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تسجيل مستخدم جديدSpatially developing turbulent boundary layer on a flat plate
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This fluid dynamics video submitted to the Gallery of Fluid motion shows a turbulent boundary layer developing under a 5 metre-long flat plate towed through water. A stationary imaging system provides a unique view of the developing boundary layer as it would form over the hull of a ship or fuselage of an aircraft. The towed plate permits visualisation of the zero-pressure-gradient turbulent boundary layer as it develops from the trip to a high Reynolds number state ($Re_tau approx 3000$). An evolving large-scale coherent structure will appear almost stationary in this frame of reference. The visualisations provide an unique view of the evolution of fundamental processes in the boundary layer (such as interfacial bulging, entrainment, vortical motions, etc.). In the more traditional laboratory frame of reference, in which fluid passes over a stationary body, it is difficult to observe the full evolution and lifetime of turbulent coherent structures. An equivalent experiment in a wind/water-tunnel would require a camera and laser that moves with the flow, effectively `chasing eddies as they advect downstream.
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The turbulent boundary layer over a flat plate is computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations as a test bed for a synthetic turbulence generator (STG) inflow boundary condition. The inlet momentum thick
ness Reynolds number is approximately 1,000. The study provides validation of the ability of the STG to develop accurate turbulence in 5 to 7 boundary layer thicknesses downstream of the boundary condition. Also tested was the effect of changes in the stabilization scheme on the development of the boundary layer. Moreover, the grid resolution required for both the development region and the downstream flow is investigated when using a stabilized finite element method.
Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state. Originally developed in numerical studies of parallel
shear flows with a linearly stable base flow, this concept is adapted here to the case of a spatially developing Blasius boundary layer. Longer time horizons fundamentally change the nature of the problem due to the loss of stability of the base flow due to Tollmien--Schlichting (TS) waves. We demonstrate, using a moving box technique, that efficient long-time tracking of edge trajectories is possible for the parameter range relevant to bypass transition, even if the asymptotic state itself remains out of reach. The flow along the edge trajectory features streak switching observed for the first time in the Blasius boundary layer. At long enough times, TS waves co-exist with the coherent structure characteristic of edge trajectories. In this situation we suggest a reinterpretation of the edge as a manifold dividing the state space between the two main types of boundary layer transition, i.e. bypass transition and classical transition.
The present numerical investigation uses well-resolved large-eddy simulations to study the low-frequency unsteady motions observed in shock-wave/turbulent-boundary-layer interactions. Details about the numerical aspects of the simulations and the sub
sequent data analysis can be found in three papers by the authors (Theo. Comput. Fluid Dyn., 23:79--107 (2009); Shock Waves, 19(6):469--478 (2009) and J. of Fluid Mech. (2011)). The fluid dynamics video illustrates the complexity of the interaction between a Mach 2.3 supersonic turbulent boundary layer and an oblique shock wave generated by a 8-degree wedge angle. The first part of the video highlights the propagation of disturbances along the reflected shock due to the direct perturbation of the shock foot by turbulence structures from the upstream boundary layer. The second part of the video describes the observed block-like back-and-forth motions of the reflected shock, focusing on timescales about two orders of magnitude longer than the ones shown in the first part of video. This gives a visual impression of the broadband and energetically-significant peak in the wall-pressure spectrum at low frequencies. The background blue-white colouring represents the temperature field (with white corresponding to hot) and one can clearly appreciate why such low-frequency shock motions can lead to reduced fatigue lifetimes and is detrimental to aeronautical applications.
We perform direct numerical simulations of rotating Rayleigh--Benard convection of fluids with low ($Pr=0.1$) and high ($Pr=5$) Prandtl numbers in a horizontally periodic layer with no-slip top and bottom boundaries. At both Prandtl numbers, we demon
strate the presence of an upscale transfer of kinetic energy that leads to the development of domain-filling vortical structures. Sufficiently strong buoyant forcing and rotation foster the quasi-two-dimensional turbulent state of the flow, despite the formation of plume-like vertical disturbances promoted by so-called Ekman pumping from the viscous boundary layer.
Three-dimensional particle tracking experiments were conducted in a turbulent boundary layer with friction Reynolds number $Re_tau$ of 700 and 1300. Two finite size spheres with specific gravities of 1.003 (P1) and 1.050 (P2) and diameters of 60 and
120 wall units were released individually from rest on a smooth wall. The spheres were marked with dots all over the surface to monitor their translation and rotation via high-speed stereoscopic imaging. The spheres accelerated strongly after release over streamwise distances of one boundary layer thickness before approaching an approximate terminal velocity. Initially, sphere P1, which had Reynolds numbers $Re_p$ of 800 and 1900, always lifts off from the wall. Similar behavior was observed occasionally for sphere P2 with initial $Re_p$ of 1900. The spheres that lifted off reached an initial peak in height before descending towards the wall. The sphere trajectories exhibited multiple behaviors including saltation, resuspension and sliding motion with small random bouncing depending on both $Re_tau$ and specific gravity. The lighter sphere at $Re_tau=1300$, which remained suspended above the wall during most of its trajectory, propagated with the fastest streamwise velocity. By contrast, the denser sphere at $Re_tau=700$, which mostly slid along the wall, propagated with the slowest streamwise velocity. After the spheres approached an approximate terminal velocity, many experienced additional lift-off events that were hypothesized to be driven by hairpins or coherent flow structures. Spheres were observed to rotate about all three coordinate axes. While the mean shear may induce a rotation about the spanwise axis, near-wall coherent structures and the spheres wake might drive the streamwise and wall-normal rotations. In all cases where the sphere propagates along the wall, sliding motion, rather than forward rolling motion, is dominant.
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