Volume 29 Issue 12
Dec.  2014
Turn off MathJax
Article Contents
Article Navigation >  Journal of Aerospace Power  > 2014  >  29(12): 2785-2794
ZHAO Guo-chang, DU Xia, SONG Li-ping, KONG Jing-ru. Similarity solutions and approximation solutions of velocity and temperature in laminar boundary layer of subsonic and supersonic wedge flows[J]. Journal of Aerospace Power, 2014, 29(12): 2785-2794. doi: 10.13224/j.cnki.jasp.2014.12.001
Citation: ZHAO Guo-chang, DU Xia, SONG Li-ping, KONG Jing-ru. Similarity solutions and approximation solutions of velocity and temperature in laminar boundary layer of subsonic and supersonic wedge flows[J]. Journal of Aerospace Power, 2014, 29(12): 2785-2794. doi: 10.13224/j.cnki.jasp.2014.12.001
shu

Similarity solutions and approximation solutions of velocity and temperature in laminar boundary layer of subsonic and supersonic wedge flows

doi: 10.13224/j.cnki.jasp.2014.12.001

  • 1. Liaoning Key Laboratory of Advanced Measurement and Test Technology for Aviation Propulsion System, Faculty of Aerospace Engineering, Shenyang Aerospace University, Shenyang 110136, China;

  • 2. Faculty of Aerospace Engineering, Shenyang Aerospace University, Shenyang 110136, China;

  • 3. Institute of High Education, Shenyang Aerospace University, Shenyang 110136, China

  • Received Date: 2014-05-25
  • Publish Date: 2014-12-28
    Abstract
  • The variations in the dimensionless velocity due to changes in similarity variables of wedge flows with different wedge angles were obtained using the Runge-Kutta method by solving the third-order nonlinear ordinary differential equation of the dimensionless stream function that was obtained through similarity transformation, which described the wedge flow in the laminar boundary layer. The second-order linear homogeneous differential equation of dimensionless temperature based on the similarity variable in the laminar boundary layer of the subsonic wedge flow and the second-order linear non-homogeneous differential equation of dimensionless temperature on the similarity variable in the laminar boundary layer of the supersonic wedge flow were derived. The general temperature distribution solutions in the laminar boundary layers of subsonic and supersonic wedge flow, the similarity solutions and exponential form approximation solutions of dimensionless temperature in the laminar boundary layers under the condition of constant wall temperature for subsonic wedge flow and the condition of adiabatic wall for supersonic wedge flow were obtained by solving the above two differential equations. The effects of compressibility and viscosity of the supersonic gas in the laminar boundary layer on velocity and temperature were investigated using the wedge flow of wedge angle of 0 as a representative example. It is shown that the maximum absolute value of relative errors between the similarity solution obtained under the condition of incompressible and constant properties and the similarity solution obtained under the condition of compressible and variable properties is less than 9.8%. Results show that: the larger the Pr of the wedge flow, the more dramatic the change in dimensionless temperature in the area close to the wall; the viscous dissipation causes the temperature of the wedge flow from the wall to the main flow in the boundary layer to first increase and then decrease under supersonic flow conditions and with temperatures lower than the adiabatic wall temperature.

     

