A new finite element method for computing the flow inside rotating machinery. (English) Zbl 0687.76062
Summary: A model is presented to simulate the flow inside a complete turbomachine in the presence of blades without physically introducing the blades but by representing their effects on the flow field. This requires that the flow be tangent to the chamber surface of the rotor or stator and permits a natural coupling of the flow field in rotating components with that of stationary parts of the machine. The new tangency condition is enforced by introducing a Lagrange multiplier which can be interpreted as the force applied by the blades on the fluid. It is shown that the blade force is constituted of a body force acting along the normal to the blade camber surface plus a distribution on the leading and trailing edges of the blade row. With this knowledge it is possible to construct an appropriate weak form of the differential equations. The primitive variable equations are solved by both a mixed and a penalty function finite element method. A numerical convergence study is conducted to assess the properties of the numerical scheme. Numerical predictions compare very well with the analytical solutions. Finally a simulation is presented for the flow in a realistic configuration.
MSC:
| 76G25 | General aerodynamics and subsonic flows |
| 76U05 | General theory of rotating fluids |
| 76M99 | Basic methods in fluid mechanics |
References:
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