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Average value of the two design objectives of individuals on the Pareto Fronts and the three CGCT-add-on cases
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A compressor blade integrated with circumferential groove casing treatment (CGCT) is optimized in this study. A hybrid aerodynamic optimization algorithm that combines the differential evolution with a radial basis function response surface is used for the multi-objective optimization via the computational fluid dynamics analysis. The sweep and lea...
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... point performance of the individuals in the two rounds of optimizations (a) design objectives of all the qualified individuals; (b) design objectives of the two Pareto Fronts, three CGCT-add-on cases, and the baseline blade. Table 5 quantitatively compares the results of the blade-only optimization, its following CGCT-add-on cases, and the blade-CGCT optimization. The blade-only optimization increases í µí± í µí±¡0,í µí±í µí±í µí±¡ and í µí¼ by 0.873% and 0.979%, respectively. ...
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This paper presents the aerodynamic design of an aircraft wing using a surrogate-assisted meta-heuristic (MH) method. The optimization problem is posed to find the wing shape in order to maximize its lift-to-drag ratio. Two surrogate-assisted MHs are presented which are the use of a surrogate model to predict the objective function directly and usi...
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... Nevertheless, in the realm of blade design, certain researchers have begun contemplating the incorporation of casing treatment. For example, Song et al. 26 showed that incorporating a casing treatment during the blade optimization process yields better results than adding a casing treatment after designing the blade. Chi et al. 27 proposed a rapid casing treatment optimization design approach based on SM assessment and data mining. ...
Experimental results indicate that wire mesh casing treatment (WMCT) enhances the stability of low-speed compressors with little reduction in efficiency. The flow resistance on the surface of the grooves, which are formed by the wire mesh, provides a new variable for the design of WMCT. This paper investigates the stability improvement induced by three different meshes through experiments and steady numerical simulations. A stability prediction model incorporating the effect of WMCT is developed to assess the stability of the steady flow field, and the results show that the predicted stall points of the compressor are close to those of the experimental data. The stability analysis model has a well-defined theoretical foundation in which the meridional flow field of the compressor is considered as the basic flow and the blade is replaced with a body force. This formulation enables fast and accurate stability assessments of compressors incorporating WMCT during the design process. Finally, based on the influence of the different meshes on the steady flow field, the stability-enhancing mechanism of WMCT is analyzed in terms of flow field details and macroscopic physical quantities. WMCT improves the flow around the tip region, shifting the tip blade loading in the aft direction and reducing the tip leakage flow. Macroscopically, the installation of WMCT makes the flow structure in the tip region less sensitive to changes in the compressor operating conditions.
... Multi-objective optimization (MOP), as an efficient design method, has been used in various fields to respond to the increasing complexity and multiple requirements in scientific research and engineering design (Song et al. 2019;Zuhal et al. 2019;Savage et al. 2021). Compared with single objective optimization, MOP usually has more complex design space and needs more sample points, which usually means more high-fidelity expensive numerical simulation is implemented. ...
To improve the optimization accuracy and efficiency, state variable and optimization potential-based multi-objective optimization (MOP) method is introduced. State variable records whether the simulation failed, which caused by ill geometry and mismatched predetermined boundary condition, and is consequently incorporated into objective function through weighted average method to improve the accuracy of surrogate model and optimization. Optimization potential, which represents the difference between present performance and ideal optimal objective, can be used to direct MOP and avoids the manual selection of weight vectors. Four optimization cases, including traditional weighted optimization, state variable based optimization, optimization potential based optimization, and the optimization combined presented two methods, are applied to optimize a typical compressor blade airfoil and demonstrate the proposed optimization method. Results show that the combination of these two methods produces the best optimization result. In which the state variable method generates most of improvement in optimal performance and the optimization potential method notably improves optimal performance under large incidences. The introduction of state variable excludes the invalid objective values at one sample point rather than directly removing or keeping, so that the accuracy of surrogate model is significantly improved and obtains better optimal results. The distribution of optimization potential among each incidence is similar to that of weight vector. Using its summation to construct objective function can be deemed as automatically assigning a preferable weight vector and the optimal result consequently presents slight preferable performance.
... With the development of computational fluid dynamics, the flow field details inside the turbomachinery passage are shown more comprehensively. It has become one of the important means to improve the aerodynamic performance of turbomachinery to remodel the high flow loss area based on the simulation results of flow field [4][5][6][7][8]. At present, the conventional simulation analysis methods usually diagnose the distribution of pressure and velocity to judge the quality of the flow field, However, the flow parameters such as pressure and velocity in most of the flow fields are basically continuously changing, and the qualitative analysis of such conventional physical quantities is limited in guiding the actual flow diagnosis and design optimisation of turbomachinery. ...
