P. Givi

Dispersion and polydispersity of droplets in stationary isotropic turbulence

Abstract A detailed parametric study is conducted of dispersion and polydispersity of liquid drops in stationary isotropic turbulence via direct numerical simulation. It is assumed that the flow is very dilute so that the effect of particles on the carrier fluid is negligible (one-way coupling). Both non-evaporating and evaporating drops are simulated; in the latter both constant and variable rates of evaporation are considered. The simulations of non-evaporating drops are used to validate the numerical methodology and to assess the effects of the particle time constant and the drift velocity on the particle velocity autocorrelation, turbulence intensity and diffusivity. The simulated results are also used to appraise the performance of some of the available theoretical models for particle dispersion in stationary isotropic turbulence. The effects of the initial drop time constant, the initial evaporation rate, and the drop Schmidt number on the probability density function (pdf) of the drop size are studied. It is found that, after an initial transient period the pdf of the drop size becomes nearly Gaussian. However, the pdf deviates from Gaussian as the mean drop time constant becomes very small. The extent of this deviation depends on the evaporation rate. The effect of the initial spray size on the pdf is also studied and it is shown that as the spray size increases, the interaction between the spray and large scale turbulence structures influences the pdf. The effect of the initial size distribution on the pdf is also investigated by varying the initial standard deviation. Both Gaussian and double-delta initial drop size pdfs are considered. In the latter it is shown that a transition to Gaussian is possible provided that the initial mean drop time constant is large and/or the initial standard deviation of the drop diameter is small.

Differential diffusion in binary scalar mixing and reaction

Abstract The phenomena of binary mixing and reaction of scalars ( A , B ) with unequal molecular diffusion coefficients ( Γ A , Γ B ) in turbulent flows are investigated by direct numerical simulation (DNS). Homogeneous turbulent flows are considered with and without the presence of constant mean scalar gradients, under both nonreacting and reacting nonpremixed conditions. The results indicate the significance of the differential diffusion ( Γ A ≠ Γ B ) effects on the low-order moments of the differential diffusivity variable (Z), the normalized scalars variance difference (ζ), the scalars cross correlation coefficient (ρ), and the moments of reacting scalars. It is suggested that the behavior of ρ and ζ are approximately characterized by the differential diffusion parameters including Γ r (the ratio of the diffusivities) and Γ d (the difference of the diffusivities), and by the reactant conversion parameters including Da (the Damkohler number), and Ŝ c (the Schmidt number corresponding to the average of the diffusivities of the reactants). In the comparative assessment of the results for non-reacting flows or reacting flows with slow chemistry, ρ and ζ are parameterized by the differential diffusion parameters. In comparisons of reacting flow results, the reactant conversion parameters characterize ρ and ζ. The influence of differential diffusion on the scalar statistics is reduced by the presence of a constant mean scalar gradient and/or by the increase of the Reynolds number. The statistical results are modified by the overall stoichiometry of the mixture.

The compositional structure and the effects of exothermicity in a nonpremixed planar jet flame

Abstract Results are presented of direct numerical simulation (DNS) of a randomly perturbed compressible, spatially developing two-dimensional planar jet under the influence of a finite rate chemical reaction of the type F + O → Product. The objectives of the simulations are to assess the compositional structure of the flame and to determine the influence of reaction exothermicity by means of statistical sampling of the DNS generated data. It is shown that even with this idealized kinetics model the simulated results exhibit features in accord with experimental data. These results indicate that the Damkohler number is an important parameter in determining the statistical composition of the reacting field and that the results are not very sensitive to the mechanism by which this parameter is varied. It is demonstrated that as the intensity of mixing is increased and the effect of finite rate chemistry is more pronounced, the magnitudes of the ensemble mean and variance of the product mass fraction decrease and those of the reactants mass fraction increase. Also, at higher mixing rates the joint probability density functions of the reactants mass fractions shift towards higher values within the composition domain, indicating a lower reactedness. These trends are consistent with those observed experimentally and are useful in portraying the statistical structure of nonequilibrium diffusion flames. The DNS-generated data are also utilized to examine the applicability of the “laminar diffusion flamelet model” in predicting the rate of the reactant conversion with finite rate chemistry. This examination indicates that the performance of the model is improved as the value of the Damkohler number is increased. Finally, the simulated results suggest that in the setting of a “turbulent” flame, the effect of the heat liberated by the chemical reaction is to increase of reactant conversion. This finding is different from those of earlier DNS results and laboratory investigations that indicate a suppressed chemical reaction with increasing heat release.

Structure of homogeneous nonhelical magnetohydrodynamic turbulence

Results are presented for three‐dimensional direct numerical simulations of nonhelical magnetohydrodynamic (MHD) turbulence for both stationary isotropic and homogeneous shear flow configurations with zero mean induction and unity magnetic Prandtl number. Small scale dynamo action is observed in both flows, and stationary values for the ratio of magnetic to kinetic energy are shown to scale nearly linearly with the Taylor microscale Reynolds numbers above a critical value of Reλ≊30. The presence of the magnetic field has the effect of decreasing the kinetic energy of the flow, while simultaneously increasing the Taylor microscale Reynolds number due to enlargement of the hydrodynamic length scales. For shear flows, both the velocity and the magnetic fields become increasingly anisotropic with increasing initial magnetic field strength. The kinetic energy spectra show a relative increase in high wave‐number energy in the presence of a magnetic field. The magnetic field is found to portray an intermittent b...

Invited Review: Reliable and Affordable Simulation of Turbulent Combustion

Large eddy simulation (LES) via the filtered density function (FDF) is now widely recognized as one of the most reliable and computationally affordable means of turbulent combustion prediction. This lecture provides an overview of the latest developments in both the basic theoretical developments and the applications of LES/FDF. Sample results are presented of some of the latest FDF simulations of turbulent reactive flows.