| The internal mechanism on the interaction between fluid and solid particles ingas-solid flow and their corresponding prediction models are very complex and needed tobe studied in depth. The characteristics of sub-grid scale (SGS) velocity fluctuations and itsinfluence on particles motion are important issues for Large eddy simulation (LES) ofgas-particle turbulence, so it is a research hot spot of multi-phase flow right now.Based on this status quo, three aspects studies on the issue about subgrid ofparticle-laden flow are carried out in this paper:First of all, the SGS statistics were obtained by the filtering operation on directnumerical simulation (DNS) of homogeneous isotropic turbulent flow. The results showthat, the SGS kinetic energy increased with filter width increased, while the kinetic energyof resolved scales (RS, or filtered DNS, FDNS) decreased; and the autocorrelations andintegral time scales of SGS and FDNS both increased as filter width increased. Contrary tothe relation TE>TLin the DNS, the SGS Lagrangian integral time scale larger than SGSEulerian integral time scale, that is δTL>δTE. The ratio of SGS Lagrangian integral timescale to SGS Eulerian integral time scale β decreased as filter width increased, and itapproaches to the limit of DNS value when filter width reach the maximum. Furthermore,we may have the conclusion that the contribution of small-scale to Lagrangian timescalemuch larger than that to Eulerian, however, the contribution of large-scale to them isreverse.Secondly, based on the results in the first part, the characteristics of subgrid fluidalong inertial particle are studied based on the point source hypothesis and special attentionhas been paid on the variation of the subgrid kinetic energy seen by particles, theautocorreltion and integral timescale of the SGS fluid seen by particles with the influenceof parameters of particle and filter width. The simulation results show that, as the Stnumber increase, the SGS kinetic energy seen by particles decreases firstly until it reachesthe minimum value, and then increases again. To the contrary, with the increase of Stnumber，the integral timescale of SGS fluid velocity seen by inertial particle increases untilreaches the maximum value and then decreases. Furthermore, the minimum value of thecurves of the subgrid kinetic energy seen by particles and the maximum of the curves of thetimescale of the SGS fluid seen by particles both shift toward larger St number as the SGS flow field tends to the full velocity field. In our opinion, this phenomenion is due to themechanism that the influence of subgrid turbulence on different St particles is not identical.For low St particles, clustering is driving by the small-scale eddies due to the centrifugingeffect. However, the large St particles have higher response times than the filtered eddiesand hence those eddies act to randomize the motion of the oarticles. Moreover, theexperience formula for the effect of inertial and filter width on the time scale of subgridfluld seen by particle has been provided, and compared with the approximation in otherreference, the result in this paper is more suitable.Finally, we systematically derived the Langevin equation of subgrid fluid seen byinertial particle, and then a closed equation is gotten based on the simulation result abovefor the key parameters. Different with the previous studies, we adopt the real subgridkinetic energy and time scale seen by inertial particles in the SGS Langevin equation,which could demonstrate the effect of inertial and filter on simulation. It is show that basedon this Langevin equation which is added to the F-DNS data the simulaition results hasbeen improved considerablely. So the Langevin model could give restruction of the subgridfluid seen by particles adequately, which means that it is important and effective to takeinto accout the effect of subgrid fluid on particle in LES frame. Therefore, we recommendthis model to be used in the following research in two-phase LES method. |
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