A high-load counter-rotating compressor is optimised based on the method of coupling aerodynamic optimisation technology and computational fluid dynamics, and the flow structures in the passage are analysed and evaluated by vorticity dynamics diagnosis. The results show that the aerodynamic performance of optimised compressor are obviously improved at both design point and off-design point. By comparing the distribution characteristics of vorticity dynamics parameters on the blade surface before and after the optimisation, it is found that BVF (boundary vorticity flux) and circumferential vorticity can effectively capture high flow loss regions such as shock waves and secondary flow in the passage. In addition, the BEF (Boundary enstrophy flux) diagnosis method based on the theory of boundary enstrophy flux is developed, which expands the application scenario of the boundary vorticity dynamics diagnosis method. The change of vorticity dynamics parameters shows blade geometric parameters’ influence on the passage’s viscous flow field, which provides a theoretical basis for the aerodynamic optimisation design.
... Multi-objective optimization has been widely used in the shape design of fluid dynamic cases such as the design of high-lift airfoil [1], heat exchanger [2], transonic axial compressor rotor with casing treatment [3], re-entry spacecraft [4], counter rotating open rotor [5], centrifugal compressor [6], and win fence of unmanned aerial vehicle [7], etc. The multi-objective optimization methods used in those applications span from metaheuristics, gradient-based and surrogatebased algorithms. ...
The multi-objective efficient global optimization (MOEGO), an extension of the single-objective efficient global optimization algorithm with the intention to handle multiple objectives, is one of the most frequently studied surrogate model-based optimization algorithms. However, the evaluation of the infill point obtained in each MOEGO update iteration using simulation tool may fail. Such evaluation failures are critical to the sequential MOEGO method as it leads to a premature halt of the optimization process due to the impossibility of updating the Kriging models approximating objectives. In this paper, a novel strategy to prevent the premature halt of the sequential MOEGO method is proposed. The key point is to introduce an additional Kriging model to predict the success possibility of the simulation at an unvisited point. Multi-objective expected improvement-based criteria incorporating the success possibility of the simulation are proposed. Experiments are performed on a set of six analytic problems, five low-fidelity airfoil shape optimization problems, and a high-fidelity axial flow compressor tandem cascade optimization problem. Results suggest that the proposed MOEGO-Kriging method is the only method that consistently performs well on analytic and practical problems. The methods using the least-square support vector machine (LSSVM) or weighted LSSVM as the predictor of success possibility perform competitively or worse compared with MOEGO-Kriging. The penalty-based method, assigning high objective values to the failed evaluations in minimization problem, yields the worst performance.
... Zhao et al. (2014) optimized the effect of casing grooves on NASA rotor 37 based on radial basis function neural network (RBFNN) and a multi-objective evolutionary algorithm. In order to improve stability and design performance, Song et al. (2019) developed a grooved casing treatment optimization method integrated with threedimensional blade design. These optimization studies were conducted on multiple grooves, using identical and equally spaced casing grooves. ...
This study concerns a multi-objective optimization of circumferential single grooved casing treatment for a low-reaction transonic rotor with ultra-high loading. The axial location, width and depth of the groove are investigated as design variables. The optimization problem seeks to fully extend the operation range of the rotor while minimizing efficiency degradation. Artificial neural network of radial basis function is applied to construct the surrogate model. The optimal groove configuration was determined using non-dominated sorting genetic algorithm II (NSGA II) in conjunction with technique for order preference by similarity to ideal solution (TOPSIS). Detailed analysis of flow field reveals that two flow features involving stability enhancement for the low-reaction rotor are the inhibition of shock/vortex interaction in the rotor tip region and the reduction or elimination of double-leakage tip gap flow. The blocking region located right downstream of the interface between the tip leakage flow and the main flow is decreased due to the tip unloading effect and recirculation flow induced by the groove. Additionally, the efficiency improvement can be observed as the intensity of tip leakage vortex decreases. Based on the single groove optimization, the prospect of a particular multiple groove casing configuration consisting of component grooves with varied geometrical dimensions is also discussed in the paper. The simulation results indicate that the new-type multiple groove configuration is more advantageous to the rotor’s performance.
... The differential evolutionary algorithm, as an improvement of the traditional genetic algorithm, can achieve a global optimal solution and has considerable utilization in aerodynamic optimization. The optimization code was validated by previous studies on airfoil optimization [37][38][39] and turbomachinery optimization 40 . The main optimization process is shown in Fig.9. ...
Propeller aircraft are widely used in general aviation. The rotating propeller has a strong effect on the aerodynamic performance of the wing. This paper uses an actuator disc to model the effect of the propeller. A wing optimization method is developed with the actuator disc method. Several wing optimizations with different slipstream settings are studied. The twist angle and airfoils of the wing are used as the design variables. The results show that the propeller slipstream and slipstream directions have a strong influence on the optimization process. Powered-on optimization with a slipstream can obtain better drag reduction results than unpowered optimization. The drag decomposition results show that most of the drag reduction comes from the form drag reduction. The symmetric “inboard-up” slipstream configuration is found to have the highest lift-to-drag ratios, which are 18.87 for the twist angle optimization and 19.15 for the airfoil optimization.
... Dinh et al. [55] varied the shape and location of air injection holes in the stator shroud to improve performance, whilst Kim et al. [134] and Song et al. [222] included the shape optimisation of casing grooves in their formulations. Li et al. [146] also used optimisation to inform the best settings for variable stators within a five-stage machine, employing a meanline analysis code. ...
