PEMP RMD M.S. Ramaiah School of Advanced Studies

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1 Radial Turbines Session delivered by: Prof. Q.H. Nagpurwala 1

2 Session Objectives This session is intended to introduce the following: Types of radial gas turbines Constructional features Radial gas turbines components Expansion process and velocity triangles Radial turbine loading parameter Radial turbine performance 2

3 Introduction A radial turbine looks similar il to a centrifugal compressor. The diffuser vanes are replaced by a ring of nozzle guide vanes. Gas flow with a high tangential velocity is directed inwards and leaves es the rotor with as small a whirl velocity as practicable near the axis of rotation. The rotor is normally followed by a diffuser at the outlet to reduce the exhaust velocity to a negligible g value. Under normal design conditions, the relative velocity at the rotor tip is radial (zero incidence) and the absolute velocity at the exit is axial (α 3 =0). Cohen and Rogers 3

4 Introduction Radial-inflow turbines have been established as a viable alternative to its axial-flow counterpart, specifically in power-system applications. Radial turbines are capable of extracting a large per-stage shaft work in situations with low mass-flow rates. Radial turbine also offers little sensitivity to tip clearances, incontrast t to axial-flow turbines. Bulkiness and heavy weight virtually prohibits its use in propulsion devices. Radial turbines are best used in microgas turbines, turbochargers and stationery power plants. 11 M. M.S. Ramaiah School School of Advanced of Advanced Studies, Studies Bangalore 4

5 Radial Turbine Radial turbine impellers Turbocharger 5

6 Turbocharger with Radial Turbine Radial lt turbine as part of a Garret make turbocharger model GTCP-85 66

7 Types of Radial Turbines Radial flow turbines may be classified as: 1. Inward flow radial (IFR) turbines Cantilever turbine 90 degree turbine 2. Outward flow radial (OFR) turbines 7

8 Cantilever Radial Turbine In cantilever IFR turbine the blades are limited to the region of the rotor tip extending from the rotor in the axial direction. The cantilever blades are usually of the impulse type (or low reaction), such that there is little change in relative velocity at inlet and outlet of the rotor. Aerodynamically, the cantilever turbine is similar to an axial-impulse turbine and can even be designed d by similar il methods. The fact thatt the flow is radially inwards hardly alters the design procedure because the blade radius ratio r 2 /r 3 is close to unity anyway. 8

9 90 Degree IFR Turbine The 90 IFR turbine or centripetal turbine is very similar in appearance to the centrifugal compressor, but with the flow direction and blade motion reversed. Nozzle blades 9

10 Outward Flow Radial Turbine Ljungström Type Outward Flow Radial Turbine 10

11 Vaned Radial Stator Vaned stator as part of the turbine non-rotating assembly 11 M. M.S. Ramaiah School School of Advanced of Advanced Studies, Studies Bangalore 11

12 Scroll Casing Configuration Vaneless versus vaned stator and typical scroll cross-section configurations 11 M. M.S. Ramaiah School School of Advanced of Advanced Studies, Studies Bangalore 12

13 Scroll Casing Excessive E i surface f roughness of the scroll interior surface leads to aerodynamic y degradation Reduction of the scroll cross-sectional area in the circumferential direction 11 M.S. Ramaiah School of Advanced Studies 13

14 90 Degree IFR Turbine Radial turbine with radial inlet flow and axial outlet flow 14

15 Expansion Process on T-s Diagram Specific work output For ideal isentropic i turbine with perfect diffuser C 0 is called the spouting velocity and is equivalent of isentropic enthalpy drop. For the ideal case For good overall efficiency, i C 0 = In terms of turbine pressure ratio Cohen and Rogers 15

