Numerical Investigation of Lid-Driven Deep Cavity with Local Grid Refinement of MRT-LBM

In the case of lid-driven deep cavity flow, the effects of different resolutions of local grid refinement have been studied in the frame of multiple relaxation times (MRT) lattice Boltzmann method (LBM). In all the cases, the aspect ratio and Reynolds number are set as 1.5 and 3.200, respectively. First, the applied method is validated by comparing it with two reported works, with which agreements are reached. Then, six separate degrees of local grid refinement at the upper left corner, i.e. purely coarse grid, including 1/64, 1/32, 1/16, 1/8, 1/4 refinements of the lattice number in the width direction have been studied in detail. The results give the following indications:① The refinement degrees lower than 1/8 produce similar results;② For single corner refinement, 1/4 refinement is adequate for clearing the noises in the singularity zone to a large extent;③ New noise around the interface between coarse and fine zones are introduced by local grid refinement. Finally, refinement of entire subzone neighboring the lid is examined to avoid introducing new noises and it has been found effective.

Mixing of miscible shear-thinning fluids in a lid-driven cavity

The concentration and velocity fields of two refractive index matched miscible shear-thinning fluids in a lid-driven cavity were investigated by using planar laser-induced fluorescence and particle image velocimetry,as well by computational fluid dynamics.Quantitative analyses show that the results obtained by flow simulations with the species transport model are in good agreement with the experimental results.The effects of different parameters were studied by using the intensity of segregation.For two fluids with the same rheological parameters,the relative amounts of liquids H_(1)/H and the power-law index n dominate the mixing process while the Reynolds number Re plays a marginal role.As for two fluids with density difference,buoyancy has significant influence on the mixing process.The dimensionless group Ar/Re(redefined such as to include shear thinning behavior)is proposed for assessing the effect of buoyancy and rheological properties on the mixing of miscible shear-thinning fluids.

Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.

The second Hopf bifurcation in lid-driven square cavity

To date, there are very few studies on the second Hopf bifurcation in a driven square cavity, although there are intensive investigations focused on the first Hopf bifurcation in literature, due to the difficulties of theoretical analyses and numerical simulations. In this paper, we study the characteristics of the second Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme recently developed by us. We numerically identify the critical Reynolds number of the second Hopf bifurcation located in the interval of(11093.75, 11094.3604) by bisection. In addition, we find that there are two dominant frequencies in its spectral diagram when the flow is in the status of the second Hopf bifurcation, while only one dominant frequency is identified if the flow is in the first Hopf bifurcation via the Fourier analysis. More interestingly, the flow phase portrait of velocity components is found to make transition from a regular elliptical closed form for the first Hopf bifurcation to a non-elliptical closed form with self-intersection for the second Hopf bifurcation. Such characteristics disclose flow in a quasi-periodic state when the second Hopf bifurcation occurs.

Transition to chaos in lid-driven square cavity flow

To date,there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity,due to the difficulties in theoretical analysis and numerical simulations.In this paper,we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us.We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of(13944.7021,13946.5333)by the method of bisection.Through Fourier analysis,it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval.Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram,Kolmogorov entropy and maximal Lyapunov exponent.The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.

SUPG finite element method based on penalty function for lid-driven cavity flow up to Re = 27500

A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.

A new failure mechanism for deep cavity and upper bound solution of supporting pressure

The investigation of supporting pressure is of great significance to the design of underground structures.Based on the kinematical approach of limit analysis,an improved failure mechanism is proposed,and the supporting pressure is investigated for deep buried cavity.Three failure mechanisms are first introduced according to the existing failure mechanisms of geotechnical structures of limit analysis.A comparison with respect to the optimal failure mechanisms and the upper bound solutions provided among these three mechanisms are then conducted in an attempt to obtain the improved failure mechanism.The results provided by the improved failure mechanism are in good agreement with those by the existing method,the numerical solution and field monitoring,which demonstrates that the proposed failure mechanism is effective for the upper bound analysis of supporting pressure.

