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The aggregation of dipolar chains driven by thermal fluctuations in an external strong (electric or magnetic) field is investigated theoretically. We discover a new simple electrostatic mechanism that rationalizes the counter-intuitive lateral coalescence of dipolar chains. There, we first demonstrate that two bent dipolar chains can either attract or repel each other depending if they possess similar or opposite curvatures, respectively. Upon bending, dipolar chains become the siege of polarization-induced local charges that in turn lead to quadrupolar couplings. This striking feature is then exploited to understand our conducted Monte Carlo simulations at finite temperature where thermal fluctuations cause local curvatures in the formed dipolar chains. The related quadrupolar attractive mode with correlated chain-curvatures is clearly identified in the simulation snapshots. Our findings shed new light on a longstanding problem in soft matter and related areas. [ABSTRACT FROM AUTHOR]

Thermal striping is a phenomenon characterized by oscillatory mixing of non-isothermal streams, which is commonly seen in industrial processes such as nuclear coolant piping, petrochemical plants and liquefied natural gas transportation. The oscillatory mixing of hot and cold fluid can produce thermal field fluctuations and pose a potential risk of high-cycle thermal fatigue failures. Predicting and evaluating spatiotemporal fluctuations in thermal striping often requires high resolution and massive computational power. Although there have been extensive studies using machine learning algorithms on surrogate modeling, research focused on spatiotemporal fluctuation predictions is very limited. Due to the high dimensionality, it often requires complex algorithms with a large amount of high-fidelity training data, which limits the adoption of such methods for industrial applications. In this research, a two-level machine learning framework based on turbulence coherent structures is proposed and its application to a practical problem is demonstrated. The two-level design leverages vortex identification and local bias correction techniques, efficiently reducing the number of full-order simulations required for training. In the first level, well-organized coherent structures are extracted by performing Proper Orthogonal Decomposition on local parameters and then a tree-based machine-learning model is used to down-select the reference structures for the field reconstruction. In the second level, a parameterized convolution neural network is trained to predict the bias introduced by reference structures approximation. The demonstration of the methodology shows that the method can accurately capture the fluctuation frequencies and amplitudes of the spatiotemporal fields in a highly variational setting. Based on the vortex identification method, the methodology is expected to be applicable to general phenomenon driven by large coherent structures. [ABSTRACT FROM AUTHOR]

Turbulent mixing noise is a vital component of jet noise, and its rapid, accurate prediction has always been persistently pursued. Recent advancement in machine learning has been applied to jet noise prediction. However, these applications are pure curve fitting and lack physical constraints. In this study, a physics-merged deep neural network (PMNN)-based prediction method was developed for turbulent mixing jet noise by merging the physics of the jet noise. This deep neural network (DNN)-based method employed recent advancements in jet turbulent mixing noise containing large- and fine-scale turbulence structures. Two simple rational functions for large- and fine-scale turbulent noise similarity spectra were proposed to replace the original complex similarity spectra functions and incorporated into the DNN-based prediction method. For comparison, we present two data-driven DNN-based prediction methods (DDNN). The first DDNN method used the sound pressure level (SPL) as the output of neural networks, directly establishing the nonlinear relationship between the input features and SPL. In the second DDNN method, the dominant modes of the jet noise spectra extracted using the proper orthogonal decomposition method were merged with DNN. These DNN-based methods were then trained using a set of experimental data over a wide range of jet operating conditions. Their performance was evaluated and compared. It was evident that all these DNN-based methods were capable of predicting turbulent mixing noise reasonably well. In contrast to the DDNN methods, the PMNN method could provide insights into the jet turbulent mixing noise components. It demonstrates that the turbulent mixing jet noise spectra at the mid polar angle is generated by the large-scale noise component at low-frequency range and by the fine-scale noise component at high-frequency range. [ABSTRACT FROM AUTHOR]

Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia, affecting over 1% of the population. It is usually triggered by irregular electrical impulses that cause the atria to contract irregularly and ineffectively. It increases blood stasis and the risk of thrombus formation within the left atrial appendage (LAA) and aggravates adverse atrial remodeling. Despite recent efforts, LAA flow patterns representative of AF conditions and their association with LAA stasis remain poorly characterized. To develop reduced-order data-driven models of LAA flow patterns during atrial remodeling in order to uncover flow disturbances concurrent with LAA stasis that could add granularity to clinical decision criteria. We combined a geometric data augmentation process with projection of results from 180 CFD atrial simulations on a universal LAA coordinate (ULAAC) system. The projection approach enhances data visualization and facilitates direct comparison between different anatomical and functional states. ULAAC projections were used as input for a proper orthogonal decomposition (POD) algorithm to build reduced-order models of hemodynamic metrics, extracting flow characteristics associated with AF and non-AF anatomies. We verified that the ULAAC system provides an adequate representation to visualize data distributions on the LAA surface and to build POD-based reduced-order models. These models revealed significant differences in LAA flow patterns for atrial geometries that underwent adverse atrial remodeling and experienced elevated blood stasis. Together with anatomical morphing-based patient-specific data augmentation, this approach could facilitate data-driven analyses to identify flow features associated with thrombosis risk due to atrial remodeling. • Novel Universal Left Atrial Appendage Coordinates (ULAAC) system. • Assessing the influence of geometric and flow parameters on LAA blood stasis. • Developing reduced-order data-driven models of hemodynamic metrics. • Identification of non-AF features by proper orthogonal decomposition (POD). [ABSTRACT FROM AUTHOR]

Wind energy in the atmospheric boundary layer serves as the primary source for energy absorption and structural load on wind turbines. However, the impact of turbulent coherent structures on the aerodynamic performance and wake characteristics of wind turbines has not been comprehensively evaluated. In this study, the proper orthogonal decomposition (POD) method is employed to assess the influence of turbulent coherent structures of varying scales on the aerodynamic performance and wake characteristics of wind turbines in the neutral atmospheric boundary layer. The results show that turbulent coherent structures are the main factor that determines the wind velocity fluctuation, aerodynamic performance and wake characteristics of wind turbine in the atmospheric boundary layer. When considering the 13th or lower order POD mode, the wind velocity fluctuation increases with the increase of energy content (more POD modes) of the turbulent coherent structures. When considering the first 19 POD modes, the dynamic loads and power of wind turbine fluctuate with high frequencies, the thrust fluctuates in an amplitude range between 2.4 % and 13.9 % around the mean value, and the power fluctuates from 4.5 % to 28.6 % of the mean value. When considering the first 40 POD modes, the average power generation of the wind turbine increases by 26 % compared to the case with no turbulent structures considered. The study of turbine wake shows that turbulent coherent structures can expand the wind turbine wake approximately to a width of 2.5 D and a height of 3 D (D is the diameter of the wind turbine), offset the wake approximately to 2 D , and move forward the position of the wake vortex beginning to dissipation approximately to 7 D behind the wind turbine. In addition, turbulent coherent structures can accelerate the wake velocity recovery by increasing the momentum exchange between the atmospheric boundary layer and wind turbine wake. • A POD-based inflow generation method is established for wind turbine simulation. • Study into the coherent structures with various energy contributions on wind turbine performance. • Obtained the most influence energy contribution of coherent structures in the ABL. • Unveil the influence of coherent structures on the expansion and deflection of wind turbine wakes. [ABSTRACT FROM AUTHOR]

