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Numerical simulation of scour around a submarine pipeline using computational fluid dynamics and discrete element method
Abstract
Scour under a submarine pipeline can lead to structural failure; hence, a good understanding of the scour mechanism is paramount. Various numerical methods have been proposed to simulate scour, such as potential flow theory and single-phase and two-phase turbulent models. However, these numerical methods have limitations such as their reliance on calibrated empirical parameters and inability to provide detailed information. This paper investigates the use of a coupled computational fluid dynamics-discrete element method (CFD-DEM) model to simulate scour around a pipeline. The novelty of this work is to use CFD-DEM to extract detailed information, leading to new findings that enhance the current understanding of the underlying mechanisms of the scour process. The simulated scour evolution and bed profile are found to be in good agreement with published experimental results. Detailed results include the contours of the fluid velocity and fluid pressure, particle motion and velocity, fluid forces on the particles, and inter-particle forces. The sediment transport rate is calculated using the velocity of each single particle. The quantitative analysis of the bed load layer is also presented. The numerical results reveal three scour stages: onset of scour, tunnel erosion, and lee-wake erosion. Particle velocity and force distributions show that during the tunnel erosion stage, the particle motion and particle–particle interactive forces are particularly intense, suggesting that single-phase models, which are unable to account for inter-particle interactions, may be inadequate. The fluid pressure contours show a distinct pressure gradient. The pressure gradient force is calculated and found to be comparable with the drag force for the onset of scour and the tunnel erosion. However, for the lee-wake erosion, the drag force is shown to be the dominant mechanism for particle movements.
... To the authors' knowledge, the CFD-DEM coupling model was first used in the analysis of the scour around a single pipeline by Zhang et al. (2015b). Later, based on the coupling model, the onset of scour, tunnel erosion and lee wake erosion were analyzed by Yang et al. (2018). The study emphasized that the single-phase models, in which the interactions of the particles cannot be considered, are inadequate to simulate the whole scour process. ...
... The behavior of the fluid is simulated by the Reynolds Averaged Navier-Stocks (RANS) equation with SST k − ω turbulence closure. The model includes the continuity and momentum equations are shown as below (Goniva et al., 2010;Yang et al., 2018;Zhu et al., 2021). ...
... The scour depth computed by Schiller Naumann model is smaller, while the other three models' results are similar. Generally, Di Felice model are always used in the previous researches of pipeline scouring and the results have been validated by experiment data (Hu et al., 2019;Yang et al., 2018;Zhang et al., 2015a). Di Felice model, Gidaspow model or Koch Hill model are suggested to be used in the simulations of the scour process around the pipelines. ...
Scour is a key issue affecting the service life of submarine pipelines. Understanding the scour process and scour mechanism around the pipelines is crucial for developing the reasonable and effective scour prevention measures. In this paper, the computational fluid dynamics and coarse-grained discrete element method (CFD-CGDEM) is used to simulate the scour process around the pipeline. The influence of the drag force model which is an important factor for analyzing the scour process of the submarine pipelines is investigated, and the results indicate that the choice of the drag force model has less influence on the simulation results. The characteristic of the CG method is studied considering different CG factors, particle radius and flow velocities. The results show that the CG method which can reduce the large need of computing resources and excessive computation time does not bring large deviation to the results, especially the scour depth beneath the pipelines. The evolution of the scour depth obtained by the CFD-CGDEM model agree well with the experimental results. A reasonable scour phenomenon around the pipeline is shown by the numerical simulation, which implies that the CFD-CGDEM model established in present study can simulate the scour process around the pipelines well.
... The CFD and DEM coupled models have been applied to geotechnical engineering problems, e.g., the seepage flow in soils, sediment transport, and sand pile formation [34][35][36]. Simulations for the scour process around a subsea pipeline were recently carried out, and the applicability of the CFD and DEM coupled model was discussed [37,38]. Zhang et al. [37] used the CFD and DEM coupled model to investigate the onset of scour, and the motion of each particle was considered in detail. ...
... Zhang et al. [37] used the CFD and DEM coupled model to investigate the onset of scour, and the motion of each particle was considered in detail. Yang et al. [38] applied the CFD and DEM coupled model to simulate the scour process and provided detailed information to better understand the scour mechanism below a pipeline. Hu et al. [39] adopted the CFD and DEM coupled model to study the effect of gap ratio and incipient velocity on a local scour around two pipelines in tandem and revealed that a scour development was closely related to the individual particle behavior. ...
... However, studies on local scour around the pipeline are still insufficient. More research on improved CFD and DEM coupled models is needed to overcome existing constraints, such as high computational cost, inaccuracies, due to the use of spherical particles, and grid dependency [21,28,37,38]. Recently, Song and Park [33] presented an improved unresolved CFD and DEM coupled solver for particulate flow. ...
In this paper, numerical studies were carried out on scour around a subsea pipeline. A coupled solver between computational fluid dynamics (CFD) and discrete element method (DEM) was selected to simulate fluid flow and particle interactions. To select and validate the numerical model parameters in the solver, angles of repose and incipient motion were simulated. From the validation studies, the selected coefficient of rolling friction with spherical particles could predict the behavior of non-spherical particles. The fluid flow around the subsea pipeline was simulated, and the motion of individual soil particles was tracked. Particle motions were generated by the drag force, due to a high velocity. Three scour development process, such as onset of scour, tunnel erosion, and lee-wake erosion, were studied and discussed. The scour depth evolution showed good agreement with the experimental data. It was confirmed that the selected solver, with numerical model parameters, predicted the scour process around a subsea pipeline well.
... Therefore, the mechanism of occurrence and expansion of the scour cavity, its depth and the factors affecting it have received considerable attention from researchers and designers. Yang et al. (2018) [4] divided the process of pipeline scour formation and development into three parts: scour initiation, tunnel erosion, and eddy erosion. When a pipe is placed in the seabed or riverbed, vortices are formed around the pipe. ...
