Exact momentum sources for gust injection in flow simulations

Abstract

Vortical gusts are unsteady flow disturbances that can affect the aerodynamic performance and stability of aircraft. Generating realistic vortical gusts in flow simulations is challenging due to the complexity and diversity of turbulence characteristics. This paper introduces a novel framework for creating vortical gusts in flow simulations using momentum sources. The method can manipulate the incoming flow with any desired divergence-free velocity perturbation at any location and avoid unwanted acoustic waves in the meanwhile. It starts from a linearized incompressible momentum equation without viscous effects. The equation has a frequency-domain representation, which is an ordinary differential equation and easy to solve. Then, several conditions are imposed to determine unknown coefficients. Expressions of source terms producing one-dimensional and two-dimensional gusts are obtained. The generated velocity field is compared to the specified gust and shows outstanding agreement. Several parameters that affect the distribution of added sources are systematically studied to find a combination that can provide optimal performance in various scenarios. Finally, the model is used to assess the aerodynamic interaction of a vortical gust and thin airfoils. The results agree well with the analytical solutions provided by the Sears model.