On a Wave Phenomenon in Turbines

The paper deals with the theoretical analysis and experimental verification of a periodic wave phenomenon occurring in running turbine stages, which until now was not recognized. This wave phenomenon can be responsible for failure of turbine blades and for loss in efficiency of turbomachines. Being periodic, it can produce a blade vibration stimulus which, in general, does not have an integral number of cycles per revolution. It consists of concentrated pressure waves (pressure pulses) which, when the conditions are favorable, are generated on the leading edges of the moving turbine blades, propagate toward the suction sides of the nozzles, are reflected back toward the turbine wheel, collide with the leading edges of the turbine blades, and are again reflected toward the nozzles. For a given turbine stage, depending on the ratio of the number of nozzles to the number of blades, on the edge-to-edge distance between the nozzles and the blades, on the nozzle angle and shape, and on the Mach number of the flow, there exist certain speed ranges (or, in the constant-speed turbines having variable inlet conditions to the stage, certain speed ratio, W/V₀, ranges) in which these waves may exist. The equations derived in this paper indicate that the ratio of the number of nozzles to the number of blades should become an important new parameter in the design of turbine stages free of the wave-produced vibration stimulus at the natural frequency of the blades. A comparison is made of the blade stimulus frequencies predicted by the method described in this paper and of the stimulus frequencies measured by the NACA on a J47 turbojet engine. Very good agreement exists between the observed and predicted stimulus frequencies. A direct observation of the reflecting waves (pressure pulses), made on a water-table model of a turbine stage, is also reported in this paper.