3Axial and Radial Flow Turbines Differences between turbine and compressor:LongShortBlade 1Last bladeCompressorTurbineWork as nozzle►Work as diffuserDirection of rotation is same asLifeDirection of rotation is oppositeto lift directionNumber of stages is small <3Number of stages are manyTemperature is high, sometimesblade cooling is requiredTemperatures are relative low
4Axial and Radial Flow Turbines Differences between Radial and Axial Types.AxialRadial(Centrifugal)Used for large engines►Used for small enginesLarge mass flow ratesSmall mass flow ratesBetter efficienciesLower efficienciesExpensiveCheapDifficult to manufactureEasy to manufacture
5Axial Flow TurbinesMost of the gas turbines employ the axial flow turbines.The chapter is concerned with axial flow turbines.The radial turbine can handle low mass flows more efficiently than the axial flow machines.
6Axial Flow Turbine Elementary Theory of Axial Flow Turbine ► Velocity Triangles.■ The velocity triangles for one axial flow turbine stage and the nomenclature employed are shown. The gas enters the row of nozzle blades with a static pressure and temperature P1, T1, and a velocity C1, is expanded to P2, T2, with an increased velocity C2 at an angle α2.■ The rotor blade angle will be chosen to suit the direction β2 of the gas velocity V2 relative to the blade at inlet.■ V2 and β2 are obtained from the velocity diagram of known C2, α2, and U.
7Axial Flow Turbine Elementary Theory The gas leaves the rotor at β3, T3, with relative velocity V3 at an angle β3.C3 and α3 can be obtained from the velocity diagram.
8Axial Flow Turbine ► Single Stage Turbine ■ C1 is axial → α1 = 0, and C1 = Cα1. For similar stages (same black shapes) C1 = C3, and α1 = α3, called repeating stage.■ Due to change of U with radius, velocity triangles vary from root to tip of the blade.
9Axial Flow Turbine ► Assumptions ■ Consider conditions at the mean diameter of the annulus will represent the average picture of what happen to total mass flow.■ This is valid for low ratio of tip radius to root radius.■ For high radii ratio, 3-D effects have to be considered.■ The change of tangential (whirl) mass is . This amount produces useful torque.■ The change in axial component produces the axial thrust on the rotor.■ Also there is an axial thrust due to P2 – P3.■ These forces (net thrust on turbine rotor) are normally balanced by the thrust on the compressor rotor.
11Axial Flow Turbine► Calculation of WorkAssume Ca= constant(1)
12Axial Flow Turbine Applying principle of angular momentum From Equation (1)Steady-state energy equation:Thus:
13Axial Flow TurbineElementary theory of axial flow turbine
14Axial Flow Turbineηs is the isentropic stage efficiency based on stagnation (total) temperature.(used for land-based gas turbines).Definingψ = blade loading coefficient (temperature drop coefficient)
15Axial Flow Turbine Thus, Degree of reaction: 0 ≤ Λ ≤ 1 For, Ca = const. and C3 = C1and relative to rotor blades no work, thus
19Axial Flow TurbineIf , Λ, and are assumed, blade angles can be determined.● For aircraft applications:3 < ψ < s, < < 1● For industrial applications: is less (more stages) is less (larger engine size)α3 < 20 (to min. losses in nozzle)● Loss coefficient:Λ and Y: The proportion of the leaving energy which is degraded by friction.
20Axial Flow Turbine Example (Mean diameter design) Given: Assumptions: Rotational speed fixed by compressor: N = 250 rpsMean blade speed: 340 m/sNozzle loss coefficient:
21Axial Flow Turbine Calculation: Λ degree of reaction at mean radius Plot velocity diagramsBlade height h, tip/root radius,Assume:The temperature drop coefficient:Assume (try):
22* To calculate degree of reaction Λ: Axial Flow Turbine* To calculate degree of reaction Λ:■ Get β3:α3 = 0■ To get Λ useThis is low as a mean radius value because Λ will be low or negative at the root.This introduce a value for α3.Take α3 = 10°
23Axial Flow Turbine Reaction at root should be checked. Thus α3 = 10°, β3 = tan = 54.96
24Axial Flow Turbine With knowledge of plot velocity diagrams.* Determine blade height h and tip/root radius ratio,.Assumption:Calculation of area at Section 2 (exit of nozzle)
29Axial Flow Turbine Mean radius using areas at stations 1,2,3 thus 3 2 Location0.10470.08330.06260.0770.06120.041.431.331.24
30Axial Flow Turbine Blade with width W Normally taken as W=h/3 Spacing s between axial blades
31Axial Flow Turbine Vortex Theory The blade speed ( u=r) changes from root to tip, thus velocity triangles must vary from root to tip.Free Vortex designaxial velocity is constant over the annulus.Whirl velocity is inversely proportional to annulus.Along the radius.
32Axial Flow TurbineFor variable density, m is given by
33Axial Flow Turbine Ex: Free vortex Results from mean diameter calculations