CST Method Research Articles

The aerodynamic optimization of hypersonic vehicles with the proper-orthogonal-decomposition-based CST method

The flight performance of traditional hypersonic vehicles is limited to a specified incoming flow condition, their aerodynamic performance significantly deteriorates outside of the design condition. We construct a data-driven design framework for aerodynamic shape optimization of hypersonic vehicles, which can be used to improve the current flexibility of designing hypersonic vehicles based on the existing shockwave shape or flowfield. The framework uses a class function/shape function transformation to set parameters for the control sections of the vehicle, then the dimensions of the parameter matrix are reduced by using the proper orthogonal decomposition, and the surrogate model with improved expectations is combined to carry out the aerodynamic shape optimization of hypersonic vehicles. The hypersonic aerodynamic optimization design of NACA 0012 airfoil is conducted, which verifies the high efficiency of the optimization method. The single-point and multi-point aerodynamic optimization designs for the Hypersonic Technology Vehicle-2 (HTV-2) type are conducted. The correlation analysis to the fundamental modes of control sections and lift-to-drag ratio is performed, which verifies the accuracy of the design. Completed the single-point and multi-point optimized design of the entire vehicle considering 48 design variables and geometry restrictions with volume not less than 95% of the baseline. The single-point optimization increases the lift-to-drag ratio by 10.91%, and the multi-point optimization ensures that the aerodynamic performance is improved at all flight conditions and reduces the drag coefficient by 4.1% at the large angle of attack condition. The vehicle shape change rule that is controlled by the positively correlated and negatively correlated fundamental modes for the three control sections coincides with the optimized trend. The study demonstrated the effectiveness and practicality of the framework in the aerodynamic design of hypersonic vehicles.

An efficient sparse surrogate model for aerodynamic characteristics of a supersonic compressor cascade with uncertain geometric deformations

The increasing demand for high-load compressors necessitates research and design of supersonic compressor blades. Geometric deformations of the blades resulting from manufacturing errors introduce uncertainties in their aerodynamic characteristics. For uncertainty analysis, Polynomial Chaos Expansion (PCE) has gained popularity among engineers in various disciplines. However, as the number of random variables used to describe uncertainties increases, the efficiency of the PCE method diminishes. To overcome this limitation, an Efficient Sparse Surrogate Model (ESSM) was first proposed. The ESSM combines PCE to approximate global characteristics and Gaussian process modeling to capture local variability, resulting in a highly accurate model. Additionally, by utilizing an iteratively diffeomorphic modulation under observable response preserving homotopy, important PCE basis functions are adaptively selected, leading to a sparse surrogate model that significantly reduces the required training samples. Then using the ESSM, efficient Uncertainty Quantification (UQ) and global sensitivity analysis were conducted to evaluate the impact of uncertain geometric deformations on the aerodynamic characteristics of a supersonic compressor cascade. Principal Component Analysis (PCA) was employed in conjunction with an Improved Class Shape Transformation (ICST) to characterize geometric deformations caused by manufacturing errors. The proposed ICST method exhibits enhanced accuracy in fitting near the leading and trailing edges compared to the CST method. PCA enables a 50% reduction in the number of random variables needed to describe geometric deformations. The UQ results establish a quantitative correlation between geometric deformations and supersonic aerodynamics, and the sensitivity analysis identifies some specific forms of geometric deformations that significantly impact the aerodynamics. Finally, the study investigated the flow mechanisms associated with typical geometric deformation forms, further providing recommendations for manufacturing and testing of supersonic blades to prevent performance deterioration.

Surrogate-based optimization of nacelle intake with fan-intake interaction: Mitigating flow separation under crosswind

Intake separation is a primary cause of distortion at the fan entrance, and crosswinds are a leading contributor to intake flow separation. Thus, improving the intake geometry to lower the distortion level during crosswind conditions is very important in engineering. As intake performance can be influenced by fan-intake interaction, in this paper, we conducted a comparative study of intake shape optimization design at a crosswind in the presence and absence of a fan stage. And a critical design point of 30-kts crosswind was considered to meet airworthiness standards. The analysis of flow mechanism inside intakes was conducted, and indicated the prominent difference of intake separation flow between fan-intake coupled simulations and intake only simulations under crosswind conditions. A POD-based CST method was conducted to obtain much fewer three-dimension nacelle parameters than the classical CST method. A Kriging-DE design model was adopted to replace the high-cost CFD simulations and searched for an optimal result. The results demonstrated that the optimization based on the fan-intake coupled simulation presented a lower intake distortion level and higher isentropic efficiency of the fan stage, highlighting the advantage of this optimization routine.

