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Luo Jian, Wang Zhihui. Compressible Couette flow and its heat transfer under vibrational nonequilibrium effects. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 83-93. DOI: 10.6052/0459-1879-21-414
Citation: Luo Jian, Wang Zhihui. Compressible Couette flow and its heat transfer under vibrational nonequilibrium effects. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 83-93. DOI: 10.6052/0459-1879-21-414

COMPRESSIBLE COUETTE FLOW AND ITS HEAT TRANSFER UNDER VIBRATIONAL NONEQUILIBRIUM EFFECTS

  • Received Date: August 20, 2021
  • Accepted Date: December 19, 2021
  • Available Online: December 20, 2021
  • Most of the new-generation hypersonic cruise vehicles have sharp leading edges and thin wings, and the flow and heat transfer downstream the stagnation point are characterized by the strong shear effects and significant nonequilibrium effects. Because of the demand on the total heat load prediction and the experimental data identification, there is an increasing engineering interest in the strongly sheared nonequilibrium flow and aerodynamic heating problems. In this paper, the theoretical modeling method, as well as the direct simulation Monte Carlo (DSMC) method, is used to study the aerodynamic force and heating performance of the compressible Couette flow under the vibrational nonequilibrium effects. Firstly, based on the reference temperature method, a theoretical formula of the reference temperature for the compressible Couette flow is deduced under the calorically perfect gas model. Then, analyses are conducted of the vibrational nonequilibrium effects on the reference temperature and the Reynolds analogy. The dimensionless criterion for the vibrational nonequilibrium effects is proposed, and the criterion is further employed to design formulas for prediction of the skin-friction and heat transfer. Finally, the theoretical results are validated and calibrated by the DSMC results. Both the analytical and numerical results in this study indicate that, the vibrational nonequilibrium effects reduce the skin-friction of the compressible Couette flow, but meanwhile, the Reynolds analogy is still valid as long as the analogy ratio is corrected to take into account of the vibrational energy transfer. The present study could enrich our understanding of the vibrational nonequilibrium shear flow, and specifically, the nonequilibrium flow criterion could be extended to investigate more practical aerodynamic heating problems which significantly involve the thermal nonequilibrium effects.
  • [1]
    周恒, 张涵信. 空气动力学的新问题. 中国科学: 物理学 力学 天文学, 2015, 45: 104709 (Zhou Heng, Zhang Hanxin. New problems of aerodynamics. Sci. Sin.-Phys. Mech. Astron., 2015, 45: 104709 (in Chinese) doi: 10.1360/SSPMA2015-00402
    [2]
    樊菁. 稀薄气体动力学: 进展与应用. 力学进展, 2013, 43(2): 185-201 (Fan Jing. Rarefied gas dynamics: advances and applications. Advances in Mechanics, 2013, 43(2): 185-201 (in Chinese)
    [3]
    Bertin JJ, Cummings RM. Critical hypersonic aerothermodynamic phenomena. Annual Review of Fluid Mechanics, 2006, 38(1): 129-157 doi: 10.1146/annurev.fluid.38.050304.092041
    [4]
    Muntz EP. Rarefied gas dynamics. Annual Review of Fluid Mechanics, 1989, 21(1): 387-422 doi: 10.1146/annurev.fl.21.010189.002131
    [5]
    Chen J, Zhou H. Rarefied gas effect in hypersonic shear flows. Acta Mechanica Sinica, 2021, 37(1): 2-17 doi: 10.1007/s10409-021-01051-9
    [6]
    Jiang W, Qiu H, Yang Y, et al. High frequency ac electric glow discharge visualization technology and application in big diameter hypersonic low-density wind tunnel. Advances in Aerodynamics, 2021, 3(1): 14
    [7]
    刘畅, 徐昆. 离散时空直接建模思想及其在模拟多尺度输运中的应用. 空气动力学学报, 2019, 38(2): 197-216 (Liu Chang, Xu Kun. Direct modeling methodology and its applications in multiscale transport process. Acta Aerodynamica Sinica, 2019, 38(2): 197-216 (in Chinese)
    [8]
    王宏宇, 王辉, 石义雷等. 一种高超声速稀薄流激波干扰气动热测量技术. 宇航学报, 2020, 41(12): 1525-1532 (Wang Hongyu, Wang Hui, Shi Yilei, et al. An aerothermodynamics measuring technique for shock interactions in hypersonic low density flow. Journal of Astronautics, 2020, 41(12): 1525-1532 (in Chinese)
