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.

Pedestrian flow through exit:Study focused on evacuation pattern

Experiments are conducted on the evacuation rate of pedestrians through exits with queued evacuation pattern and random evacuation pattern. The experimental results show that the flow rate of pedestrians is larger with the random evacuation pattern than with the queued evacuation pattern. Therefore, the exit width calculated based on the minimum evacuation clear width for every 100 persons, which is on the assumption that the pedestrians pass through the exit in one queue or several queues, is conservative. The number of people crossing the exit simultaneously is greater in the random evacuation experiments than in the queued evacuation experiments, and the time interval between the front row and rear row of people is shortened in large-exit conditions when pedestrians evacuate randomly. The difference between the flow rate with a queued evacuation pattern and the flow rate with a random evacuation pattern is related to the surplus width of the exit, which is greater than the total width of all accommodated people streams. Two dimensionless quantities are defined to explore this relationship. It is found that the difference in flow rate between the two evacuation patterns is stable at a low level when the surplus width of the exit is no more than 45% of the width of a single pedestrian stream. There is a great difference between the flow rate with the queued evacuation pattern and the flow rate with the random evacuation pattern in a scenario with a larger surplus width of the exit. Meanwhile, the pedestrians crowd extraordinarily at the exit in these conditions as well, since the number of pedestrians who want to evacuate through exit simultaneously greatly exceeds the accommodated level. Therefore, the surplus width of exit should be limited especially in the narrow exit condition, and the relationship between the two dimensionless quantities mentioned above could provide the basis to some extent.

Groundwater flow through fractured rocks and seepage control in geotechnical engineering: Theories and practices

Groundwater flow through fractured rocks has been recognized as an important issue in many geotechnical engineering practices.Several key aspects of fundamental mechanisms,numerical modeling and engineering applications of flow in fractured rocks are discussed.First,the microscopic mechanisms of fluid flow in fractured rocks,especially under the complex conditions of non-Darcian flow,multiphase flow,rock dissolution,and particle transport,have been revealed through a com-bined effort of visualized experiments and theoretical analysis.Then,laboratory and field methods of characterizing hydraulic properties(e.g.intrinsic permeability,inertial permeability,and unsaturated flow parameters)of fractured rocks in different flow regimes have been proposed.Subsequently,high-performance numerical simulation approaches for large-scale modeling of groundwater flow in frac-tured rocks and aquifers have been developed.Numerical procedures for optimization design of seepage control systems in various settings have also been proposed.Mechanisms of coupled hydro-mechanical processes and control of flow-induced deformation have been discussed.Finally,three case studies are presented to illustrate the applications of the improved theoretical understanding,characterization methods,modeling approaches,and seepage and deformation control strategies to geotechnical engi-neering projects.

Mathematical Modeling of Biological Fluid Flow Through a Cylindrical Layer with Due Account for Barodiffusion

The work proposes a model of biological fluid flow in a steady mode through a cylindrical layer taking into account convection and diffusion.The model considers finite compressibility and concentration expansion connected with both barodiffusion and additional mechanism of pressure change in the pore volume due to the concentration gradient.Thus,the model is entirely coupled.The paper highlights the complexes composed of scales of physical quantities of different natures.The iteration algorithm for the numerical solution of the problem was developed for the coupled problem.The work involves numerical studies of the considered effects on the characteristics of the flow that can be convective or diffusive,depending on the relation between the dimensionless complexes.It is demonstrated that the distribution of velocity and concentration for different cylinder wall thicknesses is different.It is established that the barodiffusion has a considerable impact on the process in the convective mode or in the case of reduced cylinder wall thickness.

EFFECT OF THE MAGNETIC FIELD ON THE PULSATILE FLOW THROUGH A RIGID TUBE

This study presents the effect of the magnetic field with constant intensity on the pulsatile flow through a rigid tube. Basing on the experimental results, the influence of the magnetic field on the blood viscosity is considered The analytic solution of the pulsatile flow through a rigid tube under constant magnetic field intensitier and the effect of the magnetic field on the velocity distribution, flow and impedance in a rigid tube are given. this investigation is valuable for understanding the influence of the magnetic field on the blood circulation.

