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Register a new userData-driven prediction of unsteady flow fields over a circular cylinder using deep learning
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Unsteady flow fields over a circular cylinder are trained and predicted using four different deep learning networks: convolutional neural networks with and without consideration of conservation laws, generative adversarial networks with and without consideration of conservation laws. Flow fields at future occasions are predicted based on information of flow fields at previous occasions. Deep learning networks are trained first using flow fields at Reynolds numbers of 100, 200, 300, and 400, while flow fields at Reynolds numbers of 500 and 3000 are predicted using the trained deep learning networks. Physical loss functions are proposed to explicitly impose information of conservation of mass and momentum to deep learning networks. An adversarial training is applied to extract features of flow dynamics in an unsupervised manner. Effects of the proposed physical loss functions, adversarial training, and network sizes on the prediction accuracy are analyzed. Predicted flow fields using deep learning networks are in favorable agreement with flow fields computed by numerical simulations.
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Unsteady laminar vortex shedding over a circular cylinder is predicted using a deep learning technique, a generative adversarial network (GAN), with a particular emphasis on elucidating the potential of learning the solution of the Navier-Stokes equations. Numerical simulations at two different Reynolds numbers with different time-step sizes are conducted to produce training datasets of flow field variables. Unsteady flow fields in the future at a Reynolds number which is not in the training datasets are predicted using a GAN. Predicted flow fields are found to qualitatively and quantitatively agree well with flow fields calculated by numerical simulations. The present study suggests that a deep learning technique can be utilized for prediction of laminar wake flow in lieu of solving the Navier-Stokes equations.
The fast and accurate prediction of unsteady flow becomes a serious challenge in fluid dynamics, due to the high-dimensional and nonlinear characteristics. A novel hybrid deep neural network (DNN) architecture was designed to capture the unsteady flow spatio-temporal features directly from the high-dimensional unsteady flow fields. The hybrid deep neural network is constituted by the convolutional neural network (CNN), convolutional Long Short Term Memory neural network (ConvLSTM) and deconvolutional neural network (DeCNN). The flow around a cylinder at various Reynolds numbers and the flow around an airfoil at higher Reynolds number are carried out to establish the datasets used to train the networks separately. The trained hybrid DNNs were then tested by the prediction of the flow fields at future occasions. The predicted flow fields using the trained hybrid DNNs are in good agreement with the flow fields calculated directly by the computational fluid dynamic solver.
A Direct Numerical Simulation (DNS) of the incompressible flow around a rectangular cylinder with chord-to-thickness ratio 5:1 (also known as the BARC benchmark) is presented. The work replicates the first DNS of this kind recently presented by Cimarelli et al (2018), and intends to contribute to a solid numerical benchmark, albeit at a relatively low value of the Reynolds number. The study differentiates from previous work by using an in-house finite-differences solver instead of the finite-volumes toolbox OpenFOAM, and by employing finer spatial discretization and longer temporal average. The main features of the flow are described, and quantitative differences with the existing results are highlighted. The complete set of terms appearing in the budget equation for the components of the Reynolds stress tensor is provided for the first time. The different regions of the flow where production, redistribution and dissipation of each component take place are identified, and the anisotropic and inhomogeneous nature of the flow is discussed. Such information is valuable for the verification and fine-tuning of turbulence models in this complex separating and reattaching flow.
Convolutional neural networks (CNNs) have recently been applied to predict or model fluid dynamics. However, mechanisms of CNNs for learning fluid dynamics are still not well understood, while such understanding is highly necessary to optimize the network or to reduce trial-and-errors during the network optmization. In the present study, a CNN to predict future three-dimensional unsteady wake flow using flow fields in the past occasions is developed. Mechanisms of the developed CNN for prediction of wake flow behind a circular cylinder are investigated in two flow regimes: the three-dimensional wake transition regime and the shear-layer transition regime. Feature maps in the CNN are visualized to compare flow structures which are extracted by the CNN from flow at the two flow regimes. In both flow regimes, feature maps are found to extract similar sets of flow structures such as braid shear-layers and shedding vortices. A Fourier analysis is conducted to investigate mechanisms of the CNN for predicting wake flow in flow regimes with different wave number characteristics. It is found that a convolution layer in the CNN integrates and transports wave number information from flow to predict the dynamics. Characteristics of the CNN for transporting input information including time histories of flow variables is analyzed by assessing contributions of each flow variable and time history to feature maps in the CNN. Structural similarities between feature maps in the CNN are calculated to reveal the number of feature maps that contain similar flow structures. By reducing the number of feature maps that contain similar flow structures, it is also able to successfully reduce the number of parameters to learn in the CNN by 85% without affecting prediction performances.
A cylinder undergoes precession when it rotates around its axis and this axis itself rotates around another direction. In a precessing cylinder full of fluid, a steady and axisymmetric component of the azimuthal flow is generally present. This component is called a zonal flow. Although zonal flows have been often observed in experiments and numerical simulations, their origin has eluded theoretical approaches so far. Here, we develop an asymptotic analysis to calculate the zonal flow forced in a resonant precessing cylinder, that is when the harmonic response is dominated by a single Kelvin mode. We find that the zonal flow originates from three different sources: (1) the nonlinear interaction of the inviscid Kelvin mode with its viscous correction; (2) the steady and axisymmetric response to the nonlinear interaction of the Kelvin mode with itself; and (3) the nonlinear interactions in the end boundary layers. In a precessing cylinder, two additional sources arise due to the equatorial Coriolis force and the forced shear flow. However, they cancel exactly. The study thus generalises to any Kelvin mode, forced by precession or any other mechanism. The present theoretical predictions of the zonal flow are confirmed by comparison with numerical simulations and experimental results. We also show numerically that the zonal flow is always retrograde in a resonant precessing cylinder (m=1) or when it results from resonant Kelvin modes of azimuthal wavenumbers m=2, 3, and presumably higher.
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