Abstract:Design requirement is as important in aerodynamic design as in other industries because it sets up the objective for the samples in design space to approach. Natural Laminar Flow (NLF) optimization belongs to the type of aerodynamic design problems featured by the combination of distinct aerodynamic performance, where the design requirement is often formulated in form of summation of laminar-related performance and pressure drag performance with different weight assignment according to different perspectives. … Show more
“…60 Each of the five new design variables is variated from the space of (À1.0, 1.0). The input number of samples for surrogate modelling is eventually 600 after geometric check, which is determined by the convergence criterion proposed in the authors' another work 36 : a dataset is presumed to be sufficient if its eigenvectors obtained via POD is converged in terms of directions, which is shown in Figure 9. The Kriging model is realized via Python package pyKriging.…”
Section: Surrogate Modellingmentioning
confidence: 99%
“…The percentage of qualified samples under posed geometric constraints from input seed population provides an estimation of the size of available design space. 36 As a closer observation of sampling, three different locations of the geometry are picked as is seen in Figure 4a, where the points from different control points contribute to the sampling of the rotor blade in different ways. The qualified is notably within the borders constituted by sampling seeds, which shows the completeness of the parametric perturbation.Figure 3.The distribution of qualified samples among total sampled data: red, triangle markers represent total sampled data while blue, round ones represent qualified ones.Figure 4.The selected three control points: their perturbation in sampling.…”
Section: Problem Descriptionmentioning
confidence: 99%
“…Geometric constraint has provided essential problem-oriented information, e.g. key geometric features, 35 limit of performance improvement, 36 optimization direction, 37 etc. Therefore, the design space is then filtered by geometric constraint, and now it contains dominant eigenvectors that can be captured by POD (Proper Orthogonal Decomposition), which results in eigenmodes presented in form of grouped FFD control point displacement.…”
Compressor blade design influences aero-engine performance mainly through its total pressure ratio and efficiency. As a volume-based geometric parameterization, Free-form Deformation (FFD) brings three-dimensionality that is essential to blade design. However, the manipulation of control points with respect to simple numeric parametric perturbation renders the use of design space low-efficient. Therefore, an improved FFD with ‘wiser’ control point lay-out is expected to identify those more important design variables. This paper proposes novel design variables that are assigned to grouping of control points’ displacement in FFD lay-out. In short, the approach is realized as: (i) establish a library of sufficient blade shape samples; (ii) filter the database with geometric constraints; (iii) extract dominant modes via (POD) Proper Orthogonal Decomposition; (iv) construct new design variables and apply them in optimization. With geometric constraint filtering, problem-oriented information is injected. With POD, the dominance of new selected geometric parameters in problem description is assured. Perfunctory details of displacement data of each control point in the lay-out can be replaced by grouped data as new design variable candidates. As a proof-of-concept study of the new approach, compressor blade Rotor 37 is selected to be the good platform of testing the feasibility of POD-aided FFD as a global and flexible yet economic geometric parameterization. Result demonstrates the feasibility of proposed POD-aided FFD approach that helps conduct an optimization involving displacement of 6 × 4 × 3 control points with as few as five new design variables, while still being capable of bringing optimization effect in three test cases.
