Figure 1- Schematic diagram of pooled stepped spillway conducted by Felder et al. (2012A): Notes: h step height (10 cm): w pool height (3.1 cm): l horizontal step length (20 cm): lw pool weir length (1.5 cm): d' is the water depth above the crest; y' is the distance normal to the crest invert

Khosro Morovati , Afshin Eghbalzadeh 
International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 3 April 2018

Abstract

많은 계단식 배수로 지오메트리 설계 지침이 평평한 단계를 위해 개발되었지만 통합 단계를 설계하는 것이 더 효율적으로 작동하는 배수로에 대한 적절한 대안이 될 수 있습니다.

이 논문은 POOL의 다른 높이에서 공기 연행과 보이드 비율의 시작점을 다루는 것을 목표로 합니다. 그 후, FLOW-3D 소프트웨어를 사용하여 POOL과 경사면의 높이를 다르게 하여 폭기된 지역과 폭기되지 않은 지역에서 압력 분포를 평가했습니다.

얻어진 수치 결과와 실험 결과의 비교는 본 연구에 사용된 모든 방류에 대해 잘 일치했습니다. POOL 높이는 시작 지점 위치에 미미한 영향을 미쳤습니다. 공극률의 값은 높은 방류에 비해 낮은 방전에서 더 많은 영향을 받았습니다.

여수로의 마루(통기되지 않은 지역)에서는 음압이 나타나지 않았으며 각 방류에서 마루를 따라 높이가 15cm인 수영장에서 최대 압력 값이 얻어졌습니다.

모든 사면에서 웅덩이 및 평평한 계단형 여수로의 계단층 부근에서는 음압이 형성되지 않았습니다. 그러나 평단식 여수로에 비해 평단식 여수로의 수직면 부근에서 음압이 더 많이 형성되어 평단식 슈트에서 캐비테이션 현상이 발생할 확률이 증가하였습니다.

Study of inception point, void fraction and pressure over pooled
stWhile many stepped spillways geometry design guidelines were developed for flat steps, designing pooled steps might be an appropriate alternative to spillways working more efficiency. This paper aims to deal with the inception point of air-entrainment and void fraction in the different height of the pools. Following that, pressure distribution was evaluated in aerated and non-aerated regions under the effect of different heights of the pools and slopes through the use of the FLOW-3D software. Comparison of obtained numerical results with experimental ones was in good agreement for all discharges used in this study. Pools height had the insignificant effect on the inception point location. The value of void fraction was more affected in lower discharges in comparison with higher ones. Negative pressure was not seen over the crest of spillway (non-aerated region), and the maximum pressure values were obtained for pools with 15 cm height along the crest in each discharge. In all slopes, negative pressure was not formed near the step bed in the pooled and flat stepped spillways. However, negative pressure was formed in more area near the vertical face in the flat stepped spillway compared with the pooled stepped spillway which increases the probability of cavitation phenomenon in the flat stepped chute.

Design/methodology/approach

압력, 공극률 및 시작점을 평가하기 위해 POOL된 계단식 여수로가 사용되었습니다. 또한 POOL의 다른 높이가 사용되었습니다. 이 연구의 수치 시뮬레이션은 Flow-3D 소프트웨어를 통해 수행되었습니다. 얻어진 결과는 풀이 압력, 공극률 및 시작점을 포함한 2상 유동 특성에 영향을 미칠 수 있음을 나타냅니다.

Findings

마루 위에는 음압이 보이지 않았습니다. 압력 값은 사용된 모든 높이와 15cm 높이에서 얻은 최대 값에 대해 다릅니다. 또한, 풀링 스텝은 플랫 케이스에 비해 음압점 감소에 더 효과적인 역할을 하였습니다. 시작 지점 위치는 특히 9 및 15cm 높이에 대해 스키밍 흐름 영역과 비교하여 낮잠 및 전환 흐름 영역에서 더 많은 영향을 받았습니다.

