Proper Orthogonal Decomposition Method Research Articles

Estimation of wind dynamic load linear transfer matrix using proper orthogonal decomposition method and genetic algorithm

ABSTRACT Due to the advantages of Laplace domain in both time and frequency domains, the dynamic analysis and control tools in engineering software like MATLAB and Python have been designed based on it. Dynamic analysis of structures requires determination of the overall transfer matrix, which is obtained by multiplying the structure's transfer matrix (TM) with the load TM. With the input vector of unit intensity white-noise processes and the overall TM, the structural responses can be obtained. Furthermore, having the load TM is crucial for implementation of active control systems. In this article, the TM of along-wind loads was estimated for a tall building using the proper orthogonal decomposition (POD) method and the genetic algorithm (GA). To evaluate the effectiveness of the proposed approach, an example of a tall building was provided. The wind load cross-power spectral matrix (XPSD) was decomposed using POD technique, followed by the truncation of higher loading modes. Subsequently, the loading TM was derived by estimating the target non-linear functions with linear transfer functions through GA technique. Then, the responses of the structure were computed using the loading TM. The results demonstrated the efficacy of the proposed method in acquiring the loading TM and predicting wind-induced responses.

Novel plasma actuator for mitigation of dynamic stall

A novel plasma actuator, the Linear Counter-flow using a Point Embedded Electrode (LCPEE), is developed for the prevention of dynamic stall for a sinusoidal pitching movement between α = 4° and α = 18°. The LCPEE is implemented on a NACA0012 airfoil and tested at a Reynolds Number of Re c = 2 × 105 and reduced frequency of k = π/16. Prior investigations using a standard linear actuator showed that the exposed electrode introduced perturbations passively which delayed dynamic stall when the actuator was off. For the LCPEE actuator, when turned off, there is least passive delay. When the LCPEE is turned on at St f = 50, the dynamic stall is prevented for the sinusoidal pitching motion of the airfoil. The LCPEE actuator is also tested for the same sinusoidal motion between α = 6° and α = 20°. Four cases are considered for the higher α range of motion: actuator off, actuator on at St f = 50 with a sinusoidal input waveform, actuator on at St f = 50 with a triangular input waveform, and actuator on at St f = 100 with a sinusoidal input waveform. Specifically for the last case, experiment shows no flow reversal demonstrating the efficacy of LCPEE in controlling the dynamic stall. The effects of LCPEE on the flow energy distribution have also been studied by using proper orthogonal decomposition (POD) method.

Aerodynamic and Aeroacoustic Optimization of UAV Rotor Based on Proper Orthogonal Decomposition Method

Aerodynamic and Aeroacoustic Optimization of UAV Rotor Based on Proper Orthogonal Decomposition Method

An augmented subspace based adaptive proper orthogonal decomposition method for time dependent partial differential equations

In this paper, we propose an augmented subspace based adaptive proper orthogonal decomposition (POD) method for solving the time dependent partial differential equations. We use the difference between the approximation obtained in the augmented subspace and that obtained in the original POD subspace to construct an error indicator, by which we obtain a general framework for augmented subspace based adaptive POD method. We then provide two strategies to construct the augmented subspaces, the residual type augmented subspace and the coarse-grid approximation type augmented subspace. We apply our new methods to two typical 3D advection-diffusion equations with the advection being the Kolmogorov flow and the ABC flow. Numerical results show that both the residual type augmented subspace based adaptive POD method and the coarse-grid approximation type augmented subspace based adaptive POD method are more efficient than the existing adaptive POD methods, especially for the advection dominated models.

Order reduction of special valve models based on pod method

Abstract The opening size of the disc-type special regulating valve (referred to as the special valve) can be used to regulate the fluid pressure and flow inside the cabin, and is an important equipment in the intake system of the high-altitude simulation test bench (referred to as the high-altitude bench). Due to the high dimensionality and complex solution of the special valve model, the calculation time is relatively long. In this paper, the Proper Orthogonal Decomposition (POD) model reduction method is applied to the mathematical model of the special valve, and the POD basis matrix is constructed through snapshots, thus obtaining a low-dimensional model and improving computational efficiency. The research results indicate that, while ensuring sufficient accuracy, this method can reduce the dimensionality of the special valve model, improve the computational speed of the simulator in calculating this case, and verify the effectiveness of the POD method.

