Aerodynamic Field Research Articles

Flow field reconstruction of compressor blade cascade based on deep learning methods

In the design process of compressors, calculating the S1 flow surface involves solving the Navier-Stokes equations, which results in slow convergence and makes determining cascade characteristics time-consuming. However, deep learning offers significant advantages in flow field reconstruction by not only automatically extracting complex flow features and reducing prediction time but also providing high accuracy in reconstruction. This paper implements the rapid reconstruction of the compressor S1 flow surface cascade flow field using two deep learning models: U-Net and 1D-CNN. Using a double-circular arc airfoil as an example, we selected four key design parameters that define the geometry and position of the airfoil, ultimately designing 5,292 sets of cascade geometries. By performing batch meshing and CFD simulations, we built a cascade flow field dataset. The U-Net neural network uses design parameters as input and outputs the aerodynamic distribution of the cascade flow field. After training, it can directly predict the flow field based on the design parameters. Since the U-Net model cannot directly obtain the aerodynamic parameter distribution and flow field aerodynamic coefficients on the airfoil surface, a 1D-CNN model is used as a complementary approach. The 1D-CNN model takes the design parameters as input and outputs the aerodynamic parameter distribution on the airfoil surface and the flow field aerodynamic coefficients. The prediction results show that the U-Net model achieves an average relative error of less than 1% in cascade flow field reconstruction, while the 1D-CNN model achieves an average relative error of less than 1% in predicting the pressure recovery coefficient and less than 2% in predicting the total pressure loss coefficient. This study presents a method for the rapid reconstruction of compressor blade cascade flow fields, which helps improve design efficiency and shorten the design cycle.

Multi-task Gaussian Processes based transient aerodynamic load reconstruction for maglev vehicle using acceleration response

The accurate estimation of aerodynamic loads is crucial for developing high-speed maglev trains, which can reach speeds of up to 600 km/h. Traditionally, this estimation has been achieved through computational aerodynamic simulation or direct pressure measurement. In this paper, we propose a novel framework for reconstructing transient aerodynamic loads on maglev vehicles using on-board acceleration measurements. In the framework, an inverse mathematical model that correlates the measured acceleration and external aerodynamic loads is derived from a well-calibrated maglev vehicle model. To avoid the ill-posed problem when solving the inverse mathematical model, a multi-task Gaussian Processes method is proposed, in which all reconstructed transient aerodynamic loads are treated as Gaussian Processes and the closed-form posterior distributions of these aerodynamic loads could be calculated. To validate the proposed framework, a set of transient vibration data collected from an operational maglev train passing through a double-track tunnel is utilized for load reconstruction. The results demonstrate that the framework offers a cost-effective and efficient means to obtain aerodynamic loads, highlighting its practical relevance for aerodynamic field testing in the context of evolving high-speed maglev technologies.

An Efficient Uncertainty Quantification Method Based on Inter-Blade Decoupling for Compressors

Abstract A compressor usually contains multiple blade rows, and its uncertainty dimensionality grows proportionally with the number of blade rows, leading to a rapid increase in required sample size for uncertainty quantification analysis. This paper proposes a new dimensionality reduction method based on inter-blade decoupling, by analyzing uncertainty propagation in compressors. Traditionally, a surrogate model with uncertainty variables of all blade rows as input is directly established and the dimensionality is high. To solve this problem, this study decomposes the compressor domain into sub-domains, each containing one blade row. For each sub-domain, a sub-model introduces aerodynamic uncertainties at the interfaces connecting different sub-domains. The dimensionality of a sub-model is roughly equal to the uncertainty factors in a single row, significantly reducing the required sample size. The uncertainties in the rotor and stator blade rows of a one-stage compressor are investigated to verify this method. Using principal component analysis and machine learning, the projection amplitudes of the interface aerodynamic flow field onto the principal modes are extracted, and sub-models are established. Results show that the original 25-dimensional model can be decoupled into a 13-dimensional sub-model for the rotor and a 16-dimensional sub-model for the stator, reducing the required sample size from 600 to 90 with similar accuracy. This dimensionality reduction method greatly reduces the cost of predicting compressor performance with uncertainty, laying a foundation for comprehensive analysis and effective control of uncertainty factors in engineering applications.

