Direct simulation of two‐dimensional turbulent flow over a surface‐mounted obstacle

Two‐dimensional turbulent flow over a surface‐mounted obstacle is studied as a numerical experiment that takes place in a wind tunnel. The transient Navier–Stokes equations are solved directly with Galerkin finite elements. The Reynolds number defined with respect to the height of the wind tunnel is 12 518. Instantaneous streamline patterns are shown that give a complete picture of the flow phenomena. Energy and enstrophy spectra yield the dual cascade of two‐dimensional turbulence and the ?1 power law decay of enstrophy. Mean values of velocities and root mean square fluctuations are compared with the available experimental results. Other statistical characteristics of turbulence such as Eulerian autocorrelation coefficients, longitudinal and lateral coefficients are also computed. Finally, oscillation diagrams of computed velocity fluctuations yield the chaotic behaviour of turbulence. Copyright © 2007 John Wiley & Sons, Ltd.     

气固两相流中颗粒弥散的拉格朗日模拟

本文提出了一种对于均匀,稳定及各向同性气固两相紊流场中圆形固体颗粒弥散的拉格朗日模拟计算方法,应用该方法对带有网栅的垂直与水平管道中均匀,稳定的气固两相流模拟计算结果与Snyder及Wells等人所做的相同情况下的试验结果进行了比较,以证明该模拟计算方法的有效性,。     

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

Heavy particle dispersion from a point source in turbulent pipe flow

Dispersion of heavy particles from a point source in high-Reynolds pipe flow was studied using large-eddy simulation, LES. A stochastic Langevin type Lagrangian model developed by Berrouk et al. was used to account for heavy particle transport by the sub-grid scale motion. In both the LES and in an experiment by Arnason, the larger particles dispersed more than the small ones. The change in diffusivity with particle size is interpreted in terms of the effect of inertia and cross-trajectory effects and qualitatively compared with the analysis of heavy particle dispersion in isotropic turbulence by Wang and Stock. Particle inertia has a much larger influence on the dispersion than the crossing-trajectories effects.     

A technique for measuring Lagrangian and Eulerian particle statistics in a turbulent flow

An experimental technique is described which has been developed to study particle dispersion in a round turbulent jet. Droplets are injected on the jet axis, and a laser sheet and position sensitive photomultiplier tube are used to track their radial displacement. Data processing is greatly simplified compared to video or photo imaging techniques which provide similar measurements. Statistically large samples are used to calculate dispersion and axial velocity as a function of axial downstream distance or particle time-of-flight. Dispersion and velocity statistics can be computed which are Lagrangian or Eulerian in nature. The technique has been demonstrated with 69 m droplets of hexadecane in a jet of air with a Reynolds number of 15,000; in principle it could be used to study the motion of very small, quasi-fluid particles.     

Computation of particle dispersion in turbulent liquid flows using an efficient Lagrangian trajectory model

The dispersion of solid particles in a turbulent liquid flow impinging on a centrebody through an axisymmetric sudden expansion was investigated numerically using a Eulerian–Lagrangian model. Detailed experimental measurements at the inlet were used to specify the inlet conditions for two-phase flow computations. The anisotropy of liquid turbulence was accounted for using a second-moment Reynold stress transport model. A recently developed stochastic–probabilistic model was used to enhance the computational efficiency of Lagrangian trajectory computations. Numerical results of the stochastic–probabilistic model using 650 particle trajectories were compared with those of the conventional stochastic discrete-delta-function model using 18 000 particle trajectories. In addition, results of the two models were compared with experimental measurements. © 1998 John Wiley & Sons, Ltd.     

Computational analysis and flow structure of a transitional separated-reattached flow over a surface mounted obstacle and a forward-facing step

Large-eddy simulation (LES) of transitional separating-reattaching flow on a two-dimensional square surface mounted obstacle and a forward facing step has been performed using a dynamic sub-grid scale model. The Reynolds number based on the uniform inlet velocity and the obstacle/step height is 4.5 × 10³. The mean LES results for both the obstacle and step flow compare reasonably well with the available experimental and DNS data.

