Search Results (337)

High-fidelity reservoir simulation is too costly for multi-query tasks such as history matching and production optimisation. Existing reduced-order models (ROMs) mitigate this cost but generally lack uncertainty quantification, spatial sparsity, and interpretable mode-to-geology mappings. We introduce USX-PGD (Uncertainty-aware, Sparse, and eXplainable Proper Generalised Decomposition), a non-intrusive ROM for two-phase immiscible flow that addresses all three gaps within a single greedy Alternating Least Squares framework. USX-PGD is benchmarked against Proper Orthogonal Decomposition (POD), standard Proper Generalised Decomposition (PGD), and an intermediate Uncertainty-aware Sparse PGD (US-PGD) variant, on a formation-aware upscaled coarse-grid ($30\times 110\times 34$ cells) representation of the SPE10 Model 2 benchmark, a heterogeneous two-phase reservoir with permeability contrasts spanning six orders of magnitude. US-PGD adds sparsity-promoting thresholding and bootstrap resampling to certify a confidence interval on reconstruction accuracy; USX-PGD further adds formation energy decomposition, mode dominance mapping, breakthrough attribution, and mode sensitivity indexing, attributing the reduced-order modes to identifiable geological formations. All four methods reproduce the reference production curves to within $11.03$–$11.05\%$ NRMS at online reconstruction times of 51–63 ms; the sparse and explainable variants achieve comparable accuracy while additionally providing $41.8\%$ spatial sparsity and a certified $95\%$ confidence interval. All four ROMs compress and replay an already-simulated trajectory, not predict new, unsimulated scenarios; USX-PGD is offered as a reproducible, physically transparent foundation for such multi-query workflows, with predictive extension identified as future work. Full article

The temperature field of a high-voltage direct-current (HVDC) cable governs its current rating and insulation lifetime and must therefore be predicted accurately across diverse operating conditions. Finite-element (FE) simulation is accurate but too costly for repeated evaluation, whereas data-driven reduced-order models (ROMs) often extrapolate poorly beyond the training-current range. This paper proposes a physics-structured POD–neural ROM to address this limitation. Specially, proper orthogonal decomposition (POD) compresses the three-dimensional temperature-rise field into a few modal coefficients, which are predicted from the operating conditions by a neural network. The key innovation is to embed the Joule-heating law directly into the architecture: the leading coefficient is represented as a current-squared factor multiplied by a learned current-independent shape. This construction guarantees the correct current scaling of the dominant mode, including its zero-current limit and extrapolation beyond the training range. On FE data for an eight-layer cross-linked polyethylene cable, the model achieves 2.4% mean relative error under current extrapolation and remains below 5% at twice the maximum training current, outperforming Gaussian-process, dynamic-mode-decomposition, autoregressive, and black-box baselines. The full field is evaluated in approximately one millisecond per condition, with a cost independent of the training-set size. Controlled ablations show that the improvement arises from structurally enforcing the scaling law rather than merely supplying $I^2$ as an input feature. Embedding known physical scaling into a surrogate architecture therefore provides a principled route to reliable extrapolation. Full article

The combustion temperature field is a key indicator of combustion stability, equipment integrity, and abnormal operating conditions. This study addresses short-horizon forecasting of laboratory-scale apparent infrared temperature fields using a Convolutional Long Short-Term Memory (ConvLSTM) network. A chronological 70/15/15 split is applied to 1800 available sequences, with the first 10 frames of each sample treated as observed inputs. Proper orthogonal decomposition (POD) is applied exclusively to the input frames at a 95% cumulative energy retention threshold, and predictions are evaluated on subsequent frames. POD is therefore used as an input-side low-rank modal preprocessing method to extract dominant coherent structures and suppress redundant variations, rather than as a reduction in the ConvLSTM network architecture itself. Performance is assessed via normalized domain PSNR/SSIM and Kelvin domain errors. The first three forecast steps maintain appreciable image similarity, while the fourth and fifth steps exhibit marked degradation. Therefore, conclusions are restricted to short-horizon forecasting, with no assertions regarding closed loop combustion control or cross-setup generalization. Simultaneously, ablation experiments with the same architecture, including and excluding the POD preprocessing step, quantified the individual contribution of the POD preprocessing step. Full article