Hydrodynamic Mixed Convection in a Lid-Driven Hexagonal Cavity with Corner Heater

Hydrodynamic mixed convection in a lid-driven hexagonal cavity with corner heater is numerically simulated in this paper by employing finite element method. The working fluid is assigned as air with a Prandtl num-ber of 0.71 throughout the simulation. The left and right walls of the hex-agonal cavity are kept thermally insulated and the lid moves top to bottom at a constant speed U0. The top left and right walls of the enclosure are maintained at cold temperature Tc. The bottom right wall is considered with a corner heater whereas the bottom remaining part is adiabatic and inside the cavity a square shape heated block Th. The focus of the work is to investigate the effect of Hartmann number, Richardson number, Grashof number and Reynolds number on the fluid flow and heat transfer characteristics inside the enclosure. A set of graphical results is presented in terms of streamlines, isotherms, local Nusselt number, velocity profiles, temperature profiles and average Nusselt numbers. The results reveal that heat transfer rate increases with increasing Richardson number and Hartmann number. It is also observed that, Hartmann number is a good control parameter for heat transfer in fluid flow in hexagonal cavity.

Effect of die cavity dimension on micro U deep drawing behaviour with T2 foil

The strips U deep drawing experiments were carried out to study the effect of die cavity dimension with an extension machine manufactured by SANS company. The effects of parameters were analyzed in deep drawing process under different experimental conditions, such as punch load, reduction of thickness, angle of U part and surface quality. The experiment results show that the punch load increases with the decrease of female radius, and larger blank holder force enlarges the range of increasing. With the increasing of blank holder force, the angle of U part increases, and the reduction of foil thickness at the corner becomes larger. Obvious scratch and accumulation at the die cavity corner were observed by SEM. The investigation results indicate that micro U deep drawing of foil is affected by micro die cavity dimension.

Mixed Convection of Bingham Fluid in a Two Sided Lid-Driven Cavity Heated From Below

This study aims to analyze mixed convection in a square cavity with two moving vertical walls by finite volume method.The cavity filled with Non-Newtonian fluid of Bingham model is heated from below and cooled by the other walls.This study has been conducted for certain parameters of Reynolds number(Re=1-100),Richardson number(Ri=1-20),Prandtl number(Pr=1-500),and Bingham number has been studied from 0 to 10.The results indicate that the increase in yield stress drops the heat transfer and the flow become flatter,while increasing Reynolds number augments it.The convective transport is dominant when increasing Richardson number which leads to enhance heat transfer in the cavity for both Newtonian and Non-Newtonian fluid.A correlation of Nusselt number is given in function of different parameters.

Polygonal Finite Element for Two-Dimensional Lid-Driven Cavity Flow

This paper investigates a polygonal finite element(PFE)to solve a two-dimensional(2D)incompressible steady fluid problem in a cavity square.It is a well-known standard benchmark(i.e.,lid-driven cavity flow)-to evaluate the numerical methods in solving fluid problems controlled by the Navier-Stokes(N-S)equation system.The approximation solutions provided in this research are based on our developed equal-order mixed PFE,called Pe1Pe1.It is an exciting development based on constructing the mixed scheme method of two equal-order discretisation spaces for both fluid pressure and velocity fields of flows and our proposed stabilisation technique.In this research,to handle the nonlinear problem of N-S,the Picard iteration scheme is applied.Our proposed method’s performance and convergence are validated by several simulations coded by commercial software,i.e.,MATLAB.For this research,the benchmark is executed with variousReynolds numbers up to the maximum Re=1000.All results then numerously compared to available sources in the literature.

Mixed Convection in a Two-Sided Lid-Driven Square Cavity Filled with Different Types of Nanoparticles:A Comparative Study Assuming Nanoparticles with Different Shapes

Steady,laminar mixed convection inside a lid-driven square cavity filled with nanofluid is investigated numerically.We consider the case where the right and left walls are moving downwards and upwards respectively and maintained at different temperatures while the other two horizontal ones are kept adiabatic and impermeable.The set of nonlinear coupled governing mass,momentum,and energy equations are solved using an extensively validated and a highly accurate finite difference method of fourth-order.Comparisons with previously conducted investigations on special configurations are performed and show an excellent agreement.Meanwhile,attention is focused on the heat transfer enhancement when different nano-particles:Cu,Ag,Al2O3,TiO2 and Fe3O4 are incorporated separately in different base fluids such as:Water,Ethylene-glycol,Methanol and Kerosene oil.In this framework,the numerical results related to several mixtures are presented and concern flow pattern and heat transfer curves for various values of Richardson number[Ri=0.1,1 and 10].It turns out that the choice of the efficient binary mixture for an optimal heat transfer depends not only on the thermophysical properties of the nanofluids but also on the range of the Richardson number.Special attention is devoted to shedding light on the effect of the shape of the nanoparticles on the heat transfer in the case of Water-Ag nanofluid.It is concluded that the spherical shape is more suitable for a better heat transfer enhancement in comparison to the cylindrical ones.

