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Numerical Study on the Effect of Non-Equilibrium Condensation on Drag Divergence Mach Number in a Transonic Moist Air Flow

천음속 익형 유동에서 비평형 응축이 Drag Divergence Mach Number에 미치는 영향에 관한 수치 해석적 연구

  • Choi, Seung Min (Institute of Green Car Parts, GyeongBuk Technopark) ;
  • Kang, Hui Bo (School of Mechanical Engineering, Kyungpook Nat'l Univ.) ;
  • Kwon, Young Doo (School of Mechanical Engineering, Kyungpook Nat'l Univ.) ;
  • Kwon, Soon Bum (School of Mechanical Engineering, Kyungpook Nat'l Univ.)
  • 최승민 (경북테크노파크 그린카부품기술연구소) ;
  • 강희보 (경북대학교 기계공학부) ;
  • 권영두 (경북대학교 기계공학부) ;
  • 권순범 (경북대학교 기계공학부)
  • Received : 2016.07.05
  • Accepted : 2016.09.01
  • Published : 2016.12.01

Abstract

In the present study, the effects of non-equilibrium condensation on the drag divergence Mach number with the angle of attack in a transonic 2D moist air flow of NACA0012 are investigated using the TVD finite difference scheme. For the same ${\alpha}$, the maximum upstream Mach number of the shock wave, Mmax, and the size of supersonic bubble decrease with the increase in ${\Phi}_0$. For the same $M_{\infty}$, ${\Phi}_0$, and $T_0$, the length of the non-equilibrium condensation zone ${\Delta}_z$ decreases with increasing ${\Phi}_0$. On the other hand, because of the attenuating effect of non-equilibrium condensation on wave drag, which is related to the interaction between the shock wave and the boundary layer, the drag coefficient $C_D$ decreases with an increase in ${\Phi}_0$ for the same $M_{\infty}$ and ${\alpha}$. For the same ${\alpha}$, $M_D$ increases with increasing ${\Phi}_0$, while $M_D$ decreases with an increase in ${\alpha}$.

본 연구에서는 NACA0012 천음속 익형 유동에 있어 비평형 응축이 항력 발산 마하수 $M_D$에 미치는 영향을 TVD 유한 차분법을 사용하여 연구하였다. 받음각 ${\alpha}$가 동일한 경우, 정체점 상대습도 ${\phi}_0$가 높을수록 충격파 직전의 최대 마하수 $M_{max}$는 작게 되고 초음속 영역의 크기도 적게 된다. 주류 마하수 $M_{\infty}$, 정체점 상대습도 ${\phi}_0$ 및 정체온도 $T_0$가 동일한 경우 받음각 ${\alpha}$가 클수록 비평형 응축영역 길이 ${\Delta}_z$은 짧게 된다. 한편, 주류 마하수 $M_{\infty}$와 받음각 ${\alpha}$가 동일한 경우 정체점 상대습도 ${\phi}_0$가 높을수록 조파저항의 감소 때문에 항력계수 $C_D$는 적어진다. $M_D$${\alpha}$가 동일한 경우 ${\phi}_0$가 클수록 크게 되며, ${\phi}_0$가 동일한 경우는 ${\alpha}$가 클수록 $M_D$는 적게 된다.

Keywords

References

  1. Schnerr, G. and Adam, S., 1995, "Unsteady Shock Formation in Transonic Flow with Nonequilibrium Phase Transition," Proc. of the 20th Int. Symposium on Shock Waves, Vol. II, pp. 1225-1230.
  2. Kim, I. W., Alam, M. M. A., Lee, S. J., Kwon, Y. D. and Kwon, S. B., 2012, "The Effect of Nonequilibrium Condensation on the Drag Coefficient in a Transonic Airfoil Flow," J. of Thermal Sci. Vol. 21, No. 6, pp. 518-524. https://doi.org/10.1007/s11630-012-0576-8
  3. Kwon, S. B. and Ahn, H. J., 2001, "Supersonic Moist Air Flow with Condensation in a Wavy Wall Channel," KSME Int. J., Vol. 15, No. 4, pp. 492-499. https://doi.org/10.1007/BF03185110
  4. Kim, J. S., Lee, S. J., Alam, M. M. A and Kwon, S. B., 2012, "Effect of Nonequilibrium Condensation on the Oscillation of the Terminating Shock in a Transonic Airfoil Flow," Trans. Korean Soc. Mech. Eng. B, Vol. 36, No 1, pp. 61-66. https://doi.org/10.3795/KSME-B.2012.36.1.061
  5. Jeon, H. K., Choi, S. M., Kwon, Y. D. and Kwon, S. B., 2015, "Effect of Nonequilibrium Condensation on Lift Divergence Mach Number at Transonic Speeds," JMST, Vol. 29, No. 7, pp. 2883-2888.
  6. Choi, S. M., Kim, J. S., Kwon, Y. D. and Kwon, S. B., 2013, "The Effect of Nonequilibrium 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.
  7. Wegener, P. P., "Gas Dynamics of Expansion Flows with Condensation and Homogeneous Nucleation of Water Vapor," Acta Mechanica, 21, pp. 165-213.
  8. Baek, S. C., Kwon, S. B. and Kim, H. D., 2004, "Passive Prandtl-Meyer Expansion Flow with Homogeneous Condensation," KSME, Int. J. Vol. 18, No. 3, pp. 407-418. https://doi.org/10.1007/BF02996106
  9. 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, 23, pp. 1736-1742.
  10. Jeon, H. K., Kim, I. W., Kwon, Y. D. and Kwon, S. B., 2014, "A Numerical Study of the Effect of Nonequilibrium Condensation on the Oscillation of the Shock Waves in a Transonic Airfoil Flow," Trans. Korean Soc. Mech. Eng. B. Vol. 38, No. 3, pp. 219-225. https://doi.org/10.3795/KSME-B.2014.38.3.219
  11. Shapiro, A. H., 1953, "The Dynamics and Thermodynamics of Compressible Fluid Flow," Ronald Press Co. New York, Vol. 1, p. 384.
  12. Tanaka M., 2006, "Study on the Effect of Non-equilibrium Heterogeneous Condensation in High-speed Internal Flow Field," Saga University, Ph. D. Thesis.
  13. Schnerr, G., 1986, "Homogene Kondensation in Stationaren Transsonischen Stromungen durch Lavaldusen und um Profile," von der Facultat fur Maschinenbau der Uni. Karlsruhe im ss 1986 Genehmigte Habilitationsschrift.
  14. Orinai, R. A. and Sundquist, B. E., 1962, "Emendation to Nucleation Theory and the Homogeneous Nucleation of Water from Vapor," J. Chem. Phys. Vol. 38, pp. 2082-2089.
  15. Dohrmann, U., 1989, "Ein Numerisches Verfahren zur Berechnung Statianarer Transonischer Stromungen mit Energiezufuhr durch Homogene Kondensation," Uni. Karlsruhe, Dr. of Eng. Dissertation, p. 19.
  16. Pai, S. I. and Luo, S., 1991, "Theoretical and Computational Dynamics of a Compressible Flow," Sci. press, Beijing, p. 299.