Computational Fluid Mechanics Research Articles

On the effect of axial inlet angle on the droplet size distribution and mixing uniformity for swirl jet mixer at high phase ratios

The “short pass” problem of liquid-liquid two-phase mixing at high phase ratios limited the development and applications of jet mixer in industrial process. In this study, the effect of the axial inlet angle on the mixing characteristics of a swirl jet mixer was investigated through laser particle size analysis and computational fluid mechanics (CFD) coupled with population balance model (PBM). The result was shown that as the axial inlet angle increased, the dispersed phase droplet sizes decreased, and the droplet size distribution was widened for the fixed mixer configuration. At Re ≤ 3.000×104, tangential inlet was more conducive to improving mixing uniformity. Conversely, the axial inlet angle of 90° was optimal at Re ≥ 3.750×104. Numerical simulations revealed that the tangential inlet effectively intensified liquid-liquid interactions, including streamlines extension, increased vorticity, improved droplet size uniformity. Additionally, the increase of the axial inlet angle resulted in increased turbulence stress and shortened decay period, the reduction in droplet size, and a wide droplet size distribution. The research findings can serve as theoretical basis for the hydraulic design and promoted applications of swirl jet mixers.

Fluid-Dynamic Modeling of Flow in Embryonic Tissue Indicates That Lymphatic Valve Location Is Not Consistently Determined by the Local Fluid Shear or Its Gradient.

Intravascular lymphatic valves often occur in proximity to vessel junctions. It is commonly held that disturbed flow at junctions is responsible for accumulation of valve-forming cells (VFCs) at these locations as the initial step in valve creation, and the one which explains the association with these sites. However, evidence in favor is largely limited to cell culture experiments. We acquired images of embryonic lymphatic vascular networks from day E16.5, when VFC accumulation has started but the developing valve has not yet altered the local vessel geometry, stained for Prox1, which co-localizes with Foxc2. Using finite-element computational fluid mechanics, we simulated the flow through the networks, under conditions appropriate to this early development stage. Then we correlated the Prox1 distributions with the distributions of simulated fluid shear and shear stress gradient. Across a total of 16 image sets, no consistent correlation was found between Prox1 distribution and the local magnitude of fluid shear, or its positive or negative gradient. This, the first direct semi-empirical test of the localization hypothesis to interrogate the tissue from invivo at the critical moment of development, does not support the idea that a feature of the local flow determines valve localization.

Non-uniform knot (NUK) SIAC post-processing of flow fields produced through unstructured grid adaptation and optimization

As the finite element method (FEM) and the finite volume method (FVM), both their traditional and high-order variants, continue their proliferation into various applied engineering disciplines, adaptive mesh refinement and optimization strategies have increased in their importance when solving real-world computational fluid mechanics applications. The post-processing and visualization of the resulting flow fields present two significant analysis and visualization challenges. The first challenge is the handling of elemental continuity, which is often only C0 continuous (in continuous Galerkin methods) or piecewise discontinuous (in discontinuous Galerkin methods). The second challenge is that, depending on the flow regime and the geometric configurations for which adaptive meshing strategies are used, the meshes generated are often highly anisotropic. The (uniform knot) line-SIAC (L-SIAC) filter has been proposed as a way of handling elemental continuity issues in an accuracy-conserving manner with the added benefit of casting the data in a smooth context even if the representation is element discontinuous. In this paper, we demonstrate that the state-of-the-art adaptive L-SIAC filter, designed for mildly anisotropic meshes, suffers degradation in the quality of the post-processed solution when applied to the types of highly anisotropic meshes produced through adaptive mesh refinement and optimization. Hence, a new Non-Uniform Knot (NUK) L-SIAC filter is proposed that automatically conforms to the underlying mesh anisotropy. We demonstrate that the new filter behaves similarly to the adaptive L-SIAC filter when applied to uniform and mildly anisotropic meshes, and furthermore we show the superiority of the NUK L-SIAC filter when applied to highly anisotropic meshes. The newly formulated filter is applied to 2D canonical scalar fields and used to visualize 2D and 3D fluid flow simulation results.

