GENERAL REYNOLDS ANALOGY RELATION ON BLUNT-NOSED BODIES

Chen Xingxing; Chen Hao; Fan Jingjing; Wen Yufen; Zhang Zheng; Ma Youlin

doi:10.6052/0459-1879-19-365

Volume 52 Issue 4

Aug. 2020

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Chinese Journal of Theoretical and Applied Mechanics > 2020 > 52(4): 1055-1062. > DOI: 10.6052/0459-1879-19-365 CSTR: 32045.14.0459-1879-19-365

Chen Xingxing, Chen Hao, Fan Jingjing, Wen Yufen, Zhang Zheng, Ma Youlin. GENERAL REYNOLDS ANALOGY RELATION ON BLUNT-NOSED BODIES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1055-1062. DOI: 10.6052/0459-1879-19-365

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GENERAL REYNOLDS ANALOGY RELATION ON BLUNT-NOSED BODIES

China Academy of Launch Vehicle Technology,Beijing 100076,China

Received Date: December 19, 2019

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Abstract

The classical Reynolds analogy relation fail on blunt-nosed bodies, as the distributions of skin frictions on curved wall surfaces differ from that on heat fluxes. With a theoretical research background on hypersonic Reynolds analogy relations, numerical simulations are presented in this paper to study the general Reynolds analogy relation on blunt-nosed bodies, as circular cylinder and power-law body, under different incoming flows. A linear relation of Reynolds analogy is obtained by theoretical analysis on the boundary layer along those surfaces. Also, numerical methods are applied to obtain solutions of N-S equations, from which skin frictions and heat fluxes and their analogy coefficients around cylinders and power-law bodies are calculated. The methods are validated by comparing the distribution of Reynolds analogy coefficients and the stagnation point heat transfer rate with former numerical and theoretical results. The convergence and grid independence are verified for the TVD method. The variation of Reynolds analogy relations are investigated in the range of $Re_\infty = 3.98\times 10^2 \sim 1.59\times 10^6$ and $M_\infty = 3\sim 12$ . The present study shows that the general Reynolds analogy relation predicts the ratio between skin frictions and heat fluxes on regimes near the stagnations point for hypersonic flows. Downstream the stagnation point of circular cylinders (where $\theta > 60^\circ$ ), the Reynolds analogy relation deviates from the theoretical linear relationship in varying degrees with the growing of Reynolds number. Numerical results demonstrate that, comparing with the general Reynolds analogy relations on circular cylinders, Reynolds analogy coefficients are lower and fit linear distributions better for power-law bodies. Analyses indicate that modifications based on the shape of noses or the Reynolds number may improve the accuracy of theoretical predictions.
- skin friction,
- heat flux,
- Reynolds analogy,
- hypersonic