We generalize certain well known orthogonal decompositions of model spaces and obtain similar decompositions for the wider class of shifted model spaces, allowing us to establish conditions for near invariance of the latter with respect to certain operators which include, as a particular case, the backward shift S*. In doing so, we illustrate the usefulness of obtaining appropriate decompositions and, in connection with this, we prove some results on model spaces which are of independent interest. We show moreover how the invariance properties of the kernel of an operator T, with respect to another operator, follow from certain commutation relations between the two operators involved. [ABSTRACT FROM AUTHOR]

Voltage‐clamp experiments are commonly utilised to characterise cellular ion channel kinetics. In these experiments, cells are stimulated using a known time‐varying voltage, referred to as the voltage protocol, and the resulting cellular response, typically in the form of current, is measured. Parameters of models that describe ion channel kinetics are then estimated by solving an inverse problem which aims to minimise the discrepancy between the predicted response of the model and the actual measured cell response. In this paper, a novel framework to evaluate the information content of voltage‐clamp protocols in relation to ion channel model parameters is presented. Additional quantitative information metrics that allow for comparisons among various voltage protocols are proposed. These metrics offer a foundation for future optimal design frameworks to devise novel, information‐rich protocols. The efficacy of the proposed framework is evidenced through the analysis of seven voltage protocols from the literature. By comparing known numerical results for inverse problems using these protocols with the information‐theoretic metrics, the proposed approach is validated. The essential steps of the framework are: (i) generate random samples of the parameters from chosen prior distributions; (ii) run the model to generate model output (current) for all samples; (iii) construct reduced‐dimensional representations of the time‐varying current output using proper orthogonal decomposition (POD); (iv) estimate information‐theoretic metrics such as mutual information, entropy equivalent variance, and conditional mutual information using non‐parametric methods; (v) interpret the metrics; for example, a higher mutual information between a parameter and the current output suggests the protocol yields greater information about that parameter, resulting in improved identifiability; and (vi) integrate the information‐theoretic metrics into a single quantitative criterion, encapsulating the protocol's efficacy in estimating model parameters. [ABSTRACT FROM AUTHOR]

A framework of the topology optimization incorporated with the phase field method considering the interfacial damage for optimizing the fracture resistance of inclusion-matrix composites is presented. The topology optimization was performed to redistribute the inclusion phase in order to reduce its volume while keeping the fracture resistance value of the initial design unchanged. The phase field method uses two scalar phase field variables: one is for the bulk crack and the other is for the interfacial crack. The decomposition of the strain tensor into compression and tension parts was incorporated into this phase field method to improve the mechanical behaviors of the materials. These compression and tension strain parts are orthogonal in the context of the inner product in which the tensor of elastic stiffness behaves as a metric. Moreover, in the simulation process, an investigation of the effects of the interfacial parameters on the numerical results was discussed. Through the obtained results, the method proposed is demonstrated to be accurate and efficient in eliminating spurious effects and singularity points on the behavior curves in the damage process. [ABSTRACT FROM AUTHOR]

This work is concerned with an adaptive reduced order model of modular structures assembled from parameter-dependent substructures. The substructures are reduced by proper orthogonal decomposition (POD) and connected by means of a tied contact formulation. We present a method to adapt the matrices of the substructures to parameter changes. We employ interpolation on Grassmann manifolds for the parametric adaption of the projection matrices. For the adaptation of the stiffness matrices, we use the direct empirical interpolation method (DEIM). Manifold interpolation of the reduced stiffness matrices, cannot be applied here since it would require semi-positive definiteness, which is here not fulfilled because of necessary rigid body motion modes. The novelty of this work is the application of these interpolation methods to the special problem class of POD-based tied contact model order reduction. Furthermore, we show a methodology to compute significant snapshots on the substructure level to compute a POD basis that can be used in different global structures. [ABSTRACT FROM AUTHOR]

AbstractThis paper presents the development of a benchmark for predicting thermal striping through simulation. This work utilized large eddy simulation and will be used to benchmark future models. The testing domain was created using both the STRUCT and the Reynolds-averaged Navier-Stokes turbulence models and is based on an earlier design of the General Atomics Fast Modular Reactor upper plenum. The plenum features two adjacent, identical hexagonal bundles each with a center-placed axial rod drive, with a hot left coolant stream and a cold right coolant stream. The simulation solves the nondimensional Navier-Stokes equations, with temperature accounted as a passive scalar. First- and second-order flow statistics were obtained after 600 convective time units of averaging. The first-order statistics reveal that the hot jet is damped by a recirculatory flow from the near wall. At the same location, the second-order statistics show strong oscillations both in velocity and temperature. The power spectral density was utilized to determine that a low-frequency oscillation occurs here that is within the range of interest for thermal striping. Furthermore, proper orthogonal decomposition was used to identify coherent structures that confirm the oscillatory behavior, indicative of thermal striping. Overall, this benchmark can aid in the development of future models for predicting thermal striping in nuclear reactors, potentially leading to improved reactor safety and performance. [ABSTRACT FROM AUTHOR]

The Schwarz domain decomposition (SDD) method is known for its high efficacy in solving large-scale systems of partial differential equations, primarily due to its parallelizability. However, the method's reliance on iteration introduces substantial computational expenses. In this study, we propose a reduced-order Schwarz domain decomposition (ROSDD) method tailored specifically for the convection-diffusion equation. Utilizing the proper orthogonal decomposition (POD) technique, the ROSDD method significantly reduces computational costs by considering only a small number of unknowns. Since the equation typically exhibits convection-dominated behavior, we employ the characteristic finite element discretization scheme. Consequently, we derive optimal a priori error estimates to assess the accuracy of our approach. Finally, we conduct some numerical experiments to validate the superiority of the ROSDD method. [ABSTRACT FROM AUTHOR]

A reconstruction framework based on proper orthogonal decomposition and the Bayesian estimation was designed for the spatial superresolution of a subsonic jet, and the simultaneous two PIV measurements of a subsonic jet with different magnifications were conducted for training and testing the framework. The measurement system successfully acquired paired particle images of broad and close-up views of the jet in the same plane, and low and high-resolution velocity fields were obtained. The artificial low-resolution velocity fields were also generated by average pooling of the measured high-resolution velocity fields, and the performance of the reconstruction framework was evaluated. The estimation accuracy of the proposed framework was compared with that of bicubic interpolation and machine learning-based reconstruction methods: convolutional neural network and downsampled skip-connection/multi-scale methods. The framework successfully reconstructed the high-resolution velocity field from the low-resolution velocity field of the artificial one and actually measured one. The minimum reconstruction error of the Bayesian estimation using actually measured low-resolution velocity field was 63%, outperforming bicubic interpolation. Although this reconstruction error of the proposed framework is almost the same as (slightly worse than) that of the neural network methods, its reconstruction process is clearer and simpler than the neural network method. The power spectra of turbulent kinetic energy showed that the proposed framework can accurately recover the original velocity field in a wide waveband compared to the other methods. Therefore, the proposed framework can be a superresolution method of experimental fluid dynamics. [ABSTRACT FROM AUTHOR]

