Abstract:

Constant-curl Laplacian equation is a new approach to study the behaviour of flows around bodies that do not present boundary-layer separation. It owns the simplicity and linearity of a potential analysis but also includes the rotational effects induced by a rotational displacement of the body such as turbine blades, manoeuvring aircrafts, etc. It assumes that this rotation is constant so that complex curved trajectories should be treated approximating the original path by a series of circular tracks. The idea is based upon a kinematic scheme that states the nullity of the velocity field Laplacian, imposing simultaneously the conditions of incompressibility and constant curl for velocity. We use 9-nodes isoparametric finite elements interpolating velocities and imposing the constant-curl condition by a modified penalty method and incompressibility by a classical one. The numerical results were compared satisfactorily against experimental data for aerodynamic forces and wake constitution on wind-turbine blades. © 2002 Elsevier Science Ltd. All rights reserved.