A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone

Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.

Numerical simulation of recalescence of 3-dimensional isothermal solidification for binary alloy using phase-field approach

A accelerated arithmetic algorithm of the dynamic computing regions was designed,and 3-dimensional numerical simulation of isothermal solidification for a binary alloy was implemented.The dendritic growth and the recalescence of Ni-Cu binary alloy during the solidification at different cooling rates were investigated.The effects of cooling rate on dendritic patterns and microsegregation patterns were studied.The computed results indicate that,with the increment of the cooling rate,the dendritic growth velocity increases,both the main branch and side-branches become slender,the secondary dendrite arm spacing becomes smaller,the inadequate solute diffusion in solid aggravates,and the severity of microsegregation ahead of interface aggravates.At a higher cooling rate,the binary alloy presents recalescence;while the cooling rate is small,no recalescence occurs.

Simulation of two-dimensional interior ballistics model of solid propellant electrothermal-chem ical launch with discharge rod plasma generator

Instead of the capillary plasma generator(CPG),a discharge rod plasma generator(DRPG)is used in the30 mm electrothermal-chemical(ETC)gun to improve the ignition uniformity of the solid propellant.An axisymmetric two-dimensional interior ballistics model of the solid propellant ETC gun(2D-IB-SPETCG)is presented to describe the process of the ETC launch.Both calculated pressure and projectile muzzle velocity accord well with the experimental results.The feasibility of the 2D-IB-SPETCG model is proved.Depending on the experimental data and initial parameters,detailed distribution of the ballistics parameters can be simulated.With the distribution of pressure and temperature of the gas phase and the propellant,the influence of plasma during the ignition process can be analyzed.Because of the radial flowing plasma,the propellant in the area of the DRPG is ignited within 0.01 ms,while all propellant in the chamber is ignited within 0.09 ms.The radial ignition delay time is much less than the axial delay time.During the ignition process,the radial pressure difference is less than 5 MPa at the place 0.025 m away from the breech.The radial ignition uniformity is proved.The temperature of the gas increases from several thousand K(conventional ignition)to several ten thousand K(plasma ignition).Compare the distribution of the density and temperature of the gas,we know that low density and high temperature gas appears near the exits of the DRPG,while high density and low temperature gas appears at the wall near the breech.The simulation of the 2D-IB-SPETCG model is an effective way to investigate the interior ballistics process of the ETC launch.The 2D-IB-SPETC model can be used for prediction and improvement of experiments.

Numerical Filling Simulation of Injection Molding Using Three-Dimensional Model

Most injection molded parts are three-dimensional, with complex geometrical configurations and thick/thin wall sections. A 3D simulation model will predict more accurately the filling process than a 2.5D model. This paper gives a mathematical model and numeric method based on 3D model, in which an equal-order velocity-pressure interpolation method is employed successfully. The relation between velocity and pressure is obtained from the discretized momentum equations in order to derive the pressure equation. A 3D control volume scheme is employed to track the flow front. Th e validity of the model has been tested through the analysis of the flow in cavity.

Application of Three-Dimensional Visual Simulation in Tidal Defense Engineering

Any tidal defense engineering involves the collection and analysis of massive information about engineering structures and their surrounding environment. Traditional method, which is carried out mainly by means of twodimensional drawings and textures, is not efficient and intuitive enough to analyze the whole project and reflect its spatial relationship. Three-dimensional visual simulation provides an advanced technical means of solving this problem. In this paper, triangular irregular network (TIN) model simplified by non-uniform rational B-splines (NURBS) technique was used to establish the digital terrain model (DTM) of a super large region. Simulation of dynamic water surface was realized by combining noise function with sine wave superposition method. Models of different objects were established with different modeling techniques according to their characteristics. Application of texture mapping technology remarkably improved the authenticity of the models. Taking the tidal defense engineering in the new coastal region of Tianjin as a case study, three-dimensional visual simulation and dynamic roaming of the study area were realized, providing visual analysis and visible demonstration method for the management and emergency decision-making associated with construction.

