Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics

This paper attempts to unravel any relations that may exist between turbulent shear flows and statistical mechanics through a detailed numerical investigation in the simplest case where both can be well defined. The flow considered for the purpose is the two-dimensional (2D) temporal free shear layer with a velocity difference Delta U across it, statistically homogeneous in the streamwise direction (x) and evolving from a plane vortex sheet in the direction normal to it (y) in a periodic-in-x domain L x +/-infinity. Extensive computer simulations of the flow are carried out through appropriate initial-value problems for a ``vortex gas'' comprising N point vortices of the same strength (gamma = L Delta U/N) and sign. Such a vortex gas is known to provide weak solutions of the Euler equation. More than ten different initial-condition classes are investigated using simulations involving up to 32 000 vortices, with ensemble averages evaluated over up to 10(3) realizations and integration over 10(4)L/Delta U. The temporal evolution of such a system is found to exhibit three distinct regimes. In Regime I the evolution is strongly influenced by the initial condition, sometimes lasting a significant fraction of L/Delta U. Regime III is a long-time domain-dependent evolution towards a statistically stationary state, via ``violent'' and ``slow'' relaxations P.-H. Chavanis, Physica A 391, 3657 (2012)], over flow time scales of order 10(2) and 10(4)L/Delta U, respectively (for N = 400). The final state involves a single structure that stochastically samples the domain, possibly constituting a ``relative equilibrium.'' The vortex distribution within the structure follows a nonisotropic truncated form of the Lundgren-Pointin (L-P) equilibrium distribution (with negatively high temperatures; L-P parameter lambda close to -1). The central finding is that, in the intermediate Regime II, the spreading rate of the layer is universal over the wide range of cases considered here. The value (in terms of momentum thickness) is 0.0166 +/- 0.0002 times Delta U. Regime II, extensively studied in the turbulent shear flow literature as a self-similar ``equilibrium'' state, is, however, a part of the rapid nonequilibrium evolution of the vortex-gas system, which we term ``explosive'' as it lasts less than one L/Delta U. Regime II also exhibits significant values of N-independent two-vortex correlations, indicating that current kinetic theories that neglect correlations or consider them as O(1/N) cannot describe this regime. The evolution of the layer thickness in present simulations in Regimes I and II agree with the experimental observations of spatially evolving (3D Navier-Stokes) shear layers. Further, the vorticity-stream-function relations in Regime III are close to those computed in 2D Navier-Stokes temporal shear layers J. Sommeria, C. Staquet, and R. Robert, J. Fluid Mech. 233, 661 (1991)]. These findings suggest the dominance of what may be called the Kelvin-Biot-Savart mechanism in determining the growth of the free shear layer through large-scale momentum and vorticity dispersal.

Effect of angle of incidence on mixed convective wake dynamics and heat transfer past a square cylinder in cross flow at Re=100

In this paper, a numerical investigation is performed to study the mixed convective flow and heat transfer characteristics past a square cylinder in cross flow at incidence. Utilizing air (Pr = 0.71) as an operating fluid, computations are carried out at a representative Reynolds number (Re) of 100. Angles of incidences are varied as, 0 degrees <= alpha <= 45 degrees. Effect of superimposed positive and negative cross-flow buoyancy is brought about by varying the Richardson number (RI) in the range -1.0 <= Ri <= 1.0. The detail features of flow topology and heat transport are analyzed critically for different angles of incidences. The thermo fluidic forces acting on the cylinder during mixed convection are captured in terms of the drag (C-D), lift (C-L), and moment (C-M) coefficients. The results show that the lateral width of the cylinder wake reduces with increasing alpha and the isotherms spread out far wide. In the range 0 degrees < alpha < 45 degrees, C-D reduces with increasing Ri. The functional dependence of C-M with Ri reveals a linear relationship. Thermal boundary layer thickness reduces with increasing angle of incidences. The global rate of heat transfer from the cylinder increases with increasing alpha. (C) 2014 Elsevier Ltd. All rights reserved.

