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Chen, Ming

Chen, Mingdong

Wei, Penglin

English

Hydraulic Engineering Repository

Conference Paper, Published VersionChen, Ming; Wei, Penglin; Chen, MingdongNumerical Modeling of Width of Turbulent Field around aLarge Diameter Cylindrical Pier under SupercriticalReynolds Number Based on LBMZur Verfügung gestellt in Kooperation mit/Provided in Cooperation with:Kuratorium für Forschung im Küsteningenieurwesen (KFKI)Verfügbar unter/Available at: https://hdl.handle.net/20.500.11970/108603Vorgeschlagene Zitierweise/Suggested citation:Chen, Ming; Wei, Penglin; Chen, Mingdong (2016): Numerical Modeling of Width ofTurbulent Field around a Large Diameter Cylindrical Pier under Supercritical ReynoldsNumber Based on LBM. In: Yu, Pao-Shan; Lo, Wie-Cheng (Hg.): ICHE 2016. Proceedings ofthe 12th International Conference on Hydroscience & Engineering, November 6-10, 2016,Tainan, Taiwan. Tainan: NCKU.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. 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In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.Verwertungsrechte: Alle Rechte vorbehaltenNumerical Modeling of Width of Turbulent Field Around a Large Diameter Cylindrical Pier  Under Supercritical Reynolds Number Based on LBM Ming Chen, Penglin Wei, Mingdong Chen National Engineering Research Center for Inland Waterway Regulation, Chongqing Jiaotong University Chongqing, P. R. China    ABSTRACT  The width of turbulent field around a cylindrical pier, relating directly to traffic safety in bridge area, is an important parameter for the determination of bridge span. The Lattice Boltzmann Model (LBM) is used to simulate the turbulent field around a large diameter cylindrical pier in straight channel under supercritical Reynolds number. The results show that the flow structure influenced by a pier is mainly dependent on the pier’s diameter and approaching flow conditions. The corresponding coupling relationship among the maximum width of turbulent field, pier’s diameter, flow velocity, and water depth is obtained.  KEY WORDS: simulation; LBM; flow field; turbulence width; Reynolds number ; pier; bridge   INTRODUCTION  The turbulent flow region around a pier (i.e. cylindrical pier) is not safe for ships passing through bridge area; hence the turbulent width is an important parameter for the determination of bridge span. Consequently, some research of the corresponding flow characteristics and turbulent width has been developed (i.e. Breuer 2000; Hu, Shen, Cheng, and Ou 2004; Salaheldin, Imran and Chaudhry 2004; Zhuang and Liu 2007; Zu 2009). However, these achievements focus mainly on the flow with low or high Reynolds number. There are a very limited number of studies addressing some of the flow with supercritical Reynolds number (Du, You, and Li 2009). In fact, for the practical bridges constructed in rivers, the large cylindrical piers (i.e. pier’s diameter D > 5 m) are usually needed and flow with high velocity (i.e. approaching velocity U > 1 m/s) is often happened. Therefore, the current with supercritical Reynolds number is easily generated in the vicinity of piers. In this case, extensive work is required for investigating the characteristics of turbulent field past a cylindrical pier. In this study a series of numerical simulations are carried out by using LBM. The objective is to provide help to confirm turbulent width by investigating the complex flow past a large cylindrical pier.   NUMERICAL METHODOLOGY  Lattice Boltzmann Method  The Lattice Boltzmann method (LBM) is originally developed as an improved modification of the Lattice Gas Automata (LGA) to remove statistical noise and achieve better Galilean invariance (Frisch, Hasslacher, and Pomeau 1986). Due to the some advantages in obtaining easily flow details and suiting to parallel computations, the LBM is becoming increasingly popular as a reliable alternative to conventional CFD approaches. In the LBM method, the basic variable is the statistical distribution functions ( ),f tα r  with real variables, preserving by construction the conservation of mass and linear momentum. The Boltzmann transport equation of discrete velocity