Flow characteristics analysis for flow past the porous spheres: wake structures and drag force coefficients

Flow past a permeable sphere is different from that of a solid sphere due to the penetration of the fluid within porous structures, which can arise a change of flow fields. In this work, flow past porous spheres with Darcy numbers (Da) ranging from [0,10−3 ] were measured using planar Particle Image Velocimetry (PIV). The whole flow fields, including both leading edge and trailing edge, were captured at six different Reynolds numbers (Re) varying from 400 to 1400. Time-average flow fields were calculated based on instantaneous flow fields within fully-developed stages. Local minimum method was used to search for stagnation point positions. The results show positions of stagnation points are nearly proportional to the logarithm of Re. For most porous spheres, positions of stagnation points are extended to farther downstream positions than that of a solid sphere. However, at some certain Darcy numbers, ranging from 5 ∗ 10−6 to 2 ∗ 10−5, positions of stagnation points are closer to the sphere centers than that of an impermeable one.

Couple stress fluid flow due to slow steady oscillations of a permeable sphere

The study of oscillating flow of a Couple Stress fluid past a permeable sphere is considered. Analytical solution for the flow field in terms of stream function is obtained using modified Bessel functions. The formula for Drag acting on the sphere due external flow is evaluated. Pressure field for the flow region past and inside the sphere is obtained. Effects of physical parameters like couple stress parameter, permeability, frequency and geometric parameters on the drag due to internal and external flows are represented graphically. It is observed that the drag for viscous fluid flow will be less than the case of couple-stress fluid flow and hence couple stress fluids offer resistance for flow.

The study of acoustic scattering from a single sound-permeable sphere

The paper presents a generalized mathematical model and numerical investigation of the problem of acoustic scattering from a single sound-permeable sphere during the passage of two types of waves - spherical from a monopole radiation source and a plane one. In solving the Helmholtz equation, a numerical technique based on the fast method of multipoles is used, which allows achieving high accuracy of the results obtained at the lowest cost of computer time. The calculations are compared with known experimental data and a good agreement is obtained. The formulas for calculating the main characteristic of the scattering field (the total scattering cross section) for a sound-permeable sphere are generalized. The effect on this characteristic of the physical parameters of media outside and inside the sphere, such as the density and speed of sound, is shown. A numerical parametric analysis of the pressure distribution around a single sound-permeable sphere for different values of the wave radius, density, and speed of sound of the outer and inner medium of the sphere is carried out. The obtained results will later be used for test verification calculations for the numerical solution of the generalized problem of acoustic scattering of a set of sound-permeable spheres (coaxial or arbitrarily located in space).