A TAYLOR-PETROV-GALERKIN ALGORITHM FOR VISCOELASTIC FLOW

被引:75
作者
CAREW, EOA [1 ]
TOWNSEND, P [1 ]
WEBSTER, MF [1 ]
机构
[1] UNIV COLL SWANSEA,INST NON NEWTONIAN FLUID MECH,DEPT COMP SCI,SWANSEA SA2 8PP,W GLAM,WALES
关键词
CONSTITUTIVE EQUATIONS; PETROV-GALERKIN STREAMLINE UPWINDING; TAYLOR-GALERKIN PRESSURE CORRECTION SCHEME; VISCOELASTIC FLOW;
D O I
10.1016/0377-0257(93)80034-9
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
A viscoelastic flow is solved using a generalised Taylor-Galerkin/pressure correction scheme that incorporates consistent Petrov-Galerkin streamline upwinding within the discretisation of the constitutive equations. The numerical approach is indirect, in the sense that fractional equation solution stages are introduced within the framework of a time-stepping scheme. The Oldroyd-B and Phan-Thien-Tanner constitutive models are considered and the proposed Taylor-streamline upwind/Petrov-Galerkin algorithm is used to simulate flow through a 4:1 planar contraction. For the Oldroyd-B model, the algorithm indicates the onset of instability as elasticity is increased and a limiting Weissenberg number is observed, with no lip vortices apparent for values less than five. For a particular class of Phan-Thien-Tanner models, it is found that the algorithm is stable at high Weissenberg numbers. In this case the solutions exhibit a lip-vortex mechanism for the establishment of recirculating regions as has been observed in some experiments. Results presented for various combinations of fluid parameters suggest that the extensional behaviour of the viscoelastic model is the single most important factor governing the stability and convergence of the algorithms for highly elastic fluids.
引用
收藏
页码:253 / 287
页数:35
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