断面分形研究中的几个问题

本文讨论了分形几何应用于断裂研究的几个基本问题．主要内容包括断面的分形特征及分维测量,分维与宏观力学性能（如断裂韧性等）的关系,分形断裂模型及分形断裂的物理机理．      

分形力学研究进展

在分形空间考虑的力学称为分形力学．本文讨论了分形力学的数学基础,在分形空间力学量的定义,力学定律的适用性．简要介绍了目前分形力学研究领域已取得的一些初步成果．     

湍流模化的现状及发展趋势

本文讨论了湍流模化研究的发展现状,提出了今后湍流模式的可能改进途径。根据一组湍流封闭假定得到了各种2阶湍流模式,如Reynolds应力模式(RSM),代数应力模式(k-ε-A)及涡粘性模式(k-ε-E)。以自由剪切流、空腔流及通过偏心槽的流动为例作出了预报。虽然至今还不存在一个完备湍流模式,但2阶湍流模式已经具备了某些预报能力。湍流模化的不完备性可能要归咎于各向同性耗散和单湍流尺度等假定的不适当。利用多重湍流尺度概念,包括利用湍流涡的分维,可以改善湍流的预报。     

锡基巴氏合金磨损表面的分形与磨损率

利用结构函数分析法研究了滑动摩擦学系统中金属磨损表面轮廓线的分形特性。结果表明：磨损表面轮廓线在小于Ｓｍ的尺度上具有分形结构。采用结构函数法可以方便地确定粗糙表面轮廓线的分形参数，即垂直于滑动方向上磨损表面轮廓线的分维Ｄ可作为磨损表面分维的特征值，它与金属磨损率的变化有着密切的关系，最佳分维Ｄｏｐｔ值对应于材料的最低磨损率。     

气流式喷嘴雾化过程的分形特征及液滴分裂模型

研究了在雾化等过程中液滴粒度分形特征，提出了—个液滴分裂服从均匀分布概率的数学模型，通过计算机模拟，计算出同代液滴的结构分维和特征分维，并用对异代液滴计算得到的结果，验证粒度分布中的结构分维，结果吻合很好．实验测定了液滴分裂的分形维数，与模拟结果相符。     

微孔洞型的分形断裂理论初探

初步研究并提出微孔洞型的分形断裂理论，建立了主裂纹与微孔洞汇合的分形模型，并以此为基础确定了分维Ｄ与连接区厚度Δ和孔洞平均半径ｒ之间的关系，推导了微孔洞与主裂纹连接的能量准则，讨论了分维与断裂韧性之间的关系。     

大理岩非分叉断裂的随机分形模型

本文建立了大理岩沿晶、穿晶及沿晶穿晶偶合断裂的随机分形模型，该模型能与大理岩的整体晶态结构自洽，且模型的分维值与测量值有很好的吻合。     

现代全球板块边界的分形特征

本文利用分形几何理论对现代全球板块边界进行了系统的分维值的测量与计算，总结出了离散介、聚敛介和转换边界的分形特征，并进一步论述了其所对应的板块边界几何复杂程度、发育程度、构造活动性和力学性质的相关性。     

完全发展的非对称槽道湍流的分形维数研究

湍流的分形维数刻画了湍流的统计正则性 ,本文利用正交子波变换对完全发展的非对称槽道湍流脉动速度的实验数据进行了分析研究。文中首先将脉动速度信号分解到各个尺度 ,然后利用正则法和盒子法两种方法计算了不同尺度信号的分形维数 ,着重于考虑分形维数的变化趋势。研究结果表明 :(1 )随着信号分解尺度的增加 ,速度信号的低频部分和高频部分的维数都逐渐减小 ;(2 )逆输运现象对速度信号的分形维数没有本质的影响 ;(3)正则法计算得到的分形维数要略大于盒子法得到的分形维数     

二维和三维湍流的分形模型

<正> 1 引言 目前分形物体已广泛引入物理学和自然科学各种现象的分析中。湍流的几何形态特别需用“自相似”方法、而不是用“欧几里德”方法来研究。人们通常考虑的是均匀分形(即具有整体严格的膨胀不变性),但我们想引入自相似性仅在平均意义下保持的一个简单模型,     

粗糙表面的分形特征与分形表达研究

得用触针轮廓仪和数据采集系统对磨削和车削表面的粗糙轮廓曲线进行了测量，并就粗糙表面的分形特征作了分析与讨论，同时还提出了粗糙表面的特征粗糙度概念及其定义，并将其用表面粗糙度水平的表述。     