Radiation Performance of Different Triangular Microstrip Patch Antenna Configuration Shapes Operating at 28 GHz

The radiation performance of different triangular microstrip patch antenna (TMPA) shapes such as right triangle (RTMPA), isosceles triangle (ITMPA), obtuse triangle (OTMPA), and equilateral triangle (ETMPA) operating at (28 GHz) are computed and compared using inset-fed techniques and Rogers-RT5880 substrate material of permittivity and (h=0.15 mm) height. The directivity, gain, efficiency, bandwidth, VSWR, S11 and 2D-radiation pattern for each mentioned triangular patch shapes are computed utilizing CST and HFSS method. The computed results reveal generally that the ETMPA provide better radiation performance whereas the OTMPA displays lower antenna radiation parameter values compared to the other considered ones. In addition, the antenna parameters of ETMPA with the use of coaxial probe fed are also simulated and the results are compared to those previously achieved experimentally and theoretically by other researchers. Generally, a good agreement between mentioned antenna parameter results is displayed and reliability of those achieved by CST with inset fed techniques is clearly observed. Moreover, the overall antenna parameter obtained, respectively, with CST and HFSS techniques for inset fed ETMPA are S11 (-28.68, -20.64), VSWR (1.076,1.20), gain (5.82, 6.29) dB, directivity (6.85, 7.09) dB, bandwidth (0.452, 0.369) GHz, efficiency (78.9%, 83.2%) and with a small antenna size of about (3.88 mm3) which is most reliable for 5G technology application systems.

Aerodynamic Shape Optimization with Grassmannian Shape Parameterization Method

The conventional method of optimizing the aerodynamic performance of an airfoil heavily depends on the confines of the design space. The design variables create a non-normalized space that is fragmented into several different clusters of airfoils. An approach that is data-driven and deforms airfoils over a Grassmannian submanifold is utilized in the work that is being presented here. The affine deformation, which includes camber and thickness, can be uncoupled from the method that is currently in use, and the operations that are performed on the airfoil shape can be made smooth enough to prevent unreasonable shapes from being produced. The CST method is also a part of the current study so that a comparison can be made between the two. A new method to describe the airfoil geometries over the Grassmannian space was generated using a dataset that contained 7007 different shapes of airfoils. These two methods are used to parameterize the subsonic (NACA0012) and transonic (RAE2822) airfoils, and the new method cuts the number of design variables from twelve to six, resulting in a reduction in overall complexity. The findings demonstrate that the new method maintains a high degree of consistency regardless of the flow conditions.

Research of Airfoil Optimization Based on CST Method and Genetic Algorithm

Aiming at the aerodynamic optimization problem of guided ammunition airfoil, genetic algorithm is used to optimize the lift-drag ratio of the airfoil based CST geometric description method with given inflow velocity and fixed angle of attack. Firstly, the parameter space generated by CST parameterized airfoil description method is performed with binary code and the basic operations of genetic algorithm such as selection, crossover and mutation. Then, the external CFD solver is called to automatically divide the grid and calculate the lift-drag ratio through the control script. Finally, the target solution is obtained by searching. The calculation results show that this method can obtain a optimal target solution in relative less generation for a group of airfoils generated randomly in a certain search space.

Dual-band passband terahertz filter based on multilayer metamaterial

We have theoretically verified the design of dual-band passband terahertz filter using multilayer metamaterial. The top and bottom layers are composed of periodically branching structure metallic patterns, which are exactly the same. The middle layer consists of a periodically metallic square aperture. The three metallic layers are separated by two thin dielectric layers. An equivalent circuit model is used to simplify the design procedure of the proposed structure. The performance of the terahertz filter is analyzed via equivalent circuit model together with the full wave CST method. The results show that the proposed structure provides two passbands. One is the center frequency of 0.32 THz with -3dB bandwidth of 164 GHz, and the other is the center frequency of 0.74 THz with -3dB bandwidth of 176 GHz.

