We propose a method to construct a reduced order model with machine learning for unsteady flows. The present machine-learned reduced order model (ML-ROM) is constructed by combining a convolutional neural network autoencoder (CNN-AE) and a long short-term memory (LSTM), which are trained in a sequential manner. First, the CNN-AE is trained using direct numerical simulation (DNS) data so as to map the high-dimensional flow data into low-dimensional latent space. Then, the LSTM is utilized to establish a temporal prediction system for the low-dimensionalized vectors obtained by CNN-AE. As a test case, we consider flows around a bluff body whose shape is defined using a combination of trigonometric functions with random amplitudes. The present ML-ROMs are trained on a set of 80 bluff body shapes and tested on a different set of 20 bluff body shapes not used for training, with both training and test shapes chosen from the same random distribution. The flow fields are confirmed to be well reproduced by the present ML-ROM in terms of various statistics. We also focus on the influence of two main parameters: (1) the latent vector size in the CNN-AE, and (2) the time step size between the mapped vectors used for the LSTM. The present results show that the ML-ROM works well even for unseen shapes of bluff bodies when these parameters are properly chosen, which implies great potential for the present type of ML-ROM to be applied to more complex flows
In this short note we apply the recently proposed data-driven RANS closure modelling framework of Schmelzer et al. (2020) to fully three-dimensional, high Reynolds number flows: namely wall-mounted cubes and cuboids at Re=40,000, and a cylinder at Re=140,000. For each flow, a new RANS closure is generated using sparse symbolic regression based on LES or DES reference data. This new model is implemented in a CFD solver, and subsequently applied to prediction of the other flows. We see consistent improvements compared to the baseline $k-ω$ SST model in predictions of mean-velocity in the complet…
A series of reduced-order numerical simulations on a specific bluff body type (v-gutters) in a subsonic duct flow is done to assess the unsteady wake dynamics. Two of the v-gutter's geometrical parameters are varied: the v-gutter's base angle ($θ$) and the size of a slit ($ξ$) at the leading-edge of the v-gutter. Turbulent flow kinematics and pressure field are analyzed to evaluate the unsteadiness at a freestream Mach number of $M_\infty = 0.25$ and a freestream Reynolds number based on bluff body's transverse length (L) of $Re_L=0.1 \times 10^6$. Five v-gutter angles are considered ($θ$, $^\…
We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent method. Of particular interest is to predict the unsteady fluid forces for different bluff body shapes at low Reynolds number. The discrete convolution process with a nonlinear rectification is employed to approximate the mapping between the bluff-body shape and the fluid forces. The deep neural network is fed by the Euclidean distance function as the input a…
FR3D: Three-dimensional Flow Reconstruction and Force Estimation for Unsteady Flows Around Extruded Bluff Bodies via Conformal Mapping Aided Convolutional Autoencoders
Aerodynamic pressure field over bluff bodies immersed in boundary layer flows is correlated both in space and time. Conventional approaches for the analysis of distributed aerodynamic pressures, e.g., the proper orthogonal decomposition (POD), can only offer relevant spatial patterns in a set of coherent structures. This study provides an operator-theoretic approach that describes dynamic pressure fields in a functional space rather than conventional phase space via the Koopman operator. Subsequently, spectral analysis of the Koopman operator provides a spatiotemporal characterization of the p…
The impact of fluidic actuation on the wake and drag of a three-dimensional blunt body is investigated experimentally. Jets blowing tangentially to the main flow allow to force the wake with variable frequency and amplitude. Depending on the forcing conditions, two flow regimes can be distinguished. First, in case of broadband actuation with frequencies comprising the natural wake time scale, the convection of the jet structures enhances wake entrainment, shortens the length of the recirculating flow and increases drag. Secondly, at higher actuation frequencies, shear-layer deviation leads to …