A novel method is introduced to estimate phase-averaged pressure and acceleration of the coherent structures. It is applied and validated in the near wake of a two-dimensional bluff body. The method is validated using synthetic data generated by simulating an unsteady laminar flow around a D-shaped bluff body; the effect of noise is investigated to simulate an experimental scenario. The acceleration terms, required for the closure of flow-governing equations, are accurately estimated using this approach. The findings demonstrate that the methodology outputs consistent results for the pressure field while combined with a divergence-correction scheme, based on Helmholtz decomposition, and an optimal control method using sparse sensor measurements. The approach is later validated on experimental data obtained in the turbulent wake of a bluff body by means of "Particle Image Velocimetry" (PIV). Triple-decomposed flow fields are provided as input, where triple-decomposition refers to the instantaneous flow fields split into a mean flow, coherent and incoherent structures. The coherent structures are extracted using the method of "Proper Orthogonal Decomposition" (POD). Coherent lift coefficients, estimated using integral budgets of momentum, remain within the sensor-measured range, whereas coherent drag coefficients show excellent agreement. Moreover, a significant reduction in the residuals, arising from the balance of the flow-governing equations, is achieved. Although the temporal information is lost when computing POD modes, the proposed method is able to recover it and estimate the pressure. Accordingly, the method can be extended to any time-dependant modal decomposition, thereby providing a low-cost alternative to expensive "time-resolved" PIV (tr-PIV) measurements. [ABSTRACT FROM AUTHOR]

The efficient and prompt mixing of fuel is crucial in the operation of scramjet engines. This paper presents the findings from wind tunnel experiments that examined the influence of plasma energy deposition on transverse jets at a Mach number of 6.13. The study took into account various inlet flow total pressures and momentum flux ratios between the jet and the main flow. Utilizing a database containing time-resolved intensities from instantaneous schlieren images, we perform turbulence analysis employing various techniques such as the root mean square, fast Fourier transform, proper orthogonal decomposition, and the two-point correlation method. Specifically, we aim to compare and analyze the pulsation characteristics and spatial self-organization of the jet flow field, both with and without energy deposition control. The findings reveal that intermittent "hot bubbles" created by plasma energy deposition interact with the bow shock induced by the jet, resulting in the formation of an array of large-scale vortices. These vortices emerge as the dominant structures within the jet, effectively amplifying its pulsations. At low inlet flow pressures, energy deposition primarily disrupts the jet, causing large-scale vortices to propagate primarily within the jet plume region. However, at high inlet flow pressures, the impact of energy deposition extends to both the jet and the turbulent boundary layer, encompassing their respective disturbance ranges. Increasing the inlet flow pressure constraints the evolution of large-scale vortices, thus limiting the efficacy of energy deposition in governing the mixing process. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics governing turbulent momentum exchange and heat transfer between pore flow within porous media and the turbulent flow passing over it. Employing high-fidelity pore-scale large eddy simulation, our investigation explores the fundamental mechanisms driving these phenomena. Modal analysis based on snapshot proper orthogonal decomposition (POD) is employed to quantify the modes of interaction between porous and non-porous regions, providing a comprehensive understanding of the underlying processes. Spatial and temporal modes reveal the existence of localized flow structures at the pore scale, contributing to time-varying patterns of information exchange. At the commencement of the porous block, the mean flow (Mode = 0) from the porous to non-porous region is the dominant mechanism in momentum exchange and heat transfer. This mode facilitates convective heat transfer from the porous to the non-porous region through upward and forward flow movements, showcasing positive flow leakage. In addition to the mean flow, the turbulent flux inherent in alternate POD modes (Mode ≠ 0) plays a substantial role in information propagation, influencing diverse directions. Spatial modes, complemented by statistical analysis, uncover a significant likelihood of observing negative vertical velocity values in the wake of the porous ligaments at the porous-fluid interface, indicative of negative flow leakage. This negative flow leakage precisely corresponds to the local penetration of fluid from the non-porous region into the porous region. Furthermore, our study reveals that information exchange via turbulence fluctuations manifests through complex outward and inward interactions in regions characterized by substantial positive flow leakage. Notably, these regions exhibit a distinct tendency for high-momentum streamwise-oriented flow to migrate outward from the porous region into the non-porous region (outward interactions). Conversely, inward interactions arise in these regions when the instantaneous magnitude of positive flow leakage is smaller than the mean value of positive flow leakage, emphasizing the pulsating nature of positive flow leakage. Finally, the distribution of the Nusselt number highlights that more than 60% of total heat transfer occurs within the initial one-third of the porous block length. Significantly, a notable portion of the porous ligaments experiences insufficient cooling due to positive flow leakage, underlining the critical implications of these findings for the understanding of turbulent momentum exchange and heat transfer in a composite porous-fluid system. [ABSTRACT FROM AUTHOR]

This study employs time-resolved particle image velocimetry technology to investigate the flow field characteristics of a double-wall jet structure under both stationary and rotating conditions. The jet rotation number range from 0 to 0.08, covering both clockwise and counterclockwise rotations, with a jet Reynolds number of 4000. The dimensionless jet-to-target spacing is 2. In order to elucidate the flow mechanisms based on experimental results and provide complementary insight, validated numerical simulations under conditions identical to the experiments were conducted. This paper considers average velocity and Reynolds stress and utilizes the proper orthogonal decomposition method to study flow characteristics. The results indicate that the rotation-induced Coriolis force, centrifugal force, and radial pressure gradient in the radial direction influence the jet to deflect. The pressure gradient generated by the centrifugal force weakens its effect, making the jet deflection primarily dominated by the Coriolis force. The deflection direction and degree of the jet differ with the rotation direction and increase with the rotation number. When the rotation direction is reversed, differences in the direction of the force acting on the fluid lead to variations in the secondary flow structures of the jet; the secondary flow structures within the impingement holes exhibit two-vortex or four-vortex structures under counterclockwise or clockwise rotation, respectively. At the highest rotation number, jet deflection intensifies mixing with the surrounding fluid, resulting in a reduction of about 30% in the velocity peak compared to the stationary state but an increase of approximately 0.6 times in turbulent kinetic energy. [ABSTRACT FROM AUTHOR]

