A RANS modeling of backward-facing step turbulent flow in an open channel

Byungjoo Kim; Joongcheol Paik

doi:10.3741/JKWRA.2022.55.2.147

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2022 Vol.55, Issue 2 Preview Page Next Page

Research Article

A RANS modeling of backward-facing step turbulent flow in an open channel 개수로에서의 후향단차 난류 흐름 RANS 수치모의

28 February 2022. pp. 147-157

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Abstract

The backward-facing step (BFS) is a benchmark geometry for analyzing flow separation occurred at the edge and resulting development of shear layer and recirculation zone that are occupied by turbulent flow. It is important to accurately reproduce and analyze the mean flow and turbulence statistics of such flows to design physically stable and performance assurance structure. We carried out 3D RANS computations with widely used, two representative turbulence models, k-ω SST and RNG k-ε, to reproduce BFS flow at the Reynolds number of 23,000 and the Froude number of 0.22. The performance of RANS computations is evaluated by comparing numerical results with an experimental measurement. Both RANS computations with two turbulence models appear to reasonably well reproduce mean flow in the shear layer and recirculation zone, while RNG k-ε computation results in about 5% larger velocity between the outer edge of boundary layer and the free surface above the recirculation zone than k-ω SST computation and experiment. Both turbulence models underestimate the shear stress distribution experimentally observed just downstream of the sharp edge of BFS, while shear stresses computed in the boundary layer downstream of reattachment point are agree reasonably well with experimental measurement. RNG k-ε modeling reproduces better shear stress distribution along the bottom boundary layer, but overestimates shear shear stress in the approaching boundary layer and above the bottom boundary layer downstream of the BFS.

Keywords

Backward-facing step

Turbulent flow

RANS modeling

Recirculating flow

Shear stress

후향단차 수공구조물의 모서리에서는 흐름분리가 발생하며 이로 인해 형성되는 전단층과 재순환 흐름 영역에서의 흐름은 복잡한 난류가 지배적이다. 물리적으로 안정하면서 성능이 보장되는 구조물 설계를 위해서는 이러한 난류 흐름의 거동을 정확하게 예측하고 분석하는 것이 중요하다. 이 연구에서는 공학적으로 널리 이용되고 있는 대표적인 난류 모형인 k-ω SST 모형과 RNG k-ε 모형을 이용한 3차원 RANS 계산을 통해서 개수로에 설치된 후향단차를 통과하는 난류 흐름을 레이놀즈 수 23,400과 후르드 수 0.22의 조건에서 수치모의하고, 해석 결과를 기존 실험자료와 비교 분석하여 수치해석의 성능을 평가하고자 한다. 두 가지 난류 모형을 이용하여 구한 평균유속 분포를 보면 모두 경계층에서 관측된 실험값을 양호하게 잘 재현하는 것으로 나타났다. 재순환 영역 상부에서 계산된 평균유속을 보면 RNG k-ε 모형이 k-ω SST 모형보다 중앙부에서의 유속을 약 5% 정도 크게 계산하는 것으로 나타났다. 난류 통계량 관점에서 보면 두 난류 모형 모두 단차 모서리 직하류에서 흐름 분리로 인해 발생하는 레이놀즈 전단응력을 현저히 과소산정하는 한편, 재부착점 하류에서는 실험값을 상대적으로 양호하게 재현하는 것으로 나타났다. RNG k-ε 모형은 수로 바닥 부근 경계층에서의 전단응력 분포를 k-ω SST 모형보다는 우수한 정확도로 실험값을 계산하는 반면에 접근수로 경계층에서 그리고 단차 하류부에서는 경계층 상부에서 전단응력을 과대 산정하는 것으로 나타났다.