Towards safer hydrogen refuelling stations: Insights from computational fluid dynamics on LH₂ leakage

Scaling hydrogen as a key clean energy carrier necessitates a comprehensive understanding of the safety aspects of hydrogen including liquid hydrogen (LH₂). Hence, this study presents a detailed computational fluid mechanics analysis to explore accidental LH₂ leakage and dispersion in a hydrogen refuelling station under varied conditions which is essential to prevent fire and explosion. The correlated impact of influential parameters including wind direction, wind velocity, leak direction, and leak rate were analysed. The study shows that hydrogen dispersion is significantly impacted by the combined effect of wind direction and surrounding structures. Additionally, the leak rate and leak direction have a significant effect on the development of the flammable cloud volume (FCV), which is critical for estimating the explosion hazards. Increasing wind velocity from 2 to 4 m/s at a constant leak rate of 0.06 kg/s results in an 82% reduction in FCV. The minimum FCV occurs when leak and wind directions oppose at 4 m/s. The most critical situation concerning FCV arises when the leak and wind directions are perpendicular, with a leak rate of 0.06 kg/s and a wind velocity of 2 m/s. These findings can aid in the development of optimised sensing and monitoring systems and operational strategies to reduce the risk of catastrophic fire and explosion consequences.

Multiphysics performance evaluation of thermoelectric generator arrays

Thermoelectric generators (TEGs) are widely used nowadays in heat recovery and power generation applications. TEGs are connected in series and/or parallel configurations in an array to meet the voltage and/or current requirements of electric load. Therefore, it is necessary to examine the electrical performance of different TEG array configurations employed in TEG systems. In the present study, an experimentally validated hydro-thermoelectric multiphysics computational model is employed by integrating the computational fluid dynamics (CFD) approach with the TEG model to test the electrical performance of various TEG array configurations and determined load voltage, current, associated power, and conversion efficiency. Each TEGs array configuration’s performance is evaluated by varying the hot water temperature from 27 °C to 42 °C as well as hot and cold water flowrate from 0.5 L/min to 2 L/min. Various configurations including series and a combination of series and parallel connections were designed. The findings show that the series configuration of the TEGs array generates higher electric power than series and parallel combined configurations whereas the latter achieves the maximum power point at a higher electric current than the series configuration. The comparative analysis of CFD model with the experimental results indicates a maximum discrepancy of 7 %. For thermoelectric power-generating systems, the proposed model might serve as a benchmark for optimizing TEGs array configurations according to the electric load requirements.

Water quality assessment using Bi-LSTM and computational fluid dynamics (CFD) techniques

Assessment of water quality is imperative for informed decision-making, ecological preservation, and sustainable water resource management, particularly in light of escalating anthropogenic pollution. Traditional approaches often face complexities and inaccuracies in forecasting, necessitating advancements in modelling techniques. Machine learning methods, particularly deep learning, present promising avenues for accurate water quality estimation, albeit with challenges. This study aims to enhance water quality forecasting through the integration of deep learning, specifically Bi-directional Long Short-Term Memory (Bi-LSTM) networks, with computational fluid dynamics (CFD). The objective is to address the limitations of existing methods by leveraging the synergies between deep learning and fluid dynamics simulations, thereby improving predictive accuracy and efficiency. By proposing a novel framework that combines Bi-LSTM networks with computational fluid mechanics, this study introduces an innovative approach to water quality assessment. The integration of these techniques offers a comprehensive solution to overcome the complexities inherent in traditional methods, promising greater reliability and efficiency in predicting water quality parameters. The study employs Bi-LSTM networks alongside CFD simulations to model contaminant movement and diffusion in water bodies, particularly focusing on the Yamuna River. Utilizing empirical data on Chemical Oxygen Demand (COD) and Biological Oxygen Demand (BOD), the framework aims to predict key factors influencing water quality. The ANSYS software, operating within a Windows environment, facilitates the execution of the proposed methodology. Evaluation of the proposed model demonstrates superior performance compared to traditional methods, exhibiting higher predictive reliability and lower margins of error. Through a comprehensive comparison study, the Bi-LSTM and CFD-based approach surpasses existing techniques in accurately forecasting water quality parameters, thus highlighting its efficacy and potential for practical application. The integration of Bi-LSTM networks with computational fluid dynamics presents a promising avenue for enhancing water quality evaluation. The study underscores the significance of leveraging advanced computational techniques to address the challenges associated with forecasting water quality, ultimately contributing to informed decision-making and sustainable water resource management.

