Axial Turbine Stacking - Best Practices for Secondary Flow Suppression

Axial turbines are used in a wide range of applications, from aero-engines to electricity generation in thermal power plants. They are employed in both gas and steam turbine applications where high work output with light weight and high efficiency is required.

Turbine Design Process

The first step in the design of any turbine is to identify the required specific speed regime of the turbine. This will dictate the meridional shape and hence the general flow direction through the machine. For example, a low specific speed turbine is likely to be a radial inflow type, whereas a high specific speed one is likely to be of mixed or axial flow type.

From the required specific speed, we can identify the main flow phenomena and loss mechanisms dominant in that particular range. For example, as the NsDs turbine chart in Figure 1 shows, leakage and secondary flow effects are more dominant in the lower ranges, whereas shocks and profile losses take priority in the higher ranges.

 

Figure 1: NsDs turbine chart [1]

In fact, with inverse design, it is possible to come up with a set of optimal design guidelines based on these fluid dynamic considerations of reducing the dominant flow losses for your turbine. However, when it comes to high and intermediate pressure stages of axial turbines, the loss mechanisms are dominated by the secondary flows or passage vortices near the hub and shroud endwalls.

Problem Statement

The design of HP and IP axial turbine nozzles, such as those used in the early stages of aero-engines and land-based steam and gas turbines, is a complex problem because:

• While conventional stacking methods like compound lean can suppress the passage vortex development near the endwalls, but it increases the loss around the midspan.
• This also makes the flow exiting the nozzle highly non-uniform, which in turn can increase the downstream mixing losses.
• It may also require modifications to the downstream rotor to be able to match this non-uniform flow profile.

This is why traditional methods often involve inefficient geometrical trial-and-error in trying to achieve control of the nozzle exit velocity, which consumes a lot of computational time and resources. So the question is whether it’s possible to come up with a rapid design technique which can perform all of this in a single design iteration, that is, which can suppress the dominant secondary flows but without adversely impacting the midspan region and the exit velocity distribution in your axial turbine nozzle, and this is what we aim to explore through this work.

Figure 2 shows the specifications of this axial turbine nozzle which has previously been studied both numerically and experimentally [2], and will be used to design the nozzles with various stacking conditions in this work.

 

Figure 2: Axial turbine nozzle specifications and schematic of test section [2]

Conventional Radial (Straight) Stacking

The first nozzle geometry is created in a CAD tool by simply extruding the hub profile in the radial direction, which is the conventional radial stacking method as presented in Figure 3.

 

 Figure 3: Axial turbine nozzle with radial stacking

Once the radially stacked nozzle is ready, a CFD analysis is run to check the actual performance. As Figure 4 shows, ANSYS TurboGrid is used for the fully structured grid of the nozzle passage and CFX for the flow analysis. Here are the different CFD settings where the inlet and outlet boundary conditions are taken from the original publication [2].

• P₀₁, T₀₁ = 171500 Pa, 388 K
• P₂ = 90703.2 Pa (radial equilibrium at hub radius)
• Turbulence model: k-omega SST
• Total mesh size ≈ 0.8 M
• Average blade y⁺ ≈ 8

 

Figure 4: Axial turbine nozzle CFD setup

Once the CFD run is complete, the results are converted into a total pressure loss coefficient using this expression which is commonly used for axial turbine nozzles, as reported in Figure 5. Next, this loss contour is plotted at the nozzle exit and finally converted into a spanwise mass-averaged profile. It can be observed that although the midspan has low loss value, there are high loss peaks corresponding to the secondary vortex flows near both hub and shroud endwalls.

 

Figure 5: Total pressure loss coefficient calculation for axial turbine nozzle

Conventional Compound Stacking

A second nozzle geometry is created in CAD using the conventional compound stacking method by arranging the same radial profile in such a way, that the pressure surface makes an acute angle with both hub and shroud endwalls as illustrated in Figure 6.

 

Figure 6: Axial turbine nozzle with compound stacking

Figure 7 reveals that when CFD analysis is repeated on the compound lean nozzle, the loss peak near the endwalls due to passage vortices is found to be lower but the loss at the midspan has increased due to greater loading in this area compared to radial stacking.

 

                                                      Figure 7: Axial turbine nozzle loss comparison between radial and compound stacking

Case for Controlled Stacking using 3D Inverse Design

Therefore, it is evident that while one type of stacking works well for the midspan loss, it makes the endwall loss worse and vice versa. So this brings us to a unique type of stacking method called controlled stacking which combines the best of both worlds using the 3D inverse design method. As Figure 8 shows, the mid-section is straight which maintains a low loss at the midspan whereas both hub and shroud endwalls have compound lean which suppresses the loss from passage vortices. Furthermore, the inverse design method ensures that the exit velocity distribution is not disturbed as a result of the stacking method.

