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.

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.

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.

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.

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.

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.

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.

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.

MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method

This paper investigates the magnetohydrodynamic （MHD） boundary layer flow of an incompressible upper-convected Maxwell （UCM） fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear prob- lem is solved by using the successive Taylor series linearization method （STSLM）. The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.

A review of methods,applications and limitations for incorporating fluid flow in the discrete element method

The past decade has witnessed the substantial growth in research interests and progress on the subject of coupled hydro-mechanical processes in rocks and soils,driven mainly by the surge of research in unconventional hydrocarbon reservoirs and associated hazards.Many coupling techniques have been developed to include the effects of fluid flow in the discrete element method(DEM),and the techniques have been applied to a variety of geomechanical problems.Although these coupling methods have been successfully applied in various engineering fields,no single fluid/DEM coupling method is universal due to the complexity of engineering problems and the limitations of the numerical methods.For researchers and engineers,the key to solve a specific problem is to select the most appropriate fluid/DEM coupling method among these modeling technologies.The purpose of this paper is to give a comprehensive review of fluid flow/DEM coupling methods and relevant research.Given their importance,the availability or unavailability of best practice guidelines is outlined.The theoretical background and current status of DEM are introduced first,and the principles,applications,and advantages and disadvantages of different fluid flow/DEM coupling methods are discussed.Finally,a summary with speculation on future development trends is given.

Numerical simulation of single bubble rising in shear-thinning fluids by level set method

The behavior of single bubble rising in quiescent shear-thinning tlmds was lnvestlgateO numerically by level set metnoa. number of bubbles in a large range of Reynolds number and Eotvos number were investigated including spherical, oblate and spherical. The bubble shape and drag coefficient were compared with experimental results. It is observed that the simulated results show good conformity to experimental results over a wide range of Reynolds number. In addition, the detailed flow field based on the reference coordinate system moving with the bubble is obtained, and the relationship among flow field, bubble shape and velocity is discussed.

Application of Multi-Step Differential Transform Method on Flow of a Second-Grade Fluid over a Stretching or Shrinking Sheet

In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.

Unstructured Grid Immersed Boundary Method for Numerical Simulation of Fluid Structure Interaction

This paper presents an improved unstructured grid immersed boundary method.The advantages of both immersed boundary method and body fitted grids which are generated by unstructured grid technology are used to enhance the computation efficiency of fluid structure interaction in complex domain.The Navier-Stokes equation was discretized spacially with collocated finite volume method and Euler implicit method in time domain.The rigid body motion was simulated by immersed boundary method in which the fluid and rigid body interface interaction was dealt with VOS(volume of solid) method.A new VOS calculation method based on graph was presented in which both immersed boundary points and cross points were collected in arbitrary order to form a graph.The method is verified with flow past oscillating cylinder.

Stabilization for Equal-Order Polygonal Finite Element Method for High Fluid Velocity and Pressure Gradient

This paper presents an adapted stabilisation method for the equal-order mixed scheme of finite elements on convex polygonal meshes to analyse the high velocity and pressure gradient of incompressible fluid flows that are governed by Stokes equations system.This technique is constructed by a local pressure projection which is extremely simple,yet effective,to eliminate the poor or even non-convergence as well as the instability of equal-order mixed polygonal technique.In this research,some numerical examples of incompressible Stokes fluid flow that is coded and programmed by MATLAB will be presented to examine the effectiveness of the proposed stabilised method.

MHD Falkner-Skan flow of Maxwell fluid by rational Chebyshev collocation method

The magnetohydrodynamics （MHD） Falkner-Skan flow of the Maxwell fluid is studied. Suitable transform reduces the partial differential equation into a nonlinear three order boundary value problem over a semi-infinite interval. An efficient approach based on the rational Chebyshev collocation method is performed to find the solution to the proposed boundary value problem. The rational Chebyshev collocation method is equipped with the orthogonal rational Chebyshev function which solves the problem on the semi-infinite domain without truncating it to a finite domain. The obtained results are presented through the illustrative graphs and tables which demonstrate the affectivity, stability, and convergence of the rational Chebyshev collocation method. To check the accuracy of the obtained results, a numerical method is applied for solving the problem. The variations of various embedded parameters into the problem are examined.

Differential Quadrature Method for Steady Flow of an Incompressible Second-Order Viscoelastic Fluid and Heat Transfer Model

The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.