An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications.

Particulate flow modelling in a spiral separator by using the Eulerian multi-fluid VOF approach

The Euler-Euler model is less effective in capturing the free surface of flow film in the spiral separator,and thus a Eulerian multi-fluid volume of fluid(VOF)model was first proposed to describe the particulate flow in spiral separators.In order to improve the applicability of the model in the high solid concentration system,the Bagnold effect was incorporated into the modelling framework.The capability of the proposed model in terms of predicting the flow film shape in a LD9 spiral separator was evaluated via comparison with measured flow film thicknesses reported in literature.Results showed that sharp air–water and air-pulp interfaces can be obtained using the proposed model,and the shapes of the predicted flow films before and after particle addition were reasonably consistent with the observations reported in literature.Furthermore,the experimental and numerical simulation of the separation of quartz and hematite were performed in a laboratory-scale spiral separator.When the Bagnold lift force model was considered,predictions of the grade of iron and solid concentration by mass for different trough lengths were more consistent with experimental data.In the initial development stage,the quartz particles at the bottom of the flow layer were more possible to be lifted due to the Bagnold force.Thus,a better predicted vertical stratification between quartz and hematite particles was obtained,which provided favorable conditions for subsequent radial segregation.

Computational fluid dynamics-discrete element method simulation of stirred tank reactor for graphene production

Liquid phase exfoliation(LPE)process for graphene production is usually carried out in stirred tank reactor and the interactions between the solvent and the graphite particles are important as to improve the production efficiency.In this paper,these interactions were revealed by computational fluid dynamics–discrete element method(CFD-DEM)method.Based on simulation results,both liquid phase flow hydrodynamics and particle motion behavior have been analyzed,which gave the general information of the multiphase flow behavior inside the stirred tank reactor as to graphene production.By calculating the threshold at the beginning of graphite exfoliation process,the shear force from the slip velocity was determined as the active force.These results can support the optimization of the graphene production process.

Effect of fracture fluid flowback on shale microfractures using CT scanning

The field data of shale fracturing demonstrate that the flowback performance of fracturing fluid is different from that of conventional reservoirs,where the flowback rate of shale fracturing fluid is lower than that of conventional reservoirs.At the early stage of flowback,there is no single-phase flow of the liquid phase in shale,but rather a gas-water two-phase flow,such that the single-phase flow model for tight oil and gas reservoirs is not applicable.In this study,pores and microfractures are extracted based on the experimental results of computed tomography(CT)scanning,and a spatial model of microfractures is established.Then,the influence of rough microfracture surfaces on the flow is corrected using the modified cubic law,which was modified by introducing the average deviation of the microfracture height as a roughness factor to consider the influence of microfracture surface roughness.The flow in the fracture network is simulated using the modified cubic law and the lattice Boltzmann method(LBM).The results obtained demonstrate that most of the fracturing fluid is retained in the shale microfractures,which explains the low fracturing fluid flowback rate in shale hydraulic fracturing.

非定常自由面流动模拟的反扩散VOF算法研究

VOF(Volume of Fluid)方法由于其良好的守恒性和网格适应性,且具有计算资源需求相对较小等优点,成为船舶水动力学领域自由面流动CFD(Computational Fluid Dynamics)模拟的主流方法。但原始的VOF方法存在较为严重的界面扩散问题,导致模拟的界面厚度过大、空间分辨率不够,进而影响流场相关变量的计算精度,这一问题在非定常自由面流动模拟中尤为明显。本文针对上述问题,通过在VOF控制方程中引入人工对流项以达到抑制界面扩散、压缩界面厚度的目的,并采用隐式离散人工对流项的方式提高计算稳定性,形成了反扩散VOF算法。经Zalesak和剪切场等经典算例在不同数量网格下的测试验证,表明反扩散VOF算法能够大幅压缩界面厚度,同时明显减小质量误差。随后的三维无障碍溃坝算例和破舱进水算例,进一步证明了反扩散VOF算法在实际非定常流动模拟中能够更好地捕捉自由面并提高计算精度。

A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction.In this work,a novel scheme based on a specific level set ghost fluid method and an implicit-explicit(IMEX)flux splitting is proposed to overcome this timestep restriction.A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface.In this part of the domain,the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases.It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method.Applica-tions to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.

