Extension of the KDO turbulence/transition model to account for roughness

Wall roughness significantly influences both laminar-turbulent transition process and fully developed turbulence. A wall roughness extension for the KDO turbulence/transition model is developed. The roughness effect is introduced via the modification of the k and νt boundary conditions. The wall is considered to be lifted to a higher position. The difference between the original position and the higher position, named as equivalent roughness height, is linked to the actual roughness height. The ratio between the two heights is determined by reasoning. With such a roughness extension, the predictions of the KDO RANS model agree well with the measurements of turbulent boundary layer with a sand grain surface, while the KDO transition model yields accurate cross-flow transition predictions of flow past a 6:1 spheroid.

Generalization enhancement of artificial neural network for turbulence closure by feature selection

Feature selection targets for selecting relevant and useful features, and is a vital challenge in turbulence modeling by machine learning methods. In this paper, a new posterior feature selection method based on validation dataset is proposed, which is an efficient and universal method for complex systems including turbulence. Different from the priori feature importance ranking of the filter method and the exhaustive search for feature subset of the wrapper method, the proposed method ranks the features according to the model performance on the validation dataset, and generates the feature subsets in the order of feature importance. Using the features from the proposed method, a black-box model is built by artificial neural network (ANN) to reproduce the behavior of Spalart-Allmaras (S-A) turbulence model for high Reynolds number (Re) airfoil flows in aeronautical engineering. The results show that compared with the model without feature selection, the generalization ability of the model after feature selection is significantly improved. To some extent, it is also demonstrated that although the feature importance can be reflected by the model parameters during the training process, artificial feature selection is still very necessary.

Characteristics of secondary droplets produced by the impact of drops onto a smooth surface

This work investigates the splashing behaviors of droplets impacting on solid surfaces and mainly focuses on the characteristics of secondary droplets. According to the experimental results, two different splashing patterns, corona splash and levitating-lamella breakup, are observed. A new breakup mode, named rim-segmenting, is found during the levitating-lamella breakup. In particular, the detailed information of the splashing secondary droplets, including the size, velocity, angle, and total volume of the splashing secondary droplets is obtained from the experimental data. The size distribution of the splashing secondary droplets obeys the gamma distribution function. The average diameter and splashing angle of the secondary droplets are mainly related to the Reynolds number Re, and can be expressed as functions of Re. High impact velocity and liquid viscosity will result in a wider size distribution range of splashing secondary droplets. We also put forward an empirical model to predict the total splashing volume, which is consistent with the experimental data both in this work and previous studies. This work is believed to provide insights on the prediction of the characteristics of splashing secondary droplets.

Transfer learning for deep neural network-based partial differential equations solving

Deep neural networks (DNNs) have recently shown great potential in solving partial differential equations (PDEs). The success of neural network-based surrogate models is attributed to their ability to learn a rich set of solution-related features. However, learning DNNs usually involves tedious training iterations to converge and requires a very large number of training data, which hinders the application of these models to complex physical contexts. To address this problem, we propose to apply the transfer learning approach to DNN-based PDE solving tasks. In our work, we create pairs of transfer experiments on Helmholtz and Navier-Stokes equations by constructing subtasks with different source terms and Reynolds numbers. We also conduct a series of experiments to investigate the degree of generality of the features between different equations. Our results demonstrate that despite differences in underlying PDE systems, the transfer methodology can lead to a significant improvement in the accuracy of the predicted solutions and achieve a maximum performance boost of 97.3% on widely used surrogate models.

Evolutionary understanding of airfoil lift

This review attempts to elucidate the physical origin of aerodynamic lift of an airfoil using simple formulations and notations, particularly focusing on the critical effect of the fluid viscosity. The evolutionary development of the lift problem of a flat-plate airfoil is reviewed as a canonical case from the classical inviscid circulation theory to the viscous-flow model. In particular, the physical aspects of the analytical expressions for the lift coefficient of the plate-plate airfoil are discussed, including Newton’s sine-squared law, Rayleigh’s lift formula, thin-airfoil theory and viscous-flow lift formula. The vortex-force theory is described to provide a solid foundation for consistent treatment of lift, form drag, Kutta condition, and downwash. The formation of the circulation and generation of lift are discussed based on numerical simulations of a viscous starting flow over an airfoil, and the evolution of the flow topology near the trailing edge is well correlated with the realization of the Kutta condition. The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.