... At the detailed design stage, where three-dimensional optimisation of the blade geometry is performed, the use of data-fit models in surrogate based optimisation (SBO) frameworks has become standard practice [156,209]. Response surfaces are built from an initial dataset generated using design of experiments techniques, with several different methodologies employed to construct the low-fidelity models including Kriging [55,96,122,128,131,154,155], artificial neural networks [126,146,179] and radial basis functions (RBFs) [64,144,222]. The surrogates are used to predict performance within an optimisation loop, often being updated sequentially as in BO (see Section 3.2.2.3) to improve their accuracy as the optimisation progresses. ...
There is commercial pressure to design axial compressors exhibiting high levels of performance more quickly. This is despite the performance of these machines approaching an asymptote in recent years, with further gains becoming increasingly difficult to achieve. One tool that can be used to help is optimisation, effectively harnessing the speed of computational analysis to accelerate the design process and unlock additional performance improvements. The greatest potential for optimisation exists at the preliminary design stage, however, current methodologies struggle when applied at this early point in the design process due to inadequate problem formulations, an inability to fulfil the role of enhancing designer understanding and a lack of high-fidelity analysis due to computational cost. The goal of this thesis is to facilitate the use of optimisation in the preliminary aerodynamic design of axial compressors by developing an improved methodology that overcomes these limitations. The multiple dominance relations (MDR) formulation enables a larger number of performance parameters to be incorporated in a way that accurately reflects the desires of the designer. This is implemented within a Tabu Search (TS) that is capable of providing interpretable design development information to enhance designer understanding. The combined MDRTS algorithm, overcoming the limitations associated with formulation and understanding, outperforms existing methods when applied to analytic, aerofoil and six-stage axial compressor test cases, generating computational savings of up to 80%. Multi-fidelity techniques are used to accelerate the search by conducting analysis on a "need-to-know'' basis. Computational savings of over 70% are observed compared to the single-fidelity version of the algorithm across the analytic, aerofoil and six-stage axial compressor test cases, enabling high-fidelity analysis to be employed in a computationally efficient manner. The resultant methodology represents a novel and inherently flexible multi-level multi-fidelity optimisation technique. Application to an N-stage axial compressor test case, in which the optimiser is given control over the number of stages in the machine, demonstrates the capabilities of the accelerated MDRTS approach. The complex design space is effectively navigated, generating computational savings of over 90% compared to existing methodologies and producing designs that are more likely to be of interest to the designer. Interpretable design development information is also provided for this problem to enhance designer understanding. These results show that the improved methodology successfully facilitates the use of optimisation in the preliminary aerodynamic design of axial compressors, overcoming the problems associated with formulation, understanding and speed that limit existing approaches.
... Qin et al. [13] conducted an optimization of casing grooves, with the groove quantity and height as optimal variables. Zhao et al. [14] combined the non-dominated sorting genetic algorithm II (NSGA II) and the radial basis function (RBF) methods to optimize circumferential grooves for NASA Rotor 37. Song et al. [15] investigated a multi-objective optimization, in which the circumferential grooves and the rotor shapes are considered together. Upon the analysis of the optimal solutions in these studies, it is found that the optimization method is suitable for casing treatments design, which normally can obtain the solutions with quite good effects. ...
A multi-objective optimization of a coupled casing treatment for an axial transonic compressor is performed in this study. The coupled casing treatment is the basis axial slots with a circumferential groove located at various positions along the slots. During the optimization stage, five important parameters to control the geometry are used as the optimal variables. The stall margin and the peak efficiency are selected as the optimal objectives. Nondominated sorting genetic algorithm II coupled with radial basis function approximation is used to search for Pareto-optimal solutions. Then, four optimal configurations are selected from Pareto-front for further analysis. As shown in the simulation results with and without the coupled casing treatments, the leakage flow is reenergized and the blocking region near the blade leading edge at rotor tip is decreased by use of these structures under the low flow rate condition, which is the main reason for stability enhancement. Besides, a coupled casing treatment with the groove settled near the end of the basis slots have potential to generate more injection flow and extend the operating range of compressor further.
... The radial basis function response surface method [38] is chosen as the surrogate model. The optimization code was verified by previous studies on airfoil [39] and turbine optimizations [40]. ...
The present study proposes a new configuration of an internally blown flap based on a multielement airfoil for the high-lift system of an amphibious aircraft. Triobjective optimization based on computational fluid dynamics is carried out. The optimization results show that the present configurations have efficient lift enhancement and reach the tradeoff of the lift to drag ratio and low angle-of-attack performance. The optimized configuration also has good stall behavior and better poststall performance. A parametric analysis is conducted to test the sensitivity of each design parameter, and the results prove the robustness of the configuration. The results of different jet momentum coefficients show that two critical values exist that separate the lift versus jet momentum curve into three segments corresponding to different flow phenomena, which indicates that the circulation control rule for a multielement airfoil with a blown flap is different and more complicated.
