基于广义Richardson外插方法的阻力预测精度分析
收稿日期: 2014-10-16
修回日期: 2014-12-30
网络出版日期: 2015-01-23
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
Received date: 2014-10-16
Revised date: 2014-12-30
Online published: 2015-01-23
Supported by
National Basic Research Program of China (2014CB744801); National Natural Science Foundation of China (11102098, 11372160)
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。
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 . DOI: 10.7527/S1000-6893.2015.0005
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.
[1] Deng X G, Zong W G, Zhang L P, et al. Verification and validation in computational fluid dynamics[J]. Advances in Mechanics, 2007, 37(2): 279-288 (in Chinese). 邓小刚, 宗文刚, 张来平, 等. 计算流体力学中的验证与确认[J]. 力学进展, 2007, 37(2): 279-288.
[2] Morrison J H. Fifth AIAA CFD drag prediction workshop[EB/OL]. (2012-05-19)[2014-09-20]. http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw.
[3] Rumsey C. Second AIAA CFD high lift prediction workshop[EB/OL]. (2014-01-23)[2014-09-20]. http://hiliftpw.larc.nasa.gov/.
[4] AIAA. Second AIAA propulsion aerodynamics workshop[EB/OL]. (2014-08-01)[2014-09-20]. http://aiaapaw.tecplot.com/.
[5] Zhang H X. On the uncertainty about CFD results[J]. Acta Aerodynamica Sinica, 2008, 26(1): 47-49 (in Chinese). 张涵信. 关于CFD计算结果的不确定度问题[J]. 空气动力学学报, 2008, 26(1): 47-49.
[6] Zhang H X, Zha J. The uncertainty and truth-value assessment in the verification and validation of CFD[J]. Acta Aerodynamica Sinica, 2010, 28(1): 39-45 (in Chinese). 张涵信, 查俊. 关于CFD验证确认中的不确定度和真值估算[J]. 空气动力学学报, 2010, 28(1): 39-45.
[7] Chen J Q, Zhang Y R. Verification and validation in CFD based on the Richardson extrapolation method[J]. Acta Aerodynamica Sinica, 2012, 30(2): 176-183 (in Chinese). 陈坚强, 张益荣. 基于Richardson插值法的CFD验证和确认方法的研究[J]. 空气动力学学报, 2012, 30(2): 176-183.
[8] Yan C, Xi K, Yuan W, et al. Review of the drag prediction workshop series[J]. Advances in Mechanics, 2011, 41(6): 776-784 (in Chinese). 阎超, 席柯, 袁武, 等. DPW系列会议述评与思考[J]. 力学进展, 2011, 41(6): 776-784.
[9] Xu J, Liu Q H, Cai J S, et al. Drag prediction based on overset grids with implicit hole cutting technique[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(2): 208-217 (in Chinese). 徐嘉, 刘秋洪, 蔡晋生, 等. 基于隐式嵌套重叠网格技术的阻力预测[J]. 航空学报, 2013, 34(2): 208-217.
[10] Wang Y T, Sun Y, Wang G X, et al. High-order numerical simulation of DLR-F6 wing-body configuration[J/OL]. Acta Aeronautica et Astronautica Sinica, DOI: 10.7527/S1000-6893. 2015. 0124.[2015-05-15].http: //www. cnki.net/kcms/detail/11. 1929. V. 20150515. 1317. 002. html (in Chinese). 王运涛, 孙岩, 王光学, 等. DLR-F6翼身组合体的高阶精度数值模拟[J/OL]. 航空学报, DOI: 10.7527/S1000-6893. 2015. 0124.[2015-05-15].http: //www. cnki.net/kcms/detail/11. 1929. V. 20150515. 1317. 002. html.
[11] Levy D W, Laflin K R, Tinoco E N, et al. Summary of data from the fifth computational fluid dynamics drag prediction workshop[J]. Journal of Aircraft, 2014, 51(4): 1194-1213.
[12] Baker T J. Mesh generation: Art or science[J]. Progress in Aerospace Sciences, 2005, 41(1): 29-63.
[13] Salas M D. Digital flight: The last CFD aeronautical grand challenge[J]. Journal of Scientific Computing, 2006, 28(2-3): 479-505.
[14] Vassberg J C, Jameson A. In pursuit of grid convergence for two-dimensional Euler solutions[J]. Journal of Aircraft, 2010, 47(4): 1152-1166.
[15] Freeman J A, Roy C J. Verification and validation of Reynolds-averaged Navier-Stokes turbulence models for external flow[J]. Aerospace Science and Technology, 2014, 32(1): 84-93.
[16] Roache P J. Discussion: "factors of safety for richardson extrapolation"[J]. Journal of Fluids Engineering-Transactions of the ASME, 2011, 133(11): 115501.
[17] Rumsey C. Turbulence modeling resource[EB/OL]. (2014-08-06)[2014-09-20]. http://turbmodels.larc.nasa.gov/.
[18] Chen H X, Fu S, Li F W. Navier-Stokes simulations for transport aircraft wing/body high-lift configurations[J]. Journal of Aircraft, 2003, 40(5): 883-890.
[19] Zhang Y F, Chen H X, Fu S, et al. A practical optimization design method for transport aircraft wing/nacelle integration[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(11): 1993-2001 (in Chinese). 张宇飞, 陈海昕, 符松, 等. 一种实用的运输类飞机机翼/发动机短舱一体化优化设计方法[J]. 航空学报, 2012, 33(11): 1993-2001.
[20] Zhang W S, Chen H X, Zhang Y F, et al. Nacelle strake's aerodynamic characteristics effects on high-lift configuration of transport aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(1): 76-85 (in Chinese). 张文升, 陈海昕, 张宇飞, 等. 短舱扰流片对运输机增升装置气动特性的影响[J]. 航空学报, 2013, 34(1): 76-85.
[21] Xu K Z, Zhang Y F, Chen H X, et al. Numerical study of induced nonlinear rolling moment of finned missile at high angle of attack[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(1): 97-104 (in Chinese). 徐柯哲, 张宇飞, 陈海昕, 等. 导弹大迎角下非线性诱导滚转力矩数值研究[J]. 航空学报, 2014, 35(1): 97-104.
[22] Menter F R. Two-equation eddy-viscosity turbulence models for engineering applications[J]. AIAA Journal, 1994, 32(8): 1598-1605.
[23] Spalart P R, Allmaras S R. A one-equation turbulence model for aerodynamic flows, AIAA-1992-0439 [R]. Reston: AIAA, 1992.
[24] Hue D. Fifth drag prediction workshop: ONERA investigations with experimental wing twist and laminarity[J]. Journal of Aircraft, 2014, 51(4): 1311-1322.
[25] Park M A, Laflin K R, Chaffin M S, et al. CFL3D, FUN3D, and NSU3D contributions to the fifth drag prediction workshop[J]. Journal of Aircraft, 2014, 51(4): 1268-1283.
[26] Hue D. Fifth drag prediction workshop: Computational fluid dynamics studies carried out at ONERA[J]. Journal of Aircraft, 2014, 51(4): 1295-1310.
/
〈 | 〉 |