Uniqueness of two-dimensional and three-dimensional flow solutions in a symmetric sudden expansion channel

Two-dimensional (2D) and three-dimensional (3D) flow models were established for the fluid flow in the symmetrical sudden expansion channel. Analysis revealed that the 3D model yielded a 2D solution akin to the 2D model. Numerical simulations provided the velocity distribution of the flow field in both models at varying Re. The nonlinear characteristics and variances in flow between the 2D and 3D models were scrutinized based on the numerical findings. The results demonstrated that under different Re, both models exhibited nonlinear phenomena, such as pitchfork bifurcation. In the absence of bifurcation, both model types exhibit a unique, symmetrical, and steady-state velocity field, with the 2D solution fully aligning with the 3D solution. In cases of weak bifurcation, the solutions for both models become non-unique, yielding a pair of antisymmetric steady-state asymmetric solutions. The 2D and 3D models maintain identical solutions, with no emergence of 3D flow characteristics. Conversely, in scenarios of strong bifurcation, 3D flow develops within the channel, rendering the 2D model's solutions inadequate to replace those of the 3D model. These findings delineate the conditions under which 3D problems can be simplified to 2D ones in experimental and numerical simulation. When the spanwise length remains constant, the flow corresponding to solid wall boundary conditions exhibits greater stability. Conversely, when the spanwise boundary conditions are uniform, an increase in spanwise length correlates with increased flow instability. This article further elucidates the physical mechanisms underlying the generation of spanwise flow.