Large eddy simulations and direct numerical simulations of high speed turbulent reacting flows

This research is involved with the implementations of advanced computational schemes based on large eddy simulations (LES) and direct numerical simulations (DNS) to study the phenomenon of mixing and its coupling with chemical reactions in compressible turbulent flows. In the efforts related to LES, a research program was initiated to extend the present capabilities of this method for the treatment of chemically reacting flows, whereas in the DNS efforts, focus was on detailed investigations of the effects of compressibility, heat release, and nonequilibrium kinetics modeling in high speed reacting flows. The efforts to date were primarily focussed on simulations of simple flows, namely, homogeneous compressible flows and temporally developing hign speed mixing layers. A summary of the accomplishments is provided

Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) for the computational analyses of high speed reacting flows

The principal objective is to extend the boundaries within which large eddy simulations (LES) and direct numerical simulations (DNS) can be applied in computational analyses of high speed reacting flows. A summary of work accomplished during the last six months is presented

A note on the Schur multiplier of a nilpotent Lie algebra

For a nilpotent Lie algebra $L$ of dimension $n$ and dim$(L^2)=m$, we find the upper bound dim$(M(L))\leq {1/2}(n+m-2)(n-m-1)+1$, where $M(L)$ denotes the Schur multiplier of $L$. In case $m=1$ the equality holds if and only if $L\cong H(1)\oplus A$, where $A$ is an abelian Lie algebra of dimension $n-3$ and H(1) is the Heisenberg algebra of dimension 3.Comment: Paper in press in Comm. Algebra with small revision

PSEUDOSPECTRAL LEAST SQUARES METHOD FOR STOKES-DARCY EQUATIONS

We investigate the first order system least squares Legendre and Chebyshev pseudospectral method for coupled Stokes-Darcy equations. A least squares functional is defined by summing up the weighted L-2-norm of residuals of the first order system for coupled Stokes-Darcy equations and that of Beavers-Joseph-Saffman interface conditions. Continuous and discrete homogeneous functionals are shown to be equivalent to a combination of weighted H(div) and H-1-norms for Stokes and Darcy equations. The spectral convergence for the Legendre and Chebyshev methods is derived. Some numerical experiments are demonstrated to validate our analysisopen0

Large eddy simulations and direct numerical simulations of high speed turbulent reacting flows

This research is involved with the implementation of advanced computational schemes based on large eddy simulations (LES) and direct numerical simulations (DNS) to study the phenomenon of mixing and its coupling with chemical reactions in compressible turbulent flows. In the efforts related to LES, a research program to extend the present capabilities of this method was initiated for the treatment of chemically reacting flows. In the DNS efforts, the focus is on detailed investigations of the effects of compressibility, heat release, and non-equilibrium kinetics modelings in high speed reacting flows. Emphasis was on the simulations of simple flows, namely homogeneous compressible flows, and temporally developing high speed mixing layers

Mesoporous Coatings with Simultaneous Light‐Triggered Transition of Water Imbibition and Droplet Coalescence

A systematic study of gating water infiltration and condensation into ceramic nanopores by carefully adjusting the wetting properties of mesoporous films using photoactive spiropyran is presented. Contact angle measurements from the side reveal significant changes in wettability after irradiation due to spiropyran/merocyanine-isomerization, which induce a wetting transition from dry to wet pores. The change in wettability allows the control of water imbibition in the nanopores and is reflected by the formation of an imbibition ring around a droplet. Furthermore, the photoresponsive wettability is able to overcome pinning effects and cause a movement of a droplet contact line, facilitating droplet coalescence, as recorded by high-speed imaging. The absorbed light not only effectuates droplet merging but also causes flows inside the drop due to heat absorption by the spiropyran, which results in gradients in the surface tension. IR imaging and particle tracking is used to investigate the heat absorption and temperature-induced flows, respectively. These flows can be used to manipulate, for example, molecular movement inside water and deposition inside solid mesoporous materials and are therefore of great importance for nanofluidic devices as well as for future water management concepts, which include filtering by imbibition and collection by droplet coalescence. © 2021 The Authors. Advanced Materials Interfaces published by Wiley-VCH Gmb

Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions

We calculate the dynamic structure factor S (omega, q) of spinless fermions in one dimension with quadratic energy dispersion k^2/2m and long range density-density interaction whose Fourier transform f_q is dominated by small momentum-transfers q << q_0 << k_F. Here q_0 is a momentum-transfer cutoff and k_F is the Fermi momentum. Using functional bosonization and the known properties of symmetrized closed fermion loops, we obtain an expansion of the inverse irreducible polarization to second order in the small parameter q_0 / k_F. In contrast to perturbation theory based on conventional bosonization, our functional bosonization approach is not plagued by mass-shell singularities. For interactions which can be expanded as f_q = f_0 + f_0^{2} q^2/2 + O (q^4) with finite f_0^{2} we show that the momentum scale q_c = 1/ | m f_0^{2} | separates two regimes characterized by a different q-dependence of the width gamma_q of the collective zero sound mode and other features of S (omega, q). For q_c << q << k_F we find that the line-shape in this regime is non-Lorentzian with an overall width gamma_q of order q^3/(m q_c) and a threshold singularity at the lower edge.Comment: 33 Revtex pages, 17 figure

Spreading of a viscoelastic drop on a solid substrate

We study the spreading of viscous and viscoelastic drops on solid substrates with different wettability. In the early stages of spreading, we find that the viscoelastic drop spreads with faster and a different power law than the Newtonian drop (i.e. aqueous glycerine solution) for the same zero shear rate viscosity. We argue that the effect of viscoelasticity is only observable for experimental time scales in the order of the internal relaxation time of the polymer solution or longer times. Near the contact line, the effective viscosity is lower for the viscoelastic drop than for the Newtonian drop. Together with its shear rate dependency, this difference in effective viscosity can explain the different spreading dynamics. We support our experimental findings with a simple perturbation model that qualitatively agrees with our findings