All Issue

2026 Vol.59, Issue 9 Preview Page
Numerical simulation and Rouse number-based quantitative analysis of turbulence damping parameter for high-concentration sediment transport in pressurized pipes

관수로 고농도 유사이송의 수치해석 및 난류 감쇠 매개변수의 Rouse 수 기반 정량 분석

Yongjun Kwona
,
Seung Ho Hongb
,
Hyung-Suk Kimc*
권 용준a
,
홍 승호b
,
김 형석c*
aPh.D Student, Department of Civil & Environment Engineering, Kunsan National University, Gunsan, Korea
bProfessor, Department of Civil and Environmental Engineering, Hanyang University ERICA, Ansan, Korea
cAssociate Professor, Department of Civil Engineering, Kunsan National University, Gunsan, Korea
a국립군산대학교 토목환경공학부 박사과정
b한양대학교 에리카 건설환경공학과 교수
c국립군산대학교 토목공학과 부교수
*Corresponding Author
30 September 2026. pp. 1115-1129
PDF XML Citation
Abstract

Three-dimensional numerical simulations of high-concentration fluid-sediment mixture flow in a circular pipe were conducted using the OpenFOAM-based sedInterFoam solver, with the previously reported experimental results adopted as the validation benchmark. The inverse Schmidt number (SUS) specification method and the governing factors of the turbulence damping parameter B were quantitatively investigated. A mesh convergence study was performed under a uniform SUS = 1.0 condition, and the optimal mesh of N5 (982,800 cells) was selected based on a composite assessment of MAPE for both velocity profiles and sediment concentration distributions. A locally computed SUSlocal, derived from a previously published empirical formula, was subsequently applied. For d = 0.09 mm, SUSlocal = 1.016–1.024, deviating from SUS = 1.0 by only 1.6–2.4%, resulting in a marginal improvement in concentration profile accuracy (MAPE: 4.92% → 3.79%). For d = 0.27 mm, SUSlocal = 1.91–3.0 was obtained, and the enhanced turbulent diffusivity substantially alleviated the near-bed concentration over-accumulation, yielding a marked improvement in predictive accuracy (MAPE: 47.98% → 14.70%). The Rouse number was introduced as a sediment transport regime classifier to identify the governing factors of parameter B. In the wash-load regime (Z < 0.8), B ≤ 10-4 was obtained for Z = 0.218–0.269, while a constant value of B ≈ 0.22 was observed for Z = 0.453–0.641. In the suspended- and bed-load dominant regime (Z ≥ 0.8), B varied from 0.07 to 0.24 over Z = 1.645–2.901, exhibiting a stepwise change in the magnitude of B with regime transition. This hierarchical governing structure of B is quantitatively established for the first time under high-concentration sediment transport conditions in a circular pipe. A predictive relationship between the dimensionless sediment concentration C* and B, given by B=0.0162 × (C*)-1.066(R2 = 0.975), is proposed for the Z ≥ 0.8 regime.

Keywords
SedInterFoam
Sediment transport
Schmidt number
Turbulence damping parameter
Rouse number
Mesh sensitivity analysis

OpenFOAM 기반 sedInterFoam 솔버를 활용하여 원형 단면 관수로 내 고농도 유체-유사 혼합류에 대한 3차원 수치모의를 수행하였으며, 기존 문헌의 수리실험 결과를 검증 기준으로 채택하였다. Schmidt 수의 역수(SUS) 산정 방법 및 난류 감쇠 매개변수 B의 지배 인자를 정량적으로 분석하였다. 균일 SUS = 1.0 조건에서 격자 해상도에 대한 수렴성 검토를 수행하였으며, 유속 및 유사 농도 MAPE의 종합 평가를 통해 최적 격자를 결정하였다. 기존 문헌의 경험식에 기반하여 국부적으로 산정하는 SUSlocal을 적용하였다. d = 0.09 mm 조건에서는 SUSlocal=1.016~1.024로 SUS = 1.0과의 차이가 1.6~2.4%에 불과하여 농도 분포 재현성 개선 효과가 제한적이었으며(MAPE 4.92%→3.79%), d = 0.27 mm 조건에서는 SUSlocal=1.91~3.0이 산정되어 난류 확산 증가에 따라 관 하부 집중되는 농도 분포의 완화와 함께 수리실험 재현성이 현저히 향상되었다(MAPE 47.98%→14.70%). Rouse 수(Z = ws/κu*)를 유사 이송 체제 분류 지표로 도입하여 매개변수 B의 지배 인자를 분석하였다. Z < 0.8의 완전부유 체제에서는 Z = 0.218~0.269 범위에서 B ≤ 10-4, Z = 0.453~0.641 범위에서 B ≈ 0.22의 일정한 값이 각각 나타났으며, Z ≥ 0.8의 부유사–소류사 복합 체제에서는 Z = 1.645~2.901에 걸쳐 B=0.07~0.24로 체제 전환에 따라 B의 크기 수준이 단계적으로 변화하였다. 이러한 B의 단계적 지배 구조는 관수로 고농도 유사이송 조건에서 정량적으로 규명되었다. 또한 Z ≥ 0.8 조건에서 무차원 유사 농도 C*와 B의 관계식 B = 0.0162 × (C*)-1.066 (R2=0.975)을 제시하였다.