The real-time computation of a three-dimensional pipe network flow is crucial for both pipe design and operational maintenance. This study devises a novel reduced-order configuration approach that combines the advantages of the acceleration characteristics of the reduced-order model and the structural applicability of the configuration model. First, a configuration model is established by categorizing sub-pipes extracted from a pipe network into sets based on the sub-pipes' type. Subsequently, reduced-order configurations are realized by a reduced-order model established for each type of configuration, enabling real-time computation of individual sub-pipes. Thus, the concatenation of sub-pipes allows the computation of an entire pipe network. A complex boundary–deep learning–reduced-order configuration model and a complex boundary–deep learning–reduced-order configuration–multi-source data–reduced-order configuration model integrated with a local multi-physical–discrete empirical interpolation method and a multi-source data fusion model are devised. These models were employed for the real-time computation and prediction of a three-dimensional velocity field for 300 snapshots composed of one to four sub-pipes extrapolated from a dataset of 294 pipe network snapshots composed of one to three sub-pipes. The maximum relative errors for snapshots from the dataset were similar to the limit precision of the proper orthogonal decomposition, with more precise accuracy than the relevant studies, indicating the excellent performance of our reduced-order configuration approach. [ABSTRACT FROM AUTHOR]

The fuel rod bundles are the core part of pressurized water reactors (PWRs), and its heat transfer characteristics directly impact the safety of PWRs. A computational fluid dynamics (CFD) model of 5 × 5 fuel rod bundles with a spacer grid is established, and the numerical simulation results are in excellent agreement with the experimental results. Then, the effects of four turbulence models, namely shear stress transport model, standard k–ε model, re-normalization group k–ε model, and realizable k–ε model on the thermal-hydraulic characteristics of the 5 × 5 fuel rod bundles are systematically investigated. Furthermore, two data-driven methods, namely proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are used to analyze the flow fields of the 5 × 5 fuel rod bundles. The two methods can extract key modes or features to enhance the comprehension and description of the dynamic behaviors within the flow fields of 5 × 5 fuel rod bundles. Finally, two reduced-order models (ROMs), called the POD-radial basis function neural network surrogate model and DMD method, are constructed, which can enable rapid prediction of the flow fields for 5 × 5 fuel rod bundles with high accuracy. The CFD simulation results presented in this paper can provide valuable insights for studying the thermal-hydraulic characteristics of the 5 × 5 fuel rod bundles. The two ROMs proposed in this paper can significantly reduce the computational costs associated with studying the thermal-hydraulic characteristics of 5 × 5 fuel rod bundles. [ABSTRACT FROM AUTHOR]

The present investigation seeks to analyze the fluid dynamics associated with tidal turbines in the context of the EU (European Union) project NEMMO (The Next Evolution in Materials and Models for Ocean Energy, nemmo.eu). A pair of counter-rotating tidal turbines is employed for propelling a ship. The separation between these turbines is approximately one rotor diameter. Consequently, the power output of the downstream turbine is adversely affected by the heightened turbulence generated by the rotation of the upstream turbine. This power imbalance poses a substantial challenge in terms of power management. Therefore, this study concentrates on conducting a flow analysis of these counter-rotating turbines. Large Eddy Simulation (LES) of a dual tidal turbine rotating in opposite directions is conducted using the actuator line method. The flow is scrutinized by employing proper orthogonal decomposition (POD). The flow field is then reconstructed using the reduced order method. It is observed that a reduced number of modes is sufficient to reconstruct the flow between the tidal turbines. However, more modes are necessary to replicate the flow beyond the downstream turbine. The utilization of fewer modes proves effective in comprehending the flow at the inlet of the downstream turbine, ultimately resulting in reduced computational power requirements through faster matrix operations and lower memory usage for the POD decomposition. [ABSTRACT FROM AUTHOR]

Aiming at fast and accurate spatiotemporal prediction of interfacial flow fields, a novel deep learning model combining Convolutional AutoEncoder (CAE) and long short-term memory with spatial and temporal attention (LSTM-STA) is proposed and named as CAE-LSTM-STA (hybrid model of CAE and LSTM-STA) in this article. To enable a fast calculation process, CAE is first utilized to compress the high-dimensional snapshots of flow fields into the low-dimensional latent space by its encoder. Then, the latent space serves as the input feature for LSTM-STA to temporally evolve the state of the low-dimensional latent space. Finally, the low-dimensional latent space at future time steps is fed back into the decoder of CAE to derive the full-order snapshots of the flow fields. The prediction performance of the proposed model is evaluated via two representative benchmark cases, including the dam break case and the rising bubble case. The capability of CAE in dimension reduction is found to be much better than that of the widely used Proper Orthogonal Decomposition, while LSTM-STA is observed that outperforms the original LSTM in multivariant temporal prediction. These promising results indicate that the proposed CAE-LSTM-STA model is able to effectively capture and advance the spatiotemporal characteristics of the interfacial flow fields, therefore making it an advanced surrogate model for fast and precise generation of the temporally continuous interfacial flow fields. [ABSTRACT FROM AUTHOR]

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of nonlinear system identification techniques, namely SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a linear system to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs). [ABSTRACT FROM AUTHOR]

In this paper, a non-intrusive reduced-order model (ROM) for parametric reactor kinetics simulations is presented. Time-dependent ROMs are notoriously data intensive and difficult to implement when nonlinear multiphysics phenomena are considered. These challenges are exacerbated when parametric dependencies are included. The proper orthogonal decomposition mode coefficient interpolation (POD-MCI) ROM presented in this work can be constructed directly from lower-dimensional full-order model (FOM) outputs and is independent of the underlying model. This greatly alleviates the data requirement of many existing ROMs and can be used without modification on arbitrarily complex models or experimental data. The POD-MCI ROM is demonstrated on a number of examples and yields accurate characterizations of the parametric behaviors of both FOM outputs and derived quantities of interest within the selected parameter spaces, at extremely attractive computational speedup factors relative to FOMs. [ABSTRACT FROM AUTHOR]

Aerodynamic shape optimization processes are often used for complex problems that meet single or multiobjective design requirements. The robust aerodynamic shape optimization techniques with a high number of design variables that consider uncertainties have a huge computational burden compared to the traditional aerodynamic shape optimization techniques without considering uncertainties. To overcome this issue, in this study, the proper orthogonal decomposition is integrated with the inductive design exploration method to use for the robust shape optimization of the ONERA M6 wing. The proper orthogonal decomposition method is utilized for reducing the number of design variables of the wing geometry. The cost due to the computational fluid dynamics analysis is mitigated by incorporating the proper orthogonal decomposition with a surrogate modeling technique called the radial basis function. The robust optimization is conducted by the proposed approach based on the inductive design exploration method by accounting for uncertainties of the Mach number in the transonic flow regime. The agreement between the performance predictions of the robust designs and the computational fluid dynamics analysis results showed the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The convolutional neural network-based deep generative model (DGM) is a powerful tool for handling image datasets that opens up strategies for fast synthesis of optimum designs at unseen boundary conditions. Existing DGMs for design synthesis are typically based on O (10000) training data, which limits the engineering applications. This paper explores the feasibility of improving DGM data efficiency with O (100) training data through prior constraints. A two-stage data-efficient deep generative model (DE-DGM) is proposed which leverages the first-stage design synthesis from probabilistic proper orthogonal decomposition and the second-stage enhancement from encoder-decoder convolutional neural network. Four topology optimization cases have been adopted, including compliance minimization, heat conduction, airplane bearing bracket design, and three-dimensional machine tool column structure design. The proposed DE-DGMs could be trained with 100–200 data and synthesize the main features of the design at unseen boundary conditions. The overall computation cost of warm-start topology optimization leveraging DE-DGM predictions reduces to 36 %–58 % of the standard cases. [ABSTRACT FROM AUTHOR]

