We present a comparative computational study of two stabilized Reduced Order Models (ROMs) for the simulation of convection-dominated incompressible flow (Reynolds number of the order of a few thousands). Representative solutions in the parameter space, which includes either time only or time and Reynolds number, are computed with a Finite Volume method and used to generate a reduced basis via Proper Orthogonal Decomposition (POD). Galerkin projection of the Navier-Stokes equations onto the reduced space is used to compute the ROM solution. To ensure computational efficiency, the number of POD modes is truncated and ROM solution accuracy is recovered through two stabilization methods: i) adding a global constant artificial viscosity to the reduced dimensional model, and ii) adding a different value of artificial viscosity for the different POD modes. We test the stabilized ROMs for fluid flow in an idealized medical device consisting of a conical convergent, a narrow throat, and a sudden expansion. Both stabilization methods significantly improve the ROM solution accuracy over a standard (non-stabilized) POD-Galerkin model.
We performed a comparative study of extraction of large-scale flow structures in Rayleigh Bénard convection using proper orthogonal decomposition (POD) and {\em Fourier analysis}. We show that the free-slip basis functions capture the flow profiles successfully for the no-slip boundary conditions. We observe that the large-scale POD modes capture a larger fraction of total energy than the Fourier modes. However, the Fourier modes capture the rarer flow structures like flow reversals better. The flow profiles of the dominant POD and Fourier modes are quite similar. Our results show that the Fou…
Oklahoma State University（俄克拉荷马州立大学）；Norwegian University of Science and Technology（挪威科技大学）；SINTEF Digital（挪威科技工业研究院数字研究所）；Virginia Tech（弗吉尼亚理工大学）
Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed noni…
Technische Universität Ilmenau（伊尔默瑙工业大学）；New York University（纽约大学）
Reservoir computing is applied to model the large-scale evolution and the resulting low-order turbulence statistics of a two-dimensional turbulent Rayleigh-Bénard convection flow at a Rayleigh number ${\rm Ra}=10^7$ and a Prandtl number ${\rm Pr}=7$ in an extended domain with an aspect ratio of 6. Our data-driven approach which is based on a long-term direct numerical simulation of the convection flow comprises a two-step procedure. (1) Reduction of the original simulation data by a Proper Orthogonal Decomposition (POD) snapshot analysis and subsequent truncation to the first 150 POD modes whi…
Optimal control of turbulent mixed-convection flows has attracted considerable attention from researchers. Numerical algorithms such as Genetic Algorithms (GAs) are powerful tools that allow to perform global optimization. These algorithms are particularly of great interest in complex optimization problems where cost functionals may lack smoothness and regularity. In turbulent flow optimization, the hybridization of GA with high fidelity Computational Fluid Dynamics (CFD) is extremely demanding in terms of computational time and memory storage. Thus, alternative approaches aiming to alleviate …
Technische Universität Ilmenau（伊尔默瑙工业大学）；New York University（纽约大学）
Recurrent neural networks are machine learning algorithms which are suited well to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by supervised machine learning without solving the underlying nonlinear mathematical equations. In this work, we apply an echo state network to approximate the evolution of two-dimensional moist Rayleigh-Bénard convection and the resulting low-order turbulence statistics. We conduct long-term direct numerical simulations in order to obtain training and test data fo…
Motivated by the aero-acoustic feedback loop phenomenon in high speed free jets and impinging jets, a thorough examination of a POD (Proper Orthogonal Decomposition)-Galerkin method to determine the average convection velocity of coherent structures in the shear layer is presented in this paper. The technique is shown to be applicable to both time resolved as well as time unresolved data, if the data set meets certain requirements. Using a detailed sensitivity analysis on a synthetic data set, a quantitative estimate on the required time resolution for the technique has been found, which can b…
In this paper, we propose a new evolve-then-filter reduced order model (EF-ROM). This is a regularized ROM (Reg-ROM), which aims at the numerical stabilization of proper orthogonal decomposition (POD) ROMs for convection-dominated flows. We also consider the Leray ROM (L-ROM). These two Reg-ROMs use explicit ROM spatial filtering to smooth (regularize) various terms in the ROMs. Two spatial filters are used: a POD projection onto a POD subspace (Proj) and a new POD differential filter (DF). The four Reg-ROM/filter combinations are tested in the numerical simulation of the three-dimensional flo…
We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive reduced order modeling technique. For non-intrusive ROMs, we consider two frameworks. The first is using dynamic mode decomposition (DMD), and the second is based on artificial neural networks (ANNs). For ANN, we utilized a residual deep neural network, and for DMD we have studied two versions of DMD approaches; one with hard thresholding and the other with…
A data-driven, model-free framework is introduced for calculating Reduced-Order Models (ROMs) capable of accurately predicting time-mean responses to external forcings, or forcings needed for specified responses, e.g., for control, in fully turbulent flows. The framework is based on using the Fluctuation-Dissipation Theorem (FDT) in the space of a limited number of modes obtained from Dynamic Mode Decomposition (DMD). Using the DMD modes as the basis functions, rather than the commonly used Proper Orthogonal Decomposition (POD) modes, resolves a previously identified problem in applying FDT to…
Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modeling convection has given rise to the development of chaos theory and the reduced-order modeling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh-Benard convectio…
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 …
Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two but the novel non-intrusive approach presented in this study is an attempt at taking all three into account effectively compared to their traditional counterparts. Based on dimensionality reduction using proper orthogonal decomposition (POD), we introduce a long short-term memory (LSTM) neural network architecture together with a principal interval decomposition (PID) framework …
A term-by-term variational multiscale method with dynamic subscales for incompressible turbulent aerodynamics
Computational Heat and Fluid Flow Lab, Universidad de Santiago de Chile（圣地亚哥智利大学计算热与流体流动实验室）；Department of Mechanical Engineering, University of Santiago de Chile（圣地亚哥智利大学机械工程系）；Chair for Computational Analysis of Technical Systems, RWTH Aachen University（亚琛工业大学技术系统计算分析教席）；Chair of Methods for Model-based Development in Computational Engineering, RWTH（亚琛工业大学计算工程基于模型开发方法教席）；Center for Simulation and Data Science (JARA-CSD), RWTH Aachen University（亚琛工业大学仿真与数据科学中心（JARA-CSD））
We conduct two- and three-dimensional simulations for double diffusive convection in the diffusive regime, where the fluid flow is driven by a destabilizing temperature gradient and stabilized by a stably stratified salinity gradient. We study how the heat flux, Reynolds number, and flow structures change with the density ratio $Λ$, which is the ratio of the buoyancy force induced by the salinity gradient to that by the temperature gradient. When $Λ$ increases from zero, the flow first behaves similarly as in pure Rayleigh-Bénard (RB) convection, both with respect to flow structure and to heat…
This paper treats topology optimization of natural convection problems. A simplified model is suggested to describe the flow of an incompressible fluid in steady state conditions, similar to Darcy's law for fluid flow in porous media. The equations for the fluid flow are coupled to the thermal convection-diffusion equation through the Boussinesq approximation. The coupled non-linear system of equations is discretized with stabilized finite elements and solved in a parallel framework that allows for the optimization of high resolution three-dimensional problems. A density-based topology optimiz…
The hydrodynamic and thermal characteristics of a freely-vibrating circular cylinder in mixed convection flow are numerically investigated at low Reynolds numbers. The numerical investigations are conducted for a range of parameters, Ur = [2.0, 10], Pr = [0.7, 10] and Ri = [0.5, 2.0]. Whereas the Reynolds number, the mass ratio and the damping ratio are fixed. A secondary VIV lock-in region is found in the cases of high Richardson number Ri=2.0 for high reduced velocity values, in which the buoyancy-driven flow is non-trivial. A wide VIV lock-in region is formed with tremendous energy transfer…
Global instabilities in swirling flows can significantly alter the flame and flow dynamics of swirl-stabilized flames, such as those in modern power generation gas turbine engines. In this study, we characterize the interaction between the precessing vortex core (PVC), which is the consequence of a global hydrodynamic instability, and thermoacoustic instabilities, which are the result of a resonant coupling between combustor acoustics and the unsteady heat release rate of combustion. This characterization is performed using experimental data obtained from a model gas turbine combustor system e…
Direct numerical simulations are conducted for double diffusive convection (DDC) bounded by two parallel plates, with fluid properties similar to the values of seawater. The DDC flow is driven by an unstable salinity difference and stabilized at the same time by a temperature difference. For these conditions the flow can be in the finger regime. We develop scaling laws for three key response parameters of the system: The non-dimensional salinity flux $Nu_S$ mainly depends on the salinity Rayleigh number $Ra_S$, which measures the strength of the salinity difference, and exhibits a very weak de…
A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for each of the fluid flows. A single design variable is used to describe the physical fields. The solid interface and the fluid domains are generated using an erosion-dilation based identification technique, which guarantees well-separated fluids, as well as a minimum wall thickness between them. Under the assumption of laminar steady flow, the two fluids are m…
The present work numerically investigates vortex-induced vibrations (VIV) of a two-dimensional circular cylinder with an axisymmetric slit at Reynolds number 500. The study examines the effects of slit shape (i.e., converging, diverging, and parallel slits), the effect of slit-area ratios, slit-width, and its angle with the freestream velocity on aerodynamic forces, vibration response, and associated flow characteristics. The results demonstrate that the addition of the slit assists the VIV suppression by adding an extra amount of flow to the main flow. It results in the stabilized wake with t…
A One-Dimensional (1D) Reduced-Order Model (ROM) has been developed for a 3D Rayleigh-Bénard convection system in the turbulent regime with Rayleigh number $\mathrm{Ra}=10^6$. The state vector of the 1D ROM is horizontally averaged temperature. Using the Green's Function (GRF) method, which involves applying many localized, weak forcings to the system one at a time and calculating the responses using long-time averaged Direct Numerical Simulations (DNS), the system's Linear Response Function (LRF) has been computed. Another matrix, called the Eddy Flux Matrix (EFM), that relates changes in the…