The flow structures upstream of the surface-mounted obstacle (referred to hereafter as obstacle) and the forward-facing step (referred to hereafter as FFS) consist of unstable two-dimensional structures and coherent rib-shaped structures. These structures with the aid of 3D streamline visualisation strongly indicate that the upstream separation bubble is a closed one rather than an open one in the sense that there is little evidence to suggest that there is fluid injection from the upstream separation region into the downstream separated region for the two geometries. The spectra and time history for the velocities and pressure fields at locations immediately upstream of the obstacle and FFS (including the recirculation region) were analysed using both the Fourier and wavelet transforms and revealed the unsteady nature of the recirculation region upstream of the obstacle and FFS.

The transition process has been elucidated using both 2D and 3D flow visualisation of the flow. In both geometries (obstacle and FFS), the separated boundary layer downstream of the leading edge shows 2D nature and roll-up shortly downstream of the separation line leading to 2D K-H rolls to be shed from the leading edge. Coherent structures such as the λ-shaped and rib-like vortices commonly associated with a flat plate boundary layer and also found in the separated-reattached flow of a blunt leading edge plate aligned horizontally to a flow are not common in the separated-reattached flow over the obstacle and FFS.     

Large eddy simulation of droplet dispersion for inhomogeneous turbulent wall flow

A large eddy simulation (LES) coupled with a Lagrangian stochastic model has been applied to the study of droplet dispersion in a turbulent boundary layer. Droplets are tracked in a Lagrangian way. The velocity of the fluid particle along the droplet trajectory is considered to have a large-scale part and a small-scale part given by a modified three-dimensional Langevin model using the filtered subgrid scale (SGS) statistics. An appropriate Lagrangian correlation timescale is considered in order to include the influences of gravity and inertia. Two-way coupling is also taken into account. The inter-droplet collision has been introduced as the main mechanism of secondary breakup. A stochastic model for breakup has been generalized for coalescence simulation, thereby two phenomena, coalescence and breakup are simulated in the framework of a single stochastic model. The parameters of this model, selectively for coalescence and for breakup, are computed dynamically by relating them to the local resolved properties of the dispersed phase compared to the main fluid. The model is validated by comparison with an agglomeration model and with experimental results on secondary breakup. The LES coupled with Lagrangian particle tracking and the model for droplet coalescence and breakup is applied to the study of the atmospheric dispersion of wet cooling tower plumes. The simulations are done for different droplet size distributions and volume fractions. We focused on the influence of these parameters on mean concentration, concentration variance and mass flux profiles.     

Relative particle velocity in a turbulent flow

On the basis of a statistical approach using a probability density function for the coordinates of two particles in a turbulent flow, the parameters of the relative particle motion are investigated. For the functions describing particle entrainment in the turbulence, rigorous results are obtained using a 3D turbulence spectrum. A method of calculating the particle relative-velocity rate with account for particle trajectory correlation is presented. The effects of particle inertia and velocity slip on the parameters of the relative particle motion are studied. Simple approximating formulas for calculating the relative particle motion in a turbulent flow are proposed. The calculation results are compared with the data of direct numerical simulation of stochastic particle trajectories in an isotropic turbulent field.     

On the flow instabilities in the end-wall region of a surface mounted obstacle

Visualization of flow in the around a surface mounted obstacle revealed that the pressure gradients imposed on the boundary layer amplified the formation of turbulent spots in the end-wall region. It was observed that the juncture vortices exhibited Λ waveform instability even during the stretching phase that was followed by a rapid amplification and formation of a turbulent spot. The turbulent spot spread laterally as it convected past the attachment and corner region of the end-wall flow. At the Reynolds number used in this investigation the instabilities were always initiated in the region where the primary singular point is located.     