A stencil-like volume of fluid (VOF)method for tracking free interface

A stencil-like volume of fluid （VOF） method is proposed for tracking free interface. A stencil on a grid cell is worked out according to the normal direction of the interface, in which only three interface positions are possible in 2D cases, and the interface can be reconstructed by only requiring the known local volume fraction information. On the other hand, the fluid-occupying-length is defined on each side of the stencil, through which a unified fluid-occupying volume model and a unified algorithm can be obtained to solve the interface advection equation. The method is suitable for the arbitrary geometry of the grid cell, and is extendible to 3D cases. Typical numerical examples show that the current method can give ＂sharp＂ results for tracking free interface.

An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic

We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and Xin.These methods can use the CFL number larger or equal to unity on regular Cartesian meshes for the multi-dimensional case.These kinetic models depend on a small parameter that can be seen as a"Knudsen"number.The method is asymptotic preserving in this Knudsen number.Also,the computational costs of the method are of the same order of a fully explicit scheme.This work is the extension of Abgrall et al.(2022)[3]to multidimensional systems.We have assessed our method on several problems for two-dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions.

Parametric resonance of axially functionally graded pipes conveying pulsating fluid

Based on the generalized Hamilton's principle,the nonlinear governing equation of an axially functionally graded(AFG)pipe is established.The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam.Via the direct multi-scale method,the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method(DQEM).The influence of Young's modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions.In general,the pipe in the supercritical region is more sensitive to the pulsating excitation.The nonlinearity changes from hard to soft,and the non-trivial equilibrium configuration introduces more frequency components to the vibration.Besides,the increasing Young's modulus gradient improves the critical pulsating flow velocity of the parametric resonance,and further enhances the stability of the system.In addition,when the temperature increases along the axial direction,reducing the gradient parameter can enhance the response asymmetry.This work further complements the theoretical analysis of pipes conveying pulsating fluid.

Numerical Study on the Aerodynamic and Fluid−Structure Interaction of An NREL-5MW Wind Turbine

A 5-MW wind turbine has been modeled and analyzed for fluid-structure interaction and aerodynamic performance.In this study, a full-scale model of a 5-MW wind turbine is first developed based on a computational fluid dynamics(CFD) approach, in which the unsteady, noncompressible Reynolds Averaged Navier-Stokes(RANS) method is used. The main focus of the study is to analyze the tower shadow effect on the aerodynamic performance of the wind turbine under different inlet flow conditions. Subsequently, the finite element model is established by considering fluid/structure interactions to study the structural stress, displacement, strain distributions and flow field information of the structure under the uniform wind speed. Finally, the fluid-structure interaction model is established by considering turbulent wind and the tower shadow effect. The variation rules of the dynamic response of the one-way and two-way fluid-structure interaction(FSI) models under different wind speeds are analyzed, and the numerical calculation results are compared with those of the centralized mass model. The results show that the tower shadow effect and structural deformation are the main factors affecting the aerodynamic load fluctuation of the wind turbine, which in turn affects the aerodynamic performance and structural stability of the blades. The structural dynamic response of the coupled model shows significant similarity, while the structural displacement response of the former exhibits less fluctuation compared with the conventional centralized mass model. The one-way fluid-structure interaction(FSI)model shows a higher frequency of stress-strain and displacement oscillations on the blade compared with the two-way FSI model.

Sensitivity of diagnosis of spontaneous bacterial peritonitis is higher with the automated cell count method

BACKGROUND Spontaneous bacterial peritonitis(SBP)is one of the most important complications of patients with liver cirrhosis entailing high morbidity and mortality.Making an accurate early diagnosis of this infection is key in the outcome of these patients.The current definition of SBP is based on studies performed more than 40 years ago using a manual technique to count the number of polymorphs in ascitic fluid(AF).There is a lack of data comparing the traditional cell count method with a current automated cell counter.Moreover,current international guidelines do not mention the type of cell count method to be employed and around half of the centers still rely on the traditional manual method.AIM To compare the accuracy of polymorph count on AF to diagnose SBP between the traditional manual cell count method and a modern automated cell counter against SBP cases fulfilling gold standard criteria:Positive AF culture and signs/symptoms of peritonitis.METHODS Retrospective analysis including two cohorts:Cross-sectional(cohort 1)and case-control(cohort 2),of patients with decompensated cirrhosis and ascites.Both cell count methods were conducted simultaneously.Positive SBP cases had a pathogenic bacteria isolated on AF and signs/symptoms of peritonitis.RESULTS A total of 137 cases with 5 positive-SBP,and 85 cases with 33 positive-SBP were included in cohort 1 and 2,respectively.Positive-SBP cases had worse liver function in both cohorts.The automated method showed higher sensitivity than the manual cell count:80%vs 52%,P=0.02,in cohort 2.Both methods showed very good specificity(>95%).The best cutoff using the automated cell counter was polymorph≥0.2 cells×10^(9)/L(equivalent to 200 cells/mm^(3))in AF as it has the higher sensitivity keeping a good specificity.CONCLUSION The automated cell count method should be preferred over the manual method to diagnose SBP because of its higher sensitivity.SBP definition,using the automated method,as polymorph cell count≥0.2 cells×10^(9)/L in AF would need to be considered in patients admitted with decompensated cirrhosis.