RADIAL EXTRUSION PROCESS BY THREE-DIMENSIONAL RIGID-PLASTIC FEM SIMULATION

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Three-dimensional simulation of sintering crunodes of metal powders or fibers by level set method

The difference of sintering crunodes of metal powders and fibers is discussed. The mathematical model of the surface diffusion described by the difference in mean curvature is defined as a Hamilton-Jacobi-type equation, and the model is numerically solved by the level set method. The three-dimensional numerical simulations of two metal powders and fibers(the fiber angle is 0° or 90°) are implemented by this mathematical model, respectively. The numerical simulation results accord with the experimental ones. The sintering neck growth trends of metal powders and metal fibers are similar. The sintering neck radius of metal fibers is larger than that of metal powders. The difference of the neck radius is caused by the difference of geometric structure which makes an important influence on the curvature affecting the migration rate of atoms.

THE SYSTEM SIMULATION OF THREE-DIMENSIONAL RADAR

To provide a test platform for Electronic Warfare (EW) system, it is needed to simulate the radar received Intermediate Frequency (IF) signals and radar system functions.This letter gives a description of a radar system simulation software developed for frequencyphase scanning three-dimensional (3-D) radar. Experimental results prove that the software could be used for system evaluation and for training purposes as an attractive alternative to real EW system.

Simulation-Based Construction of Three-Dimensional Process Model for Punching Cartridge Cases

A method of constructing three-dimensional process model for the punching cartridge cases is presented based on DEFORM simulation analysis. Using DEFORM software,the finite element simulation models for the punching and forming process of cartridge cases are established,and the corresponding simulation result model of each intermediate procedure is obtained by continuously performing the forming process simulation. The simulation model cannot annotate size and process information due to poor interface between DEFORM software and CAD software. Thus,a 3D annotation module is developed with secondary development technology of UG NX software. Consequently,the final process model with dimension and process information is obtained. Then,with the current 3D process management system,the 3D punching and forming process design of cartridge cases can be completed further. An example is also provided to illustrate that the relative error between the simulation process model and the physical model is less than 2%,which proves the validity and reliability of the proposed method in this study.

Three-dimensional discrete element numerical simulation of Paleogene salt structures in the western Kuqa foreland thrust belt

Taking the Paleogene salt strata in the west of Kuqa foreland thrust belt as study object, the deformation features of salt structure in the compression direction and perpendicular to the compression direction were examined to find out the control factors and formation mechanisms of the salt structures. By using the three-dimensional discrete element numerical simulation method, the formation mechanisms of typical salt structures of western Kuqa foreland thrust belt in Keshen and Dabei work areas were comprehensively analyzed. The simulation results show that the salt deformation in Keshen and Dabei work areas is of forward spread type, with deformation concentrated in the piedmont zone;the salt deformation is affected by the early uplift near the compression end, pre-existing basement faults, synsedimentary process and the initial salt depocenter;in the direction perpendicular to the compression direction, salt rocks near the compression end have strong lateral mobility with the velocity component moving towards the middle part, and the closer to the middle, the larger the velocity will be, so that salt rocks will aggregate towards the middle and deform intensely, forming complex folds and separation of salt structures from salt source, and local outcrop with thrust faults. Compared with 2 D simulation, 3 D simulation can analyze salt structures in the principal stress direction and direction perpendicular to the principal stress, give us a full view of the formation mechanisms of salt structures, and guide the exploration of oil and gas reservoirs related to salt structures.

Three-Dimensional Finite Element Numerical Simulation and Physical Experiment for Magnetism-Stress Detecting in Oil Casing

The casing damage has been a big problem in oilfield production. The current detection methods mostly are used after casing damage, which is not very effective. With the rapid development of China's offshore oil industry, the number of offshore oil wells is becoming larger and larger. Because the cost of offshore oil well is very high, the casing damage will cause huge economic losses. What's more, it can also bring serious pollution to marine environment. So the effective methods of detecting casing damage are required badly. The accumulation of stress is the main reason for the casing damage. Magnetic anisotropy technique based on counter magnetostriction effect can detect the stress of casing in real time and help us to find out the hidden dangers in time. It is essential for us to prevent the casing damage from occurring. However, such technique is still in the development stage. Previous studies mostly got the relationship between stress and magnetic signals by physical experiment, and the study of physical mechanism in relative magnetic permeability connecting the stress and magnetic signals is rarely reported. The present paper uses the ANSYS to do the three-dimensional finite element numerical simulation to study how the relative magnetic permeability works for the oil casing model. We find that the quantitative relationship between the stress' s variation and magnetic induction intensity's variation is: Δδ =K* ΔB, K = 8.04×109, which is proved correct by physical experiment.

