John K. Eaton

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.

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

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 Re θ = 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.

A Review of Research on Subsonic Turbulent Flow Reattachment

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.

Particle response and turbulence modification in isotropic turbulence

The effect of turbulence on particle concentration fields and the modification of turbulence by particles has been investigated using direct numerical simulations of isotropic turbulence. The particle motion was computed using Stokes’ law of resistance and it was also assumed the particle volume fraction was negligible. For simulations in which the particles do not modify the turbulence field it was found that light particles collect preferentially in regions of low vorticity and high strain rate. For increased mass loading the particle field attenuated an increasing fraction of the turbulence energy. Examination of the spatial energy spectra showed that the fraction of turbulence kinetic energy in the high wave numbers was increased relative to the energy in the low wave numbers for increasing values of the mass loading. It was also found that the turbulence field was modified differently by light particles than by heavy particles because of the preferential collection of the light particles in low‐vorticity, high‐strain‐rate regions. Correlation coefficients between the second invariant of the deformation tensor and pressure showed little sensitivity to increased loading while correlations between enstrophy and pressure were decreased more by the light particles than by the heavy particles for increased mass loading.

Particle response and turbulence modification in fully developed channel flow

The interactions between small dense particles and fluid turbulence have been investigated in a downflow fully developed channel in air. Particle velocities of, and fluid velocities in the presence of, 50 μm glass, 90 μm glass and 70 μm copper spherical beads were measured by laser Doppler anemometry, at particle mass loadings up to 80%. These particles were smaller than the Kolmogorov lengthscale of the flow and could respond to some but not all of the scales of turbulent motion. Streamwise mean particle velocity profiles were flatter than the mean fluid velocity profile, which was unmodified by particle loading. Particle velocity fluctuation intensities were larger than the unladen-fluid turbulence intensity in the streamwise direction but were smaller in the transverse direction. Fluid turbulence was attenuated by the addition of particles; the degree of attenuation increased with particle Stokes number, particle mass loading and distance from the wall. Turbulence was more strongly attenuated in the transverse than in the streamwise direction, because the turbulence energy is at higher frequencies in the transverse direction. Streamwise turbulence attenuation displayed a range of preferred frequencies where attenuation was strongest.

Preferential concentration of heavy particles in a turbulent channel flow

An investigation of the instantaneous particle concentration at the centerline of a turbulent channel flow has been conducted. The concentration field was obtained by digitizing photographs of particles illuminated by a spanwise laser sheet and identifying individual particles. The resulting distribution was then compared to the expected distribution for the same number of particles randomly distributed throughout the volume. Significant departures from randomness have been found and the differences are strongly dependent on the time constants of the particles. Five different particle classes were investigated and the maximum departure from randomness was found when the ratio of the particle’s aerodynamic response time to the Kolmogorov time scale of the flow was approximately one. The length scales of the particle clusters were found to change with the particle size. The correlation dimension was used to produce a single parameter describing the degree of concentration regardless of the scale on which it...

Combined Heat Transfer and Fluid Dynamic Measurements Downstream of a Backward-Facing Step

Combined heat transfer and fluid dynamic measurements in a separated and reattaching boundary layer, with emphasis on the near-wall region, are presented. A constant heat-flux surface behind a single-sided sudden expansion is used to obtain Stanton number profiles as a function of Reynolds number and boundary-layer thickness at separation. Fluctuating skin-friction and temperature profiles demonstrate the importance of the near-wall region in controlling the heat transfer rate. The fluctuating skin friction controls the heat transfer rate near reattachment, while the conventional Reynolds analogy applies in the redeveloping boundary layer beginning two or three step heights downstream of reattachment.

Measurements of particle dispersion obtained from direct numerical simulations of isotropic turbulence

Measurements of heavy particle dispersion have been made using direct numerical simulations of isotropic turbulence. The parameters affecting the dispersion of solid particles, namely particle inertia and drift due to body forces were investigated separately. In agreement with the theoretical studies of Reeks, and Pismen & Nir, the effect of particle inertia is to increase the eddy diffusivity over that of the fluid (in the absence of particle drift). The increase in the eddy diffusivity of particles over that of the fluid was between 2 and 16%, in reasonable agreement with the increases reported in Reeks, and Pismen & Nir. The effect of a deterministic particle drift is shown to decrease unequally the dispersion in directions normal and parallel to the particle drift direction. Eddy diffusivities normal and parallel to particle drift are shown to be in good agreement with the predictions of Csanady and the experimental measurements of Wells & Stock.

Experimental study of the development of longitudinal vortex pairs embedded in a turbulent boundary layer

The mean streamwise development of pairs of longitudinal vortices embedded in an otherwise two-dimensional turbulent boundary layer was studied. Planes of closely spaced measurements of the three components of mean velocity were obtained at several streamwise locations, and the vorticity and circulation were calculated. Skin-friction measurements were also made. It was found that the rate of vorticity spreading in a vortex was greatly increased by close proximity of other vortices. The rate of streamwise circulation decrease was significantly greater for corotating vortices than for counter rotating vortices. Boundary-layer thinning and increased skin friction occured in regions where the secondary flow induced by the pairs was directed toward the wall; the boundary layer was thickened and skin friction reduced where the secondary flow was directed away from the wall.

Experimental investigation of flow through an asymmetric plane diffuser

John K. Eaton 11. Motivation and objectivesThere is a need for experimental measurements in complex turbulent flows thatoriginate from very well-defined initial conditions. Testing of large-eddy simulationsand other higher-order computation schemes requires inlet boundary condition datathat are not normally measured. The use of fully developed upstream conditionsoffers a solution to this dilemma in that the upstream conditions can be adequatelycomputed at any level of sophistication. Unfortunately, experimenters have onlyrecently been sensitized to this issue and there are relatively few appropriate datasets.The plane diffuser experiment by Obi et al. (1993) has received a lot of atten-tion because it has fully-developed inlet conditions and it includes separation froma smooth wall, subsequent reattachment, and redevelopment of the downstreamboundary layer. Each of these features offers challenges for modern turbulencemodels. In particular, Durbin and Kaltenbach of CTR have devoted considerableeffort in developing several different computations of the flow. Unfortunately, theyfound that the experiment had several deficiencies as they began careful comparisonto the data. The most glaring problem is the fact that the data set does not appearto satisfy mass conservation, a problem that is most likely due to three-dimensionaleffects in the diffuser.The objective of this study is to provide careful qualification and detailed mea-surements in a re-creation of the Obi experiment. The work will include extensivedocumentation of the flow two-dimensionality and detailed measurements requiredfor testing of flow computations.2. AccomplishmentsThe diffuser geometry as specified by Obi et al. is shown in Fig. 1. The expectedflow includes flow separation approximately midway along the diffuser followed byreattachment in the tailpipe. The problem with this flow is that separation islikely to occur on the end-walls, causing an acceleration of the mid-plane flow.Our approach has been to modify an existing blower wind-tunnel to accommodatea very high aspect ratio version of the diffuser in hopes of minimizing end-walleffects. Unfortunately, the separated regions on the end-wall can be quite large andhave a significant effect on the mid-plane flow. After construction, the majority ofour efforts have been in controlling the end-wall boundary layer separation.