Software Testing for cyber Security

Software testing plays a vital role in software security because hackers attack on a system through back channels which they can easily find if there is any error or bug exists in the software. The software security failure can cause the unbearable loss for IT companies and other organizations. Cyber security is another big issue for computer users' personal data as all their information is vulnerable because of easy excess, visibility and availability. Therefore, software testing is also useful to secure the personal information. In this article, cyber security testing based on particle swam optimization algorithm (CST) is proposed for testing of software cyber security testing. CSTPSOA is a PSO base technique which is used to solve the complex multi-level problems and is also used for optimization. In the CST method PSO is used for the optimization of test cases for cyber security testing.

Effect of Leading-Edge Optimization on the Loss Characteristics in a Low-Pressure Turbine Linear Cascade

This paper presents a numerical study on the aerodynamics loss reduction characteristics after the leading-edge (LE) optimization in a low-pressure turbine linear cascade. The LE was optimized with a simple and practical method of “Class Function/Shape Function Transformation Technique” (CST). The simulation conditions, covering the whole working range, were independently determined by incidence, Reynolds number and Mach number. Quantitative loss analyses were carried out with a loss breakdown method based on volumetric integration of entropy production rates. To understand the reason of loss reduction, the local sources at different operating points were identified with entropy production rates. The results showed that LE optimization with the CST method played a positive role in decreasing the total losses, and the working range with lower loss was extended. The profile loss and the endwall loss were significantly reduced by the LE optimization, which were also verified to be the major causes of the total loss reduction by loss breakdown. The decrease of profile loss can be attributed to the boundary layer near the LE region and the boundary layer of downstream at off-design incidence. The reduction mostly came from the pressure side at negative incidence, while came from the suction side at the positive incidence. The endwall loss was decreased markedly about 2.5%–5% by the LE optimization at the incidence of‒12°, which was 1% at the incidence of 12°. The mechanism for the endwall loss reduction at different incidences was different from each other. At negative incidence, the LE optimization diminished the corner separation vortex on the pressure side. While at positive incidence, the benefits came from three aspects, i.e., reduced suction LE separation bubbles close to the endwall, reduced passage vortex strength, and weakened shear process between passage vortex and trailing shed vortex. The loss of the downstream zone was relatively lower than that of the profile losses and the endwall losses. The effect of LE optimization on the loss of the downstream zone at different conditions was complex and it depended both on the profile boundary layer behavior at the suction trailing edge and on the passage vortex strength.

Improved aerofoil parameterisation based on class/shape function transformation

ABSTRACTA new aerofoil parameterisation method is put forward to represent an aerofoil by combining the leading edge modification class/shape function transformation (LEM CST) method and improved Hicks–Henne bump function’s method. The new class/shape function transformation (NEW CST) method has two additional basis functions comparing the original CST method. In order to confirm these two basis functions, the radial basis functions neural network (RBF) model is trained by some samples which are generated by the Latin hypercube design (LHD) method and Genetic Algorithm (GA) is proposed to achieve the basis functions of the NEW CST method. The NEW CST method has been evaluated in fitting precision of 1,545 aerofoils by comparison with the LEM CST method and the original CST method. And the improved ability of the NEW CST at the leading edge and trailing edge is verified by a series of complex aerofoil case studies within 1,545 aerofoils. The results indicate that the NEW CST method can represent the whole aerofoils and possesses the intuitive property as well as the original CST. Moreover, the number of control parameters (NCP) to parameterise aerofoils is the fewest among these three methods. Furthermore, when the NCP of the NEW CST and LEM CST is the same, the NEW CST method has the higher accuracy and smaller root mean square errors (RMSE) especially at the leading edge and trailing edge.

