Point-particle direct numerical simulations of particle-laden flows have been conducted to investigate the complex coupling between inertial particles, buoyancy force, and strong shear flows in an unstably stratified turbulent boundary layer over a flat plate. Two-way coupling and particle-particle collisions, i.e., four-way coupling, are considered in the dilute gas-solid flows. The simulation results indicate that the presence of inertial particles with diameter smaller than the Kolmogorov length scale tends to reduce the thermal displacement thickness and enthalpy thickness, while increasing the mean skin-friction coefficient and Nusselt number. The feedback force exerted by the particles on the fluid is found to contribute largely to the drag enhancement. The turbulence intensities and temperature fluctuations are significantly attenuated in the particle-laden flows with respect to the unladen flow. The budgets of the turbulent kinetic energy show that the particles have direct and indirect effects on the modulation of turbulence. On the one hand, the production and the viscous dissipation rate are suppressed by the particles in most regions of the boundary layer. On the other hand, the particle-turbulence interactions produce an extra energy source in the inner layer, while causing an additional energy sink in the outer layer of the boundary layer. These combined effects lead to the pronounced turbulence attenuation observed in this study.
The spatiotemporal evolution of the tip clearance vortical structures behind a flat hydrofoil immersed in a turbulent boundary layer over a flat plate was investigated by means of direct numerical simulation, with focus on the unsteady behaviors of the tip-leakage vortex (TLV) and their effects on the flow blockage. It is found that the TLV evolutionary processes can be characterized by three typical phases: the formation phase, the vortex wandering phase, and the vortex splitting and breakdown phase. In the second phase, the TLV is subject to the wall-normal low-frequency wandering motion, which is excited by the induced vortex. The abrupt increase in vortex wandering intensity near the trailing edge of the hydrofoil can be attributed to the frequent occurrence of vortex splitting and breakdown events in the third phase. The time-averaged vortex intensity of the TLV increases gradually in the first and second phases. On the other hand, instantaneous vortex intensity shows an initially decreasing and then increasing trend, as a result of the breakdown of the TLV and the formation of the secondary TLV, respectively. In addition, the investigation of flow blockage caused by the TLV indicates that along the streamwise direction, the time-averaged blockage area and blockage coefficient both follow an exponential distribution. The present results provide a qualitative and quantitative characterization for the spatiotemporal evolution of the TLV, which is critical for improving the efficiency loss and mechanical vibration caused by the unsteady behaviors of the TLV.
We investigate the interaction of a stationary sphere with turbulent flows in a spatially developing boundary layer over a flat plate by means of fully resolved direct numerical simulations. The diameter of the sphere [Formula: see text] is much larger than the Kolmogorov length scale. The sphere Reynolds number [Formula: see text] is changed by varying the sphere diameter, while the gap ratio is held constant with [Formula: see text], where [Formula: see text] is the distance between the bottom of the sphere and the flat plate. The simulation results indicate that there exist complex interactions between the small-scale vortex in the wake of the sphere and the large-scale coherent structures inside the turbulent boundary layer. The jet-like flow through the gap is deflected away from the wall, and the level of deflection increases with [Formula: see text]. As a result, asymmetrical flow structures are observed in the recirculation zone. In addition, the mean recirculation length is found to decrease with the increase in [Formula: see text]. Concerning the turbulence modulation, statistics show that the skin-friction drag and boundary layer thickness are decreased in the recirculation region with respect to the undisturbed flow, whereas the displacement thickness is increased due to the presence of reverse flow. These effects become more pronounced as [Formula: see text] increases. The budget of the turbulent kinetic energy in the sphere wake is also examined. It is revealed that the turbulent production and viscous dissipation rate are significantly enhanced under the effect of the sphere with size of the same order of magnitude as the local boundary layer thickness.
This study is concerned with accurately determining the mean skin friction in a zero-pressure-gradient turbulent boundary layer. By assuming a linear relation for the weighted total shear stress in the near-wall region, an integral method to evaluate the skin friction is proposed. The method requires the wall-normal profiles of the mean streamwise velocity and Reynolds shear stress within the range of [Formula: see text] at only one streamwise location, where [Formula: see text] is the boundary layer thickness. A number of direct numerical simulation and experimental data available in the literature are employed to validate the accuracy of the method over a wide range of Reynolds numbers. The skin friction coefficient obtained using the proposed method is found to be within [Formula: see text] in agreement with the published values in both the smooth- and rough-wall turbulent boundary layers. A comparison of the present approach with several existing methods is presented, showing that the proposed skin friction relation is robust and accurate.
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