摘要
安全评价中如何预测和模拟气体储罐完全破裂后介质在瞬间泄漏的动态扩散过程目前还没有合适的模型,通常只能借用环保领域中的高斯模型和Su tton模型,但环保领域的模型为稳态扩散模型,不含时间变量,并不适合动态扩散过程.目前开发的用有限元方法求解的计算机模型只能针对具体的装置进行模拟.本文根据F ick定律建立了气体扩散的动态模型,再限定气体储罐形状为最常见的圆柱形,确定了模型的初始条件和边界条件.通过坐标变换和两个积分变换:Fourier变换和适用于圆柱函数(Bessel函数)的H ankel变换,求出了此条件下扩散方程的解析解.
As there is no mathematical model suitable for evaluating the consequence of diffusion when the gas container explodes and all the gas in it leak out immediately, a universal dynamic model is established to simulate the dynamic dispersing course based on the Grads Theory. AS the form of gas container has a shape of column, the initial conditions and boundary condition can be made certain. And then by coordinate transformation method and two kinds of integral transformations： Fourier Integral Transformation and Hankel Integral Transformation （suitable for Bessel function）, the differential equation is solved and the analytic solution is obtained.
出处
《数学的实践与认识》
CSCD
北大核心
2006年第6期110-114,共5页
Mathematics in Practice and Theory
关键词
气体
储罐
泄漏
扩散
动态模型
gas container
leakage
diffusion
dynamic model
