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A hybrid RANS/HILES method (HRILES) is developed by combining the RANS-SST model and high order implicit large eddy simulation method (HILES) and employed with the Ffowcs Williams-Hawkings (FW-H) equation to predict the slat noise of 30P30N high-lift airfoil. Comparison has been made between the HRILES method and the traditional DDES based on the full-turbulence model SST by simulating the single cylinder case with
$Re_{{d}}=4.3\times10^4$ . The HRILES method is able to predict the transition phenomenon and the small-scale separation bubble in the sub-critical wake region while the DDES can't and get a better mean wall pressure distribution than DDES. The amplitude and frequency spectrum of the far-field sound pressure level are in good agreement with the experimental data. In the simulation of 30P30N high-lift airfoil, the famous IDDES model is also used for comparison, both results are compared with experimental measurements. The computational mesh is provided by Japan Aerospace Exploration Agency (JAXA) in the Workshop on Benchmark problems for Airframe Noise Computations (BANC). The HRILES method obtains quantitative agreement with experimental data in terms of mean wall pressure coefficient, frequency spectrum of pressure fluctuations on the slat surface, and the mean flow statistics in the slat cusp shear layer. The IDDES model slightly underestimate the suction effect on the upper surface of the slat, and delays the instabilities in the slat cusp shear layer. The near-field noise spectra are compared with measurements obtained in JAXA low-speed Wind Tunnel. Narrow band peaks present are well recovered by both methods, while IDDES model overestimate the broadband noise. Far-field noise directivity results of every components, filtered in the band [256Hz–10KHz], are compared with each other, and the slat cove is confirmed to dominate the sound noise levels. The slat and flap noises show a typical dipole distribution, while the main wing noise's directivity is not apparent. Computational results show that the HRILES method, as one kind of generalized Hybrid RANS/LES method, HRILES can smoothly switch between the SST model and the HILES method. HRILES has the high-resolution simulation capability of the HILES in the LES region, and can reduce the requirements of the HILES method on the near-wall grid distribution by using the SST model in the inner boundary layer. As a result, the HRILES method has advantages in simulations at high reynolds numbers and aeroacoustic problems. Further research will be carried out in the applications at higher reynolds number flows with complex geometry in the future.[1] Busquin M 2001 http://www.acare4europe.org/sites/acare4europe.org/files/document/Vision%2020200.pdf [2019-5-22]
[2] Dobrzynski W 2010 J. Aircraft 47 2
[3] Pott P, Alvarez G, Dobrzynski W 2003 9th AIAA/CEAS Aeroacoustics Conference and Exhibit South Carolina, USA, May 12–14, 2003 p3228
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[6] Slotnick J, Khodadoust A, Alonso J http://ntrs.nasa.gov/search.jsp?=20140003093/ [2019-5-22]
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[13] Ishiko K, Shimada T 2010 48th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition Orlando, Florida, January 4−7, 2010 p923
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[26] Wang S, Deng X, Wang G, Xu D, Wang D 2016 Inter. J. Comput. Fluid Dynamics 30 7
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[35] Pascioni K, Cattafesta L, Choudhari M 2014 20th Aiaa/ceas Aeroacoustics Conference Atlanta, Georgia, June 16−20, 2014 p3062
[36] Murayama M, Nakakita K, Yamamoto K, Ura H, Ito Y 2014 20th AIAA/CEAS Aeroacoustics Conference Atlanta, GA, June 16−20 2014 p2014
[37] Gao J, Li X, Lin D 2017 23th AIAA/CEAS Aeroacoustics Conference Denver, Colorado, June 5−9, 2017 p3363
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图 1 圆柱表面平均压力系数分布
Figure 1. Mean wall pressure coefficient distribution of the rod
图 2 流线分布 (a) HRILES; (b) SST-DDES
Figure 2. Distribution of streamlines: (a) HRILES; (b) SST-DDES
图 3 远场
$ \theta = 90^\circ $ ,$ r = 180d $ 观测点声压级功率谱密度Figure 3. Farfield acoustic result of the rod: PSD at (
$ \theta = 90^\circ,$ $ r = 180d $ ).
