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2025 Vol.18, Issue 2

Original Article

Prediction of Turbulent Flows in a Square Duct Subjected to Lorentz Force

로렌츠 힘이 작용하는 정사각 덕트 내 난류유동 해석

In-Gyu Jeon1
,
Ho-Yong Park1
,
Dong-Kurl Kwak2*
,
Jong-Keun Shin2*
전 인규1
,
박 호용1
,
곽 동걸2*
,
신 종근2*
1Ph.D. Course, Graduate School of Disaster Prevention, Kangwon National University
2Professor, Graduate School of Disaster Prevention, Kangwon National University
1강원대학교 방재전문대학원 박사과정
2강원대학교 방재전문대학원 교수
*Corresponding Author
30 June 2025. pp. 1-12
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Abstract

This study was conducted to understand the effects of a magnetic field on mean velocity and turbulent characteristics in fully developed turbulent magnetohydrodynamic (MHD) flow through a square duct. Based on the coupled Navier-Stokes MHD equations, an extended Reynolds stress transport model including the Lorentz force effect was applied, and the analysis was performed using an in-house computational fluid dynamics code. In order to directly apply the Lorenz force effect to the turbulent MHD flow, models related to the generation and dissipation rate of the Lorenz force were additionally applied to the Reynolds stress and dissipation rate equations, and the indirect effect was also considered through the modification of the velocity-pressure gradient correlation model of the Reynolds stress equation. In addition, the model coefficients of the models related to the Lorenz force were tuned using the fully developed channel MHD data so that they could be linked to the elliptic-blending Reynolds stress model and then the square duct flow was analyzed. The prediction results were validated through comparison with the direct numerical simulation (DNS) data of Chaudhary et al. (2010), confirming the flattening of the mean velocity distribution and the suppression trends of turbulence intensity and shear stress. The results of the analysis show that the proposed extended model contributes to improving the predictive accuracy of MHD-affected flow fields and suggests its applicability to various engineering applications involving complex boundary conditions.

Keywords
magnetohydrodynamic
Reynolds stress transport equation
turbulence model
elliptic-blending
Lorentz force

본 연구는 정사각형 단면을 갖는 덕트 내 완전 발달된 난류 자기유체역학(magnetohydrodynamic, MHD) 유동에서 자기장이 평균속도와 난류 특성에 미치는 영향을 이해하기 위하여 수행되었다. 결합된 형태의 나비에-스토크스(Navier-Stokes) MHD 방정식들을 기반으로 로렌츠 힘 효과를 포함한 확장된 형태의 레이놀즈응력 수송 모형을 적용하였으며, 이 해석은 전산 유체역학을 위한 자체 개발 코드로 수행되었다. 난류 MHD 유동에 로렌츠 힘 효과를 직접적으로 부여하기 위하여 레이놀즈응력과 소멸률 방정식들에 로렌츠 힘 관련 생성과 소멸에 관한 모형들을 추가하였으며, 레이놀즈응력 방정식의 속도-압력구배 상관관계 모형의 수정을 통해서도 간접적인 효과를 발휘하도록 고려하였다. 또한, 본 연구에서는 타원-혼합 레이놀즈응력 모형과 연계되도록 로렌츠 힘과 관련된 모형계수들을 완전 발달된 평판 MHD 자료들을 활용하여 조율하는 과정을 거친 후에 사각덕트 유동을 해석하였다. 예측된 결과는 Chaudhary et al.(2010)의 직접수치모사(direct numerical simulation, DNS) 자료와 비교하여 타당성을 검증하였으며, 평균속도 분포의 평탄화와 난류강도 및 전단응력의 억제 경향을 확인하였다. 해석 결과는 제안한 확장형 모형이 자기장 영향을 받는 유동장의 예측 정확도 향상에 기여할 수 있음을 보여주고 복잡한 경계조건을 갖는 다양한 공학적 응용 분야에서 활용 가능성을 제시한다.

