The row of last-stage blades (LSBs) in a steam turbine's low-pressure (LP) section is a key element of the turbine's design because it defines the machine's overall performance, dimensions, and number of casings. Historically, efforts to increase overall turbine efficiency focused on the high- and intermediate-pressure (HP and IP) sections. Over the past few years, however, turbine manufacturers also have begun targeting the LP section, which may produce up to 50% of the turbine's total power (Figure 1). One way to increase that section's efficiency at certain exhaust pressure values is to lengthen its LSBs. Doing so either decreases the number of LP modules needed or increases power output at lower condenser pressures for the same number of modules.
1. Biggest contributor. The low-pressure section may account for as much as 50% of the power produced by a utility-scale steam turbine. Courtesy: Bechtel Power Corp.
The push to lengthen LSBs comes not only from designers of large coal-fired power plants but also from developers of relatively smaller combined-cycle plants. There are significant differences between turbines designed for combined cycles and for conventional steam plants. Because feedwater heaters are not normally used in the thermal design of a bottoming cycle, for the same HP main steam flow the LP exhaust steam flow in a bottoming cycle can be up to 35% greater than in a comparably sized conventional turbine. In addition, bottoming plant designs may use duct firing to compensate for the reduction in gas turbine output at high ambient temperatures or for peak loading the plant, when doing so is economically justified. It has become quite common in the U.S. to use massive amounts of supplementary firing to almost double steam turbine output.
This article explores the fundamental features of modern LSB interdisciplinary (aerodynamic and mechanical) design, including the ever-increasing role of complex computational fluid dynamics (CFD) analysis. Our purpose is to investigate how turbine performance and operability are affected by the current trend of lengthening LSBs. The article concludes with a test case that delineates the real-world options available in selecting a suitable LSB system.
Aero design fundamentals
Conventional LSB design (subsonic inflow at the tip of the rotating blade) reaches aerodynamically acceptable limits sooner than blade mechanical limits. To address this shortcoming, turbine original equipment manufacturers (OEMs) have devoted considerable effort to understanding and improving the design of stationary and rotating blades. Changes from the existing traditional design boundaries, such as supersonic relative inflow at the tip of the rotating blade, have been evaluated during extensive analytical and experimental trials to gain user acceptance.
Only a fully developed 3-D stage flow analysis can provide an optimum blade profile capable of minimizing the losses from shock waves resulting from supersonic flow. The accuracy of modern 3-D analysis as a prediction tool has vastly improved—it can now account for nonequilibrium condensation flows with different steam wetness conditions and phase change variations.
For large LP LSBs, the relative exit Mach number is an important design parameter for assessing the operating range and exhaust losses. The longer the blade, the higher the exit Mach number, due mainly to a strong mid-stage pressure gradient.
Figure 2 shows a typical static pressure and Mach number distribution. The low pressure at the hub of the rotating blade (Ps1) produces a low root reaction, which eventually leads to flow separation within the rotating blade. The Mach number at the stationary blade exit (M1) has a very strong gradient, raising the inlet Mach numbers (Mw1) at the hub and tip of the rotating blade. The high pressure at the tip produces high absolute values of the exit Mach numbers at the hub of the stationary vanes and high relative inflow Mach numbers at the tip and hub of the rotating blade, which trigger shocks within the rotor passage.
2. Tracking the field. Typical Mach numbers and static pressure distribution of a steam turbine last-stage blade. Source: H. Stüer, ASME GT2005-68746
A true 3-D design will influence the flow field to "control" this positive radial pressure gradient and avoid its detrimental effects. Several options are available, and can be used in combination, to achieve this goal.
The pressure gradient is mainly dependent on the streamline curvature and the swirl velocity. In a 2-D analysis, selecting a free vortex to control the pressure gradient will result in extremely twisted rotor blades for low hub-to-tip ratio and low hub reaction, thus generating high exit losses. A design based on using a forced vortex has the advantage of reducing the relative inlet velocity of the rotating blade.
However, achieving a true optimized flow field design with minimum losses requires an approach based on a 3-D analysis. Commonly used 3-D shapes are known as "blade lean" and "blade sweep." For a fixed hub configuration, a tangential lean is defined as the shifting of the stacking line tangentially to the pressure side. A blade sweep occurs when the stacking line is modified toward the inflow as the blade radius increases.
In some designs, the LSB lean is applied tangentially and axially. Combined with flow path contouring, the stationary vanes" tangential lean reduces the pressure gradient at the exit of the stationary vanes, raising the root reaction and allowing for a lower hub/tip ratio.
The stationary vanes" axial lean increases the vane-to-blade spacing at the tip, giving water droplets more time to accelerate before entering the rotating blade. This type of acceleration also mitigates the effects of erosion on the blade. In another application, the stationary vanes lean in the tangential direction, forcing the pressure side of the vane radically inward. Due to the action of body forces in this configuration, the increased pressure at the inner end walls causes a decrease in velocity and smaller pressure gradients, reducing turbine secondary losses. In a compound axial and tangential lean arrangement, the stationary vanes curve in the spanwise direction, and the pressure side surfaces intersect with the hub and tip endwalls at angles. This reduces the pressure gradients on the walls and consequently decreases secondary flow losses. A stator vane combining sweep and lean is the most advantageous configuration.
Depending on the design's exit Mach number at the stationary blade hub, the profile is either convergent for subsonic and transonic inlet Mach numbers up to 1.3 or convergent-divergent for higher Mach numbers. A decision to use the convergent-divergent profile must be based on the results of a detailed 3-D analysis at design and off-design conditions rather than consideration of the exit Mach number. However, convergent-divergent passages for stationary vanes have not been used due to their sensitivity to varying exit conditions that occur during off-design operation.
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