Unsteady Aerodynamic Modeling for Coflow Jet Airfoils

Abstract This study develops an improved state-space model for coflow jet (CFJ) airfoils by incorporating the jet momentum coefficient into the internal state-variable equation. The key contributions are summarized as follows. First, to quantitatively characterize flow separation characteristics of CFJ airfoils, steady and unsteady aerodynamic separation evaluation metrics α * and τ 1 are mathematically formulated. These two indicators clarify the modulation laws of jet parameters on dynamic stall initiation, aerodynamic hysteresis morphology, and aerodynamic force recovery. Embedding the proposed separation metrics into the classic Goman state-space framework yields the improved CFJ-based state-space model. Second, 18 unknown parameters of the model are calibrated via a multistart quasi-global optimization strategy, where 20 random initial guesses are sampled within ± 50 % of the baseline parameters. Validations indicated that the coefficient of determination R 2 of the presented model is above 0.99, verifying excellent predictive precision. Additional generalization tests revealed slightly elevated out-of-sample errors relative to fitting errors, yet the majority of generalization R 2 values exceeded 0.95, and the model faithfully reproduced the evolutionary features of aerodynamic hysteresis loops. This study delivers a robust unsteady aerodynamic modeling tool for CFJ airfoil performance analysis and underpins the engineering implementation of active flow control for aircraft dynamic-load manipulation, overcoming the inherent drawback of conventional state-space models in describing how active jet control modulates dynamic-stall evolution.