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The low-boom inverse design method is of great interest for the preliminary design of supersonic transport (SST), owing to its good capability of reducing sonic boom at low computational cost. However, the main challenge is how to prescribe an attainable target. This paper proposes an inverse design method using a new target-generation strategy to address this challenge. Unlike existing methods such as the Jones–Seebass–George–Darden method and the mixed-fidelity inverse design method [the Li–Shields–Geiselhart (LSG) method], the proposed method directly parameterizes the near-field overpressure distribution of a reference configuration and minimizes the ground perceived level in decibels (PLdB) predicted by solving the augmented Burgers equation to obtain an optimal target distribution, subject to cruise lift and volume constraints. The proposed method is demonstrated by the Japan Aerospace Exploration Agency (JAXA) Wing Body case, which shows that it mitigates sonic boom under lift constraint and achieves a reduction of 2.07 PLdB more than the LSG method. The proposed method is applied to the low-boom design of a large SST configuration called NPU-T7104, which is close in size to the Tupolev Tu-144; results show that aerodynamic performance is maintained while shock wave coalescence is effectively prevented, and ground-boom intensity is dramatically reduced.

The flapping motion has a great impact on the aerodynamic performance of flapping wings. In this paper, a surging motion is added to an airfoil performing pitching-plunging combined motion to figure out how it influences the lift performance and flow pattern of flapping airfoils. Firstly, the numerical methods are validated by a NACA0012 airfoil pitching case and a NACA0012 airfoil plunging case. Then, the E377m airfoil which has typical geometric characteristics of the bird-like airfoil is selected as the calculation model to study how phase differences φ1 between surging motion and plunging motion affect the aerodynamic performance of flapping airfoils. The results show that the airfoil with surging motion has comprehensively better lift performance and thrust performance than the airfoil without surging motion when 15°

Accurate prediction of tip vortices is crucial for predicting the hovering performance of a helicopter rotor. A new high-order scheme (we call it WENO-K) proposed by our research group is employed to minimize numerical dissipation and extended to numerical simulation of unsteady compressible viscous flows dominated by tip vortices over hovering rotors. WENO-K is referred to as an adaptively optimized WENO scheme with Gauss-Kriging reconstruction, and its advantage is to reduce dissipation in smooth regions of flow while preserving high-resolution around discontinuities. Here WENO-K scheme is adopted to reconstruct left and right state values within the Roe Riemann solver updating the inviscid fluxes on a structured dynamic overset grid. To minimize the accuracy loss for high-order reconstruction on artificial boundaries of overset grid, a method of multilayer fringes is proposed to carry out interpolation between background grid and blade grid. Massively parallel computing considering automatic load balance on averagely partitioned overset grid is developed to reduce the wall-clock time of an unsteady simulation. Numerical results for Caradonna-Tung (C-T) rotor in hover at the conditions of subsonic and transonic tip Mach numbers show that the thrust coefficient error for the result of WENO-K scheme is no more than 3%. Compared with WENO-JS scheme, WENO-K scheme achieves about 40% improvement on accuracy of predicting rotor thrust with only 4.1% extra computational cost. More importantly, WENO-K scheme can capture more sophisticated unsteady flow structures and resolve tip vortices to a larger wake age with an increment of about 270° compared to WENO-JS scheme.

To improve robustness and efficiency of automatic transition prediction in aerodynamic design, a reduced model of linear stability analysis is usually adopted, such as eN-envelope or eN-database me...

Crossflow instability (CFI) is crucial for triggering boundary-layer flow transition over a transonic natural laminar flow (NLF) wing, whose leading edge is swept for reducing wave drag. This paper...

