Compressible and Geometrical Effects on Shearless Turbulent Mixing
An, Eunhye
2023
Abstract
Compressible turbulent mixing plays an important role in a variety of astrophysical and engineering problems ranging from combustion engines to star formation in space. These flows involve complex physics, such as entrainment, mass/momentum transfer, and viscous dissipation. While incompressible, homogeneous turbulence is relatively well understood, compressibility and inhomogeneity pose challenges to classical theory due to different energy transfer and dissipation mechanisms. Our aim is to conduct high-fidelity numerical simulations to investigate how compressible turbulent flows mix and decay, and how heterogeneity affects these dynamics. We first propose an improved process for generating an initial velocity field that obtains an equilibrium turbulence state with desired properties such as Reynolds number, turbulent Mach number, and the most energetic wavenumber. The rescaled field exhibits the expected k^{-5/3} energy spectrum from time zero. This approach provides a systematic procedure to initialize homogeneous isotropic turbulent fields, which results in the quasi-equilibrium state with higher Reynolds numbers. This enables us to investigate the mixing mechanisms in early stages such as entrainment. Using this initialization procedure, we investigate shearless compressible turbulent/non-turbulent mixing. We juxtapose an initially shearless homogeneous isotropic turbulent field with a stationary fluid. Near the turbulent/non-turbulent interface, turbulent eddies entrain, and viscous stresses at smaller scales impart vorticity to the irrotational region; then the mixing region develops. The growth of the mixing region follows a self-similar power law of 2/3 in time, consistent with (Barenblatt,1987). Moreover, we find that compressibility effects through acoustic waves cause energy losses and result in an enhanced decay of turbulent kinetic energy because kinetic energy is transferred to less energetic flow regions. We propose the new scaling law for the decay of turbulent kinetic energy to account for this compressibility in turbulent/non-turbulent mixing, which we validate using direct numerical simulations. We then extend this study to investigate shearless compressible turbulent mixing with gradients in turbulent intensity. The flow is initialized by juxtaposing two homogeneous isotropic turbulent fields of different turbulent intensities. The higher-intensity flow has a broader range of scales; it penetrates extensively into the lower-energy region with intermittency. Therefore, there is net energy transfer from the higher- to the lower-intensity regions by dilatation along the inhomogeneous direction. These inhomogeneity and compressibility effects are represented as energy loss and gain in the scaling for the decay of turbulent kinetic energy, leading to delayed and enhanced decay rates. Geometrical effects on compressible turbulent/non-turbulent mixing are investigated for the propagation of a decaying turbulent front in planar and cylindrical geometries. We show that the cylindrical interface propagates as a power law in time with an exponent of 1/2, which is confirmed by dimensional analysis. The turbulent kinetic energy is determined by the dissipation rate and the triple moment of velocity derivatives; the dissipation rate is independent of the geometry of turbulence because there are no energy production mechanisms. On the other hand, dilatational energy transfer, which is represented as a triple moment of velocity derivatives is subject to the dimension of turbulent fields. Therefore, cylindrical turbulence exhibits more significant energy losses due to acoustic waves propagating to the non-turbulent region compared to planar turbulence. This physics is well described by the new scaling law with appropriate coefficients. This study can improve the understanding and prediction of the complex turbulent flows of engineering relevance and the development of turbulent models.Deep Blue DOI
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Compressible Turbulent Mixing
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