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Simulation study reveals aerodynamic hysteresis between accelerated and decelerated flight around an airfoil, highlighting shock wave persistence during deceleration.
Effects of acceleration and deceleration on aerodynamic characteristics at levels typical for commercial aircraft have not yet been investigated. This study examines these effects by solving the two-dimensional Euler equations on moving Cartesian meshes that follow a flying body. Computational accuracy is validated by comparing computed standoff distances of a bow shock wave ahead of a decelerating sphere with results from previous experiments and simulations. Subsequently, unsteady flow simulations are performed around a NACA 0012 airfoil with a chord length of 20 m under standard atmospheric conditions at an altitude of 10 km. A flight Mach number varies between 0.5 and 1.2, with acceleration and deceleration rates of [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. The results reveal distinct flow behaviors among cruising, accelerated, and decelerated flight. In accelerated flight, the aerodynamic coefficients exhibit trends similar to those in cruising flight. Conversely, in decelerated flight, they differ significantly in transonic flow regimes due to the persistence of the rear shock wave, followed by its sudden upstream movement. This leads to a hysteresis phenomenon between accelerated and decelerated flight. This hysteresis is amplified with increasing acceleration and deceleration rates and is largely independent of the angle of attack.
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Rei Yamashita (2026) studied this question.
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