Dynamic modelling and engineering simulation of fluid mechanics in water injectors

To study the fluid dynamic response mechanism under the working condition of water injection well borehole,based on the microelement analysis of fluid mechanics and the classical theory of hydrodynamics,a fluid microelement pressure-flow rate relationship model is built to derive and solve the dynamic distribution of fluid pressure and flow rate in the space of well borehole.Combined with the production data of a typical deviated well in China,numerical simulations and analyses are carried out to analyze the dynamic distribution of wellbore pressure at different injection pressures and injection volumes,the delayed and attenuated characteristics of fluid transmission in tube,and the dynamic distribution of wellbore pressure amplitude under the fluctuation of wellhead pressure.The pressure loss along the wellbore has nothing to do with the absolute pressure,and the design of the coding and decoding scheme for wave code communication doesn’t need to consider the absolute pressure during injecting.When the injection pressure is constant,the higher the injection flow rate at the wellhead,the larger the pressure loss along the wellbore.The fluid wave signal delay amplitude mainly depends on the length of the wellbore.The smaller the tubing diameter,the larger the fluid wave signal attenuation amplitude.The higher the target wave code amplitude(differential pressure identification root mean square)generated at the same well depth,the greater the wellhead pressure wave amplitude required to overcome the wellbore pressure loss.

Analysis of a Propeller Wake Flow Field Using Viscous Fluid Mechanics

The computational fluid dynamics （CFD） method is used to numerically simulate a propeller wake flow field in open water. A sub-domain hybrid mesh method was adopted in this paper. The computation domain was separated into two sub-domains, in which tetrahedral elements were used in the inner domain to match the complicated geometry of the propeller, while hexahedral elements were used in the outer domain. The mesh was locally refined on the propeller surface and near the wake flow field, and a size function was used to control the growth rate of the grid. Sections at different axial location were used to study the spatial evolution of the propeller wake in the region ranging from the disc to one propeller diameter （D） downstream. The numerical results show that the axial velocity fluctuates along the wake flow; radial velocity, which is closely related to vortices, attenuates strongly. The trailing vortices interact with the tip vortex at the blades＇ trailing edge and then separate. The strength of the vortex shrinks rapidly, and the radius decreases 20% at one diameter downstream.

A Unified Variational Principle of Fluid Mechanics and Application on Solitary Subdomain or Point

-According to basic equations of fluid mechanics, this paper presents a unified variational principle of fluid mechanics (UVPFM) by using the optimization method of weighted residuals (OMWR). The advantages are as follows, the establishment of the functional and the variational principle is easy, it can change various problems of fluid mechanics derived by basic equations into a unified optimization problem, and the solution is the optimum one in some sense. According to the OMWR for the solitary subdomain, this paper uses UVPFM onto any solitary subdomain and gives the solution of the hydrodynamics equation which is suitable only for that solitary subdomain. According to the OMWR for solitary point, this paper uses UVPFM to any solitary point and gives the solution of the hydrodynamics equation (point solution) which is suitable only for that solitary point. As the solution for the solitary subdomain or solitary point is developed independently, the compatibility with other subdomain or other points, does not need to be considered, but all the boundary conditions and the supplementary derived residual equations obtained by running the derivative operations to the differential equation should be taken into account.

A two-phase type-curve method with multiscale fluid transport mechanisms in hydraulically fractured shale reservoirs

The quantitative understanding of hydraulic fracture(HF)properties guides accurate production forecasts and reserve estimation.Type curve is a powerful technique to characterize HF and reservoir properties from flowback and long-term production data.However,two-phase flow of water and hydrocarbon after an HF stimulation together with the complex transport mechanisms in shale nanopores exacerbate the nonlinearity of the transport equation,causing errors in type-curve analysis.Accordingly,we propose a new two-phase type-curve method to estimate HF properties,such as HF volume and permeability of fracture,through the analysis of flowback data of multi-fractured shale wells.The proposed type curve is based on a semianalytical solution that couples the two-phase flow from the matrix with the flow in HF by incorporating matrix influx,slippage effect,stress dependence,and the spatial variation of fluid properties in inorganic and organic pores.For the first time,multiple fluid transport mechanisms are considered into two-phase type-curve analysis for shale reservoirs.We analyze the flowback data from a multi-fractured horizontal well in a shale gas reservoir to verify the field application of the proposed method.The results show that the fracture properties calculated by the type-curve method are in good agreement with the long-time production data.

