Turbulent jet reactors: Mixing time scales

Reactor scale-up and numerical simulation of reactor performance require an estimate of the time scale of turbulent mixing. In the present paper, time scales for mixing within free turbulent jets are discussed. In particular, it is demonstrated that both the Kolmogoroff time (v/epsilon)(1/2) and eddy dissipation time kappa/epsilon are proportional throughout the isotropic flowfield of fully developed free jets that are commonly used in reactor design. The constant of proportionality between both times is shown to depend on the jet Reynolds number. Scaling laws are derived in the Limiting case of either jet-to-tube velocity u/v --> 1 or u/v --> infinity plus one intermediate value u/v --> 3. Both time scales are also compared with the yield from a mixing-controlled parallel reaction occurring within a free jet where it is demonstrated that the smaller Kolmogoroff value correlates the yield in the limit of a small scale reactant feed. The eddy dissipation time, however, is shown to correlate data for larger but fixed reactant feed streams, but a complete correlation was not possible.