图 4 30P30N计算网格
Figure 4. Mesh of 30P30N airfoil
图 5
$ QC/U_{\infty} = 5000 $ 等值面 (a) IDDES; (b) HRILESFigure 5. The isosurfaces of the Q-criterion (
$ QC/U_{\infty} = 5000 $ ): (a) IDDES; (b) HRILES
图 6 平均展向涡量云图 (a) IDDES; (b) HRILES
Figure 6. Contours of meanmean spanwise vorticity: (a) IDDES; (b) HRILES
图 7 平均流线分布 (a) 缝翼; (b) 襟翼
Figure 7. Distribution of streamlines: (a) Slat; (b) flap
图 8 壁面压力系数分布
Figure 8. Distribution of wall pressure coefficient
图 9 缝翼表面压力系数脉动均方根分布
Figure 9. RMS of the fluctuating pressure coefficient on the surface of the slat
图 10 各个站位的平均速度分布
Figure 10. Mean velocity magnitudes along the seven lines across
图 11 各个站位的平均展向涡量分布
Figure 11. Mean spanwise vorticity along the seven lines across
图 12 各个站位的平均湍动能分布
Figure 12. Mean turbulent kinetic energy along the seven lines across
图 13 脉动压力功率谱密度分布 (a)
$ P_1 $ ; (b)$ P_4 $ Figure 13. Frequency spectra of pressure fluctuations: (a)
$ P_1 $ ; (b)$ P_4 $ 
图 14 瞬态脉动压力云图
Figure 14. Contours of pressure fluctuation
图 15
$ r = 2.19C,\; \theta = 287.5^\circ $ 观测点声压级功率谱Figure 15. Power spectra density of sound pressure level at
$ r = 2.19C,\; \theta = 287.5^\circ $ 
图 16
$ r = 10C $ , 远场声压级指向图Figure 16. Directivity of SPL at
$ r = 10C $ 
图 17 各部件远场(
$ r = 10C $ )声压级指向对比图 (a) IDDES; (b) HRILESFigure 17. Directivity of components' SPL at
$ r = 10C $ : (a) IDDES; (b) HRILES表 1 单圆柱算例流动参数统计结果
Table 1. Statistical results of aerodynamic coefficients for the single cylinder
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[1] Busquin M 2001 http://www.acare4europe.org/sites/acare4europe.org/files/document/Vision%2020200.pdf [2019-5-22]
[2] Dobrzynski W 2010 J. Aircraft 47 2
[3] Pott P, Alvarez G, Dobrzynski W 2003 9th AIAA/CEAS Aeroacoustics Conference and Exhibit South Carolina, USA, May 12–14, 2003 p3228
[4] Souza D, Rodríguez D, Simões L, Medeiros M 2015 Aerosp. Sci. Technol. 44 108
Google Scholar
[5] Choudhari M, Lockard D, Khorrami M, Mineck R 2011 INTER-NOISE and NOISE-CON Congress and Conference Proceedings Reston, VA, September 4−7, 2011 p3583
[6] Slotnick J, Khodadoust A, Alonso J http://ntrs.nasa.gov/search.jsp?=20140003093/ [2019-5-22]
[7] Grinstein F, Fureby C 2002 J. Fluids Eng.-Tran. ASME 124 848
Google Scholar
[8] Hahn M, Drikakis D 2005 Int. J. Numner. Methods Fluids 47 971
Google Scholar
[9] Fureby C, Grinstein F 1999 AIAA J. 37 544
Google Scholar
[10] Fureby C, Grinstein F 2002 J. Comput. Phys. 181 68
Google Scholar
[11] Ishiko K, Ohnishi N, Sawada K 2013 Aiaa Aerospace Sciences Meeting & Exhibit Reno, Nevada, January 9−12, 2006 p703
[12] Ishiko K, Shimada T 2010 26th AIAA Applied Aerodynamics Conference Honolulu, Hawaii, August 18−21, 2008 p6579
[13] Ishiko K, Shimada T 2010 48th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition Orlando, Florida, January 4−7, 2010 p923
