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Compressibility effects on the transition to turbulence in a spatially developing plane free shear layer

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Abstract

The compressibility effects on the transition to turbulence in a spatially developing, compressible plane free shear layer are investigated via direct numerical simulation using a high-order discontinuous spectral element method for three different convective Mach numbers of 0.3, 0.5, and 0.7. The location of the laminar–turbulent transition zone is predicted by the analyses of vorticities, Reynolds stresses, and the turbulent dissipation rate. In the turbulence transition and self-similar turbulence regions, the effects of compressibility on the flow properties, such as the velocity autocorrelation function, integral time scale, momentum thickness, Reynolds stress, and turbulent kinetic energy budget, are investigated. The compressibility effects on the onset and length of the turbulence transition zone are studied based on the analyses of such flow properties. The mean velocity, momentum thickness, and Reynolds stress profiles compare well with published experimental data. Vorticity contours and iso-surface of the second invariant of velocity gradient tensor identify the characteristic of flow structures. The two-point correlation functions of velocity components, the one-dimensional (1D) spanwise energy spectrum, and the balance of the turbulent kinetic energy transport equation validate the domain size and resolution of the adopted grid for turbulence simulation. An increase in the convective Mach number leads to a reduction in the sizes of the largest-scale structures, resulting in a significant decrease in Reynolds stresses and turbulence production. The onset of turbulence transition and the location where the transition completes shift downstream, while the length of the transition zone increases with increasing convective Mach number.

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Acknowledgements

Part of the computational resources for this study was provided by the ACER at the University of Illinois at Chicago. This research was also in part supported by the Blue Waters sustained-petascale computing project, which is sponsored by the National Science Foundation (Awards OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications. The Program Development Company GridPro provided us with troubleshooting support and license to access its meshing software, which was used to create the meshes for the simulations presented in this study.

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Correspondence to Farzad Mashayek.

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Li, D., Komperda, J., Ghiasi, Z. et al. Compressibility effects on the transition to turbulence in a spatially developing plane free shear layer. Theor. Comput. Fluid Dyn. 33, 577–602 (2019). https://doi.org/10.1007/s00162-019-00507-w

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Keywords

  • Direct numerical simulation
  • Transition
  • Compressible flow
  • Plane free shear layer
  • Compressibility effect
  • Spatially developing flow