Fractals and Scaling in Fracture Induced by Microcrack Coalescence

A numerical model is proposed to simulate fracture induced by the coalescence of numerous microcracks, in which the condition for coalescence between two randomly nucleated microcracks is determined in terms of a load-sharing principle. The results of the simulation show that, as the number density of nucleated microcracks increases, stochastic coalescence first occurs followed by a small fluctuation, and finally a newly nucleated microcrack triggers a cascade coalescence of microcracks resulting in catastrophic failure. The fracture profiles exhibit self-affine fractal characteristics with a universal roughness exponent, but the critical damage threshold is sensitive to details of the model. The spatiotemporal distribution of nucleated microcracks in the vicinity of critical failure follows a power-law behaviour, which implies that the microcrack system may evolve to a critical state.

Frequency characteristics and dynamical behaviors of self-modulation in vertical-cavity surface-emitting lasers

The frequency characteristics of a VCSEL with a quarter-wave plate (QWP) and an external reflector are investigated with the translation matrix of the vectorial field. Two series of eigenmode with a shift of half the free spectrum range are linearly polarized, respectively, along the neutral axes of QWP. We also numerically explore the polarization self-modulation phenomenon by using a vectorial laser equation and considering the inhomogeneous broadening of the gain medium. If the external cavity is so short that the shift is bigger than the homogeneous broadening, two stable longitudinal modes oscillate, respectively, on the neutral axes of QWP because they consume different carriers. With a long external cavity, the competition of the modes for the common carriers causes the intensity fluctuation of the modes with a period of one round-trip time of the external cavity.

水位变化引起分层边坡滑坡的实验研究

通过对分层的边坡在水位变化时滑坡的模拟实验,考察了分层坡体的滑坡模式、坡体变形、破坏和渗流引起的滑坡,重点考察了水位涨落速度对坡体稳定的影响,以及坡面从产生张拉裂缝直到形成滑面的整个过程,并对这类滑坡中的现象给出了定性解释.最后用有限元对实验坡体进行了应力和位移的静力场分析,计算结果与实验结果基本一致.

Fluid-Solid Interaction in Particle-Laden Flows

Liu Qingquan, Singh V.P

下倾管段塞流液塞频率波动的非线性分析

利用非线性分析技术中的分形理论,在长24.73 m、内径0.05 m的小型气液两相流实验装置上对下倾管空气-水段塞流中的液塞频率波动特性进行了研究.结果表明,液塞频率的波动是对初始条件敏感的混沌振荡,遵循分形统计规律,具有持久性.折算液速小时,液塞频率波动的长程相关性随着混合速度的增大而减弱,液塞频率波动对初始条件的敏感程度增强,折算液速较大时则相反.管线倾角越大,液塞频率对初始条件的敏感程度受混合速度的影响越小.折算液速和混合速度均较大时,液塞频率的混沌程度受管线倾角的影响较小.

Simulation of Coal Combustion by AUSM Turbulence-Chemistry Char Combustion Model and a Full Two-Fluid Model

An algebraic unified second-order moment (AUSM) turbulence-chemistry model of char combustion is introduced in this paper, to calculate the effect of particle temperature fluctuation on char combustion. The AUSM model is used to simulate gas-particle flows, in coal combustion in a pulverized coal combustor, together with a full two-fluid model for reacting gas-particle flows and coal combustion, including the sub-models as the k-epsilon-k(p) two-phase turbulence niodel, the EBU-Arrhenius volatile and CO combustion model, and the six-flux radiation model. A new method for calculating particle mass flow rate is also used in this model to correct particle outflow rate and mass flow rate for inside sections, which can obey the principle of mass conservation for the particle phase and can also speed up the iterating convergence of the computation procedure effectively. The simulation results indicate that, the AUSM char combustion model is more preferable to the old char combustion model, since the later totally eliminate the influence of particle temperature fluctuation on char combustion rate.