A rapid prediction framework for multi-physics field distributions in coal mine airways of variable lengths is presented. The framework integrates a Computational Fluid Dynamics model, a Proper Orthogonal Decomposition model, and machine learning techniques. The study first obtains multi-physics field distributions of temperature, velocity, species mass fraction, etc., in mining airways using CFD simulations under various operating parameters. It then constructs a POD model to decompose the high-dimensional raw snapshot data into mean field and pulsation field components, performing singular value decomposition on the pulsation field to obtain POD spatial modes and corresponding POD coefficients. Machine learning algorithms, including GA-BPNN and Bayes-XGBoost, are employed to construct predictive models of the POD coefficients. The results show that after fitting the relationship between operating parameters and POD coefficients, the multi-physics field distribution within the training parameter range can be rapidly predicted. When the cumulative energy contribution of POD modes exceeds 0.99 of the total energy, the Bayes-XGBoost model achieves minimum R² values of 0.9448, 0.9999, and 0.9996 for velocity, temperature, and oxygen mass fraction predictions, respectively. This work provides a practical engineering solution for real-time prediction of multi-physical fields in variable-length mine airways, and achieves fast and accurate prediction within the training parameter range. Full article

Nonlinear correlations among modal coefficients enable interpretable reduced-order models (ROMs) for microfluidic flows. In this study, flow around a cylinder in a microchannel at Re = 100 is investigated using proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and POD + DMD. The sparse identification of nonlinear dynamics (SINDy) is employed to identify nonlinear correlations among modal coefficients. The results show that the first POD mode contains 33% of the total kinetic energy, and the first 14 modes capture 99.2% of the energy. A minimal ROM with only two degrees of freedom is constructed, in which the real and imaginary parts of active modal coefficients differ in phase by π/2 and their magnitude equals the vortex-shedding fundamental frequency (1.067 Hz). Among sparse regression algorithms, the FROLS method yields the sparsest representation (sparsity rate 0.05), whereas other methods give sparsity rate > 0.3. Reducing the temporal resolution from 0.01 to 0.1 increases the manifold dynamics coefficient error from 0% to 0.56%. Only the ROMs built from POD + DMD and DMD preserve essential kinematic resolution. The POD-based ROM fails to maintain correct energy levels over long-time integration. Therefore, the nonlinear correlation between POD + DMD modal coefficients is recommended for developing ROMs in microchannel flows when accuracy, interpretability, and stability are considered together. Full article

Predicting the wind field around military vehicles during extended missions is crucial to avoid detectability by infrared (IR) devices. This is a challenging task because of the geometric complexity of the vehicles and the unpredictable nature of wind direction, which can shift abruptly and have a significant impact on the flow field and heat transfer. Computational fluid dynamics (CFD) is routinely used to calculate flow fields around ground vehicles. However, this requires extensive computational time and memory, making it unsuitable for real-time analysis. To address these challenges, this paper focuses on machine learning (ML) techniques for accurate wind field prediction in real time for unseen wind directions within the sampled range. Reduced order modeling (ROM) is used for dimensionality reduction of flow field data derived from high-fidelity CFD simulations. ML models are trained using low-dimensional data from the ROM, and the predicted low-dimensional data for unseen wind directions by the trained ML model is used to reconstruct the flow field. ROM, in conjunction with ML techniques, offers a substantial reduction in analysis time while maintaining the ability to predict the flow field accurately. In this study, a neural network architecture with three output formulations trained using ROM data was used for the predictions, and the accuracy of the formulations was evaluated by comparing them with the CFD results. An optimal ML model is identified by varying the number of hidden layers and neurons within those layers. The developed ROM- and ML-based approach was able to predict the unseen flow field in less than a second, while a single CFD simulation required approximately 2.6 h per wind direction. Full article

The snapshot proper orthogonal decomposition (POD) method relies on synchronously sampled datasets, significantly limiting its utility for analyzing asynchronous measurements in unsteady flow studies. This paper proposes a frequency-domain proper orthogonal decomposition (FDPOD) method tailored for mode extraction and flow field reconstruction from asynchronously sampled data. The FDPOD framework integrates three key components: frequency-domain transformation to decouple phase discrepancies inherent in asynchronous sampling, power spectral density (PSD) analysis combined with segmented ensemble averaging to suppress spectral leakage errors, and eigenvalue decomposition of energy-ranked frequency components to identify dominant coherent structures. Validated through numerical simulations of a subsonic jet and experimental measurements from a low-speed mixed-flow fan, the method demonstrates exceptional performance under asynchronous conditions: cumulative energy errors are reduced to 0.3% across the first 50 modes, while flow field reconstruction achieves 99.5% accuracy. Dominant mode structures exhibit remarkable consistency with those derived from synchronous conditions, with hot-wire measurement errors remaining below 0.03% for both asynchronous and temporally shuffled datasets. These results position FDPOD as a robust and practical tool for analyzing complex unsteady flows where synchronous data acquisition proves impractical, particularly in large-scale or spatially distributed measurement systems. Full article