Numerical method and analysis of computational fluid mechanics for photoelectric semiconducting detector

We propose a modified upwind finite difference fractional step scheme for the computational fluid mechanics simulations of a three-dimensional photoelectric semiconductor detector. We obtain the optimal l^2-norm error estimates by using the techniques including the calculus of variations, the energy methods, the induction hypothesis, and a priori estimates. The proposed scheme is successfully applied to the simulation of the photoelectric semiconductor detectors.

Painlevé Analysis,Soliton Solutions and Bcklund Transformation for Extended (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations in Fluid Mechanics via Symbolic Computation

This paper is to investigate the extended(2+1)-dimensional Konopelchenko-Dubrovsky equations,which can be applied to describing certain phenomena in the stratified shear flow,the internal and shallow-water waves, plasmas and other fields.Painleve analysis is passed through via symbolic computation.Bilinear-form equations are constructed and soliton solutions are derived.Soliton solutions and interactions are illustrated.Bilinear-form Backlund transformation and a type of solutions are obtained.

Feature Selection with Fluid Mechanics Inspired Particle Swarm Optimization for Microarray Data

Deoxyribonucleic acid（ DNA） microarray gene expression data has been widely utilized in the field of functional genomics,since it is helpful to study cancer,cells,tissues,organisms etc.But the sample sizes are relatively small compared to the number of genes,so feature selection is very necessary to reduce complexity and increase the classification accuracy of samples. In this paper,a completely newimprovement over particle swarm optimization（ PSO） based on fluid mechanics is proposed for the feature selection. This newimprovement simulates the spontaneous process of the air from high pressure to lowpressure,therefore it allows for a search through all possible solution spaces and prevents particles from getting trapped in a local optimum. The experiment shows that,this newimproved algorithm had an elaborate feature simplification which achieved a very precise and significant accuracy in the classification of 8 among the 11 datasets,and it is much better in comparison with other methods for feature selection.

Using Image Processing Technology and General Fluid Mechanics Principles to Model Smoke Diffusion in Forest Fires

In the present study,the laws of smoke diffusion during forest fires are determined using the general principles of fluid mechanics and dedicated data obtained experimentally using an“ad hoc”imaging technology.Experimental images mimicking smoke in a real scenario are used to extract some“statistics”.These in turn are used to obtain the“divergence”of the flow(this fluid-dynamic parameter describing the amount of air that converges to a certain place from the surroundings or vice versa).The results show that the divergence of the smoke depends on the outside airflow and finally tends to zero as time passes.Most remarkably,compared with clouds and fog,smoke has a unique dynamic time-evolution curve.The present study demonstrates that as long as image processing technology and intelligent monitoring technology are used to monitor the gas flow in a forest,the occurrence of forest fires can be quickly diagnosed.

A UNIVERSAL VARIATIONAL FORMULATION FOR TWO DIMENSIONAL FLUID MECHANICS

A universal variational formulation for two dimensional fluid mechanics is obtained. which is subject to the so-called parameter-constrained equations (the relationship between parameters in two governing equations). By eliminating the constraints the generalized variational principle (GVPs) can be readily derived from the formulation The formulation can be applied to any conditions in case the governing equations can be converted into conservative forms. Some illustrative examples are given to testify the effectiveness and simplicity of the method.

FLUID MECHANICS OF MICROVASCULAR VASOMOTION AND THE EFFECTS OF BLOOD VISCOELASTICITY

This paper deals with blood flow caused by microvascular vasomotion with the focus on the effects of blood viscoelasticity on the pressure rise and wall resistance. It is shown that microvascular vasomotion plays a role of the 'second heart' of the body which is of importance in conveying blood, and that the effects of blood viscoelasticity greatly depend on the Weissenberg number and mean flow rate.

