Prediction Of Velocity Fields Research Articles

Fast Spatiotemporal Sequence Graph Convolutional Network-based transient flow prediction around different airfoils

A novel Spatiotemporal Sequence Graph Convolutional Network (ST-SGCN) data-driven model is proposed to predict transient fluid dynamics around airfoils using complex and unstructured flow field data, with the aim of reducing dimensions and expediting predictions. Graph Neural Networks directly interact with the flow field grid, capturing spatiotemporal physical features of grid nodes and their interconnections, while eliminating the need for complex preprocessing steps. The ST-SGCN model integrates a Graph Convolutional Network and a Graph Attention Network with a Deep Recurrent Neural Network that uses a Gate Recurrent Unit as the kernel, adeptly extracting spatial and temporal physical features of the flow field to accurately predict transient flow states. Preliminary airfoil flow experiments demonstrated the model's ability to continuously predict transient flow fields, achieving an average accuracy of 97% for both velocity and pressure field predictions, with a maximum error of approximately 10% in the testing dataset. Further experiments, varying angles of attack, airfoils, and Reynolds numbers, demonstrated the model's generalizability, extensibility, and adaptability, with prediction errors below 5% and a speedup of over 20 times.

Toward ultra-efficient high-fidelity predictions of wind turbine wakes: Augmenting the accuracy of engineering models with machine learning

This study proposes a novel machine learning (ML) methodology for the efficient and cost-effective prediction of high-fidelity three-dimensional velocity fields in the wake of utility-scale turbines. The model consists of an autoencoder convolutional neural network with U-Net skipped connections, fine-tuned using high-fidelity data from large-eddy simulations (LES). The trained model takes the low-fidelity velocity field cost-effectively generated from the analytical engineering wake model as input and produces the high-fidelity velocity fields. The accuracy of the proposed ML model is demonstrated in a utility-scale wind farm for which datasets of wake flow fields were previously generated using LES under various wind speeds, wind directions, and yaw angles. Comparing the ML model results with those of LES, the ML model was shown to reduce the error in the prediction from 20% obtained from the Gauss Curl hybrid (GCH) model to less than 5%. In addition, the ML model captured the non-symmetric wake deflection observed for opposing yaw angles for wake steering cases, demonstrating a greater accuracy than the GCH model. The computational cost of the ML model is on par with that of the analytical wake model while generating numerical outcomes nearly as accurate as those of the high-fidelity LES.

ST-LSTM-SA: A New Ocean Sound Velocity Field Prediction Model Based on Deep Learning

ST-LSTM-SA: A New Ocean Sound Velocity Field Prediction Model Based on Deep Learning

Fast Aerodynamic Prediction of Airfoil with Trailing Edge Flap Based on Multi-Task Deep Learning

Conventional methods for solving Navier–Stokes (NS) equations to analyze flow fields and aerodynamic forces of airfoils with trailing edge flaps (TEFs) are known for their significant time cost. This study presents a Multi-Task Swin Transformer (MT-Swin-T) deep learning framework tailored for swift prediction of velocity fields and aerodynamic coefficients of TEF-equipped airfoils. The proposed model combines a Swin Transformer (Swin-T) for flow field prediction with a multi-layer perceptron (MLP) dedicated to lift coefficient prediction. Both networks undergo gradient updates through the shared encoder component of the Swin Transformer. Such a trained network model for computational fluid dynamics simulations is both effective and robust, significantly improving the efficiency of complex aerodynamic shape design optimization and flow control. The study further investigates the impact of integrating multi-task learning loss functions, skip connections, and the network’s structural design on prediction accuracy. Additionally, the effectiveness of deep learning in improving the aerodynamic simulation efficiency of airfoils with TEF is examined. Results demonstrate that the multi-task deep learning approach provides accurate predictions for TEF airfoil flow fields and lift coefficients. The strategic combination of these tasks during network training, along with the optimal selection of loss functions, significantly enhances prediction accuracy compared with the single-task network. In a specific case study, the MT-Swin-T model demonstrated a prediction time that was 1/7214 of the time necessitated by CFD simulation.