An efficient partitioned framework to couple Arbitrary Lagrangian-Eulerian and meshless vector form intrinsic finite element methods for fluid-structure interaction problems with deformable structures

The Vector Form Intrinsic Finite Element (VFIFE) is an advanced meshless Lagrangian structural solver. This study introduces a partitioned framework to integrate Arbitrary Lagrangian-Eulerian and VFIFE methods into fluid-structure interaction (FSI) problems featured by large structural displacements and deformations. The VFIFE method enables the FSI simulations with deformable structures due to the nature of Lagrangian particles, which is challenging for traditional computational fluid mechanics techniques. In addition, the VFIFE can be effectively equipped with the partitioned coupling schemes because of the versatility of governing equations. In this algorithm system, several matrix problems in finite element methods and mapping and interpolation in the fluid-structure interface can be avoided. The significant potential of this algorithm in tackling complex FSI problems is demonstrated through various benchmarks, encompassing scenarios like Taylor-Green vortex, flow over a rigid cylinder (Re = 40 ∼ 200), forced vibration of a rigid cylinder, vortex-induced vibration (VIV) of an elastically mounted cylinder, and VIV of a rigid cylinder with an attached flexible cantilever beam. Finally, an experiment on flow past a curtain in a water tank is conducted to further evaluate the precision and stability of the current coupling strategy in three dimensions, demonstrating the feasibility of such methods in flexible structures.

A radial basis function partition of unity method for steady flow simulations

A methodology is presented for the numerical solution of nonlinear elliptic systems in unbounded domains, consisting of three elements. First, the problem is posed on a finite domain by means of a proper nonlinear change of variables. The compressed domain is then discretised, regardless of its final shape, via the radial basis function partition of unity method. Finally, the system of nonlinear algebraic collocation equations is solved with the trust-region algorithm, taking advantage of analytically derived Jacobians. We validate the methodology on a benchmark of computational fluid mechanics: the steady viscous flow past a circular cylinder. The resulting flow characteristics compare very well with the literature. Then, we stress-test the methodology on less smooth obstacles—rounded and sharp square cylinders. As expected, in the latter scenario the solution is polluted by spurious oscillations, owing to the presence of boundary singularities.

Finite Element Analysis for NEG coated vacuum chamber based on ANSYS Workbench

The Hefei Advanced Light Facility (HALF) is a diffraction limited storage ring (DLSR) being constructed. As the main component of the storage ring vacuum system, the vacuum chamber transports the beam and withstands the thermal effect of synchrotron radiation simultaneously. The thermal and mechanical condition of the vacuum chamber of HALF were quantitatively analysed by means of ANSYS Workbench in this work. Combining the Computational Fluid Mechanics (CFD) and Finite Elements Analysis (FEA), the temperature and thermal stress maps of the vacuum chamber were calculated. The CFD calculation displays that the heat transfer coefficient between the water and the chamber is 7966-13093 W/(m2·°C). The thermal-mechanical simulation shows that the maximum temperature and thermal stress are 53.5 °C and 42.1 MPa, respectively. The static structural analysis was performed on vacuum chamber under the ultra-high vacuum condition, with the maximum stress of 1.7 MPa and the maximum deformation of 0.0003 mm. These results show that the vacuum chamber meets the design requirements and provide a critical theoretical basis for the design of the vacuum system of HALF.