... Therefore, the mechanism of occurrence and expansion of the scour cavity, its depth and the factors affecting it have received considerable attention from researchers and designers. Yang et al. (2018) [4] divided the process of pipeline scour formation and development into three parts: scour initiation, tunnel erosion, and eddy erosion. When a pipe is placed in the seabed or riverbed, vortices are formed around the pipe. ...
... As Dey and Singh (2008) [3] mentioned, when the water depth was more than 5 times the diameter of the pipe ( > 5 ), scour under the pipe would be independent of water depth. In all the experiments in this study > 5 , term was omitted from equation (4). Also, since during the tests, the bed material, the geometric standard deviation of sediments and the bed slope were also constant, the and S parameters could be removed from equation (4). ...
This study, experimentally investigated scouring around submarine pipelines grouped into (1) two pipes with the same diameter, (2) two pipes with different diameters, (3) three pipes with the same diameter, and (4) three pipes with different diameters. Experiments were conducted in a flume 13 m long, 0.46 m wide, and 1 m deep, with a flow discharge of 122 lit/s. To validate the experimental findings, a number of single-pipe tests were performed and the test results of single-pipe and double-pipe with the same diameter were compared with the results of similar tests done by Westerhorstmann et al. (1992) , Zhang et al. (2017) and Dey and Singh (2008) . Results of this study showed that for minimum scour depth the optimal combination of two-and three-pipe systems with the same diameter was related to a distance of G=0.5D from each other, where D is the diameter of the pipe. For two pipes with different diameters, the minimum scour was when the pipes were exposed to the flow in a descending manner and had a distance of G=0.5D' from each other, D' indicates the ratio of large diameter to small diameter (DB/DS) equal to 1.25 and 1.6, D'=DS and for DB/DS=2, D '=DB. It was also observed that the development of scour holes in the case of three pipes with different diameters was similar to the case of two pipes with different diameters.
... They showed favorable results with comparable accuracy when compared to the experimental data of Mao (1987) for pipeline scour in the live-bed regime (Mathieu et al., 2019). Two-phase flow models for pipeline scour based on Lagrangian point-particle approach are also available, such as the coupled Computational Fluid Dynamics-Discrete Element (CFD-DEM) (e.g Yang et al., 2018;Zhang et al., 2015) and Smoothed Particle Hydrodynamics (SPH) (e.g. Zanganeh et al., 2012) models. ...
... With the use of semiempirical relationships to provide both hydrodynamic force and torque acting on each particle (fluid/sediment), this approach can provide more detailed information on the particle interactions and dynamics compared to the Eulerian-Eulerian models. However, the accuracy is highly dependent on the number of particles, resulting in extremely high computational cost (Yang et al., 2018). ...
Current-induced scour around a submarine pipeline during onset and tunnel erosion are investigated in both
clear-water and live-bed regimes using an Eulerian–Eulerian two-phase model for sediment transport. The
Hybrid Fictitious Domain-Immersed Boundary (HFD-IB) method is adopted to simulate the pipeline structure.
The model is validated against two published experimental data: (1) flow past a pipeline near a rigid bed and
(2) scour around a pipeline over a sand-bed, showing favorable results for the flow and scour patterns around
the pipe. The driving mechanisms of the onset and tunnel erosion are investigated by examining the detailed
fluid–sediment interactions around the pipe in both regimes. The driving mechanisms for the onset and tunnel
erosion are found similar in both regimes, except their time and magnitude scales. The onset is triggered by
the piping mechanism induced by the upstream–downstream pressure gradient beneath the pipe. Meanwhile,
the jet flow is the driving mechanism for the tunnel erosion. The simulated live-bed condition shows a higher
upstream–downstream pressure gradient beneath the pipe, faster piping mechanism, more intense jet flow
velocity and sediment flux compared to the clear-water condition. The model well capture these underlying
mechanisms, suggesting its promising capability as a predictive tool for scouring.
... Discrete element method (DEM) refers to a class of computational models that are widely used to model the mechanical behaviors of particulate systems. The method was originally introduced by Cundall and Strack [1] for geomaterials, and has since been applied and gained tremendous popularity in various engineering disciplines (e.g., [2][3][4][5][6][7][8] ) to study particulate systems. In DEM, every particle is explicitly modeled in the Lagrangian framework using particle models, with the interactions between particles described by contact models and the motion and kinematics of particles governed by the Newton-Euler equations [9,10] . ...
... where the three terms on the left side come from Eqs. (13) , (8) , and (B.2) , respectively. By observing Eq. (19) , it is found that u (2) x is proportional to the Young's modulus and is nonlinearly correlated with the Poisson's ratio and term R/a . ...
The Hertzian contact model is prominent for characterizing the contact behaviors of particles in three dimensions (3D), while its two-dimensional (2D) version in the tangential direction has not been well-established yet. In this work, a semianalytical Hertzian frictional contact model in 2D is developed, with an analytical solution for the normal contact behavior and a semianalytical solution with a variable penalty factor for the tangential contact behavior. Numerical analyses with finite element simulations are performed to characterize the penalty factor and validate the proposed contact model. The results show that the penalty factor increases with the contact width and Poisson’s ratio based on which an empirical equation of the penalty factor is provided. Using the penalty factor calculated from the empirical equation, the contact behaviors evaluated from the proposed contact model match fairly well with those of finite element simulations. The proposed contact model is implemented in a discrete element code. Quantitative analyses of a bi-axial compression test on polydispersed particles demonstrate the stability and effectiveness of the proposed contact model. The proposed contact model could be useful to the computational mechanics of particles in 2D and parallel-axis cylinders with strip contacts in 3D.
