Direct numerical simulation and subgrid analysis of a transitional droplet laden mixing layer

Abstract

A priori subgrid analysis of temporal mixing layers with evaporating droplets Physics of Fluids 12, 1573 (2000); 10.1063/1.870405Direct numerical simulation and subgrid analysis of a transitional droplet laden mixing layer Richard S. Miller a) and Josette Bellan Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109-8099 ͑Received 13 February 1999; accepted 1 December 1999͒ Direct numerical simulations of a temporally developing, droplet laden mixing layer undergoing transition to mixing turbulence are conducted. The formulation includes complete two-way couplings of mass, momentum, and energy. As many as 18ϫ10 6 grid points are used to discretize the Eulerian gas phase equations and up to 5.7ϫ10 6 initially polydisperse evaporating droplets are tracked in the Lagrangian reference frame. The complete transition to mixing turbulence is captured for several of the higher Reynolds number simulations and it is observed that increasing the droplet mass loading ratio results in a more ''natural'' turbulence characterized by increased rotational energy and less influence of the initial forcing perturbations. An increased mass loading also results in increased droplet organization within the layer. An a priori subgrid analysis is then conducted which shows that neglecting subgrid velocity fluctuations in the context of large eddy simulations may result in significant errors in predicting the droplet drag force for Stokes numbers Stϳ1 ͑with the flow time scale based on the mean velocity difference and initial vorticity thickness͒. Similar possible errors of lesser magnitude are also observed for the droplet heat flux and evaporation rate when thermodynamic subgrid fluctuations are neglected. An extension of the eddy interaction model commonly used in Reynolds-averaged simulations is then proposed in order to account for the missing subgrid information. Probability density functions ͑PDFs͒ of the subgrid fluctuations calculated across homogeneous planes are shown to be highly intermittent, particularly near the laminar-turbulent boundaries of the mixing layer. However, the actual subgrid PDFs calculated locally are much less intermittent and may be adequately modeled by the Gaussian distribution throughout the majority of the mixing layer. A scale similarity model is then employed to predict both the velocity and thermodynamic subgrid variances. The similarity model is well correlated with the actual subgrid variances and shows good agreement in predicting the local fluctuation intensities when a filter width-dependent model constant is used. The subgrid fluctuation variances acting on the droplets are then shown to be well modeled if the Eulerian subgrid variance model is interpolated to the droplet locations.

Direct numerical simulation of gaseous mixing layers laden with multicomponent-liquid drops: liquid-specific effects

“…Configuration, boundary and initial conditions, and numerics Figure 1 illustrates the mixing layer and shows the streamwise, x 1 , cross-stream, x 2 , and spanwise, x 3 , coordinates with lengths L 1 = 4l 1 = 29.16δ ω,0 , L 2 = 1.1L 1 , and L 3 = 4l 3 = 0.6L 1 , with L 1 = 0.2 m, where l 1 and l 3 are forcing wavelengths in the x 1 -and x 3 -directions, which are used to perturb the layer so as to promote roll-up and pairing (Miller & Bellan 1999;Moser & Rogers 1991;Miller & Bellan 2000). The perturbations used to excite the layer are described elsewhere (Moser & Rogers 1991;Miller & Bellan 1999); their relative amplitudes with respect to the circulations are 10 % and 2.25 % in the spanwise and streamwise directions, respectively.…”

“…Re was relatively small compared to full turbulence values) in these pre-transitional simulations. All thermodynamic properties were calculated as in Harstad et al (2003) or Miller & Bellan (2000) and are given in Appendix A.…”

Large-eddy simulation of particle-laden turbulent flows

“…In Bini & Jones (2007), a model for the LES unresolved fluctuations upon particle dynamics is formulated and it is shown how the model is capable of reproducing the experimentally observed heavy-tailed probability distribution of particle acceleration. In the present work, this model is applied in LES and the applicability of various alternative formulations, such as those of Miller & Bellan (2000) and Okong'o & Bellan (2004), are also reviewed and discussed. The structure of the paper is as follow: first, it will be shown how the separate probabilistic treatment of the dispersed phase, when coupled with the LES of the gas phase, can be viewed in the frame of a spatially filtered probability density function (PDF) transport equation.…”

“…As discussed in earlier sections, the neglect of SGS fluctuations can lead to significant error and subgrid-scale models are thus required for χ k . The formulation of stochastic models has been discussed in Miller & Bellan (2000) and Okong'o & Bellan (2004), where it was proposed that the random contribution of a flow variable φ be related to a realization of a random variable having a standard deviation proportional to the standard deviation of the SGS fluctuations of that variable, i.e. σ 2 sgs = ( φ 2 −φ 2 ).…”

“…From the LES literature it is well known that in single-phase flows the main role of the model for the subgrid scale stress is to mimic the effect of the unresolved scales upon the resolved ones and thereby provide the correct amount of dissipation. The question of how the subgrid scale (SGS) models developed for single-phase flows may be adapted to droplet-laden flows has been addressed in the direct numerical simulation (DNS) studies of Bellan (2000), Okong'o & Bellan (2000) and Miller & Bellan (2000). An aspect of primary importance in dense spray flows is the influence of the droplet dynamics on the dissipation rate.…”