The physical characteristics and evolution of a large-scale helium plume are examined through a series of numerical simulations with increasing physical resolution using adaptive mesh refinement (AMR). The five simulations each model a 1-m-diameter circular helium plume exiting into a $$(4~\hbox {m})^3$$ ( 4 m ) 3 domain and differ solely with respect to the smallest scales resolved using the AMR, spanning resolutions from 15.6 mm down to 0.976 mm. As the physical resolution becomes finer, the helium–air shear layer and subsequent Kelvin–Helmholtz instability are better resolved, leading to a shift in the observed plume structure and dynamics. In particular, a critical resolution is found between 3.91 and 1.95 mm, below which the mean statistics and frequency content of the plume are altered by the development of a Rayleigh–Taylor (RT) instability near the centerline in close proximity to the plume base. Comparisons are made with prior experimental and computational results, revealing that the presence of the RT instability leads to reduced centerline axial velocities and higher puffing frequencies than when the instability is absent. An analysis of velocity and scalar gradient quantities, and the dynamics of the vorticity in particular, show that gravitational torque associated with the RT instability is responsible for substantial vorticity production in the flow. The grid-converged simulations performed here indicate that very high spatial resolutions are required to accurately capture the near-field structure and dynamics of large-scale plumes, particularly with respect to the development of fundamental flow instabilities.

中文翻译：

---

使用自适应网格细化对浮力驱动流动进行数值模拟：大型氦羽流的结构和动力学

通过使用自适应网格细化 (AMR) 提高物理分辨率的一系列数值模拟来检查大规模氦羽流的物理特性和演化。这五个模拟每个模拟一个直径为 1 米的圆形氦羽流进入 $$(4~\hbox {m})^3$$ ( 4 m ) 3 域，并且仅在使用以下方法解析的最小尺度方面有所不同AMR，分辨率从 15.6 毫米到 0.976 毫米不等。随着物理分辨率变得更精细，氦-空气剪切层和随后的开尔文-亥姆霍兹不稳定性得到更好的解决，导致观察到的羽流结构和动力学发生变化。特别是，在 3.91 和 1.95 毫米之间发现了一个临界分辨率，在此之下，羽流的平均统计数据和频率含量会因靠近羽流底部的中心线附近的瑞利-泰勒 (RT) 不稳定性的发展而改变。与先前的实验和计算结果进行了比较，表明与不存在不稳定性时相比，RT 不稳定性的存在会导致中心线轴向速度降低和抽吸频率更高。对速度和标量梯度量的分析，特别是涡度的动力学，表明与 RT 不稳定性相关的重力扭矩是流动中产生大量涡度的原因。此处执行的网格收敛模拟表明，需要非常高的空间分辨率才能准确捕捉大尺度羽流的近场结构和动力学，