... There are many examples of applications, for instance the circular piers in a river, marine piling, marine riser, pipeline, and cable on seabed and etc. There has been numerous investigations on this flow field in order to understand the behaviour of water flow over a circular cylinder to reduce drag force (Morison et al., 1950;Huang et al., 2011;Zhou et al., 2015) and effect of scouring (Elnikhely, 2017;Hamidi and Siadatmousavi, 2017;Jiecheng, 2018). Huang et al. (2011) and Zhou et al. (2015) had observed a reduction of drag force due to surface texture changes by experimental works. ...
... The drag coefficient dropped to 0.5 for free moving cylinder using two-dimensional k- SST model. Jiecheng et al., (2018) numerically investigated scouring around a submarine pipeline using a coupled CFD and Discrete Element Method (DEM) to simulate scouring evolution as published experimental works. A good agreement has been achieved with the published experimental results of Mao (1986), except at the initial unstable stage (t < 1.04). ...
Flow around a marine riser in water was investigated using numerical modelling. In this regime, the drag coefficient drops off at a certain Reynolds number due to a change from laminar to turbulent flow. The aim of this study is to investigate the capability of FLOW-3D, a three-dimensional computational fluid dynamic (CFD) transient solver through quantitative comparisons against existing numerical models and experiment by Maritime Research Institute Netherlands (MARIN). The k-epsilon turbulence model was employed. Six Reynolds numbers, similar to the test case, were considered. The current modelled mean drag coefficient, CD, for Reynolds numbers from 6.31 × 10^4 to 2.52 × 10^5 depart slightly from the experimental results. However, for Reynolds numbers ranging from 3.15 × 10^5 to 7.57 × 10^5 , a better accuracy of the mean CD was achieved. Therefore, it can be concluded that FLOW-3D, by means of the standard k-epsilon turbulence model, can only provide a good approximation at high turbulence regime.
... One of the most pressing issues today is introducing innovative methods in water production, first of all, modern water and resource-saving technologies, the use of highefficiency agricultural machinery and technology [1]. There are several developments in this area; the main issue in developing the theoretical basis of water trancmission and lifting devices, as well as improving the operating mode, is to increase the efficiency of water lifts [2,3]. Based on the above, this article presents methods for calculating the resource-saving design parameters of a structured water lift. ...
The current article considers a method of improvement based on the laws of flow motion in developing resource-saving devices based on the analytical analysis of research on using air ejectors in the national economy. The hydraulic parameters of the jet lift and air ejector are theoretically based, and the connections obtained are tested experimentally. Based on the experiments, the economical parameters of the inlet water lift and air ejector were determined. It was determined that the working pressure of the laboratory water intake device for taking water from a well at a depth of 1 m to a height of 2 m is Hi = 1 m, working flow consumption Q=29.52·10-5 m3/s. Based on theoretical research and experimental data, the consumption characteristics of the structured water lift and air ejector were constructed.
... These two models proceed independently, while the coupling of them at certain time intervals is implemented through the momentum exchange via CFDEMcoupling , developed by Kloss et al. (2012). This coupled LES-DEM model has been widely validated and applied (Blais et al. 2016;Yang et al. 2018;Wang & Shen 2022), especially for TC simulations in our previous work (Xie et al. 2022). In the following, the equations for the fluid phase are described in § 2.1, and the equations for the particle phase and the fluid-particle interaction forces are given in § 2.2. ...
The turbidity current (TC), a ubiquitous fluid–particle coupled phenomenon in the natural environment and engineering, can transport over long distances on an inclined terrain due to the suspension mechanism. A large-eddy simulation and discrete element method coupled model is employed to simulate the particle-laden gravity currents over the inclined slope in order to investigate the auto-suspension mechanism from a Lagrangian perspective. The particle Reynolds number in our TC simulation is $0.01\sim 0.1$ and the slope angle is $1/20 \sim 1/5$ . The influences of initial particle concentration and terrain slope on the particle flow regimes, particle movement patterns, fluid–particle interactions, energy budget and auto-suspension index are explored. The results indicate that the auto-suspension particles predominantly appear near the current head and their number increases and then decreases during the current evolution, which is positively correlated with the coherent structures around the head. When the turbidity current propagates downstream, the average particle Reynolds number of the auto-suspension particles remains basically unchanged, and is higher than that of other transported particles. The average particle Reynolds number of the transported particles exhibits a negative correlation with the Reynolds number of the current. Furthermore, the increase in particle concentration will enhance the particle velocity, which allows the turbidity current to advance faster and improves the perpendicular support, thereby increasing the turbidity current auto-suspension capacity. Increasing slope angle will result in a slightly larger front velocity, while the effect of that on the total force is insignificant.
... Unlike TFM, CFD-DEM in the Euler-Lagrange framework treats the solid phase as a discrete phase, considers solid particle interactions, and uses Lagrangian particle tracking to capture the force state, motion trajectory, and other information of sediment particles, which is critical for understanding the mesoscopic mechanism of local scour [22]. The CFD-DEM method has been widely applied to the field of deep-sea mineral pipeline transportation [23,24], submarine pipeline scours [25][26][27], fluidised-bed [28,29], and other fields of particle multiphase flow. However, its application in the local scour of pile foundations is still limited. ...
