Investigation Of The Particle Transport In Developing Flat-Plate Boundary Lavers With A Hemispherical Roughness Element By Direct Numerical Simulation

In order to investigate the mechanism of transition of boundary layer induced by roughness elements without acuate edges, a direct numerical simulation method based on finite difference was used to simulate the transition of smooth flat-plate boundary layer induced by a hemispherical roughness element with two different Reynolds numbers. In order to investigate the effect of heavy particles on the vortex regeneration in the boundary layer flows, and the mechanisms dominating particle deposition and local concentration, the direct numerical simulation method and a Lagrangian particle-tracking technique were used to simulate the motion of heavy particles with density 2000 times greater than the fluid in these transition flows of boundary layer and a developing turbulent boundary layer flow with a moderate Reynolds number. A combined multi-direct force and immersed boundary method was employed to calculate the force acted on the fluid by the surface of the hemisphere. Direct number simulations of two-dimensional flat-plate boundary layer were performed to generate proper inlet velocity boundary conditions for three-dimensional transition simulations. Slip-shear and slip-rotation lift forces affecting significantly the deposition of particles in the near-wall region were calculated, and the collision of particles with solid surfaces was taken into account by a hard-sphere model.At two roughness Reynolds numbers Rek=332 and 550 (Re=819 and 1157, respectively), the shedding frequencies of hairpin vortex downstream the hemisphere and profiles of streamwise mean velocity and velocity fluctuation at three different streamwise locations obtained through direct numerical simulations of transition boundary layer agree well with experimental results of Klebanoff et al. (1992). At Rek=332, the simulating result shows clearly the evolution process of single hairpin. Evidences are provided to confirm that disturbances induced by the hemisphere experience a transient growth process in the downstream flow field. At Rek=550, results show the regeneration of streamwise vortex and hairpin vortex, and the formation and growth of hairpin packets.In the by-pass transition of flat-plate boundary layer induced by a hemisphere, with different mass loads, heavy particles with various inertias influence the processes of generation and growth of primary hairpin vortices and subsidiary vortices in different degree. Particles with small inertia are entrained by the fluid into the low-pressure zone behind the hemisphere and concentrate in the upper fringe of this zone. These concentrated particles hinder the spiral motion of the outer fluid into the low-pressure zone, decelerate the process of vorticity concentration, and depress the shedding of hairpins downstream of the low-pressure zone effectively. As the inertia of particles increases, the possibility of particles appearing in the low-pressure zone increases. Particles with great inertia affect the generation of hairpins by increasing the pressure in the entire low-pressure zone. Because of the continue transfer of momentum from the fluid to ambient particles, particles with small inertia following the fluid reduce the strength of primary hairpins and subsidiary vortices existing in the boundary layer simultaneously. Particles with great inertia show their "low-pass filter" property clearly, and damp the sweep and ejection event induced by primary hairpins to depress the generation of secondary and other subsidiary vortices. It was observed that particles with various inertias tend to concentrate in the high-stress region, and appear in the high-vorticity region scarcely. The local concentration of particles with smaller inertia in the boundary layer flows is more visible than that of particles with greater inertia. The distribution of particles with great inertia along the wall-normal direction depends on their inertia. By examining the influence of particles with various inertias and different mass loads on the drag force acted on the flat plate, it is suggested that this friction drag is determined by the vortex structures existing in the region very close to the wall. Meanwhile, the effect of particles on the friction drag is significant in some local region, and is worth of some attention.Results of the direct numerical simulation of a developing turbulent boundary layer with a moderate Reynolds number show that the hemispherical roughness element with an enough height is one of important factors that affect the development into the fully-developed state of flat-plate boundary layer. The investigation on the vortex regeneration in the transiting boundary layer flows induced by a hemisphere extends the knowledge of the turbulence self-sustaining in the boundary layer. The effect of particles with various inertias on the vortex regeneration suggests the feasibility of utilizing solid particles as "smart roughness elements" to implement the control of turbulence. How to use three-dimensional roughness elements to control the distribution of particles in the near-wall region effectively deserves further investigations.