The Influence of Reduced Frequency on H-VAWT Aerodynamic Performance and Flow Field Near Blades

Studies demonstrate that the reduced frequency k is influenced by the incoming wind speed U0 and the rotor speed n. As a dimensionless parameter, k characterizes the stability of the flow field, which is a critical factor affecting the performance of vertical-axis wind turbines (VAWTs). This paper investigates the impact of k on the performance of straight-blade vertical-axis wind turbines (H-VAWT). The findings indicate that 0.05 is the critical value of k. The same k results in a similar flow field structure, yet the performance changes vary with different U0. A decrease in n or an increase in U0 leads to an increase in the average value and fluctuation of k, which subsequently reduces the rotor rotation torque Cm and decreases the maximum wind energy utilization rate Cpmax. This reduction in Cpmax weakens the stability of the flow field. Additionally, the high-speed area of the blade’s trailing edge velocity trajectory at θ=0°, θ=120°, and θ=240° expands with increasing range. Velocity dissipation in the high-speed area of the trailing edge affects the stability of the flow field within the rotor.

Energy harvesting from transverse galloping using a two-degree-of-freedom flow energy harvester

Abstract A two degree-of-freedom (2-DOF) galloping piezoelectric energy harvesting system where both oscillators are excited by the incoming flow is studied in this paper. A coupled lumped-parameter model is developed to simulate the electro-fluid-structural coupling behaviour assuming a quasi-steady aerodynamic flow field. The differential equations governing the dynamics of the lumped system are converted into nonlinear algebraic equations employing the harmonic balance method (HBM) and then solved using Newton’s method. The approximate analytical solutions are compared to the solutions obtained by numerical integration, and the results agree, both qualitatively and quantitatively. The solutions were subsequently used to investigate the effects of the bluff body dimension, mechanical, electrical, aerodynamic, and electromechanical parameters on the performance of the harvester and to illustrate how to optimise some of these parameters to reduce the cut-in wind speed and maximise the power output of the energy harvester. It will be shown that the energy harvesting performance could be significantly improved by introducing piezoelectric transducers on both oscillators and including both masses in the incoming flow. A comparative study between the proposed 2-DOF flow energy harvesting system, a single-degree-of-freedom (SDOF) galloping piezoelectric energy harvester (GPEH), and other configurations of 2-DOF GPEH shows that the present 2-DOF GPEH generates the largest power peak.

Denoising graph neural network based on zero-shot learning for Gibbs phenomenon in high-order DG applications

With the availability of high-performance computing technology and the development of advanced numerical simulation methods, Computational Fluid Dynamics (CFD) is becoming more and more practical and efficient in engineering. As one of the high-precision representative algorithms, the high-order Discontinuous Galerkin Method (DGM) has not only attracted widespread attention from scholars in the CFD research community, but also received strong development. However, when DGM is extended to high-speed aerodynamic flow field calculations, non-physical numerical Gibbs oscillations near shock waves often significantly affect the numerical accuracy and even cause calculation failure. Data driven approaches based on machine learning techniques can be used to learn the characteristics of Gibbs noise, which motivates us to use it in high-speed DG applications. To achieve this goal, labeled data need to be generated in order to train the machine learning models. This paper proposes a new method for denoising modeling of Gibbs phenomenon using a machine learning technique, the zero-shot learning strategy, to eliminate acquiring large amounts of CFD data. The model adopts a graph convolutional network combined with graph attention mechanism to learn the denoising paradigm from synthetic Gibbs noise data and generalize to DGM numerical simulation data. Numerical simulation results show that the Gibbs denoising model proposed in this paper can suppress the numerical oscillation near shock waves in the high-order DGM. Our work automates the extension of DGM to high-speed aerodynamic flow field calculations with higher generalization and lower cost.

