한국항공우주학회지 (Journal of the Korean Society for Aeronautical & Space Sciences)

  • 제49권6호
  • /
  • Pages.449-456
  • /
  • 2021
  • /
  • 1225-1348(pISSN)
  • /
  • 2287-6871(eISSN)
한국항공우주학회 (The Korean Society for Aeronautical and Space Sciences)
권호 표지
DOI QR코드

DOI QR Code

비압축성 유동 해석을 위한 압축성 유동 해석자 확장

Extension of Compressible Flow Solver to Incompressible Flow Analysis

  • Kim, Donguk (Department of Aerospace Engineering, Inha university) ;
  • Kim, Minsoo (Department of Aerospace Engineering, Inha university) ;
  • Lee, Seungsoo (Department of Aerospace Engineering, Inha university)
  • 투고 : 2020.12.08
  • 심사 : 2021.04.05
  • 발행 : 2021.06.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 연구에서는 저마하수 예조건화 기법이 적용된 기존 압축성 해석자의 해석 범위를 최소한의 수정으로 비압축성 유동해석이 가능하도록 확장하는 전략을 제시하였다. 이를 위해 압축성 총 에너지 방정식과 동일한 형태의 에너지 방정식을 사용하였다. 이러한 에너지 방정식은 비압축성 지배방정식인 연속방정식, 열에너지 방정식과 역학적 에너지방정식의 선형 조합을 통해 얻어진다. 이렇듯 압축성 방정식과 동일한 형태를 갖는 비압축성 지배방정식에 시간 전진 기법을 적용하기 위해 Turkel의 가상 압축성 기법을 적용하였다. 또한 Roe 평균이 공통의 압축성/비압축성 지배방정식에서 모두 유효함을 보였다. 압축성 해석자에 위 내용을 적용하여 비압축성 해석이 가능하도록 확장하는 과정은 본래의 압축성 해석자를 이용한 압축성 해석에 아무런 영향이 없다. 확장된 해석자를 통한 비압축성 해석 검증을 위해 비점성, 층류 그리고 난류 유동에 대한 순차적 해석을 수행하였다.

In this paper, we present a strategy to extend solution capability of an existing low Mach number preconditioned compressible solver to incompressible flows with a little modification. To this end, the energy equation that is of the same form of the total energy equation of compressible flows is used. The energy equation is obtained by a linear combination of the thermal energy equation, the continuity equation and the mechanical energy equation. Subsequently, a modified artificial compressibility method in conjunction with a time marching technique is applied to these incompressible governing equations for steady flow solutions. It is found that the Roe average of the common governing equations is equally valid for both the compressible and incompressible flow conditions. The extension of an existing compressible solver to incompressible flows does not affect the original compressible flow analysis. Validity for incompressible flow analysis of the extended solver is examined for various inviscid, laminar and turbulent flows.

