提高煤层气水平井玻璃钢管固井顶替效率技术研究

煤层气玻璃钢管固井可以有效的防止后期采煤作业时电火花和摩擦火花的产生,降低采煤作业瓦斯爆炸的风险.然而由于玻璃钢管的密度较低,固井时玻璃钢管在水平井眼内的位置及居中情况与钢制套管有较大差异,需要根据玻璃钢管固井的特点制定相应的顶替效率提高措施.根据水平段玻璃钢管固井顶替时的受力变形、居中度以及顶替界面形态分析,提出了针对煤层气水平井玻璃钢管固井的"本体悬浮、居中度优化、整体平直下偏心"三项顶替效率提高技术,从而保证顶替界面的最小掺混长度以及顶替界面的整体近似匀速移动,为煤层气水平井玻璃钢管固井参数设计提供了理论依据与方法.     

双材料接合半无限体三维矩形界面裂纹应力强度因子分析

基于体积力法,研究了双材料接合半无限体三维矩形界面裂纹的应力强度因子问题．在数值计算中,未知的体积力密度采用基本密度函数和多项式乘积的形式来近似,其中基本密度函数是根据界面裂纹应力的振荡奇异性来选取的．计算结果表明,基于本算法得到的数值结果其收敛精度和计算误差都是令人满意的．算例中,给出了应力强度因子随矩形形状及双材料参数的变化规律．     

热传导对气-液射流界面不稳定性的作用机理研究

研究了平面分层气-液射流在非线性温度分布条件下的界面不稳定性性质.考虑了气体的可压缩性、液体的粘性、以及气体热导率和密度随温度变化等事实.并应用正则模态方法将问题转化为四阶变系数常微分方程,用数值积分和多重打靶法对模型的空间模式进行了计算,研究了不稳定模态随各物理参量的变化趋势.计算表明模型所体现的不稳定性特征与其它模型的计算结果是一致的.同时计算还得出气体和液体的温差越小、雷诺数越大、热导率变大均将有利于液体射流有效雾化的结果.该结论与HJE.Co.Inc(Glens Falls,NY,USA)的实验数据是定性吻合的.     

线性密度分层流体中垂向湍流扩散的势能模型

本文研究在线性密度分层流体系统中垂向密度界面的无平均剪切湍流扩散规律,从分析湍流动能方程出发,提出一种湍流扩散的势能模型,得到湍流扩散距离随时间的变化以及无量纲扩散速率与当地Richardson数的关系.同时进行了实验检验,其结果与理论预测符合良好.     

重力对水平Bridgman生长系统中固液界面形状变化的影响

采用有限元方法和自动网格生成技术对水平Bridgman生长系统中的对流效应和相界面形状变化进行了研究 .结果表明 ,强烈的对流使得界面很深地凹向晶相 .在很小Ma数条件下 ,当重力水平大于 1 0 ^-2 g时 ,相界面随重力的增加而急剧扭曲 ;而如果重力小于 1 0^-3 g ,相界面则基本上为一平面 .另一方面 ,即使是在 1 0 ^-6 g的重力水平下 ,不同的生长速率仍然可能对界面形状有很大的影响 .     

准一维xPPP/yPA共聚物的激发态

建立了描述共聚物xPPP/yPA晶格及电子结构的紧束缚模型,在该模型的基础上计算了共聚物的基态及掺杂激发态的晶格结构和净电荷密度分布,并得出了激发态可能的形式. 两均聚物的配比及界面间耦合的强弱等对共聚物的掺杂激发态均有影响. 两均聚物的界面相当于一个能垒(energy barrier),耦合常数小时,界面能垒较高,电荷不易传输;反之,则界面能垒较低,电荷易于传输.     

