TY - JOUR

T1 - The effect of nozzle geometry on the turbulence evolution in an axisymmetric jet flow

T2 - A focus on fractals

AU - Seo, Yongwon

AU - Ko, Haeng Sik

AU - Son, Sangyoung

N1 - Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korea government ( NRF-2019R1A2C1089109 & NRF-2016R1D1A1B03930893 ).

PY - 2020/7/15

Y1 - 2020/7/15

N2 - 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 (αmin) 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.

AB - 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 (αmin) 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.

KW - Box-Count method

KW - Multifractal

KW - Nozzle geometry

KW - Reynolds-averaged Navier–Stokes equations

KW - Statistical turbulence model

KW - Turbulence intensity

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U2 - 10.1016/j.physa.2020.124145

DO - 10.1016/j.physa.2020.124145

M3 - Article

AN - SCOPUS:85083907363

VL - 550

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

M1 - 124145

ER -