VISUALIZATION OF FLOW THROUGH A ROTATING U-BEND DUCT

The flow through a rotating U bend duct is investigated by means of visualization. The U bend duct has a cross section of 50 mm×50 mm and a ratio of bend mean radius R c to hydraulic diameter of the duct D of 0.65. The rotation axis is parallel with the bend axis. Three cases with rotation number of Ro=-0.2, 0 and 0.2, respectively, are studied at a Reynolds number of 100 000. The results show that the combined effect of rotation and bend curvature strongly influences the flow field, especially in the downstream region of the bend. The evident difference among the flow patterns with different rotation number shows that the secondary flow induced by Coriolis force takes an important role in determining the flow structure.

CARBON WIRE AMPEROMETRIC FLOW THROUGH DETECTOR

A carbon wire amperometric flow through detector is described which is easily constructed at low cost for application to flow injection analysis,continuous stream analysis and liquid chromatography.The theoretical limiting current of the detector is 2.14×10~6nCD^(2/3)u_f^(1/3) with 36% actual current efficiency.By use of flow injection analysis,the detecting limits for Ag(I)and Cr(VI)had achieved 1 ppb and 0.4 ppb respectively with 1.2%(n=20)relative standard deviation after preliminary experiments.

SIMULATION OF GAS AND LIQUID TWO-PHASE FLOW THROUGH THE BLAST FURNACE DROPPING ZONE

A three-dimensional mathematical model,based on differential balances of mass and momentum,hasbeen developed to describe the two-phase flow of gas and liquid through the dropping zone of the blast fur-nace.Agreement between observed and calculated values verifies the validity of this model.On the basis of this model,various parameters for the surrounding of the dry zone of Blast FurnaceNo.I-BF of the Beijing Iron and Steel Company have been computed,from which a diagram for demar-cation of fluidization of coke and flooding of slag has been proposed.

Time-Frequency Signal Processing for Gas-Liquid Two Phase Flow Through a Horizontal Venturi Based on Adaptive Optimal-Kernel Theory

A time-frequency signal processing method for two-phase flow through a horizontal Venturi based on adaptive optimal-kernel （AOK） was presented in this paper.First,the collected dynamic differential pressure signal of gas-liquid two-phase flow was preprocessed,and then the AOK theory was used to analyze the dynamic differ-ential pressure signal.The mechanism of two-phase flow was discussed through the time-frequency spectrum.On the condition of steady water flow rate,with the increasing of gas flow rate,the flow pattern changes from bubbly flow to slug flow,then to plug flow,meanwhile,the energy distribution of signal fluctuations show significant change that energy transfer from 15-35 Hz band to 0-8 Hz band;moreover,when the flow pattern is slug flow,there are two wave peaks showed in the time-frequency spectrum.Finally,a number of characteristic variables were defined by using the time-frequency spectrum and the ridge of AOK.When the characteristic variables were visu-ally analyzed,the relationship between different combination of characteristic variables and flow patterns would be gotten.The results show that,this method can explain the law of flow in different flow patterns.And characteristic variables,defined by this method,can get a clear description of the flow information.This method provides a new way for the flow pattern identification,and the percentage of correct prediction is up to 91.11%.

The micropolar fluid model for blood flow through a tapered artery with a stenosis

A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter （referred to as the shape parameter）. The model is also used to study the effect of the taper angle Ф. Flow parameters such as the velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis （stenosis throat） have been computed for different values of the shape parameter n, the taper angle Ф, the coupling number N and the micropolar parameter m. It is shown that the resistance to flow decreases with increasing the shape parameter n and the micropolar parameter m while it increases with increasing the coupling number N. So, the magnitude of the resistance impedance is higher for a micropolar fluid than that for a Newtonian fluid model. Finally, the velocity profile, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis are discussed for different values of the parameters involved on the problem.

Heat transfer of copper/water nanofluid flow through converging-diverging channel

The main objective of this work is to investigate analytically the steady nanofluid flow and heat transfer characteristics between nonparallel plane walls. Using appropriate transformations for the velocity and temperature, the basic nonlinear partial differential equations are reduced to the ordinary differential equations. Then, these equations have been solved analytically and numerically for some values of the governing parameters, Reynolds number, Re, channel half angle, α, Prandtl number, Pr, and Eckert number, Ec, using Adomian decomposition method and the Runge-Kutta method with mathematic package. Analytical and numerical results are searched for the skin friction coefficient, Nusselt number and the velocity and temperature profiles. It is found on one hand that the Nusselt number increases as Eckert number or channel half-angle increases, but it decreases as Reynolds number increases. On the other hand, it is also found that the presence of Cu nanoparticles in a water base fluid enhances heat transfer between nonparallel plane walls and in consequence the Nusselt number increases with the increase of nanoparticles volume fraction. Finally, an excellent agreement between analytical results and those obtained by numerical Runge-Kutta method is highly noticed.

