Modeling, numerical methods, and simulation for particle-fluid two-phase flow problems

In this paper, we study the issues of modeling, numerical methods, and simulation with comparison to experimental data for the particle-fluid two-phase flow problem involving a solid-liquid mixed medium. The physical situation being considered is a pulsed liquid fluidized bed. The mathematical model is based on the assumption of one-dimensional flows, incompressible in both particle and fluid phases, equal particle diameters, and the wall friction force on both phases being ignored. The model consists of a set of coupled differential equations describing the conservation of mass and momentum in both phases with coupling and interaction between the two phases. We demonstrate conditions under which the system is either mathematically well posed or ill posed. We consider the general model with additional physical viscosities and/or additional virtual mass forces, both of which stabilize the system. Two numerical methods, one of them is first-order accurate and the other fifth-order accurate, are used to solve the models. A change of variable technique effectively handles the changing domain and boundary conditions. The numerical methods are demonstrated to be stable and convergent through careful numerical experiments. Simulation results for realistic pulsed liquid fluidized bed are provided and compared with experimental data. (C) 2004 Elsevier Ltd. All rights reserved.

Three-dimensional crack problem analysis using boundary element method with finite-part integrals

A set of hypersingular integral equations of a three-dimensional finite elastic solid with an embedded planar crack subjected to arbitrary loads is derived. Then a new numerical method for these equations is proposed by using the boundary element method combined with the finite-part integral method. According to the analytical theory of the hypersingular integral equations of planar crack problems, the square root models of the displacement discontinuities in elements near the crack front are applied, and thus the stress intensity factors can be directly calculated from these. Finally, the stress intensity factor solutions to several typical planar crack problems in a finite body are evaluated.

An improvement on the theoretical model for the large-scale coherent structures in the outer region of a turbulent boundary layer

According to the experimental results, there exist large-scale coherent structures in the outer region of a turbulent boundary layer, which have been studied by many authors.As experimental results, Antonia (1990) showed the phase- aver aged streamlines and isovorticity lines of the large-scale coherent structures in a turbulent boundary layer for different Reynolds numbers. Based on the hydrodynamic stability theory, the 2-D theoretical model for the large-scale structures was proposed by Luo and Zhou, in which the eddy viscosity was defined as a complex function of the position in the normal direction. The theoretical results showed in ref. were in agreement with those in ref. However, there were two problems in the results. One is that in the experimental results, there were divergent focuses between two saddle points in the streamlines, but in the theoretical results, there were centers. The other is that the stretched parts of the isovorticity lines appear at the location of centers in the theoretical results, while in the experimental results they located somewhere between the focuses and saddle points. The reason is that the computations were based on a 2-D model.

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.

Cauchy singular integral equation method for transient antiplane dynamic problems

In this paper, by use of the boundary integral equation method and the techniques of Green basic solution and singularity analysis, the dynamic problem of antiplane is investigated. The problem is reduced to solving a Cauchy singular integral equation in Laplace transform space. This equation is strictly proved to be equivalent to the dual integral equations obtained by Sih [Mechanics of Fracture, Vol. 4. Noordhoff, Leyden (1977)]. On this basis, the dynamic influence between two parallel cracks is also investigated. By use of the high precision numerical method for the singular integral equation and Laplace numerical inversion, the dynamic stress intensity factors of several typical problems are calculated in this paper. The related numerical results are compared to be consistent with those of Sih. It shows that the method of this paper is successful and can be used to solve more complicated problems. Copyright (C) 1996 Elsevier Science Ltd

Molecular dynamics studies on the dislocation gliding near a tilt boundary

The gliding behavior of edge dislocation near a grain boundary(QB) in copper under pure shear stresses is simulated by using molecular dynamics(MD) method. Many-body potential incorporating the embedded atom method (EAM) is used. The critical shear stresses for a single disocation to pass across GB surface are obtained at values of sigma(c)=23MPa similar to 68 MPa and 137 MPa similar to 274 MPa for Sigma=165 small angle tilt GB at 300 K and 20 K, respectively. The first result agrees with the experimental yield stress sigma(y)(=42 MPa) quite well. It suggests that there might be one of the reasons of initial plastic yielding caused by single dislocation gliding across GB. In addition, there might be possibility to obtain yield strength from microscopic analysis. Moreover, the experimental value of sigma(y) at low temperature is generally higher than that at room temperature. So, these results are in conformity qualitatively with experimental fact. On the other hand, the Sigma=25 GB is too strong an obstacle to the dislocation. In this case, a dislocation is able to pass across GB under relatively low stress only when it is driven by other dislocations. This is taken to mean that dislocation pile-up must be built up in front of this kind of GB, if this GB may take effect on the process of plastic deformation.

Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.

Interaction of linear waves with infinitely long horizontal cylinders studied by boundary element method

The two-dimensional problems concerning the interaction of linear water waves with cylinders of arbitrary shape in two-layer deep water are investigated by use of the Boundary Integral Equation method (BIEM). Simpler new expressions for the Green functions are derived, and verified by comparison of results obtained by BIEM with these by an analytical method. Examined are the radiation and scattering of linear waves by two typical configurations of cylinders in two-layer deep water. Hydrodynamic behaviors including hydrodynamic coefficients, wave forces, reflection and transmission coefficients and energies are analyzed in detail, and some interesting physical phenomena are observed.

