Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Detached-eddy simulation (DES) is well understood in thin boundary layers, with the turbulence model in its Reynolds-averaged Navier–Stokes (RANS) mode and flattened grid cells, and in regions of massive separation, with the turbulence model in its large-eddy simulation (LES) mode and grid cells close to isotropic. However its initial formulation, denoted DES97 from here on, can exhibit an incorrect behavior in thick boundary layers and shallow separation regions. This behavior begins when the grid spacing parallel to the wall Δ∥ becomes less than the boundary-layer thickness δ, either through grid refinement or boundary-layer thickening. The grid spacing is then fine enough for the DES length scale to follow the LES branch (and therefore lower the eddy viscosity below the RANS level), but resolved Reynolds stresses deriving from velocity fluctuations (“LES content”) have not replaced the modeled Reynolds stresses. LES content may be lacking because the resolution is not fine enough to fully support it, and/or because of delays in its generation by instabilities. The depleted stresses reduce the skin friction, which can lead to premature separation.

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A new version of detached-eddy simulation, resistant to ambiguous grid densities

An introduction to heat transfer

Jets, ie collimated streams of matter, occur from the microscale up to the large-scale structure of the universe Our focus will be mostly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science, for example in nuclear fission, DNA sampling, medical diagnostics, sprays, agricultural irrigation and jet engine technology Liquid jets thus serve as a paradigm for free-surface motion, hydrodynamic instability and singularity formation leading to drop breakup In addition to their practical usefulness, jets are an ideal probe for liquid properties, such as surface tension, viscosity or non-Newtonian rheology They also arise from the last but one topology change of liquid masses bursting into sprays Jet dynamics are sensitive to the turbulent or thermal excitation of the fluid, as well as to the surrounding gas or fluid medium The aim of this review is to provide a unified description of the fundamental and the technological aspects of these subjects

Physics of liquid jets

▪ Abstract We review the direct numerical simulation (DNS) of turbulent flows. We stress that DNS is a research tool, and not a brute-force solution to the Navier-Stokes equations for engineering problems. The wide range of scales in turbulent flows requires that care be taken in their numerical solution. We discuss related numerical issues such as boundary conditions and spatial and temporal discretization. Significant insight into turbulence physics has been gained from DNS of certain idealized flows that cannot be easily attained in the laboratory. We discuss some examples. Further, we illustrate the complementary nature of experiments and computations in turbulence research. Examples are provided where DNS data has been used to evaluate measurement accuracy. Finally, we consider how DNS has impacted turbulence modeling and provided further insight into the structure of turbulent boundary layers.

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DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research

Turbulent dispersed multiphase flows are common in many engineering and environmental applications. The stochastic nature of both the carrier-phase turbulence and the dispersed-phase distribution makes the problem of turbulent dispersed multiphase flow far more complex than its single-phase counterpart. In this article we first review the current state-of-the-art experimental and computational techniques for turbulent dispersed multiphase flows, their strengths and limitations, and opportunities for the future. The review then focuses on three important aspects of turbulent dispersed multiphase flows: the preferential concentration of particles, droplets, and bubbles; the effect of turbulence on the coupling between the dispersed and carrier phases; and modulation of carrier-phase turbulence due to the presence of particles and bubbles.

Turbulent Dispersed Multiphase Flow

Preferential concentration of particles by turbulence

Direct numerical simulation of isotropic turbulence was used to investigate the effect of turbulence on the concentration fields of heavy particles. The hydrodynamic field was computed using 643 points and a statistically stationary flow was obtained by forcing the low‐wave‐number components of the velocity field. The particles used in the simulations were time advanced according to Stokes drag law and were also assumed to be much more dense than the fluid. Properties of the particle cloud were obtained by following the trajectories of 1 000 000 particles through the simulated flow fields. Three values of the ratio of the particle time constant to large‐scale turbulence time scale were used in the simulations: 0.075, 0.15, and 0.52. The simulations show that the particles collect preferentially in regions of low vorticity and high strain rate. This preferential collection was most pronounced for the intermediate particle time constant (0.15) and it was also found that the instantaneous number density was as much as 25 times the mean value for these simulations. The fact that dense particles collect in regions of low vorticity and high strain in turn implies that turbulence may actually inhibit rather than enhance mixing of particles.