Keywords

Citation

Morovati, K. and Eghbalzadeh, A. (2018), “Study of inception point, void fraction and pressure over pooled stepped spillways using Flow-3D”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 4, pp. 982-998. https://doi.org/10.1108/HFF-03-2017-0112

Figure 1- Schematic diagram of pooled stepped spillway conducted by Felder et al. (2012A): Notes: h  step height (10 cm): w pool height (3.1 cm): l horizontal step length (20 cm): lw pool weir length (1.5 cm):  d' is the water depth above the crest; y' is the distance normal to the crest invert
Figure 1- Schematic diagram of pooled stepped spillway conducted by Felder et al. (2012A): Notes: h step height (10 cm): w pool height (3.1 cm): l horizontal step length (20 cm): lw pool weir length (1.5 cm): d’ is the water depth above the crest; y’ is the distance normal to the crest invert
Figure 2- meshing domain and distribution of blocks
Figure 2- meshing domain and distribution of blocks
Figure 3- Comparison of numerical simulation with experimental data by Felder et al. (2012A);  mesh convergence analysis; pooled stepped spillway (slope: 26.6 0 )
Figure 3- Comparison of numerical simulation with experimental data by Felder et al. (2012A); mesh convergence analysis; pooled stepped spillway (slope: 26.6 0 )
Figure 4- Comparison of numerical simulation with experimental data by Felder et al. (2012A);  Flat stepped spillway (slope: 0 26 6. )
Figure 4- Comparison of numerical simulation with experimental data by Felder et al. (2012A); Flat stepped spillway (slope: 0 26 6. )
Figure 5-Comparison of numerical simulation with experimental data by Felder et al. (2012B); pooled  and flat stepped spillways (slope: 0 9.8 )
Figure 5-Comparison of numerical simulation with experimental data by Felder et al. (2012B); pooled and flat stepped spillways (slope: 0 9.8 )
Figure 6- TKE distribution on steps 8, 9 and 10 for four different mesh numbers: 261252 (model 1),  288941 (model 2), 323578 (model 3) and 343154 (model 4)
Figure 6- TKE distribution on steps 8, 9 and 10 for four different mesh numbers: 261252 (model 1), 288941 (model 2), 323578 (model 3) and 343154 (model 4)
Figure 7- Comparison of obtained Void fraction distribution on step 10 in numerical simulation with  experimental work conducted by Felder et al. (2012A); (slope 26.60 )
Figure 7- Comparison of obtained Void fraction distribution on step 10 in numerical simulation with experimental work conducted by Felder et al. (2012A); (slope 26.60 )
Figure 8- Results of inception point of air entrainment in different height of the pools: comparison with  empirical correlations (Eqs 8-9), experimental (Felder et al. (2012A)) and numerical data
Figure 8- Results of inception point of air entrainment in different height of the pools: comparison with empirical correlations (Eqs 8-9), experimental (Felder et al. (2012A)) and numerical data
Figure 9- Void fraction distribution for different pool heights on steps 10; slope 26.6 0
Figure 9- Void fraction distribution for different pool heights on steps 10; slope 26.6 0
Figure 10- Comparison of pressure distribution between numerical simulation and experimental work  conducted by Zhang and Chanson (2016); flat stepped spillway (slope: 0 45 )
Figure 10- Comparison of pressure distribution between numerical simulation and experimental work conducted by Zhang and Chanson (2016); flat stepped spillway (slope: 0 45 )
Figure 11- A comparison of the pressure distribution above the crest of the spillway; B comparison of the  free surface profile along the crest of the spillway.  Note: x' indicates the longitudinal distance from the starting point of the crest.
Figure 11- A comparison of the pressure distribution above the crest of the spillway; B comparison of the free surface profile along the crest of the spillway. Note: x’ indicates the longitudinal distance from the starting point of the crest.
Figure 12- pressure distribution along crest of spillway in different discharges; slope 26.6
Figure 12- pressure distribution along crest of spillway in different discharges; slope 26.6
Figure 13- Pressure distribution near the last step bed for different slopes and discharges: x'' indicatesthe  longitudinal distance from the intersection of the horizontal and vertical faces of step 10; y" is the distance from the intersection of the horizontal and vertical faces in the vertical direction
Figure 13- Pressure distribution near the last step bed for different slopes and discharges: x” indicatesthe longitudinal distance from the intersection of the horizontal and vertical faces of step 10; y” is the distance from the intersection of the horizontal and vertical faces in the vertical direction
Figure 14- Pressure distribution adjacent the vertical face of step 9 for different discharges and slopes
Figure 14- Pressure distribution adjacent the vertical face of step 9 for different discharges and slopes
Table1- Used discharges for assessments of mesh convergence analysis and hydraulic  characteristics
Table1- Used discharges for assessments of mesh convergence analysis and hydraulic characteristics