This study investigates the coupling between flow dynamics, acoustic response, and convective heat transfer in a rectangular impinging jet striking on a heated slotted plate at two closely spaced Reynolds numbers (Re = 3550 and Re = 3750). Velocity fields were obtained using Particle Image Velocimetry (PIV), and coherent structures were analyzed using Proper Orthogonal Decomposition (POD) while acoustic measurements were used to characterize the tonal behavior. Infrared thermography was employed to determine local and mean Stanton numbers. The mean Stanton number increased by 6.6% when the Reynolds number increased from Re = 3550 to Re = 3750, while the sound pressure level decreased from 78 dB to 71 dB. At Re = 3550, the acoustic spectrum exhibited multi-tone behavior associated with distributed modal energy. In contrast, at Re = 3750, a single dominant frequency governed the flow dynamics. The energy of the first POD mode nearly doubled when passing from Re = 3550 to Re = 3750. The cross-correlation coefficients between the first POD mode and the acoustic field increase from 0.76 to 0.93 when changing from Re = 3550 to Re = 3750. These findings show that the dominant vortex mode which contains nearly 20% of the fluctuating energy (for Re = 3750), significant influences the energy transfer from the dynamic field to the acoustic field resulting in a strong noise reduction. Simultaneously, convective heat transfer increases, highlighting the key role of coherent flow organization on both acoustic and thermal behavior of the system. Full article

In the design of structural wind resistance, it is necessary to consider the combination of load effect extremum caused by each wind component. The existing combination rules for Gaussian wind load effects are not applicable to the combination of non-Gaussian wind load effects. The Hermite polynomial transformation model is employed to transform the non-Gaussian wind effect process based on a potential standard Gaussian process in this paper. The probability distributions of the non-Gaussian wind effect process and the non-Gaussian peak factor are deduced. A simplified TR1 (Turkstra) combination equation for the two-component non-Gaussian wind effect process and a numerical integration expression for the TR2 combination rule are proposed. The improved simplified CQC (complete quadratic combination) equations for two-component non-zero-mean softening and hardening non-Gaussian wind effect processes are derived. The accuracy and validity of these simplified combination equations are verified using the Monte Carlo simulation method. Full article

Local scour and vortex-induced vibrations around cylindrical structures in curved channels pose significant risks to the safety and stability of critical hydraulic infrastructure, such as bridge piers. To address these engineering challenges and elucidate the underlying flow mechanisms, this study conducts numerical simulations of flow past two side-by-side circular cylinders of equal diameter in a curved channel under subcritical conditions at Re = 3900, using the Realizable kε turbulence model. Spectral Proper Orthogonal Decomposition (SPOD) is introduced to quantitatively characterize the energy distribution and dominant coherent structures. Taking the spacing ratio L/D and the placement angle α as key design parameters, the flow field characteristics, modal energy distribution, and coherent structure evolution are systematically investigated for two side-by-side cylinders in three-dimensional straight and curved channels. The numerical results show that, in the straight channel, as L/D increases from 2 to 4, the flow field evolves from strong coupled interference to weak interaction. The vortex shedding frequency structure evolves from a single dominant frequency to a multi-frequency distribution with rich harmonic components, indicating a transition in wake dynamics from energy concentration to multimodal dispersion, accompanied by a significant improvement in flow stability. Under curved channel conditions, the results reveal an asymmetric flow field caused by pronounced energy concentration on the inner side of the channel. SPOD analysis further indicates that as the placement angle α increases from 30° to 90°, the modal energy distribution changes from concentrated to dispersed, the frequency spectrum broadens with enhanced harmonic components, and flow instability gradually intensifies. Overall, the spacing ratio L/D mainly governs the wake-interference pattern, whereas the placement angle α regulates the frequency structure and energy distribution. Among all the cases investigated, relatively favorable flow stability is achieved at L/D = 4 and α = 30°. The SPOD-derived modal energy distributions show that the streamwise fluctuation length of the dominant-mode energy is approximately 0.25 m at α = 30°, compared with 0.5 m at α = 90°, with the energy bandwidth nearly doubling. The combined CFD-SPOD approach effectively captures energy evolution and coherent structure characteristics of complex flows across spatial, temporal, and spectral dimensions. This enables a shift from conventional flow-field description to frequency-based mechanism analysis and provides a theoretical basis for structural layout optimization and scour protection in hydraulic engineering. Full article