    [9]
    Candler GV. Rate effects in hypersonic flows. Annual Review of Fluid Mechanics, 2019, 51(1): 379-402 doi: 10.1146/annurev-fluid-010518-040258
    [10]
    李志辉, 梁杰, 李中华等. 跨流域空气动力学模拟方法与返回舱再入气动研究. 空气动力学学报, 2018, 36(5): 826-847 (Li Zhihui, Liang Jie, Li Zhonghua, et al. Simulation methods of aerodynamics covering various flow regimes and applications to aerodynamic characteristics of re-entry spacecraft module. Acta Aerodynamica Sinica, 2018, 36(5): 826-847 (in Chinese) doi: 10.7638/kqdlxxb-2018.0121
    [11]
    Coumar S, Lago V. Influence of Mach number and static pressure on plasma flow control of supersonic and rarefied flows around a sharp flat plate. Experiments in Fluids, 2017, 58(6): 74
    [12]
    Wu L, Reese JM, Zhang Y. Solving the Boltzmann equation deterministically by the fast spectral method: application to gas microflows. Journal of Fluid Mechanics, 2014, 746: 53-84 doi: 10.1017/jfm.2014.79
    [13]
    Ivanov MS, Gimelshein SF. Computational hypersonic rarefied flows. Annual Review of Fluid Mechanics, 1998, 30(1): 469-505 doi: 10.1146/annurev.fluid.30.1.469
    [14]
    Oran ES, Oh CK, Cybyk BZ. Direct simulation Monte Carlo: recent advances and applications. Annual Review of Fluid Mechanics, 1998, 30(1): 403-441 doi: 10.1146/annurev.fluid.30.1.403
    [15]
    Anderson JD. Hypersonic and High-Temperature Gas Dynamics, 2nd Edn. Reston: American Institute of Aeronautics and Astronautics, 2006
    [16]
    Kasen S. Thermal management at hypersonic leading edges. [PhD Thesis]. Virginia: University of Virginia, 2013
    [17]
    Schwartz RN, Slawsky ZI, Herzfeld KF. Calculation of vibrational relaxation times in gases. The Journal of Chemical Physics, 1952, 20(10): 1591-1599 doi: 10.1063/1.1700221
    [18]
    Schwartz RN, Herzfeld KF. Vibrational relaxation times in gases (three-dimensional treatment). The Journal of Chemical Physics, 1954, 22(5): 767-773 doi: 10.1063/1.1740190
    [19]
    Shuler KE. Studies in non-equilibrium rate processes. II. The relaxation of vibrational non-equilibrium distributions in chemical reactions and shock waves. The Journal of Physical Chemistry, 1957, 61(7): 849-856
    [20]
    Montroll EW, Shuler KE. Studies in nonequilibrium rate processes. I. The relaxation of a system of harmonic oscillators. The Journal of Chemical Physics, 1957, 26(3): 454-464
    [21]
    Boyd ID, Josyula E. State resolved vibrational relaxation modeling for strongly nonequilibrium flows. Physics of Fluids, 2011, 23(5): 57101 doi: 10.1063/1.3584128
    [22]
    Tong H. Effects of dissociation energy and vibrational relaxation on heat transfer. AIAA Journal, 1966, 4(1): 14-18 doi: 10.2514/3.3377
    [23]
    Mori Y, Himeno N, Hijikata K, et al. Effects of vibrational relaxation of multi-atomic molecules on stagnation heat transfer. International Journal of Heat and Mass Transfer, 1980, 23(12): 1625-1633 doi: 10.1016/0017-9310(80)90221-5
    [24]
    Schubert BS. Vibrational nonequilibrium stagnation shock layers at hypersonic speed and low Reynolds number. International Journal of Heat and Mass Transfer, 1978, 21(8): 1041-1048 doi: 10.1016/0017-9310(78)90102-3
    [25]
    Bird GA. The DSMC Method. CreateSpace Independent Publishing Platform, 2013
    [26]
    Treanor CE, Marrone PV. Effect of dissociation on the rate of vibrational relaxation. The Physics of Fluids, 1962, 5(9): 1022 doi: 10.1063/1.1724467
    [27]
    Marrone PV, Treanor CE. Chemical relaxation with preferential dissociation from excited vibrational levels. The Journal of Chemical Physics, 1963, 6(9): 1215
    [28]
    Heims SP. Moment equations for vibrational relaxation coupled with dissociation. The Journal of Chemical Physics, 1963, 38(3): 603-606 doi: 10.1063/1.1733712
    [29]
    彭傲平, 李志辉, 吴俊林等. 含振动能激发Boltzmann模型方程气体动理论统一算法验证与分析. 物理学报, 2017, 66(20): 204703 (Peng Aoping, Li Zhihui, Wu Junlin, et al. Validation and analysis of gas-kinetic unified algorithm for solving Boltzmann model equation with vibrational energy excitation. Acta Physica Sinica, 2017, 66(20): 204703 (in Chinese) doi: 10.7498/aps.66.204703
