arXiv subjects

Kazuhiro Inagaki

Publications and source records attributed to Kazuhiro Inagaki.

6 recordsLinked to original sources

arXiv2024

Explanation of constant mean angular momentum in high-Reynolds-number Taylor--Couette turbulence in terms of history effects

This study discusses the mechanism of the emergence of nearly constant mean angular momentum profiles, which are widely observed in curved turbulent flows including the bulk region of Taylor--Couette (TC) flows. For high-Reynolds-number TC flows where the inner and outer cylinders are weakly counter-rotating and co-rotating, both the bulk and boundary layers become turbulent without Taylor rolls, referred to as the featureless ultimate regime (UR). Thus, we utilize the Reynolds-averaged Navier--Stokes (RANS) equations to explain the mechanism of the nearly constant mean angular momentum. High-Reynolds-number experiments of TC turbulence are performed for reference, where the angular velocity ratio $a = -\omega_\mathrm{out}/\omega_\mathrm{in}$ is in the range $-0.5 \le a \le 0.1$. Verification of the RANS based on the conventional algebraic Reynolds stress model suggests that convection of the Reynolds stress is essential for predicting the angular momentum profile. This indicates that the physical origin of the nearly constant angular momentum is the history effect of the Reynolds stress. To rigorously incorporate the convection effect into the Reynolds stress, we employ the Jaumann derivative as a covariant time derivative. The model that takes into account the history effect involving the normal stress difference successfully predicts the nearly constant mean angular momentum in the co-rotating cases. This study suggests the significance of the history effects for understanding curved or rotating turbulent flows in terms of the statistical analysis.

physics.flu-dyn↗

arXiv2023

Analysis of anisotropic subgrid-scale stress for coarse large-eddy simulation

This study discusses the necessity of anisotropic subgrid-scale (SGS) stress in large-eddy simulations (LESs) of turbulent shear flows using a coarse grid resolution. We decompose the SGS stress into two parts to observe the role of SGS stress in turbulent shear flows in addition to the energy transfer between grid-scale (GS or resolved scale) and SGS. One is the isotropic eddy-viscosity term, which contributes to energy transfer, and the other is the residual anisotropic term, which is separated from the energy transfer. We investigate the budget equation for GS Reynolds stress in turbulent channel flows accompanied by the SGS stress decomposition. In addition, we examine the medium and coarse filter length cases; the conventional eddy-viscosity models can fairly predict the mean velocity profile for the medium filter case and fails for the coarse filter case. The budget for GS turbulent kinetic energy shows that the anisotropic SGS stress has a negligible contribution to energy transfer. In contrast, the anisotropic stress has a large and non-dissipative contribution to the streamwise and spanwise components of GS Reynolds stress when the filter size is large. Even for the medium-size filter case, the anisotropic stress contributes positively to the budget for the spanwise GS Reynolds stress. Spectral analysis of the budget reveals that the positive contribution is prominent at a scale consistent with the spacing of streaks in the near-wall region. Therefore, we infer that anisotropic stress contributes to the generation mechanism of coherent structures. Predicting the positive contribution of the anisotropic stress to the budget is key to further improving SGS models.

physics.flu-dyn↗

arXiv2022

Transport and modeling of subgrid-scale turbulent kinetic energy in channel flows

To develop a more convenient subgrid-scale (SGS) model that performs well even in coarse grid cases, we investigate the transport and modeling of SGS turbulent kinetic energy (hereafter SGS energy) in turbulent channel flows based on the stabilized mixed model (SMM). In this paper, we try to increase the convenience of the SMM by replacing the modeled transport equation for the SGS energy with an algebraic model. The SMM quantitatively adequately predicts the total turbulent kinetic energy of the direct numerical simulation (DNS) even in coarse grid cases. For both the filtered DNS (fDNS) and large-eddy simulation (LES), the statistically averaged production term balances with the dissipation in the region away from the wall in the SGS energy transport equation. In contrast, we reveal that the correlation coefficient between the production and dissipation terms is high for the modeled transport equation in LES, whereas that for the fDNS is low. Based on the high correlation or local equilibrium between the production and dissipation observed in the LES, we demonstrate the reduction of the SMM into a zero-equation SMM (ZE-SMM). We construct a new damping function based on the grid-scale Kolmogorov length to reproduce the near-wall behavior of the algebraic model for the SGS energy. The ZE-SMM provides quantitatively the same performance as the original SMM that employs the SGS energy transport model. This result suggests that the local equilibrium model for the SGS energy provides the equivalent performance as the transport model in wall-bounded turbulent flows even in coarse grid cases.

