A huge amount of engineering and computational resources goes into the design of turbomachinery especially to meet multi-point, multi-objective, multi-disciplinary problems. This is especially true for centrifugal compressors, which, in almost all circumstances are range operating machines, where the ability to perform consistently at low to high speeds and low to high pressure ratios is as important as peak efficiency at the nominal ‘design point’.
The ongoing quest for map-width has, until now, been something of an empirical affair, especially when it comes to the design of the rotor itself, i.e. ignoring treatments that can be applied to the casing, diffuser and inlet. Rotor map-width and peak efficiency tend (but not always) to be a trade-off, meaning that you can have one but not the other.
Ideally then, we would want to optimize compressor rotor designs to give the very best efficiency and map-width possible for a given shaft and tip-speed (so - multi-point optimization). The traditional obstacle to this aim has been the sheer amount of high-fidelity simulation that has to be done in order to sufficiently explore a very complex and high dimensional design space, at multiple operating points. What if we could leverage a small dataset of high-fidelity data to accurately drive an optimization algorithm using Machine Learning methods?
At ADT we have considered very carefully how one might leverage the power of Machine Learning to the specific and highly complex problem of turbomachinery blade design.
● 3D Inverse Design - the enabling technology for Machine Learning
● An example of how Machine Learning can optimize a legacy compressor design
● Optimization via Machine Learning
● Design choices and performance gains
● Validation
● Conclusions
3D Inverse Design - the enabling technology for Machine Learning
In a previous blog, we showed how ADT have constructed and assembled the necessary building blocks to enable a turbomachinery Machine Learning system that can rapidly and efficiently home in on optimized designs.
In that case the application was an axial fan, but as you’d expect, the system can be configured to work on any turbomachinery design challenge.
Very briefly, the advantages of 3D Inverse Design over conventional design are:
An example of how Machine Learning can optimize a legacy compressor design
We are going to use a 20-blade, 400mm diameter compressor rotor as our baseline. This is based on the well-known Eckardt impeller. In this case it runs at 14000 rpm for a stage pressure ratio of between 1.9:1 and 1.75:1.
Firstly, we establish the baseline performance of this design by running CFD across the speedline. The pre-processing, solving and post-processing in this step is all automatically controlled from within TURBOdesign1 (TD1) , and we can choose the solver that we wish to use (i.e. it could be Ansys-CFX, Simcenter STAR-CCM+, Cadence Fine Turbo etc).
We are essentially running a pre-define template for centrifugal compressor analysis across the operating points, and TD1 is managing the generation of the data.
Figure 1: Baseline characteristics for efficiency and Pressure Ratio
Once we have our baseline established. We can turn the problem over to a Machine Learning algorithm which will attempt to redesign the rotor in order to meet the design objectives that we set.
Optimization via Machine Learning
The power of 3D Inverse Design means that we can use just 8 input parameters to create a large and rich design space wherein we hope to find a significantly better performing optimal design.
4 of the parameters relate the distribution of blade loading across the blade, 3 control the meridional shape, and 1 parameter controls the blade stacking at the trailing edge. With this small but power parameter set we have enough control and variation in the blade shape to produce a wide variety of candidate designs.
TD1 also uses an Machine Learning algorithm to recommend appropriate ranges for input variables, so that the design space is not too wide, resulting in ‘impossible’ designs, nor too narrow which might preclude a genuine, usable optimum being found.
Figure 2: 8 Input parameters describe the entire blade design space
Constraints
All good optimization algorithms work with constraints in order to efficiently explore the design space. RRS + CAE recognizes constraint violations and knows to move the search away from these areas. In this case we constrain the throat area to maintain the same swallowing capacity in the rotor as the baseline and to control the position of the peak efficiency on the speedline.
