The traditional method for obtaining aerodynamic parameters of airfoils by solving Navier–Stokes equations is a time-consuming computing task. In this article, a novel data-driven deep attention network (DAN) is proposed for reconstruction of incompressible steady flow fields around airfoils. To extract the geometric representation of the input airfoils, the grayscale image of the airfoil is divided into a set of patches, and these are input into the transformer encoder by embedding. The geometric parameters extracted from the transformer encoder, together with the Reynolds number, angle of attack, flow field coordinates, and distance field, are input into a multilayer perceptron to predict the flow field of the airfoil. Through analysis of a large number of qualitative and quantitative experimental results, it is concluded that the proposed DAN can improve the interpretability of the model while obtaining good prediction accuracy and generalization capability for different airfoils and flow-field states.

Boundary layer transition over a lifting body of 1.6 m length at $2^\circ$ angle of attack has been simulated at Mach 6 and a unit Reynolds number $1.0 \times 10^7$ m $^{-1}$ . The model geometry is the same as the Hypersonic Transition Research Vehicle designed by the China Aerodynamics Research and Development Center. Four distinct transitional regions are identified, i.e. windward vortex region, shoulder vortex region, windward cross-flow region and shoulder cross-flow region. Multi-dimensional linear stability analyses by solving the two-dimensional eigenvalue problem (spatial BiGlobal approach) and the plane-marching parabolized stability equations (PSE3D approach) are further carried out to uncover the dominant instabilities in the last three regions as well as the shoulder attachment-line region. The shoulder vortex is conducive to both inner and outer modes of shear-layer instability, of which the latter most likely trigger the vortex breakdown. A novel method is presented to substantially reduce the computational cost of BiGlobal and PSE3D in resolving the cross-flow instabilities in cross-flow regions. The peak frequencies of cross-flow modes lie between 15 and 45 kHz. Whereas oblique second Mack modes are marginally unstable in the windward cross-flow region, they could be strong enough to compete with the cross-flow modes in the shoulder cross-flow region. In the shoulder attachment-line region, there exists only one unstable mode of Mack instability, differing from previous studies that show a hierarchy of modes in the context of symmetrical attachment-line flows. Results of the numerical simulation and multi-dimensional stability analyses are compared when possible, showing a fair agreement between the two approaches and highlighting the necessity of considering non-parallel effects.

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_∞ = 2.25 and a Reynolds number Re_τ = 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_τ 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.

The characteristics of wall heat flux (WHF) beneath a supersonic turbulent boundary layer interacting with an impinging shock wave with a 33.2° angle at Mach 2.25 are analyzed using direct numerical simulation. It is found that the QP85 scaling, defined as the ratio of the mean WHF and wall pressure, changes across the interaction. The probability density function of the WHF fluctuations normalized by the local root-mean-squared value is similar to that of wall shear stress. Comparing the WHF and wall pressure spectra shows that the low-frequency shock unsteadiness exhibits little influence on the spectrum. The space–time correlation of the fluctuating WHF reveals that both the streamwise correlation length scale and the convection velocity experience a sharp decrease in the separation region and subsequent recovery in the downstream region. Moreover, the mean WHF in an incident shock interaction is decomposed for the first time. An analysis of the velocity and temperature fluctuations based on bidimensional empirical mode decomposition is performed to evaluate the contribution of turbulent structures with specific spanwise length scales to the mean WHF generation. The decomposed results indicate that the contribution associated with the large-scale structures in the outer region is greatly amplified by the shock interaction and has the leading role in the generation downstream of the interaction.

In this paper, a direct numerical simulation is performed to study the wake structures of a micro-ramp vortex generator in the hypersonic flow. The whole evolution process of vortical structures of the wake flow has been carefully analyzed. First, the scaling laws for the profiles of mean velocities and fluctuations have been explored. The results show that the scaling laws based on the supersonic experiments can be directly applied in the hypersonic wake flow with a few discrepancies near the wall. Then, the detailed structures of arc-like vortices are examined, and the legs of vortices are found not being connected with each other. No full vortex ring is detected in the present simulation. At the downstream of the wake flow, the intensity of arc-like vortices has been augmented when passing the separation shock. The results reveal that a vortex train composed of arc-like vortices and shear layer is formed. With the help of the proper orthogonal decomposition, the impact of arc-like vortices on the heat flux has been revealed. The alternative positive and negative strips in the streamwise direction suggest the impinging process of arc-like vortices. The frequencies of the corresponding modes further prove that the strips are the footprint of arc-like vortices.