---

The main object of current study is investigation of instability threshold of flow in a gradual expansion from symmetric to asymmetric situations. The expansion ratio is 1:3 and expansion angles are 30, 45, 60 and 90 degree. Discretization of governing equations is performed using finite volume method based on PISO algorithm on a staggered mesh. The CFD code is validated based on the results of sudden expansion reported in previous works. Here, the effects of expansion angle and Reynolds number on flow instability in transition from symmetric situation to two and three asymmetric vortices are investigated and the first and second critical Reynolds numbers are obtained. The bifurcation diagrams of vortices and velocity profile in centerline are plotted for each case and the effects of instability on flow field are discussed based on them. Unlike the previous studies which have been focused on the planar flow in sudden expansions, the flow instability in gradual expansions with different expansion angles is investigated which is the main innovation of current study.

---

Due to the diversity and width applications of polymeric fluids in various industries the investigation of viscoelastic fluids is noted by many researchers. In this study, non-creep flow of viscoelastic fluid has investigated inside planar channel with gradual expansion for the expansion ratio of 1:3. The laminar and incompressible flow of viscoelastic fluid has been simulated numerically using finite volume method and PISO algorithm. The nonlinear PTT rheological model has been applied to study effect of elasticity property on the length of vortices in polymeric fluid flow. The investigation of symmetric and asymmetric vortices length in a wide range of Reynolds and Weissenberg numbers is the main purpose of present study. The three angles of 30, 45 and 60 degrees have been considered for influence of the expansion angles on the length of vortices. The study of polymeric fluids flow through the planar channel with gradual changes in cross section (with expansion angles less than 90 degrees) is the innovation of this research. Also the critical values of first and second for Reynolds and Weissenberg numbers have been expressed in various expansion angles and furthermore length of second and third vortices has been presented as a function of Reynolds and Weissenberg numbers. The length of symmetric vortices decreases with increment of elastic property at all expansion angles for values of Weissenberg numbers less than one. Whereas the growth of expansion angle leads to increase in the length of symmetric and asymmetric vortices for low Reynolds and Weissenberg numbers.