Figure 8-1. Influence of Reynolds number on turbine stage efficiency
The radial-inflow turbine is especially attractive when the Reynolds num-ber (Re二 ρUD叫μ) becomes low enough (Re二 105-106) that the efficiencyof the axial-flow turbine is below that of a radial-inflow turbine， as shown in Figure 8-1. The effect of specific speed Ns二 N 叫H3叫4and specific
二 DH1叫oQQQQ oQQQQ diameter Ds4叫 on the efficiency of a turbine is shown in Figure 8-2. Radial-inflow turbines are more efficient at a Reynolds number between 105 and 106 and specific speeds below Ns二 10.
Description
The radial-inflow turbine has many components similar to those of a centrifugal compressor.However， the names and functions differ. There are two types of radial-inflow turbines: the cantilever radial-inflow turbine and the mixed-flow radial-inflow turbine. Cantilever blades are often two-dimensional and use nonradial inlet angles. There is no acceleration of the
Figure 8-2. NsDs diagram for a turbine stage Efficiency is on a total-to-total basis;thatis，itisrelatedtoinletandexitstagnationconditions Diagramvaluesaresuitable for machine Reynolds number Re三 106(Balje，O E ，""AStudyofReynoldsNumberEffectsinTurbomachinery，""JournalofEngineeringforPower，ASMETrans，Vol 86，Series A， p 227 )
flow through therotor， which is equivalent to an impulse or low-reaction turbine. The cantilever-type radial-inflow turbine is infrequently used because of low efficiency and production difficulties. This type of turbine also has rotor blade flutter problems.
The radial-inflow turbine can be the cantilever type as shown in Figure 8-3， or the mixed-flow type as shown in Figure 8-4. The mixed-flow radial-inflow turbine is a widely used design. Figure 8-5 shows the components. The scroll or collector receives the flow from a single duct. The scroll usually has a decreasing cross-sectional area around the circumference. In some designs the scrolls are used as vaneless nozzles. The nozzle vanes are omitted for economy to avoid erosion in turbines where fluid or solid particles are trapped in the air flow. Frictional flow losses in vaneless designs are greater than in vaned nozzle designs because of the nonuniformity of the flow and the greater distance the accelerating air flow must travel. Vaneless nozzle configurations are used extensively in turbochargers where efficiency is notimportant， since in most engines the amount of energy in the exhaust gases far exceeds the energy needs of the turbocharger.
Figure 8-3. Cantilever-type radial-inflow turbine
Figure 8-.. Mixed-flow-type radial-inflow turbine
The nozzle blades in a vaned turbine design are usually fitted around the rotor to direct the flow inward with the desired whirl component in the inlet velocity. The flow is accelerated through these blades. In low-reaction tur-bines the entire acceleration occurs in the nozzle vanes.
The rotor or impeller of the radial-inflow turbine consists of ahub， blades，and in somecases， a shroud. The hub is the solid axisymmetrical portion of the rotor. It defines the inner boundary of the flow passage and is sometimes called the disc. The blades are integral to the hub and exert a normal force on the flow stream. The exit section of the blading is called an exducer and it is constructed separately like an inducer in a centrifugal compressor. The exducer is curved to remove some of the tangential velocity force at the outlet.
The outlet diffuser is used to convert the high absolute velocity leaving theexducer into static pressure. If this conversion is not done， the efficiency of the unit will be low. This conversion of the flow to a static head must be donecarefully， since the low-energy boundary layers cannot tolerate great adverse pressure gradients.
Theor叩
The general principles of energy transfer in a radial-inflow turbine are similar to those already outlined in the compressor section. Figure 8-6 shows the velocity vectors in turbine rotor flow.
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