Regularization modeling for large-eddy simulation of diffusion flames

We analyze the evolution of a diffusion flame in a turbulent mixing layer using large-eddy simulation. The large-eddy simulation includes Leray regularization of the convective transport and approximate inverse filtering to represent the chemical source terms. The Leray model is compared to the more conventional dynamic mixed model. The location of the flame-center is defined by the 'stoichiometric' interface. Geometrical properties such as its surface-area and wrinkling are characterized using an accurate numerical level-set quadrature method. This allows to quantify flame-properties as well as turbulence modulation effects due to coupling between combustion and turbulent transport. We determine the active flame-region that is responsible for the main part of the chemical conversion in the flame and compare direct and large-eddy simulation predictions

Buoyant turbulent mixing in shear layers

Buoyancy effects in unstably stratified mixing layers express themselves through gravity currents of heavy fluid which propagate in an ambient lighter fluid. These currents are encountered in numerous geophysical flows, industrial safety and environmental protection issues. During transition to turbulence a strong distortion of the separating interface between regions containing `heavy' or `light' fluid arises. The complexity of this interface will be used to monitor the progress of the mixing. We concentrate on the enhancement of surface-area and `surface-wrinkling' of the separating interface as a result of gravity-effects. We also show that this process can be simulated quite accurately using large-eddy simulation with dynamic subgrid modeling. However, the subgrid resolution, defined as the ratio between filter-width Delta and grid-spacing h, should be sufficiently high to avoid contamination due to spatial discretization error effects.Comment: 4 pages, 5 figures; to appear in Proceedings ETC9, Eds: I.P. Castro and P.E. Hancock, CIMNE, Barcelona, 200

The reptating rope model: Viscometric functions for concentrated polymer solutions and melts in shear flow

The viscometric functions for shear flow as predicted by the inextensible reptating rope model have been analysed numerically and analytically. The results obtained are compared with the predictions of the Curtiss—Bird theory. It is shown that if the correlation length of the rope is small as compared to its contour length significant deviations from the Curtiss—Bird theory are obtained. Results are presented for: (a) the onset of shear flow, (b) steady state shear flow and (c) small amplitude oscillatory shear flow

Magnitude control of commutator errors

Non-uniform filtering of the Navier-Stokes equations expresses itself, next to the turbulent stresses, in additional closure terms known as commutator errors. These terms require explicit subgrid modeling if the non-uniformity of the filter is sufficiently pronounced. We derive expressions for the magnitude of the mean flux, the turbulent stress flux and the commutator error for individual Fourier modes. This gives rise to conditions for the spatial variations in the filter-width and the filter-skewness subject to which the magnitude of the commutator errors can be controlled. These conditions are translated into smoothness requirements of the computational grid, that involve ratios of first -, second - and third order derivatives of the grid mapping

Regularization modeling for large-eddy simulation

A new modeling approach for large-eddy simulation (LES) is obtained by combining a `regularization principle' with an explicit filter and its inversion. This regularization approach allows a systematic derivation of the implied subgrid-model, which resolves the closure problem. The central role of the filter in LES is fully restored, i.e., both the interpretation of LES predictions in terms of direct simulation results as well as the corresponding subgrid closure are specified by the filter. The regularization approach is illustrated with `Leray-smoothing' of the nonlinear convective terms. In turbulent mixing the new, implied subgrid model performs favorably compared to the dynamic eddy-viscosity procedure. The model is robust at arbitrarily high Reynolds numbers and correctly predicts self-similar turbulent flow development.Comment: 16 pages, 4 figures, submitted to Physics of Fluid

Complexes of block copolymers in solution: tree approximation

We determine the statistical properties of block copolymer complexes in solution. These complexes are assumed to have the topological structure of (i) a tree or of (ii) a line-dressed tree. In case the structure is that of a tree, the system is shown to undergo a gelation transition at sufficiently high polymer concentration. However, if the structure is that of a line-dressed tree, this transition is absent. Hence, we show the assumption about the topological structure to be relevant for the statistical properties of the system. We determine the average size of the complexes and calculate the viscosity of the system under the assumption that the complexes geometrically can be treated as porous spheres

Fractional exponential decay in the capture of ligands by randomly distributed traps in one dimension

In many biophysical and biochemical experiments one observes the decay of some ligand population by an appropriate system of traps. We analyse this decay for a one-dimensional system of radomly distributed traps, and show that one can distinguish three different regimes. The decay starts with a fractional exponential of the form exp[− (t/t0)1/2], which changes into a fractional exponential of the form exp[− (t/t1)1/3] for long times, which in its turn changes into a pure exponential time dependence, i.e. exp[−t/t2] for very long times. With these three regimes, we associate three time scales, related to the average trap density and the diffusion constant characterizing the motion of the ligands

Development of regularization modeling and error-control in large-eddy simulation

Numerical simulation is developing into a viable research-tool to help understand dispersion and structure in turbulence. In order to make progress toward simulating flows under realistic flow-conditions and in complex flow-domains, large-eddy simulation appears an essential stepping-stone. This requires a combination of accurate numerical treatment and proper (subgrid) modeling of the dynamic effects of small-scale turbulence. It will be shown that accurate subgrid models may be systematically derived from mathematical regularization principles. This will be illustrated for the Leray and \mbox{NS-$\alpha$} models. Moreover, a database analysis of interacting modeling and simulation errors in large-eddy simulation will be discussed in terms of error-landscapes. The optimality of the dynamic procedure will be quantified and a new inverse polynomial interpolation method will be proposed with which model parameters can be optimized to approximate the `optimal refinement strategy'