Numerical study of turbulent flow over two‐dimensional surface‐mounted ribs in a channel

This study accurately predicts the cases of turbulent flow around a surface‐mounted two‐dimensional rib with varying lengths. The numerical method employs a differencing scheme for integrating the elliptic Reynolds‐averaged Navier–Stokes equations and the continuity equation. A two‐equation k–ε turbulence model is employed to simulate the turbulent transport quantities and close the solving problem. The near‐wall regions of the separated sides of the rib are resolved by a near‐wall model of a two‐layer approach instead of the wall function approximation. Computations for flow over a surface‐mounted rectangular rib are conducted for the variations in the rib lengths. Results indicate that upstream of the obstacle, the length of the recirculating region remains unchanged with varying rib lengths; while the downstream length of the recirculating region is a strong function of rib length and changes nearly linearly for the varying lengths of B/H=0.1 to B/H=4.0. Reattachment on top of the rib, owing to its increasing length, affects the downstream boundary layer development. Copyright © 1999 John Wiley & Sons, Ltd.     

Large eddy simulation and a simple wall model for turbulent flow calculation by a particle method

A turbulent channel flow and the flow around a cubic obstacle are calculated by the moving particle semi‐implicit method with the subparticle‐scale turbulent model and a wall model, which is based on the zero equation RANS (Reynolds Averaged Navier‐Stokes). The wall model is useful in practical problems that often involve high Reynolds numbers and wall turbulence, because it is difficult to keep high resolution in the near‐wall region in particle simulation. A turbulent channel flow is calculated by the present method to validate our wall model. The mean velocity distribution agrees with the log‐law velocity profile near the wall. Statistical values are also the same order and tendency as experimental results with emulating viscous layer by the wall model. We also investigated the influence of numerical oscillations on turbulence analysis in using the moving particle semi‐implicit method. Finally, the turbulent flow around a cubic obstacle is calculated by the present method to demonstrate capability of calculating practical turbulent flows. Three characteristic eddies appear in front of, over, and in the back of the cube both in our calculation and the experimental result that was obtained by Martinuzzi and Tropea. Mean velocity and turbulent intensity profiles are predicted in the same order and have similar tendency as the experimental result. Copyright © 2012 John Wiley & Sons, Ltd.     

Steady waves in a stratified flow over a combined obstacle

A problem of steady internal waves in subcritical flows of a stratified liquid over a finite sequence of bottom elevations is considered. An asymptotic solution of the second order of accuracy, which takes into account nonlinear effects, is constructed by the method of perturbations in terms of the small parameter of the obstacle height. Near-field interference wave structures are studied.     

Pulsating motions of a solid particle in turbulent flow

The relations governing the transverse pulsations of a spherical particle in a turbulent flow are examined. On the basis of the resulting relations an estimate is made of the effect of several factors on the intensity of the velocity pulsations of the solid component in dispersed flow through a conduit.     

Grid-averaged Lagrangian LES model for multiphase turbulent flow

A grid-averaged Lagrangian (GAL) model for dispersed particle motion in multiphase turbulent flow is presented to provide a large eddy simulation (LES) model for multiphase turbulent flow in which a quite large number of particles are involved. The GAL model is based on an averaging operation for a Lagrangian-type equation of motion of a particle over a computational grid volume and a procedure of reallocation of a dispersed particle cloud with its centroid movement to each grid. The model is therefore a mixed Eulerian–Lagrangian model which can effectively reduce computational time compared with existing Lagrangian-type models, without losing the advantage of Lagrangian-type models that they can properly describe the dynamical evolution of particles. Since the GAL model adopts the grid-volume averaging operation it can easily provide an effective SGS model for LES modeling of multiphase turbulent flow. The validity of the multiphase LES model developed, which is named the GAL-LES model, is confirmed through its application to a particle plume, in which the present model is found to simulate large-eddy motion usually observed in a jet and plume, and to give good agreements with experimental data.