Boundary-layer receptivity under interaction of free-stream turbulence and localized wall roughness

The boundary-layer receptivity under the interaction of free-stream turbu- lence （FST） and localized wall roughness is studied by the direct numerical simulation （DNS） and the fast Fourier transform. The results show that the Tollmien-Schlichting （T-S） wave packets superposed by a group of stability, neutral, and instability T-S waves are generated in the boundary layer. The propagation speeds of the T-S wave packets are calculated. The relation among the boundary-layer receptivity response, the amplitude of the FST, the roughness height, and the roughness width is determined. The results agree well with Dietz＇s experiments. The effect of the roughness geometries on the receptivity is also studied.

Local receptivity in non-parallel boundary layer

The research on boundary-layer receptivity is the key issue for the laminarturbulent transition prediction in fluid mechanics. Many of the previous studies for local receptivity are on the basis of the parallel flow assumption which cannot accurately reflect the real physics. To overcome this disadvantage, local receptivity in the non-parallel boundary layer is studied in this paper by the direct numerical simulation （DNS）. The difference between the non-parallel and parallel boundary layers on local receptivity is investigated. In addition, the effects of the disturbance frequency, the roughness location, and the multiple roughness elements on receptivity are also determined. Besides, the relations of receptivity with the amplitude of free-stream turbulence （FST）, with the roughness height, and with the roughness length are ascertained as well. The Tollmien- Schlichting （T-S） wave packets are excited in the non-parallel boundary layer under the interaction of the FST and the localized wall roughness. A group of T-S waves are separated by the fast Fourier transform. The obtained results are in accordance with Dietz＇s measurements, Wu＇s theoretical calculations, and the linear stability theory （LST）.

Leading-edge receptivity of boundary layer to three-dimensional free-stream turbulence

The laminar-turbulent transition has always been a hot topic of fluid mechanics. Receptivity is the initial stage and plays a crucial role in the entire transition process. The previous studies of receptivity focus on external disturbances such as sound waves and vortices in the free stream, whereas those on the leading-edge receptivity to the three-dimensional free-stream turbulence (FST), which is more general in the nature, are rarely reported. In consideration of this, this work is devoted to investigating the receptivity process of three-dimensional Tollmien-Schlichting (T-S) wave packets excited by the three-dimensional FST in a flat-plate boundary layer numerically. The relations between the leading-edge receptivity and the turbulence intensity are established, and the influence of the FST directions on the propagation directions and group velocities of the excited T-S wave packets is studied. Moreover, the leading-edge receptivity to the anisotropic FST is also studied. This parametric investigation can contribute to the prediction of laminar-turbulent transition.

Mechanism of three-dimensional boundary-layer receptivity

Boundary-layer receptivity is always a hot issue in laminar-turbulent tran- sition. Most actual laminar-turbulent transitions belong to three-dimensional flows. An infinite back-swept fiat-plate boundary layer is a typical three-dimensionalflow. Study of its receptivity is important both in theory and applications. In this paper, a free- stream turbulence model is established. A modified fourth-order Runge-Kutta scheme is used for time marching, and compact finite difference schemes are used for space dis- cretization/ On these bases, whether unsteady cross-flow vortices can be excited in the three-dimensional boundary layer （the infinite back-swept flat-plate boundary layer） by free-stream turbulence is studied numerically. If so, effects of the level and the direc- tion of free-stream turbulence on the three^dimensional boundary-layer receptivity are further studied. Differences of the three-dimensional boundary-layer receptivity are then discussed by considering the non-parallel effect, influence of the leading-edge stagnation point of the flat plate, and variation of the back-swept angle separately. Intensive studies on the ＇three-dimensional boundary-layer receptivity will benefit the development of the hydrodynamic stability theory, and provide a theoretical basis for prediction and control of laminar-turbulent transition.

A High-Order Numerical Method to Study Three-Dimensional Hydrodynamics in a Natural River

A high-order numerical method for three-dimensional hydrodynamics is p-resented.The present method applies high-order compact schemes in space and a Runge-Kutta scheme in time to solve the Reynolds-averaged Navier-Stokes equations with the k-ǫturbulence model in an orthogonal curvilinear coordinate system.In ad-dition,a two-dimensional equation is derived from the depth-averaged momentum equations to predict the water level.The proposed method isfirst validated by its application to simulateflow in a 180◦curved laboratoryflume.It is found that the simulated results agree with measurements and are better than those from SIMPLEC algorithm.Then the method is applied to study three-dimensional hydrodynamics in a natural river,and the simulated results are in accordance with measurements.