Numerical study of laminar separation over an annular backstep

Abstract Numerical simulations of laminar flows with recirculation regions were performed. The vorticity-stream function representations of the Navier-Stokes equations for 2-D flow in Cartesian coordinates and for axisymmetric flow in cylindrical coordinates were solved numerically. The algorithm developed to solve these systems of coupled, nonlinear partial differential equations implements a variable step Crank-Nicolson scheme with Richardson's extrapolation to discretize the time integration. It implements a 4th-order collocation method to solve the linear elliptic problems at the core of the computations. An iterative method is applied to solve for the nonlinearities over each time step. This 4th-order finite element algorithm was verified by simulating two nonparallel flow exact solutions to the Navier-Stokes equations to within the accuracy specified by the user. Next, the laminar flow field over a planar backstep located below a free-surface was computed and compared with available experimental data. Subsequently, the method was applied to investigate the flow over an inner-radius annular backstep. Solutions for steady flows over the annular backstep for Re values from 100 to 400 were computed; the Re is based on the maximum velocity upstream of the step and the outer radius of the annulus.

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