Objectives
What do we want from this machine? Because we are integrating multi-point CFD runs into this study we can choose CFD results from off-design points as objectives. In TD1 we tell the Machine Learning system to maximize efficiency at the surge and choke sides of the speedline, and maximize pressure ratio at the design point. Holding or increasing mid-map pressure ratio stops the map from ‘flattening’ – i.e. increasing map-width at the expense of pressure ratio delivery ,which is a common issue in traditional ‘direct’ design.
Figure 3: Objectives for the Machine Learning algorithm
Once we have set the optimizer meta-parameters (number of iterations, number of new designs added per iteration, and some settings governing the surrogate model used within RRS + CAE) the Machine Learning system can be run to find the optimum solution.
Because RRS + CAE makes very selective use of high-fidelity CFD to explore the multi-objective, multi-point design space, this Machine Learning optimization took just 30 hours on 4 cores of a deskside Xeon workstation. The Machine Learning algorithm needed only 132 CFD runs to explore the entire design space, and home in on the optimum multi-point design.
Design choices and performance gains
RRS + CAE uses a combination of low- and high fidelity simulation, surrogate models and a genetic algorithm to discover the optimum designs.
In this case we discover a Pareto front of candidate designs in 3 dimensions (1 dimension for each of the objectives).
Observing how the Machine Learning system came to this optimal front reveals that the 3 objectives do not compete very strongly. That is, by maximising one objective we also seem to, in general, maximize the other two.
Therefore the overall design gradient is moderately correlated in all 3 dimensions. This makes our design choice quite easy - we do not have to compromise one objective against the others.
Nevertheless, a Pareto front is constructed, which, by definition, shows that for every ‘optimal’ design there is a mild pay-off in performance objectives against all other designs.
Figure 4: Surrogate Pareto front of optimal solutions - design point pressure ratio pressure vs surge side efficiency. All points on this plot are Pareto optimal, we are viewing a 3-dimensional front in 2 dimensions.
Figure 5: Baseline geometry (left) compared with optimized geometry (right)
For any surrogate model point we can run the candidate through 3D Inverse Design to generate the actual blade shape, and then send to CFD under the same meshing, pre-processing and boundary conditions as the baseline and optimization points to get a final assessment of performance. By doing so we find that our chosen optimum returns a very good improvement over the baseline in all objectives.
Figure 6: Performance improvement of the optimum design (red) over the baseline (blue)
The full speedline shows that we have extended map width by maintaining the surge margin (as far as can be ascertained by CFD numerical stability) and significantly increased margin on the choke side.
The gain in overall efficiency is so significant (2-4 pts) that it would be fairly straightforward to gain more surge margin by profile trimming this blade.
Incidentally the blade lean at the leading edge and the maximum circumferential blade lean have both been reduced in the optimal design.
This means that , for the same thickness distribution we would see a reduction in root stresses due to centrifugal forces when the wheel is rotating. So we have improved mechanical as well as aerodynamic performance.
Validation
It is very important to assess how accurate the design space surrogate model is. We must have confidence in the Reactive Response Surface model to correctly predict the shape of the design space, otherwise we would be adding in high-fidelity simulation to predict multi-point performance at the ‘wrong’ Pareto front. The comparison between the RRS surrogate model prediction and verification in CFD is shown below. We can see that the actual performance results are the same as the values predicted by the ML algorithm, showing that Reactive Response Surface + CAE is an extremely accurate method for predicting the design space topology.
Figure 7: Comparison between RRS prediction and a posteriori CFD results
Conclusions
In this blog we have shown that, in just a few hours on a standard workstation, RRS+CAE can discover significant centrifugal compressor performance gains with component redesign using the 3D Inverse Design approach. Moreover that design can be validated with high confidence in full-fidelity CFD to confirm what the Machine Learning model predicts.
The Reactive Response Surface + CAE model is an ideal method for delivering optimal designs in a multi-point, multi-objective design space and for a fraction of the total cost traditionally associated with large scale, high-fidelity optimisation studies involving complex geometry and flow interaction.