A Dielectric Barrier Discharge (DBD) plasma actuator can create a body force which locally accelerates the base flow leading to an attenuation of broadband disturbance to delay the transition. In this study, numerical simulation on an NLF0416 airfoil is conducted to investigate transition delay and drag reduction by a DBD plasma actuator. To simulate plasma’s effect more accurately, boundary-layer data is acquired from Reynolds Averaged Navier Stocks (RANS) equations instead of laminar boundary layer equations, although RANS equations need a much finer boundary-layer grid, and the linear stability analysis method is used to analyze the boundary layer and get the transition point. In this study, the influences of different actuation intensities and positions are investigated, and results show that if the actuation intensity is stronger and the actuation position is closer to the base transition point, more drag reduction can be obtained. However, the efficiency of plasma transition delay is really low. For example, when the actuation voltage is 16 kV, the actuation frequency is 1 kHz, and the main Mach number is 0.1, the saved power due to drag reduction is about 5.09 W, but the power consumed is about 32.61 W, and the efficiency is just 15.6%.

Rotor noise is one of the most important reasons for restricting helicopter development; hence, the optimization design of rotor blade considering aeroacoustic and aerodynamic performance at the same time has always been the focus of research attention. For complex rotor design problems with a large number of design variables, the efficiency of the traditional Kriging model needs to be improved. Thus, Hierarchical Kriging (HK) model is employed in this study for rotor optimization design. By using the validated RANS solver and acoustic method based on the FW–Hpds equation, an efficient aerodynamic/aeroacoustic optimization method for high-dimensional problem of rotors in hover based on HK model is developed. By using present HK model and new infill-sampling criteria, the number of design variables is increased from less than 20–53. Results of two analytical function test cases show that the HK model is efficient and accurate in calculation. Subsequently, the helicopter rotor blade is optimally designed for aerodynamic/aeroacoustic performance in hover based on the HK model with high dimensional design variables. The objective function is adopted to improve the rotational noise characteristics by reducing the absolute peak of the acoustic pressure. In addition, the constraints of thrust, hover efficiency, solidity, and airfoils thickness are strictly satisfied. Optimization results show that the Kriging model finds the objective of reducing the noise by 2.87 dB after 248 iterations while the HK model does it only after 164 iterations. The optimization efficiency of the HK model is significantly higher than that of the traditional Kriging model. In the case analyzed, the HK model saves 35% of the time used by the Kriging model. Keywords: Aeroacoustics, Design optimization, FW-Hpds equation, Helicopter rotor, RANS equations

A variable-fidelity method can remarkably improve the efficiency of a design optimization based on a high-fidelity and expensive numerical simulation, with assistance of lower-fidelity and cheaper simulation(s). However, most existing works only incorporate “two” levels of fidelity, and thus efficiency improvement is very limited. In order to reduce the number of high-fidelity simulations as many as possible, there is a strong need to extend it to three or more fidelities. This article proposes a novel variable-fidelity optimization approach with application to aerodynamic design. Its key ingredient is the theory and algorithm of a Multi-level Hierarchical Kriging (MHK), which is referred to as a surrogate model that can incorporate simulation data with arbitrary levels of fidelity. The high-fidelity model is defined as a CFD simulation using a fine grid and the lower-fidelity models are defined as the same CFD model but with coarser grids, which are determined through a grid convergence study. First, sampling shapes are selected for each level of fidelity via technique of Design of Experiments (DoE). Then, CFD simulations are conducted and the output data of varying fidelity is used to build initial MHK models for objective (e.g. CD) and constraint (e.g. CL, Cm) functions. Next, new samples are selected through infill-sampling criteria and the surrogate models are repetitively updated until a global optimum is found. The proposed method is validated by analytical test cases and applied to aerodynamic shape optimization of a NACA0012 airfoil and an ONERA M6 wing in transonic flows. The results confirm that the proposed method can significantly improve the optimization efficiency and apparently outperforms the existing single-fidelity or two-level-fidelity method. Keywords: Aerodynamic shape optimization, Computational fluid dynamics, Hierarchical kriging, Kriging, Surrogate model

