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Abstract
When a fan operates at supersonic tip speeds, shock waves are generated ahead of the blades. If these blades . are nonuniform, then the shock waves are also nonuniform, and tones at harmonics of the fan rotational frequency are generated. This paper presents a simple theory for the relation between the strengths of the individual shock waves, the blade stagger angles and the blade thicknesses, when the shock wave is detached from the blade leading edge. The analysis is in two parts: first a relation is found between the shock wave detachment and the blading nonuniformity. Then, weak shock wave theory is used to relate the detachment to the shock strength ahead of the fan. The results of the theory are in good agreement with experiments and so provide a theoretical basis for the blade shuffling procedures used to minimize blade-to-blade variations and to control shaft order tone generation by these variations.
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