Long-range interactions in turbulence and the energy decay problem.

We discuss the long-range interactions that arise in homogeneous turbulence as a consequence of the Biot-Savart law. We note that, somewhat surprisingly, these long-range correlations are very weak in decaying, isotropic turbulence, and we argue that this should also be true for magnetohydrodynamic, rotating and stratified turbulence. If this is indeed the case, it is possible to make explicit predictions for the rate of decay of energy in these anisotropic systems, and it turns out that these predictions are consistent with the available numerical and experimental evidence.

Projective Limit Random Probabilities on Polish Spaces

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.

ANALYSIS OF A PROBLEM INVOLVING RADIAL CONSOLIDATION.

An analytical solution is presented for the vertical consolidation of a cylindrical annulus of clay with horizontal drainage occurring to concentric internal and external drainage boundaries. Numerical results are given for various ratios of internal and external radii and it is shown that solutions for conventional one-dimensional consolidation, and for consolidation of a cylindrical block of clay with drainage only to the outer cylindrical boundary form extremes to the analysis presented here. An application of the solution to the estimation of horizontal permeability of clay is briefly described.

APPLICATION OF CENTRIFUGE MODELS IN THE STUDY OF AN INTERACTION PROBLEM.

Rigid retaining walls are considered. Both the backfill and the soil supporting the foundation of the model wall have been made of a single dry granular soil. Attention is limited to one grain.

Multi-dimensional conditional moment closure modelling applied to a heavy-duty common-rail diesel engine

A multi-dimensional combustion code implementing the Conditional Moment Closure turbulent combustion model interfaced with a well-established RANS two- phase flow field solver has been employed to study a broad range of operating conditions for a heavy duty direct-injection common-rail Diesel engine. These conditions include different loads (25%, 50%, 75% and full load) and engine speeds (1250 and 1830 RPM) and, with respect to the fuel path, different injection timings and rail pressures. A total of nine cases have been simulated. Excellent agreement with experimental data has been found for the pressure traces and the heat release rates, without adjusting any model constants. The chemical mechanism used contains a detailed NOx sub-mechanism. The predicted emissions agree reasonably well with the experimental data considering the range of operating points and given no adjustments of any rate constants have been employed. In an effort to identify CPU cost reduction potential, various dimensionality reduction strategies have been assessed. Furthermore, the sensitivity of the predictions with respect to resolution in particular relating to the CMC grid has been investigated. Overall, the results suggest that the presented modelling strategy has considerable predictive capability concerning Diesel engine combustion without requiring model constant calibration based on experimental data. This is true particularly for the heat release rates predictions and, to a lesser extent, for NOx emissions where further progress is still necessary. © 2009 SAE International.

On a classical problem of acoustic wave scattering by a free vortex: Numerical modelling

The scattering of sound from a point source by a Rankine vortex is investigated numerically by solving the Euler equations with the novel high-resolution CABARET method. For several Mach numbers of the vortex, the time-average amplitudes of the scattered field obtained from the numerical modeling are compared with the theoretical scaling laws' predictions. Copyright © 2009 by Sergey Karabasov.

Modeling evaporation effects in conditional moment closure for spray autoignition

Simulations of an n-heptane spray autoigniting under conditions relevant to a diesel engine are performed using two-dimensional, first-order conditional moment closure (CMC) with full treatment of spray terms in the mixture fraction variance and CMC equations. The conditional evaporation term in the CMC equations is closed assuming interphase exchange to occur at the droplet saturation mixture fraction values only. Modeling of the unclosed terms in themixture fraction variance equation is done accordingly. Comparison with experimental data for a range of ambient oxygen concentrations shows that the ignition delay is overpredicted. The trend of increasing ignition delay with decreasing oxygen concentration, however, is correctly captured. Good agreement is found between the computed and measured flame lift-off height for all conditions investigated. Analysis of source terms in the CMC temperature equation reveals that a convective-reactive balance sets in at the flame base, with spatial diffusion terms being important, but not as important as in lifted jet flames in cold air. Inclusion of droplet terms in the governing equations is found to affect the mixture fraction variance field in the region where evaporation is the strongest, and to slightly increase the ignition delay time due to the cooling associated with the evaporation. Both flame propagation and stabilization mechanisms, however, remain unaffected. © 2011 Taylor & Francis.