Three-dimensional Design Optimization Research Articles

Optimization of Three-Dimensional Blade and Variable Stators for Efficiency and Stability Enhancement of Multistage Axial Flow Compressor at Variable Speeds

Abstract High efficiency and wide stability at variable speeds are equally important to the design and operation of multistage axial flow compressors. However, published research works on three-dimensional design optimization of compressors are so far mainly limited to a single blade row or stage at design speed due to the curse of dimensionality. Moreover, optimization of variable inlet guide vanes (IGV)/stators for off-design operations is carried out by using a rapid but low-fidelity prediction tool and is generally independent of design optimization of blade geometry. To tackle these issues, a three-dimensional holistic design and adjustment optimization method is developed in which both three-dimensional blade geometry and variable IGV/stators are optimized simultaneously for better efficiency and stability at design and off-design conditions. Metamodel-interpreted data mining method and adaptive infilling strategy are used respectively to enhance the capability of the metamodeling and optimization. The developed method is then applied to a modern highly loaded 3.5-stage transonic axial flow compressor at both design and part-design speeds. The results show that the stall margin is extended from 8.23% to 19.65% at 70% design speed while peak efficiency is slightly improved at design speed. The flow mechanisms responsible for the efficiency enhancement at design speed are mainly associated with the reduced total pressure loss in stators as well as inter- and intra-stage loading redistribution. The stability enhancement at 70% design speed is mainly achieved by loading the front blade rows while unloading the limiting rear blade row through variable IGV/stators adjustment. The developed holistic design and adjustment optimization method with the aid of metamodel-interpreted data mining is of great application value for the design and adjustment of advanced multistage axial flow compressors.

Metamodel-Interpreted Data Mining for Stability and Efficiency Enhancement of Multistage Axial-Flow Compressors

Abstract The tradeoff between higher efficiency and wider stability of performance map is still one of the bottlenecks to hamper the further research and development of advanced multistage axial-flow compressor. The recent rapid growth of computational resources and artificial intelligence has enabled data mining as one of the most effective and potential ways to gain a deep insight into the complex correlations between aerodynamic performance and three-dimensional geometry parameters. In the open literatures, however, few research works have been found on using the data mining that is independent of design optimization to extract priori design guidelines for multistage axial-flow compressor mainly due to the lack of proper data mining method focused on the interpretation of metamodel with full use of limited time-consuming computational fluid dynamics dataset. To tackle this issue, a metamodel-interpreted data mining framework is developed in which extreme gradient boosting (XGBoost) metamodel combined with Shapley additive explanation (SHAP) model are employed to locally interpret the feature importance of each sample in the computational fluid dynamics dataset and then extract the design guidelines in terms of the most influential geometry parameters and their beneficial variation directions. The developed method is applied to data mining of design guidelines for efficiency and stability enhancement of a front 3.5-stage transonic axial-flow compressor in ship-board gas turbine usage. The results show that the aerodynamic performance of the investigated multistage compressor is most sensitive to three-dimensional geometry parameters related to blade lean, blade twist, and variable stators. Specially, the variable stators mainly affect the stall margin at part speed. The blade lean mainly influences the adiabatic efficiency at design speed as well as the stall margin at both speeds, while the blade twist mainly influences the aerodynamic performance at design speed. New designs followed by the design guidelines are obtained and critical performance indicators related to the goals of the data mining task are verified. The stall margin at part speed is widened to 5.87% with adjustment of blade lean and twist and further to 23.31% with additional adjustment of variable stators. The peak adiabatic efficiency at design speed is improved by 0.06% in spite of extremely limited potential for efficiency enhancement of the original design. The present work is of scientific significance as well as industrial application value in the three-dimensional design optimization of advanced multistage axial-flow compressor at the affordable computational cost.

Three-Dimensional Design Optimization of an Anode-Supported SOFC Using FEM

Solid oxide fuel cells (SOFCs) are promising as energy producing devices, which at this stage of development will require extensive analysis and benefit from numerical modeling. A 3D model is developed based on the FEM for a single cell planar SOFC design optimization. Ion, electron, heat, gas-phase species and momentum transport equations are implemented and coupled to the kinetics of electrochemical reactions. High current density spots are identified, where the electron transport distance is short and the oxygen concentration is high. The relatively thin cathode results in a significant oxygen mole fraction gradient in the direction normal to the main flow direction. The electron transport especially within the cathode is found to be limiting for the electrochemical reactions at positions far from the channel walls (interconnect ribs). It is concluded that an increased pore size in the cathode support layer increases the current density more than an increased pore size in the anode support layer.

Three-dimensional design optimization using the boundary integral equation method

Three-dimensional shape design optimization is demonstrated using the boundary integral equation method. Design sensitivities are obtained directly by differentiating the boundary integral equations with respect to normals to the surfaces at the design variable points. Coon's patches are employed in order to represent continuously changing design surfaces. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method which requires first-order derivative information has been adopted for the optimization part of the problems. Two examples, a perforated plate under biaxial stresses and a cantilever beam with end shear loading, are demonstrated for the smoothing of stress peaks and stress levelling.

Discrete aerodynamic sensitivity analysis on decomposed computational domains

A new scheme is presented for solving the large sparse unsymmetric systems of linear equations which arise from the application of the aerodynamic sensitivity equation to large two-dimensional as well as three-dimensional design optimization problems. Performance comparisons between a generalized minimum residual (GMRES) method and a direct solution method are performed on a single computational domain. Results show that, due to the use of preconditioning, the GMRES method requires almost the same memory allocation as that required by the direct method. Moreover, it is found that for many right-hand sides of the above systems, the GMRES method is significantly less efficient than the direct method. Since large systems cannot be solved by direct methods on a single domain, due to the computer memory limitations, the computational domain in the new scheme is divided into small manageable ones and each one is solved separately. In addition to the savings in memory requirements, this scheme can be applied easily to complex-geometry problems which cannot be represented by single computational grids. The computational performance of this scheme is assessed by considering the flow over a transonic airfoil. The sensitivity equation is solved for three cases where the computational domains are represented by different numbers of subdomains. Identical results are obtained in all cases without any visible effect due to the subdivisions of the computational grids. This indicates the scheme's high accuracy in solving the above system on decomposed computational domains.

Magnetic performance of the SSC dipole magnets

The authors report on the status of the magnetic design of the Superconducting Super Collider (SSC) dipole magnets. A two- and three-dimensional design optimization was performed that included the effects of permeable collar, yoke, cryostat, beam tube, crescent yoke end pieces, cool-down, and Lorentz loads. A field quality plan was developed that represents the approach to tuning the design for satisfying the systematic and RMS multipole specifications. The VSA tool is being used to simulate the effects of random parts, tool and process variations on the expected multipole distributions, both between many magnets, and within a single magnet. >