Prediction model of aircraft hinge moment: Compressed sensing based on proper orthogonal decomposition

By hinge moment, we mean the aerodynamic torque exerted on the rudder shaft by the airflow passing through the aircraft control surface, with obtaining high-precision results often relying on wind tunnel tests. Due to the complex aerodynamic balance insulation and installation errors that must be considered in cryogenic wind tunnels, the main method for calculating hinge moments is to directly integrate surface pressure distribution information. However, it is usually difficult to arrange enough pressure taps, resulting in the accuracy failing to meet expectations. Combining the sparse wind tunnel test data and low-precision computational fluid dynamics results, this paper introduces the compressed sensing based on proper orthogonal decomposition (CS-POD) method and presents the sub-Ma model and the full-Ma model for predicting hinge moments. The number of sensors and sensor positions are determined based on the sparsity of the numerical simulations and basis functions. Then, the CS algorithm solves the basis coefficients. Finally, the hinge moments are obtained by integrating the reconstruction pressure distribution which is calculated by linearly combining the basis functions and basis coefficients. The result shows that the full-Ma model exhibits higher prediction accuracy with approximately five sensors under subsonic and transonic cases, reducing the relative error of the sub-Ma model by 2–10 times, even at high angles of attack. The mean reconstruction accuracy for the hinge moments is 97.6%, and for the normal forces, it is 94.3%. Therefore, adding relevant terms when the number of samples is small can effectively improve modeling accuracy.

The characteristics of flows past a circular cylinder with heat transfer in the proximity to the wall at different gap ratios

In this study, two-dimensional laminar flows past a circular cylinder under isothermal and non-isothermal conditions over a flat-plate were investigated numerically at Re = 200. The gap ratio G / D ranges from 0.5 to 3.0, with G representing the distance between the lower surface of the cylinder and the wall. The effects of G / D on the flow dynamics were explored. For G / D = 0.5 , the vortex shedding of the lower cylinder surface is suppressed and there is a large recirculation region on the wall. For G / D = 1.0 , the recirculation region is small and the lower vortex begins to shed. For G / D ⩾ 1.5 , the flow exhibits similarities to that of an unbounded cylinder. The heat transfer characteristics was evaluated. When the cylinder temperature T c is higher than the air temperature T a , the mean drag coefficient C D ¯ is reduced and the root-mean-square lift coefficient C L ′ is increased. The temperature field is reconstructed using the proper orthogonal decomposition method, which is influenced by the large-scale vortical structures.

A New Reduced-Dimension Iteration Two-Grid Crank–Nicolson Finite-Element Method for Unsaturated Soil Water Flow Problem

The main objective of this paper is to reduce the dimensionality of unknown coefficient vectors of finite-element (FE) solutions in two-grid (CN) FE (TGCNFE) format for the nonlinear unsaturated soil water flow problem by using a proper orthogonal decomposition (POD) and to design a new reduced-dimension iteration TGCNFE (RDITGCNFE). For this objective, a new time semi-discrete CN (TSDCN) scheme for the nonlinear unsaturated soil water flow problem is first designed and the existence, stability, and error estimates of TSDCN solutions are demonstrated. Subsequently, a new TGCNFE format for the nonlinear unsaturated soil water flow problem is designed and the existence, unconditional stability, and error estimates of TGCNFE solutions are demonstrated. Next, a new RDITGCNFE format with the same FE basis functions as the TGCNFE format is built by the POD method and the existence, unconditional stability, and error estimates of RDITGCNFE solutions are discussed. Ultimately, the rightness of theory results and the superiority of the RDITGCNFE format are verified by two sets of numerical tests. It is worth noting that the RDITGCNFE format differs completely from all previous reduced-dimension methods, including the authors’ previous works. Therefore, the study of this paper can not only provide a new theoretical method for the dimensionality reduction of numerical models for nonlinear problems but also provide an algorithm implementation technology for the numerical simulation of practical engineering problems.

Real-time reconstruction of 3D transient non-uniform temperature field for thermal protection system based on machine learning

Reconstructed temperature field will provide critical input for monitoring the aerodynamic heating on the thermal protection system (TPS). In this paper, a novel data-driven method is proposed that allows real-time reconstruction of the 3D transient non-uniform temperature field in a TPS ceramic tile. The measured temperature is obtained by embedding sparse sensors at different layers of the tile. The spatial feature bases and time projection coefficients of the non-uniform temperature fields are extracted using the multi-parameter proper orthogonal decomposition (POD) method. The Fully-connected Long Short-Term Memory (FC-LSTM) networks are used to establish the prediction relationship between the measurements and the full-field temperatures. The problem to estimate the projection coefficients of the spatial feature bases is solved by optimizing the loss function using Adam algorithm. The numerical examples show an approximation error less than 5% and the reconstruction time-consuming less than 1 s in 3D temperature field reconstruction (TFR). The proposed reconstruction method is robust at different measurement noise levels and tested point arrangements.

