Three local self-similar solutions are obtained for the laminar planar jet flow of viscoelastic fluids, described by the FENE-P constitutive equation, through an order of magnitude simplification of the governing equations. The more general solution is shown to be more accurate than two further simplified solutions, here called the delta and the Olagunju-type solutions, at least for the profiles of conformation tensor components. In the limit of vanishing viscoelasticity, all conformation tensor components reduce to the same low elasticity asymptotic behavior, and the polymer stresses become Newtonian-like. The general solution is then used to obtain the laws of the decay of the centerline velocity and of the growth of the jet half-width and to ascertain the effects of the Weissenberg number, maximum polymer extensibility parameter and the ratio of polymer to total viscosities upon the flow characteristics. The general local self-similar solution compares well with results of numerical simulations obtained by the RheoFoam module of the freeware OpenFoam code.

通过控制方程的数量级简化，获得了由FENE-P本构方程描述的粘弹性流体的层状平面射流的三个局部自相似解。至少对于构象张量分量的分布，较通用的解决方案显示出比另外两个简化的解决方案（这里称为δ和Olagunju型解决方案）更准确。在消失的粘弹性极限内，所有构象张量分量都减小到相同的低弹性渐近行为，并且聚合物应力变成牛顿型。然后，使用一般解来获得中心线速度的衰减规律和射流半宽度的增长规律，并确定魏森伯格数的影响，最大流动性参数，以及流动特性下聚合物与总粘度的比率。通用的局部自相似解决方案与免费软件OpenFoam代码的RheoFoam模块获得的数值模拟结果相比较。