Large-eddy simulation of turbulent collision of heavy particles in isotropic turbulence

The small-scale motions relevant to the collision of heavy particles represent a general challenge to the conventional large-eddy simulation (LES) of turbulent particle-laden flows. As a first step toward addressing this challenge, we examine the capability of the LES method with an eddy viscosity subgrid scale (SGS) model to predict the collision-related statistics such as the particle radial distribution function at contact, the radial relative velocity at contact, and the collision rate for a wide range of particle Stokes numbers. Data from direct numerical simulation (DNS) are used as a benchmark to evaluate the LES using both a priori and a posteriori tests. It is shown that, without the SGS motions, LES cannot accurately predict the particle-pair statistics for heavy particles with small and intermediate Stokes numbers, and a large relative error in collision rate up to 60% may arise when the particle Stokes number is near St_K=0.5. The errors from the filtering operation and the SGS model are evaluated separately using the filtered-DNS (FDNS) and LES flow fields. The errors increase with the filter width and have nonmonotonic variations with the particle Stokes numbers. It is concluded that the error due to filtering dominates the overall error in LES for most particle Stokes numbers. It is found that the overall collision rate can be reasonably predicted by both FDNS and LES for St_K>3. Our analysis suggests that, for St_K<3, a particle SGS model must include the effects of SGS motions on the turbulent collision of heavy particles. The spectral analysis of the concentration fields of the particles with different Stokes numbers further demonstrates the important effects of the small-scale motions on the preferential concentration of the particles with small Stokes numbers.

Subgrid scale fluid velocity timescales seen by inertial particles in large-eddy simulation of particle-laden turbulence

Large-eddy simulation (LES) has emerged as a promising tool for simulating turbulent flows in general and, in recent years,has also been applied to the particle-laden turbulence with some success (Kassinos et al., 2007). The motion of inertial particles is much more complicated than fluid elements, and therefore, LES of turbulent flow laden with inertial particles encounters new challenges. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. The effects of SGS turbulent velocity field on particle motion have been studied by Wang and Squires (1996), Armenio et al. (1999), Yamamoto et al. (2001), Shotorban and Mashayek (2006a,b), Fede and Simonin (2006), Berrouk et al. (2007), Bini and Jones (2008), and Pozorski and Apte (2009), amongst others. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles (Fede et al., 2006; Shotorban and Mashayek, 2006a; Shotorban and Mashayek, 2006b; Berrouk et al., 2007; Bini and Jones, 2008; Pozorski and Apte, 2009).However, the accuracy of such a Langevin equation model depends primarily on the prescription of the SGS fluid velocity autocorrelation time seen by an inertial particle or the inertial particle–SGS eddy interaction timescale (denoted by $\delt T_{Lp}$ and a second model constant in the diffusion term which controls the intensity of the random force received by an inertial particle (denoted by C_0, see Eq. (7)). From the theoretical point of view, dTLp differs significantly from the Lagrangian fluid velocity correlation time (Reeks, 1977; Wang and Stock, 1993), and this carries the essential nonlinearity in the statistical modeling of particle motion. dTLp and C0 may depend on the filter width and particle Stokes number even for a given turbulent flow. In previous studies, dTLp is modeled either by the fluid SGS Lagrangian timescale (Fede et al., 2006; Shotorban and Mashayek, 2006b; Pozorski and Apte, 2009; Bini and Jones, 2008) or by a simple extension of the timescale obtained from the full flow field (Berrouk et al., 2007). In this work, we shall study the subtle and on-monotonic dependence of $\delt T_{Lp}$ on the filter width and particle Stokes number using a flow field obtained from Direct Numerical Simulation (DNS). We then propose an empirical closure model for $\delta T_{Lp}$. Finally, the model is validated against LES of particle-laden turbulence in predicting single-particle statistics such as particle kinetic energy. As a first step, we consider the particle motion under the one-way coupling assumption in isotropic turbulent flow and neglect the gravitational settling effect. The one-way coupling assumption is only valid for low particle mass loading.

