有限差分计算浓度场题目20140514.docxVIP

Calculation of concentration field using FDM1. The processing of carburization has important significance for industrial application. Consider 1-D carbon diffusion in a semi-infinitesteel plate. The concentration profile at time=t are described in Fig. 1-1. The carburizing temperature is T=1200.15K. The carbon diffusivity in austenite is D=1.5×10-5exp(-142100/RT) m2/s, which is associated with temperature.Fig. 1-1 The concentration profile at time=t in 1-D diffusion problemDivide appropriate grids (suggested grid number N=50 with spacingx=60μm) to calculate the carbon concentration distributions during the time of 36000s(10h). The example of results is shown in Fig. 1-2 and Fig. 1-3. Compare the calculation results with analytical solution( , ).Fig. 1-2Theconcentrationvariations of node1, 5,10, 20, 30, 50 calculated by FDM and analytical solutionFig. 1-3The concentration profile at time t=8082.3s calculated by FDM and analytical solution2. Carbonation in concrete refers to the chemical reaction between cement hydration products Ca(OH)2 and CO2 from the air in the conditions of a certain humidity. Carbonation in cracked concrete is considered as one of major deteriorations accelerating steel corrosion in reinforced concrete structures.Consider 2-D CO2diffusion in cracked concrete. The geometry, dimension and boundary conditions (ΓI, ΓII and ΓIII represent I, II and III type boundary condition, respectively) are described in Fig. 2-1. The crack is located in the middle of the bottom with a size of 0.0008 m×0.024 m. The CO2diffusivity in concrete is D = 2.6609×10-11 m2/s. The CO2diffusivity in crack is Dcr= 4.4892×10-9 m2/s since the crack is a main path for CO2 inside concrete.Fig. 2-1 2-D diffusion in concrete with a crackCalculate the concentration distributions with inner nodeduring the time of 432000s(5d). The example of results is shown in Fig. 2-2 and Fig. 2-3.Fig. 2-2Theconcentrationvariations of node (10, 24), (10, 48), (10, 72), (10, 96),(10, 120)Fig. 2-3The