Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

A Numerical Study of the Effect of Non-equilibrium Condensation on the Oscillation of Shock Wave in a Transonic Airfoil Flow

비평형 응축이 충격파 진동에 미치는 영향에 관한 수치 해석적 연구

  • Jeon, Heung Kyun (Fire Safety Management Dept., Daegu Health College) ;
  • Kim, In Won (Dept. of Mechanical Engineering, Kyungpook Nat'l Univ.) ;
  • Kwon, Young Doo (Dept. of Mechanical Engineering, Kyungpook Nat'l Univ.) ;
  • Kwon, Soon Bum (Dept. of Mechanical Engineering, Kyungpook Nat'l Univ.)
  • Received : 2013.10.23
  • Accepted : 2014.01.27
  • Published : 2014.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this study, to find the characteristics of the oscillation of a terminating shock wave in a transonic airfoil flow with non-equilibrium condensation, a NACA00-12,14,15 airfoil flow with non-equilibrium condensation is investigated through numerical analysis of TVD scheme. Transonic free stream Mach number of 0.81-0.90 with the variation of stagnation relative humidity and airfoil thickness is tested. For the free stream Mach number 0.87 and attack angle of ${\alpha}=0^{\circ}$, the increase in stagnation relative humidity attenuates the strength of the terminating shock wave and inactivates the oscillation of the terminating shock wave. For the case of $M_{\infty}=0.87$ and ${\phi}_0=60%$, the decreasing rate in the frequency of the shock oscillation caused by non-equilibrium condensation to that of ${\phi}_0=30%$ amounts to 5%. Also, as the stagnation relative humidity gets larger, the maximum coefficient of drag and the difference between the maximum and minimum in $C_D$ become smaller. On the other hand, as the thickness of the airfoil gets larger, the supersonic bubble size becomes bigger and the oscillation of the shock wave becomes higher.

본 연구에서는 NACA0012/14/15 천음속 에어포일 유동에서 비평형 응축이 충격파 진동에 미치는 영향을 TVD 수치해석을 통하여 연구하였다. 주류 마하수 0.81-0.90에 대해, 정체점 상대습도 및 에어포일의 기하학적 형상이 유동 특성에 미치는 영향이 구명되었다. 받음각 ${\alpha}=0^{\circ}$, 정체점 온도(288K) 및 주류 마하수가 0.87인 경우, 정체점 상대습도의 증가는 Terminating Shock의 충격파 강도를 약화시킨다. 정체점 상대습도가 30%인 경우 961Hz이던 충격파의 진동수가 60%일 때는 912Hz로 약 5% 감소한다. 정체점 상대습도가 동일한 경우는 주류 마하수가 클수록 충격파의 진동수 및 이동거리는 크게 된다. 또, 진동의 한 주기에 대해 항력계수의 변화도 구명되었다. 정체점 상대습도가 높을수록 최대 항력 계수는 작고, 항력계수의 변화폭 또한 감소한다. 한편 에어포일의 최대 두께가 두꺼울수록 초음속 영역의 크기는 증가하며 충격파의 진동수 및 이동거리도 증가한다.

Keywords

Acknowledgement

Supported by : 한국연구재단

References

  1. Wegener P. P., 1975, "Gas Dynamics of Expansion Flows with Condensation, and Homo geneous Nucleation of Water Vapor," Acta Mechanica, 21, pp. 165-213. https://doi.org/10.1007/BF01172836
  2. Kwon, S. B., Lee, S. J., Shin, S. Y. and Kim, S. H., 2009, "A Study on the Flow with Nonequilibrium Condensation in a Minimum Length Nozzle," JMST, Vol. 23, No. 6, pp. 1736-1742. https://doi.org/10.1007/s12206-009-0421-5
  3. Weitao, H., Weiyang, Q. and Hualing, L., 2001, "Shock-wave/Boundary-layer Interaction in a Transonic Turbine Cascade," Proc. IMechE Part G: J. Aerosp. Eng., Vol. 225 No. 1, pp. 77-85
  4. Cagliostro, D. J., 1972, "Periodic Compressible Nozzle Flow Caused by Heat Addition due to Condensation," Ph.D. Thesis, Yale Univ.
  5. Yee H. C., 1989 "A Class of High Resolution Explicit and Implicit Shock-capturing Methods," NASA, TM-89464.
  6. Lothe, J. and Pound, G. M., 1968, "Condensation of Clusters in Nucleation and the Classical Phase Integral," J. Chemi. Phys., Vol. 48, No. 4, pp. 466-477.
  7. Schnerr, G. H. and Dohrmann, U., 1990, "Transonic Flow Around Airfoils with Relaxation and Energy Supply by Homogeneous Condensation," AIAA J., Vol. 28, No. 7, pp. 1187-1193. https://doi.org/10.2514/3.25190
  8. Frenkel, J., 1946, "Kinetic Theory of Liquids," Dover Publications INC., NewYork, p. 415
  9. Mills, A. F. and Seban, R. A., 1967, "The Condensation Coefficient of Water," Int. J. Heat and Mass Transfer, Vol. 10, pp. 1815-1827. https://doi.org/10.1016/0017-9310(67)90052-X
  10. Orinai, R. A. and Sundquist, B. E., 1963, "Emendation to Nucleation Theory and the Homogeneous Nucleation of Water from Vapour," J. Chem. Phys. Vol. 38, pp. 2082-2089. https://doi.org/10.1063/1.1733936
  11. Baldwin, B. S. and Lomax, H., 1978, "Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows," AIAA J., pp. 78-257.
  12. Dohrmann, U., 1989, "Ein Numerisches Verfahren zur Berechnung Statianarer Transonischer Stromungen mit Energiezufuhr Durch Homogene Kondensation," Uni. Karlsruhe, Dr. of Eng. Dissertation, p. 19.
  13. Kim, I. W., Alam, M. M. A., Lee, S. J., Kwon, Y. D. and Kwon, S. B., 2012, "The Effect of Non-equilibrium Condensation on the Drag Coefficient in a Transonic Airfoil Flow," Journal of Thermal Science, Vol. 21, No. 6, pp. 518-524. https://doi.org/10.1007/s11630-012-0576-8
  14. Choi, S. M., Kim, J. S., Kwon, Y. D. and Kwon, S. B., 2013, "The Effect of Non-equilibrium Condensation on the Coefficients of Force with the Angle of Attack in the Transonic Airfoil Flow of NACA0012," JMST, Vol. 27, No. 6, pp. 1671-1676. https://doi.org/10.1007/s12206-013-0415-1
  15. Pai, S. I. and Luo, S., Theoretical and Computational Dynamics of a Compressible Flow, Sci. Press, Beijing, p. 299.
  16. Shapiro A. H., The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. 1," The Ronald Press, New York, p. 379.
  17. Shapiro, A. H., The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. 2," The Ronald Press Co., NewYork, p. 866.