Conclusion

본 연구에서는 자유표면을 모사하기 위해 VOF 방법과 k -ε (RNG) 난류 모델을 활용하여 FLOW-3D 소프트웨어를 사용하였고, 계단식 배수로의 유동을 모사하기 위한 목적으로 난류 특성을 모사하였다. 얻은 결과는 수치 모델이 시작점 위치, 보이드 비율 및 압력을 적절하게 시뮬레이션했음을 나타냅니다. 풀의 높이는 공기 유입 위치에 미미한 영향을 미치므로 얻은 결과는 이 문서에서 제시된 상관 관계와 잘 일치했습니다. 즉, 사용 가능한 상관 관계를 서로 다른 풀 높이에 사용할 수 있습니다. 공극률의 결과는 스텝 풀 근처의 나프 유동 영역에서 공극율 값이 다른 배출보다 더 큰 것으로 나타났다. 더욱이 고방출량 .0 113m3/s에서 수영장 높이를 변경해도 수영장 표면 근처의 공극률 값에는 영향을 미치지 않았습니다.

낮잠 및 전환 체제의 압력 분포에 대한 0 및 3cm 높이의 수영장 효과는 많은 지점에서 대부분 유사했습니다. 더욱이 조사된 모든 높이에서 여수로의 마루를 따라 부압이 없었습니다. 여수로 끝단의 바닥 부근의 압력 결과는 평평하고 고인 경우 부압이 발생하지 않았음을 나타냅니다. 수직면 부근의 음압은 웅덩이에 비해 평평한 계단형 여수로의 깊이(w=0 cm)의 대부분에서 발생하였다. 또한 더 큰 사면에 대한 풀링 케이스에서 음압이 제거되었습니다. 평단식 여수로에서는 계단의 수직면에 인접한 더 넓은 지역에서 음압이 발생하였기 때문에 이 여수로에서는 고형단식여수로보다 캐비테이션 현상이 발생할 가능성이 더 큽니다.

In this study, the FLOW-3D software was used through utilizing the VOF method and k −ε (RNG) turbulence model in order to simulate free surface, and turbulence characteristics for the purpose of simulating flow over pooled stepped spillway. The results obtained indicated that the numerical model properly simulated the inception point location, void fraction, and pressure. The height of the pools has the insignificant effect on the location of air entrainment, so that obtained results were in good agreement with the correlations presented in this paper. In other words, available correlations can be used for different pool heights. The results of void fraction showed that the void fraction values in nappe flow regime near the step pool were more than the other discharges. Furthermore in high discharge, 0.113m3/s, altering pool height had no effect on the value of void fraction near the pool surface.

The effect of the pools with 0 and 3 cm heights over the pressure distribution in nappe and transition regimes was mostly similar in many points. Furthermore, in all examined heights there was no negative pressure along the crest of the spillway. The pressure results near the bed of the step at the end of the spillway indicated that negative pressure did not occur in the flat and pooled cases. Negative pressure near the vertical face occurred in the most part of the depth in the flat stepped spillway (w=0 cm) in comparison with the pooled case. Also, the negative pressure was eliminated in the pooled case for the larger slopes. Since negative pressure occurred in a larger area adjacent the vertical face of the steps in the flat stepped spillways, it is more likely that cavitation phenomenon occurs in this spillway rather than the pooled stepped spillways.