The Interaction Between Shock Waves and Solid Spheres Arrays in a Shock Tube

When a shock wave interacts with a group of solid spheres, non-linear aerodynamic behaviors come into effect. The complicated wave reflections such as the Mach reflection occur in. the wave propagation process. The wave interactions with vortices behind each sphere's wake cause fluctuation in the pressure profiles of shock waves. This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres. A schlieren photography was applied to visualize the various shock waves passing through solid spheres. Pressure measurements were performed along different downstream positions. The experiments were conducted in both rectangular and circular shock tubes. The data with respect to the effect of the sphere array, size, interval distance, incident Mach number, etc., on the shock wave attenuation were obtained.

Probe for Measurements of Density/Conductivity in Flows of Conducting Fluids

A probe utilizing the bipolar pulse method to measure the density of a conducting fluid has been developed. The probe is specially designed such that the concentration of a stream tube can be sampled continuously. The density was determined indirectly from the measurement of solution conductivity. The probe was calibrated using standard NaCl solutions of varying molarity and was able to rapidly determine the density of a fluid with continuously varying conductance. Measurements of the conductivity profiles, corresponding density profiles, and their fluctuation levels are demonstrated in a channel flow with an electrolyte injected from a slot in one wall.

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

Numerical Study Of Heat Transfer Mechanism In Turbulent Supercritical Co2 Channel Flow

Direct numerical simulation (DNS) of supercritical CO2 turbulent channel flow has been performed to investigate the heat transfer mechanism of supercritical fluid. In the present DNS, full compressible Navier-Stokes equations and Peng-Robison state equation are solved. Due to effects of the mean density variation in the wall normal direction, mean velocity in the cooling region becomes high compared with that in the heating region. The mean width between high-and low-speed streaks near the wall decreases in the cooling region, which means that turbulence in the cooling region is enhanced and lots of fine scale eddies are created due to the local high Reynolds number effects. From the turbulent kinetic energy budget, it is found that compressibility effects related with pressure fluctuation and dilatation of velocity fluctuation can be ignored even for supercritical condition. However, the effect of density fluctuation on turbulent kinetic energy cannot be ignored. In the cooling region, low kinematic viscosity and high thermal conductivity in the low speed streaks modify fine scale structure and turbulent transport of temperature, which results in high Nusselt number in the cooling condition of the supercritical CO2.

Thermocapillary Flows In Liquid Bridges Of Molten Tin With Small Aspect Ratios

Numerical simulations were conducted to study thermocapillary flows in short half-zone liquid bridges of molten tin with Prandtl number Pr = 0.009, under ramped temperature difference. The spatio-temporal structures in the thermocapillary flows in short half-zone liquid bridges with aspect ratios As = 0.6, 0.8, and 1.0 were investigated. The first critical Marangoni numbers were compared with those predicted by linear stability analyses (LSA). The second critical Marangoni numbers for As = 0.6 and 0.8 were found to be larger than that for As = 1.0. The time evolutions of the thermocapillary flows exhibited unusual features such as a change in the azimuthal wave number during the three-dimensional stationary (non-oscillating) flow regime, a change in the oscillation mode during the three-dimensional oscillatory flow regime, and the decreasing and then increasing of amplitudes in a single oscillation mode. The effects of the ramping rate of the temperature difference on the flow modes and critical conditions were studied as well. In this paper, the experimental observability of the critical conditions was also discussed. (C) 2008 Elsevier Inc. All rights reserved.

Wind Tunnel Experimental Investigation Of Sand Velocity In Aeolian Sand Transport

Sand velocity in aeolian sand transport was measured using the laser Doppler technique of PDPA (Phase Doppler Particle Analyzer) in a wind tunnel. The sand velocity profile, probability distribution of particle velocity, particle velocity fluctuation and particle turbulence were analyzed in detail. The experimental results verified that the sand horizontal velocity profile can be expressed by a logarithmic function above 0.01 in, while a deviation occurs below 0.01 m. The mean vertical velocity of grains generally ranges from -0.2 m/s to 0.2 m/s, and is downward at the lower height, upward at the higher height. The probability distributions of the horizontal velocity of ascending and descending particles have a typical peak and are right-skewed at a height of 4 turn in the lower part of saltation layer. The vertical profile of the horizontal RMS velocity fluctuation of particles shows a single peak. The horizontal RMS velocity fluctuation of sand particles is generally larger than the vertical RMS velocity fluctuation. The RMS velocity fluctuations of grains in both horizontal and vertical directions increase with wind velocity. The particle turbulence intensity decreases with height. The present investigation is helpful in understanding the sand movement mechanism in windblown sand transport and also provides a reference for the study of blowing sand velocity. (C) 2007 Elsevier B.V All rights reserved.

