In another article on the manual design of a centrifugal pump stage, we showed that there is scope for improvement in the baseline impeller especially in terms of achieving the stage head requirement.
This article examines the use of Optima feature in TURBOdesign1 to automatically optimize the blade loading of the baseline impeller in order to improve the stage efficiency and hit the target stage head.
Figure 1 displays the workflow used by the automatic optimization, where the blade loading and stacking parameters are used to generate the blade shape in TURBOdesign1, and then the resulting performance parameters are fed into the optimizer which basically applies MOGA to drive the solution towards the optimum design.
Figure 1: Workflow used in automatic optimization
The optimization process starts by specifying the range of variation for the input parameters, which are the streamwise loading parameters and the wrap angle or stacking at the trailing edge because it also has an influence on the surface pressure distribution, as shown in Figure 2. Whereas by default the ranges are set to ± 10% of the original value for each parameter, there is a machine learning based feature in TURBOdesign1 that can provide optimized range estimates for these streamwise loading parameters. This is because we want to explore a large design space but also try and avoid infeasible solutions.
Figure 2: Default (left) and optimized (right) input parameter ranges used in automatic optimization
Figure 3 shows the constraints that were imposed on the optimizer as follows:
Finally, the optimization objectives are selected so as to minimize the profile loss and secondary flows in order to hit the desired stage head levels.
Figure 3: Constraints and objectives used in automatic optimization
Once the optimization run is complete, which is very fast and only takes about an hour or so on a single core machine, all the design candidates can be seen on a scatter plot between the two objectives as shown in Figure 4. The position of the baseline impeller relative to the candidates may also be noted.
Figure 4: Scatter plot of all optimization designs
Next as Figure 5 shows, we can choose to see the Pareto front of optimum designs from which it is possible to pick and analyse any design. For the present study, we select a design from near the middle of the Pareto front which promises a good trade-off between profile loss and secondary flows, and so we use this design for further analysis and for comparison with the baseline impeller, as indicated in the figure.
Figure 5: Pareto front of optimum designs
Figure 6 reveals what changed as a result of the optimization. For the streamwise blade loading, compared to the baseline impeller, the optimizer has tried to make the shroud highly fore-loaded in order to reduce the profile loss. But the hub is much less fore-loaded because this will help to reduce the pressure coefficient gap (as shown in the figure) which helps in suppressing secondary flows. As a result, the optimized impeller clearly appears very different from the baseline as shown alongside. Additionally, while the baseline impeller had zero stacking at the trailing edge, the optimizer has resulted in a backward stacking which helps to further reduce the pressure coefficient gap and hence the secondary flows.
Figure 6: Comparison of spanwise work and blade loading between baseline and optimized rotor
The results for the optimized impeller are presented in Figure 7, where the TURBOdesign1 parameters reveal a significant reduction in the profile loss and secondary flow parameters as a result of the optimization, with only a slight change in its throat area and diffusion ratio. When stage CFD analysis is performed with the new impeller at 85%, 100% and 115% of design flow rate, it is found that the peak impeller and stage efficiencies, along with the minimum volute loss happens at 100% design flow rate. This confirms that both the impeller throat and the volute are sized correctly for the design condition.
In terms of performance, compared to the baseline impeller, there is approximately 1 percentage point improvement in the total-to-total efficiency of both the impeller and the stage at the design flow rate. Furthermore, there is a 3% reduction in the volute loss coefficient which is because now there is a more uniform flow going into the volute, as can be seen from the relative velocity comparison at the impeller exit. Consequently, the pump is able to exceed the target stage head by 2.5%.
Figure 7: Results comparison between baseline and optimized design
Figure 8: LIVE Demo - Centrifugal Pump Stage Automatic Optimization for Centrifugal Pump Impellers
Conclusion
There are various types of loss mechanisms in pumps for different specific speed regimes, and it is important to identify those that affect your centrifugal pump stage. Essentially, with a good knowledge of flow physics gained from CFD and experiments, it is possible to arrive at the optimum blade loading for your specific centrifugal pump impeller. Our experience has shown that the choice of optimum loading for controlling profile loss or secondary flows has generality and can be applied to other similar applications. For example, we find that for profile loss control, the type of loading that we use for pumps is applicable to all types of pumps, mixed flow and centrifugal and regardless of the pump speed or size.