基于广义Richardson外插方法的阻力预测精度分析

doi:10.7527/S1000-6893.2015.0005

流体力学与飞行力学

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基于广义Richardson外插方法的阻力预测精度分析

李钊, 陈海昕, 张宇飞

清华大学航天航空学院, 北京 100084

收稿日期:2014-10-16 修回日期:2014-12-30 出版日期:2015-07-15 发布日期:2015-01-23
通讯作者: 陈海昕男, 博士, 教授。主要研究方向: 空气动力学, 计算流体力学, 气动设计。 Tel: 010-62789269 E-mail: chenhaixin@tsinghua.edu.cn E-mail:chenhaixin@tsinghua.edu.cn
作者简介:李钊男, 博士研究生。主要研究方向: 计算流体力学。 Tel: 010-62797506 E-mail: lizhao08@mails.tsinghua.edu.cn;张宇飞男, 博士, 讲师。主要研究方向: 气动设计, 计算流体力学。 Tel: 010-62792707 E-mail: zhangyufei@tsinghua.edu.cn
基金资助:
国家"973"计划(2014CB744801); 国家自然科学基金 (11102098, 11372160)

Accuracy analysis of drag prediction based on generalized Richardson extrapolation

LI Zhao, CHEN Haixin, ZHANG Yufei

School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

Received:2014-10-16 Revised:2014-12-30 Online:2015-07-15 Published:2015-01-23
Supported by:
National Basic Research Program of China (2014CB744801); National Natural Science Foundation of China (11102098, 11372160)

摘要/Abstract

摘要：

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。

关键词: 广义Richardson外插方法, 阻力预测, 网格收敛性, 验证与确认, 计算流体力学, CRM翼身组合体

Abstract:

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.

Key words: generalized Richardson extrapolation, drag prediction, grid convergence, verification and validation, computational fluid dynamics, CRM wing/body

中图分类号:

V211.3

李钊, 陈海昕, 张宇飞. 基于广义Richardson外插方法的阻力预测精度分析[J]. 航空学报, 2015, 36(7): 2105-2114.

LI Zhao, CHEN Haixin, ZHANG Yufei. Accuracy analysis of drag prediction based on generalized Richardson extrapolation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(7): 2105-2114.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于广义Richardson外插方法的阻力预测精度分析

Accuracy analysis of drag prediction based on generalized Richardson extrapolation

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