Hele-Shaw flow

About: Hele-Shaw flow is a research topic. Over the lifetime, 5451 publications have been published within this topic receiving 151320 citations.

Flow rate through microfilters: Influence of the pore size distribution, hydrodynamic interactions, wall slip, and inertia

Abstract: We examine the fluid mechanics of viscous flow through filters consisting of perforated thin plates. We classify the effects that contribute to the hydraulic resistance of the filter. Classical analyses assume a single pore size and account only for filter thickness. We extend these results to obtain an analytical formula for the pressure drop across the microfilter versus the flow rate that accounts for the non-uniform distribution of pore sizes, the hydrodynamic interactions between the pores given their layout pattern, and wall slip. Further, we discuss inertial effects and their order of scaling.

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

Abstract: A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

The two-sided lid-driven cavity: experiments on stationary and time-dependent flows

Abstract: The incompressible fluid flow in a rectangular container driven by two facing sidewalls which move steadily in anti-parallel directions is investigated experimentally for Reynolds numbers up to 1200. The moving sidewalls are realized by two rotating cylinders of large radii tightly closing the cavity. The distance between the moving walls relative to the height of the cavity (aspect ratio) is Γ = 1.96. Laser-Doppler and hot-film techniques are employed to measure steady and time-dependent vortex flows. Beyond a first threshold robust, steady, three-dimensional cells bifurcate supercritically out of the basic flow state. Through a further instability the cellular flow becomes unstable to oscillations in the form of standing waves with the same wavelength as the underlying cellular flow. If both sidewalls move with the same velocity (symmetrical driving), the oscillatory instability is found to be tricritical. The dependence on two sidewall Reynolds numbers of the ranges of existence of steady and oscillatory cellular flows is explored. Flow symmetries and quantitative velocity measurements are presented for representative cases.

Numerical Investigation of Low-Aspect-Ratio Wings at Low Reynolds Numbers

Abstract: A numerical analysis is performed to study the flow around low-aspect-ratio (LAR) wings and more particularly the resulting lift-and-drag force. The research is focused on low-Reynolds-number aerodynamics, as LAR wings are crucial for the development of microair vehicles (MAVs). The flow around LAR wings is characterized by complex three-dimensional flow phenomena. These phenomena include wing-tip vortices, flow separation and reattachment, laminar to turbulent transition, and a mutual interaction among these phenomena. The flow is studied using a commercial computational fluid dynamics (CFD) program and a strip method. The CFD code is used to investigate the three-dimensional flow aerodynamics of rectangular LAR wings with an aspect ratio between 0.5 and 2 at a Reynolds number of 1 x 10 5 . Simulations on a flat plate and a reflex-type low-Reynolds-number profile (S5010), which is representative for a flying-wing MAV, are performed and compared. Experimental data is used for comparison and validation. The effects of flow separation and low Reynolds numbers are further investigated using a strip method. Two accurate formalized methods to predict lift and drag are derived. The first method is applicable to profiled wings with moderate low-Reynolds-number effects. The second method, which is based on the strip method, is more general and is also applicable to flat plates and wings exhibiting large regions of flow separation.