Fast simulation of airfoil flow field via deep neural network

Computational Fluid Dynamics (CFD) has become an indispensable tool in the optimization design, and evaluation of aircraft aerodynamics. However, solving the Navier-Stokes (NS) equations is a time-consuming, memory demanding and computationally expensive task. Artificial intelligence offers a promising avenue for flow field solving. In this work, we propose a novel deep learning framework for rapidly reconstructing airfoil flow fields. Channel attention and spatial attention modules are utilized in the downsampling stage of the UNet to enhance the feature learning capabilities of the deep learning model. Additionally, integrating the predicted flow field values generated by the deep learning model into the NS equation solver validates the credibility of the flow field prediction results. The NACA series airfoils were used to validate the prediction accuracy and generalization of the deep learning model. The experimental results represent the deep learning model achieving flow field prediction speeds three orders of magnitude faster than CFD solver. Furthermore, the CFD solver integrated with deep learning model demonstrates a threefold acceleration compared to CFD solver. By extensively mining historical flow field data, an efficient solution is derived for the rapid simulation of aircraft flow fields

Corrected Navier-Stokes equations for compressible flows

For gas flows, the Navier-Stokes (NS) equations are established by mathematically expressing conservations of mass, momentum and energy. The advantage of the NS equations over the Euler equations is that the NS equations have taken into account the viscous stress caused by the thermal motion of molecules. The viscous stress arises from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress is proportional to the gradient of velocity1. Thus, the assumption is the only empirical element in the NS equations, and this is actually the reason why the NS equations perform poorly under special circumstances. For example, the NS equations cannot describe rarefied gas flows and shock structure. This work proposed a correction to the NS equations with an argument that the viscous stress is proportional to the gradient of momentum when the flow is under compression, with zero additional empirical parameters. For the first time, the NS equations have been capable of accurately solving shock structure and rarefied gas flows. In addition, even for perfect gas, the accuracy of the prediction of heat flux rate is greatly improved. The corrected NS equations can readily be used to improve the accuracy in the computation of flows with density variations which is common in nature.Comment: 13 pages, 7 figure

NN-augmented k-ω shear stress transport turbulence model for high-speed flows with shock-wave/boundary layer interaction

Menter k-ω shear stress transport (SST) turbulence model demonstrates excellent performance for incompressible, subsonic and transonic flows with mild separation but shows overprediction of the separation bubble of supersonic shock-wave/boundary layer interaction (SWBLI). Some efforts focus on the effect of the structure parameter in stress limiter in an ad-hoc way. Few studies attempt to construct the relation between the structure parameter and flow field variables. The motivation of this work is to construct such a relation to augment the prediction performance of the SST model by introducing a correction factor. Machine learning methods are used since the physical mechanism of SWBLI is complex and unclear. The simulation results show that the constructed relation enhances the structure parameter near the shock wave in the boundary layer when applied to the SST model. Compared with direct numerical simulation and experimental data, the pressure and skin friction coefficients along the wall and the velocity field are significantly improved. In addition, the introduced correction factor can automatically degrade for the subsonic benchmark case of NACA4412 airfoil and maintain the prediction accuracy of the original SST model, but delay the shock location of the transonic case

Wall heat flux in supersonic turbulent expansion flow with shock impingement

We perform direct numerical simulations to investigate the characteristics of wall heat flux (WHF) in the interaction of an oblique shock wave at an angle of 33.2 & DEG; and free-stream Mach number M & INFIN; = 2.25 impinging on supersonic turbulent expansion corners with deflection angles of 0o (flat plate), 6o and 12o. The effect of the expansion on the WHF characteristics is analysed by comparing it to the interaction with the flat plate under the same flow conditions and a fixed shock impingement point. In the post-expansion region, the decreased mean WHF is found to collapse onto the flat plate case when scaled with the mean wall pressure. The statistical properties of the WHF fluctuations, including probability density function, frequency spectra, and space-time correlations, are comparatively analysed. The expansion causes an increase in the occurrence probability of negative extreme events, an enhancement of high-frequency energy, and an inhibition of intermediate-frequency energy. The increased expansion angle also results in a faster recovery of characteristic spanwise length scales and an increase in convection velocity. We use the mean WHF decomposition method in conjunction with bidimensional empirical mode decomposition to quantitatively analyse the impact of expansion on scale contributions. It is demonstrated that the presence of the expansion corner has no significant impact on the decomposed results, but it significantly reduces the contribution associated with outer large-scale structures

Incident shock wave and supersonic turbulent boundarylayer interactions near an expansion corner

