Derivation of a realistic forcing term to reproduce the turbulent characteristics of round jets on the centerline

Abstract

Turbulence forcing techniques are often required in the numerical simulation of statistically stationary turbulent flows. However, the existing forcing techniques are not based on physics, but rather arbitrary numerical methods that sustain the turbulent kinetic energy. In this work, a forcing technique is devised to reproduce the centerline turbulent characteristics of round jets in a triply periodic box. It is derived from the Navier-Stokes equations by applying a Reynolds decomposition with the mean velocity of the axisymmetric jet. The result is an anisotropic linear forcing term, which is intended to be used in a three-dimensional box to create turbulence. Four direct numerical simulations with different Re_λ have been performed with these forcing terms. The budget of the terms in the kinetic energy equation is very close to the experimental measurement on the centerline. The anisotropy, kinetic energy k, and dissipation rate ɛ of the simulations are also comparable to experimental values. Finally, the kinetic energy spectrum in the axial direction, ϕ(κ_1), is presented. With appropriate normalizations, the spectrum agrees well with the round jet spectrum on its centerline.