Influence of magnetic field and Hall currents on blood flow through a stenotic artery

A micropolar model for blood simulating magnetohydrodynamic flow through a horizontally nonsymmetric but vertically symmetric artery with a mild stenosis is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the horizontal shape of the stenosis can easily be changed just by varying a parameter referred to as the shape parameter. Flow parameters, such as velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region, and its magnitude at the maximum height of the stenosis （stenosis throat）, have been computed for different shape parameters, the Hartmann number and the Hall parameter. This shows that the resistance to flow decreases with the increasing values of the parameter determining the stenosis shape and the Hail parameter, while it increases with the increasing Hartmann number. The wall shear stress and the shearing stress on the wall at the maximum height of the stenosis possess an inverse characteristic to the resistance to flow with respect to any given value of the Hartmann number and the Hall parameter. Finally, the effect of the Hartmann number and the Hall parameter on the horizontal velocity is examined.

Simulation of Variable Viscosity and Jeffrey Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis

Non-Newtonian fluid model for blood flow through a tapered artery with a stenosis and variable viscosity by modeling blood as Jeffrey fluid has been studied in this paper. The Jeffrey fluid has two parameters, the relaxation time A1 and retardation time A2. The governing equations are simplified using the case of mild stenosis. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, temperature profile, wall shear stress, shearing stress at the stenotsis throat and impedance of the artery are discussed. The results for Newtonian fluid are obtained as special case from this model.

Numerical investigation of velocity distribution of turbulent flow through vertically double-layered vegetation

The velocity structures of flow through vertically double-layered vegetation(VDLV)as well as single-layered rigid vegetation(SLV)were investigated computationally with a three-dimensional(3D)Reynolds stress turbulence model,using the computational fluid dynamics(CFD)code FLUENT.The detailed velocity distribution was explored with a varying initial Froude number(Fr),with consideration of the steady subcritical flow conditions of an inland tsunami.In VDLV flows,the numerical model successfully captured the inflection point in the profiles of mean streamwise velocities in the mixing-layer region around the top of short submerged vegetation.An upward and downward movement of flow occurred at the positions located just behind the tall and short vegetation,respectively.Overall,higher streamwise velocities were observed in the upper vegetation layer due to high porosity,with Pr=98%(sparse vegetation,where Pr is the porosity),as compared to those in the lower vegetation layer,which had comparatively low porosity,with Pr=91%(dense vegetation).A rising trend of velocities was found as the flow passed through the vegetation region,followed by a clear sawtooth distribution,as compared to the regions just upstream and downstream of vegetation where the flow was almost uniform.In VDLV flows,a rising trend in the flow resistance was observed with the increase in the initial Froude number,i.e.,Fr?0.67,0.70,and 0.73.However,the flow resistance in the case of SLV was relatively very low.The numerical results also show the flow structures within the vicinity of short and tall vegetation,which are difficult to attain through experimental measurements.

Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat trans- fer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two- and three-dimensional flow phenom- ena are also shown through graphical results.

Calculation of the ultimate depth of a scour pit after debris flow through drainage canal ribs

Drainage canals are engineering structures widely used for debris flow mitigation.When passing through a drainage canal,debris flow usually scours the gully bed at the back of the rib sill of the drainage canal,which leads to failure of the rib sill.Therefore,the scour depth at the back of the rib sill is an important design problem and it is related to the economic benefits of engineering and service years.To explore the law of the depth of the scour pit after debris flow through drainage canal ribs,we first proposed a formula for the calculation of the maximum scour depth at the back of a rib sill based on energy conservation.We then conducted a series of simulation experiments to test the proposed formula.The experimental results show that the scour depth,trench slope and the distance between ribs all increase with a decrease in debris flow density.We then compared the results of experiments and formula calculations.Through the testing analysis,we found that the calculation results of the conductedformula correspond with the experimental results better.Finally,taking Qipan Gully as an example,we designed the ultimate depth of a drainage canal for debris flow using the calculation formula.

