Spherical inflation of a class of compressible elastic bodies

Using a special model that belongs to a new class of elastic bodies wherein the Cauchy-Green stretch is given in terms of the Cauchy stress and its invariants, within the context of the spherical inflation of a spherical annulus, we show that interesting phenomena like the development of “stress boundary layers” manifest themselves. We consider two cases of boundary value problems, one in which there is a cavity in a sphere and the other in which there is a rigid spherical inclusion in a sphere. We show that in the case of a rigid inclusion, it is possible for a pronounced “stress boundary” layer to develop, in that the values of the stresses within this boundary layer that is adjacent to a spherical inclusion are much larger than external to it. We also show that in the case of both the cavity and a rigid inclusion, the stress concentration is an order of magnitude higher than the increase in the deformation gradient, that is, the stress and the stretch do not scale in a similar manner. While the stress adjacent to a rigid inclusion can be 2500 times the applied radial stress, the maximum stretch, which occurs at the rigid inclusion is about 10. While the variation in the stresses are linear in thin walled annular regions, we find that in thick walled annular regions, the variation of the stresses is non-linear.     

基于Hele-shaw模型的斜井偏心环空顶替流体密度差优化

针对斜井中顶替流体密度差及套管偏心引起的顶替界面突进两相流体掺混严重的问题,考虑斜井密度差引起的驱动力沿周向角和半径的变化,建立了斜井偏心环空稳定顶替界面形状模型,利用该模型分析了密度差对顶替界面形状的影响,得到了不同井斜角及套管偏心条件下顶替流体的最优密度差及变化规律:斜井中顶替界面突进的位置及程度取决于套管偏心与密度差的相对作用,存在合理的密度差使得顶替界面长度最短;最优顶替流体密度差随套管偏心度的增加而增大,随井斜角的增大而减小;固井顶替时在满足压稳防漏的条件下直井所选用的密度差越大越好,水平井所选用的密度差应相对最小。     

基于嵌套网格的环空流体内旋转杆柱与井筒碰撞特性研究北大核心CSCD

针对浸没在流体中杆管柱间相互接触问题,基于嵌套网格技术,该文建立了环空流体内旋转杆柱与井筒间碰撞的数值求解方法.将环空流体域分为相互嵌套的子区域:背景网格和组件网格,推导了各嵌套区域流场边界传递信息的插值计算公式,采用分域方法对环空流体域与杆柱固体域耦合进行求解.通过静止流体中球形颗粒与壁面正、斜碰撞实验对比,验证该文数值方法的正确性.研究了不同流体黏度、杆柱旋转速度条件下杆柱与井筒的碰撞特性,结果表明:1)杆柱与井筒碰撞的碰撞力、速度随黏度增大而降低,即杆柱与井筒碰撞的剧烈程度与流体黏度负相关;2)随着杆柱旋转速度增大,杆柱与井筒的碰撞力、速度也增大,即杆柱与井筒碰撞的剧烈程度与转速正相关.