키워드
sedInterFoam
관수로 유사이송
Schmidt 수
난류 감쇠 매개변수
Rouse 수
격자 민감도
References
1

Baykal, C., Sumer, B.M., Fuhrman, D.R., Jacobsen, N.G., and Fredsøe, J. (2014). “Numerical investigation of flow and scour around a vertical circular cylinder.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 373, No. 2033, pp. 1-15.

10.1098/rsta.2014.010425512595PMC4275922
2

Carnahan, N.F., and Starling, K.E. (1969). “Equation of state for nonattracting rigid spheres.” The Journal of Chemical Physics, Vol. 51, No. 2, pp. 635-636.

10.1063/1.1672048
3

Chauchat, J., Cheng, Z., Nagel, T., Bonamy, C., and Hsu, T.-J. (2017). “SedFoam-2.0: A 3-D two-phase flow numerical model for sediment transport.” Geoscientific Model Development, Vol. 10, No. 12, pp. 4367-4392.

10.5194/gmd-10-4367-2017
4

Cheng, Z., Hsu, T.J., and Calantoni, J. (2017). “SedFoam: A multi-dimensional Eulerian two-phase model for sediment transport and its application to momentary bed failure.” Coastal Engineering, Vol. 119, pp. 32-50.

10.1016/j.coastaleng.2016.08.007
5

Cheng, Z., Hsu, T.J., and Chauchat, J. (2018). “An Eulerian two-phase model for steady sheet flow using large-eddy simulation methodology.” Advances in Water Resources, Vol. 111, pp. 205-223.

10.1016/j.advwatres.2017.11.016
6

Delisle, M.-P. C., Kim, Y., Mieras, R. S., and Gallien, T. W. (2022). “Numerical investigation of sheet flow driven by a near-breaking transient wave using SedFoam.” European Journal of Mechanics / B Fluids, Vol. 96, pp. 51-64.

10.1016/j.euromechflu.2022.07.002
7

Ding, J., and Gidaspow, D. (1990). “A bubbling fluidization model using kinetic theory of granular flow.” AIChE Journal, Vol. 36, No. 4, pp. 523-538.

10.1002/aic.690360404
8

Fang, H.W., and Wang, G.Q. (2000). “Three-dimensional mathematical model of suspended-sediment transport.” Journal of Hydraulic Engineering, ASCE, Vol. 126, No. 8, pp. 578-592.

10.1061/(ASCE)0733-9429(2000)126:8(578)
9

Gillies, R.G., Shook, C.A., and Xu, J. (2004). “Modelling heterogeneous slurry flows at high velocities.” The Canadian Journal of Chemical Engineering, Vol. 82, No. 5, pp. 1060-1065.

10.1002/cjce.5450820523
10

Hsu, T.J., Jenkins, J.T., and Liu, P.L.F. (2004). “On two-phase sediment transport: sheet flow of massive particles.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 460, No. 2048, pp. 2223-2250.

10.1098/rspa.2003.1273
11

Jacobsen, N.G., Fredsøe, J., and Jensen, J.H. (2014). “Formation and development of a breaker bar under regular waves. Part 1. Model description and hydrodynamics.” Coastal Engineering, Vol. 88, pp. 182-193.

10.1016/j.coastaleng.2013.12.008
12

Jacobsen, N.G., Fuhrman, D.R., and Fredsøe, J. (2012). “A wave generation toolbox for the open-source CFD library: OpenFoam®.” International Journal for Numerical Methods in Fluids, Vol. 70, No. 9, pp. 1073-1088.

10.1002/fld.2726
13

Johnson, P.C., and Jackson, R. (1987). “Frictional-collisional constitutive relations for granular materials, with application to plane shearing.” Journal of Fluid Mechanics, Vol. 176, pp. 67-93.

10.1017/S0022112087000570
14

Kaushal, D.R., Kumar, A., Tomita, Y., Kuchii, S., and Tsukamoto, H. (2013). “Flow of mono-dispersed particles through horizontal bend.” International Journal of Multiphase Flow, Vol. 52, pp. 71-91.

10.1016/j.ijmultiphaseflow.2012.12.009
15

Kim, Y., Cheng, Z., Hsu, T.-J., and Chauchat, J. (2018). “A numerical study of sheet flow under monochromatic nonbreaking waves using a free surface resolving Eulerian two-phase flow model.” Journal of Geophysical Research: Oceans, Vol. 123, No. 7, pp. 4693-4719.

10.1029/2018JC013930
16

Klostermann, J., Schaake, K., and Schwarze, R. (2013). “Numerical simulation of a single rising bubble by VOF with surface compression.” International Journal for Numerical Methods in Fluids, Vol. 71, No. 8, pp. 960-982.