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arXiv2020

Role of various scale-similarity models in stabilized mixed subgrid-scale model

We investigate the physical role of various scale-similarity models in the stabilized mixed model [K. Abe, Int. J. Heat Fluid Flow, 39, 42 (2013); M. Inagaki and K. Abe, Int. J. Heat Fluid Flow, 64, 137 (2017)] and evaluate their performance in turbulent channel flows. Among various models in the present study, the original model combined with the scale-similarity model for the subgrid-scale (SGS)-Reynolds term yields the best prediction for the anisotropy of the grid-scale (GS) velocity fluctuations and the SGS stress, even in coarse grid resolutions. Moreover, it successfully predicts large intensities of the spectra close to the cut-off scale in accordance with the filtered direct numerical simulation, whereas other models predict a rapid decay of the spectra in the low-wavelength region. To investigate the behavior of the models close to the cut-off scale, we analyze the budget equation for the GS Reynolds stress spectrum. The result shows that the scale-similarity model for the SGS-Reynolds term plays a role in the enhancement of the wall-normal velocity fluctuation close to the cut-off scale. Thereby, it activates turbulence close to the cut-off scale, leading to a reproduction of the proper streak structures observed in wall-bounded turbulent flows. The reproduction of velocity fluctuations close to the cut-off scale and turbulent structures is a key element for further development of SGS models.

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arXiv2019

Higher-order realizable algebraic Reynolds stress modeling based on the square root tensor

In this study, realizable algebraic Reynolds stress modeling based on the square root tensor [Phys. Rev. E \textbf{92}, 053010 (2015)] is further developed for extending its applicability to more complex flows. In conventional methods, it was difficult to construct an algebraic Reynolds stress model satisfying the realizability conditions when the model involves higher-order nonlinear terms on the mean velocity gradient. Such higher-order nonlinear terms are required to predict turbulent flows with three-dimensional mean velocity. The present modeling based on the square root tensor enables us to make the model always satisfy the realizability conditions, even when it involves higher-order nonlinearity. To construct a realizable algebraic Reynolds stress model applicable to turbulent flows with three-dimensional mean velocity, a quartic-nonlinear eddy-viscosity model is proposed. The performance of the model is numerically verified in a turbulent channel flow, a homogeneous turbulent shear flow, and an axially rotating turbulent pipe flow. The present model gives a good result in each turbulent flow. Note that the mean swirl flow in an axially rotating turbulent pipe flow is reproduced because the present model involves cubic nonlinearity. Such a higher-order realizable algebraic Reynolds stress model, involving quartic nonlinearity on the mean velocity, is expected to be useful in numerically stable predictions of turbulent flows with three-dimensional mean velocity.

physics.flu-dyn↗

arXiv2018

Energy transport due to pressure diffusion enhanced by helicity and system rotation in inhomogeneous turbulence

It is known that turbulent energy is rapidly transferred in the direction of the rotation axis in a rotating system, in comparison with the non-rotating case. In this study, this phenomenon is investigated as a problem of energy diffusion expressed by the Reynolds averaged Navier-Stokes (RANS) model. The conventional gradient-diffusion approximation for the turbulent energy flux cannot account for the enhanced energy transport observed in rotating inhomogeneous turbulence. In order to adequately describe the phenomenon, we propose a new model for the energy flux due to the pressure associated with the rotational motion of a fluid. The model of the energy flux is expressed to be proportional to the turbulent helicity. This property is closely related to the group velocity of inertial waves in a rapidly rotating fluid. The validity of the model is assessed using a direct numerical simulation (DNS) of inhomogeneous turbulence under rotation. It is shown that most of the turbulent energy transport enhanced by the system rotation is attributed to the pressure diffusion term. The spatial distribution of the energy flux due to the pressure related to the system rotation is similar to that of the turbulent helicity with negative coefficient. Hence, the new model which is proportional to the turbulent helicity is able to qualitatively account for the enhanced energy flux due to the system rotation. Finally, the helical Rossby number is proposed in order to estimate the relative importance of the energy flux enhanced by the turbulent helicity and the rotation, in comparison to the conventional gradient-diffusion approximation.

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