Large-eddy simulation of flows past a flapping airfoil using immersed boundary method

The numerical simulation of flows past flapping foils at moderate Reynolds numbers presents two challenges to computational fluid dynamics: turbulent flows and moving boundaries. The direct forcing immersed boundary (IB) method has been devel- oped to simulate laminar flows. However, its performance in simulating turbulent flows and transitional flows with moving boundaries has not been fully evaluated. In the present work, we use the IB method to simulate fully developed turbulent channel flows and transitional flows past a stationary/plunging SD7003 airfoil. To suppress the non-physical force oscillations in the plunging case, we use the smoothed discrete delta function for interpolation in the IB method. The results of the present work demonstrate that the IB method can be used to simulate turbulent flows and transitional flows with moving boundaries.

Large-eddy simulation of flows past a flapping airfoil using immersed boundary method

The numerical simulation of flows past flapping foils at moderate Reynolds numbers presents two challenges to computational fluid dynamics: turbulent flows and moving boundaries. The direct forcing immersed boundary (IB) method has been developed to simulate laminar flows. However, its performance in simulating turbulent flows and transitional flows with moving boundaries has not been fully evaluated. In the present work, we use the IB method to simulate fully developed turbulent channel flows and transitional flows past a stationary/plunging SD7003 airfoil. To suppress the non-physical force oscillations in the plunging case, we use the smoothed discrete delta function for interpolation in the IB method. The results of the present work demonstrate that the IB method can be used to simulate turbulent flows and transitional flows with moving boundaries.

The variability of eddy kinetic energy in the South China Sea deduced from satellite altimeter data

We used fifteen years (1993-2007) of altimetric data, combined from different missions (ERS-1/2, TOPEX/Poseidon, Jason-1, and Envisat), to analyze the variability of the eddy kinetic energy (EKE) in the South China Sea (SCS). We found that the EKE ranged from 64 cm(2)/s(2) to 1 390 cm(2)/s(2) with a mean value of 314 cm(2)/s(2). The highest EKE center was observed to the east of Vietnam (with a mean value of 509 cm(2)/s(2)) and the second highest EKE region was located to the southwest of Taiwan Island (with a mean value of 319 cm(2)/s(2)). We also found that the EKE structure is the consequence of the superposition of different variability components. First, interannual variability is important in the SCS. Spectral analysis of the EKE interannual signal (IA-EKE) shows that the main periodicities of the IA-EKE to the east of Vietnam, to the southwest of Taiwan Island, and in the SCS are 3.75, 1.87, and 3.75 years, respectively. It is to the south of Taiwan Island that the IA-EKE signal has the most obvious impact on EKE variability. In addition, the IA-EKE exhibit different trends in different regions. An obvious positive trend is observed along the east coast of Vietnam, while a negative trend is found to the southwest of Taiwan Island and in the east basin of Vietnam. Correlation analysis shows that the IA-EKE has an obvious negative correlation with the SSTA in Nio3 (5A degrees S-5A degrees N, 90A degrees W-150A degrees W). El Nio-Southern Oscillation (ENSO) affects the IA-EKE variability in the SCS through an atmospheric bridge-wind stress curl over the SCS. Second, the seasonal cycle is the most obvious timescale affecting EKE variability. The locations of the most remarkable EKE seasonal variabilities in the SCS are to the east of Vietnam, to the southwest of Taiwan, and to the west of Philippines. To the east of Vietnam, the seasonal cycle is the dominant mechanism controlling EKE variability, which is attributed primarily to the annual cycle there of wind stress curl. In this area, the maximum EKE is observed in autumn. To the southwest of Taiwan Island, the EKE is enlarged by the stronger SCS circulation, which is caused by the intrusion branch from the Kuroshio in winter. Finally, intra-annual and mesoscale variability, although less important than the former, cannot be neglected. The most obvious intra-annual and mesoscale variability, which may be the result of baroclinic instability of the background flow, are observed to the southwest of Taiwan Island. Sporadic events can have an important effect on EKE variability.