Investigations of the Mass Transfer and Flow Field Disturbance Regulation of the Gas–Liquid–Solid Flow of Hydropower Stations

With the continuous depletion of fossil fuels, all countries attach importance to clean and sustainable development. The real-time state monitoring of multiphase flows is vital for enhancing hydropower station energy conversion. However, the material mass transfer mechanism and flow field disturbance regulation strategy faces significant challenges. To solve these problems, a computational fluid mechanics and discrete element method (CFD-DEM) coupling modeling and solution method based on a particle porosity model was proposed, and the mass transfer mechanism of gas–liquid–solid mixing flows was obtained under dynamic whirl intensity regulations. Combined with the user-defined function (UDF), the interphase forces and void ratios of fluids and particles were calculated to obtain the material mass transfer laws under dynamic disturbance regulations. The evolution characteristics of the particle flow pattern were tracked during the material mixing process. The results show that the mixed flow field had a high material transport efficiency under intensive whirl regulation, especially for the particle aggregation in the center of the reaction vessel. The maximum peak velocity and energy values of the particle transport process were 3.30 m/s and 0.27 × 10−3 m2·s−2. The higher whirl regulation improved the material transport process and conveying efficiency and enhanced the particle mixing effect in the reaction space. Relevant research results can provide theoretical references for material mass transfer mechanisms, dynamic regulation strategies, and particle flow pattern identifications and can also provide technical support for hydropower energy conversion.

Application of Artificial Neural Networks for Mathematical Modelling of Horizontal Jet Fires

Aim: This article focuses on the use of artificial neural networks to mathematically describe the parameters that determine the size of a jet fire flame. To teach the neural network, the results of a horizontal propane jet fire, carried out experimentally and using CFD mathematical modelling, were used. Project and methods: The main part of the work consisted of developing an artificial neural network to describe the flame length and propane-air mixing path lengths with good accuracy, depending on the relevant process parameters. Two types of data series were used to meet the stated objective. The first series of data came from field tests carried out by CNBOP-PIB and from research contained in scientific articles. The second type of data was provided by numerical calculations made by the authors. The methods of computational fluid mechanics were used to develop the numerical simulations. The ANSYS Fluent package was used for this purpose. Matlab 2022a was used to develop the artificial neural network and to verify it. Results: Using the nftool function included in Matlab 2022a, an artificial neural network was developed to determine the flame length Lflame and the length of the Slift-off mixing path as a function of the diameter of the dnozzle and the mass flux of gas leaving the nozzle. Using Pearson’s correlation coefficient, a selection was made of the best number of neurons in the hidden layer to describe the process parameters. The neural network developed allows Lflame and Slift-off values to be calculated with good accuracy. Conclusions: Artificial neural networks allow a function to be developed to describe the parameters that determine flame sizes in relation to process parameters. For this purpose, the results of the CFD simulations and the results of the jet fire experiments were combined to create a single neural network. The result is a ready-made function that can be used in programmes for the rapid determination of flame sizes. Such a function can support the process of creating scenarios in the event of an emergency. A correctly developed neural network provides opportunities for the mathematical description of jet fires wherever experimental measurements are not possible. Solution proposed by the authors does not require a large investment in ongoing calculations, as the network can be implemented in any programming language. Keywords: computational fluid mechanics, artificial neural networks, jet fire

Simulation of Heat Transfer during Paraffin And Gallium Melting and Solidification Processes Utilizing Star CCm+

