Direct Numerical Simulation Of Particle Saltation In Turbulent Channel Flow

Transcription

1 City University of New York (CUNY) CUNY Academic Works International Conference on Hydroinformatics Direct Numerical Simulation Of Particle Saltation In Turbulent Channel Flow Chunning Ji Ante Munjiza Eldad J. Avital John J. R. Williams Follow this and additional works at: htt://academicworks.cuny.edu/cc_conf_hic Part of the Water Resource Management Commons Recommended Citation Ji, Chunning Munjiza, Ante Avital, Eldad J. and Williams, John J. R., "Direct Numerical Simulation Of Particle Saltation In Turbulent Channel Flow" (2014). CUNY Academic Works. htt://academicworks.cuny.edu/cc_conf_hic/413 This Presentation is brought to you for free and oen access by CUNY Academic Works. It has been acceted for inclusion in International Conference on Hydroinformatics by an authorized administrator of CUNY Academic Works. For more information, lease contact

2 11 th International Conference on Hydroinformatics HIC 2014, New York City, USA DIRECT NUMERICAL SIMULATION OF PARTICLE SALTATION IN TURBULENT CHANNEL FLOW CHUNNING JI (1), ANTE MUNJIZA (2), ELDAD AVITAL (2), JOHN WILLIAMS (2) (1): State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Weijin Road, Tianjin, , China (2): School of Engineering & Materials Science, Queen Mary, University of London, Mile End Road, London, E1 4NS, United Kingdom This aer reorts on the numerical investigation of article saltation in a turbulent channel flow having a rough bed consisting of 2-3 layers of densely acked sheres. The Shield s Function is which is just above the sediment entrainment threshold to give a bed-load regime. The alied methodology is a combination of three technologies, i.e., the direct numerical simulation of turbulent flow, the combined finite-discrete element modelling of the deformation, movement and collision of the articles, and the immersed boundary method for the fluid-solid interaction. It is shown that the resence of entrained articles significantly modifies the rofiles of flow velocity and turbulent intensities in the vicinity of a rough-bed. Statistical features of article translational and angular velocities, together with sediment concentration and volumetric flux density rofiles, are resented. INTRODUCTION In the bed-load layer, sediment may be transorted via three modes: sliding, rolling or saltation and the last one is considered to be the most dominant [1]. Particle saltation in turbulent channel flow has been exerimentally investigated for several decades. Many statistical features, such as saltation length and height, mean article stream-wise velocity, incidence and take-off angles at collision, dynamic friction coefficient, etc., were reorted in the work of van Rijn [2], Abbott & Francis [3], Niño & García [4], Niño et al. [5], Lee et al. [6,7]. However, higher-order statistics of the article translation and rotation, the hydrodynamic forces and moments acting on the articles and the statistical features of the article-laden horizontal turbulent channel flow have not been studied adequately due to the fact that they are very difficult, if not imossible, to be measured directly. Besides exerimental studies, several different theoretical models were resented by Lee et al. [6], Osanloo et al. [8] and Niño & García [1]. These models are based on Newton s second law and some arameters, such as drag and lift coefficients, restitution and friction coefficients, incident and take-off angles, etc., are determined exerimentally and reasonable results on the first-order statistics were obtained. However, the fluctuation in article trajectories caused by the turbulent coherent structures and the diversity of take-off angles owing to the random acking arrangement of articles forming the rough bed were not reroduced.