Application of Three-Dimensional Simulation Model of Bioactive Ceramic Degrading Process in vivo

This paper describes the method of constructing three dimensional model of bioactive ceramic to simulate the degrading process in vivo. Based on the construction of three dimensional simulation model and realizing it by computer programming, it proves that the three dimensional stimulant model can correctly represent the real degrading process, and thus verifies its feasibility.

Three-Dimensional Simulation of Plasma Jet and Particle Groups in Plasma Spraying

The temperature field, velocity field, as well as species distribution in three-dimensional space are successfully calculated by establishing three-dimensional geometry model and solving plasma jet-substrate interaction equations, optimized particle trajecory models, as well as particle-particle heat transfer equations in space. Under typical working conditions, the flying trajectories and distribution of ZrO2 ceramic particles and Ni metal particles are also simulated. Results show that, the plasma jet becomes wider near the substrate, and the stochastic trajectory model is preferable to simulate the turbulent diffusion effect of particles. In addition, Ni metal particles penetrate relatively more deeply than ZrO2 ceramic particles due to larger density.

Two-Dimensional Fluid Simulation of Collisional Plasma Sheath over rf Powered Electrode with Cylindrical Hole

The characteristics of collisional radio-frequency (rf) sheath dynamics over an elec-trode with a cylindrical hole is simulated by means of a self-consistent model which consists of two-dimensional time-dependent fluid equations coupled with Poisson equation. In addition, an equivalent-circuit model is coupled to the fluid equations in order to self-consistently determine re-lationship between the instantaneous potential at the rf-biased electrode and the sheath thickness. Two-dimensional profiles of the potential, the ion fluid velocity, and the distributions of the ion and electron densities within the sheath are computed under various discharge conditions, such as the discharge powers and the gas pressures. The results show that the existence of the cylindrical hole on the electrode significantly affects the sheath structure and generates a potential trap in the horizontal direction, which is particularly strong when the sheath thickness is comparable to the depth of the hole. Moreover, it is found that the collisional effects have a significant influence on the sheath characteristics.

Two-Dimensional Simulation of a Dual Frequency Sheath Near an Electrode with a Cylindrical Hole

The characteristics of a collisional dual frequency （DF） sheath near an electrode with a cylindrical hole are studied by utilizing a two-dimensional model which includes time-dependent fluid equations coupled with the Poisson equation and an equivalent-circuit model, The effects of the gas pressure on the two-dimensional profiles of the potential, electric field, ion fluid velocity in a DF sheath are investigated. The simulation results show that the cylindrical hole on the electrode has a significant influence on the DF sheath structure, i.e., the sheath profile tends to wrap around the contour of the hole feature. Moreover, it is shown that the structure of the DF sheath is different from that of a single frequency （SF） sheath because the profile of the DF sheath is modulated by the combination of the high and low frequency sources. In addition the characteristics of the DF sheath are obviously affected by the collisional effects in the DF sheath.

IF signals simulation of three-dimensional radar

Based on the analysis of the principles of frequency-phase scanning 3-D （three-dimensional） radar and the scattering mechanism of 3-D radar, the target and clutter IF （intermediate frequency） signals model of frequencyphase scanning 3-D radar is presented. The IF signals model of different channels of 3-D radar is presented in one simple formula in which complex waveform effects are considered. The simulation results obtained during tests are also provided in the end.

A COMPUTER CODE FASTOR-3D FOR TRANSIENT THREE-DIMENSIONAL SIMULATION ON FLOW AND HEAT TRANS-FER WITH POROSITY APPROXIMATION

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Numerical Simulation of the Three-Dimensional Wave-Induced Currents on Unstructured Grid

By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three- dimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.

A three-dimensional Eulerian method for the numerical simulation of high-velocity impact problems

In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.

Three-Dimensional Cerebral Aneurysm Models for Surgical Simulation and Education—Development of Aneurysm Models with Perforating Arteries and for Application of Fenestrated Clips

We modified a three-dimensional cerebral aneurysm model for surgical simulation and educational demonstration. Novel models are made showing perforating arteries arising around the aneurysm. Information about perforating arteries is difficult to obtain from individual radiological data sets. Perforators are therefore reproduced based on previous anatomical knowledge instead of personal data. Due to their fragility, perforating arteries are attached to the model using hard materials. At the same time, hollow models are useful for practicing clip application. We made a model for practicing the application of fenestrated clips for paraclinoid internal carotid aneurysms. Situating aneurysm models in the fissure of a brain model simulates the real surgical field and is helpful for educational demonstrations.