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Performance of a Radial-Inflow Turbine
A turbine is designed for a single operating condition called the design point. In many applications the turbine is required to operate at conditions other than the design point. The turbine work output can be varied by adjusting the rotativespeed， pressureratio， and turbine inlet temperature. Under thesedifferent running conditions， the turbine is operating at off-design conditions.
To predict turbine characteristics， it is necessary to compute flow character-istics throughout the turbine. To perform this computation， the flow must be analyzed inside the blade passage. This analysis is done by first examining theflow in the meridional plane， sometimes called the hub-to-shroud plane. A solution is then obtained for the flow in the blade-to-blade plane. Once thissolution is obtained， the flows in the two planes can be combined to give the final quasi-three-dimensional flow. These surfaces are shown in Figure 8-13. The velocity distribution in the meridional plane varies between the hub and shroud as shown in Figure 8-14. The velocity distribution between the suction and pressure surfaces also varies. The velocity between the suction and pres-sure surfaces varies because the blades are working on the fluid and， as a result， there must be a pressure difference across the blade. The form of velocity distribution on the rotor blades at the hub and shroud and also between the pressure and suction sides is shown in Figure 8-15.
The boundary layer along the blade surfaces must be well energized so that no separation of the flow occurs. Figure 8-16 shows a schematic of the flow in a radial-inflow impeller. Off-design work indicates that radial-inflow turbine efficiency is not affected by changes in flow and pressure ratio to the extent of an axial-flow turbine.
In a radial-inflow turbine the problems of erosion and exducer blade vibration are prominent. The size of the particles being entrained decreases with the square root of the turbine wheel diameter. Inlet filtration is sug-gested for expanders in the petrochemical industry. The filter usually has to
Figure 8-1.. Meridional velocity distribution from hub to shroud along the blade length
Figure 8-15. Relative velocity distribution of suction and pressure side along the blade length
be an inertia type to remove most of the larger particles. The exducer fatigueproblem is serious in a radial turbine， although it varies with blade loading. The exducer should be designed so that it has a natural frequency four times above the blade passing frequency.
Noise problems in a radial-inflow turbine come from four sources:
1. Pressure fluctuations
2. Turbulence in boundary layers
3. Rotor wakes
4. External noise
Severe noise can be generated by pressure fluctuations. This noise is created by the passage of the rotor blades through the varying velocity fields produced by the nozzles. The noise generated by turbulent flow in boundary layers occurs on most internal surfaces.However， this noise source is negligible.
Noise generated from rotor flow is due to the wakes generated downstream in the diffuser. The noise generated by the rotor exducer is considerable. The noise consists of high-frequency components and is proportional to the eighth power of the relative velocity between the wake and the free stream. Outsidenoise sources are many， but the gear box is the primary source. Intense noise is generated by pressure fluctuations that result from tooth interactions in gearboxes. Other noises may result from out-of-balance conditions and vibra-tory effects on mechanical components and casings.
Bibliograph叩
Abidat，M.I.，Chen，H.，Baines，N.C.， andFirth，M.R.， 1992. ""Design ofa Highly Loaded Mixed FlowTurbine，''Proc. Inst. MechanicalEngineers， J2ωr7al P2wer 8 E7erAy， 206: 95-107.
Arcoumanis，C.，Martinez-Botas，R.F.，Nouri，J.M.， andSu，C.C.， 1997. ""Per-formance and Exit Flow Characteristics of Mixed FlowTurbines，'' l7ter7a-tω27al J2ωr7al2旷 R2tatω7A MaChω7ery， 3(4): 277-293.
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