References

  1. André, S. (2004), “High velocity aerated flows on stepped chutes with macro-roughness elements.” Ph.D. thesis,
    Laboratoire de Constructions Hydraulics (LCH), EPFL, Lausanne, Switzerland, 272 pages.
  2. Attarian, A. Hosseini, Kh. Abdi, H and Hosseini, M. (2014), “The Effect of the Step Height on Energy
    Dissipation in Stepped Spillways Using Numerical Simulation”. Arabian Journal for Science and
    Engineering, 39(4), 2587-2594.
  3. Bombardelli, F.A. Meireles. I. Matos, J. (2011), “Laboratory measurements and multi-block numerical
    simulations of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped
    spillways”. Environmental fluid mechanics, 11(3) 263-288.
  4. Chakib, B. (2013), “Numerical Computation of Inception Point Location for Flat-sloped Stepped Spillway”.
    International Journal of Hydraulic Engineering; 2(3): 47-52.
  5. Chakib, B. Mohammed, H. (2015), “Numerical Simulation of Air Entrainment for Flat-Sloped Stepped Spillway.
    Journal of computational multiphase flows”, Volume 7. Number 1.
  6. Chanson, H. Toombes, L. (2002), “Air–water flows down stepped chutes: turbulence and flow structure
    observations”. International Journal of Multiphase Flow, 28(11) 1737-1761
  7. Chen, Q. Dai, G. Liu, H. (2002), “Volume of Fluid Model for Turbulence Numerical Simulation
    of Stepped Spillway Overflow”. DOI: 10.1061/(ASCE)0733-9429128:7(683).
  8. Cheng, X. Chen, Y. Luo, L. (2006), “Numerical simulation of air-water two-phase flow over stepped spillways”.
    Science in China Series E: Technological Sciences, 49(6), 674-684.
  9. Cheng, X. Luo, L. Zhao, W. (2004), “Study of aeration in the water flow over stepped spillway”. In: Proceedings
    of the world water congress.
  10. Chinnarasri, Ch. Kositgittiwong, D. Julien, Y. (2013), “Model of flow over spillways by computational fluid
    dynamics”. Proceedings of the ICE – Water Management, Volume 167(3) 164 –175.
  11. Dastgheib, A. Niksokhan, M.H. and Nowroozpour, A.R. (2012), “Comparing of Flow Pattern and Energy
    Dissipation over different forms of Stepped Spillway”. World Environmental and Water Resources
    Congress ASCE.
  12. Eghbalzadeh, A. Javan, M. (2012), “Comparison of mixture and VOF models for numerical simulation of air
    entrainment in skimming flow over stepped spillway”. Procedia Engineering, 28. 657-660.
  13. Felder, S, Chanson, H. (2012), “Free-surface Profiles, Velocity and Pressure Distributions on a
    Broad-Crested Weir: a Physical study “Free-surface Profiles, Velocity and Pressure Distributions on a
    Broad-Crested Weir: a Physical study
  14. Felder, S. Fromm, Ch. Chanson, H. (2012B), “Air entrainment and energy dissipation on a 8.9 slope stepped
    spillway with flat and pooled steps”, School of Civil Engineering, The University of Queensland,.
    Brisbane, Australia.
  15. Felder, S. Chanson, H. (2014A), Triple decomposition technique in air–water flows: application to instationary
    flows on a stepped spillway. International Journal of Multiphase Flow, 58, 139-153.
  16. Felder, S. Chanson, H. (2014B), Effects of step pool porosity upon flow aeration and energy dissipation on
    pooled stepped spillways. Journal of Hydraulic Engineering, 140(4), 04014002.
  17. Felder, S. Chanson, H. (2013A), “Air entrainment and energy dissipation on porous pooled stepped spillways”.