Morphing Spoiler for Adaptive Aerodynamics by Shape Memory Alloys

The automotive industry is continuously looking for innovative solutions to improve vehicle aerodynamics and efficiency. The research introduces a significant breakthrough in the field of automotive aerodynamics by employing shape memory alloys as bistable actuators for spoilers and moving flaps. The main novelty of this research lies in the development of a bistable actuator made of shape memory alloys as a precise and accurate control mechanism for spoilers and movable flaps. The shape memory alloys, with their unique ability to maintain two stable configurations and switch rapidly from one to the other in response to thermal or mechanical stimuli, allow precise and rapid adjustment of aerodynamic surfaces. The main advantage of this technology is its ability to improve vehicle aerodynamics by optimising both drag and downforce, thereby improving vehicle performance and fuel efficiency. This research shows the promising potential of a single composition of NiTi as a revolutionary technology in the automotive industry, revolutionising the way spoilers and moving flaps are used to achieve superior vehicle performance.

Numerical investigation of tip bifurcation on aerodynamic characteristics and flow field structure in a compressor cascade

In this study, the tip bifurcation of the compressor cascade is proposed, referring to the biological characteristics of bird wing bifurcation. The influence of tip bifurcation with different structural parameters on the aerodynamic performance and flow field structure of compressor cascade at different incidence angles is studied by numerical simulation. The research shows that the tip bifurcation can make the starting position of the corner separation move backward, inhibit the separation along the pitch and blade height direction, and reduce the flow loss of the cascade. The separation control effect of the corner region first increases and then decreases as the bifurcation height increases, and gradually diminishes as the arrangement position approaches the trailing edge. When the tip bifurcation is set at the starting position of the corner separation and its height is equal to 4 %H, the flow improvement effect in the passage is the most obvious, and the cascade flow loss is reduced by 14.4 %. At the same time, the tip bifurcation cascade has effective positive incidence angle characteristics, but when the incidence angle is less than the minimum loss incidence angle, the tip bifurcation increases the cascade loss.

Effectiveness of Three Turbulence Modeling Approaches in a Crosswind–Sedan–Dune Computational Fluid Dynamics Framework

The aerodynamic loads of a sedan experience significant fluctuations when passing by a sand dune at the roadside under crosswinds, which can easily cause yawing and overturning. Computational fluid dynamics (CFD) methods, based on different turbulence modeling approaches, yield different aerodynamic results for sedans. This study aims to investigate the effects of three prevailing turbulence modeling approaches (renormalization group (RNG) k-ε, large eddy simulation (LES), and improved delayed detached eddy simulation (IDDES)) on the aerodynamic characteristics of a sedan passing by a sand dune under crosswinds. The CFD dynamic mesh models are constructed using the “mosaic” mesh technique to account for the dune–air–sedan interaction. The reliability of the CFD prediction method is verified by comparing it with field test results. The predictive capabilities of the three turbulence modeling approaches are compared in terms of aerodynamic loads and flow field characteristics. The simulation of sand particle movement is conducted through the discrete phase model, aiming to assess the impact of wind–sand flow on the aerodynamic properties of sedans. Corresponding results show that the aerodynamic loads predicted by the LES model closely match (within 4.4–7.5%) the corresponding data obtained from field tests. While the IDDES and LES models demonstrate similar abilities in characterizing the wind field details, and their results exhibit maximum differences of 8.3–15.7%. Meanwhile, the maximum difference between the results obtained by the RNG k-ε and LES models ranges from 14.8% to 18.4%, attributed to its inability to capture subtle changes in the vortex structure within the flow field. This work will provide a numerical modeling reference for studies on the wind–sand flow and the aerodynamic characteristics of sedans running through the desert, and it has implications for the safe driving of sedans under extreme conditions.