[14] Rizzetta D P, Visbal M R, Morgan P E 2008 Prog. Aerosp. Sci. 44 397
Google Scholar
[15] Deng X, Min Y, Mao M, Liu H, Tu G Zhang H 2013 J. Comput. Phys. 239 90
Google Scholar
[16] Jiang Y, Mao M, Deng X, Liu H 2014 Comput. Fluids 104 73
Google Scholar
[17] Jiang Y, Mao M, Deng X, Liu H 2015 Adv. Appl. Math. Mech. 7 407
Google Scholar
[18] Mao M, Jiang Y, Deng X, Liu H 2016 Adv. Appl. Math. Mech. 8 236
Google Scholar
[19] Argyropoulos C D, Markatos N C 2015 Appl. Math. Modell. 39 693
Google Scholar
[20] Spalart P, Jou W, Strelets M, Allmaras S 1997 Advances in DNS/LES (Columbus: Creyden Press) p137
[21] Spalart P, Deck S, Shur M, Squires K, Strelets M, Travin A 2006 Theor. Comput. Fluid Dyn. 20 181
Google Scholar
[22] Shur M L, Spalart P R, Strelets M K, et al. 2008 Int. J. Heat Fluid Flow 29 1638
Google Scholar
[23] Nichols R 2003 41st Aerospace Sciences Meeting & Exhibit Reno, Nevada, January 6−9, 2003 p0083
[24] Nichols R 2005 43rd Aiaa Aerospace Sciences Meeting & Exhibit Reno, Nevada, January 6−9, 2005 p498
[25] Deng X, Jiang Y, Mao M, Liu H, Li S, Tu G 2015 Comput. Fluids 116 29
Google Scholar
[26] Wang S, Deng X, Wang G, Xu D, Wang D 2016 Inter. J. Comput. Fluid Dynamics 30 7
Google Scholar
[27] Piomelli U 2008 Prog. Aerosp. Sci. 44 437
Google Scholar
[28] Francescantonio P 1997 J. Sound Vibration 202 491
Google Scholar
[29] Kato C, Iida A, Takano Y, Fujita H, Ikegawa M 1993 31wst Aerospace Sciences Meeting & Exhibit Reno, NV, January 11−14, 1993 p145
[30] Mustafa S, Tahir Y 2002 AIAA J. 40 1257
Google Scholar
[31] Szepessy S, Bearman P 1992 J. Fluid Mech. 234 91
[32] Seo J, Chang K, Moon Y 2006 12th AIAA/CEAS Aeroacoustics Conference Cambridge, Massachusetts, May 8−10, 2006 p2573
[33] Jacob M, Boudet J, Casalino D, Michard M 2005 Theiret. Comput. Fluid Dynamics 19 171
Google Scholar
[34] Terracol M, Manoha E, Murayama M, Yamamoto K, Kazuhisa A, Kentaro T 2015 21st AIAA/CEAS Aeroacoustics Conference Dallas, TX, June 22−26, 2015 p3132
[35] Pascioni K, Cattafesta L, Choudhari M 2014 20th Aiaa/ceas Aeroacoustics Conference Atlanta, Georgia, June 16−20, 2014 p3062
[36] Murayama M, Nakakita K, Yamamoto K, Ura H, Ito Y 2014 20th AIAA/CEAS Aeroacoustics Conference Atlanta, GA, June 16−20 2014 p2014
[37] Gao J, Li X, Lin D 2017 23th AIAA/CEAS Aeroacoustics Conference Denver, Colorado, June 5−9, 2017 p3363
[38] Zhang Y, Chen H, Wang K, Wang M 2017 AIAA Journal 55 4219
Google Scholar
[39] Pascioni K, Cattafesta L 2016 22ed AIAA/CEAS Aeroacoustics Conference Lyon, France, May 30–June 1, 2016 p2016
[40] Choudhari M, Lockard D 2015 22ed AIAA/CEAS Aeroacoustics Conference Dallas, TX, June 22−26, 2015 p2844
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