    [30]
    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 (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) doi: 10.6052/0459-1879-18-056
    [31]
    Luo J, Wang ZH. Analogy between vibrational and chemical nonequilibrium effects on stagnation flows. AIAA Journal, 2020, 58(5): 2156-2164 doi: 10.2514/1.J059010
    [32]
    Gladwell GML, Meier GEA, Sreenivasan KR, et al. IUTAM Symposium on One Hundred Years of Boundary Layer Research. Solid Mechanics and Its Applications. Dordrecht: Springer Netherlands, 2006
    [33]
    Illingworth CR. Some Solutions of the Equations of Flow of A Viscous Compressible Fluid. Cambridge: Cambridge University Press, 1950
    [34]
    Liepmann HW, Bleviss ZO. The effects of dissociation and ionization on compressible Couete flow. Douglas Aircraft Co. Report, SM-19831, 1956
    [35]
    Liepmann HW, Roshko A. Elements of Gas Dynamics. Mineola New York: Dover Publications Inc, 2001
    [36]
    Morris DL, Hannon L, Garcia AL. Slip length in a dilute gas. Physical Review A, 1992, 46(8): 5279-5281 doi: 10.1103/PhysRevA.46.5279
    [37]
    López-Lemus J, Velasco RM. Slip boundary conditions in Couete flow. Physica A: Statistical Mechanics and its Applications, 1999, 274(3-4): 454-465 doi: 10.1016/S0378-4371(99)00270-8
    [38]
    Gallis MA, Torczynski JR, Rader DJ, et al. Normal solutions of the Boltzmann equation for highly nonequilibrium Fourier flow and Couete flow. Physics of Fluids, 2006, 18(1): 17104 doi: 10.1063/1.2166449
    [39]
    Abramov AA, Butkovskii AV. The extended Reynolds analogy for the Couete problem: similarity parameters. International Journal of Heat and Mass Transfer, 2018, 117: 313-318 doi: 10.1016/j.ijheatmasstransfer.2017.10.011
    [40]
    Sarma GSR. Some parameter studies on hypersonic Couete flow. International Journal of Modern Physics C, 1994, 5(2): 237-239 doi: 10.1142/S0129183194000234
    [41]
    Rubesin MW, Johnson HA. A critical review of skin-friction and heat-transfer solutions of the laminar boundary layer of a flat plate. Transactions of the ASME, 1949, 71(4): 383-388
    [42]
    Dorrance WH. Viscous Hypersonic Flow: Theory of Reacting and Hypersonic Boundary Layers. Mineola New York: Dover Publications Inc, 2017
    [43]
    Eckert ERG. Engineering relations for heat transfer and friction in high-velocity laminar and turbulent boundary-layer flow over surfaces with constant pressure and temperature. Transactions of the ASME, 1956, 78(6): 1273-1283
    [44]
    Young GBW, Janssen E. The compressible boundary layer. Journal of the Aeronautical Sciences, 1952, 19(4): 229-236 doi: 10.2514/8.2236
    [45]
    Reynolds O. On the extent and action of the heating surface of steam boilers. Proceedings of the Manchester Literary and Philosophical Society, 1874, 14: 7-12
    [46]
    Van Driest ER. Investigation of laminar boundary layer in compressive fluids using the crocco method. NACA Technical Note 2597, 1952
    [47]
    Cohen NB. Correlation formulas and tables of density and some transport properties of equilibrium dissociating air for use in solutions of the boundary-layer equations. NASA Technical Note D-194, 1960
    [48]
    Debrestian DJ, Anderson JD. Reference temperature method and reynolds analogy for chemically reacting nonequilibrium flowfields. Journal of Thermophysics and Heat Transfer, 1994, 8(1): 190-192 doi: 10.2514/3.522
    [49]
    Ott JD, Anderson JD. Effects of nonequilibrium chemistry on the reference temperature method and Reynolds analogy. Journal of Thermophysics and Heat Transfer, 1994, 8(2): 381-384 doi: 10.2514/3.553
    [50]
    Uribe FJ, Mason EA, Kestin J. Thermal conductivity of nine polyatomic gases at low density. Journal of Physical and Chemical Reference Data, 1990, 19(5): 1123-1136 doi: 10.1063/1.555864
    [51]
    Bergman TL, Incropera FP. Fundamentals of Heat and Mass Transfer, 7th Edn. Hoboken NJ: Wiley, 2011
    [52]
    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 doi: 10.2514/1.J053168
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