Mixed Convection Heat Transfer for Nanofluids in a Lid-Driven Shallow Rectangular Cavity Uniformly Heated and Cooled from the Vertical Sides:The Opposing Case

An investigation on flow and heat transfer due to mixed convection, in a lid-driven rectangular cavity filled with Cu- water nanofluids and submitted to uniform heat flux along with its vertical short sides, has been conducted numerically by solving the full governing equations with the finite volume method and the SIMPLER algorithm. In the case of a slender enclosure, these equations are considerably reduced by using the parallel flow concept. Solutions, for the flow and temperature fields, and the heat transfer rate, have been obtained depending on the governing parameters, which are the Reynolds, the Richardson numbers and the solid volume fraction of nanoparticles. A perfect agreement has been found between the results of the two approaches for a wide range of the abovementioned parameters. It has been shown that at low and high Richardson numbers, the convection is ensured by lid and buoyancy-driven effects, respectively, whereas between these extremes, both mechanisms compete. Moreover, the addition of Cu-nanoparticles, into the pure water, has been seen enhancing and degrading heat transfer by lid and buoyancy-driven effects, respectively.

基于探地雷达的隧道衬砌空洞检测方法

隧道衬砌内部空洞等病害检测已经成为隧道检修人员的主要工作之一。本文提出一种将探地雷达与深度学习相结合的隧道衬砌空洞检测方法,通过雷达探测和仿真模拟,得到大量衬砌雷达图像,并对图像进行标注和制作数据集。基于YOLOv5(You Only Look Once version 5)目标检测模型,结合数据集目标特征,提出一种检测衬砌空洞的算法,引入特征融合模块提高网络感受野,并采用K-means聚类算法提高检测准确率。通过现场检测,本文的检测方法准确率达到了97.7%,准确可靠,可在工程中进行应用。

金丝球焊近壁键合技术

在引线键合工艺应用中,由于球焊键合工艺具有键合方向灵活、键合速度快等优势,在半导体芯片的封装互联领域被广泛应用。针对金丝球焊键合工艺中的近壁键合问题进行了研究,从键合方式、劈刀设计两个方面进行优化、改进,制定了两种不同的解决方案,并分析了两种方案的应用局限性。

具有深腔结构的刚挠结合板制作方法探讨

印制电路板(PCB)需要在有限的空间内集成更多的功能模块,因此有一种相应的深腔设计。但深腔制作存在深度控制精度差、工艺流程复杂及制作难度高等问题。以一种具有深腔结构的有机发光二极管(OLED)模组刚挠结合板为研究对象,通过解析关键制程工艺、关键控制点,以及对比不同工艺优缺点的方式,对深腔结构的制作难点进行分析,重点介绍了深腔加工的关键制作技术。

Numerical Simulations of Hydromagnetic Mixed Convection Flow of Nanofluids inside a Triangular Cavity on the Basis of a Two-Component Nonhomogeneous Mathematical Model

Nanofluids have enjoyed a widespread use in many technological applications due to their peculiar properties.Numerical simulations are presented about the unsteady behavior of mixed convection of Fe_(3)O_(4)-water,Fe_(3)O_(4)-kerosene,Fe_(3)O_(4)-ethylene glycol,and Fe_(3)O_(4)-engine oil nanofluids inside a lid-driven triangular cavity.In particular,a two-component non-homogeneous nanofluid model is used.The bottom wall of the enclosure is insulated,whereas the inclined wall is kept a constant(cold)temperature and various temperature laws are assumed for the vertical wall,namely:
θ=1(Case 1),θ=Yð1YÞ(Case 2),andθ=sinð2-YÞ(Case 3).A tilted magnetic field of uniform strength is also present in the fluid domain.From a numerical point of view,the problem is addressed using the Galerkin weighted residual finite element method.The role played by different parameters is assessed,discussed critically and interpreted from a physical standpoint.We find that a higher aspect ratio can produce an increase in the average Nusselt number.Moreover,the Fe_(3)O_(4)-EO and Fe_(3)O_(4)-H2O nanofluids provide the highest and smallest rate of heat transfer,respectively,for all the considered(three variants of)thermal boundary conditions.