Investigation on the Reduced-Order Model for the Hydrofoil of the Blended-Wing-Body Underwater Glider Flow Control with Steady-Stream Suction and Jets Based on the POD Method

The rapid acquisition of flow field characterization information is crucial for closed-loop active flow control. The proper orthogonal decomposition (POD) method is a widely used flow field downscaling modeling method to obtain flow characteristics effectively. Based on the POD method, a flow field reduced-order model (ROM) is constructed in this paper for the flow field control of a hydrofoil of a blended-wing-body underwater glider (BWB-UG) with stabilized suction and blowing forces. Compared with the computational fluid dynamics (CFD) simulation, the computational time required to predict the target flow field using the established POD-ROM is only about 0.1 s, which is significantly less than the CFD simulation time. The average relative error of the predicted surface pressure is not more than 6.9%. These results confirm the accuracy and efficiency of the POD-ROM in reconstructing flow characteristics. The timeliness problem of fast flow field prediction in BWB-UG active flow control is solved by establishing a fast prediction model in an innovative way.

Geometrically parametrised reduced order models for studying the hysteresis of the Coanda effect in finite element-based incompressible fluid dynamics

This article presents a general reduced order model (ROM) framework for addressing fluid dynamics problems involving time-dependent geometric parametrisations. The framework integrates Proper Orthogonal Decomposition (POD) and Empirical Cubature Method (ECM) hyper-reduction techniques to effectively approximate incompressible computational fluid dynamics simulations. To demonstrate the applicability of this framework, we investigate the behaviour of a planar contraction-expansion channel geometry exhibiting bifurcating solutions known as the Coanda effect. By introducing time-dependent deformations to the channel geometry, we observe hysteresis phenomena in the solution.The paper provides a detailed formulation of the framework, including the stabilised finite elements full order model (FOM) and ROM, with a particular focus on the considerations related to geometric parametrisation. Subsequently, we present the results obtained from the simulations, analysing the solution behaviour in a phase space for the fluid velocity at a probe point, considered as the Quantity of Interest (QoI). Through qualitative and quantitative evaluations of the ROMs and hyper-reduced order models (HROMs), we demonstrate their ability to accurately reproduce the complete solution field and the QoI.While HROMs offer significant computational speedup, enabling efficient simulations, they do exhibit some errors, particularly for testing trajectories. However, their value lies in applications where the detection of the Coanda effect holds paramount importance, even if the selected bifurcation branch is incorrect. Alternatively, for more precise results, HROMs with lower speedups can be employed.

Three-dimensional particle image velocimetry experimental study of transient motion characteristics of different scale vortices in gasoline engine

The paper adopted three-dimensional (3D) Particle Image Velocimetry (PIV) combined with high-speed measurement technology to study the transient motion characteristics of tumble flow induced by small and medium-sized vortices on an optical gasoline engine. Meanwhile, the Proper Orthogonal Decomposition (POD) method was introduced to analyze the evolution of transient vortices, revealing the three-dimensional motion principle of vortices with different spatial scales within the cylinder. The results showed that increasing the engine speed can cause boosted in-plane and out-of-plane velocity, especially for the in-plane velocity. However, the average velocity in the plane was higher than that out of the plane with the difference generally within an order of magnitude. The strong intake jet was the main reason for bringing turbulent kinetic energy in the cylinder. The average kinetic energy and turbulent kinetic energy in the cylinder are both significantly improved at high engine speed. From the results of this experiment, it was revealed that there exists isotropic turbulent pulsation characteristics. Overall, the corresponding flow characteristics of different decomposed modes were different. The first mode section had the lowest average velocity ratio, while the other two had the highest. Due to the dissipation of large vortices into small vortices or the shear action between flow layers, new vortices were generated, leading to the intermittent phenomenon of the motion path of the vortex cluster in the target plane. The average vortex size and velocity circularity corresponding to two varied engine speeds presented a downward trend. The average vortex size was smaller at high engine speed, while the vortex intensity was higher. In addition, increasing the engine speed would decrease the vortex scale but increase the vortex strength. This work provided new fundamental insights into analyzing the characteristics of micro-scaled vortices in turbulent flow, as well as the organization of intake in the gasoline engine.