키워드

후향단차

난류 흐름

RANS 수치모의

재순환 흐름

전단응력

References

Agelinchaab, M., and Tachie, M.F. (2008). "PIV study of separated and reattached open channel flow over surface mounted blocks." Journal of Fluids Engineering, Vol. 130, No. 6, 061206. 10.1115/1.2911677

Akselvoll, K., and Moin, P. (1993). "Large eddy simulation of a backward facing step flow." Engineering Turbulence Modelling and Experiments, Elsevier, Florence, Italy, pp. 303-313. 10.1016/B978-0-444-89802-9.50033-2

Armaly, B.F., Durst, F., Pereira, J.C.F., and Schönung, B. (1983). "Experimental and theoretical investigation of backward-facing step flow." Journal of Fluid Mechanics, Vol. 127, pp. 473-496. 10.1017/S0022112083002839

Barri, M., El Khoury, G.K., Andersson, H.I., and Pettersen, B. (2010). "DNS of backward‐facing step flow with fully turbulent inflow." International Journal for Numerical Methods in Fluids, Vol. 64, No. 7, pp. 777-792. 10.1002/fld.2176

Bosnyakov, S.M., Duben, A.P., Zheltovodov, A.A., Kozubskaya, T.K., Matyash, S.V., and Mikhailov, S.V. (2020). "Numerical simulation of supersonic separated flow over inclined backward-facing step using RANS and LES methods." Mathematical Models and Computer Simulations, Vol. 12, No 4, pp. 453-463. 10.1134/S2070048220040043

Bradshaw, P., and Wong, F.Y.F. (1972). "The reattachment and relaxation of a turbulent shear layer." Journal of Fluid Mechanics, Vol. 52, No. 1, pp. 113-135. 10.1017/S002211207200299X

Chen, L., Asai, K., Nonomura, T., Xi, G., and Liu, T. (2018). "A review of Backward-Facing Step (BFS) flow mechanisms, heat transfer and control." Thermal Science and Engineering Progress, Vol. 6, pp. 194-216. 10.1016/j.tsep.2018.04.004

Fujita, I. (2002). "Particle image analysis of open-channel flow at a backward facing step having a trench." Journal of Visualization, Vol. 5, No. 4, pp. 335-342. 10.1007/BF03182348

Gritskevich, M.S., Garbaruk A.V., Schütze, J. and Menter, F. (2012). "Development of DDES and IDDES formulations for the k-ω shear stress transport model." Flow, Turbulence and Combustions, Vol. 88, pp. 431-449. 10.1007/s10494-011-9378-4

Le, H., Moin, P., and Kim, J. (1997). "Direct numerical simulation of turbulent flow over a backward-facing step." Journal of Fluid Mechanics, Vol. 330, pp. 349-374. 10.1017/S0022112096003941

Lee, H.Y., and Hwang, S.T. (1994). "Migration of backward-facing step." Journal of Hydraulic Engineering, Vol. 120, No. 6, pp. 693-705. 10.1061/(ASCE)0733-9429(1994)120:6(693)

Liriano, S.L., Day, R.A., and Rodney White, W. (2002). "Scour at culvert outlets as influenced by the turbulent flow structure." Journal of Hydraulic Research, Vol. 40, No. 3, pp. 367-376. 10.1080/00221680209499951

Menter, F.R. (1994). "Two-equation eddy-viscosity turbulence models for engineering applications." American Institute of Aeronautics and Astronautics, Vol. 32, No. 8, pp. 1598-1605. 10.2514/3.12149

Müller, A., and Gyr, A. (1986). "On the vortex formation in the mixing layer behind dunes." Journal of Hydraulic Research, Vol. 24. No. 5, pp. 359-375. 10.1080/00221688609499314

Nakagawa, H., and Nezu, I. (1987). "Experimental investigation on turbulent structure of backward-facing step flow in an open channel." Journal of Hydraulic Research, Vol. 25, No. 1, pp. 67-88. 10.1080/00221688709499289

Nezu, I., and Nakagawa, H. (1989). "Turbulent structure of backward-facing step flow and coherent vortex shedding from reattachment in open-channel flows." Turbulent Shear Flows 6, Springer, Berlin, Heidelberg, pp. 313-337. 10.1007/978-3-642-73948-4_26

Nezu, I., Nakagawa, H., and Tominaga, A. (1985). "Secondary currents in a straight channel flow and the relation to its aspect ratio." Turbulent shear flows 4, Springer, Berlin, Heidelberg, pp. 246-260. 10.1007/978-3-642-69996-2_20

Nguyen, T.D., and Souad, H. (2015). "PIV measurements in a turbulent wall jet over a backward-facing step in a three-dimensional, non-confined channel." Flow Measurement and Instrumentation, Vol. 42, pp. 26-39. 10.1016/j.flowmeasinst.2015.01.002

Oder, J., Shams, A., Cizelj, L., and Tiselj, I. (2019). "Direct numerical simulation of low-Prandtl fluid flow over a confined backward facing step." International Journal of Heat and Mass Transfer, Vol. 142, 118436. 10.1016/j.ijheatmasstransfer.2019.118436

OpenFOAM (2021). The open source CFD toolbox, accessed 1 June, 2021, <https://www.openfoam.com/>.