    Paper presented at the International Workshop on Hydraulic Design of Low-Head Structures.
  18. Felder, S. Chanson, H. (2013B), “Aeration, flow instabilities, and residual energy on pooled stepped spillways of
    embankment dams”. Journal of irrigation and drainage engineering, 139(10) 880-887.
  19. Felder, S. Guenther, Ph. Chanson, H. (2012A). “Air-water flow properties and energy dissipation on stepped
    spillways: a physical study of several pooled stepped configurations”, School of Civil Engineering, The
    University of Queensland,. Brisbane, Australia.
  20. Flow Science, (2013). “FLOW-3D user’s manual”, version 10.1. Flow Science, Inc, Los Alamos.
  21. Frizell, K.W. Renna, F.M. Matos, J. (2012), “Cavitation potential of flow on stepped spillways”. Journal of
    Hydraulic Engineering, 139(6), 630-636.
  22. Gonzalez, C. (2005), “An experimental study of free-surface aeration on embankment stepped chutes”,
    department of civil engineering, Brisbane, Australia, Phd thesis.
  23. Gonzalez, C.A. Chanson, H. (2008), “Turbulence manipulation in air–water flows on a stepped chute: An
    experimental study”. European Journal of Mechanics-B/Fluids, 27(4), 388-408.
  24. Guenther, Ph.. Felder, S. Chanson, H. (2013), “Flow aeration, cavity processes and energy dissipation on flat and
    pooled stepped spillways for embankments”. Environmental fluid mechanics, 13(5) 503-525.
  25. Hamedi, A. Mansoori, A. Malekmohamadi, I. Roshanaei, H. (2011), “Estimating Energy Dissipation in Stepped
    Spillways with Reverse Inclined Steps and End Sill”. World Environmental and Water Resources
    Congress, ASCE.
  26. Hirt, C.W. (2003), “Modeling Turbulent Entrainment of Air at a Free Surface”. Flow Science Inc.
  27. Hunt, S.L. Kadavy, K.C. (2013), “Inception point for enbankment dam stepped spillway”. J. Hydraul. Eng.,
    139(1), 60–64.
  28. Hunt, S.L. Kadavy, K.C. (2010), “Inception Point Relationship for Flat-Sloped Stepped
    Spillways”. DOI: 10.1061/ASCEHY.1943-7900.0000297.
  29. Matos, J. Quintela, A. (2000), “Air entrainment and safety against cavitation damage in stepped spillways over
    RCC dams. In: Proceeding Intl. Workshop on Hydraulics of Stepped Spillways”, VAW, ETH-Zurich, H.E.
    Minor and W.H. Hager. Balkema. 69–76.
  30. Meireles, I. Matos, J. (2009), “Skimming flow in the nonaerated region of stepped spillways over embankment
    dams”. J. Hydraul. Eng., 135(8), 685–689.
  31. Miang-liang, ZH. Yong-ming, SH. (2008), “Three dimentional simulation of meandering river basin on 3-D
    RNG k − ε turbulence model”. Journal of hydrodynamics, 20(4): 448-455.
  32. Morovati, Kh. Eghbalzadeh, A. Javan, M. (2015), “Numerical investigation of the configuration of the pools on
    the flowPattern passing over pooled stepped spillway in skimming flow regime. Acta Mech, DOI
    10.1007/s00707-015-1444-x
  33. Morovati, Kh. Eghbalzadeh, A. Soori, S. (2016), “Numerical Study of Energy Dissipation of Pooled Stepped
    spillway”. Civil Engineering Journal. Vol. 2, No. 5.
  34. Nikseresht, A.H. Talebbeydokhti, N. and Rezaei, M.J. (2013), “Numerical simulation of two-phase flow on steppool spillways”. Scientia Iranica, A 20 (2), 222–230.
  35. Peyras, L. Royet, P. Degoutte, G. (1990), “Flow and energy dissipation over stepped gabion weirs”. ASCE