Optimal transonic buffet aerodynamic noise PSD predictions with Random Forest: Modeling methods and feature selection

To address challenges such as long computational cycles and high experimental measurement costs in obtaining Power Spectral Density (PSD) of aerodynamic noise, this study aims to enable a rapid assessment of buffet frequency and aerodynamic noise levels. The paper conducts a comparative analysis of the impact of different modeling methods and input features on prediction accuracy, proposing the time domain model, the full frequency domain model, and the single frequency model. The research reveals that the frequency domain model has an advantage over the time domain model in predicting aerodynamic noise, emphasizing the importance of selecting appropriate modeling methods. Additionally, based on whether frequency information is used as input features, the study introduces the full frequency domain model and the single frequency model. Results indicate that the single frequency model can significantly reduce the maximum relative error and Root Mean Square Error of the full frequency domain model by approximately three orders of magnitude, lowering the reconstruction error of the Proper Orthogonal Decomposition method by 2–3 orders of magnitude. Furthermore, this model demonstrates generalization across Mach numbers, angles of attack, and spatial positions, ensuring that the maximum absolute error of discrete peak frequencies is controlled within 1 Hz, and the relative error of discrete narrowband peaks is maintained at around 1 %.

Direct numerical simulations of an airfoil undergoing dynamic stall at different background disturbance levels

Thin airfoil dynamic stall at moderate Reynolds numbers is typically linked to the sudden bursting of a small laminar separation bubble close to the leading edge. Given the strong sensitivity of laminar separation bubbles to external disturbances, the onset of dynamic stall on a NACA0009 airfoil section subject to different levels of low-amplitude free stream disturbances is investigated using direct numerical simulations. The flow is practically indistinguishable from clean inflow simulations in the literature for turbulence intensities at the leading edge of ${Tu} = 0.02\,\%$ . At slightly higher turbulence intensities of ${Tu} = 0.05\,\%$ , the bursting process is found to be considerably less smooth and strong coherent vortex shedding from the laminar separation bubble is observed prior to the formation of the dynamic stall vortex (DSV). This phenomenon is considered in more detail by analysing its appearance in an ensemble of simulations comprising statistically independent realisations of the flow, thus proving its statistical relevance. In order to extract the transient dynamics of the vortex shedding, the classical proper orthogonal decomposition method is generalised to include time in the energy measure and applied to the time-resolved simulation data of incipient dynamic stall. Using this technique, the dominant transient spatiotemporally correlated features are distilled and the wave train of the vortex shedding prior to the emergence of the main DSV is reconstructed from the flow data exhibiting dynamics of large-scale coherent growth and decay within the turbulent boundary layer.

Proper Orthogonal Decomposition Based Response Analysis of Inlet Distortion on a Waterjet Pump

This study addresses the challenge of performance degradation in waterjet pumps due to non-uniform suction flow. Utilizing the Proper Orthogonal Decomposition (POD) method, it decomposes and reconstructs the flow features within a waterjet pump under non-uniform inflow into a series of modes ranked in descending order of energy. By analyzing the modes with dominant energy, which contain complex information about the flow field, it is revealed that modes 1 and 2 predominantly represent the formation of a concentrated vortex, whereas modes 3 and 4 illustrate its spatial offset. Notably, in the hub section, mode 3 exhibits a delayed flow separation caused by the reduction of circumferential vortex (CV), with a consequent lift in blade loading at the leading edge and a higher head compared to mode 1. In the shroud section, the delayed flow separation in mode 3 suppressed reverse flow and the concentrated separation vortex (CSV) and then increased the blade loading, ultimately enhancing the pump head. The findings provide significant insights into optimizing waterjet pump performance by detailing the interactions between various flow structures and pump components, effectively filling a knowledge gap in applying dimensionality reduction techniques within the distorted flow fields of water jet pumps.

Spacing Ratio Effects on the Evolution of the Flow Structure of Two Tandem Circular Cylinders in Proximity to a Wall

The flow around two tandem circular cylinders in proximity to a wall is investigated using particle image velocimetry (PIV) for Re = 2 × 103. The spacing ratios L/D are 1, 2, and 5, and the gap ratios G/D are 0.3, 0.6, and 1. The proper orthogonal decomposition (POD) method and λci vortex identification method are used to investigate the evolution of flow structure, and the influences of L/D and G/D on flow physics are shown. At L/D = 2 and G/D = 0.3, a “pairing” process occurs between the wall shear layer and the upstream cylinder’s lower shear layer, resulting in a small separation bubble behind the upstream cylinder. At L/D = 1, the Strouhal number (St) increases with decreasing G/D. At three gap ratios, the St gradually decreases as L/D increases. At G/D = 0.3, there is nearly a 49.98% decrease from St = 0.3295 at L/D = 1 to St = 0.1648 at L/D = 5, which is larger than the reductions in cases of G/D = 0.6 and G/D = 1. The effects of L/D on the evolution of flow structure at G/D = 0.6 are revealed in detail. At L/D = 1, the vortex shedding resembles that of the single cylinder. As L/D increases to 2, a squarish flow structure is formed between two cylinders, and a small secondary vortex is formed due to induction of the lower shear layer of the upstream cylinder. At L/D = 5, there is a vortex merging process between the upper wake vortices of the upstream and downstream cylinders, and the lower wake vortex of the upstream cylinder directly impinges the downstream cylinder. In addition, the shear layers and wake vortices of the upstream cylinder interact with the wake of the downstream cylinder as L/D increases, resulting in reductions in velocity fluctuations, and the production and turbulent diffusion of turbulent kinetic energy are decreased behind the downstream cylinder.