키워드
자기유체역학
레이놀즈응력 수송방정식
난류 모형
타원-혼합
로렌츠 힘
References
1

Chaudhary, R., S. P. Vanka, and B. G. Thomas. (2010). Direct Numerical Simulation of Magnetic Field Effects on Turbulent Flow in a Square Duct. Physics of Fluids. 22: 075102.

10.1063/1.3456724
2

Dey, P. K. and O. Zikanov. (2012). Turbulence and Transport of Passive Scalar in Magnetohydrodynamic Channel Flows with Different Orientation of Magnetic Field. International Journal of Heat and Fluid Flow. 36: 101-117.

10.1016/j.ijheatfluidflow.2012.01.005
3

Kenjeres, S. (2018). On Modeling and Eddy-Resolving Simulations of Flow, Turbulence, Mixing and Heat Transfer of Electrically Conducting and Magnetizing Fluids: A Review. International Journal of Heat and Fluid Flow. 73: 270-279.

10.1016/j.ijheatfluidflow.2018.09.003
4

Kenjeres, S. and K. Hanjalic. (2000). On the Implementation of the Effect of Lorentz Force in Turbulence Closure Models. International Journal of Heat and Fluid Flow. 21(3): 329-337.

10.1016/S0142-727X(00)00017-5
5

Kenjeres, S., K. Hanjalic, and D. Bal. (2004). A Direct-Numerical-Simulation-Based Second-Moment Closure for Turbulent Magnetohydrodynamic Flows. Physics of Fluids. 16(5): 1229-1241.

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Manceau, R. and K. Hanjalic. (2002). Elliptic Blending Model: A New Near Wall Reynolds Stress Turbulence Closure. Physics of Fluids. 14(2): 744-754.

10.1063/1.1432693
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Noguchi, H., Y. Ohtsubo, and N. Kasagi. (1998). DNS Database of Turbulence and Heat Transfer. https://www.thtlab.jp/

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Shin, J. K., J. S. An, Y. D. Choi, Y. C. Kim, and M. S. Kim. (2008). Elliptic Relaxation Second Moment Closure for the Turbulent Heat Fluxes. Journal of Turbulence. 9(3): 1-29.

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9

Shin, Jong Keun and Dong Kurl Kwak. (2016). Evaluation and Improvement of Turbulence Model for Prediction of Turbulent Magnetohydrodynamic Flows. Journal of the Korean Society of Mechanical Technology. 18(5): 707-714.

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Speziale, C. G., S. Sarkar, and T. B. Gatski. (1991). Modeling of the Pressure-Strain Correlation Tensor: An Invariant Dynamical Systems Approach. Journal of Fluid Mechanics. 227: 245-272.

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Thielen, L., K. Hanjalic, H. Jonker, and R. Manceau. (2004). Prediction of Flow and Heat Transfer in Multiple Impinging Jets with an Elliptic-Blending Second-Moment Closure. International Journal of Heat and Mass Transfer. 48(8): 1683-1598.

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12

Wilson, D. R., T. J. Craft, and H. Iacovides. (2015). Application of Reynolds Stress Transport Turbulence Closure Models to Flows Affected by Lorentz and Buoyancy Forces. International Journal of Heat and Fluid Flow. 55: 180-197.

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Korean References Translated from the English

1

신종근, 곽동걸 (2016). 난류 자기유체역학 유동 예측을 위한 난류모형의 평가와 개선. 한국기계기술학회지. 18(5): 707-714.

10.17958/ksmt.18.5.201610.707
Information
  • Publisher :Korean Society of Disaster and Security
  • Publisher(Ko) :한국방재안전학회
  • Journal Title :Journal of Korean Society of Disaster and Security
  • Journal Title(Ko) :한국방재안전학회 논문집
  • Volume : 18
  • No :2
  • Pages :1-12
  • Received Date : 2025-04-10
  • Accepted Date : 2025-05-12
  • DOI :https://doi.org/10.21729/ksds.2025.18.2.1
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