Axial-Flow Turbines: Mean-Line Analysis and Design
Introduction
The modern axial-flow turbine developed from a long line of inventions stretching back in time to the aeolipile of Heron (aka Hero) of Alexandria around 120 BC. Although we would regard it as a toy it did demonstrate the important principle that rotary motion could be obtained by the expansion of steam through nozzles. Over the centuries, many developments of rotary devices took place with wind and water driven mills, water driven turbines, and the early steam turbine of the Swedish engineer Carl de Laval in 1883. The main problems of the de Laval turbines arose from their enormous rotational speeds, the smallest rotors attained speeds of 26,000 rpm and the largest had peripheral speeds in excess of 400 m/s. Learning from these mistakes, Sir Charles Parsons in 1891 developed a multistage (15 stages) axial-flow steam turbine, which had a power output of 100 kW at 4800 rpm. Later, and rather famously, a Parsons steam turbine rated at 1570 kW was used to power a 30 m long ship, Turbinia, at what was regarded as an excessive speed at a grand review of naval ships at Spithead, England, in 1897. It outpaced the ships ordered to pursue it and to bring order to the review. This spectacular dash at once proved to all the capability and power of the steam turbine and was a turning point in the career of Parsons and for the steam turbine. Not long after this most capital ships of the major powers employed steam turbines rather than old-fashioned piston engines.
From this point, the design of steam turbines evolved rapidly. By 1920, General Electric was supplying turbines rated at 40 MW for generating electricity. Significant progress has since been made in the size and efficiency of steam turbines with 1000 MW now being achieved for a single shaft plant. Figure 4.1 shows the rotor of a modern double-flow low-pressure turbine with this power output.
The development of the axial-flow turbine is tied to the history of the aircraft gas turbine but clearly depended upon the design advances made previously in the field of steam turbines. In this chapter, the basic thermodynamic and aerodynamic characteristics of axial-flow turbines are presented. The simplest approach to their analysis is to assume that the flow conditions at a mean radius, called the pitchline, represent the flow at all radii. This two-dimensional (2D) analysis can provide a reasonable approximation to the actual flow, provided that the ratio of blade height to mean radius is
small. However, when this ratio is large, as in the final stages of an aircraft or a steam turbine, a more elaborate three-dimensional (3D) analysis is necessary. Some elementary 3D analyses of the flow in axial turbomachines of low hub-to-tip ratio, e.g.,are discussed in Chapter 6. One further assumption required for the purposes of mean-line analysis is that the flow is invariant along the circumferential direction (i.e., there are no significant “blade-to-blade” flow variations).
For turbines, the analysis is presented with compressible flow effects in mind. This approach is then applicable to both steam and gas turbines provided that, in the former case, the steam condition remains wholly within the vapor phase (i.e., superheat region).
The modern axial-flow turbine used in aircraft engines now lies at the extreme edge of technological development; the gases leaving the combustor can be at temperatures of around 1600oC or more whilst the material used to make turbine blades melt at about 1250oC. Even more remarkable is the fact that these blades are subjected to enormous centrifugal forces and bending loads from deflecting the hot gases. The only way these temperature and stress levels can be sustained is by an adequate cooling system of high pressure (HP) air supplied from the final stage compressor. In this chapter, a brief outline of the basic ideas on centrifugal stresses
and some of the methods used for blade cooling is given. Figure 4.2 shows the three shaft axial-flow turbine system of a Rolls Royce Trent turbofan engine.
Velocity diagrams of the axial turbine stage
The axial turbine stage comprises a row of fixed guide vanes or nozzles (often called a stator row) and a row of moving blades or buckets (a rotor row). Fluid enters the stator with absolute velocity c1 at angle α1 and accelerates to an absolute velocity c2 at angle α2 (Figure 4.3). All angles are measured from the axial (x) direction. The sign convention is such that angles and velocities as drawn in Figure 4.3 will be taken as positive throughout this chapter. From the velocity diagram, the rotor inlet relative velocity w2, at an angle β2, is found by subtracting, vectorially, the blade speed U from the absolute velocity c2. The relative flow within the rotor accelerates to velocity w3 at an angle β3 at rotor outlet; the corresponding absolute flow (c3, α3) is obtained by adding, vectorially, the blade speed U to the relative velocity w3.
When drawing the velocity triangles, it is always worth sketching the nozzle and rotor rows beside them, as shown in Figure 4.3. This helps to prevent errors, since the absolute velocities are
roughly aligned with the inlet and exit angles from the nozzle row and the relative velocities are aligned with the rotor row. Note that, within an axial turbine, the levels of turning are very high and the flow is turned through the axial direction in both the rotors and nozzles.