*How turbomachinery configurations are selected and what parameters drive the selection.*

**By Nicholas C. Baines, Concepts NREC**

Almost every type of renewable energy cycle requires a piece of turbomachinery. Compressors, fans, blowers, pumps, turbines all are critical components in a wide range of renewable energy applications, from wind energy to ocean energy to bottoming cycles to hydrogen pumping. While many people are familiar with these types of turbomachinery components in general, not everyone knows when or why a certain turbomachinery configuration is selected over other available configurations.

For instance, when is a centrifugal compressor better suited for a given application than an axial compressor? How is stage count determined (when and why can a single stage centrifugal compressor replace a multi-stage axial compressor). This article offers an overview of how turbomachinery configurations are selected and what parameters drive the selection to better educate users of turbomachinery, including users in the renewable energy field. Some classic turbomachinery selection charts will be shown and explained.

Turbomachines are devices that transfer energy between a turning shaft and a fluid. That definition encompasses a range of machines that is so wide as to be baffling for anyone charged with the task of selecting or designing a new machine for a new process. This is even truer in new green energy than in conventional applications, where the energy source is likely to be natural and highly variable and the technology base and experience that engineers can draw on is limited.

The transfer of energy can be in either direction. In a turbine, it is from the internal and kinetic energy of the fluid to mechanical energy of the rotating shaft. In a compressor or pump, mechanical energy is transferred to the fluid to increase its pressure or head. In some cases, such as pumped storage systems, the same machine must do both duties: pumping the fluid into storage when surplus energy is available and expanding it to generate power at other times. Turbomachines can be open or closed flow devices. Open flow machines such as wind turbines and marine propellers have no casing or enclosure around the moving parts. Closed flow machines include hydro turbines and a wide diversity of pumps, fans, compressors and blowers.

Turbomachines have to work with fluids of widely differing properties. A principal classification is between incompressible fluids, such as water and most liquids, where the density changes are insignificant, and compressible fluids including air and most gases, where the density changes considerably in passing through the machine. Other machines, such as steam turbines, may have to work with a mixture of the two, as the steam condenses into water droplets during the expansion through the turbine.

The ranges of size and speed are also very large. Wind turbines can be 100 meters or more in diameter and rotate at a few revolutions per minute (rpm). Hydro turbines are up to 10 meters in diameter, rotating at a few tens of rpm. At the other end of the scale, miniature turbines used in liquefying helium are less than 1 centimeter in diameter and rotate at 1 million rpm. The pressure drop across a wind turbine is small (measurable in millimeters of water), whereas the pressure rise generated by a downhole pump in an oil well is sufficient to drive fluid to the surface, a head rise of several thousand meters.

Faced with such a diversity of size, form and function, there is clearly a need to impose some order by finding suitable ways to classify and organize turbomachinery, so designers can make quick and reliable decisions when it comes to selecting machines for new applications.

## Dimensional Analysis

Experience has taught engineers not just in turbomachinery but in many other areas that a useful method of handling this type of diversity is dimensional analysis. Using this, the fundamental parameters that describe the application, including flow rate, pressure or head change and speed; the size of the machine; and the thermodynamic and physical properties of the fluid, are combined into groups that are dimensionless. Not only does this make the problem independent of the set of units used, but more importantly, it reduces the number of parameters the engineer has to handle. Instead of a large number of fundamental parameters, the machine and its performance can be represented using a smaller and more manageable set of dimensionless groups.

Dimensional analysis is a flexible tool, because it only defines mathematically how many dimensionless groups are required to specify the machine and its operation, but it does not say what those groups should be. This is up to the engineer, who can select the groups that are most useful in any set of circumstances. When selecting between the different types of turbomachine, one particular set of dimensionless groups has proved to be especially useful and these are groups that exclude the machine size. They are, therefore, functions only of the operational conditions (and if necessary the fluid properties) and are called specific speeds.

Specific speed is actually a misnomer, because although the shaft speed is invariably one of the fundamental parameters included, the group itself does not relate to any speed of, or within, the machine. Several different specific speed groups can be defined, but the one most commonly used, is Ns = N√Q/(gH)3/4, where N is the rotational speed, Q is the volume flow rate, and gH is the head change across the machine. (Different values of specific speed result from using different units for these parameters. If a consistent unit set is used, the resulting specific speed is dimensionless and this has been used in this article.) The constituent parameters all have to do with the machine’s operation or duty and not with its size. Specific speed, therefore, can be looked upon as a shape or form parameter, which gives information about the type of machine. Other information will later be necessary to determine the actual size of the machine that is required, but for the purposes of selecting the type of machine, specific speed is a valuable parameter.

Experience has shown that different types of turbomachines work best at particular specific speeds. Figures 1 and 2 are some of the classic charts compiled to aid selection. These examples show hydro turbines and pumps. Similar charts are available for other types of application. The efficiencies shown here are indicative of what is achievable, but should not be used for performance prediction. The actual efficiency will be a function of many other effects that are not represented on these graphs. The duty of the machine allows the engineer to determine the specific speed without reference to the machine size. The appropriate specific speed chart then can be used to select the machine type on which to focus attention.

The choice of specific speed defines the machine’s form, as shown in the pump example in Figure 3. A low specific speed means a combination of low flow Q and high head gH, for which the impeller shape at the left-hand end of the diagram is suitable. The low flow requires narrow channels and the high head is achieved by the large centrifuging effect created by the inlet/outlet diameter ratio of the impeller. On the other hand, a high specific speed implies a high flow and low head, at the right-hand end of the diagram. The high flow requires a large passage area, and the low head can be achieved with an axial impeller configuration.