This work introduces a parametric model order reduction (PMOR) approach that enhances an existing widely used technique based on proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM) for parametrized nonlinear dynamical systems by employing machine learning procedures performed on a Grassmann manifold. In particular, distances between parameters are first computed based on a metric defined on the Grassmann manifold of solution spaces. Then, the distance information is utilized in the K-medoids clustering algorithm to partition parameters into classes with corresponding local solution spaces, which are further used to form a dictionary of local bases. The artificial neural network (ANN) is next used to build a classifier that can automatically identify the most suitable local basis from the dictionary for a given input parameter to construct a parametrized reduced-order model by the POD–DEIM approach. This work numerically demonstrates the significance of using distance on the Grassmann manifold of the solution spaces, instead of directly using the Euclidean distance on the parameter space. To validate the proposed method, numerical studies are performed on a parametrized 1D Burger’s equation and a viscous fingering in a horizontal flow through a 2D porous media domain. The proposed method is shown to have advantage in terms of accuracy when compared to the traditional global basis approach, as well as the local reduced-order basis approach based on the Euclidean metric. [ABSTRACT FROM AUTHOR]

In this work, we address parametric non–stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation–based domain decomposition approach, we derive an optimal control problem, for which we present a convergence analysis in the case of non–stationary incompressible Navier–Stokes equations. We discretise the problem with the finite element method and we compare different model order reduction techniques: POD–Galerkin and a non–intrusive neural network procedures. We show that the classical POD–Galerkin is more robust and accurate also in transient areas, while the neural network can obtain simulations very quickly though being less precise in the presence of discontinuities in time or parameter domain. We test the proposed methodologies on two fluid dynamics benchmarks with physical parameters and time dependency: the non–stationary backward–facing step and lid–driven cavity flow. • Optimisation-based domain-decomposition algorithm for non-stationary computational fluid dynamics. • Convergence analysis for the domain-decomposition optimal control problem. • Comparison of the intrusive POD-Galerkin and a non-intrusive Neural Networks based approaches. [ABSTRACT FROM AUTHOR]

The time-averaged particle image velocimetry technique has been applied to measure flow mixing in the Michigan Multi-jet Gas-mixture Dome (MiGaDome) facility, a 1/12th, scaled-down model of the high-temperature gas-cooled reactor upper plenum. Measurements were first conducted with one jet injection into the upper plenum for various Reynolds numbers (Re = 1022, 2038, 4097, and 6021). The experimental region of interest includes a plane within the dome located above one of the jet inlets of interest. First- and second-order statistics are presented and discussed to analyze the local mixing process and turbulent characteristics under the effects of jet spreading and jet impingement. Results have shown that the normalized statistics of the jet reach asymptotic behavior as the inlet Reynolds number is increased. By investigating the two-dimensional budgets for the momentum equation on the measurement plane, it was concluded that the contribution of turbulent diffusion is minor near the enclosure surface where strong convection is present due to impingement. An additional measurement on a triple-jet injection case has shown that jet spreading is suppressed by a recirculation zone, which causes a redistribution of turbulent fluctuations. The detailed local fluctuation patterns/coherent structures have been examined through a proper orthogonal decomposition analysis. [ABSTRACT FROM AUTHOR]

Aiming at raising the efficiency of multidisciplinary optimization of UAV rotor aerodynamics and aeroacoustics, this paper established a low-order method of rotor aerodynamics and noise prediction based on lifting line theory (LLT) and FWH acoustic analogy theory. The maximum errors between the low-order method and the high-fidelity CFD results are 1.53% and 3.3 dB for the thrust and overall sound pressure level (OASPL) respectively, demonstrating the ability of design optimization by the low-order LLT method. Combined with the proper orthogonal decomposition (POD) dimension reduction technique to reduce the variable space, a multidisciplinary optimization of rotor aerodynamics and noise was implemented. The rotor thrust and OASPL were taken as the optimization objectives, and the chord length, thickness, and blade twist angle at different spanwise positions were taken as the design variables. The results show that the proposed optimization strategy effectively reduces the design space, the convergence process is greatly accelerated by coupling the low-order LLT-FWH prediction method, and the whole optimization process is only about 0.094% of the computational resource of the method based on unsteady CFD and conventional optimization method. Compared with the original rotor, the thrust at the design condition is increased by 1.66%, and the OASPL is maximally reduced by 3.10 dB. After optimization, the aerodynamic load fluctuation in the middle of the rotor blade (40%–80% spanwise) is significantly reduced, and the high vorticity area in the wake is reduced from the middle to the blade tip (45%–100% spanwise). [ABSTRACT FROM AUTHOR]

In the approach of metric-based geometric parameterization, the concept of database filtration and proper orthogonal decomposition manipulation quantitatively enhances the generation of new geometric parameters so that the problem-oriented information is reflected in aerodynamic design. Compared with the conventional approach that applies only geometric filtration, this paper incorporates performance filtration so that the problem-oriented information is no longer limited to geometric constraints, thereby enabling the guidance of optimization direction in a more informed manner. This paper focuses on the pressure distribution of samples and their relationship with geometric variations. A variational autoencoder is employed to extract the dominant features of the aerodynamic potentials that an initial geometry can attain in optimization. The authors believe that the aerodynamic potential is reflected in how the pressure distribution differs from that of the initial geometry. Then, samples have to meet the performance filtration criterion based on pressure distribution proposed by designers according to their aerodynamic understanding of the optimization problem. Finally, the remaining collection of qualified samples generates new geometric parameters via proper orthogonal decomposition. The conventional and new approaches were validated in a two-dimensional airfoil case of drag coefficient optimization; the lift-to-drag ratio improved by 17.07% using the traditional method, and by 38.20% using the new approach. The pressure distribution shows that the performance filtration approach produces more supercritical properties than the geometric filtration approach. This implies that the performance filtration approach can capture more intricate details related to the aerodynamic performance of the airfoil. [ABSTRACT FROM AUTHOR]

