The effect of nozzle geometry on the turbulence evolution in an axisymmetric jet flow: A focus on fractals

Multifractal modeling has originated from the study of turbulence to reproduce scale-invariant variations of the energy flux in different scales. Turbulent eddies partition themselves into finer ones in a multiplicative process that produces a population spread over a domain. The population generated is a union of subsets, where each subset is fractal with its own fractal dimension. In this study, we compare the multifractal exponents of jet turbulence intensities obtained through numerical simulation. Turbulence intensities were obtained from numerical jet discharge experiments based on Reynolds-Averaged Navier–Stokes (RANS) equations, where two types of nozzle geometry and two statistical turbulent closure models (i.e., k-ε model and the k-ω model) were tested. The simulation results by two closure models demonstrate in common that the RANS model reproduced hydraulic properties such as transversal velocity profile successfully compared to an analytical solution, but exhibit a limitation for reproducing the turbulence intensity decay in the longitudinal direction. Meanwhile, a common multifractal spectrum turns out to exist for turbulence intensity obtained from numerical simulation based on a statistically-averaged turbulence model. While two different turbulence models produced almost identical transverse velocity profiles, multifractal characteristics are quite distinct; the minimum Lipschitz–Hölder exponent (α_min) and entropy dimension (α₁) are dependent on the turbulence as well as outfall nozzle geometry. Consequently, it is demonstrated that the multifractal exponents capture the difference in turbulence structures of hierarchical turbulence intensities produced with different experimental conditions.