A large eddy simulation (LES) study of the flow around a 1/4 scale squareback Ahmed body at $Re_H=33,333$ is presented. The study consists of both wall-resolved (WRLES) and wall-modelled (WMLES) simulations, and investigates the bimodal switching of the wake between different horizontal positions. Within a non-dimensional time-window of 1050 convective flow units, both WRLES and WMLES simulations, for which only the near-wall region of the turbulent boundary layer is treated in a Reynolds-averaged sense, are able to capture horizontal (spanwise) shifts in the wake's cross-stream orientation. E…
We propose a novel active-flow-control (AFC) strategy for bluff bodies to hide their hydrodynamic traces from predators. A group of windward-suction-leeward-blowing (WSLB) actuators are adopted to control the wake of a circular cylinder submerged in a uniform flow. An array of velocity sensors are deployed in the near wake to provide feedback signals. Through the data-driven deep reinforcement learning (DRL), effective control strategies are trained for the WSLB actuation to mitigate the cylinder's hydrodynamic signatures, i.e., strong shears and periodically shed vortices. Only a 0.29% defici…
A networked oscillator based analysis is performed for periodic bluff body flows to examine and control the transfer of kinetic energy. Spatial modes extracted from the flow field with corresponding amplitudes form a set of oscillators describing unsteady fluctuations. These oscillators are connected through a network that captures the energy exchanges amongst them. To extract the network of interactions among oscillators, amplitude and phase perturbations are impulsively introduced to the oscillators and the ensuing dynamics are analyzed. Using linear regression techniques, a networked oscill…
This paper is concerned with the development of a hybrid data-driven technique for unsteady fluid-structure interaction systems. The proposed data-driven technique combines the deep learning framework with a projection-based low-order modeling. While the deep learning provides low-dimensional approximations from datasets arising from black-box solvers, the projection-based model constructs the low-dimensional approximations by projecting the original high-dimensional model onto a low-dimensional subspace. Of particular interest of this paper is to predict the long time series of unsteady flow …
Flow over bluff bodies has multiple engineering applications and thus, has been studied for decades. The lift and drag coefficients are practically important in the design of many components such as automobiles, aircrafts, buildings etc. These coefficients vary significantly with Reynolds number and geometric parameters of the bluff body. In this study, we have analyzed the sensitivity of lift and drag coefficients on single and tandem elliptic cylinders to cylinder aspect ratios, angles of attack, cylinder separation, and flow Reynolds number. Sensitivity analysis with Monte-Carlo algorithm r…
We propose an aerodynamic force model associated with a Galerkin model for the unforced fluidic pinball, the two-dimensional flow around three equal cylinders with one radius distance to each other. The starting point is a Galerkin model of a bluff-body flow. The force on this body is derived as a constant-linear-quadratic function of the mode amplitudes from first principles following the pioneering work of Noca (1997, 1999) and Liang & Dong (2014). The force model is simplified for the mean-field model of the unforced fluidic pinball (Deng et al. 2020) using symmetry properties and sparse ca…
A dual time-stepping strategy of gas-kinetic scheme for the simulation of unsteady flows is introduced in this work. The dual time-stepping strategy is always used in the approaches of unsteady flows, and the ability of dual time-stepping to accelerate the computation with acceptable error tolerance is evident. In our paper, we adopt the techniques of dual time-stepping methods for implicit gas-kinetic scheme to simulate the unsteady flows, which is very popular for the numerical methods based on the Navier-Stokes equations. It is carried out by (a) solving the gas-kinetic scheme in finite vol…
A growing body of work on the dynamics of eukaryotic flagella has noted that their oscillation frequencies are sufficiently high that the viscous penetration depth of unsteady Stokes flow is comparable to the scales over which flagella synchronize. Incorporating these effects into theories of synchronization requires an understanding of the global unsteady flows around oscillating bodies. Yet, there has been no precise experimental test on the microscale of the most basic aspects of such unsteady Stokes flow: the orbits of passive tracers and the position-dependent phase lag between the oscill…
