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The reheat factor can be given
ηisen
R曠二 ηpoly (8-12)
Turbine Design .onsiderations
To design a radial-inflow turbine of the highest efficiency， the exit velocity leaving the turbine must be axial.If the exit velocity isaxial， the Euler turbine equation reduces to
H二 U3V的3 (8-13)
since V的4二 0for an axial outlet velocity.
The flow entering the rotor of a radial-inflow turbine must have a certain incidence angle corresponding to the ""slip flow'' in a centrifugal impeller andnot to zero incidence. By relating this concept to the radial-inflow turbine， the following relationship can be obtained for the ratio of whirl velocity to blade tip speed:
V的3 去 D3
U3二 1 -2η.D3 -D4 (8-14)
This ratio is usually in the neighborhood of 0.8. A ratio of D3叫D4 forradial-inflow rotors is around2.2， and η. is the number of blades.
With the aid of the previous relationships， a velocity diagram for the flow entering a radial-inflow turbine can be drawn as shown in Figure 8-10.
The variation in stage efficiency can be shown as a function of the tip speed ratio. The tip speed ratio is a function of the blade speed and the theoretical spouting velocity if the entire enthalpy drop takes place in the nozzle as given by the following equation:
o二 U (8-15)
Vo
where
JQQQQQQQQQQQQQQQQQQQQ
Vo二 2ACJ嘗Ho
Figure 8-11 shows the efficiency variation with the tip speed ratio. This curve also shows the runaway speed. Runaway speed is achieved when turbine torque falls to zero at blade speeds higher than the design speed. Iffailure occurs above the tip speed， the rotor can be defined as a fail-safe rotor design.

The inlet area at the blade tip can be calculated using the continuity equation
 
A3二去D3b3 -η.t3b3二 ρV3 mcos .3  (8-16)
where b3 is the blade height and t3 the blade thickness.
At the exit of the turbine， the absolute exit velocity is axial. Since the bladespeed varies at the exit from hub to shroud， a series of blade diagrams are obtained as shown in Figure 8-12.
Losses in a Radial-Inflow Turbine
Losses in a radial-inflow turbine are similar to those in a centrifugal impeller. The losses can be divided into two categories: internal losses and external losses. Internal losses can be divided into the following categories:
1. .laZe l2aZω7A 2rZω曠曠ω sω27 l2ss. This loss is due to the type of loading in an impeller. The increase in momentum loss comes from the rapid increase in boundary-layer growth when the velocity close to the wall is reduced. This loss varies from around 7% at a high-flow setting to about 12% at a low-flow setting.

2.  FrωCtω27al l2ss. Frictional loss is due to wall shear forces. This loss varies from about 1-2% as the flow varies from a low-flow to a high-flow setting.

3.  SeC27Zaryl2ss. This loss is caused by the movement of the boundary layers in a direction different from the main stream. This loss is small in a well-designed machine and is usually less than 1%.

4.  Cleara7Ce l2ss. This loss is caused by flow passing between the stationary shroud and the rotor blades and is a function of the bladeheight and clearance. The clearance is usually fixed by tolerancesand，for smaller blade heights， the loss is usually a greater percentage. This loss varies between 1 and 2%.

5.  Heat l2ss. This loss is due to heat lost to the walls from cooling.

6.  l7CωZe7Ce l2ss. This loss is minimal at design conditions but will increase with off-design operation. These losses vary from about 1馬2-11馬2%.

7.  Exωt l2ss. The fluid leaving a radial-inflow turbine constitutes a loss of about one-quarter of the total exit head. This loss varies from about 2-5%.

 

The external losses are from disc friction， theseal， the bearings， and thegears. The disc friction loss is about 1j2%. Theseal， bearings， and gear losses vary from about 5-9%.
　
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