Eddy generation and evolution in the North Pacific Subtropical Countercurrent (NPSC) zone

The seasonal generation and evolution of eddies in the region of the North Pacific Subtropical Countercurrent remain poorly understood due to the scarcity of available data. We used TOPEX/POSEIDON altimetry data from 1992 to 2007 to study the eddy field in this zone. We found that velocity shear between this region and the neighboring North Equatorial Current contributes greatly to the eddy generation. Furthermore, the eddy kinetic energy level (EKE) shows an annual cycle, maximum in April/May and minimum in December/January. Analyses of the temporal and spatial distributions of the eddy field revealed clearly that the velocity shear closely related to baroclinic instability processes. The eddy field seems to be more zonal than meridional, and the energy containing length scale shows a surprising lag of 2-3 months in comparison with the 1-D and 2-D EKE level. A similar phenomenon is observed in individual eddies in this zone. The results show that in this eddy field band, the velocity shear may drive the EKE level change so that the eddy field takes another 2-3 months to grow and interact to reach a relatively stable state. This explains the seasonal evolution of identifiable eddies.

Vertical structure and evolution of the Luzon Warm Eddy

Eddies are frequently observed in the northeastern South China Sea (SCS). However, there have been few studies on vertical structure and temporal-spatial evolution of these eddies. We analyzed the seasonal Luzon Warm Eddy (LWE) based on Argo float data and the merged data products of satellite altimeters of Topex/Poseidon, Jason-1 and European Research Satellites. The analysis shows that the LWE extends vertically to more than 500 m water depth, with a higher temperature anomaly of 5A degrees C and lower salinity anomaly of 0.5 near the thermocline. The current speeds of the LWE are stronger in its uppermost 200 m, with a maximum speed of 0.6 m/s. Sometimes the LWE incorporates mixed waters from the Kuroshio Current and the SCS, and thus has higher thermohaline characteristics than local marine waters. Time series of eddy kinematic parameters show that the radii and shape of the LWE vary during propagation, and its eddy kinetic energy follows a normal distribution. In addition, we used the empirical orthogonal function (EOF) here to analyze seasonal characteristics of the LWE. The results suggest that the LWE generally forms in July, intensifies in August and September, separates from the coast of Luzon in October and propagates westward, and weakens in December and disappears in February. The LWE's westward migration is approximately along 19A degrees N latitude from northwest of Luzon to southeast of Hainan, with a mean speed of 6.6 cm/s.

Covariance analysis of the Coulomb explosion of ammonia induced by intense nanosecond laser at 532 nm

The Coulomb explosion of ammonia clusters induced by nanosecond laser at 532 not with an intensity of similar to 10(12) Wcm(-2) has been studied by time of flight mass spectrometry. The dominant multiply charged ions are N3+ and N2+ with kinetic energies of 110 and 50 eV respectively. The electrons generated from the multiphoton ionization are heated through inverse bremsstrahlung by the laser field when colliding with neutral or ionic particles. When their energies surpass the corresponding ionization potentials of the molecules or ions, the subsequent electron impact ionization may take place thus resulting in multi-charged nitrogen ions. Covariance analysis is made to study the possible pathways of the Coulomb explosion.

A Numerical Study for Turbulent Flow and Thermal Influence Over Inhomogenous Canopy of Roughness Elements

A large-eddy simulation with transitional structure function(TSF) subgrid model we previously proposed was performed to investigate the turbulent flow with thermal influence over an inhomogeneous canopy, which was represented as alternative large and small roughness elements. The aerodynamic and thermodynamic effects of the presence of a layer of large roughness elements were modelled by adding a drag term to the three-dimensional Navier-Stokes equations and a heat source/sink term to the scalar equation, respectively. The layer of small roughness elements was simply treated using the method as described in paper (Moeng 1984, J. Atmos Sci. 41, 2052-2062) for homogeneous rough surface. The horizontally averaged statistics such as mean vertical profiles of wind velocity, air temperature, et al., are in reasonable agreement with Gao et al.(1989, Boundary layer meteorol. 47, 349-377) field observation (homogeneous canopy). Not surprisingly, the calculated instantaneous velocity and temperature fields show that the roughness elements considerably changed the turbulent structure within the canopy. The adjustment of the mean vertical profiles of velocity and temperature was studied, which was found qualitatively comparable with Belcher et al. (2003, J Fluid Mech. 488, 369-398)'s theoretical results. The urban heat island(UHI) was investigated imposing heat source in the region of large roughness elements. An elevated inversion layer, a phenomenon often observed in the urban area (Sang et al., J Wind Eng. Ind. Aesodyn. 87, 243-258)'s was successfully simulated above the canopy. The cool island(CI) was also investigated imposing heat sink to simply model the evaporation of plant canopy. An inversion layer was found very stable and robust within the canopy.