A reduced-order model based on the proper orthogonal decomposition (POD) method is used to assess whether it can predict the highly unsteady flow in turbomachinery cascades. Three cases are considered: a transonic fan rotor called the National Aeronautics and Space Administration Rotor 67, a cascade of oscillating compressor blades called the 10th Standard Configuration, and a cascade of oscillating turbine blades called the 11th Standard Configuration. The governing equations used in this POD model, called zeta-POD, are written using the specific volume instead of density. This formulation of the governing equations allows the precomputation of the coefficients of the system of ordinary differential equations prior the flow simulation. Consequently, a significant speedup is obtained compared to the full-order model and a traditional, density-based POD. In addition, the accuracy of the zeta-POD model is compared against the full-order model and the density-based POD. [ABSTRACT FROM AUTHOR]

Large eddy simulation with the explicit fifth-order weighted compact nonlinear schemes is performed to investigate the aero-optical distortion caused by a transonic flow over a cylinder at Reynolds numbers of Re = 1 × 105, Re = 2 × 105, and Re = 4 × 105. Proper orthogonal decomposition identifies two dominant modes: the antisymmetric "shifting" mode and the symmetric "breathing" mode, both peaking at the non-dimensionalized Strouhal number StD = 0.18. Optical distortion refers to the phenomenon where a beam passes through a non-uniform and fluctuating flow field, resulting in defocus, jitter, and significant energy reduction. Optical calculations for 12 cases demonstrate that local shock waves and turbulent wakes notably exacerbate optical distortion. In terms of temporal results, the peak frequency of the beam aligns with StD = 0.18 when passing through the cylinder shockwave and falls within StD = 0.16–0.42 as it crosses the shear layer. Significant fluctuations are observed in the turbulent wake and local shock wave, with frequency peaks ranging from StD = 0.12–0.72. Additionally, streamwise flow structures are found to primarily impact optical distortion. Comparative analysis across the three Reynolds numbers indicates that optical distortion is insensitive to Reynolds number variations within the same order of magnitude. The employed grid sufficiently resolves key flow structures impacting beam transmission. [ABSTRACT FROM AUTHOR]

The spectral characterization of flow-field parameters provides a new perspective for understanding the spatiotemporal evolution of unsteady supersonic exhaust plumes and for extracting typical structures. In this study, a large-eddy simulation is performed to calculate the three-dimensional unsteady supersonic plume flow field of rocket engines, and a spectral proper orthogonal decomposition (SPOD) method with a spatiotemporal separation is established. This approach is used to extract the coherent structural features of the unsteady exhaust plume flow field and analyze the mode space structure at different frequencies. The three-dimensional reconstruction and denoising of the exhaust plume flow-field parameters can be achieved via the frequency- and time-domain reconstructions of the SPOD algorithm and oblique projection method, respectively. The ground rocket exhaust plume of ballistic evaluation motor-II is analyzed. The results indicate that the SPOD method can effectively extract the single-frequency mode structure of the reactive supersonic flow field, and that low-order behavior appears in the m = 0 and m = 1 azimuth modes. The potential core exhibits a high-frequency wave-packet structure that is affected by shock waves and shear layers. Time-domain reconstruction based on the oblique projection method facilitates the capture of the dynamic characteristics of the flow field. For the first-order SPOD mode, the frequency- and time-domain reconstruction errors are 3.3% and 1.5%, respectively. The frequency-domain reconstruction method exhibits a 4% improvement in denoising ability compared to low-pass filters. This study provides a novel method for the spectral characterization and spatiotemporal feature extraction of supersonic exhaust plume flow fields. [ABSTRACT FROM AUTHOR]

This study investigates the steady and unsteady behaviors of near-wake flow for axisymmetric models acquired with conical boattails with different slant angles under low-speed conditions. Delayed detached eddy simulation (DDES) was applied for the numerical processes. The Proper Orthogonal Decomposition (POD) was then used to reconstruct the dominant modes of the pressure at the base and velocity fields on the symmetry plane. Both near-wake and far-wake flows were considered in this study to obtain a full pattern of the wake. It was shown that the DDES allows for obtaining a highly accurate wake flow field. The large-scale structure of the base flow with two dominant modes of vortex shedding at StD = 0.19–0.24 and bubble pumping at StD = 0.06–0.08 occurs for the axisymmetric blunt-based model. At boattail angles up to 16°, those frequencies are clearly distinguished from the time series of POD modes of the velocity fluctuations. However, for higher angles, the motions of the "bubble pumping" and vortex shedding combine to generate frequencies in the range of StD = 0.07–0.15. The fully separated flow disturbs a ratio of one-third for the bubble pumping and vortex shedding frequencies, which was shown widely in previous studies. The reduction of frequency band and large-scale features for boattail angles of 16° explains the low drag generated for that configuration. [ABSTRACT FROM AUTHOR]

We present a formulation of proper orthogonal decomposition (POD) producing a velocity–temperature basis optimized with respect to an H1 dissipation norm. This decomposition is applied, along with a conventional POD optimized with respect to an L2 energy norm, to a dataset generated from a direct numerical simulation of Rayleigh–Bénard convection in a cubic cell (Ra = 10 7 , Pr = 0.707). The dataset is enriched using symmetries of the cell, and we formally link symmetrization to degeneracies and to the separation of the POD bases into subspaces with distinct symmetries. We compare the two decompositions, demonstrating that each of the 20 lowest dissipation modes is analogous to one of the 20 lowest energy modes. Reordering of modes between the decompositions is limited, although a corner mode known to be crucial for reorientations of the large-scale circulation is promoted in the dissipation decomposition, indicating suitability of the dissipation decomposition for capturing dynamically important structures. Dissipation modes are shown to exhibit enhanced activity in boundary layers. Reconstructing kinetic and thermal energy, viscous and thermal dissipation, and convective heat flux, we show that the dissipation decomposition improves overall convergence of each quantity in the boundary layer. Asymptotic convergence rates are nearly constant among the quantities reconstructed globally using the dissipation decomposition, indicating that a range of dynamically relevant scales is efficiently captured. We discuss the implications of the findings for using the dissipation decomposition in modeling and argue that the H1 norm allows for a better modal representation of the flow dynamics. [ABSTRACT FROM AUTHOR]

This work presents a post-data analysis procedure, namely, proper orthogonal decomposition (POD)–dynamic mode decomposition (DMD)–discrete Fourier transform analysis, for evaluating the dominant features of the flow fields from both energetic and dynamic perspectives. The large-eddy simulation (LES) was first employed to reproduce the flow field surrounding three types of building layouts. Subsequently, both POD and DMD were conducted according to LES simulation results. The extracted modes were classified into three types based on the POD and DMD: Type-1 mode: energetically and dynamically significant mode, Type-2 mode: energetically significant and dynamically insignificant mode, and Type-3 mode: energetically insignificant and dynamically significant mode. The findings indicate that Type-1 mode governs the primary velocity field and the predominant vortex patterns observed at the rear of the building arrays, as the reduction of inter-building widths leads to a shorter flow separation region. Type-2 mode is characterized by the presence of small-scale vortices and the high turbulent kinetic energy region, which periodically triggers pollutant increase in the vicinity of structures. Type-3 mode demonstrates a minimal energetic influence on the flow field; nevertheless, it significantly contributes to the consistent build-up of pollutants within the far-wake region. The present study also investigates the predominant coherent structures of flow fields concerning various building layouts and highlights the influence of passage widths on the efficiency of pollutant removal. This comprehensive analysis enables a systematic exploration of flow patterns within various building layouts, offering potential solutions for pollutant dispersion challenges in metropolitan areas. [ABSTRACT FROM AUTHOR]