Effect of H-2/CO Composition on Extinction Strain Rates of Counterflow Syngas Flames

This work presents a detailed experimental and numerical investigation of the effect of H-2/CO composition on extinction characteristics of premixed and nonpremixed syngas flames. Experimental measurements of local and global extinction strain rates in counterflow diffusion flames have been reported at atmospheric pressure for six different compositions of syngas fuel. The concentration of H-2 was varied from 5 to 20% with a 3% increment, and correspondingly, CO was decreased from 35 to 20% in steps of 3%. Particle imaging velocimetry has been used to determine the local extinction strain rates. Local extinction strain rates increased with an increase in the H-2/CO ratio in both nonpremixed and premixed flames. The predicted extinction strain rates for both nonpremixed and premixed counterflow flames using five different mechanisms available in the literature were compared with measurements. The Davis H-2/CO and Ranzi H-2/CO mechanisms predicted extinction strain rates within 10% of experimental values irrespective of the H-2/CO ratio. In the nonpremixed case, the Cl mechanism by Li et al., GRI 3.0, and the Ranzi H-2/CO mechanism predicted extinction strain rates well for low H-2/CO ratios (from 5:35 to 14:26) but deviated from experiments for higher H-2/CO values (17:23 and 20:20). In addition to kinetics, preferential diffusion effects were found to affect the reaction zone significantly and create distinct localized reaction zone structures in nonpremixed flames, which could contribute to discrepancies in extinction predictions.

Modeling of the non-isothermal liquid droplet impact on a heated solid substrate with heterogeneous wettability

A comprehensive numerical investigation on the impingement and spreading of a non-isothermal liquid droplet on a solid substrate with heterogeneous wettability is presented in this work. The time-dependent incompressible Navier-Stokes equations are used to describe the fluid flow in the liquid droplet, whereas the heat transfer in the moving droplet and in the solid substrate is described by the energy equation. The arbitrary Lagrangian-Eulerian (ALE) formulation with finite elements is used to solve the time-dependent incompressible Navier-Stokes equation and the energy equation in the time-dependent moving domain. Moreover, the Marangoni convection is included in the variational form of the Navier-Stokes equations without calculating the partial derivatives of the temperature on the free surface. The heterogeneous wettability is incorporated into the numerical model by defining a space-dependent contact angle. An array of simulations for droplet impingement on a heated solid substrate with circular patterned heterogeneous wettability are presented. The numerical study includes the influence of wettability contrast, pattern diameter, Reynolds number and Weber number on the confinement of the spreading droplet within the inner region, which is more wettable than the outer region. Also, the influence of these parameters on the total heat transfer from the solid substrate to the liquid droplet is examined. We observe that the equilibrium position depends on the wettability contrast and the diameter of the inner surface. Consequently. the heat transfer is more when the wettability contrast is small and/or the diameter of inner region is large. The influence of the Weber number on the total heat transfer is more compared to the Reynolds number, and the total heat transfer increases when the Weber number increases. (C) 2015 Elsevier Ltd. All rights reserved.

用环形激波聚焦实现爆轰波直接起爆的数值模拟

利用基元反应模型和有限体积法对环形激波在可燃气体中聚焦实现爆轰波直接起爆进行了数值模拟.研究结果表明,标准状态下的氢气-空气混合气体在马赫数为3.1以上的环形激波聚焦产生的高温高压区作用下会诱发可燃气体的直接起爆形成爆轰波,爆轰波与激波和接触间断相互作用产生了复杂的波系结构;爆轰波爆点位置在对称轴上并不是固定的点,而是随着初始激波马赫数的变化而发生移动;可燃气体初始温度和压力对起爆临界马赫数都有影响,但是初始温度的影响大得多.

爆轰波平掠惰性气体界面及其解耦现象的数值研究

采用基元化学反应模型和迎风TVD格式,数值研究了爆轰波平掠惰性气体界面时的物理现象及其作用机制,并用点隐方法克服化学反应源项引起的计算刚性.数值结果显示,当爆轰波平掠过惰性气体界面时,形成了爆轰波、界面、透射激波以及稀疏波相互作用的现象.在高N2比例稀释的可燃混合气体情况下,当爆轰波平掠过特定惰性气体界面时,它与惰性气体界面相互作用产生的稀疏波可以导致爆轰波的解耦.

准定常强激波马赫反射波形的数值研究

应用DCD频散控制激波捕捉格式,求解二维、多组分、带有化学反应的Euler方程组,数值模拟了准定常强激波的马赫反射问题。研究结果表明:与经典马赫反射理论相比,在强激波条件下,激波诱导的气体分子振动激发和化学反应使马赫反射的三波点轨迹角变小、马赫杆高度变低、楔顶附体激波倾角变小;马赫杆的相对突出量随入射激波马赫数和楔角的增大而增大,而气体分子的振动、离解等真实气体效应能进一步加剧马赫杆的向前突出。

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

On the influence zone and the prediction of tensile strength of particulate polymeric composites

An intended numerical investigation is carried out. The results indicate that, even if a perfect adhesive bond is preserved between the particles and matrix materials, the two-phase element cell model is unable to predict the strength increment of the particulate polymeric composites (PPC). To explore the main reinforcing mechanism, additional microscopic experiment is performed. An ''influence zone'' was observed around each particle which is measured about 2 to 10 micrometers in thickness for a glass-polyethylene mixture. Then, an improved computational model is presented to include the ''influence zone'' effect and several mechanical behaviors of PPC are well simulated through this new model.