DNS of Fractal-Generated Turbulence

An innovative approach which combines high order compact schemes, Immersed Boundary Method and an efficient domain decomposition method is used to perform high fidelity Direct Numerical Simulations (DNS) of four spatially evolving turbulent flows, one generated by a regular grid and three generated by fractal square grids. The main results which we have been able to obtain from these simulations are the following: the vorticity field appears more clustered when generated by fractal square grids compared to a regular grid; fractal square grids generate higher vorticities and turbulence intensities than a regular grid; the flow holds clear geometrical imprints of the fractal grids far downstream, a property which could be used in the future for flow design, management and passive control; the DNS obtained with fractal grids confirmed the existence of two turbulent regions, one where the turbulence progressively amplifies closer to the grid (the production region) followed by one where the turbulence decays; the energy spectra of fluctuating turbulent velocities at various locations in the production region of the flow provide some information on how the turbulence is generated at the smallest scales first near the grid where the smallest wakes are dominant, followed by progressively smaller turbulent frequencies further downstream where progressively larger wakes interact.     

稳定分层流密度界面处湍流混合与分形结构

采用室内混合箱研究稳定分层流(上层淡水、下层盐水) 无剪切密度界面处的湍流混合与分形结构. 湍流通过浸没在盐水层中的振动格栅产生, 密度界面结构通过在盐水层中添加荧光剂或染料可视化, 共进行12 组实验. 实验观测并记录了:(1) 淡、盐水密度界面距混合箱底部的平均高程(h);(2) 淡、盐水层的密度(ρ₀,ρ), (3) 淡、盐水密度界面. 其中, 淡、盐水密度界面通过照片、录像进行记录. 观测结果用于计算:(1) 盐水层密度;(2) 卷挟速度, (3) 整体理查孙数(Ri_o), (4) 二维、三维密度界面, (5) 二维、三维密度界面的分形维度. 结果分析发现:(1) 湍流卷挟率随Rio 增大而减小, 并且满足Ri_o的-3=2 或-7=4 幂律;表明随着湍流强度的减弱, 混合的速度也越来越缓慢;(2) 二维密度界面分形维度大于1, 三维密度界面分形维度大于2;表明二维、三维密度界面存在分形结构;(3) 分形维度随Ri_o的增大而减小;表明随着湍流强度的减弱, 密度界面也越来越趋于光滑.      

分形力学的数学基础

在分形空间考虑的力学称为分形力学。由于分形理论的特点,分形力学的描述需要引入新的空间概念、新的数学手段和方法。本文从介绍空间、测度和维数入手,引入了分形空间,Ｂｅｓｏｖ空间和分形插值方法,进而介绍了在分形边界和分形体中力学量和力学定律的定义。      

Fractal-Generated Turbulence in Opposed Jet Flows

The opposed jet configuration presents a canonical geometry suitable for the evaluation of calculation methods seeking to reproduce the impact of strain and re-distribution on turbulent transport in reacting and non-reacting flows. The geometry has the advantage of good optical access and, in principle, an absence of complex boundary conditions. Disadvantages include low frequency flow motion at high nozzle separations and comparatively low turbulence levels causing bulk strain to exceed the turbulent contribution at small nozzle separations. In the current work, fractal generated turbulence has been used to increase the turbulent strain and velocity measurements for isothermal flows are reported with an emphasis on the axis, stagnation plane and the distribution of mean and instantaneous strain rates. Energy spectra were also determined. The instrumentation comprised hot-wire anemometry and particle image velocimetry with the flows to both nozzles seeded with 1  $\upmu$ m silicon oil droplets providing a relaxation time of ? 3 $\upmu$ s. It is shown that fractal grids increase the turbulent Reynolds number range from 48–125 to 109–220 for bulk velocities from 4 to 8 m/s as compared to conventional perforated plate turbulence generators. Low frequency motion of the order 10 Hz could not be completely eliminated and probability density functions were determined for the location of the stagnation plane. Results show that the fluctuation in the position of the stagnation plane is of the order of the integral length scale, which was determined to be 3.1±0.1 mm at the nozzle exits through the use of hot-wire anemometry. Flow statistics close to the fractal plate located upstream of the nozzle exit were also determined using a transparent glass nozzle.     

