Optimization of a Heat Pump Compressor for Small-Scale Domestic Application

In the first part of this article on the design of a small-scale high speed centrifugal compressor for domestic heat pumps, we showed that the baseline impeller satisfies the basic requirements in terms of peak efficiency point and blade lean/bow parameters.

In this second part, we show how the aerodynamic performance of the baseline impeller can be enhanced without compromising on its structural integrity through the application of automatic optimization in TURBOdesign1.

Optimization Workflow

Figure 1 displays the workflow used by the automatic optimization, where the blade loading parameters are used to generate the blade shape in TURBOdesign1, and then the resulting performance parameters are fed into Optima which basically applies MOGA to drive the solution towards the optimum design.

Figure 1: Workflow used in automatic optimization of heat pump compressor

Optimization Setup

The optimization process starts by specifying the range of variation for the input parameters shown in Figure 2, which are the streamwise loading parameters because they have direct influence on the surface pressure distribution. Whereas by default the ranges are set to ± 10% of the baseline values for each parameter, there is a machine learning based feature in TURBOdesign1 that can provide initial 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: Input parameters used for heat pump compressor optimization

Figure 3 presents the constraints that are used. The throat is tightly restricted to control the peak efficiency point, and the overall diffusion ratio is limited to prevent flow separation. The leading-edge lean angle and bow ratio directly impact the maximum blade stress, and so they are constrained as well. An additional constraint is the maximum surface Mach number which prevents the compressor from entering the transonic regime. Finally, for the optimization objectives we want to minimize the profile loss and the secondary flow factor in order to maximize the efficiency. In this way, using these objectives and constraints we ensure that blade integrity is not compromised in the process of improving its aerodynamic performance.

Figure 3: Constraints and objectives used for heat pump compressor optimization

Software Demo - Automatic Optimization of a Heat Pump Compressor Impeller with TD1

Optimization Results

Once the optimization run is complete, which is very fast and only takes about 20 minutes or so on a single core machine, the design candidates can be seen on a scatter plot between the two objectives as shown in Figure 4, where the position of the baseline impeller relative to the candidates may also be observed. Next, we can choose to see the Pareto front of optimum designs from which we can pick and analyse any design of interest. For the present work, we select a design which promises a good trade-off between the profile and secondary losses, and so we use this design for further analysis and for comparison with the baseline impeller.

Figure 4: Scatter plot of feasible designs and Pareto front of optimum designs

Figure 5 reveals what changed as a result of the optimization. At the shroud, the optimizer decreases the fore-loading but still retains the fore-loaded distribution which helps in suppressing secondary flows. For the mid-span, the optimizer recommends slightly less aft-loading for improving the profile loss in this area. As a result of these changes, the optimized blade clearly appears very different from the baseline as shown alongside.

Figure 5: Comparison of blade loading between baseline and optimized impellers

As reported in Figure 6, it is interesting to see the effect on TURBOdesign1 parameters where there is a significant reduction in the total profile loss and the secondary flow factor as a result of the optimization. The diffusion ratio and maximum Mach number stay within the acceptable range removing the possibility of flow separation and transonic effects, and the lean angle and bow ratio are smaller than baseline implying that blade stress is not adversely impacted. Also, the change in throat area is minimal.

Figure 6: TURBOdesign1 performance parameters for the optimized heat pump compressor

Finally, when CFD analysis is performed on the new impeller, what we find is that the peak efficiency still occurs at the design flow and this is because the throat was constrained during the optimization as shown in Figure 7. More importantly, compared to the baseline impeller, we see up to half a percentage point improvement in efficiency over the entire simulated range. Consequently, the total pressure ratio has increased by about 2% over the baseline value for all of the simulated curve.

Conclusion
Small-scale high speed turbocompressors for heat pumps typically present a trade-off between the aerodynamic and structural aspects of the impeller. Essentially, using appropriate constraints and objectives, it is possible to optimize the impeller and achieve this trade-off in a matter of half an hour or so. Moreover, this methodology involves very less computational resources in terms of CFD runs compared to conventional design methods. Our experience has shown that the choice of optimum loading for controlling profile or secondary loss 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 compressors is applicable to all types of compressors, mixed flow and axial and regardless of the compressor speed or size.