Implementation of the DADI algorithm with implicit source term treatment into an unsteady Eulerian droplet solver for in-flight icing simulation

Abstract

Recent aircraft designs incorporate multiple rotating elements, such as rotors and propellers, that are highly susceptible to icing-induced performance issues and vibrations. This vulnerability highlights the critical need for thorough icing impact assessments, given the significant flow unsteadiness caused by their moving bodies. Therefore, considering this unsteadiness is critical in precise icing analysis. A comprehensive analysis must cover both the unsteady airflow and droplet behavior, which demands extensive computational resources. To address these challenges, this paper introduces a robust and efficient unsteady droplet solver. It utilizes the Diagonalized Alternating Direction Implicit (DADI) algorithm, renowned for its computational efficiency on the structured grids. The implementation of the DADI algorithm unfolded in two stages. Initially, a relaxation method was applied to enhance hyperbolicity for the diagonalization of the Jacobian matrix. Subsequently, a factor for source term was incorporated into the implicit operator for the treatment of stiff source terms. Verification and validation processes were conducted for one-dimensional Riemann problems, water impingement experiments on the NACA 23012 airfoil and NACA 64A008 swept horizontal tail wing, and icing experiments on an oscillating SC2110 airfoil. The computational results demonstrate high accuracy and efficiency in both steady-state and unsteady computations when compared to experimental results and previous numerical analyses. Notably, the solver employing the DADI method with source term treatment achieved solutions 16.4% faster than the TVD 2nd order Runge–Kutta method in steady-state calculations. Moreover, for unsteady computations, it obtained solutions 8.4% more quickly than the DADI method without the implicit treatment of the source term.