Energy storage systems are essential as the world works to minimize its dependency on fossil fuel energy for environmental and economic reasons. Because of their high capacity for latent heat storage. The numerical study of benchmark cases of solidification and melting was undertaken, and the results of these investigations are presented in this project. Numerical analysis is conducted to examine the brief solidification process of a pure liquid phase-change material within a rectangular enclosure when natural convection is present. The horizontal boundaries are both taken to be adiabatic, with one vertical barrier maintained at a temperature below the material's melting point and the other above. In this work, a numerical investigation of the melting of wax (namely N-octadecane) is presented. The numerical simulations of the experiments were carried out using STAR CCM+, and the results were compared with the results of other numerical simulations (FLOW 3D). The numerical simulations of gallium melting were carried out with a commercial code, STAR CCM+, which captures the solid-liquid interface with a fixed grid. This software captures the solid-liquid interface for phase change simulations in complex geometries with the enthalpy formulation technique. In addition, it demonstrates that computational fluid mechanics has reached a state of development where it permits reliable flow computations with solidification and melting. Casting with metal melts can be studied to provide information to engineers during the design process of new casting tools. The available simulation tools can also be used to predict existing casting processes and determine the origins of defects. The key findings are as follows: The interface shape during the solidification of gallium from above is always determined in large part by anisotropy in heat conductivity and interface growth morphology. Natural convection in the liquid slows down the rate of melting and adds more complexity to the morphology and transport mechanisms at the interface.

Computational hydraulics and hazard assessment of flooding on underground staircases

Underground flooding is intensifying due to urban expansion and more frequent extreme precipitation. Staircases are crucial for accessing underground spaces and evacuation during floods and it is of both academic and practical value to investigate how floodwater and the induced hazard evolve over underground staircases. This study examines flood dynamics on underground staircases and its relationship with staircase characteristics through a series of numerical experiments using a two-dimensional (2D) hydrodynamic model. The study also uncovers how staircase design influences flood hazard levels. Results indicate that shorter or higher steps lead to shallower water depths but higher flow velocities. The branch staircase experiences smaller water depths and flow velocities than the main one. The presence of staircase transforms a subcritical flow into a supercritical flow. Except in extremely deep floodwaters, pedestrians are more vulnerable to sliding than toppling on staircases. The stability of the human body is greater on steps with longer length and lower height (26.56°) or the branch line of the junction type. The relative stability of the human body is not necessarily a guarantee of complete safety and must be analyzed in conjunction with the comprehensive safety factor.

Computational Fluid Mechanics with Phase Transitions by Particle Methods

A computational method of simulations for processes of heterogeneous hydrodynamics with take of phase transitions will be discussed. The method is based on relevant approximation of conservation laws for mass, momentum, and energy in integral and differential forms. The time and spatial approximation is natural and numerical simulations are realized as direct computer experiments. It is supposed that the fluids are compressible and non-viscous. Heterogeneities of the fluids are considered as small drops or particles of one fluid within other fluid. Total number of the drops may be large enough and the drops may have phase transitions. Therefore, simulations of the main fluid with small transited drops dynamics are considered. The particle dynamics will be modelled as in the particle-in-cell method, and in the main fluid as in the large particle method. This approach makes it possible to simulate phase transitions under certain assumptions about heterogeneous fluids. The calculation algorithm of this method is implemented as a computer simulation of the dynamics of a multiphase carrier fluid containing particles that can undergo, for example, graphite-diamond phase transitions. Such transitions are modelled on the basis of the theory of phase transformations and the laws of thermodynamics. In fact, the method is a combination of the Harlow's particle-in-cell method, Belotserkovskii's large particles method and Bakhvalov's homogenization method. A modification of this method has also been developed to take into account the effects of viscosity when simulating the dynamics of a multiphase fluid in porous media. A model of the motion of such a liquid in a porous medium is obtained by freezing the motion of particles of the corresponding size in the presented method. The method will certainly be promising for numerical simulations of absorption and diffusion processes in complex fluids with phase transitions.

Collective effects in flow-driven cell migration.

