Viscous flow around three-dimensional macroscopic cavities in a granular material

Viscous flow around spherical macroscopic cavities in a granular material is investigated. The Stokes equation inside and the Darcy–Brinkman equation outside the cavities are considered. In particular, the interaction of two equally sized cavities positioned in tandem is examined in detail, where the asymptotic effect of the other cavity is taken into account. The present analysis gives a reasonable estimate on the volume flow into the cavity and the local enhancement of stresses. This is applicable to predict the microscale waterway formation in that material, onset of landslides, collapse of cliffs and river banks, etc.

Analysis for Flow of an Incompressible Brinkman-Type Fluid in Thin Medium with Friction

In this paper, we consider the Brinkman equation in the three-dimensional thin domain ℚ ε ⊂ ℝ 3 . The purpose of this paper is to evaluate the asymptotic convergence of a fluid flow in a stationary regime. Firstly, we expose the variational formulation of the posed problem. Then, we presented the problem in transpose form and prove different inequalities for the solution u ε , p ε independently of the parameter ε . Finally, these estimates allow us to have the limit problem and the Reynolds equation and establish the uniqueness of the solution.

PIV measurement of turbulence over a streamwise preferential porous medium

This study examines the possibility of orthotropic porous medium whose streamwise permeability is larger than the wall-normal permeability to reduce turbulent friction inspired by recent numerical studies of Rosti et al. (2018); G´omez-de Segura and Garc´ıa-Mayoral (2019). Because G´omez-de Segura and Garc´ıa-Mayoral (2019) used Brinkman equation to approximate the flow in the porous media, it is uncertain that such porous media really reduce the friction. We make a layered porous medium, which satisfies the drag reducing condition suggested by G´omez-de Segura and Garc´ıa-Mayoral (2019), and carry out particle image velocimetry measurements of turbulent square duct flows over it and examine the drag reduction probability. From the analyses of the obtained data, it is found that the friction on the porous-wall is nearly the same as that of the smooth-wall at Reb < 10000 and tends to increase at Reb > 10000.

Research on Regularities of Cyclic Air Motion through a Respirator Filter

In this paper, a solution to the problem of the change in the pressure drop in a respirator filter during cyclic air motion is suggested since the current theory of filtering is based on steady-flow processes. The theoretical dependence of the pressure drop in the respirator filter on air flow rate is determined, which is represented by the harmonic law, which characterizes the human respiration process during physical work. For the calculation, a filter model was used, which is represented by a system of parallel isolated cylinders with a length equal to the total length of the filter fibres surrounded by porous shells formed by a viscous air flow field, with a size determined by the equal velocities of the radial component of air flow and undisturbed flows. The flow-around process in the proposed model of air flow through the respirator filter is described by the Brinkman equation, which served to establish the total air flow resistance in the proposed system under conditions of velocity proportionality. It consists of two parts: the first characterizes the frictional resistance of the air flow against the surface of the cylinder, which imitates the filter fibre; the second—the inertial part—characterizes the frequency of pulsations of respiratory movements during physical performance. The divergence of the analytical results and experimental studies is no more than 20%, which allows the use of the established dependence to estimate the change in pressure drop in a respirator filter made of filter material “Elephlen” when the user carries out different physical activities. This allows the period of effective protective action of respirators with different cycles of respiration during physical activities to be specified, which is a very serious problem that is not currently regulated in health and safety regulations, and it also allows the prediction of the protective action of filters and respiratory protection in general.

ESTIMATION OF HETEROGENEITY OF THE ATMOSPHERIC AIR VELOCITY FIELD IN ADSORBERS OF FRONT-END PURIFICATION UNITS FOR AIR SEPARATION PLANTS

Assuming unidirectional motion of compressed atmospheric air through a vertical cylindrical adsorbent with a fixed granular layer of the front-end purification unit adsorbent, the mathematical model for estimating the heterogeneity of a hydrodynamic velocity field in the radial and axial directions in a turbulent regime is proposed. The model is based on the boundary layer approximation of the Darcy – Brinkman – Forchheimer phenomenological equation. The steady-state flow at low permeability of the granular layer is identified using the collocation method, and the approximate analytical solution is obtained which justifies the applicability of an ideal displacement mode when describing the carrier medium motion. Numerical integration of a boundary value problem of the model equation using the finite-difference method with Richardson extrapolation confirms the conclusion validity. The structure of an accelerated turbulent flow having constant flow velocity in the input section shows that for small Forchheimer coefficients, the Darcy – Brinkman equation is used to obtain the analytical ratio for calculating the length of the initial hydrodynamic section. The proposed mathematical model for estimating the heterogeneity of the velocity field in adsorbers with a stationary dispersed layer is applicable for a laminar flow regime. Testing of this approach by assessing velocity field uniformity for a mass-produced front-end purification unit of air separation plants has shown its efficiency.