三维无限接合体双材料多界面裂纹的超奇异微积分方程法

利用有限部积分的概念,导出了三维无限接合体中多个界面裂纹,在任意载荷作用下的超奇异微积分方程组.数值分析中,未知的位移间断采用基本分布函数和多项式乘积的形式来近似,其中基本分布函数是根据界而裂纹应力的振荡奇异性来选取的.作为典型算例,研究了存在两个矩形界面裂纹时,裂纹之间距离、裂纹形状及双材料弹性常数对应力强度因子的影响.计算表明,应力强度因子随裂纹间的距离的增大而减小.     

各向异性压电介质摩擦接触界面波动特性分析

应用Fourier(傅立叶)分析及奇异积分方程技术研究了弹性波与一般压电介质单侧接触界面的相互作用问题.以界面只产生滑移不分离的情况为例,分析了问题的求解思路和过程,给出了弹性波引起界面滑移或分离的条件.以六角晶系极化碳酸钡陶瓷材料和三角晶系石英材料为例,分析了不同材料摩擦接触界面对弹性波入射的不同反应,给出了不同的入射角及不同的外加压力和电场对界面的影响特性.界面产生滑移和分离时,问题的边界条件具有非线性,导致高频谐波出现,以石英材料为例分析了高频成分随外加条件的变化特性.     

金属泡沫材料压缩响应模式转变分析

金属泡沫材料的压缩响应是微结构相关的,低无序时以单一塌缩带的形核和扩展为主,高无序度时,主要是扩展能力很弱的弥散塌缩带形核所控制。基于考虑材料微结构Weibull分布的应变梯度塑性模型,探究了胞孔塑性屈曲时,相对强度改变和相对密度改变对变形模式转捩的影响。研究发现:当相对密度改变量为定值时,随相对强度改变量的增大,变形模式的转变在较低的无序度下发生。而强度改变量为定值时,相对密度改变量的变化对多孔材料压缩变形模式转变的临界无序度无确定的影响规律,但变形模式转捩点的应力水平随相对密度改变量的减小而下降。     

应用模糊综合评判方法识别低效循环井

在油田注水开发过程中,由于储层平面非均质性、流体非均质性及开发条件的影响,在平面上会出现注入水突进的情况.注水井中的注入水向不同方向驱油,推进往往是不均匀的,一般总有一个方向突进最快,且经过长期水洗之后,这个方向有可能发展成"水道",形成注入水的低效循环.建立了应用模糊综合评判方法识别低效循环井的数学模型,通过实例分析表明,运用综合评判方法识别低效循环井是一种客观有效的方法,该评价方法计算方便,易于操作和推广.     

Analysis of a modified two-lane lattice model by considering the density difference effect

In this paper, a modified lattice hydrodynamic model of traffic flow is proposed by considering the density difference between leading and following lattice for two-lane system. The effect of density difference on the stability of traffic flow is examined through linear stability analysis and shown that the density difference term can significantly enlarge the stability region on the phase diagram. To describe the phase transition of traffic flow, the Burgers equation and mKdV equation near the critical point are derived through nonlinear analysis. To verify the theoretical findings, numerical simulation is conducted which confirms that traffic jam can be suppressed efficiently by considering the density difference effect in the modified lattice model for two-lane traffic.     

Dynamically equilibrium shapes and directions of motion of ocean current rings

The dynamically equilibrium shapes of a uniform-density rotating mass of liquid (a ring) in the surface layer of a quiescent stratified ocean are determined. The examination is carried out in a plane tangential to the Earth, taking into account the vertical and horizontal projections of the angular velocity of its rotation. Exact solutions of the equations of motion of an ideal incompressibe fluid are obtained, making it possible, for a linearly stratified ocean, to determine the dynamic all equilibrium shape of the interfaces of water masses and the free boundaries of cyclonic and antocyclonic rings. These shapes comprise second-order surfaces inclined to the water level in the meridian plane, the type of surfaces depending on the governing parameters of the problem. Expressions are obtained for the angles of inclination of the principal axes. For small deviations from equilibrium, due to a difference in the gravitational forces and Archimedes forces, motion of the ring occurs, governed by the inclination of the principal axes and the nature of change (increase or reduction) in the average density of the ring, determined by the ratio of the rates of diffusion of heat and salt. The displacement along the parallel comprises geostrophic motion, for the velocity of which an analytical expression is obtained. The displacement along the meridian comprises motion over an inclined plane. An analytical expression is given that relates the change in the depth of the centre of mass of the ring to the velocity of motion along the meridian through the angle of inclination of the principal axes of the ring. This explains the motion of both types of Gulf Stream ring to the south-west and of the Oyasio ring to the north-east.     