Enhancing hydrofoil velocity estimation through residual learning

Recovering flow states from limited observations provides supports for flow control and super-resolution. Advances in deep learning have made it possible to construct precise state estimators. In this work, a deep learning estimator with an initialization branch and a residual branch is proposed to predict velocity fields from sparse pressure on the hydrofoil surface. In detail, on the one hand, the pre-trained proper orthogonal decomposition-based model as an initialization branch is employed to generate initial predictions. On the other hand, the U-shaped neural network-based model as the residual branch is trained to learn the residual between the initial predictions and the ground truth. Compared to previous models, the proposed model not only enhances prediction accuracy but also improves the interpretability of the model. Furthermore, the incorporation of the initialization branch has little influence on training and inference speed. Test results illustrate that residual learning provides additional model capacity for improving the prediction of transverse velocity fields and flow details. Moreover, even in the presence of intense velocity fluctuations near the trailing edge, predictions from the improved model are more consistent with ground truth. Visualization of feature maps underscores a significant advantage of the improved model over the baseline model in terms of structural features and increased distinctiveness among features, thereby facilitating interpretability enhancements.

Physics-informed neural networks for heat transfer prediction in two-phase flows

This paper presents data-driven simulations of two-phase fluid processes with heat transfer. A Physics-Informed Neural Network (PINN) was applied to capture the behaviour of phase interfaces in two-phase flows and model the hydrodynamics and heat transfer of flow configurations representative of established numerical test cases. The developed PINN approach was trained on simulation data derived from physically based Computational Fluid Dynamics (CFD) simulations with interface capturing. The present study considers fundamental problems, including tracking the rise of a single gas bubble in a denser fluid and exploring the heat transfer in the wake of a bubble rising close to a heated wall. Tracking of a rising bubble phase interface of fluids with disparate properties was performed, revealing a maximum error of only 5.2% at the interface edge and a maximum error of 2.8% at the position of the centre of mass. Inferred (hidden variable) flows are studied in addition to a purely extrapolative inverse isothermal bubble case. When no velocity data was supplied, velocity field predictions remained accurate. Rise of an inferred isothermal bubble with unseen fluid properties was found to produce a maximum mean-squared error of 0.28 and centre of mass error of 1.25%. For the case of the rising bubble with a hot wall, the maximum error in the temperature domain using specified boundary conditions was 6.8%, while the bubble position analysis reveals a maximum positional error of 3.6%. These results demonstrate that PINN is agnostic to geometry and fluid properties when studying the combined effects of convection and buoyancy on two-phase flows for the first time. This work serves as a starting point for PINN in multiphase cases involving heat transfer over a range of geometries. Eventually, PINN will be used in such cases to provide solutions for forward, inverse, and extrapolative cases. Each of which represent a dramatic saving in computational cost compared to traditional CFD.

Reconstruction and fast prediction of 3D heat and mass transfer based on a variational autoencoder

Reconstruction and fast prediction of heat and mass transfer are important for the improvement of data center operations and energy savings. In this study, an artificial neural network (ANN) and variational autoencoder (VAE) composite model is proposed for the reconstruction and prediction of 3D flowfields with high accuracy and efficiency. The VAE model is trained to extract features of the problem and to realize 3D physical field reconstruction. The ANN is employed to achieve the constructability of the extracted features. A dataset of steady temperature/velocity fields is acquired by computational fluid dynamics and heat transfer (CFD/HT) and fed to train the deep learning model. The proposed ANN-VAE model is experimentally proven to achieve promising field prediction accuracy with a significantly reduced computational cost. CFD/HT method is often incapable of occasions that require instant knowledge of heat and mass transfer. The proposed ANN-VAE method convert the time-consuming simulations into the training stage. Driven by large amount of simulation data, the trained ANN-VAE model is capable of field prediction. Compared to the CFD/HT method, the ANN-VAE method speeds up the physical field prediction by approximately 380,000 times, with mean accuracies of 97.3% for temperature field prediction and 97.9% for velocity field prediction, making it feasible for real-time prediction of heat and mass transfer.

A deep learning approach for velocity field prediction in a scramjet isolator from Schlieren images

Accurate measurements of physical parameters in a scramjet isolator are very important to promote the design and optimization of the isolator and even the scramjet. In a ground experiment, limited by the inherent characteristics of measurement technology and equipment, it is a big challenge to obtain the velocity field inside an isolator. In this study, a deep learning approach was introduced to combine data obtained from ground experiments and numerical simulations, and a velocity field prediction model was developed for obtaining the velocity field inside an isolator based on experimental Schlieren images. The velocity field prediction model was designed with convolutional neural networks as the main structure. Ground experiments of a scramjet isolator under continuous Mach number variation were carried out, and Schlieren images of the flow field inside the isolator were collected. Numerical simulations of the isolator were also carried out, and the velocity fields inside the isolator under various Mach numbers were obtained. The velocity field prediction model was trained using flow field datasets containing experimental Schlieren images and velocity field, and the mapping relationship between the experimental Schlieren images and the predicted velocity field was successfully established.