16 Spouting Velocity The term spouting velocity (originating g from hydraulic turbine practice) ce) is defined ed as that velocity that has an associated kinetic energy equal to the isentropic enthalpy drop from turbine inlet stagnation pressure p 01 to the final exhaust pressure. The exhaust pressure here can have several interpretations depending upon whether total or static conditions are used in the related efficiency definition and upon whether or not a diffuser is included with the turbine. Thus, when no diffuser is used total case static case In an ideal (frictionless) radial turbine with complete recovery of the exhaust kinetic energy and with At the best efficiency point of actual (frictional) 90 IFR turbines it is found that this velocity ratio is, generally, in the range 0.68 < U 2 /c 0 < Dixon 16

17 Spouting Velocity The expander wheel must be designed at optimum ratio of blade tip speed and spouting velocity = U/C 0,where U is the blade tip speed and C 0 is the magnitude of absolute velocity vector at nozzle exit under isentropic conditions. U/C 0 is a measure of the shape of the inlet velocity triangle in the inter space between nozzle exit and rotor inlet 17

18 Specific Work and Efficiency For C w3 = 0th 0, the specific work kis given by: For ideal isentropic i turbine with perfect diffuser, Overall isentropic efficiency of turbine and diffuser, because (T 01 -T 4 ') is the temperature equivalent of max work through isentropic expansion from inlet state t (p 01, T 01 )t to p a. 'Total to static' isentropic efficiency of turbine rotor, Cohen and Rogers 18

19 Loss Coefficients Following axial turbine practice, the nozzle loss coefficient i is defined d as, and the rotor loss coefficient is given by, Plane 2 is located at the periphery of the rotor. The nozzle loss includes the loss in the volute and in the vaneless space between the nozzle exit and rotor inlet. Considering i the small constant t pressure processes between 2' 2 and 3' 3", we can write c p. δt = T. δs, and Cohen and Rogers 19

20 Turbine Efficiency Consequently η t becomes From the velocity triangles Since, The expression for efficiency finally becomes Cohen and Rogers 20

21 Temperature Rise The temperature ratio T 3 '/T 2 ' can be expressed in terms of the major design variables. It is usually sufficiently near to unity for it have any effect on η t, and hence it is ignored. Thus we can write Now T 2 T 3 may be found by expanding the relation for specific work and making use of the velocity triangles. Since T 01 = T 02 Note that is not the same at inlet and outlet of the rotor as in axial ilflow machines because Cohen and Rogers 21

22 Temperature Rise It follows that t And finally T 2 may be expressed as λ N is usually obtained from separate tests on inlet volute and nozzle vane assembly, enabling λ R to be deduced from overall efficiency measurements with the aid of the above equations. Cohen and Rogers 22

23 Thermodynamics of 90 deg IFR Turbine Across the nozzle, h 01 = h 02 and static enthalpy drops Since the rothalpy, I, across the rotor is constant, where Hence Across the diffuser, h 03 = h 04 and static enthalpy increases due to diffusion Dixon 23

24 Thermodynamics of 90 deg IFR Turbine Specific work done by the fluid on the rotor is As h 01 = h 02 24

25 Nominal Design Point Efficiency Total to static efficiency is defined as Defining passage enthalpy loss as fraction (ξ) of the exit kinetic energy relative to the nozzle row and the rotor, i.e. The total to static efficiency e cy can be written as Dixon 25

26 Nominal Design Point Efficiency From the design velocity triangles and noting that, we can arrive at the following expression With the help of velocity triangles, an equation for T 3 /T 2 can be derived as Dixon 26

27 Nominal Design Point Efficiency Generally T 3 /T 2 has negligible effect on efficiency and hence it is ignored An alternate form of total to static efficiency is Where the spouting velocity C 0 is defined by Dixon 27

28 Relation between η tt and η ts Total-total and total-static efficiencies are connected by: x x 28 Dixon

29 Mach Number Relations Assuming the fluid to be a perfect gas, expressions can be deduced d d for the important Mach numbers in the turbine. At nozzle outlet the absolute Mach number at the nominal design point is, At rotor outlet the relative Mach number at the design point is defined by, Dixon 29