Multiscale Coupling in Complex Mechanical Systems

Multiscale coupling attracts broad interests from mechanics, physics and chemistry to biology. The diversity and coupling of physics at different scales are two essential features of multiscale problems in far-from-equilibrium systems. The two features present fundamental difficulties and are great challenges to multiscale modeling and simulation. The theory of dynamical system and statistical mechanics provide fundamental tools for the multiscale coupling problems. The paper presents some closed multiscale formulations, e.g., the mapping closure approximation, multiscale large-eddy simulation and statistical mesoscopic damage mechanics, for two typical multiscale coupling problems in mechanics, that is, turbulence in fluids and failure in solids. It is pointed that developing a tractable, closed nonequilibrium statistical theory may be an effective approach to deal with the multiscale coupling problems. Some common characteristics of the statistical theory are discussed.

Short-and resonant-range interactions between scales in turbulence and their applications

Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the short-range viscous stresses, which express the short-range interactions between contiguous scales in turbulence, were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation (LES) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.

关于Maunder极小期太阳活动的统计分析

本文通过自相关分析探讨在“Maunder极小期”期间太阳活动是否仍然存在11年活动周期.利用Eddy根据欧洲望远镜在“Maunder极小期”时观测的太阳黑子记录所作的相对黑子数年平均值进行了自相关分析,也与中国地方志在“Maunder极小期”时的有关黑子记录一起进行了同样的自相关分析.在作自相关分析时采用几种不同的方法进行比较,结果发现,11年活动周期性的存在与否与所选用的统计方法有关,因此不能绝对地说在“Maunder极小期”时太阳活动完全停止了,或者说在“Maunder极小期”时仍然存在着11年周期的活动性质.

An improvement on the theoretical model for the large-scale coherent structures in the outer region of a turbulent boundary layer

According to the experimental results, there exist large-scale coherent structures in the outer region of a turbulent boundary layer, which have been studied by many authors.As experimental results, Antonia (1990) showed the phase- aver aged streamlines and isovorticity lines of the large-scale coherent structures in a turbulent boundary layer for different Reynolds numbers. Based on the hydrodynamic stability theory, the 2-D theoretical model for the large-scale structures was proposed by Luo and Zhou, in which the eddy viscosity was defined as a complex function of the position in the normal direction. The theoretical results showed in ref. were in agreement with those in ref. However, there were two problems in the results. One is that in the experimental results, there were divergent focuses between two saddle points in the streamlines, but in the theoretical results, there were centers. The other is that the stretched parts of the isovorticity lines appear at the location of centers in the theoretical results, while in the experimental results they located somewhere between the focuses and saddle points. The reason is that the computations were based on a 2-D model.

Assessment of bursting detection methods with LES database of turbulent channel flows

Validated by comparison with DNS, numerical database of turbulent channel flows is yielded by Large Eddy Simulation (LES). Three conventional techniques: uv quadrant 2, VITA and mu-level techniques for detecting turbulent bursts are applied to the identification of turbulent bursts. With a grouping parameter introduced by Bogard & Tiedemann (1986) or Luchik & Tiederman (1987), multiple ejections detected by these techniques which originate from a single burst can be grouped into a single-burst event. The results are compared with experimental results, showing that all techniques yield reasonable average burst period. However, uv quadrant 2 and mu-level are found to be superior to VITA in having large threshold-independent range.