Turbine blades all come in the same usual shape with the only seeming variations being size and the presence of a rotating shroud or not. However, for gas turbines (GTs) of similar ratings, sometimes there are quite dramatic (if not subtle) differences. A good example—one that affects the owner/operator directly—is the number of stages in the hot section.

Some units offered have three turbine stages (generally speaking, GE), some four (Siemens, for example), at least one five (Alstom). This may be a cost concern when considering hot-gas-path replacement or performance-related issues.

The $64 question: What determines the designer’s choice in selecting the number of turbine stages for a given GT design? Next, who, how, or what decides the number of blades in a particular row.

Looking at Fig 1, the vertical axis, shaft work, is akin to the “loading” or work performed; the horizontal axis, annulus height, depends on the height of the turbine blades. The illustration represents the relationship between the amount of work extracted from the hot gas and the blade height (as expressed in terms of mass flow through the annulus). The relationship is important for determining many factors related to performance, maintenance, and the first cost of the gas turbine itself.

This article, based on an interview with Brent A Gregory of Creative Power Solutions, considers only the cost implications associated with the number of turbine stages; performance implications are for another discussion. The Fig 1 chart, developed in the 1950s by Rolls-Royce, shows that the fundamental variables strongly correlate with turbine performance as the independent variable.

This is reflected by the red contours in the figure, which are lines of constant efficiency. The highest performance is for turbines defined by lower work requirements and lower velocities in the gas path. Engineer Ron Pearson realized early in the development history of GTs that the number of fundamental factors determining performance might only be the following:

• Demand on the turbine (work output).

• Surface area of gas-path components, expressed (or normalized by algorithmic manipulation) as the axial velocity of the hot gas.

Pearson’s work was later published by a colleague, S F Smith, and the figure came to be known as the “Smith Chart,” a/k/a the “Pearson Chart.” The red contours (derived tests and field data) represent lines of constant efficiency, where turbine efficiency increases towards the lower left of the chart. The blue line (drawn somewhat arbitrarily) represents the peak efficiency for any given design of turbine. The yellow shaded area defines the margins of where the blue line may be drawn.

The significance of the chart: Given that work (the demand of the compressor and generator for land-based turbines) and wheel speed (most often 3000 or 3600 rpm for generator drivers) are fixed, the only remaining variables are the mass flow required to achieve that work and the temperature drop across the turbine, according to the following equation:

Work = Mass flow × deltaT × Cp,

where Cp is the specific heat of the gas flowing through the turbine.

This means there is only one real solution that maximizes performance of a given turbine designed to meet certain requirements, and that is given by the blue line drawn through the peak points of each red curve.

That leaves as the only variable the axial “through-flow” velocity. From the physics of flow (continuity equation), this depends on the turbine annulus height. Increasing the annulus area reduces flow velocity; decreasing the area speeds up the flow. Thus the designer may have few options with which to manipulate a turbine gas path. It also follows, indirectly, that deviations away from the blue line have an effect on blade shape and on the number of blades.

To help explain, consider the following example: Assume the point on the ordinate in Fig 1 (“A”) denotes the work required by the turbine. Using a simple straight edge, the highest performing turbine is found at point “B” on the abscissa.

This illustrates there are few options open to the engineer to complete the optimum design of the turbine. Given the annulus area is fixed at point B, the designer can set the maximum diameter, and the annulus area (a function of the tip and hub diameters) is deduced from simple math.

However, the maximum diameter usually is chosen at a point where the mechanical designer is comfortable with the maximum stresses on the turbine attachments and the blade length—typically the last-stage blade. The aerodynamic designer, who shares responsibility for the final layout of the turbine, is even more challenged in terms of available avenues to optimize all the design constraints.

But he or she can choose to divide the required shaft work into several parts—each representing a turbine stage. Referring back to Fig 1, if the work “A” is divided between two or more stages, then the corresponding point on the ordinate is lower and the blue optimum performance curve describes a new annulus area.

Note that as the designer invokes this option, the performance of each turbine stage increases. The result: Turbine performance is better than the single point described by the original “AB” point. When it comes to adding turbine stages, there is a law of diminishing returns to consider. For mid- to large-size (40 to 400 MW) gas turbines, that limit is three to four turbine stages.

