A scalable convolutional neural network approach to fluid flow prediction in complex environments

Lattice Boltzmann Method Pore-scale simulation of fluid flow and heat transfer in porous media: Effect of size and arrangement of obstacles into a channel

Turbulence in fluids has been a popular research topic for many years due to its influence on a wide range of applications. Computational Fluid Dynamics (CFD) tools are able to provide plenty of information about this phenomenon, but their computational cost often makes the use of these tools unfeasible. For that reason, in recent years, turbulence modelling using Artificial Neural Networks (ANNs) is becoming increasingly popular. These networks typically calculate directly the desired magnitude, having input information about the computational domain. In this paper, a Convolutional Neural Network (CNN) for predicting different magnitudes of turbulent flows around different geometries by approximating the equations of the Reynolds-Averaged Navier-Stokes (RANS)-based realizable k-ε two-layer turbulence model is proposed. Using that CNN, alternative network structures are proposed to predict the velocity fields of a turbulent flow around different geometries on a rectangular channel, with a preliminary stage to predict pressure and vorticity fields before calculating the velocity fields, and the obtained results are compared with the ones obtained with the basic structure. The results demonstrate that the proposed structures clearly outperform the basic one, especially when the flow becomes uncertain. In addition, considering the results, the best network configuration is proposed. That network is tested with a domain with multiple geometries and a domain with a narrowing of the channel, which are domains with different conditions from the training ones, showing fairly accurate predictions.

Electrorheological fluids have numerous potential applications in vibration dampers, brakes, valves, clutches, exercise equipment, etc. The flows in such applications are complex three-dimensional flows. Most models that have been developed to describe the flows of electrorheological fluids are one-dimensional models. Here, we discuss the behavior of two fully three-dimensional models for electrorheological fluids. The models are such that they reduce, in the case of simple shear flows with the intensity of the electric field perpendicular to the streamlines, to the same constitutive relation, but they would not be identical in more complicated three-dimensional settings. In order to show the difference between the two models, we study the flow of these fluids between eccentrically placed rotating cylinders kept at different potentials, in the setting that corresponds to technologically relevant problem of flow of electrorheological fluid in journal bearing. Even though the two models have quite a different constitutive structure, due to the assumed forms for the velocity and pressure fields, the models lead to the same velocity field but to different pressure fields. This finding illustrates the need for considering the flows of fluids described by three-dimensional constitutive models in complex geometries, and not restricting ourselves to flows of fluids described by one-dimensional models or simple shear flows of fluids characterized by three-dimensional models.

Context. Solving hydrodynamic problems is associated with high computational complexity and therefore requires considerable computing resources and time. The proposed approach makes it possible to significantly reduce the time for solving such problems by applying a combination of two improved modeling methods.
 Objective. The goal is to create a comprehensive hydrodynamic modeling method that requires significantly less time to determine the dynamics of the velocity field by using the modified lattice Boltzmann method and the pressure distribution by using a convolutional neural network.
 Method. A method of hydrodynamic modeling is proposed, which realizes the synergistic effect arising from the combination of the improved lattice Boltzmann method and a convolutional neural network with a specially adapted structure. The essence of the method consists of implementing a sequence of iterations, each of which simulates the process of changing parameters when moving to the next time layer. Each iteration includes a predictor step and a corrector step. At the predictor step, the lattice Boltzmann method works, which allows us to obtain the field of fluid velocities in the working area at the next time layer using the field of velocities at the previous layer. At the corrector step, we apply an improved convolutional neural network trained on a previously created data set. Using a neural network allows us to determine the pressure distribution on a new time layer with a predetermined accuracy. After adding the fluid compressibility correction on the new time layer, we get a refined value of the velocity field, which can be used as initial data for applying the lattice Boltzmann method at the next iteration. Calculations stop when the specified number of iterations is reached.
 Results. The operation of the proposed method was studied on the example of modeling fluid movement in a fragment of the human gastrointestinal tract. The simulation results showed that the time spent implementing the simulation process was reduced by 6–7 times while maintaining acceptable accuracy for practical tasks.
 Conclusions. The proposed hydrodynamic modeling method with a convolutional neural network and the lattice Boltzmann method significantly reduces the time and computing resources required to implement the modeling process in areas with complex geometry. Further development of this method will make it possible to implement real-time hydrodynamic modeling in threedimensional domains.

