Equilibrium similarity solution of the turbulent transport equation along the centreline of a round jet. (8th May 2015) - Sadeghi, H.; Lavoie, P.; Pollard, A.
Abstract : A novel similarity-based form is derived of the transport equation for the second-order velocity structure function of (δq)^2 along the centreline of a round turbulent jet using an equilibrium similarity analysis. This self-similar equation has the advantage of requiring less extensive measurements to calculate the inhomogeneous (decay and production) terms of the transport equation. It is suggested that the normalised third-order structure function can be uniquely determined when the normalised second-order structure function, the power-law exponent of q^2 and the decay rate constants of u^2 and v^2 are available. In addition, the current analysis demonstrates that the assumption of similarity, combined with an inverse relation between the mean velocity U and the streamwise distance x-x_0 from the virtual origin (i.e. U(x-x_0)^-1 ), is sufficient to predict a power-law decay for the turbulence kinetic energy ( q^2(x-x_0)^m ), rather than requiring a power-law decay ( m=-2 ) as an additional ad hoc assumption. On the basis of the current analysis, it is suggested that the mean kinetic energy dissipation rate, ε, varies as (x-x_0)^m-2 . These theoretical results are tested against new experimental data obtained along the centreline of a round turbulent jet as well as previously published data on round jets for 11 000Re_D184 000 over the range 10x/D90 . For the present experiments, q^2 exhibits power-law behaviour with m=-1.83 . The validity of this solution is confirmed using other experimental data where q^2 follows a power law with -1.89m-1.78 . The present similarity form of the transport equation for (δq)^2 is also shown to be closely satisfied by the experimental data.