Optimal design of midsurface of shells: Differentiability proof and sensitivity computation

We suppose that a shell submitted to a given load (self-weight or wind, for instance), has to resist as well as possible towards given criteria. We aim at the following problem: Is it possible to find an optimal design of the midsurface of the shell with respect to this criteria? This problem can be worked using gradient-type algorithms. In this paper we work on the differentiability proof and numerical computation of the gradient. For a given shape of the midsurface, we consider that the shell works in linear elastic conditions. We use the Budiansky-Sanders model for elastic shells, from which we get the displacement field in the shell. The criteria to be minimized are supposed to depend on the shape directly, and also through the displacement field. In this paper, we prove that the displacement field depends on the shape in a Fréchet-differentiable manner (for an appropriate topology on the set of admissible shapes). Then we give a way to compute the gradient of a given criteria from a theoretical point of view and from a numerical point of view. This allows us to use descent-type methods of optimization. They will lead to shapes which react better and better. Notice that we know nothing about convergence of these methods, the existence and unicity of a theoretical optimal solution. But from a practical point of view, it is quite interesting to be able to modify a given shape to obtain a better one.     

Vibration behavior of simply supported inclined single-walled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model

A mathematical model is proposed to investigate the dynamic response of an inclined single-walled carbon nanotube (SWCNT) subjected to a viscous fluid flow. The tangential interaction of the inside fluid flow with the equivalent continuum structure (ECS) of the SWCNT is taken into account via a slip boundary condition. The dimensionless equations of motion describing longitudinal and lateral vibrations of the fluid-conveying ECS are obtained in the context of nonlocal elasticity theory of Eringen. The unknown displacement fields are expressed in terms of admissible mode shapes associated with the ECS under simply supported conditions with immovable ends. Using Galerkin method, the discrete form of the equations of motion is derived. The time history plots of the normalized longitudinal and transverse displacements as well as the nonlocal axial force and bending moment of the midspan point of the SWCNT are provided for different levels of the fluid flow speed, small-scale parameter, and inclination angle of the SWCNT. The effects of small-scale parameter, inclination angle, speed and density of the fluid flow on the maximum dynamic amplitude factors of longitudinal and transverse displacements as well as those of nonlocal axial force and bending moment of the SWCNT are then studied in some detail.     

Explicit jump immersed interface method for virtual material design of the effective elastic moduli of composite materials

Virtual material design is the microscopic variation of materials in the computer, followed by the numerical evaluation of the effect of this variation on the material’s macroscopic properties. The goal of this procedure is an in some sense improved material. Here, we give examples regarding the dependence of the effective elastic moduli of a composite material on the geometry of the shape of an inclusion. A new approach on how to solve such interface problems avoids mesh generation and gives second order accurate results even in the vicinity of the interface. The Explicit Jump Immersed Interface Method is a finite difference method for elliptic partial differential equations that works on an equidistant Cartesian grid in spite of non-grid aligned discontinuities in equation parameters and solution. Near discontinuities, the standard finite difference approximations are modified by adding correction terms that involve jumps in the function and its derivatives. This work derives the correction terms for two dimensional linear elasticity with piecewise constant coefficients, i.e. for composite materials. It demonstrates numerically convergence and approximation properties of the method.      