Aerodynamic performance and flow field characteristics of wind turbines under shear incoming flow conditions

Abstract With the large size of the units, wind farms are evaluated in order to improve the accuracy of the incoming flow measurement and to improve the unit control strategy. In this paper, the turbulent wind field generated by autoregressive linear filtering using a large eddy simulation turbulence model is used to study the wind speed-induced zone under shear incoming flow conditions. At the same time, the wake and aerodynamic performances of the wind turbine under different incoming flow conditions are investigated, and conclusions are obtained. 1) The larger the shear index is, the larger the amplitude is at the first frequency component of the power and the thrust, and the larger the fatigue load is for the wind turbine. 2) For the wind turbine wake flow in the case of smaller wind turbine size, the wake velocity profiles at different shear indices cross and overlap in the transition and far wake regions. At position 0.5 D, the turbulence profiles with different shear indices basically overlap; the larger the shear index is, the more intense the wake flow exchange is and the greater the turbulence intensity in the wake region will be. 3) For the wind speed-induced region, at position −0.1 D, the incoming flow velocity distribution is subject to the combined effect of induction and shear, and the induction effect of the wind turbine wheel is a little larger. The larger the shear index, the greater the turbulence intensity.

Influences of ultra-low load operation strategies on performance of a 300 MW subcritical bituminous coal boiler

To reveal the operational characteristics of subcritical boilers under ultra-low loads, numerical simulations were conducted based on a 300 MW subcritical bituminous coal boiler. The impacts of boiler load and low-load operation strategies on coal combustion behavior, heat transfer process, and NOx emission were thoroughly examined. Results indicate that acceptable aerodynamic and temperature fields can still be formed at 25 % ultra-low load, but the boiler performance is significantly reduced, with the maximum cross-sectional average combustion temperature being reduced by 225.98 K compared with the full-load condition. At 25 % load, the use of only two layers of burners results in a substantial increase in NOx emission from 290.32 mg/m3 to 445.56 mg/m3. The position of in-service burners affects the region where the intense coal combustion and heat release process occurs, and using the middle three layers of burners helps to maintain heat absorption by the suspended heating surfaces and to minimize NOx emissions. Furthermore, increasing primary air velocity at ultra-low loads can promote coal combustion and heat transfer processes in the lower furnace, but increase NOx emission by 14.23 % when primary air velocity is increased from 14.90 m/s to 23.00 m/s at 25 % load. These findings provide valuable insights for optimizing the ultra-low load operation of subcritical boilers engaged in deep peak-shaving processes under the carbon neutrality goal.

Eulerian–Lagrangian hybrid solvers in external aerodynamics: Modeling and analysis of airfoil stall

Hybrid computational solvers that integrate Eulerian and Lagrangian methods are emerging as powerful tools in computational fluid dynamics, particularly for external aerodynamics. These solvers rely on the strengths of both approaches: Eulerian methods efficiently handle boundary layers, while Lagrangian methods excel in reducing numerical diffusion in flow convection. Building on our prior development of a two-dimensional hybrid solver that combines OpenFOAM with vortex particle method, this paper extends its application to the complex phenomena of airfoil stall at low Reynolds numbers. Specifically, we examine both static and dynamic stall conditions of a National Advisory Committee for Aeronautics (NACA) airfoil series 0012 (NACA0012) across a wide range of attack angles and oscillation frequencies, comparing our results with established data. The findings demonstrate the accuracy of hybrid Eulerian–Lagrangian solvers in replicating known stall behaviors, underscoring their potential for advanced aerodynamic studies. This work not only confirms the capability of hybrid solvers in accurately modeling challenging flows but also paves the way for their increased involvement in the field of external aerodynamics.