Fluid mechanics simulation of steady state flow in complex geometries has many applications, from the micro-scale (cell membranes, filters, rocks) to macro-scale (groundwater, hydrocarbon reservoirs, and geothermal) and beyond. Direct simulation of steady state flow in such porous media requires significant computational resources to solve within reasonable timeframes. This study outlines an integrated method combining predictions of fluid flow (fast, limited accuracy) with direct flow simulation (slow, high accuracy) is outlined that reduces computation time by an order of magnitude without loss of accuracy. A convolutional neural network (CNNs) is trained with various configurations on simulations in 2D and 3D porous media to estimate steady state velocity fields. Permeability estimation (as an average of the field) is accurate, but the velocity fields themselves are error prone, unsuitable for further transport studies. This estimate can either be used as an indicative prediction, or as initial conditions in direct simulation to reach a fully accurate result in a fraction of the compute time. Using Deep Learning predictions (or potentially any other approximation method) to accelerate flow simulation to steady state in complex structures shows promise as a technique to push the boundaries fluid flow modelling.

Nowadays, Computational Fluid Dynamics (CFD) simulations play an increasingly important role for turbine airfoil design. This high-fidelity approach is capable to provide accurate information of flow fields. Meanwhile, the calculation accuracy is always gained at the expense of numerical cost. This gap limits opportunities for design space exploration. To address this problem, surrogate models (also known as metamodels) are introduced to approximate high-fidelity CFD models. However, traditional surrogate models, such as Kriging or Radial Basis Function, construct response surface on a design space with limited dimensions. This prevents users from predicting the flow fields directly from the geometry and performing interactive design of airfoil. In the present work, we propose a Convolutional Neural Network (CNN) based surrogate model to predict flow properties on turbine vane airfoil surface from 3D airfoil profile defined by point cloud. The proposed CNN architecture adopts a symmetric expanding path that is similar to the so-called U-Net. The geometries in the training and testing dataset are generated via varying the parameters defined by the Free-Form Deformation approach. The corresponding flow fields are obtained through high-fidelity CFD simulations performed in a finite volume context. Furthermore, a gaussian process based Bayesian optimization technique is utilized to tune automatically the hyperparameters of the network. In this work, we trained the CNN based surrogate model with static pressure and temperature on the mean section of turbine vane airfoil surface. The trained model is able to predict in a reliable and efficient way the corresponding property directly from the 3D geometry, which allows engineers to agilely adjust their airfoil design.

Purpose This study aims to introduce a novel machine learning feature vector (MLFV) method to bring machine learning to overcome the time-consuming computational fluid dynamics (CFD) simulations for rapidly predicting turbulent flow characteristics with acceptable accuracy. Design/methodology/approach In this method, CFD snapshots are encoded in a tensor as the input training data. Then, the MLFV learns the relationship between data with a rod filter, which is named feature vector, to learn features by defining functions on it. To demonstrate the accuracy of the MLFV, this method is used to predict the velocity, temperature and turbulent kinetic energy fields of turbulent flow passing over an innovative nature-inspired Dolphin turbulator based on only ten CFD data. Findings The results indicate that MLFV and CFD contours alongside scatter plots have a good agreement between predicted and solved data with R2 ≃ 1. Also, the error percentage contours and histograms reveal the high precisions of predictions with MAPE = 7.90E-02, 1.45E-02, 7.32E-02 and NRMSE = 1.30E-04, 1.61E-03, 4.54E-05 for prediction velocity, temperature, turbulent kinetic energy fields at Re = 20,000, respectively. Practical implications The method can have state-of-the-art applications in a wide range of CFD simulations with the ability to train based on small data, which is practical and logical regarding the number of required tests. Originality/value The paper introduces a novel, innovative and super-fast method named MLFV to address the time-consuming challenges associated with the traditional CFD approach to predict the physics of turbulent heat and fluid flow in real time with the superiority of training based on small data with acceptable accuracy.

Introduction of roughness by ribs in flow passages is a popular method of enhancing heat transfer in the cooling passages, e.g., of turbine blades and combustors. It is essential to accurately predict the enhancement of heat transfer generated by the ribs to ensure good design decisions. In most of the studies square ribs have been considered, but in practice such ribs may appear rounded due to improper manufacturing or wear during operation. This study is focused on the effect of the rib deformations, based on computational fluid dynamics (CFD). One of the main difficulties in CFD is the reliable modeling of the underlying physics of the turbulence. This paper describes some recent efforts to validate and apply RANS-based models for predictions of turbulent flow and heat transfer in ribbed ducts, relevant to gas turbine cooling. The evaluated turbulence models include a basic low-Re k-ε model (AKN), and two promising higher order models: namely, the explicit algebraic stress model (EASM), and the V2F model. All these models are validated with available 2D experimental heat transfer and fluid flow data. Some conclusions are reached on their suitable application situations. The effect of the roundedness on heat transfer and fluid flow is presented in detail. Some possible improvements, i.e., of the deformed ribs, are proposed to suppress the hot spots, and/or to enhance the overall thermal and hydraulic performance.