Autologous chemotaxis is the process in which cells secrete and detect molecules to determine the direction of fluid flow. Experiments and theory suggest that autologous chemotaxis fails at high cell densities because molecules from other cells interfere with a given cell's signal. We investigate autologous chemotaxis using a three-dimensional Monte Carlo-based motility simulation that couples spatial and temporal gradient sensing with cell-cell repulsion. Surprisingly, we find that when temporal gradient sensing dominates, high-density clusters chemotax faster than individual cells. To explain this observation, we propose a mechanism by which temporal gradient sensing allows cells to form a collective sensory unit. We demonstrate using computational fluid mechanics that that this mechanism indeed allows a cluster of cells to outperform single cells in terms of the detected anisotropy of the signal, a finding that we demonstrate with analytic scaling arguments. Our work suggests that collective autologous chemotaxis at high cell densities is possible and requires only known, ubiquitous cell capabilities.

Applying Model Studies to Support the Monitoring of Methane Hazard during the Process of Underground Coal Mining

Abstract The process of underground mining is one of the most complex and hazardous activities. In order to maintain the continuity and efficiency of this process, it is necessary to take measures to reduce this hazard. The paper addresses this issue by presenting a developed methodology for using model studies and numerical simulations to support the process of monitoring methane hazards. Its basis is the developed model of the region of underground mining exploitation along with the ventilation phenomena occurring in it. To develop it, the ANSYS Fluent program was used, based on the finite volume method classified as computational fluid mechanics. The model reflects both the geometries and physical and chemical phenomena occurring in the studied area, as well as the auxiliary ventilation equipment used during operation. The research was conducted for two variants of methane emissions from goaf zones, the first of which concerned the actual state of the mining area, and the second of which concerned increased methane emissions from these goaf zones. The purpose of the study was to determine the distribution of methane concentrations in the most dangerous part of the studied area, which is the intersection of the longwall and the tailgate, as well as the distribution of ventilation air flow velocities affecting them. The studies for both variants made it possible to determine places particularly exposed to the occurrence of dangerous concentrations of methane in this region. The methodology developed represent a new approach to studying the impact of methane emissions from goaf zones into mine workings.

Machine learning models coupled with empirical mode decomposition for simulating monthly and yearly streamflows: a case study of three watersheds in Ontario, Canada

This paper presents a novel approach for enhancing long-term runoff simulations through the integration of empirical mode decomposition (EMD) with four machine learning (ML) models: ensemble, support vector machine (SVM), convolutional neural networks (CNN), and artificial neural networks with backpropagation (ANN-BP). The proposed methodology uses EMD to decompose precipitation and temperature time-series into intrinsic mode functions, thereby revealing underlying data patterns. Subsequently, these components are incorporated into the ML models to simulate the runoff time-series. The effectiveness of the hybrid models is evaluated using streamflow runoff data obtained from the Grand, Winnipeg, and Moosonee Rivers in Ontario, Canada. Four widely used performance indices, namely, correlation coefficient, root mean square error (RMSE), mean absolute relative error, and Nash–Sutcliffe efficiency, are employed to assess the models’ performance. The results demonstrate that the hybrid EMD-ML models exhibit significantly superior performance compared with the standalone ML methods. During the validation phase, the EMD-Ensemble, EMD-SVM, EMD-CNN, and EMD-ANN-BP models exhibit notable reductions in the RMSEs of monthly streamflow estimates for the Grand River, amounting to 11%, 22%, 8%, and 33%, respectively, compared with their non-EMD counterparts. Additionally, these hybrid models exhibit improved RMSEs for yearly simulations in the Winnipeg River, with reductions of 54%, 0.08%, 6%, and 4.5% respectively. To further enhance the accuracy of monthly and yearly streamflow estimates, an SVM-recursive feature elimination technique is employed to select a more appropriate EMD dataset in all study cases. This research underscores the potential of integrating EMD with ML models to enhance long-term runoff simulations. The outcomes highlight the superior performance of the hybrid EMD-ML models, demonstrating their ability in generating lower biases than the standalone ML methods. These findings hold significant implications for the field of computational fluid mechanics and can contribute to the understanding of hydrological processes.

