基于径向基函数的结冰收集率计算的两级插值方法

为提高飞机结冰数值模拟中粒子轨迹计算的效率,基于拉格朗日方法,提出了两级插值方法。第一级插值为收集率插值,根据水滴轨迹在壁面撞击位置的收集率,采用径向基函数插值计算所有网格的收集率；第二级插值为轨迹插值,把水滴从远场运动撞击到壁面过程分为两个部分,在距机翼较远位置计算少量水滴轨迹,在壁面附近位置加密计算大量水滴轨迹。采用收集率插值时,由于结冰累积,线性插值或者高阶样条插值方法在遮蔽区内插值不准确,引入径向基函数插值来解决该问题。给出的算例表明,两级插值方法能够极大的提高拉格朗日法计算收集率的效率,径向基函数插值能够避免遮蔽区内插值不准确的问题。

The Methods of Two-stage Interpolation for Computation of Collection Efficiency in Icing Simulation Based on Radial Basis Function

Two-stages interpolation is developed to improve the computational efficiency of trajectories of water droplets simulation based on the Lagrangian method. The first stage is collection efficiency interpolation. In this stage, the collection efficiency on all wall grid is interpolated using radial basis functions from the collection efficiency of the water droplets trajectories which strike on the wall. The second stage is trajectories interpolation. The movement of the droplets is simulated by two stages. Only a little water drops trajectories are used in the far field. Plenty of water droplets trajectories are employed near the airfoil. For the first-stage interpolation, linear interpolation or high order spline interpolation underperform under the condition of ice accumulation, especially for the blocking area. To overcome this problem, the radial basis functions interpolation method has been introduced into the collection efficiency interpolation. The results show that the computational efficiency has been improved greatly and the radial basis functions interpolation avoids miscalculation in blocking area.