Papers by Keyword: Finite Difference Method (FDM)

Abstract: This article investigates the transfer of heat with reactant (oxygen) consumption in a stockpile of reactive material. A reactive material is any carbon or hydrocarbon containing component in a stockpile that readily reacts with the oxygen due to exothermic chemical reaction, where self-ignition may take place if heat generation rate during the combustion process within the stockpile, may exceed the rate of heat release to the surrounding environment. The study is modeled in a long cylindrical pipe whose material thermal conductivity varies with the temperature at a given time. The heat and mass transfer partial differential equations governing the problem were solved numerically using the finite difference method (FDM). Kinetic parameters embedded within the reaction system were analyzed to understand their effects on the temperature and the reactant consumption process. The results shew that the parameters that influence the increase in temperature, increase also the consumption rate of the reactant.

Abstract: Burgers’ equation on an unbounded domain is an important mathematical model to treat with some external problems of fluid materials. In this paper, we study a FDM of Burgers’ equation using high-order artificial boundary conditions on the unbounded domain. First, the original problem is converted into the heat equation on an unbounded domain by Hopf-Cole transformation. Thus the difficulty of nonlinearity of Burgers’ equation is overcome. Second, high-order artificial boundary conditions are given by using Padé approximation and Laplace transformation. And the conditions confine the heat equation onto a bounded computational domain. Third, we prove the solutions of the resulting heat equation and Burgers’ equation are both stable. Fourth, we establish the FDM for Burgers’ equation on the bounded computational domain. Finally, a numerical example demonstrates the stability, the effectiveness and the second-order convergence of the proposed method.

Abstract: In this paper the heat transfer problem in transient and cylindrical coordinates will be solved by the Crank-Nicolson method in conjunction the Finite Difference Method. To validate the formulation will study the numerical efficiency by comparisons of numerical results compared with two exact solutions.

Abstract: This paper building upon studies [1‐8] describes a subset of the High Pressure Water (HPW) descaling strategy developed at Tata Steel UK to optimise descaling set-ups for range of steel grades prone to adherent primary scale such as in high alloy steels (Si, Ni, Cr). Effective primary descaling, i.e. descaling post furnace discharge via washbox or alternative technologies is imperative to obtain good surface quality and conditioning of the surface state as well as the morphology, growth and behaviour of the secondary/tertiary scale. This paper primarily focuses on analytical descaling concepts for both mechanical and thermal outputs for flat jet nozzle and process factors. This approach has been linked to recent developments for oxide scale evolution during rolling and descaling [8].

Abstract: In order to analyze the construction processing for No.1 shaft of Weihe Tunnel on Baoji-Lanzhou Passenger-dedicated Railway, a two-dimensional numerical model for the simulation of the shaft was built with the finite difference method. Mohr-Coulomb model was chosen as the soil constitutive model. The result shows that the maximum lateral displacement appears at the upper part of the shaft, and the lateral displacement is in effective constraint at the shaft’s bottom. After the construction, the maximum uplift at the shaft’s bottom is in the center, while the uplift decreases from the shaft’s center to its both sides. The maximum pressure stress turns up at the bottom sides of the shaft, and the maximum tensile stress appears at the middle of the shaft.

Abstract: Intesive research works have been done on solid particle flows for the past decades. However, prediction of accurate relationship between the particle and the surrounding fluid is still challenging. This study focuses on the experimental and numerical study of behavior of a particle flow in a lid-driven cavity of equilateral triangular shape. Numerical analysis was done using Finite Difference Method (FDM) with stream function vorticity approach. The center location of the fluid flow was treated assumed to be the particle motion. To check the validaty of the numerical results, experiment was done. The particle and fluid used for the experiment were water and silk, respectively. The particle is considered to be slightly buoyant towards water. In the experiment the fluid flow was based on horizontal translating motion where the particle was initially at rest at the bottom wall of the cavity. The fluid flow speed is set to laminar flow with Reynolds Number, Re = 0 to 1000. It was found that the silk particle moved to the preferential path of the primary vortex at equivalent time of 13 seconds. Generally, the experimetal and numerical results for the streamlines were in good agreement.

Abstract: A numerical simulation for DC PD in void is put forward based on the PD physical process. The finite difference method is used to calculate the electric field distribution, and both of the stochastic property and the accumulation of the charge after PD on the void surfaces are considering in the model. The time of PD occurring, the amount of discharge and the voltage across the void are calculated. Meanwhile, the relationship between the DC voltage and the PD time interval or repetition rate is also simulation, the results show that with the increase of the DC voltage, the PD interval corresponding decreases exponentially and the repetition rate increases exponentially.

Abstract: In the paper, by means of Laplace transform the Sobolev differential equations become to the elliptic differential equations, which can be solved by the fourth order finite difference equations in parallel. After getting the approximate solutions of the elliptic differential equations, we can achieve the numerical solutions with high accuracy for the Sobolev differential equations by using the Zakian inversion method. At last, we carry out one numerical experiment to indicate that the method in this paper is effective.

Abstract: In order to simulate the thermal stresses, thermal strains and residual stresses of steel during quenching by numerical means, it is necessary to obtain an accurate boundary condition of temperature field. The explicit finite difference method, nonlinear estimate method and the experimental relation between temperature and time during water and nitrogen-spray water quenching have been used to solve the inverse problem of heat conduction. The relations between surface heat-transfer coefficient in water and nitrogen-spray water quenching and surface temperature of cylinder have been given. In numerical calculation, the thermal physical properties of material were treated as the function of temperature. The results show that the relations between surface heat-transfer coefficient and surface temperature are non-linear during water and nitrogen-spray water quenching, the heat-transfer coefficient is bigger when water quenching than when nitrogen-spray water before 580°C, the heat-transfer coefficient is smaller when water quenching than when nitrogen-spray water after 400°C. The results of calculation coincided with the results of experiment. This method can effectively determine the surface heat-transfer coefficient during water and nitrogen-spray water quenching.

Abstract: The numerical simulation model was established by using numerical simulation tools of FLAC3D, through establishing interface for digging foundation-soil, which can consider mutual effect of digging foundation-soil. Bearing capacities of the digging foundation in slopes is calculated. The affecting factors of the bearing capacity are analyzed. The results show that the bearing capacity has a positive correlation with the distance between the foundation and the slope and has a negative correlation with the slope ratio, which can be expressed as a quadratic polynomial. Nonlinear regression analysis of calculation data are carried out and the fitting formula of the capacity ratio between pile in the slope and pile in the flat is obtained. Finally, the calculation method of horizontal bearing capacity about pile in the slope is developed, which can provide a reference to specification revision and engineering.