This article presents a novel approach for predicting transition locations over airfoils, which are used to activate turbulence model in a Reynolds-averaged Navier-Stokes flow solver. This approach combines Dynamic Mode Decomposition (DMD) with eN criterion. The core idea is to use a spatial DMD analysis to extract the modes of unstable perturbations from a steady flowfield and substitute the local Linear Stability Theory (LST) analysis to quantify the spatial growth of Tollmien–Schlichting (TS) waves. Transition is assumed to take place at the stream-wise location where the most amplified mode’s N-factor reaches a prescribed threshold and a turbulence model is activated thereafter. To improve robustness, the high-order version of DMD technique (known as HODMD) is employed. A theoretical derivation is conducted to interpret how a spatial high-order DMD analysis can extract the growth rate of the unsteady perturbations. The new method is validated by transition predictions of flows over a low-speed Natural-Laminar-Flow (NLF) airfoil NLF0416 at various angles of attack and a transonic NLF airfoil NPU-LSC-72613. The transition locations predicted by our HODMD/eN method agree well with experimental data and compare favorably to those obtained by some existing methods (LST/eN or γ-Reθt‾). It is shown that the proposed method is able to predict transition locations for flows over different types of airfoils and offers the potential for application to 3D wings as well as more complex configurations. Keywords: Airfoil, Dynamic mode decomposition (DMD), eN criterion, Navier-Stokes equations, Transition prediction

Expensive multiobjective optimization problem poses a big challenge. In many real-world engineering design problems, the time-consumed function evaluation is done by solving partial differential equations. The partial derivatives of a candidate solution can be calculated as a byproduct. Naturally, these problems can be solved more efficiently if gradient information is used. This paper proposes such a method, called MOEA/D-GEK, which combines MOEA/D and gradient-enhanced Kriging to solve expensive multiobjective problem. The gradient information is used for the construction of the Kriging model. Experimental studies on a set of test instances and a real-world aerodynamic design problem show high efficiency and effectiveness of our proposed method.

Background The prognositc factors in patient with invasive cribriform carcinoma (ICC) of breast is still remain controversal. The study aims to establish a nomogram to predict the survival outcomes in patients with ICC based on the Surveillance, Epidemiology and End Results (SEER) database. Methods We retrieved SEER database for clinical data about patients including ICC and infiltrating ductal carcinoma (IDC) from 2004 to 2015. Kaplan-Meier survival was used to compare the difference survival outcomes between ICC and IDC. ICC patients were randomly allocated to training cohort and validation cohort. A nomogram was built to predict individual patient’s 3-year and 5-year survival status for ICC. The established TMN model and the newly established nomogram was further evaluated by the concordance index (C-index) and the decision curve analysis (DCA). Results Comparing the baseline clinical data between IDC and ICC, a significant of smaller tumor mass, less infiltrated lymph nodes, lower metastases rate, better tumor differentiation degree, higher proportion of estrogen receptor (ER) and progesterone receptor (PR) positive and lower rate of chemotherapy and radiotherapy was found in ICC. Age at diagnosis, marriage status, tumor location, T stage, M stage, ER status, surgery were independent significant prognostic factors for the overall survival (OS). A significantly higher C-index was found in nomogram compared with established TNM model in validation cohort. Conclusions The prognosis of ICC patients is better than that of IDC patients. The nomogram is recommended for future patient with ICC to survival analysis.

The method of aggregating a large number of constraints into one or few constraints has been successfully applied to wing structural design using gradient-based local optimization. However, numerical difficulties may occur in the case that the local curvatures of the aggregated constraint become extremely large and then ill-conditioned Hessian matrix may be yielded. This paper aims to test different methods of constraint aggregation within the framework of a gradient-free optimization, which makes use of cheap-to-evaluate surrogate models to find the global optimum. Three constraint aggregation approaches are investigated: the maximum constraint approach, the constant parameter Kreisselmeier-Steinhauser (KS) function, and the adaptive KS function. We also explore methods of aggregating constraints over the entire structure and within sub-domains. Examples of structural optimization and aero-structural optimization for a transport aircraft wing are employed and the results show that (1) the KS function with a larger constant parameter ρ can lead to better optimization results than the adaptive method, as the active constraints are approximated more accurately; (2) lumping the constraints within sub-domains instead of all together can improve the accuracy of the aggregated constraint and therefore helps find a better design. Finally, it is concluded from current test cases that the most efficient way of handling large-scale constraints for wing surrogate-based optimization is to aggregate constraints within sub-domains and with a relatively large constant parameter.