The local scour around offshore pile foundations often seriously affects the normal operation of offshore wind power. The most widely used numerical simulation method in the study of local scour is the Euler two-fluid model (TFM). However, the contact effect between sediment particles is neglected in this model. Thus, the momentum and energy transfer between sediment particles and the fluid is not realistically reflected, which limits its significance in revealing the mesoscopic mechanism of local scour. Therefore, the computational fluid dynamics-discrete element method (CFD-DEM) numerical model was applied in this study, which fully considers the contact between solid particles and momentum transfer between two phases. The model was first verified by experimental data of a local scour test under clear water scour. Then, the mechanism of local scour was further discussed from macro and micro perspectives. The results showed that CFD-DEM could be effectively used to study the local scour around a pile foundation. The local scour was comprehensively affected by flow velocity, gravity, fluid force, drag force, and interaction between particles, etc. Although the maximum average drag force happened in the area about 90° from the direction of incoming flow, the maximum scour depth always occurred at about 45°. Corresponding findings and conclusions can be used for future reference when designing and protecting the offshore wind power pile.
... Compared with the sediment transport rate models, the CFD-DEM models cost much more computational time because the motion of all sediment particles must be predicted. As a result, CFD-DEM models are mostly used for small-scale scour study to discover the fundamental mechanism of scour of subsea pipelines [86][87][88], scour around small piers [89], jet-flow-induced scour [90] and scour in front of breakwaters [91]. The accuracy of the motion of every sediment particle in the CFD-DEM model is highly dependent on the empirical formulae for determining the hydraulic forces on the particles and the model for the collision between particles. ...
This paper reviews the recent development of numerical modelling of local scour around hydraulic and marine structures. The numerical models for simulating local scour are classified into five categories: sediment transport rate models, two-phase models, CFD-DEM models, equilibrium scour models and depth-averaged models. The sediment transport rate models are the most popularly used models because of their high calculation speed and availability of empirical formulae for predicting sediment transport rates. Two-phase models were developed to simulate sediment transport in the format of sheet flow under strong current velocity or strong turbulence. The CFD-DEM model simulates the motion of every individual sediment particle. Its speed is the slowest, but it provides the opportunity to understand fundamental mechanisms of flow–particle interaction and particle–particle interaction using small-scale simulations. Equilibrium scour models predict the final scour profile at the equilibrium stage but cannot predict scour history. The depth-averaged models that were developed early are not recommended for local scour problems because they are not able to predict three-dimensional features around structures. Although many numerical models have been developed and many studies have been conducted to investigate local scour, some challenging problems remain to be solved, for example, the effects from scaling and sediment gradation. In addition, people’s understanding of local scour of cohesive sand is still very shallow, and more experimental and numerical research in this area is needed.
... Therefore, the study of the mechanism of occurrence and expansion of the scour cavity, its depth and the factors affecting it have been considered by researchers and designers. [2] Yang et al. (2018) have divided the process of formation and development of scouring under pipeline into three parts, which are: scour initiation, tunnel erosion, and eddy erosion [3]. Mao (1986) stated that when a pipe is placed on the seabed or riverbed, vortices are formed around the pipe. ...
Submarine pipelines are an important infrastructure and constitute vital vessels for transporting water, natural gas, oil, and petroleum products. In this study, scouring in one, two, and three tube models were experimentally investigated. The aim of this study was to investigate scour profiles for cases where pipes of different diameters were placed next to each other without any gap. In this regard, 15 experiments were performed in a flume 13 meters long, 0.46 meters wide, and 0.6 meters deep. For bed material, sand with a median particle size of 0.24 mm was used. The validity of experimental results was evaluated by performing 4 experiments under one-tube conditions and comparing the results with similar studies. When two pipes of the same diameter were placed next to each other without distance, they acted as an interconnected object and the maximum scouring depth formed between the two pipes. In the case where two pipes had different diameters, the greatest scouring depth formed near the larger diameter pipe. The scour depth formed under two pipes of different diameters was less when the larger diameter pipe was placed upstream, showing the pipes were placed in descending order (in terms of diameter). The results obtained for two pipes with different diameters also applied in the case of three pipes.
... (1). The fluid drag force can be described by Eq. (7) (Felice, 1994;Yang et al., 2018), ...
Plugging shale pores and throats with nanoparticles is an efficient and economic method of preventing water invasion to sustain shale wellbore stability. The nanoparticles size distribution is the key factor affecting plugging performance. Currently, the selection of nanoparticle size is usually based on empirical plugging rules and qualitative evaluation experiments. Experimental evaluations only can reflect the macroscopic plugging performance, but cannot reveal the microscopic plugging mechanism. In addition, the experiment for shale pores plugging is complicated and costly. Thus, it is very meaningful to propose a new method for sizing plugging nanoparticles based on simulation.
The essence of particles plugging process actually is the interactions of particle-particle, particle-rock and particle-fluid. In this paper, the thought of discrete element method is adopted and the plugging nanoparticles are treated as discrete elements. A coupled computational fluid dynamics-discrete element method (CFD-DEM) model is constructed to describe the motion behaviors of nanoparticles (discrete elements) in the process of plugging shale pores. In this model, taking into account the flow action of drilling fluid and the nanoscale effect of nanoparticles, the major considered forces include inter-particle forces (i.e. elastic contact force, friction force and Van der Waals force), hydrodynamic forces (i.e. drag force, Magnus force, buoyancy force and pressure gradient force) and gravitational force. Furthermore, a plugging criterion is established to check the particles plugging status through monitoring the microscopic movements of nanoparticles. Moreover, three evaluation indexes (i.e. porosity reduction of shale, permeability and porosity of external plugging layer, plugging ratio) are proposed to evaluate the macroscopic plugging performances of nanoparticles.
Based on the constructed computational model, microscopic plugging criterion and macroscopic plugging performance evaluation indexes, a novel method of sizing plugging nanoparticles to prevent water invasion for shale wellbore stability is developed. In addition, the validation of the method is conducted and the results are similar to the previous results of plugging experiments. The proposed method can give support to the selection of plugging nanoparticles size through obtaining the microscopic plugging behaviors and macroscopic plugging performances of nanoparticles. And it can also be regarded as a fundamental method to study other kinds of particles plugging problems, such as formation damage and optimization of lost circulation materials.