Prediction of 3D Velocity Field of Reticulated Foams Using Deep Learning for Transport Analysis

Data-driven deep learning models are emerging as a new method to predict the flow and transport through porous media with very little computational power required. Previous deep learning models, however, experience difficulty or require additional computations to predict the 3D velocity field which is essential to characterize porous media at the pore scale. We design a deep learning model and incorporate a physics-informed loss function that enforces the mass conservation for incompressible flows to relate the spatial information of the 3D binary image to the 3D velocity field of porous media. We demonstrate that our model, trained only with synthetic porous media as binary data without additional image processing, can predict the 3D velocity field of real reticulated foams which have microstructures different from porous media that were studied in previous works. Our study provides deep learning framework for predicting the velocity field of porous media and conducting subsequent transport analysis for various engineering applications. As an example, we conduct heat transfer analysis using the predicted velocity fields and demonstrate the accuracy and advantage of our deep learning model.

Transition of the Flow Regime Inside of Monolith Microchannel Reactors Fed with Highly Turbulent Flow

This paper investigates the flow behaviour of monolith microchannels. Specifically, the study characterizes the flow regime within in-series monolith channels where highly turbulent flow approaches them but inside of the channels, the Reynolds number is subcritical. Results from LES and a transitional RANS model are compared to those obtained when directly assuming laminar flow inside of the channels. A space-resolved model of channels placed in series and channel Reynolds numbers ranging from 50 to 300 are considered. The results show that the flow pattern in is almost identical in the two channels and that the frequency of fluctuations tends to increase with the Reynolds number. The flow regime in both channels is unsteady laminar, containing a wide spectrum of frequencies. The tested transitional RANS model (k-kL-ω) is unable to capture the velocity fluctuations predicted by LES. Despite the differences in the velocity field prediction, the pressure drop estimation from all models is practically the same. This study provides insights into the flow behaviour of monolith reactors and is useful for reactor design and optimization.

Transient velocity field prediction and uncertainty quantification of pump-jet propulsor using variational Bayesian neural networks

The study provides a fast and accurate variational Bayesian convolution neural network (VB–CNN) framework to obtain the pump-jet propulsor (PJP) transient velocity field. In practical engineering or experiments, it can obtain the transient velocity field of PJP only by discrete pressure points for different times conditions. Compared with the computational fluid dynamics (CFD) method, it can save a lot of computing time and computing resources. This study also uses the VB-CNN method to solve the problem of poor performance of CNN in small data-sets, VB-CNN method can consider the prior knowledge of PJP transient data to improve the prediction accuracy. The predicted values, errors and variances of the PJP transient wake velocity field and stator domain at different times and different rotating speed conditions are investigated. The uncertainty of the transient flow field is analyzed using 95% confidence intervals. It also uses GPU technology to improve training speed. The research results show that VB-CNN and CNN methods can better predict the PJP transient flow field, while the VB-CNN method has higher accuracy than CNN method. The velocity gradient and velocity profile of the PJP transient velocity field are predicted accurately, the predicted velocity field is in good agreement with the CFD flow field. All linear correlation coefficients exceeds 0.99. The value of structural similarity index (SSIM) at different times exceeds 0.95.

A pre-training model based on CFD for open-channel velocity field prediction with small sample data

Abstract Accurately obtaining the distribution of the open-channel velocity field in hydraulic engineering is extremely important, which is helpful for better calculation of open-channel flow and analysis of open-channel water flow characteristics. In recent years, machine learning has been used for open-channel velocity field prediction. However, effective training of data-driven models in machine learning heavily depends on the diversity and quantity of data. In this paper, a CFD-based pre-training neural network model (CFD–PNN) is proposed for accurate open-channel velocity field prediction, allowing the adaption to the task with small sample data. Also, a cross-sectional velocity field prediction method combining the computational fluid dynamics (CFD) and machine learning is established. By comparing CFD–PNN with six other neural network algorithm models and the CFD model, the results show that, in the case of small sample data, the CFD–PNN model can predict a more reasonable open-channel velocity field with higher prediction accuracy than other models. The average error of the velocity calculation for the trapezoidal open-channel cross-section is about 3.62%. Compared with other models, the accuracy is improved by 0.3–2.8%.