Aerodynamic shape optimization of a swept natural-laminar-flow wing in the transonic regime is still challenging. The difficulty is associated with reliable prediction of laminar–turbulence transit...

The efficient global optimization method (EGO) based on kriging surrogate model and expected improvement (EI) has received much attention for optimization of high-fidelity, expensive functions. However, when the standard EI method is directly applied to a variable-fidelity optimization (VFO) introducing assistance from cheap, low-fidelity functions via hierarchical kriging (HK) or cokriging, only high-fidelity samples can be chosen to update the variable-fidelity surrogate model. The theory of infilling low-fidelity samples towards the improvement of high-fidelity function is still a blank area. This article proposes a variable-fidelity EI (VF-EI) method that can adaptively select new samples of both low and high fidelity. Based on the theory of HK model, the EI of the high-fidelity function associated with adding low- and high-fidelity sample points are analytically derived, and the resulting VF-EI is a function of both the design variables x and the fidelity level l. Through maximizing the VF-EI, both the sample location and fidelity level of next numerical evaluation are determined, which in turn drives the optimization converging to the global optimum of high-fidelity function. The proposed VF-EI is verified by six analytical test cases and demonstrated by two engineering problems, including aerodynamic shape optimizations of RAE 2822 airfoil and ONERA M6 wing. The results show that it can remarkably improve the optimization efficiency and compares favorably to the existing methods.

A novel formulation of gradient-enhanced surrogate model, called weighted gradient-enhanced kriging, is proposed and used in combination with the cheap gradients obtained by the adjoint method to a...

Multi-fidelity optimization methods promise a high-fidelity optimum at a cost only slightly greater than a low-fidelity optimization. This promise is seldom achieved in practice, due to the requirement that low- and high-fidelity models correlate well. In this article, we propose an efficient bi-fidelity shape optimization method for turbulent fluid-flow applications with Large-Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) as the high- and low-fidelity models within a hierarchical-Kriging surrogate modelling framework. Since the LES–RANS correlation is often poor, we use the full LES flow-field at a single point in the design space to derive a custom-tailored RANS closure model that reproduces the LES at that point. This is achieved with machine-learning techniques, specifically sparse regression to obtain high corrections of the turbulence anisotropy tensor and the production of turbulence kinetic energy as functions of the RANS mean-flow. The LES–RANS correlation is dramatically improved throughout the design-space. We demonstrate the effectivity and efficiency of our method in a proof-of-concept shape optimization of the well-known periodic-hill case. Standard RANS models perform poorly in this case, whereas our method converges to the LES-optimum with only two LES samples.

This study assessed the clinical efficacy of the neoadjuvant chemotherapy TAC scheme in treatment of patients with locally advanced breast cancer, and the value of the level of Ras association domain family 1A (RASSF1A) gene methylation and the Wnt inhibitory factor (WIF)-1 gene in tissue and serum of patients in clinical outcome prediction. In total, 126 patients were consecutively selected to receive TAC scheme (docetaxel, pirarubicin/epirubicin and cyclophosphamide) for at least four cycles with the total effective rate. The incidence of complications, progression-free survival and survival rate were recorded. Tumor tissues and peripheral blood samples collected in this study was used to detect methylation positive rate of RASSF1A and WIF-1 by methylation-specific PCR method and the relative level of expression of RASSF1A and WIF-1 mRNA by reverse transcription PCR method. Of the 126 patients, there were 18 cases with complete response (CR), 32 cases with partial response (PR), 50 cases with stable disease (SD), and 26 cases with disease progression (PD) with a total effective rate of 79.37%. Comparison on baseline data of effective group and ineffective group showed no difference (P>0.05), and comparison on adverse reactions occurrence showed no difference (P>0.05). Progression-free survival of the effective group was prolonged with a significant increase in survival rate (P

