Evaporating droplets in turbulent reacting flows

Three-dimensional direct numerical simulations are carried out to determine the effects of turbulence on the preferential segregation of an evaporating spray and then to study the evolution of the resulting mixture fraction topology and propagating flame. First, the mixing between an initially randomly dispersed phase and the turbulent gaseous carrier phase is studied with non-evaporating particles. According to their inertia and the turbulence properties, the formation of clusters of particles is analyzed (formation delay, cluster characteristic size and density). Once the particles are in dynamical equilibrium with the surrounding turbulent flow, evaporation is considered through the analysis of the mixture fraction evolution. Finally, to mimic ignition, a kernel of burnt gases is generated at the center of the domain and the turbulent flame evolution is described.     

Two-parameter expansion in the renormalization-group analysis of turbulence

The renormalization of the solution of the Navier-Stokes equation for randomly stirred fluid with long-range correlations of the driving force is analysed near two dimensions. It is shown that a local term must be added to the correlation function of the random force for the correct renormalization of the model at two dimensions. The interplay of the short-range and long-range terms in the large-scale behaviour of the model is analysed near two dimensions by the field-theoretic renormalization group. A regular expansion in 2ε=d-2 and δ=2-λ is constructed, whered is the space dimension and λ the exponent of the powerlike correlation function of the driving force. It is shown that in spite of the additional divergences, the asymptotic behaviour of the model near two dimensions is the same as in higher dimensions, contrary to recent conjectures based on an incorrect renormalization procedure.     

Electron-active silicon oxidation

Visible and ultraviolet light was employed in a series of refining experiments to reveal the kinetics of photon-enhanced oxidation of silicon. The experimental evidence then gave rise to an electron-active silicon oxidation process involving electron emission from Si into SiO₂ moderating the dissociation of molecular oxygen near the interface. Photonicallystimulated oxidation enhancement then straightforwardly derives from an enhanced level of electron emission. This simple model helps to clarify normal dry thermal oxidation growth kinetics, as well as thin oxide rapid growth behavior and the charged-versus-neutral oxidant controversy. Finally, attention is called to the not generally recognized but likely role that secondary electron emission from surfaces may play in moderating the chemistry of various electron, ion and photon beam-induced surface reactions.     

Gasdynamic CO laser with closed-cycle gas flow

The operation of an electrically excited gasdynamic CO laser with closed-cycle gas flow is described. Details of the gasdynamics, the recompression, and the cooling of the flowing gas are given. The electrical discharge produces contaminating gas compounds—in particular CO₂—which accumulate in the recirculating gas. The resulting transient behavior of the laser gas composition, the discharge characteristics, and the laser performance are studied and compared with the results obtained with the same CO laser in an open-flow system. It is found that the closed-cycle system may be operated for considerable time if the CO₂ contamination is removed from the laser gas.     

Acceleration statistics of inertial particles in turbulent flow

Turbulent transport of material inclusions plays an important role in many natural and industrial situations. Being able to accurately model and predict the dynamics of dispersed particles transported by a turbulent carrier flow, remains a challenge. One critical and difficult point is to develop models which correctly describe the dynamics of particles over a wide range of sizes and densities. Our measurements show that acceleration statistics of particles dispersed in a turbulent flow do exhibit specific, and so far unpredicted, size and density effects and that they preserve an extremely robust turbulent signature with lognormal fluctuations, regardless of particles size and density. This has important consequences in terms of modeling for the turbulent transport of dispersed inclusions.     

Influence of magnetic quantization on the Einstein relation in non-linear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestion for experimental determination

In this paper, we have investigated the Einstein relation for the diffusivity-to-mobility ratio (DMR) under magnetic quantization in non-linear optical materials on the basis of a newly formulated electron dispersion law by considering the crystal field constant, the anisotropies of the momentum-matrix element and the spin-orbit splitting constant, respectively, within the frame work of k·p formalism. The corresponding result for the three-band model of Kane (the conduction electrons of III-V, ternary and quaternary compounds obey this model) forms a special case of our generalized analysis. The DMR under magnetic quantization has also been investigated for II-VI (on the basis of Hopfield model), bismuth (using the models of McClure and Choi, Cohen, Lax and parabolic ellipsoidal, respectively), and stressed materials (on the basis of model of Seiler et al.) by formulating the respective electron statistics under magnetic quantization incorporating the respective energy band constants. It has been found, taking n-CdGeAs₂, n-Hg_1−xCd_xTe, p-CdS, and stressed n-InSb as examples of the aforementioned compounds, that the DMR exhibits oscillatory dependence with the inverse quantizing magnetic field due to Subhnikov de Haas (SdH) effect with different numerical values. The DMR also increases with increasing carrier degeneracy and the nature of oscillations are totally dependent on their respective band structures in various cases. The classical expression of the DMR has been obtained as a special case from the results of all the materials as considered here under certain limiting conditions, and this compatibility is the indirect test of our generalized formalism. In addition, we have suggested an experimental method of determining the DMR for degenerate materials under magnetic quantization having arbitrary dispersion laws. The three applications of our results in the presence of magneto-transport have further been suggested.     

