5 results
Energy transfer in turbulent flows behind two side-by-side square cylinders
- Yi Zhou, Koji Nagata, Yasuhiko Sakai, Tomoaki Watanabe, Yasumasa Ito, Toshiyuki Hayase
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- Journal:
- Journal of Fluid Mechanics / Volume 903 / 25 November 2020
- Published online by Cambridge University Press:
- 18 September 2020, A4
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Our previous study (J. Fluid Mech., vol. 874, 2019, pp. 677–698) confirmed that two different types of $-5/3$ energy spectra (i.e. non-Kolmogorov and quasi-Kolmogorov $-5/3$ spectra) can be found in turbulent flows behind two side-by-side square cylinders. In the upstream region (i.e. $X/T_0=6$ with $T_0$ being the cylinder thickness), albeit the turbulent flow is highly inhomogeneous and intermittent and Kolmogorov's hypothesis does not hold, the energy spectrum exhibits a well-defined $-5/3$ power-law range for over one decade. Meanwhile, the power-law exponent of the corresponding second-order structure function is 1, which is significantly larger than the expected value, i.e. $2/3$. At the downstream location, i.e. $X/T_0=26$, in contrast, the quasi-Kolmogorov $-5/3$ energy spectrum (and also the 2/3 scaling of the second-order structure) can be identified. Through decomposing the streamwise velocity fluctuations into the spanwise average of instantaneous velocity and the turbulent residual, we demonstrate that the non-Kolmogorov $-5/3$ spectrum at $X/T_0=6$ is caused by the turbulent residual part. To shed light on the physics of the scale-by-scale energy transfer, we resort to the Kármán–Howarth–Monin–Hill equation. At $X/T_0=6$, the expected balance between the nonlinear term and the dissipation term cannot be detected. Instead, the contributions from the non-local pressure, advection, nonlinear transport and turbulent transport terms are dominant. Moreover, because the corresponding flow field is highly intermittent, the magnitudes of the non-local pressure, advection, nonlinear transport and turbulent transport terms are significantly larger than that of the dissipation term. At a far downstream location, i.e. $X/T_0=26$, where the dual-wake flow is fully turbulent and becomes much more homogeneous and isotropic, within a short intermediate range the two dominant terms in the two-point turbulent kinetic energy budget are the nonlinear transport term and the dissipation term, which to some extent echoes Kolmogorov's scenario, albeit the contribution from the large-scale advection term cannot be ignored. By comparing the behaviour of the one-point and two-point energy transfer, it can be seen that the two different energy transfer processes are actually closely related, that is, the similar relative importance of the viscous dissipation and the same role of the non-negligible terms in terms of being a source or sink term.
Extreme events and non-Kolmogorov $-5/3$ spectra in turbulent flows behind two side-by-side square cylinders
- Yi Zhou, Koji Nagata, Yasuhiko Sakai, Tomoaki Watanabe
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- Journal:
- Journal of Fluid Mechanics / Volume 874 / 10 September 2019
- Published online by Cambridge University Press:
- 12 July 2019, pp. 677-698
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Turbulent flows behind two side-by-side square cylinders with three different gap ratios, namely, $L_{d}/T_{0}=4,$ 6 and 8 ($L_{d}$ is the separation distance between two cylinders and $T_{0}$ is the cylinder thickness) are investigated by using direct numerical simulations. Depending on the strength of the gap flow, the three cases can generally be characterized into two regimes, one being the weak gap flow regime and the other being the robust gap flow regime. The wake-interaction length scale can only be applied to characterize the spatial evolution of the dual-wake flow in the robust gap flow regime. And only in this regime can the so-called ‘extreme events’ (i.e. non-Gaussian velocity fluctuations with large flatness) be identified. For the case with $L_{d}/T_{0}=6$, two downstream locations, i.e. $X/T_{0}=6$ and 26, at which the turbulent flows are highly non-Gaussian distributed and approximately Gaussian distributed, respectively, are analysed in detail. A well-defined $-5/3$ energy spectrum can be found in the near-field region (i.e. $X/T_{0}=6$), where the turbulent flow is still developing and highly intermittent and Kolmogorov’s universal equilibrium hypothesis does not hold. We confirm that the approximate $-5/3$ power law in the high-frequency range is closely related to the occurrences of the extreme events. As the downstream distance increases, the velocity fluctuations gradually adopt a Gaussian distribution, corresponding to a decrease in the strength of the extreme events. Consequently, the range of the $-5/3$ power law narrows. In the upstream region (i.e. $X/T_{0}=6$), the second-order structure function exhibits a power-law exponent close to $1$, whereas in the far downstream region (i.e. $X/T_{0}=26$) the expected $2/3$ power-law exponent appears. The larger exponent at $X/T_{0}=6$ is related to the fact that fluid motions in the intermediate range can directly ‘feel’ the large-scale vortex shedding.
