Effect of gravity on the development of homogeneous shear turbulence laden with finite-size particles

Fully resolved simulations of homogeneous shear turbulence (HST) laden with sedimenting spherical particles of finite size have been performed to clarify the effects of gravity on the development of particle-laden turbulent shear flows. We consider turbulence in a horizontal flow subjected to vertical or horizontal shear. Numerical results show that the development of HST laden with finite-size particles are significantly altered by gravity. The effects of gravity lead to a slower increase in the Taylor-microscale Reynolds number, whose value is found to be well correlated with the average particle Reynolds number. The gravity also causes a slower increase in the turbulence kinetic energy (TKE) through the enhancement of energy dissipation. The change in the Reynolds shear stress (RSS) due to particles also significantly contributes to the relative change in TKE. In vertically sheared cases, RSS has high values between counter-rotating trailing vortices behind the particles, which causes a transient relative increase in TKE. In horizontally sheared cases, on the other hand, RSS is reduced in the wakes of particles, which contributes to a significant relative reduction in TKE.     

各向同性湍流中颗粒引起湍流变动的直接模拟

本文通过直接数值模拟对均匀各向同性湍流中颗粒对湍流的变动作用进行了研究.颗粒相的体积分数很小而质量载荷足够大,以至于颗粒之间的相互作用可以忽略不计,而重点考虑颗粒与湍流间能量的交换。颗粒对湍流的反向作用使得湍动能的耗散率增强,以至于湍动能的衰减速率增大.湍动能的衰减速率随颗粒惯性的增大而增大。三维湍动能谱显示,颗粒对湍动能的影响在不同的尺度上是不均匀的。在低波数段,流体带动颗粒,而高波数段则相反.     

汉克-贝塞尔光束在海洋湍流信道中的螺旋相位谱分析

携带轨道角动量的汉克-贝塞尔(Hankel-Bessel,HB)光束具有无衍射和自聚焦特性,用来作为信息传输的载体有望增大信息传输容量.基于Rytov近似理论,推导得到了HB涡旋光束经过海洋水平弱湍流信道后的螺旋相位谱的解析表达式,并利用数值仿真方法研究了海洋湍流参数对轨道角动量模式探测概率的影响.结果表明,海洋湍流导致发射轨道角动量模式的探测概率下降,出现模式串扰和螺旋相位谱扩展.海洋湍流对HB涡旋光束的负面影响随着轨道角动量模式数、传输距离、温度方差耗散率的增加而增强,随湍流动能耗散率的增加而减弱.HB涡旋光束受以盐度波动驱动的海洋湍流的负面影响更大.另外,在弱湍流及几十米传输距离条件下,HB涡旋光束的传输性能要差于最佳束腰大小设置的拉盖尔-高斯涡旋光束.这些结果有望为海洋环境水下光通信链路的实现提供一定的参考价值.     

Characteristics and generation of elastic turbulence in a three-dimensional parallel plate channel using direct numerical simulation

Direct numerical simulations(DNSs) of purely elastic turbulence in rectilinear shear flows in a three-dimensional(3D) parallel plate channel were carried out,by which numerical databases were established.Based on the numerical databases,the present paper analyzed the structural and statistical characteristics of the elastic turbulence including flow patterns,the wall effect on the turbulent kinetic energy spectrum,and the local relationship between the flow motion and the microstructures' behavior.Moreover,to address the underlying physical mechanism of elastic turbulence,its generation was presented in terms of the global energy budget.The results showed that the flow structures in elastic turbulence were 3D with spatial scales on the order of the geometrical characteristic length,and vortex tubes were more likely to be embedded in the regions where the polymers were strongly stretched.In addition,the patterns of microstructures' elongation behave like a filament.From the results of the turbulent kinetic energy budget,it was found that the continuous energy releasing from the polymers into the main flow was the main source of the generation and maintenance of the elastic turbulent status.     