Role of unsteady tip leakage flow in acoustic resonance inception of a multistage compressor

In previous studies, a theoretical model was developed after Acoustic Resonance (AR) was experimentally detected in a four-stage compressor, and AR inception was proposed to be triggered by an unknown sound source, which is a pressure perturbation of a specific frequency with a suitable circumferential propagation speed. The present paper, which is not dedicated to the simulation of acoustic field, aims to identify the specific sound source generated by the unsteady tip leakage flow using the unsteady Computational Fluid Mechanics (CFD) approach. After a comprehensive analysis of an Unsteady Reynolds Averaged Navier-Stokes (URANS) simulation, a pressure perturbation of non-integer multiple of rotor frequency is found at the blade tip. Since the essence of the tip leakage flow is a jet flow driven by the pressure difference between two sides of blade, a simplified tip leakage flow model is adopted using Large Eddy Simulation (LES) in order to simulate the jet flow through a tip clearance. It is found that the convection velocity of shedding vortices fits the expected propagation speed of the sound source, the frequency is also close to one of the dominating frequencies in the URANS simulation, and the resultant combination frequency coincides with the experimentally measured AR frequency. Since such a simplified model successfully captures the key physical mechanisms, it is concluded that this paper provides a piece of unambiguous evidence on the role of unsteady tip leakage vortex in triggering the AR inception of the multistage compressor.

Material Transport and Flow Pattern Characteristics of Gas–Liquid–Solid Mixed Flows

Flow pattern monitoring of gas–liquid–solid mixed flow has great significance to enhance the quality and efficiency of material mixing, and the material transport mechanism and dynamic control strategy are faced with significant challenges. To solve these problems, a computational fluid mechanics and discrete element method (CFD-DEM) coupling modeling and solving approach based on soft sphere and porous models is presented to explore material transport mechanisms. The user-defined function (UDF) is adopted to perform data communication, and the porosity of the porous model is calculated to achieve the bidirectional calculation of Eulerian fluid and Lagrange particle phases. Material transport processes of gas–liquid–solid mixed flows are discussed to explore material transport mechanisms of particle flow and the flow pattern evolution laws under the inflation control are obtained. The results show that the particles are not evenly distributed under the synergistic action of impeller rotation and inflation. The particles in the upper and lower impeller have similar characteristics along the radial direction, and there is an aggregation phenomenon in the impeller center. A certain degree of inflation enhances the macroscopic mixing process of turbulent vortices, promotes the particle suspension effect inside the container, and improves the material transport efficiency inside the mixing space. Relevant research results can provide theoretical references for the material transport mechanism, flow pattern tracking models, and energy transfer and can also provide technical support for chemical process separation, food processing, battery homogenate mixing, and other production processes.

Artificial neural network based correction for reduced order models in computational fluid mechanics

In this paper we propose a reduced order model (ROM) for incompressible flows based on proper orthogonal decomposition (POD) and having a finite element approximation as full order model (FOM). The main idea is to start from a purely POD-based ROM, projecting the equations onto the ROM space, and then add a nonlinear correction that depends on the ROM unknowns to enhance the final ROM model. This correction is based on the fact that we do have some available high fidelity data, namely, the snapshots. Thus, the correcting term is built as an artificial neural network (ANN) constructed with the snapshots as the training set. This correction is then introduced in the fully discrete ROM system to achieve more accurate solutions. A further feature of our approach is that we construct both the ROM and the FOM using the variational multi-scale (VMS) concept, and this allows us to understand the correction term as an approximation to the scales that are lost when passing from the FOM to the ROM. The resulting corrected ROM has a significant higher accuracy than the original one.