What are the key factors that drive the designer’s choice among two, three, four, or even five turbine stages? Brent Gregory’s career at Rolls-Royce, GE, Honeywell, and Alstom suggests that the historical progress of an OEM’s product allows the designer to generate a Smith/Pearson Chart for a given product range.

Generations of turbine designers have walked in their predecessors’ footsteps, meaning that new designs largely reflect previous designs with only very cautious introduction of new technologies. The Smith/Pearson Chart reflects the design and optimization strategies of the OEM over many years and development cycles. Thus one OEM’s Smith/Pearson Chart almost certainly will not overlay with that of another OEM’s. Each OEM has a unique optimum X or Y and the efficiency curves do not line up with one another.

These “brand” characteristics are determined by such things as empiricism derived from previous designs and the results of performance criteria derived from specific tests based on years of research in the academic world, and by emerging technologies such as Computational Fluid Dynamics (CFD).

Example: Aircraft-engine designers will develop turbines with fewer blades and vanes than the heavy-frame designer, who is impacted little by weight issues. In Fig 2, efficiency curves (“Optimum X”) for turbines having lower blade counts are driven to the right. The fundamental philosophies of design are of great importance when considering a turbine layout. That philosophy affects strategic business decisions such as first cost and lifetime costs.

It is doubtful a three-stage design could ever trump the four-stage design in terms of performance. Other factors driving the decision will determine the rationale for choosing a design, but producers of a wide range of turbines will have many choices at their disposal.

More probably should be said about the history of industrial three-stage turbines, which are incorporated in thousands of GE machines worldwide. Examples include all Frame 6Bs and Frame 7s through the Model FA.

The three-stage GT turbine evolved from steam turbines which were largely developed along high-through-flow designs because of their inherent low-pressure-ratio (lighter duty) stages. As OEMs transitioned their products from steam to gas turbines they turned to new technologies available to them from research developed for aircraft engines.

Aircraft-engine technologies drove new initiatives because of the need to increase firing temperature and the need to dramatically increase efficiency while reducing weight. In this work, the expansion across each stage determined the annulus area, so the optimums implied by the Smith/Pearson chart were largely ignored. Aircraft-engine developments have forced heavy-frame OEMs to rethink many historical paradigms.

Fig 3 illustrates the paradigm shift from the mature three-stage design, plotted on a per-stage basis, to a modern four-stage design. At least one OEM has transitioned to a four-stage turbine for its latest large frames from the three-stage design used in earlier models. The change was motivated by performance.

Even if the extra stage drives up first cost, the performance increase reflected in a lower fuel burn easily pays for the enhancement in less than a year. OEMs also have considerable advantage in using highly loaded technology in the first stage or two to allow less aggressive (read expensive) technology downstream.

If an OEM was thinking modern design, or even a retrofit, here’s what a four-stage design would look like relative to an equivalent-duty three-stage turbine (Fig 4):

• Shorter chords as a result of highly loaded airfoil technology (more work per blade). Higher loading reduces airfoil count and/or reduces the width of the blade.

• The blade shape and count are significant variables when designing turbines to the left or right of the optimum.

• Attachment areas are refined based on aircraft-engine technology or an evolution of a known “good” design practice within the OEM’s experience.

• Lower “through flow” allows the expansion of each stage to be incorporated in the same diameter as a three-stage machine, allowing the retrofit of a four-stage unit into a similar area. The casing can remain and the turbine inner flow path (hangers) can be reshaped to accommodate the new gas-path profile.

• Lower “through flow” enables efficiency optimization. Historically, the stage optimum efficiency implied by Smith/Pearson was largely ignored; a more modern design would tend to follow the optimum.

• The retrofit challenge will be to maintain the very high mechanical loads on a new last stage. Four-stage designs allow for increased performance with larger capacity flows, increasing output by as much as 20% for a given frame design. If designers can retrofit new technologies, such as those afforded by adding extra stages in the available design space, it opens up a new era for turbomachinery currently anchored in their existing facilities by 100 of tons of concrete.

However, it is highly unlikely that an OEM would seriously consider retrofitting an existing frame with more turbine stages (though it is often done in a compressor) because of the high mechanical demand placed on the rotor. Some OEMs with a long tradition of three stages can make a significant technology leap by adding a fourth stage to what traditionally would have been a three-stage machine and make a dramatic technology leap in quoted performance over the competition.