<div class="section abstract"><div class="htmlview paragraph">Analysis-driven pre-calibration of a modern automotive engine is extremely valuable in significantly reducing hardware investments and accelerating engine designs compliant with stricter emission regulations. Advanced modelling tools, such as a Virtual Engine Model (VEM) using Computational Fluid Dynamics (CFD), are often used within the framework of a Design of Experiments for Powertrain Engineering (DEPE) with the goal of streamlining significant portions of the calibration process. The success of the methodology largely relies on the accuracy of analytical predictions, especially engine-out emissions. Results show excellent agreements in engine performance parameters (with R<sup>2</sup> > 98%) and good agreements in NOx and combustion noise (with R<sup>2</sup> > 87%), while the Carbon Monoxide (CO), Unburned Hydrocarbons (HC) and Smoke emissions predictions remain a challenge even with a large n-heptane mechanism consisting of 144 species and 900 reactions and refined mesh resolution. In this study, a Machine Learning (ML) approach is presented to correlate in-cylinder images of Equivalence Ratio, Temperature, Velocity field and Turbulent Kinetic Energy (TKE) at Exhaust Valve Opening (EVO) to engine-out emissions of CO, HC and Smoke measured experimentally. The images generated from CFD simulations and experimentally measured emissions data were used to train a deep Convolutional Neural Network (CNN) based on the VGG16 architecture. The prediction performance of the trained model was evaluated on held-out data. The deep learning model led to a significant improvement in prediction of all emissions species and captured the qualitative trends as well. This model could be used as an emissions prediction sub-model in the Virtual Engine Model framework leading to significantly lower computational costs by avoiding the use of expensive chemistry solvers. Gradient-weighted Regression Activation Mapping (Grad-RAMS) was used to draw insights into image features that had a strong influence on the emissions predictions.</div></div>

A coupling algorithm is used to compute the equilibrium of a flexible anchor impeller in a stirred vessel. This coupling algorithm is based on a partitioned approach, which consists of three relatively independent modules: the computational fluid dynamics (CFD), the computational structure dynamics (CSD) and the interface. In the CFD module, the Euler formulation was used to account for the moving boundary. In the CSD module, the updated Lagrangian formulation for solving the motion of non-linear structure was used and a static study was adopted. In the interface module, an exchange of the forces and displacements was allowed. The numerical results, such as the velocity field, the turbulent kinetic energy, its dissipation rate, the turbulent viscosity and the mechanical deformation, have been presented. Particularly, we are interested in the study of the static behavior of the anchor impeller and the evolution of the displacement field of the arms during various iterations of our coupling algorithm. Accordingly, if the anchor impeller undergoes a deformation due to the flexion of the arms of the anchor impeller, the numerical results changes slightly from iteration to another. At the end of certain iteration, the anchor impeller becomes deformed and the velocity field is preserved. These results confirm that the fluid has a significant effect on the deformation of the arms of the anchor impeller during mixing depending on the velocity of the anchor impeller and the fluid flow. The numerical results were validated by a comparison with literature data.

Full-scale experimental and computational fluid dynamics (CFD) methods were used to investigate the velocity and temperature fields in a mechanically ventilated room. Detailed airflow fields were measured in three cases of ventilation air temperature: an isothermal case, a hot case and a cold case. The ventilation system created a round jet which developed near the ceiling. The experimental data were used to test two turbulence models: a first order k-ε turbulence model and a second order RSM turbulence model. The RSM model predicted the temperature and velocity fields better than the k-ε turbulence model. In particular, experimental global values of velocity and temperature were in good agreement with the RSM turbulence model. This model is recommended for simulation of ventilated enclosures with thermal effects.

One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak non–locality (dispersion) associated with an internal length scale and localized dissipation due to mixing. The non–locality introduces a dimensional surface energy; dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes. In particular, we study a non–trivial limit when both components are incompressible, the pressure is kinematic but the velocity field is non–solenoidal (quasi–incompressibility). To demonstrate the effects of quasi–incompressibility, we analyse the linear stage of spinodal decomposition in one dimension. We show that when the densities of the fluids are not perfectly matched, the evolution of the concentration field causes fluid motion even if the fluids are inviscid. In the limit of infinitely thin and well–separated interfacial layers, an appropriately scaled quasi–incompressible Euler–Cahn–Hilliard system converges to the classical sharp interface model. In order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient, we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity.