Parameters Effect on Heat Transfer Augmentation in a Cavity with Moving Horizontal Walls

Mixed convection flow is one of the essential criteria of fluid flow and heat transfer. And its application has been increased due to modernization of society. So, to compete with the global world an analysis has been investigated numerically. In this study we have considered 2D double lid driven cavity with two-sided adiabatic walls. This problem is illustrated mathematically by a collection of governing equations and the developed model has been solved numerically by using Finite Difference Method (FDM). The goal of the present study is to analyze numerically the thermal behaviour and parameters effect on heat transfer inside the 2D chamber. Also this analysis has been observed for the case where the upper wall is moving at positive direction and lower wall is moving at negative direction with constant speed. Furthermore, we have tried to analyze the velocity and temperature profiles for a vast range of dimensionless parameters namely Reynolds number (Re), Richardson number (Ri)?and Prandtl number?(Pr)?and presented graphically. Moreover, it is found that these flow parameters have significant effects in controlling the flow behavior inside the cavity. A comparison has been done to validate our code and found a good agreement. Finally, average Nusselt number (Nu)?has been studied for the effects of these parameters and presented in tabular form.

薄壁深腔小脱模斜度箱体塑件注塑模具设计

针对某办公设备上的薄壁深腔小脱模斜度箱体塑件为研究对象,根据塑件深腔、薄壁、脱模斜度小的结构特点和适用于大批量生产的技术要求,设计了一副包含:定模芯入子优先抽芯结构、动模芯入子优先抽芯结构和四边滑块侧向抽芯结构的复杂注塑模具。模具设计采用四边滑块侧向抽芯机构,解决塑件两侧脱模方向倒扣及塑件表面脱模斜度小、高度方向太深易黏定模的问题,同时可以优化分型面结构,提高加工效率;模具设计的定模芯入子优先抽芯结构,通过在两处环形筋位处设置的前模芯镶件入子,利用镶件的排气特性,解决定模侧两处环形深的筋位在注塑成型时易出现困气、烧焦及填充困难的问题,通过优先抽芯前模芯的镶件入子,解决此两处深的筋位黏模的问题;模具设计的动模芯入子优先抽芯结构解决了塑件深腔、薄壁结构包紧力过大顶出困难的问题,利用动模芯入子的优先抽芯结构,先脱出动模型芯,即可轻松顶出塑件同时不会造成顶出变形。针对塑件成型时易出现的问题,经过模具结构优化设计,模具在后续实际生产中表现优异、符合预期。

CPTU数据校准上海深层软土参数的随机力学-贝叶斯方法

城市深层地下空间的开发需要开展科学计算。合理的本构模型和准确的岩土参数是岩土力学分析的两大支撑。修正剑桥模型(modified cam-clay,MCC)的岩土参数简单直观,被广泛应用于岩土工程实践。室内土工试验由于取样扰动、试验误差等不可避免的缺陷,难以精确获得深层岩土参数。结合先验知识、室内试验数据和孔压静力触探(piezocone penetration test,CPTU)测试数据,将关键岩土参数视为随机变量,采用随机力学-贝叶斯方法,校准深层软土的关键岩土参数,如临界状态应力比、压缩系数、回弹系数和超固结比。以上海市苏州河深层排水调蓄管道系统工程——云岭竖井基坑工程为背景,以基础底板处的深部第(8)层土为研究对象。首先,利用MCC模型的柱孔扩张理论,揭示了CPTU数据(锥尖阻力、侧摩阻力和孔隙水压力)与极限扩孔应力之间的力学转换机理,利用苏格兰Bothkennar岩土试验场地的试验数据,验证CPTU测试数据力学模型的适用性;其次,建立关键岩土参数与CPTU数据之间的二次非交叉响应面,利用MCMC(Markov-chain Monte Carlo)抽样算法,获得关键岩土参数的后验统计特征;最后,结合岩土参数的后验均值,开展超深基坑工程的数值计算。结果表明,经过柱孔扩张随机力学-贝叶斯方法校准后,关键岩土参数的不确定性大幅度降低,后验均值的预测结果与监测值较为接近,证明了该方法的高效、合理性。