The non-Darcy characteristics of fault water inrush in karst tunnel based on flow state conversion theory

The fault water inrush is a key factor which leads to tunnel construction in karst regions. Based on the fluid mechanics principles, the paper addresses a numer?ical coupled model for karst fault tunnel with COMSOL Multiphysics software. Besides, the Darcy law equation, Brinkman equation, and Navier-Stokes equation are inserted to stimulate the steady flow of aquifer, the non-linear seepage of fault and the free flow in tunnel excavating area in software, respectively. Then, the pres?sure and flow velocity in three flow fields are analyzed under different permeability ratios in numerical model. It is shown that the fault permeability is the key factor affecting water inrush, and that the pressure and flow velocity change visibly in adjacent domains between two flow fields.

Study of Laminar Naturel Convection in Partially Porous Cavity in the Presence of Nanofluids

The objective of this work is the mathematical modelling and the numerical simulation of the stationary, laminar, and natural convection, in a confined square cavity (H = L) filled with two fluids (a mixture of nanoparticles of aluminum oxide and Al2O3 water) in one partition and pure water in the other partition. A porous conductive wall of thickness w (w = L/e) and thermal conductivity Keff constitutes the exchange surface between these two partitions. The fluid movement is modeled by the Navier-Stokes equations in the two partitions, while the porous medium is modelled by the Darcy–Brinkman equation. Comsol Multiphysics software is used to solve the system of differential equations that is based on the finite element method. The results are discussed with particular attention to the mean and local Nusselt number (Nu), streamlines and isotherms. A parametric study for Rayleigh number Ra (102 to 106), volume fraction j (0% to 10%), and Darcy number Da (10-7 to 10-2) is performed. The obtained findings show that the increase in Ra, Da, and j intensifies the flow and improves the thermal exchange on the cold wall. For Da £ 10-5, Nu remains practically low and the natural convection is being dominated by conduction. For Da > 10-5, an increase in Nu is observed and the flows tend towards a purely convective situation. Furthermore, an increase in the heat transfer coefficients is observed with the raise of the porous layer permeability, volume fraction and Rayleigh number.

Free Interfaces at the Tips of the Cilia in the One-Dimensional Periciliary Layer

Cilia on the surface of ciliated cells in the respiratory system are organelles that beat forward and backward to generate metachronal waves to propel mucus out of lungs. The layer that contains the cilia, coating the interior epithelial surface of the bronchi and bronchiolesis, is called the periciliary layer (PCL). With fluid nourishment, cilia can move efficiently. The fluid in this region is named the PCL fluid and is considered to be an incompressible, viscous, Newtonian fluid. We propose there to be a free boundary at the tips of cilia underlining a gas phase while the cilia are moving forward. The Brinkman equation on a macroscopic scale, in which bundles of cilia are considered rather than individuals, with the Stefan condition was used in the PCL to determine the velocity of the PCL fluid and the height/shape of the free boundary. Regarding the numerical methods, the boundary immobilization technique was applied to immobilize the moving boundaries using coordinate transformation (working with a fixed domain). A finite element method was employed to discretize the mathematical model and a finite difference approach was applied to the Stefan problem to determine the free interface. In this study, an effective stroke is assumed to start when the cilia make a 140∘ angle to the horizontal plane and the velocitiesof cilia increase until the cilia are perpendicular to the horizontal plane. Then, the velocities of the cilia decrease until the cilia make a 40∘ angle with the horizontal plane. From the numerical results, we can see that although the velocities of the cilia increase and then decrease, the free interface at the tips of the cilia continues increasing for the full forward phase. The numerical results are verified and compared with an exact solution and experimental data from the literature. Regarding the fixed boundary, the numerical results converge to the exact solution. Regarding the free interface, the numerical solutions were compared with the average height of the PCL in non-cystic fibrosis (CF) human tissues and were in excellent agreement. This research also proposes possible values of parameters in the mathematical model in order to determine the free interface. Applications of these fluid flows include animal hair, fibers and filter pads, and rice fields.