    Convention.
  36. Qun, Ch. Guang-qing, D. Feu-qing, Zh. Qing, Y. (2004). “Three-dimensional turbulence numerical simulation of
    a stepped spillway overflow”. Journal of hydrodynamics, Ser. B, 1, 74-79.
  37. Relvas, A. T. Pinheiro, A. N. (2008), Inception point and air concentration in flows on stepped chutes lined with
    wedge-shaped concrete blocks. Journal of Hydraulic Engineering, 134(8), 1042-1051
  38. Sanchez, M. (2000), “Pressure field in skimming flow over a stepped spillways”. In: Proceeding Intl. Workshop
    on Hydraulics of Stepped Spillways, VAW, ETH-Zurich, H.E. Minor and W.H. Hager. Balkema,
    137–146.
  39. Sarfaraz, M. Attari, J. Pfister, M. (2012), “Numerical Computation of Inception Point Location for Steeply
    Sloping Stepped Spillways”. 9th International Congress on Civil Engineering, May 8-10. Isfahan
    University of Technology (IUT), Isfahan, Iran.
  40. Savage, Bruce M. Michael C. Johnson. (2001), “Flow over ogee spillway: Physical and numerical model case
    study.” Journal of Hydraulic Engineering 127.8:640-649.
  41. Shahhedari, H. Jafari Nodoshan, E. Barati, R. Azhdary moghadam, M. (2014). “Discharge coeficient and energy
    dissipation over stepped spillway under skimming flow regime”. KSCE Journal of Civil Engineering, DOI
    10.1007/s12205-013-0749-3.
  42. Tabbara, M. Chatila, J. Awwad, R. (2005), “Computational simulation of flow over stepped spillways”.
    Computers & structures, 83(27) 2215-2224.
  43. Thorwarth, J. (2008), “Hydraulisches Verhalten der Treppengerinne mit eingetieften Stufen—Selbstinduzierte
    Abflussinstationaritäten und Energiedissipation” [Hydraulics of pooled stepped spillways— Self-induced
    unsteady flow and energy dissipation]. Ph.D. thesis, Univ. of Aachen, Aachen, Germany (in German).
  44. WeiLin, XU. ShuJing, LUO, QiuWen, ZH. Jing, LUO. (2015), “Experimental study on pressure and aeration
    characteristics in stepped chute flows. SCIENCE CHINA. Vol.58 No.4: 720–726. doi: 10.1007/s11431-015-
    5783-6.
  45. Xiangju, Ch. Yongcan, C. Lin, L. (2006), “Numerical simulation of air-water two-phase flow over stepped
    spillways”. Science in China Series E: Technological Sciences, 49(6), 674-684.
  46. Zare, K.H. Doering, J.C. (2012), “Inception Point of Air Entrainment and Training Wall
    Characteristics of Baffles and Sills on Stepped Spillways”. DOI: 10.1061/(ASCE)HY
    .1943-7900.0000630.
  47. Zhan, J. Zhang, J. Gong, Y. (2016), “Numerical investigation of air-entrainment in skimming flow over stepped
    spillways”. Theoretical and Applied Mechanics Letters. Volume 6. Pages 139–142.
  48. Zhang, G. Chanson, H. (2016), Hydraulics of the developing flow region of stepped spillways. II: Pressure and
    velocity fields. Journal of Hydraulic Engineering, 142(7).
  49. Zhenwei, M. Zhiyan, Zh. Tao, Zh. (2012), “Numerical Simulation of 3-D Flow Field of Spillway based on VOF
    Method”. Procedia Engineering, 28, 808-812.
  50. Zhi-yong, D. Hun-wei, L.J. (2006), “Numerical simulation of skimming flow over mild stepped channel”.
    Journal of Hydrodynamics, Ser. B, 18(3) 367-371.
  51. ZhongDong, Q. XiaoQing, H. WenXin, H. António, A. (2009), “Numerical simulation and analysis of water
    flow over stepped spillways”. Science in China Series E: Technological Sciences, 52(7) 1958-1965.