한국수자원학회논문집 (Journal of Korea Water Resources Association)

  • 제53권1호
  • /
  • Pages.1-13
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  • 2020
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  • 2799-8746(pISSN)
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  • 2799-8754(eISSN)
한국수자원학회 (Korea Water Resources Association)
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난류 흐름의 RANS 수치모의를 위한 벽함수 성능 평가

An evaluation of wall functions for RANS computation of turbulent flows

  • 유동근 (강릉원주대학교 토목공학과) ;
  • 백중철 (강릉원주대학교 토목공학과)
  • Yoo, Donggeun (Department of Civil Engineering, Gangneung-Wonju National University) ;
  • Paik, Joongcheol (Department of Civil Engineering, Gangneung-Wonju National University)
  • 투고 : 2019.07.18
  • 심사 : 2019.11.20
  • 발행 : 2020.01.31
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초록

높은 레이놀즈수를 갖는 공학적인 흐름을 예측하는 가장 일반적인 방법은 여전히 벽함수를 이용하는 난류모형에 근거한 RANS 수치모의이다. 최근 벽근처의 점성영역 관계식과 벽에서 떨어진 대수영역 관계식을 혼합하여 개발된 일반화된 벽함수들은 두 영역사이의 난류량과 유속이 부드럽게 천이하도록 한다. 이 연구는 난류운동에너지(TKE), 에너지 소산율, 비소산율, 와점성에 대해서 적용 가능한 벽함수들을 조합하여 일련을 수치 모의를 수행하여 널리 이용되고 있는 난류모형들의 성능과 수렴 특성을 분석하였다. 이 연구 결과는 RNG k-𝜖 모형의 경우 첫번째 계산격자가 완충층에 놓이게 될 때는 반복 계산시 작은 허용오차를 이용하여 주의 깊게 적용을 하여야 안정된 해를 구할 수 있음을 보여준다. 표준 k-𝜖과 RNG k-𝜖 모형은 TKE와 와점성에 대해서 적용 가능한 벽함수들 중 어느 것을 선택하여 적용하더라도 수치모의 결과가 민감하게 반응하지 않는 것으로 나타났다. 한편, k-ω SST 모형의 경우 TKE에 대해서는 kL-벽함수 그리고 와점성에 대해서는 nutUB-벽함수를 이용하여야 정확하고 안정된 경계 조건 설정을 보장할 수 있다. 레이놀즈수 155,000조건에서 적용한 후방계산흐름 수치모의 결과 격자 해상도에 상관없이 약 13% 정도 재부착 거리를 과소평가하는 모형을 제외하고 나머지 적용한 난류모형들 모두 적절히 세밀한 해상도의 격자에서 양호하게 재부착거리를 잘 예측하는 것으로 나타났다.

The most common approach for computing engineering flow problems at high Reynolds number is still the Reynolds-averaged Navier-Stokes (RANS) computations based on turbulence models with wall functions. The recently developed generalized wall functions blending between the wall-limiting viscous and the outer logarithmic relations ensure a smooth transition of flow quantities across two regions. The performances and convergence properties of widely used turbulence models with wall functions that are applicable for turbulence kinetic energy (TKE), turbulent and specific dissipation rates, and eddy viscosity are presented through a series of near wall flow simulations. The present results show that RNG k-𝜖 model should be carefully applied with small tolerance to get the stable solution when the first grid lies in the buffer layer. The standard k-𝜖 and RNG k-𝜖 models are not sensitive to the selection of wall functions for both TKE and eddy viscosity, while the k-ω SST model should be applied together with kL-wall function for TKE and nutUB-wall functions for eddy viscosity to ensure accurate and stable boundary conditions. The applications to a backward-facing step flow at Re=155,000 reveal that the reattachment length is reasonably well predicted on appropriately refined mesh by all turbulence models, except the standard k-𝜖 model which about 13% underestimates the reattachment length regardless of the grid refinement.

키워드

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