키워드

참고문헌

  1. Langtangen, H. P., Mardal, K. A. and Winther, R., "Numerical methods for incompressible viscous flow," Advances in water Resources, Vol. 25, 2002, pp. 1125~1146. https://doi.org/10.1016/S0309-1708(02)00052-0
  2. Chorin, A. J., "A numerical method for solving incompressible viscous flow problems," Journal of computational physics, Vol. 135, No. 2, 1997, pp. 118~125. https://doi.org/10.1006/jcph.1997.5716
  3. Steger, J. L. and Kutler, P., "Implicit finite-difference procedures for the computation of vortex wakes," AIAA Journal, Vol. 15, No. 4, 1977, pp. 581~590. https://doi.org/10.2514/3.60663
  4. Chang, J. and Kwak, D., "On the method of pseudo compressibility for numerically solving incompressible flows," In 22nd Aerospace Meeting, 1984, p. 252.
  5. Choi, D. and Merkle, C. L., "Application of time-iterative schemes to incompressible flow," AIAA Journal, Vol. 23, No. 10, 1985, pp. 1518~1524. https://doi.org/10.2514/3.9119
  6. Lee, H. R., Kwak, E. K. and Lee, S., "Investigation on Characteristics of Modified Artificial Compressibility Method," Proceeding of The Korean Society for Aeronautical and Space Sciences Fall Conference, November 2010, pp.39~43.
  7. Merkle, C., "Time-accurate unsteady incompressible flow algorithms based on artificial compressibility," In 8th Computational Fluid Dynamics Conference, 1987, p. 1137.
  8. Soh, W. Y. and Goodrich, J. W., "Unsteady solution of incompressible Navier-Stokes equations," Journal of computational physics, Vol. 79. No. 1, 1988, pp. 113~134. https://doi.org/10.1016/0021-9991(88)90007-1
  9. Lee, H. R., Yoo, I. Y., Kwak, E. K. and Lee, S., "Numerical Simulations of Two Dimensional Incompressible Flows Using Artificial Compressibility Method," Korean Journal of Computational Fluids Engineering, 2010, pp. 389~396.
  10. Volpe, G., "On the use and the accuracy of compressible flow codes at low Mach numbers," 22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference, 1991, pp. 1662.
  11. Venkateswaran, S., and Merkle, L., "Analysis of preconditioning methods for the Euler and Navier-Stokes equations," Lecture series-van Kareman Institute for fluid dynamics, Vol. 3, 1999, pp. B1~B155.
  12. Turkel, Eli., "Preconditioned methods for solving the incompressible and low speed compressible equations," Journal of computational physics, Vol. 72, No. 2, 1987, pp. 277~298. https://doi.org/10.1016/0021-9991(87)90084-2
  13. Roe, P. L., "Approximate Riemann solvers, parameter vectors, and difference schemes," Journal of computational physics, Vol. 43, No. 2, 1981, pp. 357~372. https://doi.org/10.1016/0021-9991(81)90128-5
  14. Panton, R. L., Incompressible flow, John Wiley & Sons, 2013.
  15. Michelassi, V., Migliorini, F. and Martelli, F., "Preconditioned scalar approximate factorization method for incompressible fluid flows," International Journal of Computational Fluid Dynamics, Vol. 7, No. 4, 1996, pp. 311~325. https://doi.org/10.1080/10618569608940768
  16. Kiris, C., Housman, J. and Kwak, D., "Comparison of artificial compressibility methods," Computational Fluid Dynamics, 2004, pp. 475~480.
  17. Turkel, E., "Review of preconditioning methods for fluid dynamics," Applied Numerical Mathematics, Vol. 12, No. 1-3, pp. 257~284. https://doi.org/10.1016/0168-9274(93)90122-8
  18. Choi, Y. H. and Merkle, C. L., "The application of preconditioning in viscous flows," Journal of computational physics, Vol. 105, No. 2, 1993, pp. 207~223. https://doi.org/10.1006/jcph.1993.1069
  19. Weiss, J. M. and Smith, W. A., "Preconditioning applied to variable and constant density flows," AIAA Journal, Vol. 33, No. 11, 1995, pp. 2050~2057. https://doi.org/10.2514/3.12946
  20. Lee, H. and Lee, S., "Convergence characteristics of upwind method for modified artificial compressibility method," International Journal of Aeronautical and Space Sciences, Vol. 12, No. 4, 2011, pp. 318~330. https://doi.org/10.5139/IJASS.2011.12.4.318
  21. Lee, S. and Whan Choi, D., "On coupling the Reynolds averaged Navier-Stokes equations with two equation turbulence model equations," International Journal for Numerical Methods in Fluids, Vol. 50, No. 2, 2006, pp. 165~197. https://doi.org/10.1002/fld.1049
  22. Dennis, S. C. R. and Chang, G. Z., "Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100," Journal of Fluid Mechanics, Vol. 42, No. 3, 1970, pp. 471~489. https://doi.org/10.1017/S0022112070001428
  23. Kawaguti, M., "Numerical solution of the Navier-Stokes equations for the flow around a circular cylinder at Reynolds number 40," Journal of the Physical Society of Japan, Vol. 8, No. 6, 1953, pp. 747~757. https://doi.org/10.1143/JPSJ.8.747
  24. Takami, H. and Keller, H. B., "Steady two dimensional viscous flow of an incompressible fluid past a circular cylinder," The Physics of Fluids, Vol. 12, No. 12, 1969, pp. II~51.