Decaying turbulence in the presence of a shearless uniform kinetic energy gradient

The decay of turbulent kinetic energy in nearly isotropic grid turbulence has been studied extensively as a fundamental point of reference for turbulence theories and numerical simulations. Most studies have focused on nearly homogeneous turbulence characterised by power-law decay. Other studies have focused on so-called shearless mixing layers, in which two regions with the same mean velocity but distinctly different kinetic energy levels slowly diffuse into each other downstream thus providing information about spatial transport of turbulence. Here, we introduce and study another type of shearless turbulent flow. It has initially a nearly uniform spatial gradient of kinetic energy of the form k ～ β(y ? y₀), where y is the spanwise position. In the experiments, this gradient is generated with the use of an active grid and screens mounted upstream of the wind-tunnel’s test section, iteratively designed to produce a uniform gradient of turbulent kinetic energy without mean velocity shear. Data are acquired using X-wire thermal anemometry at different spanwise and downstream locations. Profile measurements are used to quantify the constancy of the mean velocity and the linearity of the initial profile of kinetic energy. Measurements show that at all spanwise locations, the decay in the streamwise direction follows a power-law but with exponents n(y) that depend upon the spanwise location. The results are consistent with a decay of the form k/?u?² = β(x/x_ref)^?n(y)(y ? y₀)/M. Results for the development of integral length scale, and for velocity skewness and flatness factors are also presented. Significant deviations from Gaussianity are observed especially for the spanwise velocity component in the lower kinetic energy region. Future experiments will be needed including measurements of the dissipation rate ? at sufficient accuracy, in order to unambiguously partition the energy decay into dissipation and spatial diffusion.     

Beyond Scaling and Locality in Turbulence

An analytic perturbation theory is suggested in order to find finite-size corrections to the scaling power laws. In the frame of this theory it is shown that the first order finite-size correction to the scaling power laws has following form , where η is a finite-size scale (in particular for turbulence, it can be the Kolmogorov dissipation scale). Using data of laboratory experiments and numerical simulations it is shown shown that a degenerate case with α ₀=0 can describe turbulence statistics in the near-dissipation range r > η, where the ordinary (power-law) scaling does not apply. For moderate Reynolds numbers the degenerate scaling range covers almost the entire range of scales of velocity structure functions (the log-corrections apply to finite Reynolds number). Interplay between local and non-local regimes has been considered as a possible hydrodynamic mechanism providing the basis for the degenerate scaling of structure functions and extended self-similarity. These results have been also expanded on passive scalar mixing in turbulence. Overlapping phenomenon between local and non-local regimes and a relation between position of maximum of the generalized energy input rate and the actual crossover scale between these regimes are briefly discussed. PACS: 47.27.-i, 47.27.Gs.     

Wavelet analysis of Navier-Stokes flow

Three-dimensional turbulence is analyzed by wavelet transform. To keep the number of degrees of freedom in appropriate bounds, a reduced set of wavelets is used. Integrating the equation of motion, the following results are obtained: We find strong intermittent fluctuations of the energy dissipation rate and of the vorticity in the viscous range. The vorticity shows the tendency of alignment with the direction of least shear and is organized within elongated tubes. Inertial range properties of the flow are addressed by means of an eddy viscosity or by strongly reducing the spatial resolution of the wavelet basis. In the high Reynolds number limit there seem to be hardly any scaling corrections to the ?5/3-law in accordance with other recent results.     

有限差分格式的一个通用色散-耗散条件

通过分析显式有限差分格式的数值色散和数值耗散,导出一个适于有限差分格式的通用色散-耗散条件.根据群速度和耗散率之间的物理关系,确定了用以抑制数值解中伪高波数波所需要的适度耗散.在以往发展的低耗散加权基本无振荡格式WENO-CU6-M2上的应用表明,该条件可用作优化线性或非线性有限差分格式的色散和耗散的通用指导准则.此外,满足色散-耗散条件的改进WENO-CU6-M2格式还可选作低分辨率数值模拟,以三维Taylor-Green涡向湍流转捩和自相似能量衰减问题展现了它的这种能力.与经典的动态Smagorinsky亚网格尺度模型相比,在Reynolds数Re=400~3000条件下,无黏和黏性Taylor-Green涡的数值模拟结果均得到明显改善.在保持激波捕捉特性同时,与最新的隐式大涡模拟模型的计算效果相当.      

