基于广义Richardson外插方法的阻力预测精度分析

利用计算流体力学(CFD)方法预测阻力是飞行器气动设计中的关键环节。采用广义Richardson外插方法分别对数值方法预测二维简单构型的压差阻力、摩擦阻力和三维复杂构型的总阻力的精度进行了分析。在NACA 0012翼型无黏绕流和平板湍流边界层两个算例中验证了NSAWET程序和广义Richardson外插方法,分别得到数值算法预测压差阻力和摩擦阻力能达到的名义精度。进而模拟三维通用研究模型(CRM)翼身组合体绕流,得到的阻力名义精确值在DPW 5的统计误差带范围之内;综合DPW 5的计算结果来看,不同CFD解算器的结果之间存在一定差别,阻力预测精度总体上不符合二阶。可见,标准Richardson方法采用的二阶精度假设难以普遍适用,有必要采用广义Richardson外插方法得到名义精度。针对不合理的名义精度,采用Roache建议的方法加以限制。广义Richardson外插方法有助于提高误差分析的合理性,可以进一步降低网格对阻力预测的影响。

Accuracy analysis of drag prediction based on generalized Richardson extrapolation

Drag prediction based on computational fluid dynamics (CFD) plays a crucial role in aircraft aerodynamic design. In this study, the generalized Richardson extrapolation method is applied to the prediction accuracy analyses of pressure drag and friction drag for two-dimensional simple test cases and the total drag for a three-dimensional complex configuration. The inviscid flow around two-dimensional NACA 0012 airfoil and the turbulent boundary layer over a zero-pressure-gradient flat plate are used to validate the in-house CFD solver NSAWET and the generalized Richardson extrapolation method. The derived formal order of accuracy is considered as the theoretical drag prediction accuracy of CFD solvers. In the common reseach model (CRM) wing/body case, the predicted results for pressure drag, friction drag and total drag are within the range of the DPW 5 statistics. However, there are some differences among different CFD solvers and the prediction accuracy does not agree with second-order. All the above analyses show that the second-order accuracy adopted by the standard Richardson extrapolation may not be universally applicable and that the generalized Richardson extrapolation with restricted formal order of accuracy is thus necessary. The generalized Richardson extrapolation is able to make error analysis more reasonable and to weaken the grid effect on the drag prediction.