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[1]	Reynolds O. On the extent and action of the heating surface for steam boilers. Proc Lit Phil Soc Manchester, 1874,14(1):7-2
[2]	Blasius H. Grenzschichten in flüessigkeiten mit kleiner ribung. Zeitschrift fuer Mathematik und Physik, 1908,56(1):1-37
[3]	Li TY, Nagamatsu HT. Similar solutions of compressible boundary-layer equations. Journal of the Aeronautical Sciences, 1953,20(9):653-55
[4]	Cohen CB. Similar solutions of compressible laminar boundary-Layer equations. Journal of the Aeronautical Sciences, 1954,21(4):281-82
[5]	Chen XX, Wang ZH, Yu YL. Nonlinear shear and heat transfer in hypersonic rarefied flows past flat plates. AIAA Journal, 2015,53(2):413-419
[6]	Abramov A, Butkovskii A. Extended Reynolds analogy for the rarefied Rayleigh problem: Similarity parameters// AIP Conference Proceedings 2132,2019
[7]	Jiang LY, Campbell I. Reynolds analogy in combustor modeling. International Journal of Heat and Mass Transfer, 2008,51(1):1251-263
[8]	丛彬彬, 万田. 高速双锥绕流中热化学与输运模型影响研究. 力学学报, 2019,51(4):1012-1021
[8]	( Cong Binbin, Wan Tian. Effects of thermochemical and transport models on the high-speed double-cone flowfield. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(4):1012-1021 (in Chinese))
[9]	Van Driest ER. Turbulent boundary layer in compressible fluids. Journal of Spacecraft and Rockets, 1951,18(3):145-160
[10]	Van Driest ER. Investigation of laminar boundary Crocco method. NACA-TN-2597, 1952
[11]	Van Driest ER. The problem of aerodynamic heating. Aeronautical Engineering Review, 1956,15(1):26-41
[12]	Spalding DB, Chi SW. The drag of a compressible turbulent boundary layer on a smooth flat plate with and without heat transfer. Journal of Fluid Mechanics, 1964,18(1):117-143
[13]	Eckert ERG. Engineering relations for friction and heat transfer to surfaces in high velocity flow. Journal of the Aeronautical Sciences, 1955,22(8):585-587
[14]	蒋友娣, 董葳, 陈勇. 高超声速钝头体变熵表面热流计算. 航空动力学报, 2008,23(9):1591-1594
[14]	( Jiang Youdi, Dong Wei, Chen Yong. Surface heat flux calculation of variable entropy flow for hypersonic blunt bodies. Journal of Aerospace Power, 2008,23(9):1591-1594 (in Chinese))
[15]	Chi RW, Maleina CB, Turbulence models and Reynolds analogy for two-dimensional supersonic compression ramp flow. NASA-TM-106474, 1994
[16]	梁贤, 李新亮, 傅德薰等. Mach 8 的平板可压缩湍流边界层直接数值模拟及分析. 中国科学: 物理学力学天文学, 2012,42(3):282-293
[16]	( Liang Xian, Li Xinliang, Fu Dexun, et al. DNS and analysis of a spatially evolving hypersonic turbulent boundary layer over a flat plate at Mach 8. Sci Sin-Phys Mech Astron, 2012,42(3):282-293 (in Chinese))
[17]	She ZS, Zou HY, Xiao MJ, et al. Prediction of compressible turbulent boundary layer via a symmetry-based length model. Journal of Fluid Mechanics, 2018,857(1):449-468
[18]	姜宗林, 李进平, 胡宗民等. 高超声速飞行复现风洞理论与方法. 力学学报, 2018,50(6):1283-1291
[18]	( Jiang Zonglin, Li Jinping, Hu Zongmin, et al. Shock tunnel theory and methods for duplicating hypersonic flight conditions. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(6):1283-1291 (in Chinese))
[19]	Chen XX, Wang ZH, Yu YL. General Reynolds analogy for blunt-nosed bodies in hypersonic flows. AIAA Journal, 2015,53(8):2410-2416
[20]	Anderson JD. Hypersonic and High Temperature Gas Dynamics. 2nd ed. New York: McGraw-Hill Book Company, 2006: 270-271
[21]	Chen XX, Wang ZH, Yu YL. General Reynolds analogy on curved surfaces in hypersonic rarefied gas flows with non-equilibrium chemical reactions// 30th International Symposium on Rarefied Gas Dynamics (RGD), Victorial, Canada, 2016-7-10-15, AIP Conference Proceedings 1786, 150009, 2006
[22]	屈程, 王江峰. DSMC 计算中碰撞对取样和时间推进环节的高效处理方法. 空气动力学报, 2018,36(1):52-56
[22]	( Qu Cheng, Wang Jiangfeng. High efficient processing method for DSMC calculation in chains of collision pair selection and time integration. Acta Aeradynamics Sinica, 2018,36(1):52-56 (in Chinese))
[23]	Qian G, Ramesh KA. Computations of rarefied hypersonic blunt body flow in binary inert gas mixtures using the generalized Boltzmann equation// AIP Conference Proceedings 2132,100011, 2019
[24]	杨超, 孙泉华. 高温气体热化学反应的DSMC微观模型分析. 力学学报, 2018,50(4):722-733
[24]	( Yang Chao, Sun Quanhua. Analysis of dsmc reaction models for high temperature gas simulation. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(4):722-733 (in Chinese))
[25]	Lees L. Laminar heat transfer over blunt-nosed bodies at hypersonic flight speeds. Journal of Jet Propulsion, 1956,26(4):259-69
[26]	Fay JA, Riddell FR. Theory of stagnation point heat transfer in dissociated air. Journal of the Aeronautical Science, 1958,25(2):73-85
[27]	Wang ZH, Bao L, Tong BG. Rarefaction criterion and non-Fourier heat transfer in hypersonic rarefied flows. Physics of Fluids, 2010,22:126103
[28]	王智慧. 尖化前缘气动加热受稀薄气体效应和非平衡真实气体效应的工程理论. [博士论文]. 北京: 中国科学院研究生院, 2011
[28]	( Wang Zhihui. A theoretical modelling of aeroheating on sharpened noses under rarefied gas effects and nonequilibrium real gas effect. [PhD Thesis]. Beijing: University of Chinese Academy of Sciences, 2011 (in Chinese))
[29]	王智慧, 鲍麟, 童秉纲. 尖化前缘的稀薄气体化学非平衡流动和气动加热相似律研究. 气体物理, 2016,1(1):5-12.
[29]	( Wang Zhihui, Bao Lin, Tong Binggang. Similarity law of aero-heating to sharpened nosed in rarefied chemical nonequilibrium flows. Physics of Gases, 2016,1(1):5-12 (in Chinese))
[30]	Hoffmann KA, Siddiqui MS, Chiang ST. Difficulties associated with the heat flux computations of high speed flows by the Navier-Stokes equations. AIAA Paper 91-0467, 1991
[31]	Lee JH, Rho OH. Accuracy of AUSM+ scheme in hypersonic blunt body flow calculations. AIAA Paper 98-1538, 1998
[32]	Ashwani A, Nived MR, Nikhil NK, et al. A numerical study of shock and heating with rarefaction for hypersonic flow over a cylinder. Journal of Heat Transfer, 2020,142(1):014501
[33]	Schwartzentruber TE, Leonardo CS, Iain DB. Hybrid particle-continuum simulations of non-equilibrium hypersonic blunt body flow fields. AIAA Paper 2006-3602, 2006
[34]	Lees L. Hypersonic flow. Journal of Spacecraft and Rockets, 1955,40(5):700-735
[35]	Korobkin I. Laminar heat transfer characteristics of a hemisphere for the Mach number range 1.9 to 4.9., AIAA Paper 2006-NAVORD Report No. 3841, 1954
[36]	Pan D, Ramesh KA. Numerical drag prediction of NASA common research models using differcent turbulence models. Computers & Fluids, 2019,191(15), 104238

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