Kyle D. Squires

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.

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.

An approach to wall modeling in large-eddy simulations

Channel flow with friction Reynolds number Reτ as high as 80 000 is treated by large-eddy simulation at a moderate cost, using the subgrid-scale model designed for detached-eddy simulations. It includes wall modeling, and was not adjusted for this flow. The grid count scales with the logarithm of the Reynolds number. Three independent codes are in fair agreement with each other. Reynolds-number variations and grid refinement cause trades between viscous, modeled, and resolved shear stresses. The skin-friction coefficient is too low, on the order of 15%. The velocity profiles contain a “modeled” logarithmic layer near the wall and some suggest a “resolved” logarithmic layer farther up, but the two layers have a mismatch of several units in U+.

Direct numerical simulation of turbulence modulation by particles in isotropic turbulence

The modulation of isotropic turbulence by particles has been investigated using direct numerical simulation (DNS). The particular focus of the present work is on the class of dilute flows in which particle volume fractions and inter-particle collisions are negligible. Gravitational settling is also neglected and particle motion is assumed to be governed by drag with particle relaxation times ranging from the Kolmogorov scale to the Eulerian time scale of the turbulence and particle mass loadings up to 1. The velocity field was made statistically stationary by forcing the low wavenumbers of the flow. The calculations were performed using 96 3 collocation points and the Taylor-scale Reynolds number for the stationary flow was 62. The effect of particles on the turbulence was included in the Navier–Stokes equations using the point-force approximation in which 96 3 particles were used in the calculations. DNS results show that particles increasingly dissipate fluid kinetic energy with increased loading, with the reduction in kinetic energy being relatively independent of the particle relaxation time. Viscous dissipation in the fluid decreases with increased loading and is larger for particles with smaller relaxation times. Fluid energy spectra show that there is a non-uniform distortion of the turbulence with a relative increase in small-scale energy. The non-uniform distortion significantly affects the transport of the dissipation rate, with the production and destruction of dissipation exhibiting completely different behaviours. The spectrum of the fluid–particle energy exchange rate shows that the fluid drags particles at low wavenumbers while the converse is true at high wavenumbers for small particles. A spectral analysis shows that the increase of the high-wavenumber portion of the fluid energy spectrum can be attributed to transfer of the fluid–particle covariance by the fluid turbulence. This in turn explains the relative increase of small-scale energy caused by small particles observed in the present simulations as well as those of Squires & Eaton (1990) and Elghobashi & Truesdell (1993).

Large eddy simulation of particle‐laden turbulent channel flow

Particle transport in fully‐developed turbulent channel flow has been investigated using large eddy simulation (LES) of the incompressible Navier–Stokes equations. Calculations were performed at channel flow Reynolds numbers, Reτ, of 180 and 644 (based on friction velocity and channel half width); subgrid‐scale stresses were parametrized using the Lagrangian dynamic eddy viscosity model. Particle motion was governed by both drag and gravitational forces and the volume fraction of the dispersed phase was small enough such that particle collisions were negligible and properties of the carrier flow were not modified. Material properties of the particles used in the simulations were identical to those in the DNS calculations of Rouson and Eaton [Proceedings of the 7th Workshop on Two‐Phase Flow Predictions (1994)] and experimental measurements of Kulick et al. [J. Fluid Mech. 277, 109 (1994)]. Statistical properties of the dispersed phase in the channel flow at Reτ=180 are in good agreement with the DNS; reas...

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.

The inner-outer layer interface in large-eddy simulations with wall-layer models

The interaction between the inner and outer layer in large-eddy simulations (LES) that use approximate near-wall treatments is studied.In hybrid Reynolds-averaged Navier–Stokes (RANS)/LES models a transition layer exists between the RANS and LES regions, which has resulted in incorrect prediction of the velocity profiles, and errors of up to 15% in the prediction of the skin friction.Several factors affect this transition layer, but changes we made to the formulation had surprisingly little effect on the mean velocity.In general, it is found that the correct prediction of length- and time-scales of the turbulent eddies in the RANS region is important, but is not the only factor affecting the results.The inclusion of a backscatter model appears to be effective in improving the prediction of the mean velocity profile and skin-friction coefficient.