A new airfoil family, called NPU-MWA (Northwestern Polytechnical University Multi-megawatt Wind-turbine A-series) airfoils, was designed to improve both aerodynamic and structural performance, with the outboard airfoils being designed at high design lift coefficient and high Reynolds number, and the inboard airfoils being designed as flat-back airfoils. This article aims to design a multi-megawatt wind turbine blade in order to demonstrate the advantages of the NPU-MWA airfoils in improving wind energy capturing and structural weight reduction. The distributions of chord length and twist angle for a 5 MW wind turbine blade are optimized by a Kriging surrogate model-based optimizer, with aerodynamic performance being evaluated by blade element-momentum theory. The Reynolds-averaged Navier&ndash, Stokes equations solver was used to validate the improvement in aerodynamic performance. Results show that compared with an existing NREL (National Renewable Energy Laboratory) 5 MW blade, the maximum power coefficient of the optimized NPU 5 MW blade is larger, and the chord lengths at all span-wise sections are dramatically smaller, resulting in a significant structural weight reduction (9%). It is shown that the NPU-MWA airfoils feature excellent aerodynamic and structural performance for the design of multi-megawatt wind turbine blades.

For real-world engineering design optimizations, it is of great significance to find approximate optimal designs with least number of expensive functional evaluations. This paper proposes to use a surrogate-based multi-objective evolutionary algorithm (SBMO) to address this type of problems. The basic idea is to decompose a multi-objective optimization problem into a number of scalar optimization subproblems and to optimize them simultaneously in a simple-to-implement manner, in which global surrogate models are used to enable full cooperation between subproblems. First, initial samples are selected by design of experiments and expensive simulations are conducted to evaluate them. Second, global surrogate models for objective (and constraint) functions are built through the sampled data and the optimization subproblems are solved simultaneously to suggest new samples. Third, the surrogate models are updated and the optimization proceeds to the next generation. This process is repeated until satisfactory Pareto-front solutions are found. Thanks to decomposition strategy, the infill-sampling criteria and constraint handling dedicated for a single-objective optimization can be directly used in a SBMO. The difference between SBMO and the existing methods such as MOEA/D-EGO is that a combined infill-sampling strategy and dedicated constraint handling are used. Benchmark test cases have demonstrated that SBMO is efficient, robust and has good capability of constraint handling. SBMO has been applied to multi-objective aerodynamic shape optimization of a transonic airfoil. It has been shown that SBMO is well suited for engineering design problems where expensive numerical simulations are employed.

The surrogate-assisted optimization algorithms (SAOAs) are very promising for solving computationally expensive optimization problems (EOPs). Generally, the performance of a SAOA is determined by the quality of its surrogate model and the infill sampling criterion. In this paper, we propose a radial basis function (RBF) assisted optimization algorithm with batch infill sampling criterion for solving EOPs (short for RBFBS). In RBFBS, the quality of RBF model is adjusted by choosing a good shape parameter via solving a sub-expensive hyperparameter optimization problem. Moreover, a batch infill sampling criterion that includes a bi-objective-based sampling approach and a single-objective-based sampling approach is proposed to get a batch of samples for expensive evaluation. The experimental results on various benchmark problems show that RBFBS is very promising for expensive optimization.

For a black box data-space exploration, classical DoE method prescribes a cluster of quasi-isotropic design points following a certain space-infill criterion, however the objective function behaves. Adding new points often disturbs the original spatial-infill properties, which restricts dimension-augmentation and reusability of data. Surrogate model based sequential design considers not only the spatial features of the design space but also the characteristic of the objective function. The latter may favor a highly anisotropic design for the sake of computational effort effectiveness, especially when highly informative samples are used. This work presents a high anisotropy design solution when derivative-assisted co-Kriging method is employed. Adaptation of this method has been proposed for the special case where only one single sample appears at certain dimensions. A 2-dimensional test function with distinctive spatial properties at each dimension is composed and used to assess the validity of the proposed method.