Dielectric waveguides of arbitrary cross sectional shape

Numerical guided mode solutions of arbitrary cross sectional shaped waveguides are obtained using a finite difference (FD) technique. The standard FD scheme is appropriately modified to capture all discontinuities, due to the change of the refractive index, across the waveguides’ interfaces taking into account the shape of each interface at the same time. The method is applied to the vector Helmholtz equation formulated to describe the electric or magnetic fields in the waveguide (one field is retrieved from the other through Maxwell’s equations). Computational cost is kept to a minimum by exploiting sparse matrix algebra. The waveguides under study have arbitrary cross sectional shape and arbitrary refractive index profile.     

Experimental study on the non- specularly reflected ultrasonic beam on a liquid- solid interface

The reflected fields of a slightly divergent ultrasonic beam on a liquid-solid interface are recorded by a Schlieren system, and the lateral beam displacements on the interface are measured. The range of the incident angle_i is around the Rayleigh angle_c. The displacements are found to decrease as the incident angle increases. Theoretical calculation reveals that the displacements decrease with the increase in the incident angle for a divergent incident beam, but increase with that for a convergent one. The calculated curve of- _i are in agreement with the experimental results.     

Lattice hydrodynamic model of pedestrian flow considering the asymmetric effect

The original lattice hydrodynamic model of traffic flow is extended to single-file pedestrian movement at middle and high density by considering asymmetric interaction (i.e., attractive force and repulsive force). A new optimal velocity function is introduced to depict the complex behaviors of pedestrian movement. The stability condition of this model is obtained by using the linear stability theory. It is shown that the modified optimal velocity function has a remarkable influence on the neutral stability curve and the pedestrian phase transitions. The modified Korteweg-de Vries (mKdV) equation near the critical point is derived by applying the reductive perturbation method, and its kink-antikink soliton solution can better describe the stop-and-go phenomenon of pedestrian flow. From the density profiles, it can be found that the asymmetric interaction is more efficient than the symmetric interaction in suppressing the pedestrian jam. The numerical results are consistent with the theoretical analysis.     

Coupled wetting meniscus model for the mechanism of spontaneous capillary action

Capillarity plays a significant role in many natural and artificial processes, but the mechanism responsible for its dynamics is not completely understood. In this study, we consider capillary flow characteristics and propose a coupled wetting meniscus model for the mechanism of spontaneous capillary action. In this model, capillary action is considered as the dynamic coupling of two interfacial forces, i.e., the wall wetting force at the contact line and the meniscus restoring force on the free interface. The wetting force promotes the motion of the contact line directed toward an equilibrium contact angle, whereas the meniscus restoring force promotes a reduction in the interface curvature, which is more consistent with a 90° contact angle. The competing interaction between these two forces is coupled together via the evolution of the interface shape. The model is then incorporated into a finite volume method for a two-fluid flow with an interface. Capillary flow experiments were performed, including vertical and horizontal flows. Phenomena analysis and data comparisons were conducted to verify the proposed model. According to the results of our study, the model can explain the capillary flow process well and it can be also used to accurately guide capillary flow calculations.     

转动与摆动复合运动下脂润滑关节轴承的数值分析

建立了球面轴承的三维润滑模型,该模型将内圈的转动运动、轴颈倾斜引起的内圈倾斜和内圈的摆动运动等因素纳入考虑,推导出球坐标下适用于非Newton(牛顿)流体润滑的Reynolds(雷诺)方程.应用该模型,并考虑使用润滑脂的Ostwald流变模型,对向心关节轴承的润滑问题进行了数值计算,研究了在不同的幂律指数、内圈倾斜角度和摆动角速度下,脂润滑膜的压力分布、最大压力、承载力和流量.结果表明:在合适的操作条件下,脂润滑能产生明显的流体动压效应;在其它参数不变时,幂律指数对脂润滑膜的最大压力和承载能力影响显著,相对于Newton流体,剪切稠化流体可提高润滑膜的最大压力和承载能力,并增加周向流量,而剪切稀化流体的影响效果则相反;内圈倾斜角度对脂润滑膜最大压力和承载能力的影响较小,内圈摆动角速度的影响则较为明显.