基于拟合与插值的受油机前扰波建模与分析

Modeling and Analysis of Receiver-Aircraft Bow Wave Based on Fitting and Interpolation

在无人机软管式自动空中加油中,受油机前扰波对于空中对接有着重要的影响。针对前扰波建模的迫切需求,通过计算流体动力学(CFD)仿真,得到受油机机头附近速度场数据,基于此数据分析速度随位置的变化规律。以多项式的函数形式用最小二乘法拟合出速度沿x,y,z 3个轴向上的分布规律,根据此规律推测出速度在机头横截面上的二维解析表达式,再用多项式进行二维拟合,接着用平面插值在满足精度的条件下求解出速度与三维位置坐标的解析表达式。最后对x,y,z 3个方向分别拟合插值并选取区域进行验证,仿真结果表明了模型的有效性并且可以看出沿y轴方向进行插值误差最小。

In the hose-type air-to-air refueling of Unmanned Aerial Vehicles （UAVs）, the bow wave of the receiver-aircraft has an important impact on the docking phase in the air. To meet the urgent requirements of bow-wave modeling, the velocity field data around the nose of the receiver-aircraft is obtained through Computational Fluid Dynamics （ CFD ） simulation, based on which the change laws of velocity with the coordinated point are analyzed. Based on the polynomial function, the regularities of distribution of the velocity along the x, y and z axis are fitted by using the least square method, the two-dimension analytical expression of the velocity on the intersecting surface is speculated according to the laws above, and the two- dimension fitting is done by using the polynomial. Then, the analytical expressions of the velocity and the three-dimensional position coordinates are solved by using the plane interpolation, which meets the precision requirements. Finally, the interpolating along the x, y and z axis are conducted respectively, and an area is selected for validation. The simulation results prove the effectiveness of this model, and show that the error is the minimum when interpolating along y axis.