Journal of Aerospace System Engineering (항공우주시스템공학회지)

The Society for Aerospace System Engineering (항공우주시스템공학회)
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Partially Implicit Chebyshev Pseudo-spectral Method for a Periodic Unsteady Flow Analysis

부분 내재적 체비셰브 스펙트럴 기법을 이용한 주기적인 비정상 유동 해석

  • Im, Dong Kyun (Department of Aeronautical Maintenance and Mechanical Engineering, Cheongju University)
  • 임동균 (청주대학교 항공기계공학과)
  • Received : 2020.02.05
  • Accepted : 2020.04.10
  • Published : 2020.06.30
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Abstract

In this paper, the efficient periodic unsteady flow analysis is developed by using a Chebyshev collocation operator applied to the time differential term of the governing equations. The partial implicit time integration method was also applied in the governing equation for a fluid, which means flux terms were implicitly processed for a time integration and the time derivative terms were applied explicitly in the form of the source term by applying the Chebyshev collocation operator. To verify this method, we applied the 1D unsteady Burgers equation and the 2D oscillating airfoil. The results were compared with the existing unsteady flow frequency analysis technique, the Harmonic Balance Method, and the experimental data. The Chebyshev collocation operator can manage time derivatives for periodic and non-periodic problems, so it can be applied to non-periodic problems later.

본 연구는 Chebyshev collocation operator를 지배 방정식의 시간 미분항에 적용하여 비정상 유동해석을 해석할 수 있는 기법을 개발한 논문이다. 시간적분으로 유속항은 내재적으로 처리하였으며 시간 미분항은 Chebyshev collocation operator을 적용하여 원천항 형태로 외재적으로 처리하여 부분 내재적 시간적분법을 적용하였다. 본 연구의 방법을 검증하기 위해 1차원 비정상 burgers 방정식과 2차원 진동하는 airfoil에 적용하였으며 기존의 비정상 유동 주파수 해석기법과 시험 결과를 비교하여 나타내었다. Chebyshev collocation operator는 주기적인 문제와 비주기적인 문제에 대해서 시간 미분항을 처리할 수 있으므로 추후 비주기적인 문제에 적용할 예정이다.

Keywords

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