This study utilized high-speed camera and large eddy simulation methods to explore the cavitating flow mechanisms and turbulence structures of R134a refrigerant inside a Venturi tube under varying cavitation numbers (CNs). Data-driven modal analysis approaches, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), were introduced to identify and extract the energy hierarchy and transient characteristics within the cavitating flow. The analysis of grayscale images indicated that the cavitating flow gradually transitioned from quasi-periodic to unsteady flow as the CN decreased, and the severity of cavitation correlates with lower peak frequencies. The POD analysis facilitated the extraction of coherent structures in the cavity's temporal evolution, and the results indicate that the quasi-ordering shedding and collapse of large-scale cavity clouds predominantly occur under low cavitation intensity conditions. As the CN increases, the influence of small-scale cavity shedding becomes more significant. The first 30 most energetic modes occupied over 75% of the entire energy, and they were used to reconstruct the cavitating flow, achieving good consistency with transient flow snapshots. Additionally, the DMD results of the cavitating flow yield three frequency spans, including several prominent characteristic frequencies. These spans are closely linked to the cavity cloud structures of varying scales, unveiling the structural characteristics of unsteady cavitating flow. [ABSTRACT FROM AUTHOR]

Reduced-order models (ROMs) have been extensively employed to understand complex systems efficiently and adequately. In this study, a novel parametric ROM framework is developed to produce Eulerian–Lagrangian simulations. This study employs two typical parametric strategies to reproduce the physical phenomena of a gas–solid flow by predicting the adequate dynamics of modal coefficients in the ROM: (i) based on the radial-basis function (RBF) interpolation, termed ROM-RBF and (ii) based on a long–short term memory (LSTM) neural network, termed ROM-LSTM. In the ROM, an advanced technique, namely, Lanczos-based proper orthogonal decomposition (LPOD), is employed to efficiently transform numerical snapshots into the modal coefficients. Validation tests are conducted in a typical gas–solid flow system such as a spouted bed. The coherent structures of the gas–solid flows are shown to be captured by the LPOD technique. Besides, in comparison with the high-fidelity simulations, our proposed ROMs are shown to simulate the gas–solid flows by significantly reducing the calculation time by several orders of magnitude and faithfully predicting the macroscopic properties. In particular, compared to the ROM-RBF, the ROM-LSTM can capture the flow fields more accurately within the gas–solid flows. [ABSTRACT FROM AUTHOR]

The efficiency of adjoint-based aerodynamic shape optimization depends critically on the solution efficiency of adjoint equations. In this letter, we employ the Proper Orthogonal Decomposition (POD) method to analyze the adjoint field samples and project them from the physical space into a low-order modal space. Subsequently, the full-order adjoint equations are reduced to low-order equations using the POD modes. Thus, we can efficiently predict the initial values for pseudo-time marching, thereby accelerating the solution of adjoint equations. Results indicate that the high-order POD modes are crucial for constructing the low-dimensional system. Moreover, this method can be seamlessly integrated with our previously established Dynamic Mode Decomposition (DMD) acceleration method to form a POD+DMD acceleration approach. Application of this approach to the flow past a National Advisory Committee for Aeronautics 0012 airfoil demonstrates a noteworthy 80.9% reduction in iteration numbers when solving the adjoint equations. Even for the airfoil located on the upper boundary of sampling space, the number of iterations is still reduced by 72.6%. Therefore, we believe that the proposed method holds significant promise for improving the efficiency of adjoint-based aerodynamic shape optimization in future research. [ABSTRACT FROM AUTHOR]

The forced ignition instability and combustion instability in a scramjet engine were investigated experimentally and numerically using modal analysis. In this study, proper orthogonal decomposition (POD) was applied to OH+ chemiluminescence image data obtained during previous supersonic combustion experiments. In this scramjet combustor, a microrocket torch was installed in the cavity. First, to clarify the combustion instability phenomenon in the cavity and flow paths, a POD analysis was performed using the OH+ chemiluminescence image data. The maximum power spectrum density peak shifted to the high-frequency region in high-order modes. The combustion oscillations between 100 and 500 Hz were attributed to injector flame feedback from the fuel or torch jet gas because the fuel and torch gas were directly injected into the shear layer, where fuel combustion occurred. Next, to clarify the forced ignition instability phenomenon in the cavity, the POD modes near the torch jet orifice were investigated. The low frequencies near the torch jet orifice within the cavity were likely associated with the torch gas injector flame feedback because the frequency spectra of the inner pressure oscillations in the micro-rocket torch matched the frequency spectra peak near the torch jet orifice in the cavity. [ABSTRACT FROM AUTHOR]

The present study investigates unsteady wake dynamics in flow past an oscillating cylinder. A two-dimensional computational analysis is undertaken for flow past a sinusoidally oscillating cylinder. Operating parameters like Reynolds number, forcing frequency, amplitude, and wavelength are systematically varied, and their effect on wake dynamics is investigated. Lift and drag coefficients are plotted with cylinder position to characterize the flow. The flow field is analyzed using Proper Orthogonal Decomposition (POD). POD mode shapes and Power Spectral Density (PSD) plots characterize the flow response to cylinder oscillations. The effect of frequency ratio is examined in achieving synchronized vortex shedding. Previous studies focus on two extremes- the cylinder is either stationary or oscillating with perfect phase-locking. Flow past an oscillating cylinder where Karman and forcing frequencies compete for dominance is rarely reported. This paper considers such a scenario and demonstrates how POD can identify coherent structures, their significance, and associated frequencies. Further, non-symmetric vortex shedding, which is not a common observation, is captured and discussed. Large amplitude and large wavelength regimes are investigated, which remained unexplored in previous research. Coherent structures associated with those regimes are identified. [ABSTRACT FROM AUTHOR]

Two-body aerodynamic analysis is crucial whenever there is a store that separates from its parent body, i.e., the aircraft. Any time that a new aircraft is developed or an existing one undergoes some modification with its associated store, it has to undergo a meticulous analysis to predict the path of the separated store across a range of operating parameters (freestream conditions). The present work demonstrates an efficient albeit approximate semi-empirical technique that employs a reduced-order model based on proper orthogonal decomposition in conjunction with a multi-domain-decomposition approach for predicting the flow field around a store-aircraft dyad. Encouraging preliminary results are obtained in the verification that is pursued on a two-dimensional problem for simplicity. The approach can be readily extended to three-dimensional problems as well. [ABSTRACT FROM AUTHOR]

