Effects of the Mach number on the evolution of vortex-surface fields in compressible Taylor-Green flows

Abstract

We investigate the evolution of vortex-surface fields (VSFs) in compressible Taylor-Green flows at Mach numbers (M a) ranging from 0.5 to 2.0 using direct numerical simulation. The formulation of VSFs in incompressible flows is extended to compressible flows, and a mass-based renormalization of VSFs is used to facilitate characterizing the evolution of a particular vortex surface. The effects of the Mach number on the VSF evolution are different in three stages. In the early stage, the jumps of the compressive velocity component near shocklets generate sinks to contract surrounding vortex surfaces, which shrink vortex volume and distort vortex surfaces. The subsequent reconnection of vortex surfaces, quantified by the minimal distance between approaching vortex surfaces and the exchange of vorticity fluxes, occurs earlier and has a higher reconnection degree for larger M a owing to the dilatational dissipation and shocklet-induced reconnection of vortex lines. In the late stage, the positive dissipation rate and negative pressure work accelerate the loss of kinetic energy and suppress vortex twisting with increasing M a.

Mechanism and modelling of the secondary baroclinic vorticity in the Richtmyer–Meshkov instability

“…The two-time method (Yang & Pullin 2011; Peng & Yang 2018) is used to calculate the VSF evolution. The temporal evolution at each time step is divided into prediction and correction substeps.…”

Assessment of Low-Dissipative Shock-Capturing Schemes for the Compressible Taylor–Green Vortex

“…Throughout this work the coordinates ( = 0, 1, 2) are referred to as ( , , ), with corresponding velocity components ( , , [12] as ( ) = 1.4042 1.5 + 0.40417 .…”

“…The compressible TGV problem at higher Mach numbers is a challenging test case for numerical schemes, but has not been widely explored in the literature. One notable exception is the work of [12], which investigated the evolution of vortex-surface fields in a compressible TGV. This study was performed at a low Reynolds number of = 400.…”

Theory and applications of the vortex-surface field

“…对于高马赫(Ma)数流动中的强可压缩性作用, 涡 面场研究发现高Ma数TG流动中的涡动力学过程可分 为3个阶段 [38] : 在演化初期随Ma数增大, 流场中产生强 激波压缩作用导致球状涡面体积缩小; 在演化中期随 Ma增大, 涡面间重联发生的时刻提前, 重联程度增加; 在演化后期, 涡面扭曲成管状结构, 且随Ma增大流场中 动能向内能剧烈转化, 导致涡管扭曲程度降低, 涡动力…”

“…此外, 由方程(9)可知, 理论上涡面场可以使用固定 的等值面阈值来表征时间演化中某一特定的涡面, 因 此该方法在使用时无须人为调整等值面阈值. 此外基 于涡面所包围的控制体内质量守恒算法 [38] , 可以进一 [39,48] , 这为工程应用中发展基于流动结构的预 测模型提供了理论基础. 此外, 其他流动结构显示中所 用的三维被动标量场(如染色剂、烟线等) [61] 与涡面场 之间的偏差可由式(11)定量化.…”