Multi-objective airfoil shape optimization using an adaptive hybrid evolutionary algorithm

In this study, multi-objective aerodynamic optimization problems were conducted with a hybrid evolutionary-adaptive directional local search method for convergence enhancement. The directional search operator includes selection of search direction and one-dimensional search. Probability for the directional operator is adaptively changed based on relative effectiveness of the directional search operator and evolutionary operators such as crossover and mutation. The adaptive directional operator is combined with a baseline evolutionary multi-objective algorithm (EMOA) such as NSGA-II or MOGA. Multi-objective airfoil shape optimization examples are defined as drag minimization/lift maximization and L/D maximization at high lift and cruise conditions in subsonic and transonic regimes. The CST method and the B-spline method were used for airfoil shape parameterization. Design examples with drag minimization and L/D maximization at cruise conditions are all found to have uni-modal design spaces, and the local search operator is effective for those examples. However, lift maximization and high angle of attack cases show multi-modality in the design spaces due to flow separations and thus the local search is not effective for those cases. Design results show that the adaptive directional search method significantly enhances convergence of problems in which the directional search is effective, and also minimizes unnecessary spending of computational budget for cases in which the directional search does not produce competitive solutions. The present method improves search performance for different airfoil parameterization methods and different baseline EMOAs. Statistical tests confirm that the adaptive hybrid method is superior to the baseline EMOA.

Benchmark aerodynamic shape optimization with the POD-based CST airfoil parametric method

This paper conducts a benchmark aerodynamic shape optimization with the developed POD-based CST airfoil parametric method. The POD analysis transforms the basis functions of the CST parametric method into reduced orthogonal POD basis functions which are used to describe the geometric variation of the aerodynamic shape. A benchmark aerodynamic shape optimization for drag minimization of RAE2822 airfoil in transonic viscous flow provided by AIAA aerodynamic design optimization discussion group is used to verify the optimization effect of the developed parametric method. The optimized results indicate that developed parametric method can maintain almost the same ability to cover potential airfoils with much fewer parameters as the original high-dimensional CST method does, which can overcome the contradiction of high-dimensionality of design parameters and increase of optimization difficulty well. Moreover, the benchmark optimized results verify the optimization effect of the developed method by comparing with benchmark results optimized by other international counterparts in the field of aerodynamic shape optimization.

Rotor airfoil profile optimization for alleviating dynamic stall characteristics

In order to alleviate the dynamic stall characteristics of rotor airfoil, a high-efficient optimization method is established by coupling the SQP method with CFD method. Aiming at improving the optimized efficiency, a new strategy of linear search is established to avoid the disturbance of the penalty factors, and the optimal efficiency improves more than 30% compared with traditional line search method. In order to reduce the design variables, the CST method is employed to parameterize the airfoil section. All the flow solutions were computed by solving the URANS equations, coupled with the Spalart–Allmaras turbulence model. To reduce pitching moment and drag coefficient under dynamic stall condition, a new airfoil has been optimized based on the OA209 airfoil by employing the present optimal method. Due to the inhibition of leading edge vortex, the peaks of pitching moment and drag coefficient of the optimized airfoil are decreased about 75.8% and 44.2% at point 1, 44.0% and 41.4% at point 2 compared with the OA209 airfoil. Moreover, the optimized airfoil has better lift stall characteristics compared with the OA209 airfoil. In addition, by comparing the 3-D dynamic stall characteristics of rotor blade, it is demonstrated that the peaks of pitching moment coefficients and drag coefficients of optimized airfoil are smaller than those of OA209 airfoil at different blade radial stations.

An automated analysis process for vertical axis wind turbine

This paper presents an automated process for analyzing the performance of vertical axis wind turbine (VAWT). The details of this process will be demonstrated, which include the airfoil geometry representation using CST method, a hybrid meshing process combining structured grids and unstructured grids, CFD calculation process and processing data results to calculate the power coefficient of VAWT. These processes are designed as separate modules. CFD methods used in this research is RANS 2D using Realizable k  turbulence model. Meshing process will be done on the GAMBIT software, the CFD calculations are done on commercial ANSYS FLUENT software and these processes are controlled by mathematical software MATLAB. The formulas used to calculate the power coefficient will be also introduced in this paper.

