1. Yet Another Three Losses in Turbines
P M V Subbarao
Professor
Mechanical Engineering Department
A Set of Losses not Strictly due to Geometry of Blading….

2. Losses by stage and section for a 700 MW turbine. Source: Toshiba

3. Other Losses in Steam Turbines
Disc Friction & Windage Losses : Miscellaneous Losses
Partial Admission Losses
Wetness Losses
Leaving Losses

4. Diaphragms & Interaction with Steam

5. Generation of Windage Vortices

6. An Unwanted Fluid Mechanics : Churning?
The rotors act like a giant food mixer stirring the flow.
The blades are moving so fast that they create a lot of heat in the steam.
This causes the steam temperature to rise and the blades become hotter and they expand.
The LP casings become hotter which affects the differential movements between the rotor and casing.
Water sprays are fitted in the exhaust of large LP turbines, to keep the blades and casings cool

7. Losses due to Disc Friction and Windage
Frictional forces appear between the rotating turbine disc and the steam enveloping it.
The rotating disc drags the particles near its surface and imparts to them an accelerating force in the direction of rotation.
A definite amount of mechanical work is spent in overcoming the effect of friction and imparting this acceleration.
The enegry dissipated (heat generated ) per blade row is proportional to ρ, N3 h D4
Considerable heat can be generated in the LP stages by windage !!!

8. Estimation of Windage Losses
The magnitude of these losses is calculated using Stodola’s Empirical Formula:
Pwind: Power los in overcoming friction and windage.
λ : fluid Coefficient: 1 for air or highly superheated steam, 1.1 – 1.2 for ordinary superheated & 1.3 for saturated steam.
D : Mean diameter of the disc.
ε: Degree of partial admission.
l1: Heght of blades, in cm.
U : Velocity of blade at mean diameter, m/s.
ρ: density of steam, kg/m3.

9. Irreversible Fluid mechanics of Turbine Flow Path : Full Load

10. Irreversible Fluid mechanics of hp Drum Flow Path : Full Load

11. Partial Admission in First Stage of HP Drum
Partial admission applied as control stage yields high part load efficiency and high specific work output due to a maintained high inlet pressure for the turbine in the fully admitted sectors.

12. Full load at Design Conditions

13. Macro Thermodynamic Model for hp Drum
Three simultaneous Equations

14. Part Load Conditions

15. The thermodynamics of partial admission can be explained by a comparison to simple throttling valve.

16. Deliberate Partial Admission at Full Loads
Partial admission is sometimes deliberately used at full load in small scale turbine stages.
This helps in avoiding short blades in order to reduce the tip leakage loss and losses induced by endwall flows.
Radial dimensions of turbine blades and flow channels are primarily a function of the volumetric flow rate throughout the machine, and consequently become reduced for small turbines.
The physical size of the turbines has a great deal of importance for the isentropic turbine efficiency.
In an “ideal” machine where all the geometrical parameters could be held at a constant ratio to blade cord length, the small size would have very little impact on turbine efficiency.
This in according to similarity rules, only a decrease in Reynolds number may affect the losses.
In reality these ratios are not possible to practically uphold and the losses become large for small machines.

17. New Losses due to Partial Admission
PA improves part load efficiency due to decreased secondary losses.
There are three main concerns regarding partial admission turbines.
These are related to:
Aerodynamics/Fluid Dynamics
Thermodynamics
Aeromechanics.

18. Special Fluid Dynamics due to Partial Admission
Firstly, there are special aerodynamic losses; pumping-, emptying- and filling losses attributed to the partial admission stage.

19. New Issues due to PA
Secondly, in multistage turbines the downstream stages experience non-periodic flow around the periphery and substantial circumferential pressure gradients and flow angle variations that produce additional mixing losses.
Thirdly, compared to full admission turbines, the forcing on downstream components is also circumferentially non-periodic with rapid load changes.
This is very high for the rotor in the admission stage.

20. The Effect of Distribution of Given PA Level : 50% Load

21. Circumferential Variation of Absolute Flow Angle

22. Variation of Stage Exit Total Temperature

23. Variation of DoR

24. Estimation of PA Losses
Partial admission losses can be broken down into pumping loss, filling loss and emptying loss.
The pumping loss refers to the pumping in the inactive blade channels rotating in a fluid-filled casing.
The losses that originate from the filling and emptying of the rotor passages as the blades pass through the active sector are sometimes combined and referred to as sector loss.

