Experimental study on the P wave velocity in rocks from lower crust and crust-mantle transitional zone beneath the Hannuoba

Cenozoic basalt-borne mafic granulite-facies plagioclase pyroxenite and eclogite-facies garnet pyroxenite xenoliths from the Hannuoba, as well as nearby Archean terrain granulites, are selected for the experimental study on the P wave velocity at high temperature and high pressure in order to reveal the present-day compositional features for the lower crust and crust-mantle transitional zone. Results show that mafic xenoliths have high Vp (7.0～8.0 km/s), in contrast, the Archean terrain granulites have low Vp (<7.0 km/s). High Vp mafic xenoliths can represent the present-day compositional features for the lower crust and crust-mantle transitional zone beneath the Hannuoba. This provides new evidence for the crust vertical growth and the formation of the crust-mantle transitional zone resulting from the magma underplating. Low Vp Archean granulite still remains the characteristics of the early lower crust.     

Kinetic modeling of dilute solid-liquid two-phase flows with inelastic collisions

A kinetic model was presented for dilute solid-liquid two-phase flows with inelastic collisions by modeling the inelastic collisions with the revised BGK model （Santos and Astillero, 2005） and particle turbulence interactions with the Fokker-Planck operator. The formulated model kinetic equation was solved with the Chapman-Enskog method and the obtained approximate solution was further adopted to derive the constitutive relationships for the conservation equations of the particle phase. The new constitutive relationships would be suitable for the study on dilute solid-liquid two-phase flows such as sediment-laden flows in open channels or rivers.     

低浓度颗粒流Boltzmann方程的同伦分析方法解

同伦分析方法(homotopy analysis method, HAM)是求解强非线性问题的有力手段. 针对颗粒流的动理学理论中的非线性微分积分方程——?Boltzmann方程, 采用 HAM方法选取局域Maxwell速度分布函数作为初始猜测解, 得到了低浓度颗粒流的Boltzmann方程的一阶近似解, 与传统的Chapman-Enskog方法得到的一阶近似解表达式的结构一致, 初步显示了HAM方法求解Boltzmann方程的有效性, 为一般Boltzmann方程的HAM方法求解奠定了基础.     

Influence of gravity on narrow input forced drainage in 2D liquid foams

Liquid foam is a dense packing of gas bubbles in a small amount of liquid containing surfactants or other surface-active macromolecules, which is one of the highly organized materials and possesses hallmark rheological behaviour of soft matters. Forced foam drainage is the flow of constantly inputted liquid through the network of interstitial channels between bubbles under actions of gravity and capil-larity. This process involves two mechanisms: minimal viscous flow dissipation of liquid and minimal surface energy of bubbles. For constant surfactant solution, viscous dissipation usually varies with gravity. This work reports simulations of 2D forced foam drainage with narrow input in a Hele-Shaw cell under 8 different gravities, g, ranging from 9.8 to 0 ms?2. The spread of liquid both vertical due to gravity action, and horizontal due to capillary suction, is recorded over time. Positions of drainage wave fronts in both directions with time are found to be well described in the power law form, and the exponents are 0.536 5.29×10-3g and 0.479?7.27×10-3g, respectively, while the sum is close to a constant of 1.015 which is independent of gravity. For g=9.8 ms-2, the calculated exponents are in good agreement with experimental results by Hutzler et al. and Wang.     

Crack spacing of unsaturated soils in the critical state

The cracking mechanism of unsaturated soils due to evaporation is poorly understood, and the magnitude of crack spacing is usually hard to estimate. In this work, cracks were postulated to occur succedently rather than simultaneously, that is, secondary cracks appear after primary cracks as evaporation continues. Formulae of the secondary crack spacing and secondary trend crack spacing were then derived after stress analysis. The calculated spacing values were consistent with the published experimental data. Meanwhile, the effect of the Poisson ratio on the crack spacing was analyzed, which showed that the magnitude of crack spacing was proportional to the Poisson ratio in the range of [0.30, 0.35].     

Microscopic study on stress-strain relation of granular materials

A biaxial shearing test on granular materials is numerically simulated by distinct element method （DEM）. The evolution of the microstructures of granular materials during isotropic compression and shearing is investigated, on which a yield function is derived. The new yield function has a similar form as the one used in the modified Cam-clay model and explains the yield characteristics of granular materials under the isotropic compression and shear process through the change of the contact distribution N（θ） defining the contacts at particle contact angle θ.     

An analytical solution to Boltzmann equation of dilute granular flow with homotopy analysis method

The homotopy analysis method （HAM）, as a new mathematical tool, has been employed to solve many nonlinear problems. As a fundamental equation in non-equilibrium statistical mechanics, the Boltzmann integro-differential equation （BE） describing the movement of particles is of strong nonlinearity. In this work, HAM is preliminarily applied to dilute granular flow which is relatively simple. By choosing the Maxwell velocity distribution function as the initial solution, the concrete expression of the first-order approximate solution to BE with collision term being the BGK model is given. Furthermore it is consistent with the solution using Chapman-Enskog method but does not rely on little parameters.     

Foam drainage wave coalescing and its energy evolution

Liquid foam is a dense packing of gas bubbles in a small amount of surfactant solution. Liquid drains out of foams until equilibrium is reached due to the compromise between gravity and capillarity, which greatly affects the stability of foam. Based on a series of work on foam structure and drainage we conducted previously, this paper reports the results on coalescence of an original forced drainage wave at a low flow rate with subsequent drainage waves with higher flow rates. The evolutions of viscous energy and surface energy during the process of coalescence are theoretically analyzed.     

Numerical study of flow pattern modulation in a vertical phase separation condenser tube

The passive phase separation concept was proposed to modulate flow patterns for heat transfer enhancement. By the flow pattern modulation, the gas tends to be near the wall and the liquid tends to be in the tube core. Experiment has been performed to verify the fresh idea and the flow pattern modulation mechanism was analyzed qualitatively. This paper focuses on the numerical simulation of the bubble dynamics for a single bubble in the vertical phase separation condenser tube to quantitatively explore the flow pattern mechanism, based on a multiscale grid system and the volume-of-fluid (VOF) method. It is found that: (1) the modulated liquid film thickness can be decreased by 70% compared to that in the bare tube region; (2) the modulated bubble traveling velocity can be doubled, causing the increased liquid velocity and velocity gradient in the annular region to weaken the fluid boundary layer; (3) the significantly increased bubble traveling velocity in the annular region promotes the mass and momentum exchange between the annular region and the core region, and yields the self-sustained pulsating flow in the core region. The above three factors are benefit for the performance improvement of the heat transfer facilities.     

考虑非弹性碰撞的低浓度固液两相流动理学模型

用修正的BGK模型模拟粒间非弹性碰撞效应, 用Fokker-Planck扩散算子描述湍流-颗粒作用, 建立了低浓度固液两相流颗粒相的模型动理学方程和宏观水动力学方程组. 运用 Chapman-Enskog迭代法获得动理学方程的二阶近似解, 建立了颗粒相脉动应力和脉动能传导通量的显式本构关系. 建立的动理学模型在颗粒近乎弹性条件下简化为已有的模型, 为固液两相流模拟提供了一个实用模型.