... The scientific researches which mentioned above is the scientific works with a strong theoretical basis. As a result of the research which provided in this field, sediment transportation can be written totally as follows [8][9][10][11]: At the core of provided scientific researches sediment transportation of the flow is related with the specific physical parameters. The main disadvantage of such relations is that their usage possibility. ...
Clearing the water reservoirs from sediments is one of the most pressing problems. There are several ways to deal with this problem, and in most cases, they require enormous amounts of money and energy. Studying the motion of a muddy flow in pressure pipelines is one of the important works for solving this problem. Designed by the Department of Hydraulics and Hydroinformatics (TIIAME), the the inkjet apparatus is considered to be an energy-saving device and uses the potential of the flow itself to remove the muddy sediment from the water structures to the bottom. Typically, the flow carrying capacity depends on several hydraulic flow elements. The article discusses that fuzzy transporting ability depends on relative depth. Relative depth is the ratio of the suction height to the water head in front of the water outlet. The studies were conducted in laboratory conditions. Theoretical work is justified by the law of energy conservation. As a result, a new expression is obtained showing the relationship between the transporting ability of the flow and relative depth.
... In the DEM model, the force of the contact is mainly divided into normal force and tangential force [26,27]. Normal force is perpendicular to the contact surface, while the tangential force is tangential to the contact surface. ...
Dense solid–gas bubbling systems with combined fluid-particle motion are among one of the most extensively used fluidization forms used in the chemical industry. Therefore, it is important to have a good understanding of the hydrodynamic behavior of bubbles. In this paper, both the experiment and numerical simulations are used to investigate the flow patterns in a spouted bed. For numerical simulations, the bidirectional coupling simulations using computational fluid dynamics (CFD) with discrete element method (DEM) are conducted. The results show that the simulations can accurately predict the bubbles morphology compared with the experimental results. When the number of particles is 30,000, only a single core-annular flow pattern appears. When the number of particles is increased to 36,500, the single bubble in the spouted bed transitions into two and a double core-annular flow pattern emerges. As the number of particles is increased to 43,000, a complex multicore-annular flow pattern appears. These flow patterns are also observed in the experiments using high-speed imaging camera. This paper analyzes and explains the causes of these flow phenomena from the dynamic characteristics of particle phase and fluid phase. These results have great significance in providing guidance for optimization of dense phase bubbling spouted beds.
... Following Lee et al., 21 at the upper inlet boundary, the undisturbed approach velocity Uo is increased linearly from 0 to 0.35 m/s within 8 s for case A and from 0 to 0.87 m/s within 4 s for case B. This is a common procedure for suppressing transient instabilities in numerical simulations. 38 The boundary conditions for fluid and turbulence parameters are similar to those used in the case of Sec. III A. The difference is that now there are sediments lying above the bottom rigid boundary. ...
A new numerical model is developed to simulate and investigate scour beneath a vibrating pipe during the tunnel erosion stage. This study is motivated by the fact that existing numerical models are not able to properly simulate scour under a vibrating pipeline, and the underlying physical mechanisms are not well understood due to the complex fluid-structure-sediment interaction. The present model incorporates the hybrid fictitious domain-immersed boundary method into a recently developed rheology-based two-phase model. The present model is validated against published experiment results of flow beneath a vibrating pipeline near a rigid boundary and scour beneath a fixed pipe. The flow velocity at the gap and the scour profile beneath the pipe are generally well produced by the model. Subsequently, the proposed model is applied to simulate scour under a vibrating pipe with different vibration amplitudes and frequencies. Among other things, it is found that maximum pipe acceleration has a dominant effect on the underlying physics that induce scour, irrespective of the combination of the vibration amplitude and frequency. An explanation for this finding is proposed based on various quantitative simulated results.
... Summary of Simulation Conditions and Results체의 레이놀즈수는 동일하다. 또한, 입자 초기 운동에서 유입 속도와 임계치 속도의 비를 실험값과 동일하게 유지하였다(Yang et al., 2018). 따라서 비교 검증을 위해 실험의 세굴 깊이 를 직접 비교하는 것은 타당하다. ...
When an offshore foundation is exposed to waves and currents, local scour could develop around a pile and even lead to structural failure. Therefore, understanding and predicting the scour due to sediment transport around foundations are important in the engineering design. In this study, the flow and scour around a monopole foundation exposed to a current were investigated using a method that coupled the computational fluid dynamics (CFD) and discrete element method (DEM). The open source computation fluid dynamics library OpenFOAM and a sediment transport library were coupled in the OpenFOAM platform. The incipient motion of the particle was validated. The flow fields and sediment transport around the monopole were simulated. The scour depth development was simulated and compared with existing experimental data. For the upstream scour hole, the equilibrium scour depth could be reproduced qualitatively, and it was underestimated by about 23%.
... There are many examples of the applications, for instance the circular piers in a river, marine piling, pipeline and cable on seabed and etc. There has been a lot of researches on this flow field in order to understand the behaviour of water flow over a circular cylinder to reduce drag force [1,2,3] and effect of scouring [4,5,6]. Huang et al. [1] and Zhou et al. [2] observed reduction of drag force due to surface texture changes by experimental works. ...
Flow around a smooth cylinder was investigated by numerical modelling at subcritical Reynolds numbers ranged from 7.2 x 10^3 to 1.8 x 10^4 and compared to experimental work by previous researchers. This study aims to compare the drag force between numerical modelling to the experimental measurement with the closest condition and environment in order to define the reliability of the numerical modelling used. The computational fluid dynamics (CFD) modelling software applied for this research is a 3D commercial computational software, FLOW-3D. Cartesian mesh type was used in the modelling setup and all boundaries of the domain was specified according to experimental condition. The free-stream velocity used was varied as 0.18, 0.29, 0.37 and 0.45 m/s, corresponding to Reynolds number which are 7200, 11600, 14800 and 18000 respectively. The value of drag coefficient simulation and experimental results differ between 35% to 42%; but still within the range of other numerical results for seven CFD platforms by previous researchers.