Poletto, R., Craft, T. and Revell, A. (2013). "A new divergence free synthetic eddy method for the reproduction of inlet flow conditions for LES." Flow, Turbulence and Combustions, Vol. 91, pp. 519-539. 10.1007/s10494-013-9488-2

Pont-Vílchez, A., Trias, F.X., Gorobets, A., and Oliva, A. (2019). "Direct numerical simulation of backward-facing step flow at and expansion ratio 2." Journal of Fluid Mechanics, Vol. 863, pp. 341-363. 10.1017/jfm.2018.1000

Probst, A., Wolf, C., Radespiel, R., Knopp, T., Schwamborn, D., and Radespiel, R. (2010). "A comparison of detached-eddy simulation and Reynolds-stress modeling applied to the flow over a backward-facing step and an airfoil at stall." 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, FL, U.S., p. 920. 10.2514/6.2010-920

Sainte-Rose, B., Bertier, N., Deck, S., and Dupoirieux, F. (2009). "A DES method applied to a backward facing step reactive flow." Comptes Rendus Mécanique, Vol. 337, No. 6-7, pp. 340-351. 10.1016/j.crme.2009.06.017

Shobayo, O.O., and Walters, D.K. (2018). "Evaluation of performance and code-to-code variation of a dynamic hybrid RANS/LES model for simulation of backward-facing step flow." Fluids Engineering Division Summer Meeting, ASME, Montreal, Quebec, Canada, Vol. 51555, V001T08A002. 10.1115/FEDSM2018-83160

Smirnov, E.M., Smirnovsky, A.A., Schur, N.A., Zaitsev, D.K., and Smirnov, P.E. (2018). "Comparison of RANS and IDDES solutions for turbulent flow and heat transfer past a backward-facing step." Heat and Mass Transfer, Vol. 54, No. 8, pp. 2231-2241. 10.1007/s00231-017-2207-0

Tachie, M.F., Balachandar, R., and Bergstrom, D.J. (2001). "Open channel boundary layer relaxation behind a forward facing step at low Reynolds numbers." Journal of Fluids Engineering, Vol. 123, No, 3, 539-544. 10.1115/1.1383971

Wilcox, D.C. (1988). "Reassessment of the scale-determining equation for advanced turbulence models." American Institute of Aeronautics and Astronautics, Vol. 26, No. 11, pp. 1299-1310. 10.2514/3.10041

Xingkui, W., and Fontijn, H.L. (1993). "Experimental study of the hydrodynamic forces on a bed element in an open channel with a backward-facing step." Journal of Fluids and Structures, Vol. 7, No. 3, 299-318. 10.1006/jfls.1993.1018

Yakhot, V., Orszag, S.A., Thangam, S., Catski, T.B. and Speziale, C.G. (1992). "Development of turbulence models for shear flows by a double expansion technique." Physics of Fluids, Vol. 4, No. 7, pp. 1510-1520. 10.1063/1.858424

Yu, K.F., Lau, K.S., and Chan, C.K. (2004). "Numerical simulation of gas-particle flow in a single-side backward-facing step flow." Journal of Computational and Applied Mathematics, Vol. 163, No. 1, pp. 319-331. 10.1016/j.cam.2003.08.077

Information

Publisher :KOREA WATER RESOURECES ASSOCIATION
Publisher(Ko) :한국수자원학회
Journal Title :Journal of Korea Water Resources Association
Journal Title(Ko) :한국수자원학회 논문집
Volume : 55
No :2
Pages :147-157
Received Date : 2021-11-03
Revised Date : 2021-12-20
Accepted Date : 2021-12-29
DOI :https://doi.org/10.3741/JKWRA.2022.55.2.147

Journal of Korea Water Resources Association ISSN:2799-8746(Print) 2799-8754(Online) 한국수자원학회 논문집

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