Local equilibrium in the inertial layer of wall bounded turbulence

Recently Brouwers [Dissipation equals production in the log layer of wall-induced turbulence. Phys Fluids. 2007;19:101702] carried out an asymptotic analysis using the RANS based turbulence energy transport equation and showed that the energy dissipation equals its production in the inertial layer of wall-induced turbulence. Assuming log-law profile to the mean velocity, pressure, viscous and energy diffusion terms were estimated and shown to be negligibly small compared to the production and dissipation terms thereby proving local equilibrium. However, based on scale relations Tennekes and Lumley [A first course in turbulence. Cambridge (MA): MIT Press; 1994] have already established that the pressure and energy diffusion terms appearing in the energy transport equation are of the same order of magnitude especially in the inertial layer thus leading to a contradiction. Hence we have attempted here to re-estimate the turbulence energy budgets in a different way by invoking the Kolomogrov’s similarity hypotheses and (4/5)th law. Magnitudes of pressure and energy diffusion terms are determined explicitly and found to match well with the DNS data. The striking point of the present analysis is that no prior assumption is enforced on the mean velocity profile. Further, two main advantages of the present study are, (i) reasonable estimates for both the diffusion terms are obtained explicitly that were unavailable before and (ii) these estimates help us to tweak the production/dissipation terms to reflect the influence of turbulent diffusion mechanisms without the necessity to model them as in the case of elliptic relaxation and Reynold stress RANS models.     

A numerical analysis on flow field and heat transfer by interaction between a pair of vortices in rectangular channel flow

This paper is a numerical study of the effect of flow field and heat transfer created by interactions between a pair of vortices generated by a vortex generator in a rectangular channel flow. In order to analyze the vortices produced by the vortex generator, the pseudo-compressibility method is introduced into the Navier–Strokes (NS) equation of a three-dimensional unsteady, incompressible viscous flow. A two-layer k–ε turbulence model is used on the flat plate three-dimensional turbulence boundary to predict the turbulence characteristics of the vortices. The computational results accurately predict the vortex characteristics, which are related to Reynolds stress, turbulent kinetic energy, and flow field. Also, in the prediction of thermal boundary layers, skin friction characteristics, and heat transfers, the present results are reasonably close to the experimental results obtained by other researchers.     

Resonance oscillation damping of a scanning microscope probe by a near-surface viscous liquid layer

Viscous liquid layer motion between a probe with a tip shaped as a paraboloid of revolution and a surface is considered for semicontact-mode operation of a scanning probe microscope. The presence of a viscous liquid layer leads to energy dissipation and is one of the factors responsible for the decrease in the probe oscillation amplitude. The Reynolds equation for viscous liquid motion is used to obtain an analytic solution to the problem. The formula derived for the loss is compared with experimental data obtained for probes and layers with various curvature radii and viscosities.     

Large scale dissipation and filament instability in two-dimensional turbulence

Coherent vortices in two-dimensional turbulence induce far-field effects that stabilize vorticity filaments and inhibit the generation of new vortices. We show that the large-scale energy sink often included in numerical simulations of statistically stationary two-dimensional turbulence reduces the stabilizing role of the vortices, leading to filament instability and to continuous formation of new coherent vortices. This counterintuitive effect sheds new light on the mechanisms responsible for vortex formation in forced-dissipated two-dimensional turbulence, and it has significant impact on the temporal evolution of the vortex population in freely decaying turbulence. The time dependence of vortex statistics in the presence of a large-scale energy sink can be approximately described by a modified version of the scaling theory developed for small-scale dissipation.     

