Abstract A Full Turbulence Simulation (FTS) of turbulent channel flow at friction Reynolds number ($Re_{\tau}$) $\approx 1000$ was performed by resolving the Kolmogorov wavenumber in all spatial directions. At this Reynolds number, the intermediate layer attains a physically meaningful width. Analysis of the FTS demonstrates that the most restrictive conditions for the proposed resolution criteria occur within this region, highlighting its important role in determining DNS resolution requirements. The wall‑normal grid spacing of the FTS also confirms that, when the Kolmogorov length scale is sufficiently resolved, the second‑order central‑difference scheme introduces no adverse numerical effects in the wall‑normal direction. In the wall‑parallel directions, two resolution criteria were identified based on the present FTS: a first‑approximation DNS resolution that resolves approximately 99\% of the turbulent kinetic energy and accurately reproduces the dissipation rate ($\Delta x^{+} \approx 19$, $\Delta y^{+} \approx 8$, where $\Delta x^{+}$ and $\Delta y^{+}$ denote the stream and spanwise spatial resolutions in wall units), while a stricter full-dissipation criterion ($\Delta x^{+} \approx 7.5$, $\Delta y^{+} \approx 5.0$) is required to resolve all dissipation-spectrum contributions. The first‑approximation resolution by means of spectral method reproduces the essential turbulence statistics within approximately 1\% accuracy while requiring only one‑eighth of the grid points used in the FTS, demonstrating its practical efficiency. In contrast, even the highest‑resolution second‑order central‑difference case ($\Delta x^{+} \approx 5.0$, $\Delta y^{+} \approx 4.5$) fails to match the accuracy of the first‑approximation spectral resolution. Comparison of the dissipation spectra between $Re_{\tau}\approx1000$ and $Re_{\tau}\approx16000$ further supports the applicability of the proposed resolution criteria at substantially higher Reynolds numbers. These findings provide important resolution guidelines for high-Reynolds-number DNS, particularly for simulations at $Re_{\tau}=\mathcal{O}(10^{4})$.
Abstract Eddy viscosity models for subgrid-scale (SGS) stress are widely used in large eddy simulation (LES). However, they do not provide accurate results for coarse-grid LES. Eddy viscosity models are too dissipative and do not reproduce backscatter, that is, the local energy transfer from the SGS to the grid-scale field. Although the scale similarity term can be added to the model to reproduce backscatter, it leads to numerical instability. In this study, a nonlocal SGS model was proposed by extending the nonlocal eddy diffusivity model for the Reynolds-averaged Navier–Stokes (RANS) equation to LES. As the nonlocal RANS model can reproduce the counter-gradient diffusion of scalar and momentum transport, the proposed SGS model is expected to reproduce the energy backscatter. First, a simplified version of the nonlocal RANS model is presented and analyzed to demonstrate its numerical stability. The diffusion effect at high wavenumbers was smaller than that of the local model. Next, based on the nonlocal RANS model, a nonlocal SGS model is proposed and applied to the LES of a turbulent channel flow using a coarse grid. The mean velocity and turbulent shear stress profiles improved and a small amount of backscatter was observed. The high-wavenumber part of the energy spectra increased and the near-wall velocity structure improved compared with the local model. These results demonstrate that the nonlocal SGS model has the potential to improve the coarse-grid LES.
This paper examines the approximate formulation of a vortex ring generated behind a sphere in a steady viscous flow within the finite-Reynolds-number region using an analytical approach. The governing equation for this flow is the Navier-Stokes equation. A mathematical difficulty called the Whitehead paradox occurs when the perturbation method is applied to this problem. To avoid this paradox, scholars have developed many analytical methods, such as the Oseen approximation or matching technique. The authors also presented an analytical solution that expresses the separation behind a sphere by applying a novel perturbation technique. In this paper, we further develop a perturbation technique to derive a simplified expression for the drag coefficient and obtain closed-form formulae for the vortex ring behind a sphere in the low-to-moderate Reynolds number range. The present drag coefficient shows good agreement with the numerical results for Rd <= 30 as the relative errors are 0.5% at Rd=10, 4.6% at Rd=20 and 11.9% at Rd=30 ( Rd is the diameter-based Reynolds number). We also obtain approximate formulae for the separation angle and vortex length, which are consistent with experimental and numerical results. For example, the relative errors are 6.0% for the vortex length and 8.5% for the separation angle at Rd=50 in comparison with the numerical results. Additionally, based on the observation of the geometry of the vortex region, encompassing the interior of the sphere, we suggest that the vortex shape can be represented by an ellipse as an approximation. Its validity is assessed because the error between the approximation and the present stream function is approximately 2%.
Abstract In wind tunnel experiments, one approach to reproducing the representative flow environment around test bodies is the use of obstacles, which necessitates longer test sections. As an alternative, an active grid system, consisting of motor-driven rods with attached winglets, was introduced by Makita (1991 Fluid Dyn. Res. 8 53–64). Since then, numerous studies have investigated the effects of synchronized and independent rod motions, the influence of input parameters on the resulting flow characteristics, and the ability to generate desired profiles through parameter adjustments. The present study explores a potential method for determining the input parameters required to produce specified mean velocity and turbulence intensity profiles. To this end, a mini wind tunnel equipped with an active grid system was designed, and various combinations of input parameters were tested to generate training data for artificial neural networks (ANNs). The results were consistent with previous findings, indicating that mean velocity profiles depend primarily on the flow restriction created by the collective winglet positions, while turbulence intensity profiles are influenced by both the restricted flow areas and the rotational speeds of the rods. The ANN successfully learned to predict input parameters for target mean velocity profiles, although achieving similar performance for turbulence intensities proved more challenging. Consequently, the turbulence intensity part of the study focuses on assessing the learning potential of ANNs for turbulence intensities and provides recommendations for future research.
The study of convective transport phenomena in the presence of internal heat and mass sources is of considerable significance in understanding various natural and industrial processes. In this work, we investigate a problem where an incompressible and viscous Newtonian fluid is subjected to an internal heat source (Ri) along with two internal mass sources (Rj,Rl) in opposite sense, under isothermal and iso-solutal boundary conditions. Employing weakly nonlinear theory, the critical thermal Rayleigh number is obtained, and the corresponding Nusselt and Sherwood numbers are evaluated. Further, the Ginzburg-Landau equation is derived to describe the amplitude dynamics of the system. The resulting amplitude equation is solved numerically using MATHEMATICA, and the effects of various governing parameters on the thermal Rayleigh number (RaT0), Nusselt number (Nu), and the two Sherwood numbers (Sh1,Sh2) are systematically analyzed. It is found that the parameters Ri and Rl faster the onset, while Rj delays it. Additionally, an increase in Lewis number (Le1) leads to a rise in the Nusselt number ( Nu) and the first Sherwood number ( Sh1), whereas a decrease is observed in the second Sherwood number ( Sh2). The outcomes provide valuable insights into the stability behavior and transport characteristics of multi-component convection systems influenced by internal sources. The present study is not only theoretically significant but can also be useful in various industrial and experimental applications.