While gas-turbine combustors have received much research attention, the forced response of large atmospheric industrial flames is much less studied. To improve the understanding of thermoacoustic instabilities in industrial combustion systems, the forced response of a large natural-gas fired test furnace is computed using Scale-Adaptive Simulations (SASs) with a Flamelet Generated Manifold model. Two test burner configurations are compared. One produces a partially premixed flame (case P) and the other a non-premixed flame. Furthermore, the non-premixed configuration is simulated at both a slightly rich (case N) and a slightly lean set point (case NL). The flame is forced by perturbing the airflow using a superposition of sine waves at four discrete frequencies. That way, the gain and phase of the Flame Transfer Function (FTF) are determined in three simulations for a total of 12 discrete frequencies between 10 and 230 Hz. The results show very different behaviour of the partially premixed and non-premixed configurations. Case P is simulated to be a compact flame, with a maximum FTF gain of one around 70–80 Hz and a quasi-steady limit of 0.7. Case N and NL are characterised by slightly lifted flames acting as low-pass filters that quickly drop off towards higher frequencies. While the phase shift in case P is linearly dependent on frequency and can be related to its flame length, the non-premixed cases have a sharp initial phase shift that levels off with increasing frequency as the gain reduces to zero. Importantly, a non-zero phase shift at 0 Hz is observed for case NL. The nature of the combustion dynamics is further explored by a Proper Orthogonal Decomposition (POD) analysis. The FTFs are applied to predict the thermoacoustic stability using an Acoustic Network Model (ANM). This model is able to reproduce the stability of the cases observed in experiments. The results presented in this study provide insight on the effect of mixing and stoichiometry on the stability of large industrial furnaces. Full article

To better understand the impact that multi-scale unsteadiness has on industrial flows, we use Large Eddy Simulation (LES) data representative of a midspan compressor section operating in an idealized multi-stage environment. We collect a large number of three-dimensional flow snapshots and perform a large-scale flow decomposition using a parallel framework based on the Proper Orthogonal Decomposition (POD). Once the flow is split into orthogonal modes, we quantify kinetic energy budgets on a mode-by-mode basis. This enables us to characterize energy exchanges between these modes and analyze the flow in a multi-scale manner. As a result we are able to reconstruct an approximate energy cascade within the domain. The results provide insights into the role that various scales play in modulating the energy transfer within the flow. This work is a stepping stone towards utilizing all the information embedded in the 3D unsteady flowfield and its evolution for the purpose of informing turbulence modeling. Full article

Transient analyses of liquid-fueled molten salt reactors involve strong coupling among neutronics, delayed neutron precursor transport, thermal–hydraulics, and solid heat transfer, leading to high computational costs for repeated high-fidelity simulations. To enable fast multi-physics prediction at unseen operating conditions, a parametric non-intrusive reduced-order model (ROM) combining proper orthogonal decomposition (POD) and higher-order dynamic mode decomposition (HODMD) is developed. Coupled full-order snapshots generated from an OpenFOAM-based one-eighth symmetric core model based on a simplified MSRE benchmark configuration are used to construct reduced representations for 11 physical fields. The POD truncation rank, HODMD delay dimension, and interpolation model are selected using leave-one-out cross-validation, with polynomial, radial basis function, and Gaussian process regression models considered as interpolation candidates. For unseen parameter points, the model maintains high accuracy in both the interpolation stage and the temporal extrapolation stage. In the temporal extrapolation stage, the highest mean relative $L_2$ error for the inlet-temperature-step case is $2.112\%$, whereas all mean relative $L_2$ errors for the inlet-velocity-step case remain below $0.177\%$. The results indicate that, under the present cases and parameter settings, the proposed framework provides an accurate and rapid surrogate for multi-physics transient prediction. Full article

