A non-hybrid method for the PDF equations of turbulent flows on unstructured grids

In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A set of parallel algorithms is proposed to provide an efficient solution of the PDF transport equation, modeling the joint PDF of turbulent velocity, frequency and concentration of a passive scalar in geometrically complex configurations. An unstructured Eulerian grid is employed to extract Eulerian statistics, to solve for quantities represented at fixed locations of the domain (e.g. the mean pressure) and to track particles. All three aspects regarding the grid make use of the finite element method (FEM) employing the simplest linear FEM shape functions. To model the small-scale mixing of the transported scalar, the interaction by exchange with the conditional mean model is adopted. An adaptive algorithm that computes the velocity-conditioned scalar mean is proposed that homogenizes the statistical error over the sample space with no assumption on the shape of the underlying velocity PDF. Compared to other hybrid particle-in-cell approaches for the PDF equations, the current methodology is consistent without the need for consistency conditions. The algorithm is tested by computing the dispersion of passive scalars released from concentrated sources in two different turbulent flows: the fully developed turbulent channel flow and a street canyon (or cavity) flow. Algorithmic details on estimating conditional and unconditional statistics, particle tracking and particle-number control are presented in detail. Relevant aspects of performance and parallelism on cache-based shared memory machines are discussed.Comment: Accepted in Journal of Computational Physics, Feb. 20, 200

Joint PDF modelling of turbulent flow and dispersion in an urban street canyon

The joint probability density function (PDF) of turbulent velocity and concentration of a passive scalar in an urban street canyon is computed using a newly developed particle-in-cell Monte Carlo method. Compared to moment closures, the PDF methodology provides the full one-point one-time PDF of the underlying fields containing all higher moments and correlations. The small-scale mixing of the scalar released from a concentrated source at the street level is modelled by the interaction by exchange with the conditional mean (IECM) model, with a micro-mixing time scale designed for geometrically complex settings. The boundary layer along no-slip walls (building sides and tops) is fully resolved using an elliptic relaxation technique, which captures the high anisotropy and inhomogeneity of the Reynolds stress tensor in these regions. A less computationally intensive technique based on wall functions to represent boundary layers and its effect on the solution are also explored. The calculated statistics are compared to experimental data and large-eddy simulation. The present work can be considered as the first example of computation of the full joint PDF of velocity and a transported passive scalar in an urban setting. The methodology proves successful in providing high level statistical information on the turbulence and pollutant concentration fields in complex urban scenarios.Comment: Accepted in Boundary-Layer Meteorology, Feb. 19, 200

Flow rate of transport network controls uniform metabolite supply to tissue

Life and functioning of higher organisms depends on the continuous supply of metabolites to tissues and organs. What are the requirements on the transport network pervading a tissue to provide a uniform supply of nutrients, minerals, or hormones? To theoretically answer this question, we present an analytical scaling argument and numerical simulations on how flow dynamics and network architecture control active spread and uniform supply of metabolites by studying the example of xylem vessels in plants. We identify the fluid inflow rate as the key factor for uniform supply. While at low inflow rates metabolites are already exhausted close to flow inlets, too high inflow flushes metabolites through the network and deprives tissue close to inlets of supply. In between these two regimes, there exists an optimal inflow rate that yields a uniform supply of metabolites. We determine this optimal inflow analytically in quantitative agreement with numerical results. Optimizing network architecture by reducing the supply variance over all network tubes, we identify patterns of tube dilation or contraction that compensate sub-optimal supply for the case of too low or too high inflow rate.Comment: 11 pages, 4 figures, 8 pages supplemen

Transport of measures on networks

In this paper we formulate a theory of measure-valued linear transport equations on networks. The building block of our approach is the initial/boundary-value problem for the measure-valued linear transport equation on a bounded interval, which is the prototype of an arc of the network. For this problem we give an explicit representation formula of the solution, which also considers the total mass flowing out of the interval. Then we construct the global solution on the network by gluing all the measure-valued solutions on the arcs by means of appropriate distribution rules at the vertexes. The measure-valued approach makes our framework suitable to deal with multiscale flows on networks, with the microscopic and macroscopic phases represented by Lebesgue-singular and Lebesgue-absolutely continuous measures, respectively, in time and space