We present a novel method for the determination of N-factors in cross-flow transition scenarios. The method considers numerical simulations, in which a turbulent model is applied downstream from a predetermined point and solves a laminar flow upstream from this point. The solution is postprocessed using higher order dynamic mode decomposition to extract the leading spatial mode in several small sections along the streamwise direction. The spatial evolution of the amplitude of this mode will determine the N-factor. The results presented are compared with experimental measurements and linear stability theory, showing the good performance of this novel method, which does not assume parallel flow assumptions, is automatic and computationally efficient.

An adaptive finite-difference WENO method with Gauss-Kriging reconstruction (we call it WENO-K) is proposed to reduce dissipation in smooth regions of flow while preserving high-resolution around discontinuities for hyperbolic system of conservation laws. The method adopts a kriging model with non-polynomial Gauss exponential function to obtain new reconstruction coefficients that contain a hyper-parameter. By adaptively optimizing the hyper-parameter and automatically identifying troubled cells using newly developed indicators, the accuracy in the smooth region is obviously improved. Compared with the classical WENO-JS method, the proposed WENO-K method provides more accurate reconstructions and sharper solution profiles near discontinuities. Furthermore, the WENO-K method is easy to implement in an existing classical WENO code with less than 13%∼16% of additional computational cost. Numerical results demonstrate that the proposed method outperforms the WENO-JS method for a broad range of problems. This method is supposed to be applied to other variants of WENO scheme and offers the potential of improving their accuracy.

Surrogate models are used to dramatically improve the design efficiency of numerical aerodynamic shape optimization, where high-fidelity, expensive computational fluid dynamics (CFD) is often employed. Traditionally, in adaptation, only one single sample point is chosen to update the surrogate model during each updating cycle, after the initial surrogate model is built. To enable the selection of multiple new samples at each updating cycle, a few parallel infilling strategies have been developed in recent years, in order to reduce the optimization wall clock time. In this article, an alternative parallel infilling strategy for surrogate-based constrained optimization is presented and demonstrated by the aerodynamic shape optimization of transonic wings. Different from existing methods in which multiple sample points are chosen by a single infill criterion, this article uses a combination of multiple infill criteria, with each criterion choosing a different sample point. Constrained drag minimizations of the ONERA-M6 and DLR-F4 wings are exercised to demonstrate the proposed method, including low-dimensional (6 design variables) and higher-dimensional problems (up to 48 design variables). The results show that, for surrogate-based optimization of transonic wings, the proposed method is more effective than the existing parallel infilling strategies, when the number of initial sample points are in the range from Nv to 8Nv (Nv here denotes the number of design variables). Each case is repeated 50 times to eliminate the effect of randomness in our results.

High-subsonic and low-Reynolds-number flow is a special aerodynamic problem associated with near space propellers and Mars aircrafts. The flow around airfoils and the corresponding aerodynamic performance are different from the incompressible flow at low-Reynolds-number, due to complex shock wave-laminar separation bubble interaction. The objective of this paper is to figure out the effect of Mach number on aerodynamic performance and special flow structure of airfoil. An in-house Reynolds-averaged Navier–Stokes solver coupled with [Formula: see text] transition model is employed to simulate the flows around the E387 airfoil. The results show that the lift slope is larger than [Formula: see text] in the linear region. No stall occurs even at an attack angle of [Formula: see text]. With increase of Mach number, lift coefficient decreases when attack angle is below [Formula: see text]. However, once the angle of attack exceeds [Formula: see text], higher Mach number corresponds to higher lift coefficient. In addition, the strength and number of shock waves are very sensitive to Mach number. With increase of Mach number, the region of reverse flow vortex near transition location becomes smaller and finally disappears, while a new reverse flow vortex appears near the trailing edge and becomes larger.

With the development of smart city, the concept of smart development is integrated into the construction management, so as to promote the smart development of construction and improve the efficiency of construction management. This paper discusses the application prospect of GIS-BIM integration technology in construction schedule management, site material management and safety management of construction personnel. At the same time, it looks into the application trend of gis-bim integration technology and global wide area network, Internet of things, virtual reality and other emerging technologies in the integration of building construction management, so as to promote the intelligent and visual management development of gis-bim integration technology in building construction management.