A preserving accuracy two-grid reduced-dimensional Crank-Nicolson mixed finite element method for nonlinear wave equation

In this paper, we mainly resort to a proper orthogonal decomposition (POD) method to study the reduced-dimension of unknown mixed finite element (MFE) solution coefficient vectors in the two-grid Crank-Nicolson MFE (TGCNMFE) method for the nonlinear wave equation and build a preserving accuracy reduced-dimension extrapolated TGCNMFE (RDETGCNMFE) method for the nonlinear wave equation. For this purpose, we first build a new TGCNMFE method for the nonlinear wave equation and demonstrate the existence, unconditional stability, and error estimates for the TGCNMFE solutions. From there, we build a preserving accuracy RDETGCNMFE method for the nonlinear wave equation by using the POD method to decrease the dimension of unknown TGCNMFE solution coefficient vectors and employ the matrix analysis to analyze the existence, unconditional stability, convergence, and errors for the RDETGCNMFE solutions. We finally make use of numerical experiments to verify our theoretical results and to show the advantages of RDETGCNMFE method.

Impact of Oxygen Content on Flame Dynamics in a Non-Premixed Gas Turbine Model Combustor

In this study, large eddy simulation (LES) was used to investigate the dynamic characteristics of diffusion flames in a swirl combustion chamber at an oxygen content of 11–23 wt% and temperature of 770 K. The proper orthogonal decomposition (POD) method was employed to obtain flame dynamic modes. The results indicate that oxygen content has a significant impact on the downstream flow and flame combustion characteristics of the swirl combustion chamber. With oxygen content increasing, the size of the recirculation zone is reduced, and the flame field fluctuations are intensified. The pressure and heat release fluctuations under different oxygen contents were analyzed using frequency spectrum analysis. Finally, the flame modes were analyzed using the POD method, and it was found that the coherent structures are asymmetric relative to the local coordinate system. At an oxygen content of 11 wt%, they exhibit larger coherent structures, while at an oxygen content of 23 wt%, they exhibit numerous turbulent structures.

Nonlinear reduction using the extended group finite element method

In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the extended group finite element formulation achieves a noticeable reduction in the computational overhead associated with nonlinear finite element problems. However, the problem’s size still leads to long solution times in most applications. Aiming to make real-time and/or many-query applications viable, we consider model order reduction and complexity reduction techniques to reduce the problem size and efficiently handle the reduced nonlinear terms, respectively. For proof of concept, we focus on the proper orthogonal decomposition and discrete empirical interpolation methods. While similar approaches based on the group finite element method only focus on semilinear problems, our proposed framework is also compatible with quasilinear problems. Compared to existing methods, our reduced models prove to be superior in many different aspects as demonstrated in three numerical benchmark problems.

Large eddy simulation of non-premixed flame behavior and NOx emission characteristics in a staged combustor with multi-swirling flows

This study utilizes Large Eddy Simulation (LES) to investigate flame characteristics and NOx emission generation in a concentric staged combustor with three distinct pilot swirler arrangements. We examine the effects of multi-swirling flow on the instantaneous flow field and flame characteristics using the Proper Orthogonal Decomposition (POD) method, and assess how variations in swirler structures influence thermoacoustic instability. Furthermore, a comparison of NOx emissions between two pilot swirler configurations, with similar mean flow field and flame characteristics, highlights the precessing vortex core's role in NOx emissions. Compared to a single-swirler setup, a double-swirler configuration produces a more distinct single precessing vortex core, thereby amplifying thermoacoustic instability. The extended venturi structure in the double-swirler setup mitigates the development of the swirl-induced vortex core, reducing thermoacoustic instability. However, the expansion section in this setup impedes initial fuel and air mixing, leading to an extended flame length, which in turn results in higher NOx emissions due to a more concentrated temperature distribution. With similar mean flow field and flame structure, the double-swirler combustor proves more effective in reducing NO emissions than the triple-swirler combustor.