Sweeping jet (SWJ) actuators are widely used in active flow control, but explicitly resolving actuator-scale unsteadiness in full-configuration computational fluid dynamics (CFD) remains prohibitively expensive because of the small geometric scales and high-frequency oscillations involved. Existing reduced-order boundary-condition models constructed from exit-plane data alone can reproduce the observed switching waveform, but they treat the actuator as an input–output black box and provide limited insight into the internal dynamics that generate the response. This work develops a causal state-space reduced-order modeling framework that links internal mixing-chamber dynamics to time-resolved exit-plane boundary conditions. Proper orthogonal decomposition (POD) is used to obtain a low-dimensional representation of the internal flow, and a data-driven linear evolution operator is identified in the reduced space by least-squares regression of successive snapshot pairs. A POD truncation rank of $r=60$ is selected from cumulative-energy and validation-error sensitivity analyses, capturing well above 99% of the fluctuation energy while lying within the converged performance regime. A corresponding reduced operator is identified for the exit plane, and spectral comparison reveals near-neutrally stable oscillatory modes in both regions. Using a $\pm 1\%$ relative frequency-matching tolerance, the dominant reduced-operator modes exhibit a 28.3% frequency overlap, providing operator-level evidence that exit-plane oscillations are dynamically linked to internal coherent structures. This correspondence is further supported by cross-spectral coherence analysis between representative internal and exit-plane probe signals, which shows strong coherence at dynamically relevant frequencies. A delayed causal output mapping is then formulated in which the internal reduced state drives the exit-plane response after an identified lag of 149 time steps, corresponding to $2.98\times {10}^{-3}$ s. This delay provides a physically interpretable convective transport timescale from the mixing chamber to the actuator exit. Over the validation interval, the model maintains a mean relative $L_2$ error below 0.02, with maximum normalized errors below 0.04 for most of the prediction horizon, and localized increases are confined to rapid jet-switching events. Field-level reconstructions of streamwise velocity and total pressure show that the model captures both phases of the jet-switching cycle, with errors concentrated primarily in high-gradient shear-layer regions. Compared with exit-only reduced-order models, the proposed internal-driven formulation improves amplitude and phase fidelity over extended prediction horizons. The resulting framework provides a compact, interpretable, operator-based representation of SWJ actuator dynamics suitable for use as a CFD-embeddable dynamic boundary condition. Full article

The accurate reconstruction and real-time prediction of transient three-dimensional flow fields in hydraulic turbines are critical for ensuring operational stability under renewable energy-driven variable-load conditions, yet conventional computational fluid dynamics (CFD) approaches remain too computationally expensive for digital twin applications. This paper proposes a hybrid framework that integrates Proper Orthogonal Decomposition (POD) with Long Short-Term Memory (LSTM) networks to reconstruct and predict the unsteady flow field within the draft tube of a Francis turbine using only four sparse wall-mounted pressure sensors. The methodology begins with high-fidelity Large Eddy Simulation (LES) to establish a comprehensive flow field database under Part Load (PL), Best Efficiency Point (BEP), and High Load (HL) conditions. POD is subsequently applied to extract dominant coherent structures and their temporal coefficients, achieving a low-dimensional representation of the high-dimensional flow field. A comparative analysis between standard POD and weighted POD reveals that under the PL condition characterized by a strong double-helical vortex rope, the weighting effect is significant—standard POD captures 90% of the total energy with the first 2 modes, while weighted POD requires up to 8 modes to reach the same threshold. Under the BEP and HL conditions, the energy distributions of the two methods are nearly identical, yet weighted POD still yields cleaner spatial modes with sharper vortex boundaries and fewer spurious wall-region vortices. An LSTM network is then trained to establish a mapping between time-series signals from the four sensors and the POD temporal coefficients. The results demonstrate that LSTM prediction performance is governed by the spatial correlation between each mode and the sensor locations rather than by temporal regularity. Modes that project strongly onto the sensor locations—PL Modes 1–2 (R² = 0.85 and 0.513), BEP Mode 1 (R² = 0.96), and HL Mode 1 (R² = 0.92)—are reliably predictable, while PL Mode 3 and HL Mode 2, despite their regular temporal oscillations, yield strongly negative R² values (−3.366 and −186.6) because their spatial structures are concentrated away from the wall. With a condition-adaptive strategy predicting only sensor-correlated, energetic modes, the reconstructed pressure fields achieve mean L2 relative errors of 17.01% (PL), 7.17% (BEP), and 12.91% (HL). Because the mean flow dominates total pressure energy (86.66–98.07%), the effective absolute error is substantially lower. The proposed POD-LSTM framework successfully bridges the gap between high-fidelity CFD and real-time monitoring, enabling full-field flow state estimation from sparse sensor measurements without the computational expense of online simulations. This capability is particularly valuable for digital twin applications in hydraulic turbines operating under rapidly varying renewable energy conditions. Full article