The classical potential formulation of inviscid transonic flows is modified to account for non‐isentropic effects. The density is determined in terms of the speed as well as the pressure, which in turn is calculated from a second‐order mixed‐type equation derived via differentiating the momentum equations.
The present model differs in general from the exact inviscid Euler equations since the flow is assumed irrotational. On the other hand, since the shocks are not isentropic, they are weaker and are placed further upstream compared to the classical potential solution. Furthermore, the streamline leaving the aerofoil does not necessarily bisect the trailing edge.
Results for the present conservative calculations are presented for non‐lifting and lifting aerofoils at subsonic and transonic speeds and compared to potential and Euler solutions.
SUMMARYThe classical potential formulation of inviscid transonic flows is modified to account for non-isentropic effects. The density is determined in terms ofthe speed as well as the pressure, which in turn is calculated from a second-order mixed-type equation derived via differentiating the momentum equations.The present model differs in general from the exact inviscid Euler equations since the flow is assumed irrotational. On the other hand, since the shocks are not isentropic, they are weaker and are placed further upstream compared to the classical potential solution. Furthermore, the streamline leaving the aerofoil does not necessarily bisect the trailing edge.Results for the present conservative calculations are presented for non-lifting and lifting aerofoils at subsonic and transonic speeds and compared to potential and Euler solutions.
SUMMARYIn this work a study of the application of the finite element method to transonic flows in axial turbomachines is undertaken.Solution techniques capable of accurately predicting flows from the incompressible regime up to the establishment of shocks in the transonic regime are presented. In the subsonic and shockless transonic regimes a local linearization method capable of very rapid convergence is used. In the full transonic regime the artificial compressibility method is employed to exclude downstream influences in the supersonic regions. The two approaches can be combined in a unified package and appropriate switches introduced to select the relevant method in any flow regime.
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