can be defined as   ( ) ( ) ( ) ( )1+ , - , , ,eqf t t t f t f t f tα α α α ατ ∆ + ∆ = − − r e r r r (1)  Where ( ),f tα r  is the statistical distribution functions of discrete velocities αe  at the locations r  and time t, τ  is the relaxation time parameter related to the macroscopic viscosity υ  and can be written as follows  21=2sCυτ +                                                                                               (2)  ( ),eqf tα r  is the local equilibrium function usually expressed as  ( ) ( ) ( )222 4 2, = , 1 2 2eqs s sf t w tC C Cααα αρ ⋅⋅ + + −  e ue u ur r                                         (3) 3sCC =                                                                                                  (4)  Where sC  is the speed of sound, C  is the velocity of lattice, u  is the macroscopic velocity, wα  are weighting constants for the model D3Q15 taken as   22 22 22 9, 0= 1 9,1 72, 3ew e Ce Cαα αα == =                                                                               (5)  The macroscopic density and linear momentum can be calculated as  12th International Conference on Hydroscience & Engineering Hydro-Science & Engineering for Environmental Resilience November 6-10, 2016, Tainan, Taiwan.   ( ) ( ) ( ), = , ,eqt f t f tα ααρ =∑ ∑r r r                                                             (6) ( ) ( ) ( ), = , ,eqt e f t e f tα α α ααρ =∑ ∑r u r r                                                     (7)  LBM-LES Method  In order to accurately simulate the flow characteristics with high Reynolds number, especially supercritical Reynolds number, large eddy simulation (LES) is usually introduced to LBM method. The turbulent viscosity can be computed by the smagorinsky model in LBM-LES method. Therefore  0= + tυ υ υ                                                                                                (8)  The laminar viscosity 0υ  can be written as  0 =UDReυ                                                                                                  (9)  Where U is the approaching velocity, D is the diameter of a cylindrical pier, Re is the Reynolds number. The eddy-viscosity tυ  is expressed as  ( )2=t wC sυ ∆                                                                                        (10)  Where wC  is the smagorinsky constant taken as 0.1, ∆  the filter scale, s  is the strain rate tensor of the resolved scales usually computed as  ( ) ( ), ,eqij i js e e f t f tα α α αα = − ∑ r r                                                         (11)  Grid Technology and Boundary Conditions  Some grid technologies including uniform and non-uniform grids, body-fitted grids (i.e. structured and unstructured grids) are commonly applied in LBM. If these grid methods are used in the numerical simulations of flow around a pier under supercritical Reynolds number, a huge computer resource would be needed. In the present study, the particle-gridless hybrid method is used (Yoon, Koshizuka, and Yoshiaki 1999). Some poor grid quality including distorted and skew elements can be avoided in utilizing this method. Moreover, the particle-gridless technology performs well in the treatment of near-wall zone of a cylindrical pier. This computational domain consists of a rectangular domain and is set to dimensions of (31D×10D×2D). The pier is located at the streamwise symmetry axis and 10.5D from the inlet. The initial octree lattice structure can be generated based on the input geometries. In order to adapt to the flow patterns, the lattice structure around the pier and in the wake region may be modified later by the solver. For all the simulated cases, the similar boundary conditions are employed. At the inflow plane constant velocity is imposed. A pressure-inlet with pressure profile is specified at the outflow plane. No-slip boundary conditions are used at solid walls. In the present paper, the free surface capture method is applied to predict the variation of water surface.  