The planar laser induced hydroxyl fluorescence (OH-PLIF) technique was used to study three kinds of swirling flame, namely flames I, II, and III, by changing swirl conditions. According to the PLIF results, double structure exists in flames I and II. The inner flame burns in the inner shear layer and is anchored by vortex breakdown, which is similar to the M- or V-shaped flame. The unique outer flame is attached to the inner wall of the air annular nozzle and burns in the outer shear layer. The lean blowout (LBO) equivalent ratio of swirling flame with outer flame is lower than that without outer flame. It is interesting to compare the LBO mechanisms among the three types and the traditional swirling flame, and investigate their unsteady characteristics. Firstly, the flameout process of flames I and II starts from the local extinguishing at the root of the outer flame. However, the LBO process of flame III is consistent with that of traditional swirling flame, that is, it starts with repeated extinguishing and reigniting at the root of the inner recirculation zone (IRZ). Secondly, the unsteady characteristics of the three flames are analyzed by spectral proper orthogonal decomposition. It is found that flame oscillations, asymmetric disturbances, and longitudinal disturbances of different frequencies exist in different combinations under near-LBO conditions. In particular, asymmetric and P-wave disturbances mainly exist in the inner shear layer and jet breaking down, which further indicates the stability and anti-LBO potential of the outer flame. [ABSTRACT FROM AUTHOR]

Jet fuel-fired combustors in aero gas turbine engines have switched to lean burn to decrease nitric oxide emissions in recent years as a result of strict emission regulations. Lean operating conditions, however, exhibit a heightened sensitivity to thermoacoustic instabilities and such burners require careful consideration in design and operation. Similar to natural gas-fired combustors, they exhibit thermoacoustic instabilities, but the characteristics are more complex and less well-studied. This paper presents a numerical investigation of an airblast jet fuel swirl burner operating with preheated air at lean pressurized conditions. In order to understand the acoustic characteristics of the in-house designed burner (Magister UT burner), detached eddy simulations are performed at relevant aero engine conditions. Simulation results are then analyzed by means of our internally developed parallel modal analysis package, PARAMOUNT, to perform proper orthogonal decomposition (POD) on large datasets. The resulting modes are inspected to highlight flow features of interest and their associated acoustic frequencies at unforced conditions. Single frequency acoustic forcing is employed to study the acoustic response of the burner to perturbations at similar frequencies to its precessing vortex core. We show that parallel computation of POD modes is a viable tool to investigate the main flow features of swirl burners and is suitable for highlighting the important acoustic frequencies without the need to employ fully compressible computational fluid dynamics solvers. Additionally, the analysis method reveals the ways in which various flow structures correlate with each other and how external perturbations modify them. [ABSTRACT FROM AUTHOR]

Chaotic time series prediction is a central science problem in diverse areas, ranging from engineering, economy to nature. Classical chaotic prediction techniques are limited to short-term prediction of low- or moderate-dimensional systems. Chaotic prediction of high-dimensional engineering problems is notoriously challenging. Here, we report a hybrid approach by combining proper orthogonal decomposition (POD) with the recently developed next generation reservoir computing (NGRC) for the chaotic forecasting of high-dimensional systems. The hybrid approach integrates the synergistic features of the POD for model reduction and the high efficiency of NGRC for temporal data analysis, resulting in a new paradigm on data-driven chaotic prediction. We perform the first chaotic prediction of the nonlinear flow-induced vibration (FIV) of loosely supported tube bundles in crossflow. Reducing the FIV of a continuous beam into a 3-degree-of-freedom system using POD modes and training the three time coefficients via a NGRC network with three layers, the hybrid approach can predict time series of a weakly chaotic system with root mean square prediction error less than 1% to 19.3 Lyapunov time, while a three Lyapunov time prediction is still achieved for a highly chaotic system. A comparative study demonstrates that the POD-NGRC outperforms the other existing methods in terms of either predictability or efficiency. The efforts open a new avenue for the chaotic prediction of high-dimensional nonlinear dynamic systems. [ABSTRACT FROM AUTHOR]

In this paper, we construct a reduced-order finite element (ROFE) method holding seldom unknowns for the parabolic optimal control problem. We apply the proper orthogonal decomposition (POD) technique to develop two unsteady systems about state and co-state approximations, which efficiently reduces the number of unknowns and computational costs. Optimal a priori error estimates for the state, co-state and control approximations are derived. Finally, numerical examples are presented to verify that the ROFE method is accurate and efficient for solving the parabolic optimal control problem. [ABSTRACT FROM AUTHOR]

The second-mode instability on a 7° half-angle sharp cone at Mach 6 is analyzed using high-speed calibrated schlieren imagery at a frame rate near the expected fundamental frequency. Experiments were conducted in the NASA Langley 20-Inch Mach 6 facility at unit Reynolds numbers between 6.56 × 10 6 and 9.71 × 10 6 m - 1 . Time-resolved pixel intensity signals throughout the boundary layer are reconstructed using spatially available data in the schlieren images to recover an effective sampling rate of over 10 MHz; these are then converted to quantitative density gradients using a thin-lens-based calibration technique. A global analysis is performed on the schlieren data to investigate the nonlinear growth of the second-mode fundamental and harmonic content. Pointwise measures of the autobicoherence are used to identify specific triadic interactions and the locations of their highest levels of quadratic phase coupling. Significant resonance interactions between the second-mode fundamental and harmonic instabilities were found along with interactions between these and the mean flow. Bispectral mode decomposition is employed to educe the flow structures associated with these interactions. A similar analysis is performed for the power spectrum, with power spectral densities computed for each pixel's time-series and spectral proper orthogonal decomposition employed to derive the modal structure and energy of the flow at specific frequencies. Comparisons between the bispectral quantities and second-mode power show that nonlinear interactions, particularly resonance interactions, are closely correlated with spatiotemporal modulation of disturbances during the nonlinear stage of transition. [ABSTRACT FROM AUTHOR]

The influence of incoming freestream turbulence on an elastically mounted circular cylinder undergoing vortex-induced vibrations is investigated through simultaneous displacement and flow field measurements at a constant Reynolds number of approximately 4400. The results show that the effects of freestream turbulence are more prominent within the lower branch and desynchronization, where earlier desynchronization is observed with elevated freestream turbulence. Conversely, freestream turbulence minimally affects the structure and wake dynamics within the initial and upper branches. A comparison between a stationary cylinder wake and the wake of a cylinder free to vibrate at very low amplitudes reveals that even minor cylinder vibrations (≈ 1% of cylinder diameter) modify the separated shear layer and near wake dynamics, the result of which is a decreased sensitivity of the near wake to freestream turbulence. Proper orthogonal decomposition is used to identify changes in the vortex shedding characteristics that result in earlier desynchronization. [ABSTRACT FROM AUTHOR]