30 Nozzle Loss Coefficients Enthalpy loss coefficient Stagnation ti pressure loss coefficient i Defining velocity coefficient it can be shown that t Practical values of φ for well-designed nozzle rows in normal operation are usually in the range of 0.90 to Dixon 30

31 Rotor Loss Coefficients Enthalpy loss coefficient Stagnation ti pressure loss coefficient i Defining velocity coefficient it can be shown that t Normal range of φ for well-designed rotors is usually in the range of 0.70 to Dixon 31

32 Slip Factor Analogous to the slip factor used in centrifugal compressors, Whitfield and Baines (1990), an incidence factor, λ, The slip factor, devised by Stanitz for centrifugal compressors, is used for radial turbines also We can also obtain the relation Dixon 32

33 Specific Speed The above equation can be factorised to give For ideal 90 deg IFR turbine, And specific speed reduces to Dixon 33

34 Remarks on Specific Speed The numerical value of specific speed provides a general index of flow capacity relative to work output. Low values of specific speed are associated with relatively small flow passage area and high values with relatively large flow passage areas. Specific speed has also been widely used as a general indication of achievable efficiency. These efficiencies apply to favourable design conditions with high values of flow Reynolds number, efficient diffusers and low leakage losses at the blade tips. Over a limited range of specific speed the best radial-flow turbines match the best axial-flow turbine efficiency. But from specific speed (in radians) from 0.03 to 10, no other form of turbine, handling compressible fluids, can exceed the peak performance capability of the axial turbine. 34 Dixon

35 Performance-Related Variables Reynolds number Flow coefficient: Work coefficient Total relative properties and critical Mach number 11 M. M.S. Ramaiah School School of Advanced of Advanced Studies, Studies Bangalore 35

36 Performance Characteristics 36

37 Performance Characteristics 37

38 Radial Turbine Characteristics Larger pressure and temperature drops are achieved in a single stage compared to an axial turbine. Hence, a radial turbine can extract larger work in a single stage. The radial turbine is suitable for low mass flow, high pressure drop, and low power application. The radial turbine is more robust and is more resistant to corrosion and erosion. The cooling of a radial turbine passage is more difficult than the cooling of an axial stage. Performance characteristic of an Allison make (1980) radial turbine 1258 HP; rpm; TET = 1530K; Mass flow rate = 2.36 kg/s 38

39 Mach and Reynolds Numbers Effect of Mach number and Reynolds number on rotor efficiency 11 M. M.S. Ramaiah School School of Advanced of Advanced Studies, Studies Bangalore 39

40 Radial Turbine Components Referring to the above figure and also to the typical expansion process: Nozzle: Rotor: Diffuser: 40

41 Radial Turbine Loading Coefficient or where φ = V r2 /U 2 41

42 Radial Turbine Performance Temperature ratio Pressure ratio where 42

43 Radial Turbine Degree of Reaction Unlike axial turbines, the reaction is a function of inner and outer radii and velocities at different radial locations. For a specific case, when α 3 =0, β 2 =0, V θ1 =0, V θ2 =U 2, and V θ1 =0 (radial turbine with axial exit): If V 1 =W W 2 =VV 3, then the reaction is 50%. 43

44 Stage Reaction The stage reaction (R) is the ratio between the static and total enthalpy changes across the rotor Note that for the terms in the above equation to represent an enthalpy change (static or dynamic), each parenthesised term in this expression should be divided id d by M. M.S. Ramaiah School School of Advanced of Advanced Studies, Studies Bangalore 44

45 Session Summary Components and constructional features of radial turbines are explained. Expansion process and velocity triangles are discussed. d Various loss coefficients are defined and explained. Si ifi f i l i i l i d Significance of spouting velocity is explained Performance characteristcs of radial turbines are presented tdand ddiscussedd 45

46 Thank you 46

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