Numerical investigations of flow over a sphere in the subcritical and supercritical regimes

The flow field around a sphere in an uniform flow has been analyzed numerically for conditions corresponding to the subcritical (laminar separation) and supercritical (turbulent separation) regimes spanning a wide range of Reynolds numbers (104–106). Particular attention has been devoted to assessing predictions of the pressure distribution, skin friction, and drag as well as to understanding the changes in the wake organization and vortex dynamics with the Reynolds number. The unsteady turbulent flow is computed using detached-eddy simulation, a hybrid approach that has Reynolds-averaged Navier–Stokes behavior near the wall and becomes a large eddy simulation in the regions away from solid surfaces. For both the subcritical and supercritical solutions, the agreement with experimental measurements for the mean drag and pressure distribution over the sphere is adequate; differences in skin friction exist due to the simplistic treatment of the attached boundary layers in the computations. Improved agreement in the skin-friction distribution is obtained for the supercritical flows in which boundary layer transition is fixed at the position observed in experiments conducted at the same Reynolds numbers. For the subcritical flows the Strouhal number, St, associated with the large-scale shedding is predicted at St∼0.195 along with a higher frequency component associated with the development of the Kelvin–Helmholtz instabilities in the detached shear layers. If in the subcritical regime the wake assumes a helical-like form due to the shedding of hairpin-like vortices at different azimuthal angles, in the supercritical regime the wake structure is characterized by “regular” shedding of hairpin-like vortices at approximately the same azimuthal angle and at a much higher frequency (St∼1.3) that is practically independent of the Reynolds number and not sensitive to the position of laminar-to-turbulent transition.

Detached-Eddy Simulation With Compressibility Corrections Applied to a Supersonic Axisymmetric Base Flow

Detached-eddy simulation is applied to an axisymmetric base flow at supersonic conditions. Detached-eddy simulation is a hybrid approach to modeling turbulence that combines the best features of the Reynolds-averaged Navier-Stokes and large-eddy simulation approaches. In the Reynolds-averaged mode, the model is currently based on either the Spalart-Allmaras turbulence model or Menter’s shear stress transport model; in the largeeddy simulation mode, it is based on the Smagorinski subgrid scale model. The intended application of detached-eddy simulation is the treatment of massively separated, highReynolds number flows over complex configurations (entire aircraft, automobiles, etc.). Because of the intented future application of the methods to complex configurations, Cobalt, an unstructured grid Navier-Stokes solver, is used. The current work incorporates compressible shear layer corrections in both the Spalart-Allmaras and shear stress transport-based detached-eddy simulation models. The effect of these corrections on both detached-eddy simulation and Reynolds-averaged Navier-Stokes models is examined, and comparisons are made to the experiments of Herrin and Dutton. Solutions are obtained on several grids—both structured and unstructured—to test the sensitivity of the models and code to grid refinement and grid type. The results show that predictions of base flows using detached-eddy simulation compare very well with available experimental data, including turbulence quantities in the wake of the axisymmetric body. @DOI: 10.1115/1.1517572#

On the prediction of gas–solid flows with two-way coupling using large eddy simulation

The purpose of this paper is to examine the feasibility of large eddy simulation (LES) for predicting gas–solid flows in which the carrier flow turbulence is modified by momentum exchange with particles. Several a priori tests of subgrid-scale (SGS) turbulence models are conducted utilizing results from direct numerical simulation (DNS) of a forced homogeneous isotropic turbulent flow with the back effect of the particles modeled using the point-force approximation. Properties of the subgrid-scale field are computed by applying Gaussian filters to the DNS database. Similar to the behavior observed in single-phase flows, a priori test results show that, while the local energy flux is inaccurately estimated, the overall SGS dissipation is reasonably predicted using the conventional Smagorinsky model and underestimated using the Bardina scale-similarity model. Very good agreement between model predictions and DNS results are measured using closures whose coefficients are computed using the resolved field, th...