In this lecture... Axial flow turbine Impulse and reaction turbine stages Work and stage dynamics Turbine blade cascade

Transcription

1 Lect- 0 1

2 Lect-0 In this lecture... Axial flow turbine Ipulse and reaction turbine stages Work and stage dynaics Turbine blade cascade

3 Lect-0 Axial flow turbines Axial turbines like axial copressors usually consists of one or ore stages. The flow is accelerated in a nozzle/stator and then passes through a rotor. In the rotor, the working fluid iparts its oentu on to the rotor, that converts the kinetic energy to power output. Depending upon the power requireent, this process is repeated in ultiple stages. 3

4 Lect-0 Axial flow turbines Due to otion of the rotor blades two distinct velocity coponents: absolute and relative velocities in the rotor. This is very uch the case in axial copressors that was discussed earlier. Since turbines operate with a favourable pressure gradient, it is possible to have uch higher pressure drop per stage as copared with copressors. Therefore, a single turbine stage can drive several stages of an axial copressor. 4

5 Lect-0 Axial flow turbines Turbines can be either axial, radial or ixed. Axial turbines can handle large ass flow rates and are ore efficient. Axial turbine have sae frontal area as that of the copressor. They can also be used with a centrifugal copressor. Efficiency of turbines higher than that of copressors. Turbines are in general aerodynaically easier to design. 5

6 Axial flow turbines Nozzle/stator Rotor Lect-0 Hot gas Exhaust Disc 1 3 An axial turbine stage 6

7 Velocity triangles Lect-0 Eleentary analysis of axial turbines too begins with velocity triangles. The analysis will be carried out at the ean height of the blade, where the peripheral velocity or the blade speed is,. The absolute coponent of velocity will be denoted by, and the relative coponent by, V. The axial velocity (absolute) will be denoted by a and the tangential coponents will be denoted by subscript w (for eg, w or V w ) α denotes the angle between the absolute velocity with the axial direction and β the corresponding angle for the relative velocity. 7

8 Velocity triangles Lect-0 1 α 1 Stator/Nozzle 1 β α V Rotor V 3 β 3 α

9 Lect-0 Types of axial turbines There are two types of axial turbine configurations: Ipulse and reaction Ipulse turbine Entire pressure drop takes place in the nozzle. Rotor blades siply deflect the flow and hence have syetrical shape. Reaction turbine Pressure drop shared by the rotor and the stator The aount of pressure drop shared is given by the degree of reaction. 9

10 ΔT T 0 01 Lect-0 Work and stage dynaics Applying the angular oentu equation, P ( ) w Let ( ΔT 0 w ( w T 01 w c w3 T 01 T 3 03 w3 w3 In an axial turbine, Therefore, the work per unit ass is t The stage work ratio is, p ) ) or T 0 w t T 3 03 c. p (T 01 T 03 ) 10

11 Lect-0 Work and stage dynaics Turbine work per stage is liited by Available pressure ratio Allowable blade stresses and turning nlike copressors, boundary layers are generally well behaved, except for local pockets of separation The turbine work ratio is also often defined in the following way: w h0 w Δ t w3 11

12 Lect-0 Ipulse turbine stage 1 3 w3 3 w α 3 β 3 α V w3 V 3 V β 3 V w V β V 3 α β a Stator/Nozzle Rotor 1

13 13 Lect-0 Ipulse turbine stage α Δ α β β tan h the turbine work ratio is Or, tan ) ( V and V V Therefore, the flow. the rotor siply deflects turbine, In an ipulse a 0 a w w w w w w

14 Lect-0 50% Reaction turbine stage V 3 α β β 3 V V V 3 Stator/Nozzle Rotor 14

15 Lect-0 Ipulse turbine stage In a 50% reaction turbine, syetrical. Δh w3 ( a tan α tan α And the turbine work ratio becoes 0 Therefore, a 1 the velocity for constant ) triangles axial are velocity, 15

16 Turbine ascade Lect-0 A cascade is a stationary array of blades. ascade is constructed for easureent of perforance siilar to that used in axial turbines. ascade usually has porous end-walls to reove boundary layer for a two-diensional flow. Radial variations in the velocity field can therefore be excluded. ascade analysis relates the fluid turning angles to blading geoetry and easure losses in the stagnation pressure. 16

17 Turbine ascade Lect-0 Turbine cascades are tested in wind tunnels siilar to what was discussed for copressors. However, turbines operate in an accelerating flow and therefore, the wind tunnel flow driver needs to develop sufficient pressure to cause this acceleration. Turbine blades have uch higher caber and are set at a negative stagger unlike copressor blades. ascade analysis provides the blade loading fro the surface static pressure distribution and the total pressure loss across the cascade. 17

18 Turbine ascade Lect-0 18

19 Lect-0 Turbine ascade Fro eleentary analysis of the flow through a cascade, we can deterine the lift and drag forces acting on the blades. This analysis could be done using inviscid or potential flow assuption or considering viscous effects (in a siple anner). Let us consider V as the ean velocity that akes and angle α with the axial direction. We shall deterine the circulation developed on the blade and subsequently the lift force. In the inviscid analysis, lift is the only force. 19

20 Turbine ascade Lect-0 Inviscid flow through a turbine cascade 0

21 irculation, Γ and Lift lift, Turbine ascade L ρv Expressing lift coefficient, S(V Γ L w ρv in a non - 1 ρ V L V w1 S(V ) w V ρv w1 diensional ) S (tan α S(V ρ 1 Lect-0 for, w V tan α V 1 w1 ) )cos α 1

22 Turbine ascade Lect-0 Viscous effects anifest theselves in the for to total pressure losses. Wakes fro the blade trailing edge lead to non-unifor velocity leaving the blades. In addition to lift, drag is another force that will be considered in the analysis. The coponent of drag actually contributes to the effective lift. We define total pressure loss coefficient as: P P ω 01 1 ρv 0

23 Turbine ascade Lect-0 Viscous flow through a turbine cascade 3

24 Turbine ascade Lect-0 Drag is The L L + Therefore, S given effective ωs cos α the (tan α by, lift ρv lift D Γ + coefficient, tan α ωs cos α 1 ωs cos α )cos α + D tan α 4

25 Lect-0 Turbine ascade Based on the calculation of the lift and drag coefficients, it is possible to deterine the blade efficiency. Blade efficiency is defined as the ratio of ideal static pressure drop to obtain a certain change in KE to the actual static pressure drop to produce the sae change in KE. η b If η b we neglect 1 + D L D L L tan α cot α 1 D sin α the D ter in the lift definition, 5

26 Lect-0 In this lecture... Axial flow turbine Ipulse and reaction turbine stages Work and stage dynaics Turbine blade cascade 6

27 In the next lecture... Lect-0 Axial flow turbine Degree of Reaction, Losses and Efficiency 7