An analysis of the effects of symmetrical tilt grain boundaries on the plastic deformation

A numerical investigation on the simple polycrystals containing three symmetrical tilt grain boundaries (GBs) is carried out within the framework of crystal plasticity which precisely considers the finite deformation and finite lattice rotation as well as elastic anisotropy. The calculated results show that the slip geometry and the redistribution of stresses arising from the anisotropy and boundary constraint play an important role in the plastic deformation in the simple polycrystals. The stress level along GB is sensitive to the load level and misorientation, and the stresses along QB are distributed nonuniformly. The GB may exhibit a softening or strengthening feature, which depends on the misorientation angle. The localized deformation bands usually develop accompanying the GB plastic deformation, the impingement of the localized band on the GB may result in another localized deformation band. The yield stresses with different misorientation angles are favorably compared with the experimental results.

共用尾喷管多管脉冲爆震发动机数值模拟研究

采用基元反应模型和显式迎风TVD差分格式数值模拟方法，研究共用尾喷管多管脉冲爆震发动机（Pulse Detonation Engine，简称PDE）各爆震管之间相互影响。采用点隐算法解决化学反应引起的刚性问题，模拟了共用尾喷管内的流场，以及爆震波退化为激波遇到尾喷管收敛斜面反射及反射波向爆震管上游传播的过程。研究结果为多管PDE的共用尾喷管设计提供了理论基础。

后台阶下游床面冲刷过程数值模拟研究

以床面瞬时剪应力作为泥沙起动及输运的水动力机制,建立了结构物周围复杂流场下床面局部冲刷的数学模型。并应用大涡模拟方法对后台阶下游三维湍流流动进行数值模拟,得到台阶下游床面瞬时剪应力的分布规律。为了确定床面瞬时剪应力与泥沙上扬通量的关系,先应用数学模型对不同模型参数下,冲刷开始后5分钟时台阶下游床面形状进行试算。通过试算与实验结果的比较,确定床面瞬时剪应力与泥沙上扬通量关系中需要的模型参数。进一步对冲刷开始后30分钟内台阶下游床面演化规律进行模拟,模拟结果与实验结果相符合。

欠膨胀超声速射流不稳定性机理的数值研究

应用NND有限差分格式求解轴对称可压缩N-S方程,研究了不同驻室与环境压力比条件下欠膨胀超声速射流近场的失稳特性.计算结果表明欠膨胀超声速射流的失稳机制根据射流激波结构的特征可分为3种失稳模式:具有规则反射激波结构和单一剪切层特征的射流不稳定性;带有马赫反射激波结构和双剪切层特征的射流不稳定性;具有弯曲马赫杆和高度欠膨胀射流的不稳定性.对于欠膨胀超声速射流,沿射流方向重复出现拟周期性的射流激波结构是射流稳定发展的特征,这种射流激波结构的消失是射流开始失稳的标志.

散心柱面胞格爆轰演化数值研究

采用有限体积方法,在自适应非结构网格上求解二维含化学反应Euler方程,数值研究了柱面胞格爆轰波演化现象.化学反应计算采用单步可逆总包反应模型.数值结果演示了散心柱面胞格爆轰波演化过程中胞格结构的分裂现象,获得了与实验结果定性一致的结果.胞格结构的分裂演化在点火区近场和远场显示了不同的特点,其中爆轰波传播过程中波阵面当地曲率的变化是控制胞格分裂演化行为的关键因素.数值结果也显示胞格结构的分裂现象来自于爆轰波前锋结构中横波的自组织行为,即沿爆轰波波面传播的小扰动发展成为横波的过程,这种现象与胞格爆轰波的不稳定性密切相关.

一维过驱动爆轰波形成的数值研究

利用有限速率的基元反应模型对一维过驱动爆轰波的形成过程进行数值模拟．研究表明，在上游高温、高压、高速来流作用下首先会形成一道强激波，其波面方存在诱导区和放热区，然后诱导区和放热区界面会在来流扰动的作用下发生失稳，经过复杂的波系运动过程形成过驱动爆轰波．通过对不同初始条件下界面失稳过程的模拟和分析，研究了混合气体的组元、温度，来流的压力、温度、速度对过驱动爆轰波形成的影响．