Coupling Optimization Design of Aspirated Compressor Airfoil and Aspirated Scheme Based on Artificial Bee Colony Algorithm and CST Method

AbstractThis paper focuses on creating a new design method optimizing both aspirated compressor airfoil and the aspiration scheme simultaneously. The optimization design method is based on the artificial bee colony algorithm and the CST method, while the flow field is computed by one 2D computational program. The optimization process of the rotor tip and stator tip airfoil from an aspirated fan stage is demonstrated to verify the effectiveness of the new coupling method. The results show that the total pressure losses of the optimized stator tip and rotor tip airfoil are reduced relatively by 54% and 20%, respectively. Artificial bee colony algorithm and CST method indicate a satisfying applicability in aspirated airfoil optimization design. Finally, the features of aspirated airfoil designing process are concluded.

Investigation of Various Parametric Geometry Representation Methods for Airfoils

Abstract—This paper presents the investigation of typical parametric geometry representation methods for airfoils, namely, PARSEC method, orthogonal basis function method and CST method. The investigation assesses the fitting accuracy of these parametric methods for various airfoils including the symmetric airfoil, cambered airfoil and supercritical airfoil. The design variables of these parametric methods are solved by the methods of least squares fit. The fitting results show that the fitting accuracy of CST method is better than other parametric methods for airfoil. The aerodynamics analysis models of these typical parametric geometry representation methods for airfoil are constructed. The pressure distributions calculated for different parametric methods are compared with the corresponding experimental pressure distributions for the actual airfoil geometry. Keywords-orthogonal basis function; PARSEC; CST; fitting accuracy; pressure distributions

測定ブリッジ4辺のC分に対応した新CST方式動ひずみ測定器

測定ブリッジ4辺のC分に対応した新CST方式動ひずみ測定器

Recent extensions and applications of the ‘CST’ universal parametric geometry representation method

AbstractFor aerodynamic design optimisation as well as for multidisciplinary design optimisation studies, it is very desirable to limit the number of the geometric design variables. In Ref. 1, a ‘fundamental’ parametric aerofoil geometry representation method was presented. The method included the introduction of a geometric ‘class function/shape function’ transformation technique, CST, such that round nose/sharp aft end geometries as well as other classes of geometries could be represented exactly by analytic well behaved and simple mathematical functions having easily observed physical features. The CST method was shown to describe an essentially limitless design space composed entirely of analytically smooth geometries. In Ref. 2, the CST methodology was extended to more general three dimensional applications such as wing, body, ducts and nacelles. It was shown that any general 3D geometry can be represented by a distribution of fundamental shapes, and that the ‘shape function/class function’ methodology can be used to describe the fundamental shapes as well as the distributions of the fundamental shapes. A number of applications of the ‘CST’ method to nacelles, ducts, wings and bodies were presented to illustrate the versatility of this new methodology. In this paper, the CST method is extended to include geometric warping such as variable camber, simple flap, aeroelastic and flutter deflections. The use of the CST method for geometric morphing of one geometric shape into another is also shown. The use of CST analytic wings in design optimisation will also be discussed.

Properties of 4H-SiC by Sublimation Close Space Technique

ABSTRACTSiC is suitable for power devices but high quality SiC epitaxial layers having a high breakdown voltage are needed and thick epilayer is indispensable. In this study, CST method (Close Space Technique) was used to rapidly grow thick epitaxial layers. Source material used was 3C-SiC polycrystalline plate of high purity while 4H-SiC(0001) crystals inclined 8° off toward <1120> was used for the substrate. Quality of the epilayer was influenced significantly by pressure during growth and polarity of the substrate. A p-type conduction was obtained by changing the size of p-type source material. The carrier concentration of epilayer decreased when a lower pressure was employed. Schottky diode was also fabricated.

Precipitation and filtration of zinc, magnesium, copper and aluminium hydroxides

Filtration properties of batchwise precipitated suspensions of Zn(OH)2, Mg(OH)2 and Cu(OH)2 and continuously precipitated Al(OH)3 were studied. For batchwise precipitated suspensions was verified the theoretically predicted dependence of specific filtration resistance on initial supersaturation and for the continuously precipitated Al(OH)3 the relation between the specific filtration resistance and the mean residence time of suspension in the reactor. Dependences were also recorded between the bed porosity and concentration of precipitated solutions, specific filtration resistance and used filtration pressure and the effect of aging of the batchwise precipitated suspension of Mg(OH)2on its filtration properties. The used CST method for determination of filtration characteristics of Zn(OH)2 suspension was also studied.