Eddy genesis and transformation of Stokes flow in a double-lid-driven cavity. Part 2: deep cavities

This paper extends an earlier work [1] on the development of eddies in rectangular cavities driven by two moving lids. The streamfunction describing Stokes flow in such cavities is expressed as a series of Papkovich-Faddle eigenfunctions. The focus here is deep cavities, i.e. those with large height-to-width aspect ratios, where multiple eddies arise. The aspect ratio of the fully developed eddies is found computationally to be 1.38 > 0.05, which is in close agreement with that obtained from Moffatt's [2] analysis of the decay of a disturbance between infinite stationary parallel plates. Extended control space diagrams for both negative and positive lid speed ratios are presented, and show that the pattern of bifurcation curves seen previously in the single-eddy cavity is repeated at higher aspect ratios, but with a shift in the speed ratio. Several special speed ratios are also identified for which the flow in one or more eddies becomes locally symmetric, resulting in locally symmetric bifurcation curves. By superposing two semi-infinite cavities and using the constant velocity damping factor found by Moffatt, a simple model of a finite multiple-eddy cavity is constructed and used to explain both the repetition of bifurcation patterns and the local symmetries. The speed ratios producing partial symmetry in the cavity are shown to be integer powers of Moffatt's velocity damping factor

Direct numerical simulation of a turbulent flow over an axisymmetric hill

Direct numerical simulation (DNS) of a turbulent flow over an axisymmetric hill has been carried out to study the three-dimensional flow separation and reattachment that occur on the lee-side of the geometry. The flow Reynolds number is ReH = 6500, based on free-stream quantities and hill height (H). A synthetic inflow boundary condition, combined with a data feed-in method, has been used to generate the turbulent boundary layer approaching to the hill. The simulation has been run using a typical DNS resolution of Dxþ ¼ 12:5; Dzþ ¼ 6:5, and Dyþ1 ¼ 1:0 and about 10 points in the viscous sublayer. It was found that a separation bubble exists at the foot of the wind-side of the hill and the incoming turbulent boundary layer flow undergoes re-laminarization process around the crest of the hill. These lead to a significant flow separation at the lee-side of the hill, where a very large primary separation bubble embedded with a smaller secondary separations have been captured. The present low-Re simulation reveals some flow features that are not observed by high-Re experiments, thus is useful for future experimental studies

Lagrangian chaos in steady three-dimensional lid-driven cavity flow

Steady three-dimensional flows in lid-driven cavities are investigated numerically using a high-order spectral-element solver for the incompressible Navier–Stokes equations. The focus is placed on critical points in the flow field, critical limit cycles, their heteroclinic connections, and on the existence, shape, and dependence on the Reynolds number of Kolmogorov–Arnold–Moser (KAM) tori. In finite-length cuboidal cavities at small Reynolds numbers, a thin layer of chaotic streamlines covers all walls. As the Reynolds number is increased, the chaotic layer widens and the complementary KAM tori shrink, eventually undergoing resonances, until they vanish. Accurate data for the location of closed streamlines and of KAM tori are provided, both of which reach very close to the moving lid. For steady periodic Taylor–Görtler vortices in spanwise infinitely extended cavities with a square cross section, chaotic streamlines occupy a large part of the flow domain immediately after the onset of Taylor–Görtler vortices. As the Reynolds number increases, the remaining KAM tori vanish from the Taylor–Görtler vortices, while KAM tori grow in the central region further away from the solid walls

Structural changes of laminar separation bubbles induced by global linear instability

The topology of the composite flow fields reconstructed by linear superposition of a two-dimensional boundary layer flow with an embedded laminar separation bubble and its leading three-dimensional global eigenmodes has been studied. According to critical point theory, the basic flow is structurally unstable; it is shown that in the presence of three-dimensional disturbances the degenerate basic flow topology is replaced by a fully three-dimensional pattern, regardless of the amplitude of the superposed linear perturbations. Attention has been focused on the leading stationary eigenmode of the laminar separation bubble discovered by Theofilis; the composite flow fields have been fully characterized with respect to the generation and evolution of their critical points. The stationary global mode is shown to give rise to a three-dimensional flow field which is equivalent to the classical U-shaped separation, defined by Hornung & Perry, and induces topologies on the surface streamlines that are resemblant to the characteristic stall cells observed experimentally

MODELING OF FLOW AND PARTICLE DYNAMICS HUMAN RESPIRATORY SYSTEM USING FLUID DYNAMICS

The aim of this research is to study numerically the flow characteristics and particle transport within a human respiratory system, including the human nasal cavity and the bifurcation. Various flow rates and particle sizes are main parameters varied in order to analyze the effects on particle movements and deposition on the human respiratory system. There are three main systems considered in this research: flow around a blockage in a channel, flow in the Final particle deposition with Stokes number, St = 0.12 for inlet flow rates of: (a) 30 L/min; (b) 60 L/min in human nasal cavity, and flow in the double bifurcation. Computational Fluid Dynamics (CFD) is used to solve gas-particle flow equations using a commercial software, FLUENT. Flow around a blockage in a channel was performed to gain confidence in the CFD model that has recirculation zone behind the block. The unsteady vortices flow around this blockage is investigated for Reynolds numbers, Re = 150, 300, 600, 900, and 1200 and Stokes numbers, St = 0.01, 0.1, 0.5, 1.0 and 2.0 by solving momentum and particle model equations. A detailed airflow structures such as vortices, flow distribution are obtained. It was found that the particle distribution depends on vortical structures and Stokes number. A model of real human nasal cavity is reconstructed from computerized tomography (CT) scans. The flow structure is validated with experimental data for flowrates of 7.5 L/min (Re = 1500) and 15 L/min (Re = 3000). The total particle deposition in nasal cavity is also validated with experimental data using inertial parameter. Then the model is further investigated the effect of turbulence on particle deposition with flowrates of 20, 30 and 40 L/min. Deposition was found to increase with Stoke number for the same Reynolds number. vii Three-dimensional double bifurcations with coplanar configurations are employed to investigate the flow. Results of laminar flow (Re = 500, Re = 1036, and Re = 2000) are used to compare with experimental and numerical solution for validation. The model is further used to investigate the turbulent flow and particle deposition for heavy breathing with flowrates of 30 L/min (Re = 7300) and 60 L/min (Re = 14600). It was found that the deposition efficiency is dependent on Reynolds number and Stokes numbers. This research outcome will guide to improve the injection particle drugs to human lungs and to develop nasal mask to protect the lungs from hazardous particles