3 With the develoment of high erformance comuting technology and numerical schemes, sediment transort simulation in which the articles are well-resolved by grids resents an effective way not only to investigate the interaction between article motions and near-bed turbulence structures, but also to show the dynamic rocess of article saltation in detail in which the hydrodynamic forces and moments, collision between articles and ressure distributions on the article surface are investigated. Chan-Braun et al. [9] numerically investigated the hydrodynamic forces and torques on sherical articles fixed on a bed consisting of one layer of sheres in a square arrangement using a combination of direct numerical simulation (DNS) for the turbulent flow and the immersed boundary method (IBM) for the fluid-solid interactions. Chan-Braun et al. [10] and Kidanemariam et al. [11] further investigated the statistical features of finite-size heavy articles transort in turbulent oen channel flow. Shao et al. [12] carried out a fully resolved DNS of article-laden turbulent flow in a horizontal channel by using the direct-forcing fictitious domain method which is closely related with IBM. Ji et al. [13] studied the interaction between turbulent coherent structures and article entrainment by couling DNS and the IBM together with the combined finite-discrete element method (FDEM) which takes into account article deformability, frictional contact forces, and frictional and lastic-loss of energy. Particle movement, hydrodynamic forces and turbulent flow statistics at the inciient of entrainment were reorted. These results contributed greatly to the understanding of the underlying hysical mechanisms of article transort in turbulent channel flow. This aer further investigates the subsequent continuous saltation after the articles have been entrained by the turbulent coherent structures. It reorts on the statistical features of article translational and angular velocities, together with sediment concentration and volumetric flux density rofiles. METHODOLOGY The alied methodology is three-fold. The code used to simulate the turbulent flow is an inhouse comutational fluid dynamics (CFD) C code called CgLes [14]. It is a 3D DNS/LES (large eddy simulation) code with second order accuracy in both time and sace. The immersed boundary method, first introduced by Peskin [15] in the simulation of blood flow around the flexible leaflet of human heart, was incororated into CgLes to model the interaction between the flow and moving articles. The main advantage of the IBM is associated with its inherent simlicity in treating flows which have solids with moving boundaries. To imrove the accuracy of the IBM, an iterative direct-forcing IBM which was introduced in our revious work [16] is alied in this study. To simulate the movement and collision of articles, we couled CgLes with another in-house combined finite-discrete element method C code develoed by Munjiza et al. [17]. This code comrises a set of C libraries incororating the latest breakthroughs in discontinua simulations. It is caable of modelling the deformation, movement and collision of millions of articles of different shae and size. STATISTICS OF TURBULENT FLOW AND PARTICLE TRANSPORTATOIN Problem descrition In this study, we considered sediment transort in a fully develoed turbulent oen channel flow having a rough bed consisting of 2-3 layers of densely acked sheres (see Fig. 1). The total number of sheres was 6355 and the rough bed was water-worked meaning that the most

4 Figure 1. Channel geometry. exosed ones were removed. No-sli boundary conditions were used on both the bed and shere surfaces and the to boundary was set as a free-sli hard lid. Periodicity was imosed in both the stream-wise and san-wise directions. The following list summarizes the simulation arameters: Comutational domain sizes in x, y and z directions: 6d d 4d Number of grid nodes in x, y and z directions: Grid sacing in wall units: x y z 5.4 Kolmogorov length scale in wall units: 3.3 Particle diameter: D 0.1d Geometric height of roughness elements: k = 0.3d Equivalent roughness height: ks 0.242d Effective bed location: yb 0.252d Effective channel deth: h d yb 0.748d Density ratio: ss s / f 2.65 Shields function: w / (( s f ) gd) Reynolds number: Re h uh / 647 Particle Reynolds number: Re D ud / 86.5 Equivalent roughness height in wall units: k s ksu / 209 Reynolds number based on bulk velocity: Re b Uh b / 6417 Reynolds number based on velocity on the to surface: Re c Uh c / In the above, d is the channel deth, is the fluid kinematic viscosity, g is the gravitational acceleration, U b and U c are the bulk velocity and the velocity on the to surface resectively, s and f are the densities of article and fluid resectively, u and w are the friction velocity and the shear stress at y b resectively, suerscrit indicates quantities in wall units l / u. Note that a different definition of u has been alied in this study comared with that of Ji et al. [16] which, consequently, makes Re h, Re D and k s smaller. To facilitate the following analysis and discussion, the following terminology is adoted: single-hase flow indicates the turbulent channel flow over the fixed rough-bed and two-hase flow denotes the turbulent channel flow with sediment transort. The fluid hase of the twohase flow reresents the flow in the whole comutational domain excluding the volume occuied by sheres regardless of their state of motion whilst the disersed hase of the twohase flow is the moving sheres. Furthermore, a vertical coordinate Y y yb is adoted, where y is the vertical coordinate and y b is the effective bed location.

