The fundamental requirement that inside a SCRJ fuel/air mixing and combustion must be completed in a short length to prevent excessive friction drag motivates the need to predict turbulent mixing in a supersonic airstream. Mixing is due to vorticity and its equation shows the three modes, or terms, responsible for mixing when M >> 1. The dissipation of the kinetic energy of vorticity is a source of entropy, and the power necessary to create it determines the vehicle drag. Drag power can be estimated from the K41 turbulence model developed by Kolmogorov and valid at low M < 1 if Morkovin’s hypothesis is verified. This is likely the case of SCRJ combustors, where the entrance M is of order a few units. The cascade time to transfer scalars such as fuel from large to fine scales can be estimated and becomes also a reasonable estimate of mixing time. Compared to subsonics, the slower mixing at M > 1 is showed to depend on the inertia of the fuel and air streams and can be predicted directly from the non-dimensional vorticity equation. An analog of the K41 scaling, but valid for M > 1, is then conjectured linking wavenumber to pressure, turbulent dissipation, and density. From this relationship, the analog of Kolmogorov’s lengthscale is developed in the M > 1 regime that qualitatively satisfies the observed slower mixing observed in compressible turbulence. Finally, several fuel/air mixing strategies and their technology are analyzed and discussed.
Turbulence and Mixing
sp propuls
2023-11-28
55 pages
Article/Chapter (Book)
Electronic Resource
English
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