On the consistency of four different control surfaces used for finite area blade-to-blade flow calculations
Abstract
The consistency and order of accuracy of four spatial-discretization schemes used in finite-area-method (FAM) blade-to-blade computations of cascade flows are investigated analytically. The original hexagonal FAM control surface (CS) of McDonald (1971), the trapezoidal CS of Denton (1976), the quadrilateral CS of Essers and Kafyeke (1980), and the bitrapezoidal CS of Van Hove (1979), as developed by Arts (1982), are compared using a simple flexible grid comprising several pseudostreamlines and pitchwise lines. The hexagonal CS is shown to be unconditionally consistent with the stationary two-dimensional Euler equations on which the FAM is based and to have general first-order accuracy, while the three four-node CSs can all introduce consistency errors under certain defined conditions. Of these, the bitrapezoidal CS is found to impose the least stringent restrictions on CS geometry and to have the simplest error-correction strategy (blunt discretization at leading and trailing edges).
- Publication:
-
International Journal for Numerical Methods in Fluids
- Pub Date:
- November 1984
- DOI:
- 10.1002/fld.1650041107
- Bibcode:
- 1984IJNMF...4.1083A
- Keywords:
-
- Cascade Flow;
- Computational Fluid Dynamics;
- Control Surfaces;
- Finite Volume Method;
- Turbomachine Blades;
- Consistency;
- Discrete Functions;
- Hexagons;
- Partial Differential Equations;
- Trapezoids;
- Fluid Mechanics and Heat Transfer