Robust design using multiobjective optimisation and artificial neural networks with application to a heat pump radial compressor

Although robustness is an important consideration to guarantee the performance of designs under deviation, systems are often engineered by evaluating their performance exclusively at nominal conditions. Robustness is sometimes evaluated a posteriori through a sensitivity analysis, which does not guarantee optimality in terms of robustness. This article introduces an automated design framework based on multiobjective optimisation to evaluate robustness as an additional competing objective. Robustness is computed as a sampled hypervolume of imposed geometrical and operational deviations from the nominal point. In order to address the high number of additional evaluations needed to compute robustness, artificial neutral networks are used to generate fast and accurate surrogates of high-fidelity models. The identification of their hyperparameters is formulated as an optimisation problem. In the frame of a case study, the developed methodology was applied to the design of a small-scale turbocompressor. Robustness was included as an objective to be maximised alongside nominal efficiency and mass-flow range between surge and choke. An experimentally validated 1D radial turbocompressor meanline model was used to generate the training data. The optimisation results suggest a clear competition between efficiency, range and robustness, while the use of neural networks led to a speed-up by four orders of magnitude compared to the 1D code.

Influence of input parameters in radial compressor design algorithm on the efficiency and its sensitivity analysis

Nowadays there are lots of methods using three-dimensional or quasi three-dimensional CFD analysis. Unfortunately, this approach is still very demanding, so that quick preliminary design algorithms have still its importance, even though simplified analytical model of radial compressor gives less accurate results. Obtained results can be used in later stages of the radial compressor (RC) design, such as definition of spatial impeller geometry and CFD computation. The article presents the influence of input parameters in the radial compressor design algorithm on the efficiency. The assembled mathematical model of RC is derived from the basic laws of continuum mechanics and can be used for a quick assessment of the preliminary design concept of the RC. A sensitivity analysis is performed on input parameters to select parameters that have the dominant effect on the monitored performance indicators. On the basis of the sensitivity analysis, a multicriteria optimization process was assembled to increase the performance parameters.

Validation of a Radial Compressor CFD Analysis

In this study, a radial compressor flow at a high speed is investigated by Computational Fluid Dynamics (CFD) methods. The radial compressor of interest consists of a rotor, diffuser, and exit guide vanes and has an operational rotational speed of 21789 rpm. The geometry of the compressor and its test results such as compression ratio and adiabatic efficiency are available in literature. After extensive mesh convergence tests, steady-state CFD analysis has been performed for compressible and turbulent flow using the ideal gas approach. The main motivation of the study is the determine the appropriate CFD approach and boundary conditions of the problem that will fit best to the measurements. The CFD analysis revealed that the maximum relative errors for the adiabatic efficiency and the pressure ratio were 3.6 % and 1.3 %, respectively.

Metamodel-Assisted Multidisciplinary Design Optimization of a Radial Compressor

Kriging is increasingly used in metamodel-assisted design optimization. For expensive simulations; however, one can afford only a few samples to build the Kriging model, which consequently lacks prediction accuracy. We propose a bounded Kriging able to handle optimization problems with a small initial database. During the optimization, the proposed Kriging suggests designs close to database samples and finds optimal designs while staying in a feasible region (with respect to mesh and CFD convergence). The bounded Kriging is applied along with the ordinary Kriging to a multidisciplinary design optimization of a radial compressor. The shape of the compressor blades is optimized by considering the aero performance at different operating points and the mechanical stresses. The objective of the optimization is to maximize the efficiency at two operating points, while constraints are imposed on the maximum stress level in the material, the choke mass flow, the pressure ratio and the momentum of inertia of the impeller. While ordinary Kriging stopped prematurely because of many failing design evaluations, the bounded Kriging satisfied all constraints and reached an improvement of 2.59% in efficiency over the baseline design that does not comply with any constraints. The bounded Kriging covers a special need for robust methods in optimization able to deal with challenging geometries and a small database, which is the case for most industrial design optimizations.

Using Optimization in Industrial Multi-Point Radial Compressor Design: Map Correction

The application of Surrogate-Based Optimization (SBO) to the industrial design process for a radial compressor with two operating points is described. The design specification includes two operating points at mass flow rates differing by a factor of three, and efficiency and pressure ratio targets for each point. The base case, while roughly sized from 1D analysis, fails to achieve the pressure ratio targets. In this paper, the optimization focusses on correcting the two speed-line map of total to static pressure ratio vs. mass flow rate. “Smart parameterization”, combining independent and dependent geometric parameters, and yielding reasonable geometries for most input combinations, coupled with efficient SBO, with separate models for response surface modeling and failure prediction, yields a design achieving the targets in just 57 CFD runs. FINE/Turbo [1] is used as the CFD analysis code and FINE/Design3D [2] and MINAMO [3] as the multi-objective optimizer.

Automatic Numerical Analyses and Optimization of Operating Maps Applied to a Radial Compressor

This paper contributes to the field of radial compressor design by proposing an adaptive, automated workflow incorporating the analysis of the compressor performance for a multitude of operation points by means of the respective operating maps. Most state-of-the-art approaches do not consider that the operating map limits are not conserved while changing geometric parameters which constraints these analyses to a rather small design space. In contrast, the presented methodology considers the varying operating map limits in regards to the corresponding mass flow and with that expands the possible input parameter range. The presented workflow integrates different software solutions, starting with the automated generation of the compressor geometry based on a parametric CAD model. For each geometry a mesh is generated that is used for all subsequent CFD simulations which finally result in the operating map. For every speed line, the choke point is identified by an adaptive CFD computation (based on the principle of similarity). By using the calculated choke mass flow, supplementary CFD simulations obtain additional operating points on the current speed line by a stepwise reduction of the mass flow. However, the identification of the surge line is not within the scope of the presented approach. Therefore, the range covered by the map is determined by the mass flow at the maximum efficiency and the mass flow at the choke line. The developed framework is applied to optimize the operating map of a radial compressor. A successful optimization shows that the optimized design has an enlarged choke mass flow for lower compressor speed while the pressure ratio and polytropic efficiency are comparable. At the same time, this design has a comparable choke mass flow and efficiency for higher compressor speed, but an improved maximal pressure ratio. The obtained results from the optimization show that the methodology is applicable to a wide parameter range. By adaptively calculating the operating map limits, the approach is not restricted to a small design space.