This analysis employs a time-marching method to study unsteady transonic flow in oscillating airfoils, suggesting effective techniques for shock capturing and boundary conditions.
In this paper, the variational principle for 2-D unsteady transonic flow with shocks around oscillating airfoils developed previously is modified and improved in such a way that a time-marching finite element method can be employed, Non-reflecting far-field boundary conditions and a new unsteady Kutta condition are also incorporated. Great advantage has been taken of the functional variation with variable domain and the artificial density concept in capturing all unknown discontinuities such as shocks and free vortex sheets. For numerical realization of the variable-domain variation a special finite element with self-adjusting nodes is also suggested herein. The numerical solution show that the present method is suitable and effective and can be extended further to unsteady flow past 2- and 3-D rotor bladings of turbomachinery.
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Guo et al. (1995) studied this question.
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