RESULTS AND DISCUSSION  Vertical Variation of Flow Feature  The main objective of the present study is to investigate flow past a cylindrical pier with supercritical Reynolds number in the range 0.5×107 < Re < 3.0×107. An overview of all simulations and the corresponding detailed parameters are shown in Table 1: h = water depth in the vicinity of the pier; Fr = Froude number and is defined as Fr =U/(gh)1/2, where g = acceleration of gravity. Fig. 1 shows the simulated flow field of run 5 influenced by the pier at different water depth. In the front region of the pier, the approaching flow decelerates and flow separation occurs in the horizontal and vertical planes. As a result, the acceleration of flow velocity on the sides of the pier has been developed due to the decrease of flow area. Behind the pier, in the wake region, the complex flow patterns including circulation and reversed flow as well as downward and upward flow are caused by the wake vortex. Meanwhile, the figure clearly illustrates the vertical variation of flow velocity in the immediate vicinity of the pier. There are significant differences for flow patterns at various flow depth due to the direct result of gravity and complex three-dimensional flow structure. The current near the bottom is not strongly disturbed by the pier as compared to that at the other water depth. This is because the flow velocity near the bottom is dragged down by the shear stress generated from the effect of near-wall. Moreover, it also can be seen from Fig. 1 that the pier has the most impact on the flow field about at the layer y/h = 0.85 (see Fig. 1(e)) where y is the distance from the bottom. This simulated results of the present work are in close agreement with the experimental data of Hu, Zu, Cheng, Li, and Wang (2009). Therefore, the following results and discussion are concentrated on the flow feature at the layer y/h = 0.85.  Table 1 Parameters for numerical simulations run D (m) U (m/s) h (m) Re (×107) Fr 1 5 1 5 0.5 0.14 2 10 1.5 5 1.5 0.21 3 5 2 5 1.0 0.29 4 10 2.5 5 2.5 0.36 5 10 3 5 3.0 0.43 6 5 3.5 5 1.75 0.50   (a) 0.2 h   (b) 0.4 h 12th International Conference on Hydroscience & Engineering Hydro-Science & Engineering for Environmental Resilience November 6-10, 2016, Tainan, Taiwan.   (c) 0.6 h   (d) 0.8 h   (e) 0.85 h   (f) 0.9 h Fig. 1 Flow field past a cylindrical pier (run 5)  Turbulence Width As discussed before, the velocity distribution on the horizontal and vertical planes is obviously changed by the pier. In fact, the lateral velocity vz on the horizontal plane has more impact on the safety of ship maneuvering than the streamwise velocity vx. Besides, the vz is also a main factor to determine the bridge span in bridge area. As a consequence, at the lateral central axis of the pier, the maximum distance between the centre of the pier and the stagnant point of vz is defined unilateral turbulence width. Therefore, the total width B is two times the unilateral turbulence width. As shown in figures 2 and 3, the velocity change caused by the pier is mostly related to the parameters such as pier’s diameter D, flow velocity U and water depth h. It indicates that the relative turbulence width B/D has a close relationship with Froude number Fr =U/(gh)1/2. Moreover, the pier’s strong behavior of disturbing the vector field and streamlines around the pier with large Froude number can be observed in the figures. It implies that the relative turbulence width increases with increasing Froude number. In Fig. 4, comparison between the predicted data of the present study and the results already published shows that there is a discrepancy between the B/D calculated by LBM and that measured by Hu, Shen, Cheng, and Ou (2004). The increase of turbulence width near the pier is more pronounced in the measured results of Hu, Shen, Cheng, and Ou (2004) than that in the simulated data. Comparing with the results measured by Zhuang and Liu (2007), the value of width predicted  by LBM in the present work is slightly larger. For example, Fr = 0.43 with run 5, the turbulence width of Zhuang and Liu (2007) extends approximately two pier’s diameter, whereas the calculated value increases slightly to 2.5 times pier’s diameter. However, from this figure the LBM solution is consistent with the value reported by Zu (2009). Based on the simulated data, a fitted curve with a high correlation coefficient (r=0.9989) can be plotted