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Direct numerical simulations of the interaction of temporally evolving circular jets

Published online by Cambridge University Press:  28 April 2025

Tomoaki Watanabe Open the ORCID record for Tomoaki Watanabe [Opens in a new window] ,
Tatsuya Inagaki ,
Takahiro Mori ,
Kirari Ishizawa  and
Koji Nagata Open the ORCID record for Koji Nagata [Opens in a new window]
Tomoaki Watanabe*
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8540, Japan
Tatsuya Inagaki
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
Takahiro Mori
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
Kirari Ishizawa
Affiliation:
Undergraduate Department of Mechanical and Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
Koji Nagata
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8540, Japan
*
Corresponding author: Tomoaki Watanabe, [email protected]
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Abstract

Direct numerical simulations are performed to study turbulence generated by the interaction of multiple temporally evolving circular jets with jet Mach numbers $M_J=0.6$ and $1.6$, and a jet Reynolds number of 3000. The jet interaction produces decaying, nearly homogeneous isotropic turbulence, where the root-mean-squared (r.m.s.) fluctuation ratio between the streamwise and transverse velocities is approximately 1.1, consistent with values observed in grid turbulence. In the supersonic case, shock waves are generated and propagate for a long time, even after the turbulent Mach number decreases. A comparison between the two Mach number cases reveals compressibility effects, such as reductions in the velocity derivative skewness magnitude and the non-dimensional energy dissipation rate. For the r.m.s. velocity fluctuations, $u_{rms}$, and the integral scale of the streamwise velocity, $L_u$, the Batchelor turbulence invariant, $u_{rms}^2 L_u^5$, becomes nearly constant after the turbulence has decayed for a certain time. In contrast, the Saffman turbulence invariant, $u_{rms}^2 L_u^3$, continuously decreases. Furthermore, temporal variations of $u_{rms}^2$ and $L_u$ follow power laws, with exponents closely matching the theoretical values for Batchelor turbulence. The three-dimensional energy spectrum $E(k)$, where $k$ is the wavenumber, exhibits $E(k) \sim k^4$ for small wavenumbers. This behaviour is consistently observed for both Mach number cases, indicating that the modulation of small-scale turbulence by compressibility effects does not affect the decay characteristics of large scales. These results demonstrate that jet interaction generates Batchelor turbulence, providing a new direction for experimental investigations into Batchelor turbulence using jet arrays.

JFM classification

Wakes/Jets: Jets Turbulent Flows: Isotropic turbulence
Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1009 , 25 April 2025 , A68
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© The Author(s), 2025. Published by Cambridge University Press

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