The NPU-WA airfoils were designed at high design lift coefficient and high Reynolds number, with small sensitivity of the maximum lift coefficient to leading edge roughness and excellent geometric compatibility. Compared to the widely used airfoils, the NPU-WA airfoils have higher lift-to-drag ratio and higher maximum lift coefficient. This paper aims to design a megawatt wind turbine blade in order to demonstrate the advantage of the NPU-WA airfoils. The distributions of chord length and twist angle for a 2 MW wind turbine blade are optimized by a kriging surrogate model-based optimizer, with aerodynamic performance being evaluated by blade element-momentum theory. Results show that compared with the baseline blade, the maximum power coefficient of the optimized NPU blade is larger, and the chord lengths at all span-wise sections are smaller, which is benefit to structural weight reduction. It is shown that the NPU-WA airfoils feature excellent aerodynamic for the design of megawatt wind turbine blades.

The number of aerodynamic analysis in the design optimization of propeller has been reduced significantly by using the surrogate model, such as kriging. In this paper, a more efficient aerodynamic design optimization method of propeller is proposed by using the HK (hierarchical kriging) model. The high-fidelity model is defined as a RANS (Reynolds- Averaged Navier-Stokes) simulation for propeller and the low-fidelity model is defined as the results by blade-element/vortex theory. Initial samples are selected for two levels of fidelity via LHS (Latin Hypercube Sampling). The aerodynamic performance of varying fidelity is used to build variable-fidelity surrogate models for functions of objective (e.g. thrust) and constraint (e.g. shaft power). Infill sampling criteria, including MSP (minimizing of surrogate prediction), EI (expected improvement), PI (probability of improvement), LCB (lower-confidence bounding) and MSE (mean-squared error) are used to obtain new samples, and the surrogate models are repetitively updated until a global optimum is found. High-altitude propellers are optimized by the kriging model and hierarchical kriging model, respectively. Compared to kriging model, the number of RANS solving by the hierarchical kriging model is reduced 37.5%, and the optimization time is reduced 24.3%. The results have shown that the proposed design method for propeller can significantly improve the optimization efficiency.

Double-ended airfoils with round leading and trailing edges outperform conventional round-nose and sharp trailing-edge airfoils when used for the inboard part of a rigid coaxial rotor operating in forward flight, as reverse flow can occupy 80% surface of the retreating blade. However, aerodynamic design optimization for this kind of airfoils is challenging, since it is required to achieve drag reduction over a wider lift range in both forward and reverse flows but there is no method available currently. To address this problem, this article proposes an efficient hybrid inverse/optimization design method that combines inverse design and direct optimization within a surrogate-based optimization (SBO) framework. The weighted objective function consists of two components: prescribed pressure distributions and total drag. The resulting constrained optimization problem is solved by using kriging surrogate model and dedicated infill-sampling method. The proposed method is demonstrated by aerodynamic shape optimizations of a DBLN-526 airfoil and an elliptical airfoil and compared with direct optimization method. For DBLN-526 airfoil case, 7%–30% drag reduction is achieved in the range from zero lift to maximum lift and the optimum airfoil features better stall characteristics. For the case of elliptical airfoil of 40% thickness, significant drag reduction is achieved in both forward and reverse flows and the optimum airfoil features more robust aerodynamic performance at off-design Mach numbers. The results confirm that the proposed method outperforms the conventional direct optimization method and more practical for aerodynamic shape optimization of double-ended airfoils.

This work presents a new method to compute instabilities associated to cross-flow transition scenarios. The method analyses base flows issued from CFD simulations (RANS model) using higher order dynamic mode decomposition (HODMD). The flow field is then approximated as an expansion of modes and it is possible to identify the primary and secondary flow instabilities, in cross-flows. The good performance of this novel method is first validated by locating the transition point related to the first instability in a low-speed 2D NLF0416 airfoil. Then, 3D cross-flow instabilities over a wing with 40◦ back-sweep angle (shaped from a NACA642A015 airfoil) are presented.