Vortex stretching and compression near the turbulent/non-turbulent interface in a planar jet
- Tomoaki Watanabe, Yasuhiko Sakai, Kouji Nagata, Yasumasa Ito, Toshiyuki Hayase
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- Journal:
- Journal of Fluid Mechanics / Volume 758 / 10 November 2014
- Published online by Cambridge University Press:
- 13 October 2014, pp. 754-785
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Vortex stretching and compression, which cause enstrophy production by inviscid processes, are investigated near the turbulent/non-turbulent (T/NT) interface in a planar jet by using a direct numerical simulation (DNS). The enstrophy production is investigated by analysing the relationship among a vorticity vector, strain-rate eigenvectors and strain-rate eigenvalues. The statistics are calculated individually for three different interface orientations. The vorticity near the T/NT interface is oriented in the tangential direction to the interface. The enstrophy production is affected by the interface orientation because the intensity of vortex stretching depends on the interface orientation, and the alignment between the vorticity vector and the strain-rate eigenvectors is confined by the interface. The enstrophy production near the T/NT interface is analysed by considering the motion of turbulent fluid relative to that of the interface. The results show that the alignment between the interface and the strain-rate eigenvectors changes depending on the velocity field near the T/NT interface. When the turbulent fluid moves toward the T/NT interface, the enstrophy is generated by vortex stretching without being greatly affected by vortex compression. In contrast, when the turbulent fluid relatively moves away from the T/NT interface, large enstrophy reduction frequently occurs by vortex compression. Thus, it is shown that the velocity field near the T/NT interface affects the enstrophy production near the interface through the alignment between the vorticity and the strain-rate eigenvectors.
Turbulent Schmidt number and eddy diffusivity change with a chemical reaction
- Tomoaki Watanabe, Yasuhiko Sakai, Kouji Nagata, Osamu Terashima
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- Journal:
- Journal of Fluid Mechanics / Volume 754 / 10 September 2014
- Published online by Cambridge University Press:
- 30 July 2014, pp. 98-121
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We provide empirical evidence that the eddy diffusivity $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}D_{{t}\alpha }$ and the turbulent Schmidt number ${\mathit{Sc}}_{{t}\alpha }$ of species $\alpha $ ($\alpha =\mathrm{A}, \mathrm{B}$ or $\mathrm{R}$) change with a second-order chemical reaction ($\mathrm{A} + \mathrm{B} \rightarrow \mathrm{R}$). In this study, concentrations of the reactive species and axial velocity are simultaneously measured in a planar liquid jet. Reactant A is premixed into the jet flow and reactant B is premixed into the ambient flow. An optical fibre probe based on light absorption spectrometry is combined with I-type hot-film anemometry to simultaneously measure concentration and velocity in the reactive flow. The eddy diffusivities and the turbulent Schmidt numbers are estimated from the simultaneous measurement results. The results show that the chemical reaction increases ${\mathit{Sc}}_{t\mathrm{A}}$; ${\mathit{Sc}}_{t\mathrm{B}}$ is negative in the region where the mean concentration of reactant B decreases in the downstream direction, and is positive in the non-reactive flow in the entire region on the jet centreline. It is also shown that ${\mathit{Sc}}_{t\mathrm{R}}$ is positive in the upstream region whereas it is negative in the downstream region. The production terms of axial turbulent mass fluxes of reactant B and product R can produce axial turbulent mass fluxes opposite to the axial gradients of the mean concentrations. The changes in the production terms due to the chemical reaction result in the negative turbulent Schmidt number of these species. These results imply that the gradient diffusion model using a global constant turbulent Schmidt number poorly predicts turbulent mass fluxes in reactive flows.
Diffusion of matter by a non-buoyant plume in grid-generated turbulence
- Ikuo Nakamura, Yasuhiko Sakai, Masafumi Miyata
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- Journal:
- Journal of Fluid Mechanics / Volume 178 / May 1987
- Published online by Cambridge University Press:
- 21 April 2006, pp. 379-403
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The turbulent diffusion process is investigated for a continuous point source of a non-buoyant plume in grid-generated water turbulence. Two kinds of biplanar grids with a mesh length of 10 mm and 20 mm were used. The mesh Reynolds numbers were 1480 and 2970, respectively. The mean and fluctuating concentration fields of aqueous dye solution were measured by the light absorption method. Experimental results for both grids were compared.
For both grids, the mean concentration radial profiles proved to have a similar Gaussian shape, and the mean concentration on the plume axis obeys the hyperbolic decay law well. These mean concentration profiles and their decay show an excellent agreement with the results deduced from the similarity analysis for the mean concentration field.
Radial profiles of the fluctuation r.m.s. value and relative intensity (i.e. the ratio of the r.m.s. value to the mean concentration) were found also to be nearly similar, and the centreline r.m.s. value decays downstream as a hyperbola. The relative intensity on the centreline tends to increase slightly downstream. All experimental results obtained were much less scattered and more reliable than those reported earlier.
The similarity for the concentration fluctuation intensity has been analysed using a thin-layer approximation. Also, an approximate analysis of the fluctuating concentration field is given by replacing the fluctuating concentration signal by a randomly spaced sequence of rectangular waves with various heights and widths.