Solution of Nonhomogeneous Helmholtz Equation with Variable Coefficient Using Boundary Domain Integral Method

© 2018, Pleiades Publishing, Ltd. The Boundary Domain Integral Method (BDIM) is applied to the solution of the nonhomogeneous Helmholtz equation with variable coefficient. The analytical formulas for the integrals over the individual boundaries and domain integrals are used to increase the accuracy of the numerical approach. Comparisons of the developed BDIM with the analytical solutions for the homogeneous Helmholtz equation with constant coefficient and the nonhomogeneous Helmholtz equation with variable coefficient are given

A theoretical study of aerosol sampling by an idealized spherical sampler in calm air

The performance of an idealized spherical sampler operating in calm air for an inlet arbitrarily oriented relative to the gravity force is studied theoretically. Under potential flow assumption the air velocity field is obtained by using a model of a finite-size sink on a sphere. The particle motion equations are solved to find the limiting trajectory surface and to calculate the aspiration efficiency. The singular points of the motion equations as a function of settling velocity of particles and the sampler orientation angle are investigated. The connection between the pattern of typical zones of particle trajectories around the sampler and the location of the singular points is illustrated. The effects of partial sampling from zones without particles and of particle screening are discussed. The results of parametrical investigations of the dependence of the aspiration efficiency on the Stokes number and their analysis are presented. In the case of vertically upwards orientation of the sampler the proposed mathematical model gives fair agreement with experimental data from the work by Su and Vincent (Abstracts of sixth international aerosol conference, Taipei, Taiwan, 2002a, pp. 639-640). © 2003 Elsevier Ltd. All rights reserved

Numerical study of the respiCon sampler performance in the calm air

Results of a numerical study of the RespiCon sampler performance in the calm air are presented. The air flow is described by the Navier-Stokes equations of axisymmetric stationary viscous flow of incompressible fluid that are numerically integrated by the computational fluid dynamics (CFD) software FLUENT. The collection efficiencies of RespiCon impactor stages agree quite well with experimental data and curves of the European standards for the thoracic and respirable dust fractions. The aspiration efficiencies derived from the numerical model overestimate the experimental data in the range of particle sizes of 10 μm < dp < 40 μm; however, they correctly predict the value of maximal size of aspirated particles. A new design of the RespiCon sampler with a higher volume flow rate was developed. Copyright © 2014 American Association for Aerosol Research

Inertial deposition of suspended particles in a flow around a porous cylinder

The results of studying a dispersed airflow around a single porous cylinder are presented. The flow field of carrying medium outside the cylinder is described within the framework of the Navier-Stokes equations for incompressible gas; inside the porous cylinder the Darcy-Brinkman extended equations for averaged velocity are used. The numerical solution of the medium equations is achieved in the FLUENT package. In the found field of carrying medium velocities the suspended particle trajectories are calculated. Also given are the dependences of the particle inertial deposition effectiveness on the Stokes number at various values of the Darcy number. © 2012 Allerton Press, Inc

Solution of stokes flow problem using biharmonic equation formulation and multiquadrics method

© 2016, Pleiades Publishing, Ltd.The biharmonic equation formulation of the Stokes flow problem for multiquadrics method is developed. The main advantage of the approach is the iteration free method to find the solution. The numerical method is applied for the problem of steady incompressible fluid flow past a cylinder in the periodic cell of the Kuwabara model. The comparison with known analytical solution and the analysis of absolute and relative errors show that proposed approach gives satisfactory accuracy. The nonmonotonic dependence of the relative errors on the shape parameter typical for multiquadrics method is observed

Numerical study of the respiCon sampler performance in the calm air

Results of a numerical study of the RespiCon sampler performance in the calm air are presented. The air flow is described by the Navier-Stokes equations of axisymmetric stationary viscous flow of incompressible fluid that are numerically integrated by the computational fluid dynamics (CFD) software FLUENT. The collection efficiencies of RespiCon impactor stages agree quite well with experimental data and curves of the European standards for the thoracic and respirable dust fractions. The aspiration efficiencies derived from the numerical model overestimate the experimental data in the range of particle sizes of 10 μm < dp < 40 μm; however, they correctly predict the value of maximal size of aspirated particles. A new design of the RespiCon sampler with a higher volume flow rate was developed. Copyright © 2014 American Association for Aerosol Research