Fast and accurate prediction of air temperature and velocity field in non-uniform indoor environment under complex boundaries

The thermal environment in a built indoor space is usually non-uniform in temperature and many other index distributions. Simulation, analysis and understanding the non-uniform indoor environment is critical to a healthy, energy-efficient and comfort indoor space. Conventional CFD model consumes huge computational resources and time for a final result, which may not be suitable for coupling with energy system, and some other applications that needs fast simulation. This study proposes a new model that is built upon Proper Orthogonal Decomposition (POD) method and Radial Basis Function (RBF), with a special Taguchi method served for data preparation. A series of tests are conducted and the results show that the POD-RBF model is fast in computation, accurate in prediction, robust in implementation, and flexible in applications. The construction of the model takes less than 3 s and each case computation takes less than 1 s. The averaged model error in predicting temperature and velocity field is about 0.3% and 8% across different tests.

Parametrized non intrusive space-time approximation for explicit dynamic fem applications

In the following work, a benchmark of different non-intrusive model reduction approaches is performed on an explicit dynamic contact 3D-problem. The main purpose of this work is to evaluate the stability of the reduced model with respect to time along with the precision of these approaches with respect to the true solutions of interest. These solutions are the prediction of displacement and velocity fields. The precision of these approaches is also evaluated with respect to the evolution of some materials parameters. Six parameters vary in this study and we would like to predict the whole transient fast dynamic impact response with respect to each parameters. To this end, several models are trained : Proper Orthogonal Decomposition (POD) and Deep convolutional Neural Network (DcNN), in addition, a vectorized version of Interpolation in Grassman Manifolds is proposed. The benchmark performed illustrate that using DcNN’s allows to achieve the best precision and stability in predicting physical fields.

Towards real-time prediction of velocity field around a building using generative adversarial networks based on the surface pressure from sparse sensor networks

In this study, we used machine learning techniques to predict instantaneous velocity fields around a single building, where a limited amount of surface pressure data obtained from sparse sensor networks were used as the model input. We found that the model based on mean square error (MSE) can reproduce large flow structures appropriately by mapping their relationships to the surface pressure data. However, this model tends to average the effects of small structures, resulting in their absence in the predicted field and significant underestimations of the turbulent kinetic energy and Reynolds stresses. On the other hand, the velocity fields generated by generative adversarial networks (GANs) provide authentic flow structures and can provide relatively accurate statistics. However, this model is unconstrained in generating large flow structures, resulting in unnecessary errors. The blending of GAN and MSE losses with an appropriate blending factor provides a balance, wherein the predictable large flow structures were learnt by minimizing MSE, and the unpredictable small flow structures were generated by GAN with reasonable statistics. Finally, the model needs sufficient surface pressure monitors to predict flow structures, but the prediction results are not sensitive to the number of monitoring points when it exceeds the critical number.

Wind velocity field estimation from aircraft derived data using Gaussian process regression.

Wind velocity field knowledge is crucial for the future air traffic management paradigm and is key in many applications, such as aircraft performance studies. This paper addresses the problem of spatio-temporal windc velocity field estimation. The north and east wind components within a given air space are estimated as a function of time. Both wind velocity field reconstruction in space for a past or present time instant and short-term prediction are performed. Wind data are obtained indirectly from the states of the aircraft broadcast by the Mode-S and ADS-B aircraft surveillance systems. The Gaussian process regression method, which is a flexible and universal estimator, is employed to solve both problems. Under general conditions, the method is statistically consistent, meaning that the method converges to the ground truth when increasingly more data are available, which is especially interesting, since aircraft data availability is expected to grow in the future through the deployment of the European System-Wide Information Management. Besides estimation, the Gaussian process regression method provides the probability distribution of any particular estimate, allowing confidence intervals to be computed. Moreover, the spatial modelling is performed using raw data without relying on grids and estimation can be performed at any spatio-temporal location. Furthermore, since the training phase of the method described in this paper is fast, requiring less than 5 minutes on a standard desktop computer, it can be used online to continuously track the state of the wind velocity field, thus allowing for data assimilation. In the case study presented in this paper, the Gaussian process regression method is tested on different days with different wind intensities. The available data set is split into several training and testing data sets, which are used to check the consistency of the results of wind velocity field reconstruction and prediction. Finally, the Gaussian process regression method is validated using the European Centre for Medium-Range Weather Forecasts ERA5 meteorological reanalysis data. The obtained results show that Gaussian process regression can be used to reliably estimate the wind velocity field from aircraft derived data.

