A computational approach to the modeling of the glaciation of sea offshore gas pipeline

作者：Krivovichev Gerasim V^*

来源：International Journal of Heat and Mass Transfer, 2017, 115: 1132-1148.

DOI：10.1016/j.ijheatmasstransfer.2017.08.117

• Natural gas pipeline
• Glaciation
• Stefan problem
• Finite-element method
• FreeFem plus
• Dirac delta function
• Numerical simulation

In the, present study a computational approach to the modeling of the glaciation of sea offshore pipelines completely exposed to the seawater is proposed. The phase transform "seawater - ice" is taken into account and Stefan condition on the phase change boundary is considered. The mathematical model is based on Dirichlet problem for the nonlinear heat equation in the domain with fixed boundaries. The model is obtained by transformation of classical unsteady Stefan problem in the ice layer, which is considered as domain with unknown moving boundary. The calculations based on the proposed model may be realized by the implicit methods, which are convenient for numerical solution of two-and three-dimensional problems. The temperature of the gas flow and thermal layers of the pipe is input as a time function.
The finite-element formulation of the Dirichlet problem for the nonlinear heat equation is proposed. The iterative method for the practical calculations based on the solution of the linear problem on every iteration is considered. The method does not use Jacobi matrix. Algorithm of the method may be easily realized on modern programming languages and software packages.
Some problems of the practical realization of the implicit method are solved. The methods of the estimation of the length of heat boundary layer and Dirac delta function definition interval are proposed. Several types of the approximating functions for the Dirac delta function and the coefficient of the thermal conductivity are considered. For one-dimensional problem, it is shown that the piecewise constant approximations are preferable. The program of the algorithm of the implicit method for a solution of two-dimensional problems is realized in the FreeFem++ software package in the case of fixed mesh.
Two model problems are considered: the problem of the uniform glaciation of the pipe and the problem of weakly asymmetric glaciation with a model profile of the initial ice layer.

• 出版日期2017-12