Radial inflow turbines are used in a wide range of applications, from big geothermal power plants to small gas turbines and turbochargers for automotive engines. They are found suitable for several industries encompassing ship, aircraft and space power systems where compact sizes and high expansion ratios are 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 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-speed turbines, there is usually a trade-off between the aerodynamic and structural aspects of the rotor, and this brings us to our problem statement.
Problem Statement
High speed radial turbines, like those used in turbochargers, operate under a very demanding environment and so it is a common practice to use modifications like radial filament. However, while this reduces the stress levels in the rotor making its operation safer, it takes a heavy toll on its efficiency. This is why, in a previous paper [2], we used an inverse design-based approach involving multiple CFD and FEA runs in order to ensure that the appropriate trade-off was achieved, where the designs were purely radial-filament due to some post modification on the 3D geometry.
This resulted in a highly optimized design with high efficiency and stress levels that were well within the material strength, and so we are going to refer to this as the baseline design for reference and for comparison in the present study.
Figure 2: Radial turbine performance maps from previous study [2]
Despite being highly effective, such an approach can still consume a lot of computational time and resources. So the question is whether it is possible to come up with a rapid optimization methodology which can match the performance levels of computationally expensive methods, while avoiding a large number of CFD and FEA runs and also avoiding the radial filament modification, and this is what we aim to explore through this work.
This is based on one of ADT’s technical papers that was presented at the 15th IMechE turbocharger conference [3].
Optimization Methodology
To put things in perspective, Figure 3 shows the previous optimization workflow and how it compares to the present one.
While the previous study started from an initial design and took several days to complete using multiple CFD and FEA runs and achieve an optimized design which we refer to as baseline in this work, the present approach goes from the initial design straight to TD1 optimization which is much quicker and still results in an equivalent performance to the baseline. Of course, some CFD and FEA is performed but this is only to validate the final design.
Figure 3: Workflow for rapid optimization of radial turbines
3D Blade Design of Rotor
Here are the specifications that are used to design the radial inflow turbine rotor:
- Expansion Ratio: 2.2
- Rotational Speed: 71,000 rpm
- Flow Rate: 0.22 m3/s
Figure 4 presents the meridional shape which is directly used from the optimized design from the previous study, and the duty point sits in the good efficiency region of the specific speed diagram and so this means that using the above specifications, it should be possible to design a radial turbine with a good performance level.
Figure 4: Meridional shape of radial turbine rotor and duty point verification in specific speed diagram
Figure 5 presents the setup for the baseline radial inflow turbine stage in our 3D inverse design software TURBOdesign1, where it is possible to impose your own custom thickness profile as shown, and which is very important for stress considerations. The spanwise work distribution is forced vortex, and so it has some variation from hub to shroud. Also, the initial loading distribution is fore-loaded at the hub and aft loaded at the shroud, and then these inputs result in 3D geometry of the rotor wheel.
Figure 5: 3D blade design of radial turbine rotor
In the second part of this article, we present a rapid methodology to optimize the initial rotor design to a less 3D blade (not completely radial-filament), and quickly obtain the desired trade-off between its aerodynamic and mechanical performance.
References
[1] O. E. Balje, “TURBOMACHINES : A Guide to Design, Selection, and Theory”, A Wiley-Interscience Publication, (1981)
[2] Zhang, J., Zangeneh, M., “Multidisciplinary and multi-point optimisation of radial and mixed-inflow turbines for turbochargers using 3D inverse design method”, 14th International Conference on Turbochargers and Turbocharging, Institution of Mechanical Engineers, ISBN: 978-0-367-67645-2
[3] Zhang, J., Zhang, L., Zangeneh, M., “A 3D inverse design based rapid multi-disciplinary optimization strategy for radial-inflow turbines”, 15th International Conference on Turbochargers and Turbocharging, Institution of Mechanical Engineers, ISBN: 978-1-032-55154-8
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