Langevin Dynamics Simulation of Transport and Aggregation of Soot Nano-particles in Turbulent Flows

The present paper uses Langevin dynamics (LD) to investigate the aggregation of soot nano-particles in turbulent flows. Interparticle forces are included, and the computation of the individual particles by LD is retained even after aggregate formation such that collision events and locations can be based on center-to-center particle distances without invoking any modelling assumptions of aggregate shape and/or collision frequency. We focus on the interactions between the specific hydrodynamic conditions and the particle properties and their effect on the resulting agglomerates’ morphologies. The morphology is characterized by the fractal dimension, D _f . Computations of particle aggregation in homogeneous isotropic turbulence and in shear flows dominated by counter-rotating vortices with a wide range of turbulence intensities and particle sizes indicate that the evolution of the agglomerates’ shapes can be adequately parameterized by the size of the agglomerates and the Knudsen and Péclet numbers, the latter being based on the smallest turbulence scales. The computations further suggest that the shapes of agglomerates of certain sizes are relatively independent of time and relatively insensitive to larger turbulence structures. The fractal dimensions are modelled as functions of radius of gyration, Kn and Pe. The fitted expressions show good agreement with the LD simulations and represent the entire growth process of the agglomerates. A direct comparison of selected aggregates with experimental data shows very good qualitative agreement. A thorough quantitative validation of the evolution of the computed aggregate characteristics is, however, presently hindered by the challenges for and therefore lack of suitable experiments under appropriately controlled conditions.     

Experimental analysis of liquid–gas interface at low Weber number: interface length and fractal dimension

The present paper reports an experimental investigation on atomizing liquid flows produced by simplified cavity nozzles. The Weber number being kept low, the sprays produced by these injectors depend on the liquid flow characteristics only, and more precisely, on the non-axial kinetic energy and of the turbulent kinetic energy at the nozzle exit. The investigation reported here concentrates on the characterization of liquid flows during atomization by measuring the spatial variation of the local interface length and of the local interface fractal dimension. Both parameters were found representative of the physics of atomization process: they depend on the characteristics of the flow issuing from the nozzle and they are related to the subsequent drop size distribution. The local interface length is representative of the amount of liquid–gas interface surface area, and is a function of both the non-axial and the turbulent kinetic energies at the nozzle exit. The fractal dimension is representative of the tortuosity of the liquid–gas interface and, as expected, is mainly related to the turbulent kinetic energy at the nozzle exit. As far as the drop size distribution is concerned, it is found that the local interface length at the instant of break-up determines a representative drop diameter of some kind, whereas the fractal dimension at the same instant controls the dispersion of the distribution.     

环形通道内湍流旋流流动的数值模拟

本文应用一种考虑湍流－旋流相互作用及湍流脉动各向异性的新的代数Ｒｅｙｎｏｌｄｓ应力模型,对环形通道内的湍流旋流流动进行了数值模拟,研究了改主为旋流流数,进口轴向速度及半径比等参数对环形通道内湍流流动的影响,以及对强化环形通道内传热的作用。     

Non-equilibrium turbulent phenomena in the ?ow over a backward-facing ramp

Non-equilibrium turbulence phenomena have raised great interests in recent years. Significant efforts have been devoted to non-equilibrium turbulence properties in canonical flows, e.g., grid turbulence, turbulent wakes, and homogeneous isotropic turbulence(HIT). The non-equilibrium turbulence in non-canonical flows, however, has rarely been studied due to the complexity of the flows. In the present contribution, a directnumerical simulation(DNS) database of a turbulent flow is analyzed over a backwardfacing ramp, the flow near the boundary is demonstrated, and the non-equilibrium turbulent properties of the flow in the wake of the ramp are presented by using the characteristic parameters such as the dissipation coefficient C and the skewness of longitudinal velocity gradient Sk, but with opposite underlying turbulent energy transfer properties. The equation of Lagrangian velocity gradient correlation is examined, and the results show that non-equilibrium turbulence is the result of phase de-coherence phenomena, which is not taken into account in the modeling of non-equilibrium turbulence. These findings are expected to inspire deeper investigation of different non-equilibrium turbulence phenomena in different flow conditions and the improvement of turbulence modeling.     

摩擦信号分形维数与载荷和速度的关系研究

在立式万能摩擦磨损试验机上对GCr15/45#钢摩擦副进行不同接触载荷和滑动速度下的摩擦磨损试验,对初始滑动距离1 000 m内的摩擦系数信号进行数据采集,运用结构函数测度方法对摩擦系数信号进行分形表征,计算不同载荷和速度下的分形维数,研究摩擦信号的分形维数随载荷和速度的变化规律.结果表明,摩擦系数信号具有显著的分形特征,其分形维数随载荷和速度而变化.在相同载荷下,分形维数随滑动速度增加而增大;在相同速度下,分形维数随着接触载荷增加而增大.磨损率与摩擦系数信号的分形维数正相关.