5 Statistical features of the two-hase turbulent flow Figure 2 shows the lane (binned) and time-averaged stream-wise velocity of the fluid (disersed) hase of the two-hase flow, together with that of the single-hase flow for comarison. Here, the lane averaging of Eulerian quantities on the DNS grids was erformed over the fluid-occuied domain in the wall-arallel lanes and the binned averaging of the Lagrangian quantities related to articles was erformed over the articles with their center in the wall-arallel bins with a thickness of D/10. As seen in Figure 2, the velocity rofile of the fluid hase is retarded above the highest crests of the roughness elements of the single-hase flow case (referred to as P1, hereafter), comaring with that of the single-hase flow, due to the resence of the entrained articles. Below this osition, the flow is accelerated because the moving articles cause less momentum exchange with the fluid hase. The mean stream-wise velocity of the disersed hase is always smaller than that of the fluid hase and shows a quasilinear rofile although there are small fluctuations in the to region of the bed-load layer due to the samling of an insufficient number of articles visiting there. The height of the bed-load layer, calculated as the distance from the effective bed location of the single-hase flow case (referred to as P2, hereafter) to the highest osition that moving articles center can reach, is aroximately 0.29h (2.1D). The mean velocity rofile of the fluid hase verifies the logarithmic law-of-the-wall above Y / h 0.29, as shown in the inset of Figure 2. However, the transition from a concave curve to a convex one as shown in the mean velocity rofile of the single-hase flow is absent from the mean velocity rofile of the fluid hase. Figure 2. Comarison of the mean stream-wise velocity rofiles. Figure 3. Comarison of turbulence quantities between the single and two-hase flow cases.

6 Figure 3 shows the turbulence quantities for both the single and two-hase flow cases. The modifications to the turbulence quantities due to the resence of the disersed hase is clearly seen, esecially near and below P1. Secifically, the near-wall eak of the stream-wise comonent urms / u of the fluid hase is smoothed and shifted downward and also decreases slightly in magnitude comared with that of the single-hase flow. This is in agreement with the exerimental results of Kiger & Pan [18] and the numerical results of Chan-Braun et al. [10] and Shao et al. [12]. However, the fluid velocity fluctuations deviate only marginally from the single hase counterart in the numerical results of Kidanemariam et al. [11] which is attributed to their small solid volume fraction of 0.05%. It should be noted that the near-wall eak values of urms / u for the single and two-hase flow cases of the resent study are aroximately 2.1 and 2.0, resectively, which are much lower than the value of 2.7 for the article-free and article-laden cases in Kidanemariam et al. [11], owing to the near-wall coherent streaky structures of turbulent flow being destroyed by the large article size and solid volume fraction in the resent study. This lower-eak trend is also shown in the results of Shao et al. [12] and becomes more ronounced with increasing article size and solid volumetric fraction. The sanwise velocity fluctuations of the two-hase flow are only marginally different from the singlehase case. However, the vertical velocity fluctuations show a erceivable increase which could be the result of high-seed articles in the outer region landing and colliding on the rough-bed and introducing small-scale vortices in the near-wall region. Below P2, the turbulence intensities of the single-hase flow show small fluctuations, while the ones of the two-hase flow are smoother. In contrast to their counterarts of the fluid hase, the turbulence intensities of the disersed hase in the vertical and san-wise directions are almost identical in the near-wall region where the greater occurrence of collisions leads to a more isotroic distribution of shere fluctuation energy in the vertical and san-wise directions and is in agreement with the findings of Chan-Braun et al. [10] and Kidanemariam et al. [11]. The stream-wise comonent is generally larger than the other two and, above Y / h 0.2, large fluctuations are observed in all three comonents due to insufficient number of samles. All three turbulence intensities of the disersed hase are consistently smaller than their fluid hase counterarts and is a result that does not agree with the findings of Chan-Braun et al. [10] who found that the vertical velocity fluctuations of the disersed hase are larger than their fluid hase counterarts in the near-wall region, and also the findings of Kidanemariam et al. [11] who found that both vertical and sanwise velocity fluctuations of the disersed hase are larger than their fluid hase counterarts. This discreancy could be due to the lower solid-fluid density ratio, i.e., ss s / f 1.7, and the smaller grain-size in their study - lighter and smaller articles are more easily accelerated by the surrounding flow, and their motion thus more turbulent. Statistics of translation and rotation of the entrained articles Figure 4 shows the binned and time-averaged velocity comonents of the disersed hase. The mean vertical and san-wise velocity rofiles are almost zero throughout the channel deth, desite the small fluctuations observed in the to region of the bed-load layer. The volumetric flux density function q and the sediment concentration C are also resented in Figure 4 in which q and C are normalized by gd and C s, resectively, where Cs 0.63 is the average sediment concentration of the static rough-bed. The flux density shows a symmetric rofile and eaks at P1. Beyond that, the flux density function and the sediment concentration decrease exonentially with height and agrees with the numerical results of Durán et al. [19].