GLOBAL EXISTENCE AND BLOW-UP PHENOMENA OF CLASSICAL SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA

By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.

Nonlinear fluid flow through three-dimensional rough fracture networks:Insights from 3D-printing,CT-scanning,and high-resolution numerical simulations

Nonlinear flow behavior of fluids through three-dimensional(3D)discrete fracture networks(DFNs)considering effects of fracture number,surface roughness and fracture aperture was experimentally and numerically investigated.Three physical models of DFNs were 3D-printed and then computed tomography(CT)-scanned to obtain the specific geometry of fractures.The validity of numerically simulating the fluid flow through DFNs was verified via comparison with flow tests on the 3D-printed models.A parametric study was then implemented to establish quantitative relations between the coefficients/parameters in Forchheimer’s law and geometrical parameters.The results showed that the 3D-printing technique can well reproduce the geometry of single fractures with less precision when preparing complex fracture networks,numerical modeling precision of which can be improved via CT-scanning as evidenced by the well fitted results between fluid flow tests and numerical simulations using CT-scanned digital models.Streamlines in DFNs become increasingly tortuous as the fracture number and roughness increase,resulting in stronger inertial effects and greater curvatures of hydraulic pressure-low rate relations,which can be well characterized by the Forchheimer’s law.The critical hydraulic gradient for the onset of nonlinear flow decreases with the increasing aperture,fracture number and roughness,following a power function.The increases in fracture aperture and number provide more paths for fluid flow,increasing both the viscous and inertial permeabilities.The value of the inertial permeability is approximately four orders of magnitude greater than the viscous permeability,following a power function with an exponent a of 3,and a proportional coefficient b mathematically correlated with the geometrical parameters.

Computation of flow through the oesophagogastric junction

Whilst methods exist to indirectly measure the effects of increased flow or gastro-oesophageal refluxing, they cannot quantitatively measure the amount of acid travelling back up into the oesophagus during reflux, nor can they indicate the flow rate through the oesophagogastric junction (OGJ). Since OGJ dysfunction affects flow it seems most appropriate to describe the geometry of the OGJ and its effect on the flow. A device known as the functional lumen imaging probe (FLIP) has been shown to reliably measure the geometry of and pressure changes in the OGJ. FLIP cannot directly measure flow but the data gathered from the probe can be used to model flow through the junction by using computational flow dynamics (CFD). CFD uses a set of equations known as the Navier-Stokes equations to predict flow patterns and is a technique widely used in engineering. These equations are complex and require appropriate assumptions to provide simplifications before useful data can be obtained. With the assumption that the cross-sectional areas obtained via FLIP are circular, the radii of these circles can be obtained. A cubic interpolation scheme can then be applied to give a high-resolution geometry for the OGJ. In the case of modelling a reflux scenario, it can be seen that at the narrowest section a jet of fluid squirts into the oesophagus at a higher velocity than the fluid surrounding it. This jet has a maximum velocity of almost 2 ms-1 that occurs where the OGJ is at its narrowest. This simple prediction of acid ‘squirting’ into the oesophagusillustrates how the use of numerical methods can be used to develop a better understanding of the OGJ. This initial work using CFD shows some considerable promise for the future.

Mathematical modeling and parametric investigation of blood flow through a stenosis artery

In this study,a mathematical model is formulated to examine the blood flow through a cylindrical stenosed blood vessel.The stenosis disease is caused because of the abnormal narrowing of flow in the body.This narrowing causes serious health issues like heart attack and may decrease blood flow in the blood vessel.Mathematical modeling helps us analyze such issues.A mathematical model is considered in this study to explore the blood flow in a stenosis artery and is solved numerically with the finite difference method.The artery is an elastic cylindrical tube containing blood defined as a viscoelastic fluid.A complete parametric analysis has been done for the flow velocity to clarify the applicability of the defined problem.Moreover,the flow characteristics such as the impedance,the wall shear stress in the stenotic region,the shear stresses in the throat of the stenosis and at the critical stenosis height are discussed.The obtained results show that the intensity of the stenosis occurs mostly at the highest narrowing areas compared with all other areas of the vessel,which has a direct impact on the wall shear stress.It is also observed that the resistive impedance and wall shear pressure get the maximum values at the critical height of the stenosis.