Convergence enhancement of SIMPLE-like steady-state RANS solvers applied to airfoil and cylinder flows

Abstract

Iterative steady Reynolds-averaged Navier–Stokes (RANS) solvers are widely used to obtain polars representing the aerodynamic characteristics of airfoils. Unsteadiness is encountered in the flow for many of the simulated angles of attack due to phenomenon such as vortex shedding and separation bubbles. In such cases, the steady RANS solver may become numerically unstable. As a consequence it is unable to find a converged solution, with the solver residuals often entering limit cycle oscillations. The BoostConv method is an alternative to the classical Newton’s method to compute unstable steady-state solutions of dynamical systems. It has been previously applied for obtaining steady laminar solutions of the Navier–Stokes equations. However, it demonstrated a lack of robustness by failing to always find the steady-state turbulent solutions of the RANS equations. To overcome this problem, we propose a modification in the application of the BoostConv method to compute steady-state turbulent solutions of the RANS equations. The modified BoostConv method is coupled with an iterative steady RANS solver for computing converged two-dimensional steady-state flows over airfoils. The proposed modification in the application procedure introduces a relaxation parameter that improves the convergence and robustness of the BoostConv method. We show this by finding lift and drag curves with angles of attack spanning 360°for airfoils representative of those used in modern wind turbines. The flow solutions are converged to machine precision at all angles of attack using the novel application procedure of the BoostConv method. Additionally, for flow cases convergent with the original BoostConv method, the modified BoostConv method showed faster convergence rates. The proposed modification provides an enhancement of the BoostConv method that can be easily integrated into existing implementations. By improving the method’s robustness and convergence rates in finding steady-state turbulent solutions of the RANS equations, it opens up the modified BoostConv method to be used in a wide variety of industrial flow cases.