Unsteady Interacting Boundary Layer Method

Within this study an unsteady, two-dimensional interacting boundary layer method is presented for the incompressible flow around wind turbine rotor blade sections. The main approach is to divide the flow field in to two regions; the one in the vicinity of the surface where the viscosity is effective (so called boundary layer) and the one away from the surface where the flow can be assumed as inviscid. The solutions obtained from these two regions are matched with a quasi-simultaneous viscous-inviscid interaction scheme. For the viscous flow, unsteady integral boundary layer equations together with laminar and turbulent closure sets are solved employing a high-order quadrature-free discontinuous Galerkin method. Laminar to turbulent transition is modeled with the eNmethod. The potential flow is solved by using the linear-strength vortex panel method. It is shown that introducing the interaction scheme leads to non-conservative mechanisms in the system. The discontinuous Galerkin method is extended to handle these non-conservative flux terms. Furthermore it is shown that this numerical method achieves the designed order of accuracy for smooth problems. Results are presented for the individual numerical solution methods which are verified on various test cases and subsequently for the coupled system which is applied on a chosen test case. Evaluation of a laminar flow over an airfoil section is shown and the results (converged to a steady state solution) are compared with other numerical solutions as well as with the experimental data where available. It is shown that the results of the developed numerical solution method are in good agreement with the experimental data and other computational methods.

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