Estimating turbulent kinetic energy and dissipation with internal flow loss coefficients

Abstract

Estimating the turbulent kinetic energy at the nozzle outlet is necessary to model turbulent jet breakup. We identified errors in a model of nozzle turbulence developed by Huh et al. which made the model inaccurate. To develop an improved model, we derived a generalized form of the Bernoulli equation for non-cavitating flows. The equation can be used to estimate turbulent kinetic energy, k, and dissipation, ε, in internal flows given loss coefficients or friction factors and a turbulence model. The equation allows turbulent kinetic energy and dissipation to be estimated without computational fluid dynamics. The estimates can be used as-is where turbulent kinetic energy or dissipation are desired, or as a more accurate boundary condition for computational fluid dynamics. A model for fully developed pipe flow is developed and compared against experimental data. A nozzle turbulence model which could replace Huh et al.'s is also developed, but the model has not been validated due to a lack of experimental data.