Despite extensive study, there remain significant questions about the Reynolds-number scaling of the zero-pressure-gradient flat-plate turbulent boundary layer. While the mean flow is generally accepted to follow the law of the wall, there is little consensus about the scaling of the Reynolds normal stresses, except that there are Reynolds-number effects even very close to the wall. Using a low-speed, high-Reynolds-number facility and a high-resolution laser-Doppler anemometer, we have measured Reynolds stresses for a flat-plate turbulent boundary layer from Reθ = 1430 to 31 000. Profiles of u′2, v′2, and u′v′ show reasonably good collapse with Reynolds number: u′2 in a new scaling, and v′2 and u′v′ in classic inner scaling. The log law provides a reasonably accurate universal profile for the mean velocity in the inner region.

Reynolds-number scaling of the flat-plate turbulent boundary layer

Introduction T reattachment of a turbulent shear layer is an important process in a large number of practical engineering configurations, including diffusers, airfoils with separation bubbles, buildings, and combustors. In order to predict these complicated flows, we must understand and be able to predict the behavior of reattaching shear layers. However, our current understanding of the reattachment process is poor, a fact demonstrated by our inability to predict simple reattaching flows over a wide range of parameters. In fact, a complete list of the parameters that affect reattachment has yet to be formulated. Among two-dimensional flows, the backward-facing step is the simplest reattaching flow. The separation line is straight and fixed at the edge of the step, and there is only one separated zone instead of two, as seen in the flow over a fence or obstacle. In addition, the streamlines are nearly parallel to the wall at the separation point, so significant upstream influence occurs only downstream of separation. Although they are not always stated explicitly, these are the reasons why most of the research on reattachment has been done in backward-facing step flows. The backward-facing step is also used as a building block flow for workers developing turbulence models. Therefore, it is important to supply data which can be used to test codes and information that may aid the development of future codes. Bradshaw and Wong reviewed the experimental data for reattaching flows in 1972. Since that time there has been a proliferation of new research in the area, particularly since the advent of the laser anemometer and the pulsed-wire anemometer. This research has been conducted by a number of independent groups, and therefore the net result is somewhat disorganized. Very little systematic study has been done on the effect of the governing parameters on reattachment. In addition, most of the experiments, when viewed separately, have failed to cast any new light on the underlying physics of the reattachment process. The purpose of this paper is twofold. The primary purpose is to review the available data for turbulent flows over backward-facing steps, including some new data of our own and other previously unpublished data. Second, we suggest several areas of research that we feel could lead to improvements in our ability to predict flows with separation bubbles. Several physical mechanisms will be proposed to explain some of the phenomena that have been observed. It is our hope that these suggestions will provoke further thought, comment, and research. The review covers subsonic flows over backward-facing steps in which the Reynolds number is high enough to insure that the separated shear layer is fully turbulent. Important work on laminar and transitional reattaching shear layers has been performed by Goldstein et al. and Armaly et al. but will not be referred to here. Primary emphasis is on planar flows, but some data from axisymmetric flows will be utilized. Double-sided, sudden expansion flows in which the flow is asymmetric are not considered here, because these flows are even more complicated than flows with a single separation bubble. A companion paper examines the uncertainty of the available data in more detail. It also assesses the usefulness of the various data sets as test cases for computational procedures.

John K. Eaton

Papers

Turbulent Dispersed Multiphase Flow

Preferential concentration of particles by turbulence

Preferential concentration of particles by turbulence

Reynolds-number scaling of the flat-plate turbulent boundary layer

A Review of Research on Subsonic Turbulent Flow Reattachment