Aerodynamic force characteristics and flow field mechanism of multiple square cylinders in a tandem arrangement

Wind tunnel tests and large eddy simulations were employed to obtain the aerodynamic coefficients and flow fields of two and three tandem square cylinders across various spacing ratios. The spacing ratio L/D, defined as the ratio of the center-to-center spacing between adjacent square cylinders to their width, ranges from 1.2 to 8. By analyzing these results, the aerodynamic force characteristics and their generation mechanism of the three tandem square cylinders at a high Reynolds number (Re = 3.2 × 104) were revealed. By comparing the results of the two and three tandem square cylinders, the effect of adding a third square cylinder behind the two tandem square cylinders on its aerodynamic characteristics was clarified. The results show that unlike the two tandem square cylinders, the three tandem square cylinders exhibit two critical spacing ratios, (L/D)cr1 = 2.5–3 and (L/D)cr2 = 3.5–4, respectively. Based on these two critical spacing ratios, the flow around the three tandem square cylinders is identified as single blunt body, reattachment, and co-shedding regimes. In the single blunt body and reattachment regimes, the addition of a third square cylinder behind significantly alters the flow around the two tandem square cylinders, leading to reduced mean drag coefficients, fluctuating lift coefficients, and Strouhal numbers, along with an increased critical spacing ratio. In the co-shedding regime, this addition has little effect on the flow.

Numerical investigation of cylinder rotors with various endplates

For a finite-length cylinder rotor, rotation induces unique pattern tip vortices at the free end, significantly altering the aerodynamic characteristics of the rotor. Endplates are often applied to finite-length cylinders as a means of restraining end effects. The endplates change the aerodynamic characteristics of the rotor by affecting the end axial flow. In the present study, cylinder rotors with static and rotating endplates of various diameters are investigated by means of large eddy simulation. By analyzing the aerodynamic force, wind pressure, and flow field characteristics of the rotors, the varying patterns and reasons for the aerodynamic characteristics of rotors with static and rotating endplates are clarified. The results show that the endplate induces disk vortices and changes the vortex patterns at the free end of the rotor, and the static endplates show little effect on the development of tip vortices, so the wake vortices show the triple vortex pattern, whereas the rotating endplates enhance the intensity of the plate vortices and inhibit the tip vortices development, leading to the double vortex pattern, which in turn produces a different pattern of aerodynamic characteristics compared to the rotor with the static endplates. The mechanism of the variation in the aerodynamic characteristics and vortex patterns is partially explained by analyzing and discussing the flow field results.

Experimental Study of Trailing-Edge Bluntness Noise Reduction by Porous Plates

The acoustic and aerodynamic fields of blunt porous plates are examined experimentally in an effort to mitigate trailing-edge bluntness noise. The plates are characterized by a single dimensionless porosity parameter identified in previous works that controls the influence of porosity on the sound field. Hot-wire anemometry interrogates the velocity field to connect turbulence details of specific regions to flow noise directivity and beamforming source maps. Porous plates are demonstrated to reduce the bluntness-induced noise by up to 17 dB and progressively suppress broadband low-frequency noise as the value of the porosity parameter increases. However, an increase in this parameter also increases the high-frequency noise created by the pores themselves. The same highly perforated plate characterized by a large value of the porosity parameter reduces the bluntness-induced vortex shedding that is present in the wake of the impermeable plate. Lastly, pore shape and positional alignment are shown to have a complex effect on the acoustic field. Among the porosity designs considered, plates with circular pores are most effective for low-frequency noise reductions but generate high-frequency noise. No meaningful difference is found between the acoustic spectra from plates of the same open-area fraction with pores aligned along or staggered about the flow direction.

Flow over traveling and rotating cylinders using a hybrid Eulerian–Lagrangian solver