Shock related unsteadiness over axisymmetric spiked body configurations is experimentally investigated at a freestream supersonic Mach number of 2.0 at 0$^\circ$ angle of attack. Three different forebody configurations mounted with a sharp spike-tip ranging from blunt to streamlined (flat-face, hemispherical, and elliptical) are considered. Steady and unsteady pressure measurements, short-exposure high-speed shadowgraphy, shock footprint analysis from $x-t$ plots, and identification of dominant spatiotemporal modes through modal analysis are carried out to explain the unsteady flow physics. Th…
Although the stability properties of the wake past impervious bluff bodies have been widely examined in the literature, similar analyses regarding the flow around and through porous ones are still lacking. In this work, the effect of the porosity and permeability on the wake patterns of porous rectangular cylinders is numerically investigated at low to moderate Reynolds numbers in the framework of direct numerical simulation combined with local and global stability analyses. A modified Darcy-Brinkman formulation is employed here so as to describe the flow behavior inside the porous media, wher…
We present a new higher-order accurate finite difference explicit jump Immersed Interface Method (HEJIIM) for solving two-dimensional elliptic problems with singular source and discontinuous coefficients in the irregular region on a compact Cartesian mesh. We propose a new strategy for discretizing the solution at irregular points on a nine point compact stencil such that the higher-order compactness is maintained throughout the whole computational domain. The scheme is employed to solve four problems embedded with circular and star shaped interfaces in a rectangular region having analytical s…
A network community-based reduced-order model is developed to capture key interactions amongst coherent structures in high-dimensional unsteady vortical flows. The present approach is data-inspired and founded on network-theoretic techniques to identify important vortical communities that are comprised of vortical elements that share similar dynamical behavior. The overall interaction-based physics of the high-dimensional flow field is distilled into the vortical community centroids, considerably reducing the system dimension. Taking advantage of these vortical interactions, the proposed metho…
We investigate the hovering dynamics of rigid bodies with up-down asymmetry placed in oscillating background flows. Recent experiments on inanimate pyramid-shaped objects in oscillating flows with zero mean component demonstrate that the resulting aerodynamic forces are sufficient to keep the object aloft. The mechanisms responsible for this lift production are fundamentally unsteady and depend on the shed vorticity. Here, we consider a model system of a two-dimensional flyer and compute the unsteady, two-way coupling between the flyer and the surrounding fluid in the context of the vortex she…
Formation of recirculating wakes is a prominent feature of inertial flow around bluff bodies. Below the onset of vortex shedding in uniform unbounded flows, the fluid in the recirculating wake region moves on closed planar orbits. The steady wake is thus an isolated zone in the flow and does not exchange fluid with the free stream. In this work, we utilize lattice-Boltzmann simulations and microfluidic experiments to demonstrate that in microchannel inertial flow of Newtonian fluids, the recirculating wake is replaced by a three-dimensional vortical flow. Spiraling streamlines generate a conti…
Machine learning techniques have received attention in fluid dynamics in terms of predicting, clustering and classifying complex flow physics. One application has been the classification or clustering of various wake structures that emanate from bluff bodies such as cylinders or flapping foils, creating a rich diversity of vortex formations specific to flow conditions, geometry, and/or kinematics of the body. When utilizing oscillating foils to harvest energy from tidal or river flows, it is critical to understand the intricate and nonlinear relationship between flapping kinematics and the dow…
Cluster-based reduced-order modelling of a mixing layer
提出了一种新的基于聚类的非定常流降阶建模策略。CROM结合了Gunzburger小组（Burkardt et al. 2006）开创的聚类分析和Eckhardt小组（Schneider et al. 2007）在流体动力学中引入的过渡矩阵模型。CROM构成了一个潜在的替代POD模型和推广的Ulam-Galerkin方法经典地用于动力系统，以确定一个有限秩近似的Perron-Frobenius算子。该策略分两步处理时间分辨的流快照序列。首先，快照数据被聚类成状态空间中的少量代表性状态，称为质心。这些质心将状态空间划分为互补的非重叠区域（质心Voronoi单元）。从标准算法出发，确定聚类的概率，并通过分析转移矩阵对状态进行排序。其次，使用马尔可夫过程动态地建模状态之间的转换。然后通过对马尔可夫过程的精细分析来提取物理机制，例如使用有限时间李雅普诺夫指数和熵方法。该CROM框架被应用到Lorenz吸引子（作为说明性的例子），空间发展的不可压缩混合层和三维湍流尾流的钝体的速度场。对于这些例子，CROM被证明是以无监督的方式识别非平凡的准吸引子和过渡过程。CROM有许多潜在的应用系统识别的物理机制的复杂的动态，比较流动演变模型，识别的前兆，希望和不希望的事件，并利用非线性驱动动力学的流量控制应用。
