Development of a laminar-turbulent transition model and blended time-marching schemes for rotorcraft CFD application

Abstract

This work focuses on improving rotorcraft Computational Fluid Dynamic (CFD) simulations through the incorporation of an appropriate Galilean invariant transition model suitable for rotating flows and a blended implicit time-marching scheme to reduce unphysical early tip-vortex breakdown. A correlation-based Galilean invariant transition model is coupled to the Spalart-Allmaras (S-A) turbulence model. The transition model is derived from Menter's 1-eq transition model and reformulated to incorporate with the S-A turbulence model. A constant freestream turbulence is applied for local correlations to account for wind tunnel test conditions in CFD simulations. Convergence of the model is improved for implicit time methods by applying the positivity in the implicit operators. The model is extended with two crossflow transition models, one proposed by Langtry et al. and the other one by Menter and Smirnov. The extended model has capability to predict the natural transition, bypass transition, separation-induced transition, and cross flow transition. Calibrations of the transition model are performed based on results of plate cases, and a new set of the model constants are proposed. The model is validated against various 2-D airfoils and 3-D cases. Accuracy and robustness of the transition model is demonstrated with comparisons with experimental data. For a 3-D hovering rotor case, the transition model shows similar trends with other CFD for integrated quantities, but without nonphysical behaviors in transition locations. The wake breakdown of a hovering rotor in CFD simulations is investigated with a focus on the effect of time marching. Several factors are tested such as 1) time step sizes, 2) temporal accuracy of time-marching schemes (BDF2 and BDF1), and 3) adding temporal damping to the BDF2 scheme. For this purpose, a blended formulation of the BDF2 and BDF1 schemes is derived with a temporal damping variable. Numerical studies are performed for NASA Langley's PSP hovering rotor, and results are compared such as wake structures, integrated rotor performance, and FFT analysis of the thrust coefficient. The results show that adding a small amount of temporal damping to the BDF2 scheme makes the integrated rotor performance settled down and reduces unphysical secondary vortex braid instability in wake structure. It is shown that the blended BDF scheme with a temporal damping can be used as an engineering solution of the wake structure breakdown in CFD rotor simulations without significant loss of temporal accuracy.