A many-body dissipative particle dynamics with energy conservation study of droplets icing on microstructure surfaces

Droplets icing has important applications in real life. The icing process of droplets on microstructure is explored based on the MDPDE method in this study. Firstly, the correctness of the heat transfer model was verified by one-dimensional heat conduction simulation, and then the feasibility of the phase change model was verified by investigating the icing process of droplets. The influence of cold surface temperature, droplet volume and contact angle on freezing time of droplets was discussed, and it was found that the temperature of cold surfaces had a greater effect on freezing. We finally explored the influence of different microstructure surfaces on the icing of droplets, and results showed that the presence of microstructures greatly enhanced the anti-icing effect of the surface. In our research, the contact angle is a relatively large factor affecting the icing of droplets. In addition, it was discovered that the droplet had the strongest ability to delay freezing on the surface of triangle microstructures with a contact angle of 157.1°.

A decomposition formula for the wall heat flux of a compressible boundary layer

Understanding the generation mechanism of the heat flux is essential for the design of hypersonic vehicles. We proposed a novel formula to decompose the heat flux coefficient into the contributions of different terms by integrating the conservative equation of the total energy. The reliability of the formula is well demonstrated by the direct numerical simulation results of a hypersonic transitional boundary layer. Through this formula, the exact process of the energy transport in the boundary layer can be explained and the dominant contributors to the heat flux can be explored, which are beneficial for the prediction of the heat and design of the thermal protection devices.

An improved third-order HWCNS for compressible flow simulation on curvilinear grids

Due to the very high requirements on the quality of computational grids, stability property and computational efficiency, the application of high-order schemes to complex flow simulation is greatly constrained. In order to solve these problems, the third-order hybrid cell-edge and cell-node weighted compact nonlinear scheme (HWCNS3) is improved by introducing a new nonlinear weighting mechanism. The new scheme uses only the central stencil to reconstruct the cell boundary value, which makes the convergence of the scheme more stable. The application of the scheme to Euler equations on curvilinear grids is also discussed. Numerical results show that the new HWCNS3 achieves the expected order in smooth regions, captures discontinuities sharply without obvious oscillation, has higher resolution than the original one and preserves freestream and vortex on curvilinear grids.

Direct numerical simulation of hypersonic boundary layer transition over a lifting-body model HyTRV

Direct numerical simulation (DNS) of transition over a hypersonic lifting body model HyTRV developed by China Aerodynamics Research and Development Center is performed. The free-stream parameters are: the free-stream Mach number is 6, the unit Reynolds number is 10000/mm, the free-stream temperature is 79 K, the angle of attack is 0, and the wall temperature is 300 K. Weak random blowing-and-suction perturbations in the leading range are used to trigger the transition. A high order finite-difference code OpenCFD developed by the authors is used for the simulation, and grid convergence test shows that the transition locations are grid-convergence. DNS results show that transition occurs in central area of the lower surface and the concaved region of the upper surface, and the transition regions are also the streamline convergence regions. The transition mechanisms in different regions are investigated by using the spectrum and POD analysis.

Data-driven nonlinear constitutive relations for rarefied flow computations

To overcome the defects of traditional rarefied numerical methods such as the Direct Simulation Monte Carlo (DSMC) method and unified Boltzmann equation schemes and extend the covering range of macroscopic equations in high Knudsen number flows, data-driven nonlinear constitutive relations (DNCR) are proposed first through the machine learning method. Based on the training data from both Navier-Stokes (NS) solver and unified gas kinetic scheme (UGKS) solver, the map between responses of stress tensors and heat flux and feature vectors is established after the training phase. Through the obtained off-line training model, new test cases excluded from training data set could be predicated rapidly and accurately by solving conventional equations with modified stress tensor and heat flux. Finally, conventional one-dimensional shock wave cases and two-dimensional hypersonic flows around a blunt circular cylinder are presented to assess the capability of the developed method through various comparisons between DNCR, NS, UGKS, DSMC and experimental results. The improvement of the predictive capability of the coarse-graining model could make the DNCR method to be an effective tool in the rarefied gas community, especially for hypersonic engineering applications.