Linear motion of multiple superposed viscous fluids

In this paper the small-amplitude motion of multiple superposed viscous fluids is studied as a linearized initial-value problem. The analysis results in a closed set of equations for the Laplace transformed amplitudes of the interfaces that can be inverted numerically. The derived equations also contain the general normal mode equations, which can be used to determine the asymptotic growth-rates of the systems directly. After derivation, the equations are used to study two different problems involving three fluid layer. The first problem is the effect of initial phase difference on the development of a Rayleigh-Taylor instability and the second is the damping effect of a thin, highly viscous, surface layer.Comment: 22 pages and 9 figure

Computational analysis of shock-induced flow through stationary particle clouds

We investigate the shock-induced flow through random particle arrays using particle-resolved Large Eddy Simulations for different incident shock wave Mach numbers, particle volume fractions and particle sizes. We analyze trends in mean flow quantities and the unresolved terms in the volume averaged momentum equation, as we vary the three parameters. We find that the shock wave attenuation and certain mean flow trends can be predicted by the opacity of the particle cloud, which is a function of particle size and particle volume fraction. We show that the Reynolds stress field plays an important role in the momentum balance at the particle cloud edges, and therefore strongly affects the reflected shock wave strength. The Reynolds stress was found to be insensitive to particle size, but strongly dependent on particle volume fraction. It is in better agreement with results from simulations of flow through particle clouds at fixed mean slip Reynolds numbers in the incompressible regime, than with results from other shock wave particle cloud studies, which have utilized either inviscid or two-dimensional approaches. We propose an algebraic model for the streamwise Reynolds stress based on the observation that the separated flow regions are the primary contributions to the Reynolds stress.Comment: 33 pages, 23 figures, 3 table

Particle-resolved simulations of shock-induced flow through particle clouds at different Reynolds numbers

This study investigates the Reynolds-number dependence of shock-induced flow through particle layers at 10\% volume fraction, using ensemble-averaged results from particle-resolved large eddy simulations. The advantage of using large eddy simulations to study this problem is that they capture the strong velocity shears and flow separation caused by the no-slip condition at the particle surfaces. The shock particle cloud interaction produces a reflected shock wave, whose strength increases with decreasing particle Reynolds number. This results in important changes to the flow field that enters the particle cloud. The results show an approximate proportionality between the mean flow velocity and the flow fluctuation magnitudes. Maximum particle drag forces are in excellent agreement with previous inviscid studies, and we complement these results with statistics of time-averaged particle forces as well as the variation of temporal oscillations. The results of this work provides a basis for development of improved simplified dispersed flow models.Comment: 30 pages, 15 figure

Numerical modelling of aerosol dispersion inside a rotating aerosol chamber

Numerical simulation of the airflow inside a slowly rotating aerosol chamber is carried out using a high resolution LES and several RANS based turbulence models. The result of the LES revealed a complex turbulent flow field which none of the RANS models were able to faithfully reproduce. Simulations of passive aerosol transport based on the RANS flow fields did reveal that they possibly can be used for this purpose, as the results did not contradict observations of the aerosol deposition