Inertial deposition of aerosol particles in a periodic row of porous cylinders

© 2015 American Association for Aerosol Research. The aerosol flow through a periodic row of parallel porous cylinders is investigated. The air flow field outside the cylinders is described by the Navier-Stokes equations of viscous incompressible fluid. The extended Darcy-Brinkman equations are used to calculate the flow velocity inside a porous cylinder. The dependence of the efficiency of the deposition of aerosol particles by inertial impaction and interception on the Stokes number for various values of the Darcy number is studied. Comparison of the results obtained from the numerical model and an approximate analytical model is given. The combined approximate formula for the deposition efficiency of a cylindrical fiber in a parallel array proposed by Müller et al. (2014) is extended for the porous cylindrical fiber. The aerosol flow through the porous body composed by a random array of cylinders is calculated to estimate the interior deposition

Modeling of fluid flow in periodic cell with porous cylinder using a boundary element method

© 2016 Elsevier Ltd. All rights reserved.The problem of viscous incompressible flow past a periodic array of porous cylinders (a model of flow in an aerosol filter) is solved. The approximate periodic cell model of Kuwabara is used to formulate the fluid flow problem. The Stokes flow model is then adopted to model the flow outside the cylinder and the Darcy law of drag is applied to find the filtration velocity field inside the porous cylinder. The boundary value problems for biharmonic and Laplace equations for stream functions outside and inside the porous cylinder are solved using a boundary elements method. A good agreement of numerical and analytical models is shown. The analytical formulas for the integrals in the expressions for the stream function, vorticity and Cartesian velocity components are obtained. It is shown that the use of analytical integration gives considerable advantage in computing time

Modelling of the evolution of a droplet cloud in a turbulent flow

The effects of droplet inertia and turbulent mixing on the droplet number density distribution in a turbulent flow field are studied. A formulation of the turbulent convective diffusion equation for the droplet number density, based on the modified Fully Lagrangian Approach, is proposed. The Fully Lagrangian Approach for the dispersed phase is extended to account for the Hessian of transformation from Eulerian to Lagrangian variables. Droplets with moderate inertia are assumed to be transported and dispersed by large scale structures of a filtered field in the Large Eddy Simulation (LES) framework. Turbulent fluctuations, not visible in the filtered solution for the droplet velocity field, induce an additional diffusion mass flux and hence additional dispersion of the droplets. The Lagrangian formulation of the transport equation for the droplet number density and the modified Fully Lagrangian Approach (FLA) make it possible to resolve the flow regions with intersecting droplet trajectories in the filtered flow field. Thus, we can cope successfully with the problems of multivalued filtered droplet velocity regions and caustic formation. The spatial derivatives for the droplet number density are calculated by projecting the FLA solution on the Eulerian mesh, resulting in a hybrid Lagrangian–Eulerian approach to the problem. The main approximations for the method are supported by the calculation of droplet mixing in an unsteady one-dimensional flow field formed by large-scale oscillations with an imposed small-scale modulation. The results of the calculations for droplet mixing in decaying homogeneous and isotropic turbulence are validated by the results of Direct Numerical Simulations (DNS) for several values of the Stokes number

Numerical studies on the performance of an aerosol respirator with faceseal leakage

© Published under licence by IOP Publishing Ltd.We studied the efficiency of a facepiece filtering respirator (FFR) in presence of a measurable faceseal leakage using the previously developed model of a spherical sampler with porous layer. In our earlier study, the model was validated for a specific filter permeability value. In this follow-up study, we investigated the effect of permeability on the overall respirator performance accounting for the faceseal leakage. The Total Inward Leakage (TIL) was calculated as a function of the leakage-to-filter surface ratio and the particle diameter. A good correlation was found between the theoretical and experimental TIL values. The TIL value was shown to increase and the effect of particle size on TIL to decrease as the leakage-to- filter surface ratio grows. The model confirmed that within the most penetrating particle size range (∼50 nm) and at relatively low leakage-to-filter surface ratios, an FFR performs better (TIL is lower) when the filter has a lower permeability which should be anticipated as long as the flow through the filter represents the dominant particle penetration pathway. An increase in leak size causes the TIL to rise; furthermore, under certain leakage-to-filter surface ratios, TIL for ultrafine particles becomes essentially independent on the filter properties due to a greater contribution of the aerosol flow through the faceseal leakage. In contrast to the ultrafine fraction, the larger particles (e.g., 800 nm) entering a typical high- or medium-quality respirator filter are almost fully collected by the filter medium regardless of its permeability; at the same time, the fraction penetrated through the leakage appears to be permeability- dependent: higher permeability generally results in a lower pressure drop through the filter which increases the air flow through the filter at the expense of the leakage flow. The latter reduces the leakage effect thus improving the overall respiratory protection level. The findings of this study provide valuable information for developing new respirators with a predictable actual workplace protection factor