Le travail de thèse est réalisé dans le cadre du projet de recherche CUBISM - Développement de capteurs d'humidité et de pression pour suivre le séchage de matériaux réfractaires, qui s'inscrit dans le programme de coopération transfrontalière INTERREG V France-Wallonie-Vlaanderen. Le séchage des matériaux réfractaires est une des étapes les plus délicates lors de la première chauffe d'une installation. En effet, lors de la montée en température, l'eau ajoutée au mélange initial peut se transformer en vapeur et engendrer une augmentation de pression dans le matériau. Si cette pression devient supérieure à la résistance mécanique, on peut voir apparaître des fissures voire une explosion du garnissage des installations. À ce jour, aucun système de contrôle n'est disponible pour garantir l'intégrité du réfractaire durant la mise en route de l'installation, et plus tard en service. L'objectif du projet CUBISM est de proposer des capteurs d'humidité et de pression intégrés dans le matériau, pour un monitoring efficace du cycle de mise en œuvre. Les capteurs de pression développés seront de type ultrasonore, exploitant la propagation d'ondes de surface (capteur SAW) sur un substrat poreux piézoélectrique. Sous l'action de la pression, le substrat pourra subir une déformation mécanique et modifier le parcours de l’onde. Il s'agira d'étudier numériquement l'influence de la pression de gaz interne sur le comportement mécanique d'un matériau poreux en fonction de l'architecture (taille et distribution des pores,…). On s'intéressera dans un premier temps à l'étude du comportement mécanique du matériau, à la prédiction de l'endommagement et à la réponse vibratoire du matériau sous sollicitations. Dans cette première phase d'étude, le doctorant sera amené à reprendre des outils de conception de Volumes Élémentaires Représentatifs (VER), à savoir des motifs géométriques représentatifs du matériau et de sa microstructure, et à modéliser par des éléments discrets. Dans un second temps, le travail s'élargira au cadre d'un comportement multi-physique de type thermo-hydro-mécanique où le doctorant devra, après étude bibliographique approfondie, apporter des solutions de couplage adaptées aux conditions considérées (températures montant à près de 500°C et pression dépassant les 60 bars). Il sera également amené à développer ses propres routines au sein du code multiCAMG dédié à la modélisation de milieux à microstructures complexes, et au sein du code MULTICOR dédié à la modélisation par éléments discrets
Submarine pipelines, as an important tool for oil and gas transportation, have been distributed in offshore oil and gas fields worldwide. Under extreme waves, a large number of submarine pipelines have been damaged in the past decades. In order to investigate the effect of extreme marine environments on the pipelines, the joint effect of solitary waves and background currents on the pipelines is numerically studied in this paper by using a numerical wave tank developed with a free surface tracking approach and the immersed boundary method. The sediment transport module including packed and suspended sediment is incorporated with the flow module. In order to ensure the calculation accuracy of this model, three verification cases related to the wave propagation profile, the hydrodynamic force on the cylinder and the scour hole profile are simulated and the numerical results match the experimental and analytical results well. Given the combined wave exerts on the different pipelines, the environmental variables consider the background current velocity and wave height, and the pipeline arrangement includes the different diameters and the suspended pipeline and tandem pipeline. It is noted that the hydrodynamic characteristics, the forces and the local scour around the pipeline are closely related to the background current and the diameter and layout of the pipeline. It is anticipated that the findings in this paper will enhance our understanding of the damage mechanism of submarine pipeline by waves and may also be useful in future design practices for pipelines.
Hydro transport is characterized by the combined movement of liquid and solid particles, which in a mixture form two-phase or multiphase flows with different physical and mechanical properties. One of the main tasks of hydraulic transport is to study the throughput of pipelines, where taking into account the distribution of sediment concentration over the cross section of the pipeline formed under the influence of gravitational force is of great importance in describing the nature of the two-phase flow. Pressure-bearing suspended flows in hydro transport systems are usually characterized by high volumetric concentrations and a wide range of sizes and densities of solid particles that are part of hydraulic mixtures. The flows under consideration are more complex in their structure than turbulent flows of homogeneous liquids in pipes. Therefore, the methods for calculating these flows are much more complicated than the usual methods of hydraulics of pressure flows of homogeneous liquids. To develop scientif-ically based methods for calculating the parameters of the movement of hydraulic mixtures in pipes, widely used the averaged equations of the weighted flow and experimental data. When moving slurries through pipes, gravity plays a significant role. The article discusses the influence of gravity on the throughput of pressure systems with different slopes and obtains new dependences of the flow rate of turbid flow on the slope of the pressure pipe.
In the field of offshore oil and gas engineering, the arrangement of multiple pipelines are becoming more common, the spacing between the pipelines and the incoming stream velocity will significantly affect the scouring process around the pipelines. In this study, the effect of space ratio (G/D) and the stream velocity on the scouring process around two pipelines in tandem are investigated using the coupled approach of computational fluid dynamics (CFD) and discrete element method (DEM). Here G is the spacing between the pipelines and D is the diameter of the pipeline. Specifically, the effect of space ratio and the stream velocity are discussed by simulating the gap ratio (G/D) between two pipelines ranging from 1 to 3 with an interval of 1, under the stream velocity U = 0.5,1 and 2 m/s, The results indicate that when G/D ≤ 2, the equilibrium scour depth below the upstream pipeline (S1) is slightly larger than that under the downstream pipeline (S2), S1 and S2 slightly increase as the gap ratio increases. Whereas for G/D > 2, the equilibrium scour depth beneath the upstream pipeline is slightly smaller than that under the downstream pipeline, S1 and S2 slightly decrease as the gap ratio increases. Furthermore, the scour depths are highly dependent on and positively related to the incoming stream velocity, the equilibrium bed profiles are similar under the same incident stream velocity with different gap ratios.
