Wolfgang Gerlinger

Numerical simulation of the mixing of passive and reactive scalars in two-dimensional flows dominated by coherent vortices

Abstract The present paper comprises direct numerical simulation of the mixing of passive and reactive scalars in two-dimensional flows dominated by coherent vortices. By means of highly accurate pseudo-spectral methods the instationary Navier–Stokes and convection–diffusion–reaction equations are numerically integrated on the torus. We present the evolution of typical vortex arrangements and analyze their ability to mix scalars. Furthermore, we attribute the influence of vortices on the mixing to the formation of spirals and to the merging of vortices. As a way of quantifying the mixing, we consider global and local mixing time scales which describe the overall and the early variance decay, respectively. Moreover, the influence of the Schmidt number and of a chemical reaction on mixing processes are investigated.

Numerical simulation of three-dimensional instabilities of spherical flame structures

The paper is concerned with the non-stationary numerical simulation of freely propagating spherically symmetric flame structures at low Lewis number in a lean hydrogen-air mixture. The three-dimensional thermodiffusive equations with a single-step chemical reaction with Arrhenius-like temperature dependence of the reaction rate and a Stefan-Boltzmann-type radiation are integrated by means of a highly accurate Fourier-pseudo-spectral method with a semi-implicit time scheme in a parallelized version. This computational effort is necessary to fulfill the requirements resulting from the wide range of scales which are present in this reaction-diffusion problem. The algorithm is applied to compute the evolution of thermodiffusive flames, where we particularly investigate the influence of the initial flame radius and the radiative heat loss onto the development of freely evolving spherical flames. In the computations we obtain different scenarios of expanding flame structures as found in recent experimental studies under microgravity conditions, for example, the extinction because of excessive heat loss, the splitting due to cellular instability, and the observation of quasi-steady three-dimensional flame balls. Furthermore, we show the necessity of simulations in all physical dimensions to incorporate three-dimensional instabilities which in rotationally symmetric calculations cannot be included. Finally, we show the time evolution of flame structures which are initially disturbed by an artificial function to simulate natural perturbation of flame balls.

Numerical simulations on the stability of spherical flame structures

The paper presents investigations concerning the stability of spherical flames in a premixed lean hydrogen-air atmosphere and their evolution in case of instabilities. This is done by means of numerical simulations using the thermo-diffusive model with one-step finite rate chemical reaction and radiative heat loss under optically thin conditions. In the first part spherical symmetry is imposed leading to a one-dimensional problem. The results obtained in this way are compared with the asymptotic analysis and the numerical simulations from the literature. In the second part these solutions are employed as initial conditions for fully three-dimensional simulations using a high-resolution pseudo-spectral method. It allows the investigation of the nonlinear transient behavior of spherical flames with respect to three-dimensional perturbations. Different scenarios of their evolution are observed: extinction, spherical growth, and splitting. Also, for the first time, a steady flame ball is computed in a three-dimensional simulation. The different numerical and physical issues are discussed in detail and are related to available experimental observations as well as to theoretical analyses.

Mass transport characteristics of alkyl amines in a water/n-decane system.

Water-in-decane emulsions can be applied as reaction system for the precipitation of nanoparticles. Herein the precipitation reaction is induced once an oil as well as water soluble compound (here: alkyl amines) diffuses from the continuous oil phase into a water based droplet, loaded with the reaction partner. Thus, the mass transfer and adsorption characteristics of the alkyl amine at the interface are key parameters to understand particle formation in emulsion droplets. For this reason, the effective diffusion coefficients and the interfacial tension of different alkyl amines in a water/n-decane system were estimated. Furthermore, emulsifiers necessary for the stability of the emulsion might represent a diffusion barrier. In order to determine its influence, diffusion experiments were also conducted in the presence of emulsifier. The effective diffusion coefficients were measured using an adapted photometric method. To identify relevant adsorption characteristics of the water/n-decane/alkyl amine systems, the interfacial tension was studied with the pendant drop technique. According to the results, we can draw three conclusions: First, the effective diffusion coefficient depends on the molecular structure of the amines. Second, regarding our materials, the surface activity and surface coverage proved to be a governing parameter to describe differences in the transport mechanism. And third, the presence of additional surface active compounds leads to a decrease of the effective diffusion coefficient.

Simulation and Analysis of Mixing in Two-Dimensional Turbulent Flows Using Fourier and Wavelet Techniques

This paper presents direct numerical simulations of mixing of passive and reactive scalars in two-dimensional flows. By means of pseudo-spectral methods the governing equations are numerically integrated. As an application we study a temporally growing mixing layer where we focus on the role of coherent vortices. Wavelet techniques are applied to obtain local spectral information about vorticity and scalars. We show that the local generation of fine scales in shear zones is strongly correlated with locally enhanced mixing. Furthermore, we examine the influence of chemical reactions.