This same effect can be seen for a range of Francis turbine runners in Figure 4. The low specific speed runners are characterized by passages of small area and a large radius change from inlet to exit, giving a large expansion of the flow from its incoming high head to exit at ambient conditions. For this purpose a radial or centrifugal runner is required. The high specific speed runners have a much larger passage area and a much lower inlet to exit radius ratio. Unlike the high specific speed axial pump, the incoming flow is still radial and undergoes a change of direction to axial in the runner. The turning effect, however, is not the key to work transfer from the fluid, it is the radius change that for high specific speed applications must be small to match the low head of the incoming flow.

Specific speed is not the only dimensionless group that is useful for selecting turbomachines. Two other groups to be considered are the head and flow coefficients. The head coefficient is the specific work transfer (that is, power per unit mass flow rate) divided by the square of the rotor blade tip speed. The flow coefficient is defined as the meridional velocity of the fluid (that is, the axial velocity in the case of an axial machine or the radial velocity in the case of a radial or centrifugal machine) divided by the tip speed. Since meridional velocity is volume flow rate per unit area, it is apparent how this coefficient relates to the machine’s flow rate. Both coefficients also emphasize the importance of the tip speed of the rotor in determining machine performance characteristics.

Two further selection charts, now showing head and flow coefficients, are depicted in Figures 5 and 6, for work-absorbing (pumps and compressors) and work-producing (turbines) machines, respectively. Taking the former, the air and marine propellers are examples of machines that have high flow, low head characteristics, and this is the area of the diagram in which they are found. The axial fan found in turbofan engines is another example of a high flow turbomachine. In this case, however, it is a highly refined aerospace product capable of higher pressure rises (and hence head coefficient) than more mainstream fans. This is an example where the level of technical refinement adds some complexity to machine selection. It also emphasizes that with all of these experience-based charts, the limits of machine performance are somewhat fuzzy.

Axial, mixed flow and centrifugal compressors form a spectrum covering the range of flow coefficients, so the choice will depend strongly on the flow rate requirements. In the chart, single and multistage centrifugal compressors are differentiated and this highlights another design decision to be made: the number of stages. Many turbomachines can be made with multiple stages to share the work and pressure or head change. If the work requirements are too great for a single stage, multiple stages must be considered. Areas of overlap always exist where the same effect could be achieved using a small number of highly-loaded stages (that is, high head coefficient per stage) or a larger number of lightly-loaded stages. Since lightly-loaded stages are usually easier to design and more efficient than highly-loaded stages, an incentive exists to increase the stage number, providing the manufacturing costs and installation size do not become excessive. So the multistage compressor in Figure 5 comprises stages with lower head coefficients than the single stage compressor.

A similar pattern can be seen for expanders in Figure 6. Wind turbines and Kaplan (hydro) turbines are examples of high flow, low head turbines. The axial gas turbine is another high flow turbine because for airplane applications the size of the engine must be kept to a minimum to limit the aerodynamic drag of the engines. This forces the turbomachine stages to have high flow coefficients, or high flow per unit area. To limit the number of stages and hence engine weight, however, the head coefficient per stage is raised. Various forms of gas and steam turbines occupy the high head regime of the chart, and for high head, low flow applications, the Pelton wheel is best suited.

Because of the dimensional analysis, dimensionless groups are interrelated and specific speed can be expressed as a function of head and flow coefficients. Lines of constant specific speed are also plotted in Figures 5 and 6 to emphasize the point that high specific speed coincides with high flow, low head applications and low specific speed with low flow, high head, applications.

The use of head and flow coefficients goes beyond the initial machine selection and is influential in choosing the number of stages, as noted above. It also affects the turbomachine design itself. In many applications, a need exists to maximize the power transfer per stage and minimize the number of stages. Excessively high stage loading, however, limits the efficiency that is achievable. The stage loading coefficient can be reduced by increasing the number of stages or by increasing the blade tip speed. The former increases the machine’s complexity, size and cost and the latter increases the centrifugal stress in the blades and may limit the life of the machine.

Selecting a small flow coefficient means keeping the fluid velocity low in the blade passages, which is conducive to high efficiency, but also means that the flow passage area must be large. To minimize the size of the machine, a higher flow coefficient must be selected. As with head coefficient, the flow coefficient can be reduced by increasing the blade tip speed, at the cost of blade stress. Figure 7 illustrates the designer’s dilemma: high efficiency requires low head and flow coefficients, whereas machine size and life goals may require high head and flow coefficients. The designer’s skill lies in choosing the right compromise between conflicting requirements such as these, but head and flow coefficients allow the problem to be expressed in simple terms that are easily understood.

Author: Dr. Nick Baines is a distinguished corporate fellow at Concepts NREC and has worked for the company in a variety of positions including director of education and publications. Dr. Baines has extensive experience teaching turbomachinery topics to a broad range of clients. He has worked in the field of turbomachinery for more than 30 years. He has a wide knowledge of turbomachinery for various applications and has been responsible for a large number of projects requiring the selection and design of turbomachinery. Dr. Baines received his BA and MA in Engineering from St. Catharine’s College in Cambridge and his Ph.D from the University of Bath.

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