Abstract
The power spectrum of concentration fluctuation of high Schmidt number dye (\({\rm Sc}\simeq 2.9\times 10^3\)) was measured in a liquid-phase axisymmetric turbulent jet at the jet Reynolds number of \(2.0\times 10^4\). We used the optical fiber LIF probe which has a spatial resolution of 2.8 \(\mu\)m and a working distance of 140 \(\mu\)m. It is confirmed that the probe can achieve high signal-to-noise ratio by using high concentration dye, which enabled us to examine the spectral shape almost up to the Batchelor scale for the present experimental condition. The measured power spectrum captures the transition from the inertial–convective range to the viscous–convective range at around \(k\eta _K=0.03\) (\(\eta _K\): Kolmogorov scale). The \(k^{-1}\) scaling law for the power spectrum almost holds in the viscous–convective range. However, the spectrum does not perfectly follow the \(k^{-1}\) scaling but has a small bump in the range. It is also shown that the small-scale concentration fluctuation largely contributes to the r.m.s value of concentration fluctuation.
Graphic abstract
References
Batchelor GK (1959) Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivity. J Fluid Mech 5(1):113–133. https://doi.org/10.1017/S002211205900009X
Clay MP (2017) Strained turbulence and low-diffusivity turbulent mixing using high performance computing. PhD thesis, Georgia Institute of Technology
Dahm WJ, Dimotakis PE (1990) Mixing at large Schmidt number in the self-similar far field of turbulent jets. J Fluid Mech 217:299–330. https://doi.org/10.1017/S0022112090000738
Donzis DA, Sreenivasan KR, Yeung PK (2010) The batchelor spectrum for mixing of passive scalars in isotropic turbulence. Flow, Turbul Combust 85:549–566. https://doi.org/10.1007/s10494-010-9271-6
Dowling DR, Dimotakis PE (1990) Similarity of the concentration field of gas-phase turbulent jets. J Fluid Mech 218:109–141. https://doi.org/10.1017/S0022112090000945
Friehe CA, Van Atta CW, Gibson CH (1972) Jet turbulence: dissipation rate measurements and correlations. Turbulence Shear Flows, AGARD Conference Proceedings 93:18
Gibson CH, Lyon RR, Hirscnsohn I (1970) Reaction product fluctuations in a sphere wake. AIAA J 8(10):1859–1863. https://doi.org/10.2514/3.6001
Grant HL, Hughes Ba, Vogel WM, Moilliet A (1968) The spectrum of temperature fluctuations in turbulent flow. J Fluid Mech 34(03):423. https://doi.org/10.1017/S0022112068001990
Lavertu TM, Mydlarski L, Gaskin SJ (2008) Differential diffusion of high-Schmidt-number passive scalars in a turbulent jet. J Fluid Mech 612:439–475. https://doi.org/10.1017/S0022112008003224
Miller PL, Dimotakis PE (1996) Measurements of scalar power spectra in high Schmidt number turbulent jets. J Fluid Mech 308:129–146. https://doi.org/10.1017/S0022112096001425
Takeichi T, Sakai Y, Terashima O, Nagata K, Ito Y (2014) Study on the concentration measurement in a liquid jet by the optical fiber LIF method. J JSEM 14:s30–s35. https://doi.org/10.11395/jjsem.14.s30
Acknowledgements
The work was partially supported by JSPS KAKENHI Grant Number 18H01369 and Foundation of Public interest of Tatematsu.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Iwano, K., Hosoi, J., Sakai, Y. et al. Power spectrum of high Schmidt number scalar in a turbulent jet at a moderate Reynolds number. Exp Fluids 62, 129 (2021). https://doi.org/10.1007/s00348-021-03216-5
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-021-03216-5