并增加较大直径的固体。颗粒动力学理论用于推导由于阻力和附加质量力两者而在颗粒和流体之间交换的功,以适应任何颗粒/流体密度比,包括气泡、液滴和重固体。对于较大的颗粒,我们设计了一个新的模型,涡脱落引起的颗粒之间的滑移和湍流,由于颗粒的惯性。通过渐近分析,得到了湍流调制的简单近似公式。固体颗粒的总体效果是,大直径固体的增强是由于旋涡脱落,而小直径的湍流抑制主要是由于湍流阻力和额外的流体耗散。在$D/l = 0.1$周围从抑制到增强的转变对于大范围的粒子雷诺数和斯托克斯数是一个鲁棒的特征,但是我们不能证明这是一个理论基础上的一般关系。实际上,对于较大直径,气泡和液滴可能根本不显示湍流增强,这是由于防止破碎所需的中等湍流水平,并且颗粒和流体之间的速度差可能因此太低而不能发生涡旋脱落。在该模型的基础上,我们发现,在垂直气流中的固体的一些数据显示非常大的湍流增强,只能是由于重力沉降。

英文摘要:

A large amount of published data show that particles with diameter above 10\% of the turbulence integral length scale ($D/l >0.1$) tend to increase the turbulent kinetic energy of the carrier fluid above the single-phase value, and smaller particles tend to suppress it. A revised phenomenological model of the $k-ε$ type was developed to reproduce these effects with the correct asymptotic limit of no turbulence modulation for small particles, and augmentation for larger diameter solids. Particle-kinetic theory was used to derive the work exchanged between the particles and the fluid due to both drag and added mass forces to accommodate any particle/fluid density ratios including bubbles, droplets and heavy solids. For the larger particles, we devised a new model for vortex shedding induced by the slip between the particles and the turbulent flow, due to particle inertia. Simple approximate formulae for the turbulence modulation were obtained through asymptotic analysis. The overall effect for solid particles is that augmentation for large diameter solids is due to vortex shedding, and turbulence suppression for small diameters is due to mainly to turbulent drag forces and extra fluid dissipation. The transition from suppression to augmentation around $D/l = 0.1$ is a robust feature for a wide range of particle Reynolds and Stokes numbers, but we could not prove this to be a general relation on a theoretical basis. Indeed, bubbles and droplets may not display turbulence augmentation at all for the larger diameters due to moderate turbulence levels needed to prevent breakup, and the velocity difference between particles and fluid may therefore be too low for vortex shedding to occur. On the basis of the model we find that some data for solids in vertical gas flow show very large turbulence augmentation that can only be due to gravitational settling.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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