Modelling extinction and reignition in turbulent flames

The presented work attempts to extend the conditional moment closure method for noon-premixed. turbulent combustion to predict extinction and reignition phenomena in turbulent flames. The conditional moment closure method is one of a????class of conserved scalar modelling approaches in turbulent non-premixed combustion. where chemistry is treated as mainly dependend on the mixing of oxidizer and fuel. However. as designers of combustion devices aim for higher turbulence rates to enhance mixing and promote combustion, chemical conversion is not solely determined by the rate at which fuel and oxidizer are mixed, but kinetic effects become important. Therefore it is necessary in these cases. to consider a second variable to govern the evolution of the chemical system. This variable will parameterize the chemical conversion process from cold. mixed reactants at fixed eguivalence ratio to an eguilibrium state. Equations describing the chemical system as a function of these two variables, the conserved scalar, commonly referred to as mixture fraction and the progress variable. can be derived and constitute the doubly conditioned moment closure equations. However, solution of this set of equations is computationally expensive and key parameters describing the rate of dissipation of the progress variable, which is a reactive scalar, are not yet fully understood. By considering conditional fluctuations of the progress variable, applying simple relationships for scalar dissipation and using a pre-computed functional dependence of conditional moments on the progress variable, the effect of double conditioning on the chemical source term and on the overall chemistry predictions can be examined. The methodology is tested for its capability to predict the turbulent. piloted flames of the Sandia D-F series. These laboratory flames show an increasing degree of local extinction and reignition due to varying turbulence levels. Hence they provide an ideal benchmark for the study of models trying to predict these phenomena.Imperial Users onl

From individual behaviour to an evaluation of the collective evolution of crowds along footbridges

This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real world problems is tested by considering the pedestrian traffic along footbridges, of interest for Structural and Transportation Engineering. The genuinely macroscopic quantitative description of the crowd flow directly matches the engineering need of bulk results. However, three issues beyond the sole modelling are of primary importance: the pedestrian inflow conditions, the numerical approximation of the equations for non trivial footbridge geometries, and the calibration of the free parameters of the model on the basis of in situ measurements currently available. These issues are discussed and a solution strategy is proposed.Comment: 23 pages, 10 figures in J. Engrg. Math., 201

The effect of stellar feedback on the formation and evolution of gas and dust tori in AGN

Recently, the existence of geometrically thick dust structures in Active Galactic Nuclei (AGN) has been directly proven with the help of mid-infrared interferometry. The observations are consistent with a two-component model made up of a geometrically thin and warm central disk, surrounded by a colder, fluffy torus component. In an exploratory study, we investigate one possible physical mechanism, which could produce such a structure, namely the effect of stellar feedback from a young nuclear star cluster on the interstellar medium in centres of AGN. The model is realised with the help of the hydrodynamics code TRAMP. We follow the evolution of the interstellar medium by taking discrete mass loss and energy ejection due to stellar processes, as well as optically thin radiative cooling into account. In a post-processing step, we calculate observable quantities (spectral energy distributions and images) with the help of the radiative transfer code MC3D. The interplay between injection of mass, supernova explosions and radiative cooling leads to a two-component structure made up of a cold geometrically thin, but optically thick and very turbulent disk residing in the vicinity of the angular momentum barrier, surrounded by a filamentary structure. The latter consists of cold long radial filaments flowing towards the disk and a hot tenuous medium in between, which shows both inwards and outwards directed motions. This modelling is able to reproduce the range of observed neutral hydrogen column densities of a sample of Seyfert galaxies as well as the relation between them and the strength of the silicate 10 micron spectral feature. Despite being quite crude, our mean Seyfert galaxy model is even able to describe the SEDs of two intermediate type Seyfert galaxies observed with the Spitzer Space Telescope.Comment: 16 pages, 11 figures, accepted by MNRAS, high resolution version can be downloaded from: http://www.mpe.mpg.de/~mschartm/papers/schartmann_2008b.pd