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将基于润滑理论的水膜-冰层模型推广到在任意二维截面上建立的正交曲线坐标系,得到描述二维型线表面水膜流动和积冰的偏微分控制方程.采用一种隐式-显式有限差分格式建立控制方程组的代数形式,给出求解非稳态控制方程组的数值方法.为验证模型和数值解法的有效性,在典型的航空积冰和传输线积冰环境下对翼型和传输线表面的积冰算例进行数值模拟.将水膜-冰层模型的冰形计算结果与传统Messinger模型的模拟结果以及冰风洞试验结果进行对比,低温明冰条件下采用当前方法计算的翼型表面冰形接近于Messinger模型的模拟冰形曲线;相对高温条件下的计算结果比传统Messinger模型更为精确.低速积冰环境下Messinger模型难以模拟的传输线表面积冰同样可以采用水膜-冰层模型进行有效预测.
The water film-ice model based on lubrication theory is extended to the orthogonal curvilinear coordinate system established on any two-dimensional cross section, and the partial differential equations governing the flow and the ice accretion on the two-dimensional line surface are obtained. In this paper, we establish the algebraic form of the governing equations by using the explicit finite difference scheme and give the numerical method for solving the unsteady governing equations.In order to verify the validity of the numerical solution and the numerical solution, Numerical simulations of the ice accretion on the airfoil and transmission line surface were carried out.Comparing the ice-shape calculation results of the water film-ice model with those of the conventional Messinger model and the ice-wind tunnel test results, the current ice- The calculated ice shape of the airfoil on the airfoil is close to the simulated ice curve of the Messinger model. The calculated results under the relatively high temperature are more accurate than those of the traditional Messinger model. The surface ice accretion on the transmission line which is difficult to be simulated by the Messinger model under low- Membrane - ice model for effective prediction.