金川镍矿岩体移动与开采稳定性研究

The two major issues in mining industry are work safety and protection of ground environment when carrying on underground mining activities. Cut-and-fill mining method is increasingly applied in China owing to its advantages of controlling ground pressure and protecting the ground environment effectively. However, some cut-and-fill mines such as Jinchuan nickel mine which has big ore body, broken rock mass and high geostress have unique characteristics on the law of ground pressure and rock mass movement that distinguish from other mining methods. There are still many problems unknown and it is necessary for the further analysis. In this dissertation, vast field survey, geology trenching and relative data analysis are carried out. The distribution of ground fissures and the correlation of the fissures with the location of underground ore body is presented. Using of monitoring data by three-dimension fissure meter and GPS in Jinchuan Deposit Ⅱ, the rule of the surface deformation and the reason of ground fissures generation are analyzed. It is shown that the stress redistribution in surrounding rocks resulting from mining, the existence of the void space underground and the influence of on-going mining activities are three main reasons for the occurrence of ground fissures. Based on actual section planes of No.1 ore body, a large-scale 3D model is established. By this model, the complete process of excavation and filling is simulated and the law of rock mass movement and stability caused by Cut-and-fill Mining is studied. According to simulation results, it is concluded that the deformation of ground surface is still going on developing; the region of subsidence on the ground surface is similar with a circle; the area on the hanging wall side is larger than one on the lower wall side; the contour plots show the centre of subsidence lay on the hanging wall side and the position is near the ore body boundary of 1150m and 1250m where ore body is the thickest. Along strike-line of Jinchuan Deposit Ⅱ, the deformation at the middle of filling body is larger than that in the two sides. Because of the irregular ore body, stress concentrates at the boundary of ore body. With the process of excavation and filling, the high stress release and the stress focus disappear on the hanging wall side. The cut-and-fill mechanism is studied based on monitoring data and numerical simulation. The functions of filling body are discussed. In this dissertation, it is concluded that the stress of filling body is just 2MPa, but the stress of surrounding rock mass is 20MPa. We study the surface movement influenced by the elastic modulus of backfill. The minimal value of the elastic modulus of backfill which can guarantee the safety production of cut-and-fill mine is obtained. Finally, based on the real survey results of the horizontal ore layer and numerical simulation, it is indicated that the horizontal ore layer has destroyed. Key words: cut-and-filling mining, 3D numerical simulation, field monitoring, rock mass movement, cut-and-filling mechanism, the elastic modulus of backfill, the horizontal ore layer

高分辨率非线性岩性物性联合反演方法和应用

In the prediction of complex reservoir with high heterogeneities in lithologic and petrophysical properties, because of inexact data (e.g., information-overlapping, information-incomplete, and noise-contaminated) and ambiguous physical relationship, inversion results suffer from non-uniqueness, instability and uncertainty. Thus, the reservoir prediction technologies based on the linear assumptions are unsuited for these complex areas. Based on the limitations of conventional technologies, the thesis conducts a series of researches on various kernel problems such as inversions from band-limited seismic data, inversion resolution, inversion stability, and ambiguous physical relationship. The thesis combines deterministic, statistical and nonlinear theories of geophysics, and integrates geological information, rock physics, well data and seismic data to predict lithologic and petrophysical parameters. The joint inversion technology is suited for the areas with complex depositional environment and complex rock-physical relationship. Combining nonlinear multistage Robinson seismic convolution model with unconventional Caianiello neural network, the thesis implements the unification of the deterministic and statistical inversion. Through Robinson seismic convolution model and nonlinear self-affine transform, the deterministic inversion is implemented by establishing a deterministic relationship between seismic impedance and seismic responses. So, this can ensure inversion reliability. Furthermore, through multistage seismic wavelet (MSW)/seismic inverse wavelet (MSIW) and Caianiello neural network, the statistical inversion is implemented by establishing a statistical relationship between seismic impedance and seismic responses. Thus, this can ensure the anti-noise ability. In this thesis, direct and indirect inversion modes are alternately used to estimate and revise the impedance value. Direct inversion result is used as the initial value of indirect inversion and finally high-resolution impedance profile is achieved by indirect inversion. This largely enhances inversion precision. In the thesis, a nonlinear rock physics convolution model is adopted to establish a relationship between impedance and porosity/clay-content. Through multistage decomposition and bidirectional edge wavelet detection, it can depict more complex rock physical relationship. Moreover, it uses the Caianiello neural network to implement the combination of deterministic inversion, statistical inversion and nonlinear theory. Last, by combined applications of direct inversion based on vertical edge detection wavelet and indirect inversion based on lateral edge detection wavelet, it implements the integrative application of geological information, well data and seismic impedance for estimation of high-resolution petrophysical parameters (porosity/clay-content). These inversion results can be used to reservoir prediction and characterization. Multi-well constrains and separate-frequency inversion modes are adopted in the thesis. The analyses of these sections of lithologic and petrophysical properties show that the low-frequency sections reflect the macro structure of the strata, while the middle/high-frequency sections reflect the detailed structure of the strata. Therefore, the high-resolution sections can be used to recognize the boundary of sand body and to predict the hydrocarbon zones.