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Register a new userPrediction of laminar vortex shedding over a cylinder using deep learning
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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.
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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.
An investigation of optimal feedback controllers performance and robustness is carried out for vortex shedding behind a 2D cylinder at low Reynolds numbers. To facilitate controller design, we present an efficient modelling approach in which we utilise the resolvent operator to recast the linearised Navier-Stokes equations into an input-output form from which frequency responses can be computed. The difficulty of applying modern control design techniques to complex, high-dimensional flow systems is thus overcome by using low-order models identified from these frequency responses. The low-order models are used to design optimal control laws using $mathcal{H}_{infty}$ loop shaping. Two distinct control arrangements are considered, both of which employ a single-input and a single-output. In the first control arrangement, a velocity sensor located in the wake drives a pair of body forces near the cylinder. Complete suppression of shedding is observed up to a Reynolds number of $Re=110$. Due to the convective nature of vortex shedding and the corresponding time delays, we observe a fundamental trade-off: the sensor should be close enough to the cylinder to avoid any excessive time lag, but it should be kept sufficiently far from the cylinder to measure any unstable modes developing downstream. It is found that these two conflicting requirements become more difficult to satisfy for larger Reynolds numbers. In the second control arrangement, we consider a practical setup with a body-mounted force sensor and an actuator that oscillates the cylinder according to the lift measurement. It is shown that the system is stabilised only up to $Re=100$, and we demonstrate why the performance of the resulting feedback controllers deteriorates much more rapidly with increasing Reynolds number. The challenges of designing robust controllers for each control setup are also analysed and discussed.
The present article represents part of the PhD. dissertation by C. Josserand. We discuss the nucleation of quantized vortices in the nonlinear Schr{o}dinger equation (NLS) for a flow around a disk in two spatial dimensions. It appears that the vortices are nucleated when the flow becomes locally (at the edge of the disk) supersonic. A detailed study of the phase equation for the complex field $psi$ gives an Euler-Tricomi type equation for the stationary solutions below threshold. This equation is closely related to the one known in shock wave dynamics for gas. Then using solvability condition, we extract a time-dependent scenario for the evolution of the amplitude of the solution, which we, finally, relate to a known family solution of NLS which gives rise to a vortex nucleation. We also give a first order correction at the Landau velocity of nucleation, taking into account the geometry of the flow.
Efficiently predicting the flowfield and load in aerodynamic shape optimisation remains a highly challenging and relevant task. Deep learning methods have been of particular interest for such problems, due to their success for solving inverse problems in other fields. In the present study, U-net based deep neural network (DNN) models are trained with high-fidelity datasets to infer flow fields, and then employed as surrogate models to carry out the shape optimisation problem, i.e. to find a drag minimal profile with a fixed cross-section area subjected to a two-dimensional steady laminar flow. A level-set method as well as Bezier-curve method are used to parameterise the shape, while trained neural networks in conjunction with automatic differentiation are utilized to calculate the gradient flow in the optimisation framework. The optimised shapes and drag force values calculated from the flowfields predicted by DNN models agree well with reference data obtained via a Navier-Stokes solver and from the literature, which demonstrates that the DNN models are capable of predicting not only flowfield but also yield satisfactory aerodynamic forces. This is particularly promising as the DNNs were not specifically trained to infer aerodynamic forces. In conjunction with the fast runtime, the DNN-based optimisation framework shows promise for general aerodynamic design problems.
Vortex-induced vibration (VIV) exists widely in natural and industrial fields. The main approaches for solving VIV problems are numerical simulations and experimental methods. However, experiment methods are difficult to obtain the whole flow field information and also high-cost while numerical simulation is extraordinary time-consuming and limited in low Reynolds number and simple geometric configuration. In addition, numerical simulations are difficult to handle the moving mesh technique. In this paper, physics informed neural network (PINN) is proposed to solve the VIV and wake-induced vibration (WIV) of cylinder with high Reynolds number. Compared to tradition data-driven neural network, the Reynolds Average Navier-Stokes (RANS) equation, by implanting an additional turbulent eddy viscosity, coupled with structures dynamic motion equation are also embedded into the loss function. Training and validation data is obtained by computational fluid dynamic (CFD) technique. Three scenarios are proposed to validate the performance of PINN in solving VIV and WIV of cylinders. In the first place, the stiffness parameter and damping parameter are calculated via limited force data and displacement data; secondly, the flow field and lifting force/drag force are inferred by scattered velocity information; eventually, the displacement can be directly predicted only through lifting forces and drag forces based on LSTM. Results demonstrate that,compared with traditional neural network, PINN method is more effective in inferring and re-constructing the unknown parameters and flow field with high Reynolds number under VIV and WIV circumstances.
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