10.1002/fld.3692
17

Lee, C.H., Xu, C., and Huang, Z. (2019). “A three-phase flow simulation of local scour caused by a submerged wall jet with a water-air interface.” Advances in Water Resources, Vol. 129, pp. 373-384.

10.1016/j.advwatres.2017.07.017
18

Li, M.Z., He, Y.P., Liu, Y.D., and Huang, C. (2018). “Effect of interaction of particles with different sizes on particle kinetics in multi-sized slurry transport by pipeline.” Powder Technology, Vol. 338, pp. 915-930.

10.1016/j.powtec.2018.07.088
19

Mathieu, A., Chauchat, J., Bonamy, C., and Nagel, T. (2019). “Two-phase flow simulation of tunnel and lee-wake erosion of scour below a submarine pipeline.” Water, Vol. 11, No. 8, pp. 1727-1743.

10.3390/w11081727
20

Mathieu, A., Kim, Y., Hsu, T.-J., Bonamy, C., and Chauchat, J. (2025). “sedInterFoam 1.0: a three-phase numerical model for sediment transport applications with free surfaces.” Geoscientific Model Development, Vol. 18, No. 5, pp. 1561-1573.

10.5194/gmd-18-1561-2025
21

Meyer-Peter, E., and Müller, R. (1948). “Formulas for bed-load transport.” Proceedings of the 2nd Meeting of the International Association of Hydraulic and Structural Research, Stockholm, Sweden, pp. 34-64.

22

Ota, K., Sato, T., and Nakagawa, H. (2015). “3D numerical model of sediment transport considering transition from bed-load motion to suspension: Application to a scour upstream of a cross-river structure.” Journal of Japan Society of Civil Engineers, Vol. 4, pp. 173-180.

10.2208/journalofjsce.4.1_173
23

Revil-Baudard, T., Chauchat, J., Hurther, D., and Barraud, P.-A. (2015). “Investigation of sheet-flow processes based on novel acoustic highresolution velocity and concentration measurements.” Journal of Fluid Mechanics, Vol. 767, pp. 1-30.

10.1017/jfm.2015.23
24

Rouse, H. (1937). “Modern conceptions of the mechanics of turbulence.” Transactions of the American Society of Civil Engineers, Vol. 102, pp. 463-505.

10.1061/TACEAT.0004872
25

Rusche, H. (2003). Computational fluid dynamics of dispersed two-phase flows at high phase fractions. Ph.D. dissertation, Imperial College London, London, UK, pp. 15-20.

26

Sabbagh-Yazdi, S.R., and Jamshidi, M. (2013). “Depth-averaged hydrodynamic model for gradual breaching of embankment dams attributable to overtopping considering suspended sediment transport.” Journal of Hydraulic Engineering, ASCE, Vol. 139, No. 6, pp. 580-592.

10.1061/(ASCE)HY.1943-7900.0000706
27

Schiller, L., and Naumann, A. (1933). “Uber die grundlegenden berechungen bei der schwerkraftaufbereitung.” Verein Deutscher Ingenieure, Vol. 77, pp. 318-320.

28

Sumer, B.M., Kozakiewicz, A., Fredsoe, J., and Deigaard, R. (1996). “Velocity and concentration profiles in sheet-flow layer of movable bed.” Journal of Hydraulic Engineering, ASCE, Vol. 122, No. 10, pp. 549-558.

10.1061/(ASCE)0733-9429(1996)122:10(549)
29

Van Rijn, L.C. (1984). “Sediment transport, part ii: suspended load transport.” Journal of Hydraulic Engineering, ASCE, Vol. 110, No. 11, pp. 1613-1641.

10.1061/(ASCE)0733-9429(1984)110:11(1613)
30

Xie, H., Cai, H., Wang, H., Fu, D., Xu, N., and Xu, D. (2025). “Mechanism of turbulence modulation of sediment-laden flow for the case of equilibrium suspended-load transport.” Frontiers in Physics, Vol. 13, pp. 1-15.

10.3389/fphy.2025.1449056
Information
  • Publisher :KOREA WATER RESOURECES ASSOCIATION
  • Publisher(Ko) :한국수자원학회
  • Journal Title :Journal of Korea Water Resources Association
  • Journal Title(Ko) :한국수자원학회 논문집
  • Volume : 59
  • No :9
  • Pages :1115-1129
  • Received Date : 2026-06-23
  • Revised Date : 2026-07-29
  • Accepted Date : 2026-08-08
  • DOI :https://doi.org/10.3741/JKWRA.2026.59.9.1115
Journal Informaiton Journal of Korea Water Resources Association Journal of Korea Water Resources Association
Online Submission
Archives
  • scopus
  • KCI-수자원
  • NRF
  • KOFST
  • KISTI Current Status
  • KISTI Cited-by
  • crosscheck
  • orcid
  • open access
  • ccl
Journal Informaiton Journal Informaiton - close