7 3 The non-dimensional volume flux qs / ( s / f 1) gd is which agrees well with exerimental data and several well-known bed-load transort equations values, ranging from 0.01 to 0.04, at comiled by Wiberg & Smith [20] (refer to Fig. 7 of their work). The volumetric sediment flux q s is calculated according to 3 qs D /(6 A) u, where A is the channel area and u is the sum of mean velocity over all sheres. It should be noted that U indicates the binned and time-averaged stream-wise velocity of the disersed hase whereas u reresents the time-averaged stream-wise velocity of an individual article. Figure 5 shows the binned and time-averaged angular velocities, normalized by u / D, of the disersed hase. The mean stream-wise and vertical angular velocities, i.e. x and y, are generally zero excet fluctuations in the to region of the bed-load layer, while the one in the san-wise direction z decreases with height and reaches a negative lateau with D z / u 2.2 before it lummets at Y / h 0.23 owing to the insufficient samling. The negative san-wise angular velocity indicates that the entrained articles redominately rotate clockwise in the x-y lane (flow is from left to right). All standard deviations of the angular velocities show a similar trend excet that the sanwise comonent, z, have a larger value see Figure 6. Below the effective bed location y x y x, while beyond that. This is due to the fact that the y-rotation of articles is caused by the relative velocities in z and x directions of contacting articles while the x-rotation is related with those in y and z directions and the fact that the mean velocity and its standard deviation in x direction are much larger than those in y and z directions see Figures. 3 and 4. Figure 4. Mean article velocity rofiles, normalized sediment concentration and normalized volumetric flux density of the disersed hase. Figure 5. Mean angular velocity of the disersed hase.

8 Figure 6. Angular velocity standard deviation of the disersed hase. CONCLUSIONS In this study, article saltation in a turbulent channel flow has been numerically investigated using a methodology which combines the DNS of turbulence flow, the FDEM of article dynamics and the IBM for the fluid-solid interaction. Statistics of the article-laden turbulent flow, article translation and rotation, together with the sediment concentration and the volumetric flux density rofiles, have been resented. It was found that the resence of the disersed hase significantly modifies the statistical features of the turbulent flow in the vicinity of the rough-bed. For examle, our numerical results have showed a distinct velocity lag between the single and two-hase mean stream-wise flow rofiles and the reason has been attributed to a larger article size and solid volume fraction. The articles mean stream-wise velocity shows a quasi-linear rofile, while their mean angular velocity in the san-wise direction is almost constant. ACKNOWLEDGEMENT This work was suorted by a Marie Curie International Incoming Fellowshi within the 7th Euroean Community Framework Programme (Grant No. PIIF-GA ). The first author acknowledges the financial suort of the Science Fund for Creative Research Grous of the National Natural Science Foundation of China (Grant no ), National Natural Science Foundation of China (Grant Nos and ), and Natural Science Foundation of Tianjin (Grant no. 12JCQNJC02600). We thank UKTC for HECToR comuter time and facilities. REFERENCES [1] Niño Y. and García M., Gravel saltation: 2. Modeling, Water Resour. Res., Vol. 30, No. 6, (1994), [2] van Rijn L. C., Sediment transort, art I: bed load transort, J. Hydraul. Eng.-ASCE, Vol. 110, No. 10, (1984), [3] Abbott J. E. and Francis J. R. D., Saltation and susension trajectories of solid grains in a water stream, Phil. Trans. R. Soc. Lond. A, Vol. 284, (1977),

