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Mixing Delays in Non-Equilibrium High-Speed Turbulence

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[Technical Report, Memorandum Report]

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This paper uses NRLs Coherent Structure Dynamics CSD model coupled to Surrogate Fluid Dynamics SFD on a triply-periodic, cubical domain to estimate the additional mixing time delays that occur in separated fuel and oxidizer systems when turbulence is quiescent initially. Mixing delays occur as the turbulent energy cascades dynamically from macroscopic driving flows to the much smaller scales where molecular mixing happens. If the turbulence is fully excited initially, the molecular mixing still takes some time but it can begin much earlier. CSD-SFD is an incompressible model in which the computations are at least three orders of magnitude faster than in Computational Fluid Dynamics CFDsimulations of comparable resolution. Further the SFD algorithms are implemented with no numerical diffusion and no Courant stability limit so timesteps can be appreciably longer. Added diffusion must be explicitly supplied at the grid scale to ensure fuel and oxidizer mix locally. Multiple realizations of the 3D SFD flow field can be constructed, each obeying the single time-dependent, multi-scale spectrum computed by the CSD model. In this paper, matching pairs of 3D simulations are used, one starts with a laminar large-scale stirring flow where turbulence takes time to develop while the second simulation begins with a fully equilibrated turbulent spectrum. The elapsed time at which specific levels of mixing occur in each simulation is differenced to compute the non-equilibrium mixing delay. This is done for fast flows in this paper to estimate how much the reaction process will be delayed, for example, in a supersonic combustor. In a Mach 3 flow at 1 kmsec, velocities driving the turbulence of .5 kmsec, .3 kmsec, and .2 kmsec are considered. The extra distances needed for combustion are 1.0, 1.6, and 2.4 meters respectively when the initial turbulence is far from equilibrium.

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  • Fluid Mechanics

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[A, Approved For Public Release]