The dynamic interaction between pipeline vibration and local scour is investigated numerically. The sediment scour model is adopted to calculate the local scour below pipeline. The general moving objects (GMO) model fully coupled with the fluids is established to simulate the pipeline vibration. The present results are consistent with the previous experimental results and show good agreement. The scour depth and scour hole scale are closely related to the amplitude of pipeline vibration. The effects of initial gap-to-diameter ratio, reduced velocity, and pipeline diameter on the local scour and pipeline vibration are investigated.
A mathematical model of the problem of nonlinear oscillations of a viscoelastic pipeline conveying fluid is developed in the paper. The Boltzmann–Volterra integral model with weakly singular kernels of heredity is used to describe the processes of pipeline strain. Using the Bubnov–Galerkin method, the mathematical model of the problem is reduced to the study of a system of ordinary integro-differential equations, where time is an independent variable. The solution of integro-differential equations is determined by a numerical method based on the elimination of the singularity in the relaxation kernel of the integral operator. Using the numerical method for unknowns, a system of algebraic equations is obtained. To solve a system of algebraic equations, the Gauss method is used. A computational algorithm is developed to solve the problems of the dynamics of viscoelastic pipelines with a flowing fluid. The algorithm of the proposed method makes it possible to investigate in detail the effect of rheological parameters on the character of vibrational strength of viscoelastic pipelines with a fluid flow, in particular, in the study of free oscillations of pipelines based on the theory of ideally elastic shells. On the basis of the computational algorithm developed, a set of applied computer programs has been created, which makes it possible to carry out numerical studies of pipeline oscillations. The influence of singularity in the heredity kernels and the geometric parameters of the pipeline on the vibrations of structures possessing viscoelastic properties is numerically investigated. It is shown that an account of viscoelastic properties of pipeline material leads decrease in the amplitude and frequency of oscillation. It is established that to reveal the influence of viscoelastic properties of structure material on the pipeline oscillations, it is necessary to use the Abel-type weakly singular kernels of heredity. The obtained results of numerical simulation can be used in the enterprises of oil and gas industries, as well as in design organizations.
Sediment transport is fundamentally a two-phase phenomenon involving fluid and sediments; however, many existing numerical models are one-phase approaches, which are unable to capture the complex fluid-particle and inter-particle interactions. In the last decade, two-phase models have gained traction; however, there are still many limitations in these models. For example, several existing two-phase models are confined to one-dimensional problems; in addition, the existing two-dimensional models simulate only the region outside the sand bed. This paper develops a new three-dimensional two-phase model for simulating sediment transport in the sheet flow condition, incorporating recently published rheological characteristics of sediments. The enduring-contact, inertial, and fluid viscosity
effects are considered in determining sediment pressure and stresses, enabling the model to be applicable to a wide range of particle Reynolds number. A k − ε turbulence
model is adopted to compute the Reynolds stresses. In addition, a novel numerical scheme is proposed, thus avoiding numerical instability caused by high sediment concentration and allowing the sediment dynamics to be computed both within and outside the sand bed. The present model is applied to two classical problems, namely, sheet flow and scour under a pipeline with favorable results. For sheet flow, the computed velocity is consistent with measured data reported in the literature. For pipeline scour, the computed scour rate beneath the pipeline agrees with previous experimental observations. However, the present model is unable to capture vortex shedding; consequently, the sediment deposition behind the pipeline is overestimated. Sensitivity analyses reveal that model parameters associated with turbulence have strong influence on the computed results.
Numerical modelling using computational fluid mechanics (CFD) and discrete element method (DEM) becomes increasingly prevalent for the exploration of agglomeration and deagglomeration in dry powder inhalers (DPIs). These techniques provide detailed information of air flow and particle-particle/wall interaction, respectively. Coupling of CFD and DEM enables an in-depth investigation of the mechanisms at microscopic level. This paper reviews the applications of CFD and DEM in DPI development and optimisation. The recent progress in modelling of two key processes in DPIs, i.e. agglomeration and deagglomeration, is presented. It has been demonstrated that DEM-CFD is a promising numerical approach to investigate the underlying agglomeration and deagglomeration mechanisms for DPIs. With further advance in computing capacity, it is expected that DEM-CFD will be capable of addressing more realistic and complicated issues for DPI improvement.
We present a multi-purpose CFD-DEM framework to simulate coupled fluid-granular systems. The motion of the particles is resolved by means of the Discrete Element Method (DEM), and the Computational Fluid Dynamics (CFD) method is used to calculate the interstitial fluid flow. We first give a short overview over the DEM and CFD-DEM codes and implementations, followed by elaborating on the numerical schemes and implementation of the CFD-DEM coupling approach, which comprises two fundamentally different approaches, the unresolved CFD-DEM and the resolved CFD-DEM using an Immersed Boundary (IB) method. Both the DEM and the CFD-DEM approach are successfully tested against analytics as well as experimental data.
The primary objective of this study is to improve understanding of the mechanism causing scour in unidirectional current. Experiments have shown how local scour develops around submarine pipelines in noncohesive sediments. The study shows that piping is the dominant cause of the initiation of scour. Piping and the stagnation eddy combine to undermine the pipeline, and mark the onset of scour. The critical hydraulic gradient associated with the initiation of scour is equal to the flotation gradient of the bed sediment. The pressure drop between the stagnation pressure upstream and wake pressure downstream of the pipe induces this hydraulic gradient. When a pipe is just embedded, the onset of scour does not occur if the ratio of the flow depth to pipe diameter exceeds 3.5. Similarly, the onset of scour does not occur for half-buried pipes. The reduction in pressure gradient across the pipeline for these flow/pipe combinations accounts for the lack of scour. The onset of scour can be prevented by placing an impermeable membrane underneath the pipeline.
