Fluid Mechanics and Flight Mechanics

Entropy correction method for high accuracy drag prediction with mixed grids

  • ZHANG Peihong ,
  • ZHANG Yaobing ,
  • ZHOU Guiyu ,
  • CHEN Jiangtao ,
  • DENG Youqi
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  • Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China

Received date: 2018-01-15

  Revised date: 2018-03-17

  Online published: 2018-04-09

Supported by

National Specialized Fund for Strategic High-tech Research and Development of China (17H86303ZT001018)

Abstract

The Roe flux-difference splitting scheme is widely used to simulate subsonic and transonic flow fields due to its characteristics of small dissipation, high resolution, etc. However, an entropy correction method should be proposed when the space is discrete. And the entropy correction will increase dissipation and affect the prediction accuracy of drags. Based on the characteristics of entropy correction for the Roe scheme of the unstructured hybrid grid, a new entropy correction method is presented by improving the original Harten-Yee entropy correction method. To validate the new method, a numerical simulation of the DLR-F4 wing-body configuration is performed. The numerical results are analyzed and compared with that of the original Harten-Yee entropy correction method and no-entropy method. The results indicate that the same residual convergence and more accurate results can be obtained with the new method, and the results show a good agreement with experiment results and the results obtained with no-entropy method. It is found that the new method not only retains the advantages such as robustness, but also minimizes the effect on the prediction accuracy of drags. That verifies the effectiveness of the new method. The DLR-F6 wing-body model of the 3th AIAA Drag Prediction Workshop is studied elaborately using the new method. The influences of grid convergence and Reynolds numbers are studied. The results demonstrate that the new method is much more suitable for viscous calculation of the unstructured hybrid grid, and the precision is similar to the corresponding CFD software. The drag prediction accuracy of the new method is further verified.

Cite this article

ZHANG Peihong , ZHANG Yaobing , ZHOU Guiyu , CHEN Jiangtao , DENG Youqi . Entropy correction method for high accuracy drag prediction with mixed grids[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018 , 39(9) : 122019 -122030 . DOI: 10.7527/S1000-6893.2018.22019