    • FullText(HTML)
  • loading
    • References(22)
  • [1]
    赵以强,刘世英,邓立君.高超声速楔形体前缘优化[J].内燃机与动力装置,2013,30(2):36-39. ZHAO Yiqiang,LIU Shiying,DENG Lijun.Optimization of power law leading edges in hypersonic flow[J].Internal Combustion Engine and Power Plant, 2013,30(2):36-39.(in Chinese)
    [2]
    杨鹏飞,方洋旺,黄春蓉,等.高超声速楔形模型飞行流场数值模拟[J].飞行力学,2013,31(2):113-117. YANG Pengfei,FANG Yangwang,HUANG Chunrong,et al.Numerical simulation of hypersonic flow fields around wedge model[J].Flight Dynamics, 2013, 31(2):113-117.(in Chinese)
    [3]
    Santos F N W,Lewis J M.Aerodynamic heating performance of power law leading edges in rarefied hypersonic flow[C]//Proceedings of 36th AIAA Thermophysics Conference.Orlando,US:AIAA,2003:1-11.
    [4]
    Lovett A J,Brogan P T,Philippona S D,et al.Development needs for advanced afterburner designs[R].Fort Lauderdale,US:40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference,2004.
    [5]
    王燕,郝英立.机翼表面结冰数值模拟[J].东南大学学报:自然科学版,2009,139(5):956-960. WANG Yan,HAO Yingli.Numerical simulation of ice accretion on airfoil[J].Journal of Southeast University:Natural Science Edition,2009,139(5):956-960.(in Chinese)
    [6]
    Dufour E,Bouchez M.Computational analysis of a kero-sene-fueled scramjet[R].Kyoto,Japan:AIAA/NAL-NASDA-ISAS 10th International Space Planes and Hyper-sonic Systems and Technologies Conference,2001.
    [7]
    Kodera M,Sunami T,Nakahashi K,et al.Numerical study of mixing and combustion process of a scramjet engine model[R].Kyoto,Japan:AIAA/NAL-NASDA-ISAS 10th In-ternational Space Planes and Hypersonic Systems and Technologies Conference,2001.
    [8]
    孙冰,郑力铭.超燃冲压发动机支板热环境及热防护方案[J].航空动力学报,2006,21(2):336-341. SUN Bing,ZHENG Liming.Research of scramjet strut thermal environment and thermal protection scheme[J].Journal of Aerospace Power,2006,21(2):336-341.(in Chinese)
    [9]
    宋冈霖,田亮,冮强,等.超燃冲压发动机支板热性能研究[J].推进技术,2006,21(2):809-816. SONG Ganglin,TIAN Liang,JIANG Qiang,et al.A study for scramjet strut thermal performance[J].Journal of Propulsion Technology,2006,21(2):809-816.(in Chinese)
    [10]
    杨强生,蒲保荣.高等传热学[M].上海:上海交通大学出版社,1996.
    [11]
    凯斯·W M,克拉福特·M E.对流传热与传质[M].陈熙,翟殿春,译.北京:科学出版社,1986.
    [12]
    Goldstein R J,Howarth L.Modern development in fluid dynamics:high speed flow[M].Qxford:Clarendon Press,1953.
    [13]
    孙雁,钟万勰.二维边界层方程的迭代求解[J].计算力学学报,2010,27(3):385-390. SUN Yan,ZHONG Wanxie.Iterative solution for two-dimensional boundary layer equations[J].Chinese Journal of Computational Mechanics,2010,27(3):385-390.(in Chinese)
    [14]
    郑连存,温安国,张欣欣.Falkner-Skan方程的近似解析解[J].计算力学学报,2008,25(4):506-510. ZHENG Liancun,WEN Anguo,ZHANG Xinxin.Approximate analytical solution for Falkner-Skan equation[J].Chinese Journal of Computational Mechanics,2008,25 (4):506-510.(in Chinese)
    [15]
    施梨,张世杰,叶松.大椭圆星载轨道预报系统设计[J].航天控制,2010,28(6):43-48. SHI Li,ZHANG Shijie,YE Song.The onboard orbit propagation system design of large elliptical orbit[J].Aerospace Control,2010,28(6):43-48.(in Chinese)
    [16]
    Eckert E R G,Drake R M Jr.Analysis of heat and mass transfer[M].New York:McGraw Hill,1972.
    [17]
    章梓雄,董曾南.黏性流体力学[M].北京:清华大学出版社,2011.
    [18]
    张靖周.高等传热学[M].北京:科学出版社,2009.
    [19]
    杨强生.对流传热与传质[M].北京:高等教育出版社,1985.
    [20]
    王补宣.工程传热传质学[M].北京:科学出版社,1998.
    [21]
    Toro P G P,Rusak Z,Nagamatsu H T,et al.Self-similar compressible laminar boundary layers[R].AIAA 97-0767,1997.
    [22]
    何霖.超声速边界层及激波与边界层相互作用的实验研究[D].长沙:国防科学技术大学,2011. HE Lin.Experimental investigation of supersonic boundary layer and shock wave/boundary layer interaction[D].Changsha:National University of Defense Technology,2011.(in Chinese)
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Get Citation
    PDF(1166.0KB)
    XML

    Article Metrics

    Article views (1762) PDF downloads(1450) Cited by()
    Proportional views
    Related

    Copyright © 《Journal of Aerospace Power》 All Rights Reserved.

    Supported by: Beijing Renhe Information Technology Co., Ltd.  

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return