Direct numerical simulations of incident shock wave and supersonic turbulent boundary layer interactions near an expansion corner are performed at Mach number M-infinity = 2.9 and Reynolds number Re-infinity = 5581 to investigate the expansion effect on the characteristic features of this phenomenon. Four expansion angles, i.e. alpha = 0(0) (flat-plate), 2(0), 5(0) and 10(0) are considered. The nominal impingement point of the oblique shock wave with a flow deflection angle of 12(0) is fixed at the onset of the expansion corner, and flow conditions are kept the same for all cases. The numerical results are in good agreement with previous experimental and numerical data. Various flow phenomena, including the flow separation, the post-shock turbulent boundary layer and the flow unsteadiness in the interaction region, have been systematically studied. Analysis of the instantaneous and mean flow fields indicates that the main effect of the expansion corner is to significantly decrease the size and three-dimensionality of the separation bubble. A modified scaling analysis is proposed for the expansion effect on the interaction length scale, and a satisfactory result is obtained. Distributions of the mean velocity, the Reynolds shear stress and the turbulent kinetic energy show that the post-shock turbulent boundary layer in the downstream region experiences a faster recovery to the equilibrium state as the expansion angle is increased. The flow unsteadiness is studied using spectral analysis and dynamic mode decomposition, and dynamically relevant modes associated with flow structures originated from the incoming turbulent boundary layer are clearly identified. At large expansion angle (alpha=10(0)), the unsteadiness of the separated shock is dominated by medium frequencies motions, and no low frequency unsteadiness is observed. The present study confirms that the driving mechanism of the low frequency unsteadiness is strongly related to the separated shock and the detached shear layer. (C) 2019 Elsevier Ltd. All rights reserved

Wall shear stress and wall heat flux in a supersonic turbulent boundary layer

We report the characteristics of wall shear stress (WSS) and wall heat flux (WHF) from direct numerical simulation (DNS) of a spatially developing zero-pressure-gradient supersonic turbulent boundary layer at a free-stream Mach number M-& INFIN; = 2.25 and a Reynolds number Re-tau = 769 with a cold-wall thermal condition (a ratio of wall temperature to recovery temperature T-w/T-r = 0.75). A comparative analysis is performed on statistical data, including fluctuation intensity, probability density function, frequency spectra, and space-time correlation. The root mean square fluctuations of the WHF exhibit a logarithmic dependence on Re-tau similar to that for the WSS, the main difference being a larger constant. Unlike the WSS, the probability density function of the WHF does not follow a lognormal distribution. The results suggest that the WHF contains more energy in the higher frequencies and propagates downstream faster than the WSS. A detailed conditional analysis comparing the flow structures responsible for extreme positive and negative fluctuation events of the WSS and WHF is performed for the first time, to the best of our knowledge. The conditioned results for the WSS exhibit closer structural similarities with the incompressible DNS analysis documented by Pan and Kwon [ "Extremely high wall-shear stress events in a turbulent boundary layer, " J. Phys.: Conf. Ser. 1001, 012004 (2018)] and Guerrero et al. [ "Extreme wall shear stress events in turbulent pipe flows: Spatial characteristics of coherent motions, " J. Fluid Mech. 904, A18 (2020)]. Importantly, the conditionally averaged flow fields of the WHF exhibit a different mechanism, where the extreme positive and negative events are generated by a characteristic two-layer structure of temperature fluctuations under the action of a strong Q4 event or a pair of strong oblique vortices. Nevertheless, we use the bi-dimensional empirical decomposition method to split the fluctuating velocity and temperature structures into four different modes with specific spanwise length scales, and we quantify their influence on the mean WSS and WHF generation. It is shown that the mean WSS is mainly related to small-scale structures in the near-wall region, whereas the mean WHF is associated with the combined action of near-wall small-scale structures and large-scale structures in the logarithmic and outer regions

Effect of expansion on the wall heat flux in a supersonic turbulent boundary layer

Direct numerical simulation of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.25 and a friction Reynolds number of Re-tau = 769 subjected to an expansion corner with a deflection angle of 12 degrees is performed to investigate the effect of expansion on the characteristics of the wall heat flux (WHF). The effect of expansion on the statistical and structural properties of the fluctuating WHF is analyzed systematically in terms of probability density function, frequency spectra, and space-time correlations. Normalization using the local root mean square value yields good collapse of the probability density function curves. Unlike with wall pressure frequency spectra, it is found that expansion has little influence on the low-frequency components of the WHF spectrum. The correlation results show that the main effect of expansion is to increase the characteristic length scales and convection velocity of the WHF fluctuation in the post-expansion region. Furthermore, a direct comparison between the conditionally averaged flow fields and those presented in the authors' previous work [Tong et at, Phys. Fluids 34, 015127 (2022)] is performed to uncover the effect of expansion on the flow structures associated with extreme positive and negative WHF fluctuation events. We highlight that the extreme positive event emerges below a small hot spot under the action of a strong Q4 event, whereas the extreme negative event is relatively insensitive to expansion and still occurs between a pair of strong oblique vortices. In addition, we decompose the mean WHF into seven physics-informed contributions and quantify the effect of expansion on the dominating components with the aid of the bidimensional empirical mode decomposition method. The scale-decomposed results demonstrate quantitatively that expansion decreases the contribution of the large-scale structures in the outer region but the small-scale structures in the near-wall region contribute heavily to the mean WHF generation in the downstream region. Published under an exclusive license by AIP Publishing