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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°

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...

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

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.

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.

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.

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.

Aerodynamic shape optimization of a hypersonic transport aircraft over a wide Mach-number range is challenging. The difficulty is not only associated with the large computational cost of high-fidelity CFD (computational fluid dynamics) simulations but also linked to the reasonable compromise between aerodynamic performances of aircraft at different speed ranges. This article proposes to use efficient global optimization based on surrogate models to address this type of problems. A RANS (Reynolds averaged Navier-Stokes) flow solver is adopted to evaluate objective and constraint functions; Kriging surrogate model combined with a parallel infill-sampling method and a multi-round strategy are employed to find the global optimum. First, a profile optimization with baseline airfoil of NACA64A-204 is conducted to achieve high lift-to-drag ratio ( L / D ) at both hypersonic ( Ma = 6.0 ) and transonic ( Ma = 0.8 ) regimes with up to 18 design variables, and significant improvement has been observed. Then, multi-objective wing optimizations of maximizing both hypersonic and transonic L / D s with up to 54 design variables are performed and multiple optimizations with various sets of weight coefficients are investigated. The optimized wings are further evaluated and compared with the baseline wing at the flow regimes from subsonic to hypersonic speeds. Results show that by using the optimized profile, hypersonic and transonic L / D s of a typical wing configuration are increased by 13.85% and 7.32%, respectively. After 3-D optimizations, the L / D s at hypersonic and transonic design points are further improved by 4.47% and 3.19%, respectively, and a better performance over a wide Mach-number range is obtained. It is shown that a multi-round surrogated-based optimization is feasible and effective for aerodynamic shape optimization of hypersonic transport aircrafts over a wide Mach-number range.

Variable-fidelity surrogate modeling offers an efficient way to generate aerodynamic data for aero-loads prediction based on a set of CFD methods with varying degree of fidelity and computational expense. In this paper, direct Gradient-Enhanced Kriging (GEK) and a newly developed Generalized Hybrid Bridge Function (GHBF) have been combined in order to improve the efficiency and accuracy of the existing Variable-Fidelity Modeling (VFM) approach. The new algorithms and features are demonstrated and evaluated for analytical functions and are subsequently used to construct a global surrogate model for the aerodynamic coefficients and drag polar of an RAE 2822 airfoil. It is shown that the gradient-enhanced GHBF proposed in this paper is very promising and can be used to significantly improve the efficiency, accuracy and robustness of VFM in the context of aero-loads prediction.

This paper aims to develop an efficient global optimization method for design of transonic natural-laminar-flow (NLF) airfoils and wings, based on high-fidelity computational fluid dynamics (CFD) solver. The CFD solver features functionality of automatic transition prediction, by coupling Reynolds-averaged Navier-Stokes (RANS) equations with the linear-stability-theory-based dual e N method for Tollmien-Schlichting and crossflow instabilities. An A320-sized transonic NLF wing with a laminar supercritical airfoil is designed for cruise condition at Mach=0.74, Re=20 million, CL=0.515. In order to further improve the cruise efficiency, this NLF wing is optimized at higher Mach number of 0.75 via an in-house surrogate-based optimizer. The optimization is formulated as a drag minimization problem with constraints on lift, pitching moment and geometric thickness. Through only 130 CFD evaluations, 12.1 counts drag reduction is obtained, while all constraints are strictly satisfied. Further study shows that the drag reduction is contributed by both of shock-wave weakening and laminar-flow extension. On suction side, the favorable pressure gradient is maintained while shock wave is weakened; on pressure side, the crossflow (CF) instability is effectively suppressed and thereby the laminar flow region is dramatically extended. The improvement of aerodynamic performance is observed not only at design point but also over a certain range of off-design lift coefficients.