in Fig. 5 and the corresponding computational formula for turbulence width can be written in the form  0.674.42869 rB D F=                                                                               (12)  Applying Eq. 12, the turbulence width past a large diameter cylindrical pier in a straight channel can be calculated and provides an important parameter to determine bridge span. As a matter of fact, there are other factors to affect the turbulence width, i.e., cross section type of a pier, approaching flow direction and river pattern. Therefore, the further studies associated with pier’s behavior of influencing the flow field with different conditions are deserved to carry out.   (a) Fr=0.21   (b) Fr=0.36   (c)Fr=0.50 Fig. 2 Flow field past a cylindrical pier with different Froude number 12th International Conference on Hydroscience & Engineering Hydro-Science & Engineering for Environmental Resilience November 6-10, 2016, Tainan, Taiwan.    (a) Fr=0.21   (b) Fr=0.36   (c) Fr=0.50 Fig. 3 Flow streamlines past a cylindrical pier with different Froude number   Fig. 4 Computed turbulence width in comparison with Hu’s data (2004), Zu’s work (2009) and Zhuang’s work (2007)  CONCLUSION  In this study, numerical simulations using LBM method have been conducted to investigate the turbulence characteristics of flow past a large diameter cylindrical pier with supercritical Reynolds number. The results show that the relative turbulent width around a pier increases with increasing Froude number. Meanwhile, the corresponding function relationship between them is established. Furthermore, the achievements can effectively contribute to the determination of bridge span.  ACKNOWLEDGMENTS  This work is supported by the National Natural Science Foundation of China (Grant No. 51509027) and Foundation of Chongqing Municipal Commission of Education of China (Grant No. KJ1400322). The authors gratefully appreciate the support.  REFERENCES  Breuer, M. (2000). A challenging test case for large eddy simulation: high Reynolds number circular cylinder flow. International Journal of Heat and Fluid Flow, 21, 648-654. Du, Q.G., You, Y.X. and Li, W. (2009). Three-dimensional numerical simulations of the viscous flow past a large diameter cylinder of the spar platform under supercritical reynolds number. Journal of Shanghai Jiaotong University, 43, 1267-1272. (in Chinese) Frisch, U., Hasslacher, B. and Pomeau, Y. (1986). Lattice-gas automata for the navier-stokes equation, Physical review letters, 56, 1505-1508. Hu, X.Y., Shen, X.X., Cheng, Y.Z. and Ou, Y.F. (2004). Experimental investigation on width of superficial eddy area around cylindrical pier. Journal of Changsha University of Science and Technology(Natural Science), 1, 39-42. (in Chinese) Hu, X.Y., Zu, X.Y., Cheng, Y.Z., Li, Y.F. and Wang, Q.Y. (2009). Experimental study of lateral turbulent flow width at round ended pier. Hydro-Science and Engineering, 3, 8-13. (in Chinese) Salaheldin, T.M., Imran, J. and Chaudhry, M.H. (2004). Numerical modeling of three-dimensional flow field around circular piers. Journal of Hydraulic Engineering, 130, 91-100. Yoon, H.Y., Koshizuka, S. and Yoshiaki (1999). Particle-gridless hybrid method for incompressible flows. International journal for numerical methods in fluids, 30, 407-424. Zhuang, Y. and Liu, Z.Y. (2007). Experimental investigation on turbulent flow width around bridge pier. Navigation of China, 3, 5-9,44. (in Chinese) Zu, X.Y. (2009). Experimental study of turbulent flow width and the characteristic of the turbulence around round-ended pier. Master’s thesis, Changsha University of Science and Technology, Changsha, China. (in Chinese)   12th International Conference on Hydroscience & Engineering Hydro-Science & Engineering for Environmental Resilience November 6-10, 2016, Tainan, Taiwan.  

Numerical Modeling of Width of Turbulent Field around a Large Diameter Cylindrical Pier under Supercritical Reynolds Number Based on LBM

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Numerical Modeling of Width of Turbulent Field around a Large Diameter Cylindrical Pier under Supercritical Reynolds Number Based on LBM

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