二阶非牛顿流体蠕流精确解

二阶流体是工业界常见的非牛顿流体,因为其本构关系简单而被广泛采用和研究.逆方法预先假定流场满足某类特定的物理的或几何的特性,从而求出流体运动方程的精确解.本文通过假定平面定常二阶非牛顿流体的涡量场与受到扰动的流函数相等这一特定形式,采用求解非线性微分方程常用的逆方法,推导并获得了平面二阶蠕流流场的精确解,由此容易进一步获得流场的压力.所获得的精确解包含了Poiseuille,简单Couette平行流动以及两相向流体的相互作用等流动.这些精确解为实验,数值以及渐进解的检验提供了借鉴和参考.     

微分约束方法在求解二阶流体精确解上的应用

利用微分约束方法研究了二阶流体的精确解,通过使用一阶微分约束条件,不仅获得了具有抽吸作用下的Couette和Poiseuille平行流、碰撞射流、平面拉伸流等具有明确物理意义的流动解,而且获得了两类新的精确解,所得精确解表明二阶流体的流动特性不仅依赖于物质粘性参数,而且依赖物质弹性参数.此外讨论了部分边值问题.     

Application of differential constraint method to exact solution of second-grade fluid

A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, and planar elongational flows are derived. In addition, two new classes of exact solutions for a second-grade fluid flow are found. The obtained exact solutions show that the non-Newtonian second-grade flow behavior depends not only on the material viscosity but also on the material elasticity. Finally, some boundary value problems are discussed.