25. The Pumping Power Loss

26. The Sector Losses
The sector loss, associated with the emptying and filling of rotor passages as the blades pass by the active stator arc, is found to be
where Ks is a loss coefficient representing the decrease of the momentum of the fluid passing through the rotor compared to the available energy of the fluid.
η efficiency of full-admission turbine
η p efficiency of partial-admission turbine
Kw exit-to-inlet relative velocity ratio ( Vre/Vri)
SR rotor blade pitch

27. Effect of PA on Number of Stages

28. Old Last Stage LP Blade

29. Adiabatic Expansion of Steam in Last Few Stages
The liquid in the LP turbine expansion flow field is considered to progressively appear, with lowering pressure, in four forms, namely as:
A fine mist (or fog) suspended in the steam;
As a water stream running in rivulets along the casing (mainly OD);
As a water film moving on the surface of the blades (mainly stator; not particularly evident on the rotor blades owing to centrifugal-flinging action);
As larger droplets created when the water flowing along the surface of the blades reaches the trailing edge.

30. Notional Diagram of Path Break Down in LP Stages
Re-entrained
Coarse water
Coarse water spray centrifuged from blade
Deposition of Part of Fog and Coarse water
Coarse water spray
Impact & Splashing of Coarse water
Fog
Impact & Splashing of Coarse water
Centrifuging of deposited Fog and Coarse water

31. Notionally envisaged progressive process
Formation of fog that continues to appear in the through-flow, some of which is deposited.
Deposition of fog droplets on blade surfaces.
Coarse water re-entrained in through-flow primarily from fixed blades.
Impact of coarse water on the moving blades.
Coarse water re-entrained in through-flow from moving blades
Coarse water entering the next stage (fixed blades).
Continued process, with more fog formation and some deposition, in the successive stages.

32. Deviation of Eater Droplets
Velocity triangles for coarse water droplets
Velocity triangles for steam

33. Transport Losses
Impact of droplets on blade surfaces, with strong resulting momentum exchange.
Slip of the droplets relative to the main steam flow, causing drag between the droplets and the dry steam.
This is because of the high-density water droplets that cannot accelerate as fast as the dry steam under the same pressure gradient.

34. Limit on Allowable Wetness
The level of allowable moisture in the last stages of the LP turbine has been a practical limit on the usable temperatures and pressures of steam since the earliest turbine designs.
Severe erosion was found in LP blades of early turbine designs and lead to the imposition of a limitation of about 12% on exit wetness.
A second, although less limiting effect, was characterized by Baumann as early as 1910: that the efficiency, of wet stages of the LP decreases approximately 1% for every 1% increase in wetness in the stage.

35. Losses Vs Wetness

36. Exhaust Diffuser For L P Turbine

38. Steam Turbine Exhaust Size Selection
The steam leaving the last stage of a condensing steam turbine can carry considerably useful power to the condenser as kinetic energy.
The turbine performance analysis needs to identify an exhaust area for a particular load that provides a balance between exhaust loss and capital investment in turbine equipment.

39. Typical exhaust loss curve showing distribution of component loss
Condenser flow rate
Percentage of Moisture at the Expansion line end point
SP.Volume
Annulus restriction loss
Annulus velocity (m/s)
Annulus area
Total Exhaust Loss 50
Turn-up loss 40
Gross hood loss
Exhaust Loss, kJ/kg of dry flow 30 20
Actual leaving loss 10
120
240
180
240
300
360
Annulus Velocity (m/s)

40. Optimal Design of Exhaust Hood
Total Exhaust Losses
Thermodynamic Optimum
Axial Leaving Losses
Economic Optimum

41. Thermodynamic Quality of Turbine Blade

42. Thermodynamic Quality of Turbine Stage

43. Characteristic Curves for Stages with symmetric Blading

44. Characteristic Curves for Stages with asymmetric Blading : Low Aspect Ratio

45. Characteristic Curves for Stages with symmetric Blading : High Aspect Ratio