Numerical Solutions of the Classical and Modified Buckley-Leverett Equations Applied to Two-Phase Fluid Flow

Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.

基于VOF方法的超临界二氧化碳——水两相流动孔隙尺度数值模拟

二氧化碳(CO_(2))捕集与封存技术有利于减少CO_(2)的排放量,近年来针对CO_(2)地质封存形成了从纳米尺度到油气藏尺度的大量研究成果,大多数研究只针对单一维度多孔介质中流动行为开展研究,且物理实验方法受许多不确定性因素影响,十分耗费时间和成本。为了从微观角度深入理解CO_(2)地质封存过程中的渗流行为,提高CO_(2)地质埋存量,基于追踪两相界面动态变化的VOF(Volume of Fluid)方法,分别建立了2D和3D模型,开展了超临界CO_(2)-水两相流动数值模拟研究,对比了不同润湿性、毛细管数、黏度比条件下的CO_(2)团簇分布特征、CO_(2)饱和度变化规律,揭示了孔隙尺度CO_(2)埋存的内在机理。研究结果表明:①随着岩石对CO_(2)润湿性增加,CO_(2)波及范围扩大,同时CO_(2)团簇的卡断频率减少,CO_(2)埋存量增加;②随着毛细管数的增加,驱替模式由毛细指进转变为稳定驱替,CO_(2)埋存量增加;③随着注入超临界CO_(2)黏度逐渐接近水的黏度,两相流体之间的流动阻力降低,促进了“润滑效应”,CO_(2)相的渗流能力提高,CO_(2)埋存量增加;④润湿性、毛细管数、黏度比在不同维度多孔介质模型中对CO_(2)饱和度的影响程度不同。结论认为,基于VOF方法的CO_(2)-水两相渗流模拟研究在孔隙尺度上揭示了CO_(2)地质封存过程中的渗流机理,对CCUS技术的发展有指导意义,也为更大尺度的CO_(2)地质封存研究提供了理论指导和技术支撑。

基于VOF方法的可调参数对气泡聚并过程计算精度与成本的影响

气泡聚并通过改变气液两相间界面面积,影响相间的传热和传质,而聚并时间和液膜厚度是描述2个气泡聚并过程的重要物理参数。采用流体体积(VOF)方法对气泡聚并过程进行数值模拟时,合理设置计算流程中可调参数(例如网格尺寸、最大库朗数以及方程循环次数等),有助于提高求解过程的收敛性、节省计算时间。因此,本文基于OpenFOAM开源软件,采用VOF方法与自适应网格相结合的方法,以同轴两气泡聚并过程为例,探究最大库朗数Co_(max)、相方程循环次数nα和控制方程循环次数n_(pimple)这3个参数对气泡聚并过程数值模拟的计算量与计算精度的影响,同时,得到气泡间液膜厚度在可调参数不同取值时随时间的变化规律。研究结果表明:气泡间液膜的变薄速度与最大库朗数Co_(max)成反比,与相方程循环次数nα和控制方程循环次数n_(pimple)成正比,这主要是由于减小最大库朗数Co_(max)以及增大相方程循环次数nα和控制方程循环次数n_(pimple)提高了计算精度,改善了流体在网格单元上移动滞后的现象,加快了两气泡聚并以及液膜减薄过程;综合考虑计算精度与计算成本,得到了基于VOF方法的气泡聚并数值模拟较优的可调参数组合,即(Co_(max),nα,n_(pimple))=(0.05,3,8)。