Deep Learning Applied to Computational Mechanics:A Comprehensive Review,State of the Art,and the Classics

Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.

Introducing CFD and Wind Tunnel Testing in an Undergraduate Fluid Mechanics Course

CFD （computational fluid dynamics） is following the trend of CAD and FEA （finite element analysis） to undergraduate education especially with recent advances in commercial codes. It will soon take its place as an expected skill for new engineering graduates. CFD was added as a component to an experiment in a junior level fluid mechanics course. The objectives were to introduce CFD, as an analysis tool, to the students and to support the theoretical concepts of the course. The students were asked to complete an experimental two-dimensional study for a wing in a wind tunnel, to use CFD to simulate the flow, and to predict the aerodynamic lift using CFD as well as the experimentally obtained pressure distribution. In addition, they had to compare their results to published data for the studied wing. Details of the course, the wind tunnel test and the CFD simulations are presented. Samples from the students＇ work are used in the discussion. The lab activities were successfully completed by the students and the learning objectives were well addressed. One of the valuable outcomes from this lab was the opportunity for the students to integrate multiple fluid mechanics analysis tools and learn about the limits for each tool. CFD also enhanced the learning in the lab activities and increased students＇ interest in the subject.

MY WORK IN THE FIELD OF FLUID MECHANICS

I graduated from the National Peiyang University (now called Tianjin University) in 1950, majoring in hydraulic engineering. Starting from 1952, my teaching work was basically in mechanics.My first academic probe was in cybernetics, resulting in the publication of the first Chinese paper concerning optimal control. After 1963, I worked on the theory of hydrodynamic stability. My explorative thrust is at the eigenvalues of the Orr Sommerfeld Equation,a non-self adjoint problem in

Mass transfer enhancement and hydrodynamic performance with wire mesh coupling solid particles in bubble column reactor

It is of vital significance to investigate mass transfer enhancements for chemical engineering processes.This work focuses on investigating the coupling influence of embedding wire mesh and adding solid particles on bubble motion and gas-liquid mass transfer process in a bubble column.Particle image velocimetry(PIV)technology was employed to analyze the flow field and bubble motion behavior,and dynamic oxygen absorption technology was used to measure the gas-liquid volumetric mass transfer coefficient(kLa).The effect of embedding wire mesh,adding solid particles,and wire mesh coupling solid particles on the flow characteristic and kLa were analyzed and compared.The results show that the gas-liquid interface area increases by 33%-72%when using the wire mesh coupling solid particles strategy compared to the gas-liquid two-phase flow,which is superior to the other two strengthening methods.Compared with the system without reinforcement,kLa in the bubble column increased by 0.5-1.8 times with wire mesh coupling solid particles method,which is higher than the sum of kLa increases with inserting wire mesh and adding particles,and the coupling reinforcement mechanism for affecting gas-liquid mass transfer process was discussed to provide a new idea for enhancing gas-liquid mass transfer.

Optimizing the Diameter of Plugging Balls in Deep Shale Gas Wells

Deep shale gas reserves that have been fractured typically have many relatively close perforation holes. Due to theproximity of each fracture during the formation of the fracture network, there is significant stress interference,which results in uneven fracture propagation. It is common practice to use “balls” to temporarily plug fractureopenings in order to lessen liquid intake and achieve uniform propagation in each cluster. In this study, a diameteroptimization model is introduced for these plugging balls based on a multi-cluster fracture propagationmodel and a perforation dynamic abrasion model. This approach relies on proper consideration of the multiphasenature of the considered problem and the interaction force between the involved fluid and solid phases. Accordingly,it can take into account the behavior of the gradually changing hole diameter due to proppant continuousperforation erosion. Moreover, it can provide useful information about the fluid-dynamic behavior of the consideredsystem before and after plugging. It is shown that when the diameter of the temporary plugging ball is1.2 times that of the perforation hole, the perforation holes of each cluster can be effectively blocked.