Minimum state for high Reynolds and Péclet number turbulent flows

Direct numerical simulations (DNS) or experiments for the very high Reynolds (Re) and Péclet (Pe) number flows commonly exceed the resolution possible even when use is made of the most advanced computer capability or most sophisticated diagnostics and physical capabilities of advanced laboratory facilities. In practice use is made of statistical flow data bases developed at the highest Re and Pe levels achievable within the currently available facility limitations. In addition, there is presently no metric to indicate whether and how much of the fully resolved physics of the flow of interest has been captured within the facilities available. In this Letter the authors develop the necessary metric criteria for homogeneous, isotropic and shear layer flows. It is based on establishing a smaller subset of the total range of dynamic scale interactions that will still faithfully reproduce all of the essential, significant, influences of the larger range of scale interactions. The work identifies a minimum significant Re and Pe level that must be obtained by DNS or experiment in order to capture all of the significant dynamic influences in data which is then scaleable to flows of interest. Hereafter this is called the minimum state. Determination of the minimum state is based on finding a minimum scale separation for the energy-containing scales of the flow and scalar fields sufficient to prevent contamination by interaction with the (non-universal) velocity dissipation and scalar diffusivity inertial range scale limits.     

Flame growth and wrinkling in a turbulent flow

High-speed planar laser-induced fluorescence (PLIF) and 3-D large eddy simulations (LES) are used to study turbulent flame kernel growth, wrinkling and the formation of separated flame pockets in methane/air mixtures. Turbulence was effected by a set of rotary fans situated in a cylindrical enclosure. Flame wrinkling was followed on sequential 2-D OH images captured at kHz repetition rates. Under stoichiometric conditions and low turbulence levels the flame kernel remains singly connected and close to spherical in shape. By increasing turbulence or reducing the stoichiometry of the mixture the formation of separated pockets could be observed and studied. The mechanisms behind these phenomena are investigated qualitatively by LES of a level-set G-equation describing the flame surface propagation in turbulent flows. Received: 12 April 2000 / Revised version: 26 June 2000 / Published online: 5 October 2000     

Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

Intermittency in a turbulent low temperature gaseous helium jet

We analyse experimental velocity measurements on the axis of a low temperature gaseous helium jet. From independent increments arguments, we reproduce the behaviour of structure functions. We show where this approach fails and how the intermittency phenomenon is a small correction. The physical arguments under the multiplicative cascade models for this intermittency imply an acceleration of this cascade close to the dissipative range, which we are able to evidence. This acceleration could be responsible of the apparent Extended Self Similarity between structure functions of various orders. Received 13 October 1999 and Received in final form 19 May 2000     

Self-organized criticality in 1D stochastic traffic flow model

Results of computer simulations of a 1D particle hopping model of traffic flow are presented. The model is characterized by parallel update and fully asymmetric stochastic hopping dynamics which allows unbounded series of jumps to empty neighbour sites on the right. The considered case of open boundary conditions can be used to model a “bottleneck” situation in traffic. Evidence for self-organized criticality is found in two aspects: the presence of long-range spatial correlations manifested in the shape of density profiles, and long-time temporal correlations showing up in the low-frequency behaviour of the spectral density of the total particle number and flow. A plausible conjecture is to interpret the observed qualitative changes in these features, as a function of the injection rate and the hopping probability, in terms of a nonequilibrium phase transition between a low-density phase and a maximal current phase. This conjecture is supported by the phase diagram obtained in mean-field approximation.     

Lattice Boltzmann model for three-dimensional decaying homogeneous isotropic turbulence

We implement a lattice Boltzmann method (LBM) for decaying homogeneous isotropic turbulence based on an analogous Galerkin filter and focus on the fundamental statistical isotropic property. This regularized method is constructed based on orthogonal Hermite polynomial space. For decaying homogeneous isotropic turbulence, this regularized method can simulate the isotropic property very well. Numerical studies demonstrate that the novel regularized LBM is a promising approximation of turbulent fluid flows, which paves the way for coupling various turbulent models with LBM.     

Analysis of a turbulent compressed flow by a second-order model

This paper is concerned with the simulation of a turbulent flow submitted to a cyclic one-dimensional compression and expansion between two parallel flat pistons moving with opposite velocities in the direction of their perpendicular axis. The turbulence model used is the second-order model developed at a low Reynolds number by Craft and Launder. Numerical results show that the turbulent field may be considered as homogeneous in an extended part of the domain. The confinement effect appears mainly in the vicinity of the moving walls while the central region is especially influenced by the compression effect. The evolution of the heat flux, transferred from the fluid through the moving walls, tends to a zero limit cycle in the turbulent flow and to a non-zero limit cycle in the laminar flow. The disappearance of the turbulent energy is not predicted by the k-l model.     

Ripple formation in weakly turbulent flow

The formation of granular ripples under liquid shear flow in an annular channel is studied experimentally. The erodible granular bed is subject to weakly turbulent flows without a defined sharp boundary layer close to the granular bed. The flow field and the degree of turbulence is characterized quantitatively by using a particle image velocimeter and a laser-Doppler velocimeter, respectively. A new range of particle Reynolds numbers at the lower limit of the Shields diagram were explored. Quantitative measurements of the granular flow on the surface reveal that the threshold for particle motion coincides within the order of one percent with the threshold for ripple formation. In fully developed ripples it was found that on the leeward side of the ripples regions of low-velocity gradients exist where granular motion is scarce, indicating that the coupling between the ripples is mainly caused by the flow field of the liquid.     

Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method

In this paper, we discuss the incorporation of dynamic subgrid scale (SGS) models in the lattice-Boltzmann method (LBM) for large-eddy simulation (LES) of turbulent flows. The use of a dynamic procedure, which involves sampling or test-filtering of super-grid turbulence dynamics and subsequent use of scale-invariance for two levels, circumvents the need for empiricism in determining the magnitude of the model coefficient of the SGS models. We employ the multiple relaxation times (MRT) formulation of LBM with a forcing term, which has improved physical fidelity and numerical stability achieved by proper separation of relaxation time scales of hydrodynamic and non-hydrodynamic modes, for simulation of the grid-filtered dynamics of large-eddies. The dynamic procedure is illustrated for use with the common Smagorinsky eddy-viscosity SGS model, and incorporated in the LBM kinetic approach through effective relaxation time scales. The strain rate tensor in the SGS model is locally computed by means of non-equilibrium moments of the MRT-LBM. We also discuss proper sampling techniques or test-filters that facilitate implementation of dynamic models in the LBM. For accommodating variable resolutions, we employ conservative, locally refined grids in this framework. As examples, we consider the canonical anisotropic and inhomogeneous turbulent flow problem, i.e. fully-developed turbulent channel flow at two different shear Reynolds numbers Re_∗ of 180 and 395. The approach is able to automatically and self-consistently compute the values of the Smagorinsky coefficient, C_S. In particular, the computed value in the outer or bulk flow region, where turbulence is generally more isotropic, is about 0.155 (or the model coefficient ) which is in good agreement with prior data. It is also shown that the model coefficient becomes smaller and approaches towards zero near walls, reflecting the dampening of turbulent length scales near walls. The computed turbulence statistics at these Reynolds numbers are also in good agreement with prior data. The paper also discusses a procedure for incorporation of more general scale-similarity based SGS stress models.     

Second-order phase transition in two-dimensional cellular automaton model of traffic flow containing road sections

Two-dimensional cellular automaton model has been broadly researched for traffic flow, as it reveals the main characteristics of the traffic networks in cities. Based on the BML models, a first-order phase transition occurs between the low-density moving phase in which all cars move at maximal speed and the high-density jammed phase in which all cars are stopped. However, it is not a physical result of a realistic system. We propose a new traffic rule in a two-dimensional traffic flow model containing road sections, which reflects that a car cannot enter into a road crossing if the road section in front of the crossing is occupied by another car. The simulation results reveal a second-order phase transition that separates the free flow phase from the jammed phase. In this way the system will not be entirely jammed (“don’t block the box” as in New York City).     

Reanalysis and semi-empirical predictions of the hyperfine structure of in the model space

On the basis of most of the earlier hyperfine-structure (hfs) experimental results, the hfs of the atomic zirconium has been reanalyzed by the simultaneous parameterization of the one- and two-body interactions for the model space (4 d + 5 s ) ⁴ . The values of the one- and two-body hfs parameters have been determined and the nuclear quadrupole moment, free of Sternheimer corrections up to second order, has been evaluated. Moreover, the values of the magnetic-dipole A and the electric-quadrupole B constants for all known levels of this model space have been predicted. Received: 22 December 1997 / Revised: 15 May 1998 / Accepted: 1 July 1998     

Stretching of polymers in a random three-dimensional flow

Behavior of a dilute polymer solution in a random three-dimensional flow with an average shear is studied experimentally. Polymer contribution to the shear stress is found to be more than 2 orders of magnitude higher than in a laminar shear flow. The results indicate that the polymer molecules are strongly stretched by the random motion of the fluid.     

A scale-entropy diffusion equation to describe the multi-scale features of turbulent flames near a wall

Multi-scale features of turbulent flames near a wall display two kinds of scale-dependent fractal features. In scale-space, an unique fractal dimension cannot be defined and the fractal dimension of the front is scale-dependent. Moreover, when the front approaches the wall, this dependency changes: fractal dimension also depends on the wall-distance. Our aim here is to propose a general geometrical framework that provides the possibility to integrate these two cases, in order to describe the multi-scale structure of turbulent flames interacting with a wall. Based on the scale-entropy quantity, which is simply linked to the roughness of the front, we thus introduce a general scale-entropy diffusion equation. We define the notion of “scale-evolutivity” which characterises the deviation of a multi-scale system from the pure fractal behaviour. The specific case of a constant “scale-evolutivity” over the scale-range is studied. In this case, called “parabolic scaling”, the fractal dimension is a linear function of the logarithm of scale. The case of a constant scale-evolutivity in the wall-distance space implies that the fractal dimension depends linearly on the logarithm of the wall-distance. We then verified experimentally, that parabolic scaling represents a good approximation of the real multi-scale features of turbulent flames near a wall.