Numerical simulation of solitary and random wave propagation through vegetation based on VOF method

A vertical two-dimensional numerical model has been applied to solving the Reynolds Averaged Navier- Stokes （RANS} equations in the simulation of current and wave propagation through vegetated and non- vegetated waters. The k-e model is used for turbulence closure of RANS equations. The effect of vegeta- tion is simulated by adding the drag force of vegetation in the flow momentum equations and turbulence model. To solve the modified N-S equations, the finite difference method is used with the staggered grid system to solver equations. The Youngs＇ fractional volume of fluid （VOF） is applied tracking the free sur- face with second-order accuracy. The model has been tested by simulating dam break wave, pure current with vegetation, solitary wave runup on vegetated and non-vegetated channel, regular and random waves over a vegetated field. The model reasonably well reproduces these experimental observations, the model- ing approach presented herein should be useful in simulating nearshore processes in coastal domains with vegetation effects.

DIFFERENTIAL QUADRATURE METHOD TO STABILITY ANALYSIS OF PIPES CONVEYING FLUID WITH SPRING SUPPORT

It is a new attempt to extend the differential quadrature method(DQM) to stability analysis of the straight and curved centerlinepipes conveying fluid. Emphasis is placed on the study of theinfluences of several parameters on the critical flow velocity.Compared to other methods, this method can more easily deal with thepipe with spring support at its boundaries and asks for much lesscomputing effort while giving ac- ceptable precision in the numericalresults.

Preparation of TiO_2-MoO_3 nano-composite photo-catalyst by supercritical fluid dry method

A series of TiO 2-MoO 3 nano-composite photocatalysts were prepared by supercritical fluid dry method(SCFD) and an impregnation technique with TiCl 4 and (NH 4) 6Mo 7O 24 ·4H 2O as the starting materials. The catalysts were characterized by the means of XRD, TEM and UV-Vis. Methyl orange was used as model compound for the evaluation of their catalytic activities. The results indicated that the photo-catalyst prepared by SCFD had the advantages of small size(12.84 nm), narrow distribution and good dispersivity. The presence of small amount of Mo in composite catalyst gives rise to the red shift of its absorbance wavelength, decrease of its energy gap and increase of the utility of visible light. Furthermore, higher surface acidity of the photo-catalyst was obtained as the result of the addition of MoO 3. Compared with pure TiO 2, the catalytic activity of the TiO 2-MoO 3 nano-composite photo-catalyst was improved significantly. As the doping concentration of the composite catalysts was controlled at 0.6%(molar percentage), 100% degradation of methyl orange was achieved with in 1.2 h irradiation time.

An Irregular Wave Maker of Active Absorption with VOF Method

A numerical irregular wave flume with active absorption of re-reflected waves is simulated by use of volume of fluid （VOF） method. An active ＇absorbing wave-maker based on linear wave theory is set on the left boundary of the wave flume. The progressive waves and the absorbing waves are generated simultaneously at the active wave generating-absorbing boundary. The absorbing waves are generated to eliminate the waves coming back to the generating boundary due to reflection from the outflow boundary and the structures. SIRW method proposed by Frigaard and Brorsen （1995） is used to separate the incident waves and reflected waves. The digital filters are designed based on the surface elevation signals of the two wave gauges. The corrected velocity of the wave-maker paddle is the output from the digital filter in real time. The numerical results of regular and irregular waves by the active absorbing-generating boundary are compared with the numerical results by the ordinary generating boundary to verify the performance of the active absorbing-generator boundary. The differences between the initial incident waves and the estimated incident waves are analyzed.

A GHOST FLUID BASED FRONT TRACKING METHOD FOR MULTIMEDIUM COMPRESSIBLE FLOWS

Recent years the modify ghost fluid method （MGFM） and the real ghost fluid method （RGFM） based on Riemann problem have been developed for multimedium compressible flows. According to authors, these methods have only been used with the level set technique to track the interface. In this paper, we combine the MCFM and the RGFM respectively with front tracking method, for which the fluid interfaces are explicitly tracked by connected points. The method is tested with some one-dimensional problems, and its applicability is also studied. Furthermore, in order to capture the interface more accurately, especially for strong shock impacting on interface, a shock monitor is proposed to determine the initial states of the Riemann problem. The present method is applied to various one- dimensional problems involving strong shock-interface interaction. An extension of the present method to two dimension is also introduced and preliminary results are given.