Hybrid Eulerian–Lagrangian solvers have gained increasing attention in the field of external aerodynamics, particularly when dealing with strong body–vortex interactions. This approach effectively combines the strengths of the Eulerian component, which accurately resolves boundary layer phenomena, and the Lagrangian component, which efficiently evolves the wake downstream. This study builds on our team’s previous work by enhancing the capabilities of a two-dimensional hybrid Eulerian–Lagrangian solver. We aim to upgrade our solver which was initially designed for static cases, to now also simulate cases involving moving objects. To ensure the reliability and applicability of a new solver, it is essential to validate its performance in complex cases. Here, the solver is validated across the case of a traveling cylinder and the case of a rotating cylinder in two different rotational speeds at low Reynolds numbers. In the realm of Eulerian solvers, such as OpenFOAM (utilized for the Eulerian component of this hybrid approach), traditional techniques include the use of morphing meshes, overset meshes, and Arbitrary Mesh Interfaces (AMI) to model body motion. The proposed methodology involves extending the Eulerian mesh up to a short distance from the solid boundary and moving it entirely as a solid entity. Then the Lagrangian solver is responsible for calculating the updated boundary conditions, thereby completing the hybrid solver’s functionality. This approach is very similar to the overset mesh technique. However, unlike the traditional method where an Eulerian mesh moves on top of a static one, our method involves the motion of an Eulerian mesh over a Lagrangian grid. We compared the results from our hybrid solver with those from a purely Eulerian solver, specifically OpenFOAM. The comparison demonstrates that our solver can replicate OpenFOAM’s results with high accuracy. Another interesting point highlighted in this study is the presence of high-frequency oscillations in the body forces in hybrid solvers that incorporate the redistribution of Lagrangian particles and do not utilize surface elements such as vortex panels, specifically when dealing with dynamic mesh simulations. When the Eulerian mesh travels on top of the Lagrangian grid of particles, the positions of the particles with respect to the Eulerian mesh continuously change. This results in a constant shift of particles near the solid body, where the highest vorticity is observed. Particles that are close to the solid boundary at one time step may find themselves inside the boundary at the next time step, leading to their removal. This pattern continuously changes during the simulation, causing fluctuations in the boundary conditions of the Eulerian solver and manifesting as oscillations in the forces acting on the body. It is shown that this issue can be alleviated either by increasing the spatial resolution of the Lagrangian solver or by synchronizing the movement of the Lagrangian grid with the motion of the Eulerian mesh. The results of the study make the solver trustworthy and pave the way for more demanding external aerodynamic simulations.

Prediction of the aerodynamic noise of an airfoil via the hybrid methods of aeroacoustics

The accurate prediction of the trailing-edge noise and the determination of its sources are essential to reduce fans and propellers noise. This noise component is due to the scattering of the turbulent boundary layer into acoustic waves by the trailing edge. In this paper, the noise emanating from a CD (Controlled-Diffusion) airfoil is simulated and computed via the hybrid methods of aeroacoustics. In these methods, the aerodynamic and acoustic fields are computed separately. The flow data are obtained using the in-house LES solver SFELES. ACTRAN acoustic solver has been used to solve the acoustics and to provide the near and far fields propagation via Lighthill’s analogy. Curle’s analogy is applied as well in its integral compact formulation which takes the presence of walls into account. Curle’s formulation is applied proposing an approach where the volume and surface integrals have been implemented in SFELES to be calculated simultaneously with the flow in order to avoid the storage of noise sources which requires a huge space. In Lighthill’s analogy, sources and near field maps show that the turbulent boundary layer and wake are the more efficient sources and the center of radiation is the trailing edge. The comparison of the numerical results with the experimental measurements, performed by Moreau and Roger and Moreau et al. , shows an overall excellent agreement confirming the capability of SFELES (LES sources) combined with ACTRAN (Lighthill’s analogy) to predict correctly the noise generated by turbulent flows around airfoils. The acoustic spectrum presents an overprediction up to 5 dB at the frequencies 300 Hz and 550 Hz and an underprediction about 5 dB at the frequencies 1100 Hz and 1750 Hz. The sound pressure level (SPL) obtained using the proposed approach of Curle’s analogy matches very well the experimental results. Thus, Curle’s analogy can be used to obtain a fast, approximated and acceptable results about the noise radiation of airfoils avoiding the storage of noise sources which requires a huge space and time.