Effects Of Subgrid-Scale Modeling On Lagrangian Statistics In Large-Eddy Simulation

The application of large-eddy simulation (LES) to turbulent transport processes requires accurate prediction of the Lagrangian statistics of flow fields. However, in most existing SGS models, no explicit consideration is given to Lagrangian statistics. In this paper, we focus on the effects of SGS modeling on Lagrangian statistics in LES ranging from statistics determining single-particle dispersion to those of pair dispersion and multiparticle dispersion. Lagrangian statistics in homogeneous isotropic turbulence are extracted from direct numerical simulation (DNS) and the LES with a spectral eddy-viscosity model. For the case of longtime single-particle dispersion, it is shown that, compared to DNS, LES overpredicts the time scale of the Lagrangian velocity correlation but underpredicts the Lagrangian velocity fluctuation. These two effects tend to cancel one another leading to an accurate prediction of the longtime turbulent dispersion coefficient. Unlike the single-particle dispersion, LES tends to underestimate significantly the rate of relative dispersion of particle pairs and multiple-particles, when initial separation distances are less than the minimum resolved scale due to the lack of subgrid fluctuations. The overprediction of LES on the time scale of the Lagrangian velocity correlation is further confirmed by a theoretical analysis using a turbulence closure theory.

Thermal fatigue on pistons induced by shaped high power laser. Part I: Experimental study of transient temperature field and temperature oscillation

Thermal fatigue behavior is one of the foremost considerations in the design and operation of diesel engines. It is found that thermal fatigue is closely related to the temperature field and temperature fluctuation in the structure. In this paper, spatially shaped high power laser was introduced to simulate thermal loadings on the piston. The incident Gaussian beam was transformed into concentric multi-circular beam of specific intensity distribution with the help of diffractive optical element (DOE), and the transient temperature fields in the piston similar to those under working conditions could be achieved by setting up appropriate loading cycles. Simulation tests for typical thermal loading conditions, i.e., thermal high cycle fatigue (HCF) and thermal shock (or thermal low cycle fatigue, LCF) were carried out. Several important parameters that affect the transient temperature fields and/or temperature oscillations, including controlling mode, intensity distribution of shaped laser, laser power, temporal profile of laser pulse, heating time and cooling time in one thermal cycle, etc., were investigated and discussed. The results show that as a novel method, the shaped high power laser can simulate thermal loadings on pistons efficiently, and it is helpful in the study of thermal fatigue behavior in pistons. (C) 2007 Elsevier Ltd. All rights reserved.

Numerical Study on Flow Field and Temperature Distribution in Growth Process of 200 mm Czochralski Silicon Crystals

The melt flow and temperature distribution in a 200 mm silicon Czochralski furnace with a cusp magnetic field was modeled and simulated by using a finite-volume based FLUTRAPP ( Fluid Flow and Transport Phenomena Program) code. The melt flow in the crucible was focused, which is a result of the competition of buoyancy, the centrifugal forces caused by the rotations of the crucible and crystal, the thermocapillary force on the free surfaces and the Lorentz force induced by the cusp magnetic field. The zonal method for radiative heat transfer was used in the growth chamber, which was confined by the crystal surface, melt surface, crucible, heat shield, and pull chamber. It was found that the cusp magnetic field could strength the dominant counter-rotating swirling flow cell in the crucible and reduce the flow oscillation and the pulling-rate fluctuation. The fluctuation of dopant and oxygen concentration in the growing crystal could thus be smoothed.