In part 1 of this blog, we discussed how to construct the essential elements of a Machine Learning system that could reliably and efficiently be applied to the problem of parameterizing, evaluating and optimizing a turbomachinery blade geometry.
Now let’s look at how this system, based on ADT’s Reactive Response Surface + CAE, is applied to an industrial application, by optimizing the multi-point performance of an axial fan.
● Establishing a baseline design and characteristic
● Setting up the optimization
● Inputs
● Constraints
● Outputs
● Reactive Response Surface + CAE
● Running Machine Learning system to obtain multi-objective, multi-point optimal solutions and selecting final design
● Verifying performance and comparison with baseline
● Conclusions
Establishing a baseline design and characteristic
With a basic specification for speed and flowrate, number of blades and outer diameter, we can rapidly obtain a baseline design that will meet the specifications using TURBOdesign-Pre to generate the meanline design and TURBOdesign1 (TD1) to create the 3D blade shape.
TD1 creates an inviscid estimate of performance and a noise calculation based on the Ffowcs-Williams Hawkings equation for dipole sources to give ‘thickness noise’ and ‘loading noise’ which are the primary noise signals for subsonic rotating flow.
The characteristic Pressure-flow (P-Q) curve for low- design- and high-flow operating points is, in this case, created by running Simcenter Star-CCM+ at these points, but another high-fidelity CFD solver can be used.
Domain creation, meshing, pre-processing, running the solver and post-processing are templated, scripted processes, managed by TD1, so we get consistency of analysis time after time.
Figure 1: TD1 automatically integrates multi-point CFD analysis to establish a baseline fan characteristic
Setting up the optimization
The entire blade design space is described by just 10 parameters, linked to blade loading distribution and the position of the leading edge. Not only is this an incredibly efficient way of parameterizing a complex 3D shape, it also means that all candidates in the design space are guaranteed to meet the required duty (pressure rise at a given flow rate and rotor speed) so we do not spend any time evaluating non-compliant candidates. Our only consideration is how well each design meets the duty requirements, we do not have to worry if they actually will or not.
Figure 2: Definition of the 10 blade definition input parameters
The design space candidates are constrained by an upper limit on the pressure rise at the high flow point, candidates which fall outside this limit still run, but are marked as ‘non-feasible’ and the optimizer knows to move away from such designs. This constraint is one way of making sure of a rising P-Q curve, i.e. one where the delivery pressure rises as the flow rate falls, so we are in the ‘stable, usable’ region of the fan characteristic.
We are targeting peak efficiency, flow range and noise performance, recognising that these objectives can compete with each other, leading to payoff (or Pareto optimal) designs. We direct TD1 to maximise efficiency at the design point and maximise pressure rise at the low flow point to maintain a rising P-Q curve and extend range on the stall side of the characteristic. We also mandate to minimize tone noise at the design point.
Figure 3: Objectives (blue) and constraint (red) shown on the fan characteristic
Reactive Response Surface + CAE
ADT’s Reactive Response Surface (RRS) + CAE is an incredibly efficient way to conduct focussed searches in a multi-dimensional design space.
It enables rapid convergence to a global optimum using a small dataset. In this case we specify an initial design matrix of 40 candidates to establish the design space, followed by 4 iterative steps that add 5 candidates each time - so 20 additional points.
In reality 3 of the additional points are found to be non-feasible, breaking our pressure-rise at high-flow limit, so only 17 additional points are added.
That means 40+17 candidates run across 3 operating points (low-, design- and high-flow rates) so 57 x 3 = 171 CFD runs. Between the iterative steps, RRS+CAE will interrogate the design space using a MOGA of 100 generations of 100 children, so 10,000 samples of the space.
Although this sounds like a heavy computation, it will use the surrogate model to generate responses, so will take hardly any time at all.
Running the Machine Learning system to obtain multi-objective, multi-point optimal solutions
Everything we need to run the study is now set up, and a single mouse click sets the study underway which will run autonomously from end-to-end. This took 19 hours on 32 cores of a Xeon workstation.
Because we are running multi-objective optimization, and those objectives pay-off against each other, our optimal solution is actually a 3-dimensional (1 dimension for each objective) Pareto front.
Any point on this front is an optimal compromise between the 3 competing objectives. So we can select a final design based on what priorities we choose - effectively weighting the objectives based on relative importance.
Let’s select the optimal candidate which gives the absolute best pressure rise at the low-flow point (so best range) and the best design point efficiency, compromising on the acoustic objective.
It is important to note that, because the design is taken from the Pareto front, it is still the best performing acoustically from the 1000s of considered points in the overall design space, for a design which also delivers maximum gain on the other two objectives.
Figure 4: Selection of an optimum solution from the Surrogate model predicted 3D Pareto front
Verifying performance and comparison with baseline
We run the selected optimum in CFD to verify its performance and find the improved characteristic meets our performance objectives. We have improved peak efficiency by more than 3 points whilst increasing the slope of the P-Q curve, thus extending the range on the stall side. We pay a very small penalty in predicted total noise output going from 56.8 dB for the baseline design to 56.9 dB on the optimised design. There are other candidates in the design space that are quieter, but with smaller improvements in efficiency and pressure rise across the operating range.
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.
We find that the actual performance results agree very well with the predicted values to within a maximum error of around 1% on all objectives. showing that Reactive Response Surface + CAE is an extremely accurate method for predicting the design space topology.
For the acoustic performance, the validation is taken from the TD1 calculation of noise (Ffowcs-Williams Hawkins equation) as we do not do an acoustic simulation in CFD.
Figure 6: RRS (surrogate model) prediction accuracy vs CFD/TD1 data for Optimal Design 1
Conclusions
In this article, along with part 1 of this blog, we have seen how realizing a set of requirements for building a Machine Learning system can lead to usable and efficient gains in component performance.
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.