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What unexpected phenomenon limits the size of turbine fans due to the speed of the outside tip of the fan blade in power plants?
Well it's not really a phenomenon, nor is it unexpected. What limits the diameter of turbine wheels, and flywheels, is actually the tensile strength of the materials used to build the turbine rotor (shaft, wheel, keys, caps, straps and seals). The centrifugal force pushing the outer tip of the turbine away from the center of rotation is a measurable and calculable force. When this force exceeds the tensile strength of the material it will tear the wheel apart. For must materials (steels) used to make turbine wheels this force is between 55,000 and 65,000 pounds force per square inch of cross section of material. This equates directly to a calculated "tip speed" of the turbine wheel, where if the outer rim of the wheel exceeds a particular velocity it will rip the turbine apart. For most steels this tip speed is about 5500 feet per second. (for wooden flywheels it is about 4500 FPS.)
Thus the maximum wheel diameter is determined by the maximum rotational speed (RPM) of the turbine. Turbine wheels up to 18 feet in diameter have been built for slow rotating (1200 rpm) turbines. For 3600 RPM machines 6 foot diameter wheels are more commonly the largest where a factor of safety of 3 times is built into the machine. An 18 to 19 foot wheel would be destroyed at about 3600 rpm (the tip speed would exceed 5500 fps). Some turbines run at 30,000 rpm (a 6" DeLaval pump drive turbine is one) and others have run at 600 rpm to generate electricity on a 12 pole generator.
**Note: several turbines are designed to operate at greater than the speed of sound (1126 fps). The harmonic vibration that occurs while passing through the sound barrier could destroy a turbine if allowed to build up. Most turbines do not operate at more than 2000 fps. The velocity of the steam through the turbine, depending on the design, will be between 1 to 2 times the velocity of the rotating outer edge of the wheel. Most turbines are designed so that harmonic vibrations (steam velocity, tip speeds of each wheel, seal and bearing surface along with axial vibrations) occur at about 65 to 75 % of the operating speed of the turbine, for small variable speed turbines these harmonics are designed to occur at greater than the maximum operating speed.
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