Subsea pumps and compressors must withstand multiphase flows whose gas volume fraction (GVF) or liquid volume fraction (LVF) varies over a wide range. Gas or liquid content as a dispersed phase in the primary stream affects the leakage, drag torque, and dynamic forced performance of secondary flow components, namely seals, thus affecting the process efficiency and mechanical reliability of pumping/compressing systems, in particular during transient events with sudden changes in gas (or liquid) content. This paper, complementing a parallel experimental program, presents a computational fluid dynamics (CFD) analysis to predict the leakage, drag power, and dynamic force coefficients of a smooth surface, uniform clearance annular seal supplied with air in oil mixture whose inlet GVF varies discretely from 0.0 to 0.9, i.e., from a pure liquid stream to a nearly all-gas content mixture. The test seal has uniform radial clearance Cr = 0.203 mm, diameter D = 127 mm, and length L = 0.36 D. The tests were conducted with an inlet pressure/exit pressure ratio equal to 2.5 and a rotor surface speed of 23.3 m/s (3.5 krpm), similar to conditions in a pump neck wear ring seal. The CFD two-phase flow model, first to be anchored to test data, uses an Euler–Euler formulation and delivers information on the precise evolution of the GVF and the gas and liquid streams' velocity fields. Recreating the test data, the CFD seal mass leakage and drag power decrease steadily as the GVF increases. A multiple-frequency shaft whirl orbit method aids in the calculation of seal reaction force components, and from which dynamic force coefficients, frequency-dependent, follow. For operation with a pure liquid, the CFD results and test data produce a constant cross-coupled stiffness, damping, and added mass coefficients, while also verifying predictive formulas typical of a laminar flow. The injection of air in the oil stream, small or large in gas volume, immediately produces force coefficients that are frequency-dependent; in particular the direct dynamic stiffness which hardens with excitation frequency. The effect is most remarkable for small GVFs, as low as 0.2. The seal test direct damping and cross-coupled dynamic stiffness continuously drop with an increase in GVF. CFD predictions, along with results from a bulk-flow model (BFM), reproduce the test force coefficients with great fidelity. Incidentally, early engineering practice points out to air injection as a remedy to cure persistent (self-excited) vibration problems in vertical pumps, submersible and large size hydraulic. Presently, the model predictions, supported by the test data, demonstrate that even a small content of gas in the liquid stream significantly raises the seal direct stiffness, thus displacing the system critical speed away to safety. The sound speed of a gas in liquid mixture is a small fraction of those speeds for either the pure oil or the gas, hence amplifying the fluid compressibility that produces the stiffness hardening. The CFD model and a dedicated test rig, predictions and test data complementing each other, enable engineered seals for extreme applications.

The aim of this article is to evaluate the ability of a convolutional neural network (CNN) to predict velocity and pressure aerodynamic fields in heavy vehicles. For training and testing the developed CNN, various CFD simulations of three different vehicle geometries have been conducted, considering the RANS-based k-ω SST turbulent model. Two geometries correspond to the SC7 and SC5 coach models of the bus manufacturer SUNSUNDEGUI and the third one corresponds to Ahmed body. By generating different variants of these three geometries, a large number of representations of the velocity and pressure fields are obtained that will be used to train, verify, and evaluate the convolutional neural network. To improve the accuracy of the CNN, the field representations obtained are discretized as a function of the expected velocity gradient, so that in the areas where there is a greater variation in velocity, the corresponding neuron is smaller. The results show good agreement between numerical results and CNN predictions, being the CNN able to accurately represent the velocity and pressure fields with very low errors. Additionally, a substantial improvement in the computational time needed for each simulation is appreciated, reducing it by four orders of magnitude.

Advanced nuclear reactors are essential for the future of sustainable energy production, with their ability to provide large-scale, low-carbon electricity. A critical factor in the design and optimization of these reactors is the efficient management of heat transfer, which ensures operational safety and enhances performance. This paper presents a detailed study on the use of Computational Fluid Dynamics (CFD) to analyze and improve heat transfer in advanced nuclear reactors. The study evaluates the effectiveness of CFD models in predicting fluid flow, temperature distribution, and heat removal under various operating conditions. The research discusses the advantages of using CFD simulations to optimize reactor designs, highlighting their potential in improving thermal efficiency and ensuring safety. A comparative analysis of various CFD techniques is presented, with an emphasis on the application of the models in the design of next-generation reactors such as Small Modular Reactors (SMRs). The findings from this study contribute to a deeper understanding of the thermal behavior in advanced reactors, facilitating better decision-making in reactor design and operation.