References

[1] ROE P L. Approximate Riemann solvers parameter vectors and difference schemes[J]. Journal of Computational Physics, 1981, 43(2):357-372.
[2] 周禹, 阎超. Roe格式中不同类型熵修正性能分析[J]. 北京航空航天大学学报, 2009, 35(3):356-360. ZHOU Y, YAN C. Entropy correction analyses for Roe scheme[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(3):356-360(in Chinese).
[3] TADMOR E. Entropy stability theory for difference approximations of nonlinear conservation laws and related time dependent problem[J]. Acta Numerica, 2003, 12(12):451-512.
[4] KERMANI M J, PLETT E G. Modified entropy correction formula for the Roe scheme:AIAA-2001-0083[R]. Reston, VA:AIAA, 2001.
[5] ALEKSANDAR J, HRVOJE J. Entropy stable multi-dimensional dissipation function for the Roe scheme on unstructured meshes:AIAA-2012-0569[R]. Reston, VA:AIAA, 2012.
[6] PHONGTHANAPANICH S, DECHAUMPHAI P. Flux-difference splitting scheme with modified multidimensional dissipation on unstructured meshes[J]. Journal of the Chinese Institute of Engineers, 2004, 27(7):981-992.
[7] HARTEN A, HYMAN J. Self-adjusting grid method for one dimensional hyperbolic conservation laws[J]. Journal of Computational Physics, 1983, 50(2):235-269.
[8] PERRY K M, IMLAY S T. Blunt body flow simulations:AIAA-1998-2904[R]. Reston, VA:AIAA, 1998.
[9] ROBINET J C, GRESSIER J, CASALIS G, et al. Shock wave instability and the carbuncle phenomenon:same intrinsic origin[J]. Journal of Fluid Mechanics, 2011, 417:237-263.
[10] HARTEN A. High resolution scheme for hyperbolic conservation laws[J]. Journal of Computational Physics, 1983, 49(3):357-393.
[11] VAN LEER B, LEE W T, POWELL K G, et al. Sonic-point capturing:AIAA-1989-1945[R]. Reston, VA:AIAA, 1989.
[12] 张培红, 张耀冰, 周桂宇, 等. 面向混合网格高精度阻力预测的梯度求解方法[J]. 航空学报, 2018, 39(1):121415. ZHANG P H, ZHANG Y B, ZHOU G Y, et al. Gradient calculation method of unstructured mixed grids for improving drag prediction accuracy[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(1):121415(in Chinese).
[13] VASSBERG J C, TINOCO E N, MANI M, et al. Summary of the Third AIAA CFD Drag Prediction Workshop[J]. Journal of Aircraft, 2008, 45(3):781-798.
[14] LEVY D W, ZICKUHR T, VASSBERG J C, et al. Summary of data from the First AIAA CFD Drag Prediction Workshop:AIAA-2002-0841[R]. Reston, VA:AIAA, 2002.
[15] LAFLIN K R, KLAUSMEYER S M, ZICKUHR T, et al. Summary of the Second AIAA CFD Drag Prediction Workshop[J]. Journal of Aircraft, 2005, 42(5):1165-1178.
[16] JOSEPH H M, MICHAEL J H. Statistical analysis of the AIAA Drag Prediction Workshop CFD solutions:AIAA-2007-0254[R]. Reston, VA:AIAA, 2007.
[17] SLOTNICK J, KHODADOUST A, ALONSO J, et al. CFD vision 2030 study:A path to revolutionary computational aero-sciences:NASA/CR-2014-218178[R]. Washington, D.C.:NASA, 2014.
[18] BARTH T J. An overview of combined uncertainty and a posteriori error bound estimates for CFD calculations:AIAA-2016-1062[R]. Reston, VA:AIAA, 2016.
[19] 王运涛, 孟德虹, 孙岩, 等. DLR-F6/FX2B翼身组合体构型高精度数值模拟[J]. 航空学报, 2016, 37(2):484-490. WANG Y T, MENG D H, SUN Y, et al. High-order ac-curacy numerical simulation of DLR-F6/FX2B wing-body configuration[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(2):484-490(in Chinese).
[20] 张耀冰, 邓有奇. DLR-F6翼身组合体数值计算[J]. 空气动力学学报, 2011, 39(2):163-169. ZHANG Y B, DENG Y Q. Drag prediction of DLR-F6 using MFlow unstructured mesh solver[J]. Acta Aerodynamica Sinica, 2011, 39(2):163-169(in Chinese).
[21] 张健, 邓有奇, 李彬, 等. 一种适用于三维混合网格的GMRES加速收敛新方法[J]. 航空学报, 2016, 37(11):3226-3235. ZHANG J, DENG Y Q, LI B, et al. A new method to accelerate GMRES's convergence applying to three-dimensional hybrid grid[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(11):3226-3235(in Chinese).
[22] 张扬, 张来平, 赫新, 等. 基于非结构/混合网格的脱体涡模拟算法[J]. 航空学报, 2015, 36(9):2900-2910. ZHANG Y, ZHANG L P, HE X, et al. Detached-eddy simulation based on unstructured and hybrid grid[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(9):2900-2910(in Chinese).
[23] 刘强, 白鹏, 李峰, 等. 不同雷诺数下翼型气动特性及层流分离现象演化[J]. 航空学报, 2017, 38(4):120338. LIU Q, BAI P, LI F, et al. Aerodynamic characteristics of airfoil and evolution of laminar separation at different Reynolds numbers[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(4):120338(in Chinese).
[24] 王运涛, 孙岩, 孟德虹, 等. CRM翼身组合体模型高阶精度数值模拟[J]. 航空学报, 2017, 38(3):120298. WANG Y T, SUN Y, MENG D H, et al. High-order numerical simulation of CRM wing-body model[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(3):120298(in Chinese).
[25] 张露, 李杰. 基于RANS/LES方法的超声速底部流场数值模拟[J]. 航空学报, 2017, 38(1):120102. ZHANG L, LI J. Numerical simulations of super-sonic base flow field based on RANS/LES approaches[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(1):120102(in Chinese).
[26] 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. 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).
[27] 王运涛, 李松, 孟德虹, 等. 梯形翼高升力构型的数值模拟技术[J]. 航空学报, 2014, 35(12):3213-3221. WANG Y T, LI S, MENG D H, et al. Numerical simulation technology of high lift trapezoidal wing configuration[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(12):3213-3221(in Chinese).
[28] 康忠良, 阎超. 适用于混合网格的约束最小二乘重构方法[J]. 航空学报, 2012, 33(9):1598-1605. KANG Z L, YAN C. Constrained least-squares recon-struction method for mixed grids[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(9):1598-1605(in Chinese).
[29] 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 Z, CHEN H X, ZHANG Y F. Accuracy analysis of drag prediction based on generalized Richardson extrapolation[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(7):2105-2114(in Chinese).
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