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….

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

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

Diaphragms & Interaction with Steam

Generation of Windage Vortices

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

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 !!!

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.

Irreversible Fluid mechanics of Turbine Flow Path : Full Load

Irreversible Fluid mechanics of hp Drum Flow Path : Full Load

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.

Full load at Design Conditions

Macro Thermodynamic Model for hp Drum Three simultaneous Equations

Part Load Conditions

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

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.

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.

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

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.

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

Circumferential Variation of Absolute Flow Angle

Variation of Stage Exit Total Temperature

Variation of DoR

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.

The Pumping Power Loss

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

Effect of PA on Number of Stages

Old Last Stage LP Blade

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.

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

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.

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

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.

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.

Losses Vs Wetness

Exhaust Diffuser For L P Turbine

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.

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)

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

Thermodynamic Quality of Turbine Blade

Thermodynamic Quality of Turbine Stage

Characteristic Curves for Stages with symmetric Blading

Characteristic Curves for Stages with asymmetric Blading : Low Aspect Ratio

Characteristic Curves for Stages with symmetric Blading : High Aspect Ratio