9 [4] Niño Y. and García M. H., Exeriments on saltation of sand in water, J. Hydraul. Eng. - ASCE, Vol. 124, (1998), [5] Niño Y., García M. and Ayala L., Gravel saltation: 1. Exeriments, Water Resour. Res. Vol. 30, No. 6, (1994), [6] Lee H. Y., Chen Y. H., You J. Y. and Lin Y. T., Investigations of continuous bed load saltating rocess, J. Hydraul. Eng. -ASCE, Vol. 126, No. 9, (2000), [7] Lee H. Y., You J. Y. and Lin Y. T., Continuous saltating rocess of multile sediment articles, J. Hydraul. Eng. -ASCE, Vol. 128, No. 4, (2002), [8] Osanloo F., Kolahchi M., McNamara R. S. and Herrmann H. J., Sediment transort in the saltation regime, Physical Review E, Vol. 78, No. 1, (2008), [9] Chan-Braun C., Garcia-Villalba M. and Uhlmann M., Force and torque acting on articles in a transitionally rough oen channel flow, J. Fluid Mech., Vol. 684, (2011), [10] Chan-Braun C., Garcia-Villalba M. and Uhlmann M., Direct numerical simulation of sediment transort in turbulent oen channel flow. High Performance Comuting in Science and Engineering'10, (2011), [11] Kidanemariam A.G., Chan-Braun C., Doychev T. and Uhlmann M., Direct numerical simulation of horizontal oen channel flow with finite-size, heavy articles at low solid volume fraction, New J. Phys., Vol. 15, No. 2, (2013), [12] Shao X., Wu T. and Yu Z., Fully resolved numerical simulation of article-laden turbulent flow in a horizontal channel at a low Reynolds number, Journal of Fluid Mechanics, Vol. 693, (2012), [13] Ji C., Munjiza A., Avital E., Ma J. and Williams J. J. R., Direct numerical simulation of sediment entrainment in turbulent channel flow, Physics of Fluids, Vol. 25, No. 5, (2013), [14] Thomas T. G. and Williams J. J. R., The develoment of a arallel code to simulate skewed flow over a bluff body, J. Wind Eng. Ind. Aero., Vol , (1997), [15] Peskin C. S., Flow atterns around heart valves: a numerical method, J. Com. Phys., Vol. 10, (1972), [16] Ji C., Munjiza A. and Williams J. J. R., A novel iterative direct-forcing immersed boundary method and its finite volume alications, J. Com. Phys., Vol. 231, No. 4, (2012), [17] Munjiza, A. A., Knight, E. E. and Rougier, E., Comutational mechanics of discontinua, John Wiley & Sons, (2011). [18] Kiger K. T. and Pan C., Susension and turbulence modification effects of solid articulates on a horizontal turbulent channel flow, J. Turbul., Vol. 3, (2002), N19. [19] Durán O., Andreotti B. and Claudin P., Numerical simulation of turbulent sediment transort, from bed load to saltation, Phys. Fluids, Vol. 24, (2012), [20] Wiberg P. L. and Smith J. D., Model for calculating bed load transort of sediment, J. Hydraul. Eng., Vol. 115, (1989),