The Jaffa Transform for Hessian Matrix Systems and the Laplace Equation

Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation.

Computational Fluid-dynamics of Liquid Phase Flow on Distillation Column Trays

A computational fluid-dynamics model is presented for predictingthe two-phase two-dimensional liquid phase flow on a distillationcolumn tray based on the modification of Navier-Stokes Equation byconsidering both the resistance and the enhanced turbulence createdby the uprising vapor. Experimental measurement of the local liquidphase velocity on an air-water simulator of 1.2 m in diameter byusing the hot film anemometer is briefly described. Two of theconventional fluid-dynamic constants are readjusted for the case ofliquid flow on a tray by fitting the experimental data.

A multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone

The transport of fluid, nutrients, and signaling molecules in the bone lacunar-canalicular system （LCS） is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching （FRAP） approach to quantify load-induced fluid and solute transport in the LCS in situ, but the measurements were limited to cortical regions 30-50 μm underneath the periosteum due to the constrains of laser penetration. With this work, we aimed to expand our understanding of load-induced fluid and solute transport in both trabecular and cortical bone using a multiscaled image-based finite element analysis （FEA） approach. An intact murine tibia was first re-constructed from microCT images into a three-dimensional （3D） linear elastic FEA model, and the matrix deformations at various locations were calculated under axial loading. A segment of the above 3D model was then imported to the biphasic poroelasticity analysis platform （FEBio） to predict load-induced fluid pressure fields, and interstitial solute/fluid flows through LCS in both cortical and trabecular regions. Further, secondary flow effects such as the shear stress and/or drag force acting on osteocytes, the presumed mechano-sensors in bone, were derived using the previously developed ultrastructural model of Brinkman flow in the canaliculi. The material properties assumed in the FEA models were validated against previously obtained strain and FRAP transport data measured on the cortical cortex. Our results demonstrated the feasibility of this computational approach in estimating the fluid flux in the LCS and the cellular stimulation forces （shear and drag forces） for osteocytes in any cortical and trabecular bone locations, allowing further studies of how the activation of osteocytes correlates with in vivo functional bone formation. The study provides a promising platform to reveal potential cellular mechanisms underlying the anabolic power of exercises and physical activities in treating patients with skeletal deficiencies.

Sensitivity Analysis and Optimization of Geometric Parameters of a New Fluid Bag Buffer Mechanism on Buffering Performance

A new fluid bag buffer mechanism,which can provide large axial stiffness under the small displacement,is designed.The dynamic change laws of the mechanism stiffness and the internal pressure of the fluid bag are studied when it is subjected to impact load.According to the protection performance for the flexible joint and the pressure change in the fluid bag during the impact process,the sensitivity of the geometric parameters of the fluid bag to the axial stiffness is analyzed by using the orthogonal experimental method,and the optimal parameter combination of the geometric parameters of the fluid bag under impact is obtained,leading to the displacement of the inner shell reduce by 41.4%.The results show that the internal pressure of the fluid bag is a rising process of oscillation and fluctuation.The sensitivity of the geometric parameters of the fluid bag to the displacement of the inner shell from high to low is as follows:Height H,radius r,wall thickness t,chamfer A.The correlation between the geometric parameters of the fluid bag and its internal pressure is:H is negatively correlated with the internal pressure,while the r,t,and A are positively correlated with the internal pressure.

ANALYTICAL SOLUTIONS OF SINGULARITIES MOVING WITH AN ARBITRARY PATH WHEN TWO FLUIDS ARE PRESENT

The derivations are carried out for the velocity potentials of singularities moving with an arbitrary path either in the upper fluid or in the lower fluid with or without a horizontal bottom when two fluids are present. In such a case, the pressure distribution is no longer equal to a constant or zero at the free interface. Taking the influence of an upper fluid upon the lower fluid into consideration, a series of fundamental solutions in closed forms are presented in this paper.