An efficient method based on the surrogate-management framework has been excised to optimize the actuation parameters of active flow control over an airfoil via a synthetic jet. In this approach, sample points are chosen by the design of experiments method, and approximation models are built based on the sampled data obtained from unsteady Reynolds-averaged Navier―Stokes simulations. The accuracy of these approximation models is evaluated at some test points by comparing the approximated values with the accurate values obtained from unsteady Reynolds-averaged Navier―Stokes simulations. Three types of approximation models (quadratic response-surface model, kriging model, and radial-basis-function neutral network) are built from the same data set. The model with highest accuracy is chosen as the surrogate model to be used to replace the unsteady Reynolds-averaged Navier― Stokes analysis during optimization. The optimization objective is to maximize the lift coefficient of a NACA 0015 airfoil at given angles of attack (14 to 22°), with the jet momentum coefficient, nondimensional frequency, and jet angle being the design variables. The surrogate model is coupled with a simulated annealing genetic algorithm optimizer to efficiently obtain the global optimum. As a result of the optimization process, the lift coefficient at an angle of attack of 16° is increased by 16.9% and the corresponding drag is decreased by 13.4% with respect to the initial controlled flow. It is preliminarily shown that the presented method is efficient and applicable for optimization of active flow control via a synthetic jet.

Design of airfoils specially tailored for wind turbine blades has dramatic influence on the performance of a wind turbine. The traditional way for wind turbine airfoil design is a kind of trial and error process. In order to improve the design efficiency was well as the performance of the design, numerical optimization methods coupling optimization algorithm with CFD codes in an automatic process chain are of great interest. This study is focused on the development of efficient numerical optimization design methods for wind turbine airfoils. The main feature is to use surrogate-based optimization. Surrogate-based optimization is very efficient and has the capability of finding global optima; it can be classified as the third-type optimization method other than the traditional gradient-based methods and gradient-free searching methods, such as evolutional algorithms. Optimization designs of FFA-W3-211, inverse design of NPU-WA-300 and realistic numerical optimization of NPU-WA-250 are exercised. Examples show that the developed methods are efficient and robust, with sufficient flexibility of handling both geometric and aerodynamic constraints, multi-points design and multi-objective design.

Gradient-based optimization using adjoint method has proved effective for automatic aerodynamic shape optimization via high-fidelity Computational Fluid Dynamics (CFD) methods. Past experience suggests that its optimization efficiency and robustness are crucially affected by the step size along a direction of descending. In this paper, a surrogate modeling method based on gradient-enhanced Kriging is exercised to determinate the step size of adjoint-based optimization and a routine for adjoint-based aerodynamic design has been proposed. Representative results are presented for the inverse design of a RAE 2822 airfoil. It is found that the efficiency as well as robustness of adjoint-based aerodynamic optimization can be dramatically improved. Nomenclature

A Variable-Fidelity Modeling (VFM) method has been developed as an efficient and accurate aerodynamic data modeling strategy. In this approach, a set of CFD methods with varying degrees of fidelity and computational expense is exercised to reduce the number of expensive high-fidelity computations. Kriging-based bridge functions are constructed to match the low- and high fidelity CFD data. The method is demonstrated by constructing a global approximation model of the aerodynamic coefficients of an RAE 2822 airfoil based on sampled data. The model is adaptively refined by inserting additional samples. It is shown that the method is promising for efficiently generating accurate aerodynamic models that can be used for the rapid prediction of aerodynamic data across the flight envelope.

Cokriging is a statistical interpolation method for the enhanced prediction of a less intensively sampled primary variable of interest with assistance of intensively sampled auxiliary variables. In the geostatistics community it is referred to as two- or multi-variable kriging. In this paper, a new cokriging method is proposed and used for variable-fidelity surrogate modeling of aerodynamic data obtained with an expensive high-fidelity CFD code, assisted by data computed with cheaper lower-fidelity codes or by gradients computed with an adjoint version of the high-fidelity CFD code, or both. A self-contained derivation as well as the numerical implementation of this new cokriging method is presented and the comparison with the autoregressive model of Kennedy and O’Hagan is discussed. The developed cokriging method is validated against an analytical problem and applied to construct global approximation models of the aerodynamic coefficients as well as the drag polar of an RAE 2822 airfoil based on sampled CFD data. The numerical examples show that it is efficient, robust and practical for the surrogate modeling of aerodynamic data based on a set of CFD methods with varying degrees of fidelity and computational expense. It can potentially be applied in the efficient CFD-based aerodynamic analysis and design optimization of aircraft.