Scaling and Trimming in Axial Compressors and Fans

Introduction

Despite the deepening understanding of the essence of gas-dynamic processes and the development of computational methods, simpler design methods such as scaling and trimming remain in demand in turbomachinery engineering. The main advantage of these approaches over design from scratch is simplicity and its inexpensive nature due to the small-time expenditure and lower demand from computational resources. Good predictive accuracy of the performance and efficiency of the resulting machines is based on the use of an existing machine with well-known characteristics as a prototype.

Conversely, using the prototype imposes restrictions on the use of scaling and trimming methods. It is almost impossible to get a new design with pressure and efficiency higher than that of the prototype. Also, in cases where it is required to obtain performance that is significantly different from the prototype, the inherent reliability of the original prediction may be insufficient.

Scaling Method

Easy to apply and general, valid, scaling laws are needed for design and application engineers. The scaling laws are needed for the purposes of:

  1. Predicting the full-scale performance machine from model test data obtained from a scaled machine
  2. Obtaining a family of machines with different performances on the basis of one well-tested machine

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Experimental performance and efficiency testing on a full-size model of large machines such as fans to ventilate tunnels and mines or to move combustion air and smoke gas in power plants may be impractical due to the high energy costs and geometric limitations of the experimental stand. In these cases, a scale model is used. And although complete similarity is not maintained, for example, in terms of the Reynolds number, the correction factors in most cases are well known and the prediction accuracy is high.

The method involves the implementation of the flow path of the designed fan or compressor on a scale to the prototype. This means that all linear dimensions (e.g. diameters, blade chord, axial length, etc.) must be multiplied by the scaling factor (SF). The angular dimensions (e.g. blade angles at inlet and outlet, stagger angle, etc.) remain unchanged.

When scaling, it is assumed that parameters such as Pressure Ratio, circumferential velocity (U), and axial velocity (Cz) are equal for the designed machine and the prototype. Thus:

Trimming and Scaling Formula 1

The condition of equality of the Reynolds criteria is not ensured, since the designed compressor and the prototype do not have the same diameters of the rotor with the equality of other parameters that determine the number of Rew. This design guarantees the practical accuracy of the calculated characteristics, provided that the gas movement in the flow path is turbulent. It is known that for “physical” values of the Reynolds numbers

Trimming and Scaling Formula 2

the flow remains turbulent and the inequality of the Reynolds numbers of the designed compressor and the prototype has little effect on the gas-dynamic characteristics.

To determine the efficiency of low-pressure fans, a well-known formula is usually used:

Trimming and Scaling Formula 3

An example of obtaining a stage of an axial compressor by the scaling method is shown in Figure 1.

Figure 1 - Axial Compressor Stage Scaling
Figure 1 – Axial Compressor Stage Scaling

The disadvantages of the scaling method include the need to change the rotor speed. This can be relevant for industrial installations, where the rotation speed is often limited and tied to the frequency of the electrical network current. Additionally, the need to change the overall dimensions can be a limiting factor, especially if it is necessary to increase productivity significantly, and the installation location for the turbomachine is limited. In some cases, maintaining full geometric similarity is impossible for technological or constructive reasons. For example, the minimum value of the tip clearance may be limited by the operating conditions of the rotor (not touching the rotor against the housing) or the impossibility of obtaining a small clearance if the scaling is carried out from a large prototype to a small model.

Trimming Method

Fan rotor trimming is a common industrial practice and serves several different purposes. In applications where low cost is more important than high efficiency, cast impellers may be machined later in the process to produce impellers with different operating characteristics from a single die. Similarly, a single high-flow design can be expanded to become a family of fans through successive trimming to cover a wide flow range. In addition to these, it can be very useful to modify an existing impeller design for a new performance requirement rather than perform a “clean sheet” design on a new impeller. The advantage of trimming is the ability to reduce the fan performance without changing the rotor speed, as well as minimal changes to the housing parts.

One of the methods for designing axial compressors is to obtain a multistage compressor using one initial (model) stage. Axial velocity control along the flow path is carried out by reducing the inlet annulus area of each stage. For this, the blade is trimmed along the shroud of the hub or on both sides (Figure 2).

Figure 2 - The Main Types of Flow Parts Obtained by the Trimming Method
Figure 2 – The Main Types of Flow Parts Obtained by the Trimming Method

Compressor stages can have a different distribution of total pressures and axial velocities along the blade height. For example, in the stages designed according to the free vortex law, the theoretical distribution of total pressures and axial velocities is uniform along the blade height. Therefore, for this type of stage, trimming will not affect the summary value of the axial velocity or total pressure.

In reality, however, numerous studies show that it is not possible to obtain a uniform diagram of axial velocities and total pressures for stages even designed according to the free vortex law. Figure 3 shows a stage scheme with axial velocity and total pressure plots. In the zones near the surfaces of the hub and shroud, the values of the axial velocity and total pressure drop sharply due to losses in the boundary layer.

Figure 3 - Plots of Total Pressures and Axial Velocities in an Isolated Real Stage
Figure 3 – Plots of Total Pressures and Axial Velocities in an Isolated Real Stage

When trimming, axial velocity and total pressure diagrams are obtained by parallel displacement of the near-wall zones of velocity and pressure drop. An increase in trimming leads to a reduction in the area of uniform distributions of parameters (flow core) and until the disappearance of the flow core and the merging of the near-wall zones of parameters drop.

As a rule, in real stages, the value of the total pressure increases from the hub to the shroud, while the diagram of the total pressure is uniform at the inlet to the stage. With hub trimming, the average total pressure downstream of the stage increases. However, with over trimming, when the near-wall zones of parameters drop merge the average total pressure of the stage drops. With shroud trimming, the average pressure downstream of the stage always drops.

The change in the head coefficient  (formula below) of a stage due to trimming is determined empirically.

Trimming and Scaling Formula 4

Experience shows that in real compressor stages, the total pressure diagrams can have a different degree of unevenness with different near-wall zones of parameters drop. Therefore, the value of the Ktrimmed coefficients is different for different stages (see below formula).

Trimming and Scaling Formula 5

For example, Figure 4 shows the Ktrimmed distribution for the K-100-4 stage for hub and shroud trimming.

Figure 4 - Dependence Plots of the Ktrimmed Coefficient for the K-100-4 Stage
Figure 4 – Dependence Plots of the Ktrimmed Coefficient for the K-100-4 Stage

Conclusion

Simple methods of obtaining a new design such as scaling and trimming have a number of advantages over modern design methods and have their applications in turbomachinery engineering today. Scaling and moderate trimming results in highly predictable designs, and can be cheaper and more easily completed than undergoing a new clean-sheet design.

The main disadvantages of the scaling and trimming methods include the impossibility of obtaining a design with a significant increase in pressure than that of the prototype. Additionally, the accuracy of the prediction of the parameters may decrease if the scaling and trimming are performed at a large value.

Are you looking for ways to better increase your scaling and trimming capabilities? Or perhaps you’re looking to obtain trimmed and scaled designs faster in order to bid on a design contract? Then you don’t want to miss our upcoming webinar on turbomachinery trimming and scaling, happening on November 10th, 2021 at 10:00AM EST. Register for free here.

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