Abstract
A highly efficient numerical method is developed for three-dimensional, periodic, vortical flows around a cascade of loaded airfoils. The method uses the approximation of the rapid distortion theory and thus fully accounts for the effects of distortion of the vortical disturbances as they propagate through the spatially varying mean flow. The numerical scheme is based on the splitting of the unsteady velocity into a vortical part which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and a potential part satisfying a nonconstant-coefficient, inhomogeneous, convective wave equation. A new downstream out-flow boundary condition is derived to complete the unsteady boundary value problem. By writing the downstream condition in terms of the unsteady pressure, the difficulties associated with the singular behavior of the unsteady vortical velocity are avoided. This condition is relatively simple and suitable for numerical computations. By using a body-fitted coordinate system, the unsteady potential is computed in the frequency domain. Results are presented to demonstrate the effects of mean blade loading on the aerodynamic response of a cascade to vortical gust excitations.
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Fang, J., Atassi, H.M. (1993). Compressible Flows with Vortical Disturbances Around a Cascade of Loaded Airfoils. In: Atassi, H.M. (eds) Unsteady Aerodynamics, Aeroacoustics, and Aeroelasticity of Turbomachines and Propellers. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9341-2_8
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DOI: https://doi.org/10.1007/978-1-4613-9341-2_8
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