 

Figure 8: Controlled stacking approach for axial turbine nozzle

Controlled Stacking using TURBOdesign1

Now, we'll  demonstrate how an axial turbine nozzle with controlled stacking can be designed using TURBOdesign1, and how it improves the aerodynamic performance compared to conventional stacking methods.

Figure 9 presents the setup for the nozzle with controlled stacking in our 3D inverse design software TURBOdesign1, where the meridional design, thickness and all these settings can be directly used as design inputs. The controlled stacking condition shown is imposed at 40% of the axial chord which is clearly a combination of radial stacking at the midspan and compound stacking near the endwalls.

The loading distribution is aft loaded at both hub and shroud as commonly seen in axial turbines, and the spanwise swirl distribution at the nozzle inlet and exit is preserved regardless of the loading or stacking condition, and then these inputs result in 3D geometry of the nozzle.

 

Figure 9: Controlled stacking approach for axial turbine nozzle 

Performance Comparison

CFD analysis is performed on the new nozzle design with controlled stacking, leading to some very interesting results reported in Figure 10. The hub side loss peak is suppressed by about 13% as a result of the controlled stacking condition, close to what we had with compound stacking. However, there is no increase in midspan loss, which is actually almost coincident with the radial stacking result. This provides confirmation that this unique stacking method is able to cut down the overall losses in the nozzle.

 

Figure 10: Total pressure loss coefficient of axial turbine nozzle with controlled stacking

Figure 11 compares the exit flow profiles from the different stacking methods, and clearly the controlled stacking results in a very uniform meridional velocity compared to the conventionally stacked designs. The main advantage from this is that it makes the exit flow angle distribution very uniform, whereas compound stacking produces a large variation of almost 10 degrees from hub to shroud, which can be highly detrimental to the performance of the downstream rotor. Above all, the controlled stacking is performed in a single design iteration, whereas to achieve the same using conventional compound stacking would certainly require significant trial-and-error.

 

Figure 11: Axial turbine nozzle exit flow angle comparison

In order to understand this improvement from controlled stacking, Figure 12 reveals that the loss cores corresponding to passage vortices are reduced in depth compared to radial stacking near both hub and shroud. This is true with compound stacking as well, but the wake is much wider at the midspan leading higher loss figures in this region.

 

Figure 12: Axial turbine nozzle exit total pressure loss contours

Another result of interest is contours of helicity displayed in Figure 13, which clearly shows that both hub and shroud passage vortices are weakened as a result of controlled stacking. However, while compound stacking is able to produce a similar effect near the shroud, it presents a much stronger helicity towards the hub compared to controlled stacking.

 

Figure 13: Axial turbine nozzle exit helicity contours

Finally, difference contours of loss coefficient are also studied to understand which areas of flow result in a loss increase or decrease compared to the radially stacked design, as reported in Figure 14. With controlled stacking, there is a notable reduction in loss inside the passage vortex cores, with only a slight increase towards blade pressure side. However, with compound stacking, the loss reduction at the midspan gets compromised by a significant increase on the pressure side, resulting in an overall higher loss value.

 

Figure 14: Axial turbine nozzle exit loss difference contours

Conclusion

In summary, high and intermediate pressure axial turbine stages typically show a predominance of passage vortex losses near the endwalls. While conventional methods such as compound stacking are good for suppressing these endwall vortices, they can worsen the midspan loss and also make the exit flow non-uniform.

Essentially, controlled stacking with inverse design makes it possible to bring about an overall loss improvement without compromising on the exit flow uniformity. Moreover, this methodology does not involve any trial-and-error as opposed to conventional design methods.

Our experience has shown that the choice of optimum stacking for controlling profile or endwall losses has generality and can be applied to other similar applications. For example, we find that for endwall loss control, the type of stacking that we use for turbines is applicable to all types of turbines, mixed flow and radial and regardless of the turbine speed or size.

References
[1] O. E. Balje, “TURBOMACHINES : A Guide to Design, Selection, and Theory”, A Wiley-Interscience Publication, (1981)
[2] Watanabe, H., Harada, H., “Suppression of Secondary Flows in a Turbine Nozzle with Controlled Stacking Shape and Exit Circulation by 3D Inverse Design Method”, International Gas Turbine & Aeroengine Congress & Exhibition, June 7-10, 1999, Indianapolis, Indiana, USA