A study on turbulence modulation via an analysis of turbulence anisotropy-invariants

We investigate the turbulence modulation by particles in a turbulent two-phase channel flow via an analysis of turbulence anisotropy-invariants. The fluid turbulence is calculated by a large eddy simulation with a point-force two-way coupling model and particles are tracked by the Lagrangian trajectory method. The channel turbulence follows the two-component turbulence state within the viscous sub-layer region and outside the region the turbulence tends to follow the right curve of the anisotropy-invariant....     

Effect of spherical aberration on scintillations of Gaussian beams in atmospheric turbulence

The effect of spherical aberration on scintillations of Gaussian beams in weak, moderate and strong turbulence is studied using numerical simulation method. It is found that the effect of the negative spherical aberration on the on-axis scintillation index is quite different from that of the positive spherical aberration. In weak turbulence, the positive spherical aberration results in a decrease of the on-axis scintillation index on propagation, but the negative spherical aberration results in an increase of the on-axis scintillation index when the propagation distance is not large. In particular, in weak turbulence the negative spherical aberration may cause peaks of the on-axis scintillation index, and the peaks disappear in moderate and strong turbulence, which is explained in physics. The strong turbulence leads to less discrepancy among scintillations of Gaussian beams with and without spherical aberration.     

Interaction of solid particles with a tangle of vortex filaments in a viscous fluid

Homogeneous isotropic turbulence consists of coherent filamentary vortex structures superimposed to a more incoherent background. The question which we address is the effect of these structures on the dynamics of small, neutrally buoyant solid particles. Rather than generating the turbulence by direct numerical simulation (DNS) of the Navier-Stokes equations, we use a model of turbulence based entirely on viscous vortex filaments which interact via inertial forces and reconnect with each other. Using this model, we show that solid particles can become trapped around vortex filaments, something difficult to achieve with DNS. Unlike most studies, we have not neglected inviscid inertial effects. By comparing the Stokes, local, and convective components of the particle's acceleration, we also show that the convective part clearly identifies the trapping.     

Instability of a charged layer of a viscous liquid on the surface of a solid spherical core

The dispersion relation for the spectrum of capillary waves of a spherical layer of a viscous liquid coating a solid spherical core with a layer of finite thickness is introduced and analyzed. It is shown that the existence of two mechanisms for the viscous dissipation of the energy of the capillary-wave motions of the liquid, viz., damping in the bulk of the layer and on the solid core, leads to restriction of the spectrum of the realizable capillary waves of the liquid on both the high-and low-mode sides. At a fixed value of the system charge which is supercritical for the first several capillary modes, the maximum growth rates in the case of a small solid core are possessed by modes from the middle of the band of unstable modes, while in thin liquid layers the highest of the unstable modes have the largest growth rates. This points out differences in the realization of the instability of the charged surface of the spherical layer for small and large relative sizes of the solid core. Zh. Tekh. Fiz. 67, 8–13 (September 1997)     

On clustering of aerosol particles in homogeneous turbulent shear flows

The objective of this paper is to present a model for predicting clustering of aerosol particles in uniformly sheared turbulent flows laden with small heavy particles. The background of the model for predicting clustering is based on a kinetic equation for the two-point probability density function of the relative velocity distribution of two particles. The effect of clustering of particles in homogeneous turbulent shear flows is demonstrated and compared with known results of direct numerical simulations. It is shown that the universality of the clustering process can take place if the characteristic cluster size is smaller than the shear scale.     

Direct numerical simulation study of the interaction between the polymer effect and velocity gradient tensor in decaying homogeneous isotropic turbulence

Direct numerical simulation of decaying homogeneous isotropic turbulence (DHIT) of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase "strain generation resistance" and "vorticity generation resistance", i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.