Flow around a pair of 2D cylinders using a hybrid Eulerian-Lagrangian solver

The field of external aerodynamics encompasses various engineering disciplines with a significant impact on wind energy technology. Aerodynamic investigations provide insights not only into the characteristics of individual blades or standalone wind turbines but also into entire wind farms. As advancements in wind turbine design continue, understanding the interactions between turbines in close proximity becomes crucial, presenting a multi-body problem. Researchers require efficient and accurate tools to comprehensively study such dynamics. This paper presents a hybrid Eulerian-Lagrangian solver designed to leverage the strengths of Eulerian solvers in resolving boundary layers and Lagrangian solvers in convecting wakes downstream without introducing significant numerical diffusion. The solver adeptly handles multi-body simulations, allowing the construction of independent Eulerian meshes that communicate seamlessly through Lagrangian particles. In this way, the computational study of multibody problems does not require very large and dense meshes. Validation in single-body cases has already been conducted, with this paper demonstrating the solver’s application to a pair of cylinders in different configurations. A comparative performance analysis is carried out against pure Eulerian solvers. The results highlight that the hybrid solver efficiently reproduces the accuracy of the Eulerian solver, demonstrating its effectiveness in handling complex aerodynamic simulations.

Aerodynamic flow field analysis of vortex interactions on multi-swept wing configurations

The underlying flow physics of vortex breakdown and vortex-vortex interactions at moderate to high angles of attack is not well understood. This lack of understanding is a challenge to the development of optimized wing designs for fighter aircraft. The goal of this study is to gain insight into the breakdown of vortices on multi-swept wing configurations. Two generic models were considered, one with a gradual vortex breakdown and one with a rapid (abrupt) breakdown. Aerodynamic forces were calculated from the US Air Force Academy (USAFA) subsonic wind tunnel to validate the experimental setup using computational fluid dynamics (CFD) and previous work. Stereoscopic particle imaging velocimetry (SPIV) was used to visualize vortex-vortex interactions, measure vortex strengths, and identify vortex breakdown locations. The measured lift and drag forces showed flow physics that agreed with previous experiments and CFD, supporting the validity of the new experimental setup. Analysis of SPIV and CFD data improved our understanding of the different types of vortex interactions observed for both models. The only difference between the models was the location of the secondary sweep angle on the chord. The C4L80 model, with a secondary sweep angle at 40% of the root chord, had a large shear layer along the leading edge, which led to vortex merging and gradual vortex breakdown at lower angles of attack than its counterpart. The C6L80 model, with a secondary sweep angle at 60% of the root chord, had no such shear layer and instead developed strong, isolated vortices that were characterized by vortex braiding and abrupt breakdown at high angles of attack. These vortices were entrained into the main vortex at the leading edge of the strake (inboard vortex), creating a balanced vortex system that enhanced lift and delayed the onset of gradual vortex breakdown seen in the C4L80 model.

Automated optimal experimental design strategy for reduced order modeling of aerodynamic flow fields

Aerodynamic flow fields reveal essential physical insights (such as shocks) that substantially affect aerodynamic performance. However, conventional flow field computations require time-consuming simulations. Alternatively, reduced-order models (ROMs) allow fast flow field predictions, enabling real-time decision-making. Efficient sampling is required to train ROMs without incuring prohibitive costs. In this paper, we propose a fully automated optimal experimental design (Auto-OED) strategy on proper orthogonal decomposition (POD) for ROM-based rapid flow field predictions. Auto-OED uses two individual optimal experimental design (OED) strategies, automatically selects the number of POD bases for the first sampling strategy, and intelligently switches to the second strategy on the fly. We showcased the Auto-OED strategy on airfoil flow field predictions in the transonic regime. OED-based ROMs were constructed over 20 trials for robustness tests with a total of 40 training samples in each trial, including 16 random initial samples by Latin hypercube sampling (LHS) and 24 OED samples. The results demonstrated that the ROM predictions completely based on LHS had an error of 1.6×10−3 while the existing OED strategies-based ROMs over 20 trials achieved a mean error (μerr) of 7.5×10−4 with a standard deviation (σerr) of 9.0×10−5. In contrast, the best Auto-OED ROM achieved the lowest μerr of 7.5×10−4 and lowest σerr of 6.2×10−5. These error reductions confirm the viability of the proposed Auto-OED-based ROM in fluid field predictions and potentially other engineering applications of a similar type.