基于润滑理论的二维积冰数值模拟

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.

Numerical simulation of two dimensional ice accretion based on lubrication theory

Water film-ice layer model based on lubrication theory was extended to two-dimensional orthogonal curvilinear coordinate system on arbitrary sections. Two governing partial differential equations of water film flow and ice accretion on curved sections were obtained. The numerical methods for solving these unsteady governing equations were presented. An implicit-explicit discrete scheme was applied to obtain the algebraic form of governing equations. Examples of numerical icing calculation were verified on NACA0012 airfoil and circle cylinder section in typical aero icing and structural icing environment. The results of calculation using current model were compared with ice shapes of simulation using traditional Messinger model and results from ice wind tunnel tests. Ice shapes on airfoil obtained using this numerical method were close to icing curves calculated by Messinger model in low temperature glaze icing conditions. In relatively high temperature icing conditions, more accurate results were obtained than Messinger model compared with results of ice tunnel experiments. Ice accretion on transmission line wires which cannot be predicted properly by traditional Messinger model was also effectively predicted by current model in structural icing conditions.