“…60 Each of the five new design variables is variated from the space of (À1.0, 1.0). The input number of samples for surrogate modelling is eventually 600 after geometric check, which is determined by the convergence criterion proposed in the authors' another work 36 : a dataset is presumed to be sufficient if its eigenvectors obtained via POD is converged in terms of directions, which is shown in Figure 9. The Kriging model is realized via Python package pyKriging.…”
Section: Surrogate Modellingmentioning
confidence: 99%
“…The percentage of qualified samples under posed geometric constraints from input seed population provides an estimation of the size of available design space. 36 As a closer observation of sampling, three different locations of the geometry are picked as is seen in Figure 4a, where the points from different control points contribute to the sampling of the rotor blade in different ways. The qualified is notably within the borders constituted by sampling seeds, which shows the completeness of the parametric perturbation.Figure 3.The distribution of qualified samples among total sampled data: red, triangle markers represent total sampled data while blue, round ones represent qualified ones.Figure 4.The selected three control points: their perturbation in sampling.…”
Section: Problem Descriptionmentioning
confidence: 99%
“…Geometric constraint has provided essential problem-oriented information, e.g. key geometric features, 35 limit of performance improvement, 36 optimization direction, 37 etc. Therefore, the design space is then filtered by geometric constraint, and now it contains dominant eigenvectors that can be captured by POD (Proper Orthogonal Decomposition), which results in eigenmodes presented in form of grouped FFD control point displacement.…”
Compressor blade design influences aero-engine performance mainly through its total pressure ratio and efficiency. As a volume-based geometric parameterization, Free-form Deformation (FFD) brings three-dimensionality that is essential to blade design. However, the manipulation of control points with respect to simple numeric parametric perturbation renders the use of design space low-efficient. Therefore, an improved FFD with ‘wiser’ control point lay-out is expected to identify those more important design variables. This paper proposes novel design variables that are assigned to grouping of control points’ displacement in FFD lay-out. In short, the approach is realized as: (i) establish a library of sufficient blade shape samples; (ii) filter the database with geometric constraints; (iii) extract dominant modes via (POD) Proper Orthogonal Decomposition; (iv) construct new design variables and apply them in optimization. With geometric constraint filtering, problem-oriented information is injected. With POD, the dominance of new selected geometric parameters in problem description is assured. Perfunctory details of displacement data of each control point in the lay-out can be replaced by grouped data as new design variable candidates. As a proof-of-concept study of the new approach, compressor blade Rotor 37 is selected to be the good platform of testing the feasibility of POD-aided FFD as a global and flexible yet economic geometric parameterization. Result demonstrates the feasibility of proposed POD-aided FFD approach that helps conduct an optimization involving displacement of 6 × 4 × 3 control points with as few as five new design variables, while still being capable of bringing optimization effect in three test cases.
“…In [5], a new formulation of the design requirements in Natural Laminar Flow (NLF) optimization tasks is presented to make them less experience-based and much more grounded on quantitative criteria. The paper shows the impact of the proposed formulation on the result of NLF optimization in the design of transonic airfoils and aero-engine compressor blades from two perspectives: Pareto front convergence and the improving effect of accessory performance.…”
Section: Requirements In Design Processes: Open Issues Relevance and ...mentioning
Requirements play a key role in the design process by affecting analysis, synthesis and evaluation activities at different levels and in different ways [...]
“…Altogether, 550 samples are obtained via sampling: three parameters from the supplementary CST for the wing root and another three for the wing tip (therefore, all the parameters that are served as design variables are related only to the leading-edge region). The sample amount is appropriate for the optimization problem with six parameters 35 ; the optimization method is to select the best among the samples (i.e., enumeration among the samples in design space). The main idea of the optimization is to demonstrate the effect that can be brought by the supplementary CST method.…”
Geometrical representation method plays a fundamental role in aerodynamic design in that it makes preparation for design space. A good design space should be composed of design variables that are more likely to attain the solution to the problem than others. This study finds that due to the characteristics of Bernstein polynomials, a conventional class-shape transformation (CST) geometrical representation method is insufficiently focused on the leading-edge region of airfoils/wings. However, more aerodynamic attention is required there because it has strong relationship with the aerodynamic performance of whole geometry. The lack of design variables assigned to the leading-edge region is likely to compromise the effort in finding better optimization results in design space. While maintaining the convenience and accuracy of conventional CST, this study proposes two types of modifications to add more aerodynamic insights into the leading-edge region: (1) an approach of supplementary vertical CST aiming to describe the leading-edge region upon the fitting result of conventional CST; (2) an approach of globally transforming airfoil surfaces into a single-value function with respect to x-direction so that the leading-edge region avoids being split up into two separate parts. With those two modifications, the leading edge can be put to the center of geometric description by rotating the local coordinate system after tackling some other issues that come with the operation. Modification 1 is intuitive, although it requires additional attention to some parameters for the continuity between the leading-edge region and other regions of the airfoil. Modification 2 is convenient to implement, but has limitations on accuracy control because the result of shape error has to account for the introduction global transforming function. Two modifications are illustrated, and their applications are discussed in the study, showing the perspective of being utilized in aerodynamic design that involves delicate difference of aerodynamic performance brought by variations of leading-edge shape.
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