Understanding of turbulence modulation and particle response in a particle-laden jet from direct numerical simulations

Abstract Point-particle direct numerical simulations have been employed to quantify the turbulence modulation and particle responses in a turbulent particle-laden jet in the two-way coupled regime with an inlet Reynolds number based on bulk velocity and jet diameter $({D_j})$ of ~10 000. The investigation focuses on three cases with inlet bulk Stokes numbers of 0.3, 1.4 and 11.2. Special care is taken to account for the particle–gas slip velocity and non-uniform particle concentrations at the nozzle outlet, enabling a reasonable prediction of particle velocity and concentration fields. Turbulence modulation is quantified by the variation of the gas-phase turbulent kinetic energy (TKE). The presence of the particle phase is found to damp the gas-phase TKE in the near-field region within $5{D_j}$ from the inlet but subsequently increases the TKE in the intermediate region of (5–20)Dj. An analysis of the gas-phase TKE transport equation reveals that the direct impact of the particle phase is to dissipate TKE via the particle-induced source term. However, the finite inertia of the particle phase affects the gas-phase velocity gradients, which indirectly affects the TKE production and dissipation, leading to the observed TKE attenuation and enhancement. Particle response to the gas-phase flow is quantified. Particles are found to exhibit notably stronger response to the gas-phase axial velocity than to the radial velocity. A new dimensionless figure is presented that collapses both the axial and radial components of the particle response as a function of the local Stokes number based on their respective integral length scales.

Framework for a variational Bayesian convolutional network for velocity field prediction and uncertainty quantification of a pump-jet propulsor

This study provides the framework for a variational Bayesian convolutional neural network (VB-CNN) to quickly predict the wake velocity field of a pump-jet propulsor and quantify uncertainty. For engineering application and experiments, the wake velocity field of the propulsor can be obtained by using discrete pressure points when the model is trained. The weight distribution of the neural network is altered from a point distribution to a probability distribution using the variational Bayesian method, which also takes into account the prior knowledge of datasets. VB-CNN produces superior results to the convolutional neural network method in small datasets and can quantify uncertainty. This study investigates the differences between the velocity field of computational fluid dynamics and the predictions for the velocity field obtained by the CNN method and the VB-CNN method. The uncertainty distribution of the predicted velocity fields is analyzed according to the 95% confidence interval. Different geometric models are used to verify the generalization of the VB-CNN and CNN models. The results indicate that the VB-CNN method has higher accuracy than the CNN method. Furthermore, the VB-CNN method has superior prediction performance for the velocity field contour and velocity gradient. The maximum error for the velocity field prediction is within 2.33% at different axial positions. The best linear correlation coefficient reached 0.9911. The VB-CNN and CNN models have lower uncertainty at lower rotation speeds and higher uncertainty at higher rotation speeds.

CNN-based flow control device modelling on aerodynamic airfoils

Wind energy has become an important source of electricity generation, with the aim of achieving a cleaner and more sustainable energy model. However, wind turbine performance improvement is required to compete with conventional energy resources. To achieve this improvement, flow control devices are implemented on airfoils. Computational fluid dynamics (CFD) simulations are the most popular method for analyzing this kind of devices, but in recent years, with the growth of Artificial Intelligence, predicting flow characteristics using neural networks is becoming increasingly popular. In this work, 158 different CFD simulations of a DU91W(2)250 airfoil are conducted, with two different flow control devices, rotating microtabs and Gurney flaps, added on its Trailing Edge (TE). These flow control devices are implemented by using the cell-set meshing technique. These simulations are used to train and test a Convolutional Neural Network (CNN) for velocity and pressure field prediction and another CNN for aerodynamic coefficient prediction. The results show that the proposed CNN for field prediction is able to accurately predict the main characteristics of the flow around the flow control device, showing very slight errors. Regarding the aerodynamic coefficients, the proposed CNN is also capable to predict them reliably, being able to properly predict both the trend and the values. In comparison with CFD simulations, the use of the CNNs reduces the computational time in four orders of magnitude.

Data-driven turbulence modelling using symbolic regression

The study is focused on the performance of machine-learning methods applied to improve the velocity field predictions in canonical turbulent flows by the Reynolds-averaged Navier–Stokes (RANS) equation models. A key issue here is to approximate the unknown term of the Reynolds stress (RS) tensor needed to close the RANS equations. A turbulent channel flow with the curved backward-facing step on the bottom has the high-fidelity LES data set. It is chosen as the test case to examine possibilities of GEP (gene expression programming) of formulating the enhanced RANS approximations. Such a symbolic regression technique allows us to get the new explicit expressions for the RS anisotropy tensor. Results obtained by the new model produced using GEP are compared with those from the LES data (serving as the target benchmark solution during the machine-learning algorithm training) and from the conventional RANS model with the linear gradient Boussinesq hypothesis for the Reynolds stress tensor.