Recent studies on turbulent friction drag reduction by wavy surfaces are reviewed. Special focus is laid upon numerical studies of fully developed flow in a channel having wavy surfaces. Both the surfaces driven by the flow (i.e., passive surfaces) and those driven by the external power (i.e., active surfaces) are considered. In addition, the drag reduction by traveling wave-like blowing and suction, which is closely related to the wavy surfaces, is also discussed in detail.

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Vortex methods are a group of Lagrangian and semi-Lagrangian methods based on the vorticity-streamfunction or vorticity-velocity formulation of the Navier-Stokes equation, and provide an interesting alternative to grid based methods for external flows dominated by unsteady vortical motion. In the present review article, we will assess the advantages and disadvantages of vortex methods for the simulation of incompressible turbulent flows, based on the speed and accuracy benchmarks that have been performed recently. Our goal is to objectively and quantitatively evaluate the performance of this non-standard method, by directly comparing it's speed and accuracy against finite difference and pseudo-spectral DNS codes under identical calculation conditions. We also present examples of vortex methods in engineering applications of turbulent flows.

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Spatial direct numerical simulation results are presented for transitional/turbulent supersonic isothermal flat plate boundary layers at M = 2.0 and impinging shock wave-boundary layer interactions. The numerical results show the formation and development of three-dimensional vortical structures such as hairpin packets and streak-breakdown, and secondary and tertiary hairpins as well. These characteristic vortical structures create a significant fraction of the supersonic turbulent boundary layer structure. An incident shock wave impinging upon the transitional boundary layer with streaks and hairpins, and unsteady reflected waves from the mildly separation boundary layer are observed. Expansion waves after the impinging point and compression waves due to the boundary layer reattachment are also identified. Across the interacting shock, turbulence is enhanced with finer hairpins generated inside, and it undergoes a relaxation process to higher Reynolds turbulent boundary layers far downstream.

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2-dimensional direct numerical simulation (DNS) of autoignition and flame propagation of turbulent premixed mixture has been conducted to investigate the turbulent combustion mechanism in homogeneous charge compression ignition (HCCI) engines. CH₄-air mixtures with spatial inhomogeneity of temperature and equivalence ratio are investigated by considering a detailed kinetic mechanism. Since the combustion process depends on local characteristics of the mixture, an identification method of ignition or flame propagation is proposed based on behaviors of elementary reactions related to OH radical. The proposed identification method shows that the area fraction of the flame propagation region increases drastically with the increase of initial temperature fluctuations.

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The present work deals with a computational strategy coupling near-wall, eddyviscosity-based RANS models with LES within a zonal Hybrid LES/RANS (HLR) framework. Key questions concerning the coupling of both methods, the inherently steady RANS method and highly-unsteady LES method, are closely connected to the treatment at the interface separating both sub-regions. Large attention was paid to this problem and following three issues were highlighted: (1) the exchange of the variables across the LES/RANS interface was adjusted by implicit imposition of the condition of equality of the modelled turbulent viscosities (by assuming the continuity of their resolved contributions across the interface), enabling a smooth transition from the near-wall RANS layer to the off-wall LES sub-region; (2) utilisation of a dynamic, flow-dependent interface position in the course of the simulation. The control parameter k^* representing the ratio of the modelled (SGS) to the total turbulent kinetic energy in the LES region, averaged over all grid cells at the interface on the LES side, is adopted; (3) the third issue, the present work is focussing on, addresses the usage of a special forcing technique, which compensates the loss of information due to strong damping caused by the presence of the RANS region (the typical outcome of such a circumstance is the so-called velocity mismatch in the region of interface) by creation of artificial and correlated fluctuations using a method originating from a digital-filter-based generation of inflow data for spatially developing DNS and LES due to Klein et al. (2003). Herewith, the recovery of the fluctuations on the LES side of the interface is accelerated and the afore-mentioned velocity bump is eliminated to a largest extent. The performances of the model are illustrated against the available DNS and fine-grid LES of periodic flows in a plane channel and over a 2-D smoothly contoured hill respectively.

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Attention was focused on the statistical properties of pressure fluctuation, which is caused by fine-scale vortices in turbulent flow. The aim is improvement in the prediction of cavitation inception due to fine-scale turbulence vortices, which are usually in subgrid-scale (SGS) in Large-eddy simulation (LES). We conducted a finely-resolved direct numerical simulation (DNS) of a spatially-developing turbulent mixing layer in cavitating and non-cavitating (single-phase) conditions. The result under cavitating condition suggested that low-pressure region corresponding to the core of fine-scale vortices could become an origin of cavitation. We applied filtering technique to DNS database under non-cavitating condition to model the low-pressure region of subfilter vortices observed in result under cavitating condition. Filtering volume is corresponding to that in the probable LES. In fully developed turbulence, proportional relation was found out between intensity of SGS pressure fluctuation and turbulent kinetic energy. In addition, Gaussian profile reasonably approximated instantaneous pressure distribution within a filtering volume. We therefore think the possibility of cavitation inception can be accurately estimated by using the intensity of SGS kinetic energy in couple with filtered pressure field.

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Flows around vortex generators (VGs), which serve as one of the important flow control methods, are investigated by solving Reynolds-Averaged Navier-Stokes (RANS) equations. The influences on the main flow of VGs are intended to explore. To validate computational schemes, the flow around a single VG on a flat plane is computed to acquire basic knowledge of this kind of flow. Then transonic flow past a standard model, named by ONERA-M6 wing, is predicted to investigate the flow features of shockwave/boundary-layer interactions (SWBLI). Investigation is focused on a supercritical wing. Firstly, the effects of a row of VGs on the airfoil with the same cross-section design are calculated with periodical boundaries in transonic conditions. Then, VGs on the whole supercritical wing are analyzed with strong SWBLI. Lastly, VGs are mounted more upwind (about 3.5% local chord) to explore the effects at low speed and high incidence condition. The numerical results show that seven VGs on the wing can effectively suppress the separations behind the strong SWBLI and decrease spanwise flow and wing-tip vortex in transonic condition. VGs can also decrease the large scope of separation over the wing at low speed with high angle of attack.

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Sand erosion is a phenomenon whereby solid particles impinging on a wall cause serious mechanical damage to the wall surface. This phenomenon is a typical gas-solid two-phase turbulent flow and can be considered as a multi-physics problem in which the flow field, particle trajectory, and wall deformation interact. On the other hand, aircraft engines operating in a particulate environment are subjected to performance and lifetime deterioration due to sand erosion. In particular, the compressors of aircraft engines can be severely damaged. In order to consider sand erosion in the design phase, it is important to develop a prediction method and to obtain basic data. In the present study, we apply our three-dimensional sand erosion prediction code to a single-stage axial flow compressor. The numerical results for the eroded surface geometry and the performance deterioration showed the same tendency as the experimental results. Moreover, the change in the flow field and the particle trajectories are investigated in order to clarify the erosion mechanisms of the compressor.

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