This paper examines and reviews published results relating to local scour around submarine pipelines. It highlights the limitations of existing methods for estimating scour depth at the pipeline. Based on experimental results, the study proposes an empirical function relating the amount of gap flow through the scour hole for given flow conditions. With the aid of this function, it is possible to predict the maximum Scour depth at submarine pipelines for given flow and geometric boundary conditions. Published results suggest that the maximum equilibrium scour depth occurs when the pipeline is just lying on a plane bed and subjected to a pure unidirectional current. The undisturbed bed shear stress is equal to the critical shear stress for sediment entrainment. This condition implies that there is no general sediment transport away from the pipeline. The predicted maximum scour depth using the iterative method proposed in this study compares well with experimental results.
A three-dimensional CFD-DEM model is proposed to investigate the aeolian sand movement. The results show that the mean particle
horizontal velocity can be expressed by a power function of heights. The probability distribution of the impact and lift-off
velocities of particles can be described by a log-normal function, and that of the impact and lift-off angles can be expressed
by an exponential function. The probability distribution of particle horizontal velocity at different heights can be described
as a lognormal function, while the probability distribution of longitudinal and vertical velocity can be described as a normal
function. The comparison with previous two-dimensional calculations shows that the variations of mean particle horizontal
velocity along the heights in two-dimensional and three-dimensional models are similar. However, the mean particle density
of the two-dimensional model is larger than that in reality, which will result in the overestimation of sand transportation
rate in the two-dimensional calculation. The study also shows that the predicted probability distributions of particle velocities
are in good agreement with the experimental results.
Keywordsaeolian sand movement-CFD-DEM-three-dimensional simulation
The local granular rheology is investigated numerically in idealised turbulent bedload transport configurations. Using a coupled fluid-discrete element model, the stress tensor is computed as a function of the depth for a series of simulations varying the Shields number, the specific density and the particle diameter. The results are analyzed in the framework of the $\mu(I)$ rheology and exhibit a collapse of both the shear to normal stress ratio and the solid volume fraction over a wide range of inertial numbers. The effect of the interstitial fluid on the granular rheology is shown to be negligible, supporting recent work suggesting the absence of a clear transition between the free-fall and the turbulent regime. In addition, the data collapse is observed up to unexpectedly high inertial numbers $I\sim2$, challenging the existing conceptions and parametrization of the $\mu(I)$ rheology. Focusing upon bedload transport modelling, the results are pragmatically analyzed in the $\mu(I)$ framework in order to propose a granular rheology for bedload transport. The proposed rheology is tested using a 1D volume-averaged two-phase continuous model, and is shown to accurately reproduce the dense granular flow profiles and the sediment transport rate over a wide range of Shields number. The present contribution represents a step in the upscaling process from particle-scale simulations toward large scale applications involving complex flow geometry.
In this study, shear flows of dry flexible fibres are numerically modelled using the discrete element method (DEM), and the effects of fibre properties on the flow behaviour and solid-phase stresses are explored. In the DEM simulations, a fibre is formed by connecting a number of spheres in a straight line using deformable and elastic bonds. The forces and moments induced by the bond deformation resist the relative normal, tangential, bending and torsional movements between two bonded spheres. The bond or deforming stiffness determines the flexibility of the fibres and the bond damping accounts for the energy dissipation in the fibre vibration. The simulation results show that elastically bonded fibres have smaller effective coefficients of restitution than rigidly connected fibres. Thus, smaller solid-phase stresses are obtained for flexible fibres, particularly with bond damping, compared with rigid fibres. Frictionless fibres tend to align with a small angle from the flow direction as the solid volume fraction increases, and fibre deformation is minimized due to the alignment. However, jamming, with a corresponding sharp stress increase, large fibre deformation and dense contact force network, occurs for fibres with friction at high solid volume fractions. It is also found that jamming is more prevalent in dense flows with larger fibre friction coefficient, rougher surface, larger stiffness and larger aspect ratio.
The performance of the standard k-epsilon, Wilcox high-Reynolds-number k-omega, Wilcox low-Reynolds-number k-omega and Smagorinsky's subgrid scale (SGS) turbulence models is examined against the flow around a circular cylinder 0.37 diameter above a rigid wall. The governing equations are solved using finite difference method in a non-orthogonal boundary-fitted curvilinear coordinate system. A mesh dependence study for the four turbulence models is carried out on computational meshes with different densities. In addition, the performance of the k-omega models with either wall function or no-slip boundary condition on the cylinder surface is examined on the finest mesh. It is found that the SGS model over-predicts the shedding of vortices from the cylinder and is sensitive to the computational mesh and the model constant C-s used. The standard k-epsilon and the Wilcox k-omega models predict the mean velocity field quite well but generally under-predict the velocity and hydrodynamic force oscillations using wall functions on the cylinder surface. It is also found that the Wilcox k-omega models with the no-slip boundary condition on the cylinder surface give better predictions on the shedding of vortices than their counterparts using the wall function boundary condition.
A numerical model for the description of fluid flow, and suspended and bed-load sediment transport, is presented. Density effects are included in the momentum (Reynolds) equations and in the turbulence (it and e) equations. Changes in bed levels are calculated from sediment continuity, and the finite-element grid is adapted to the geometry. The Reynolds equations and the transport equation for suspended sediment are solved numerically using a Taylor-Galerkin finite-element method. The flow at a surface mounted cylinder in a steady flow is predicted in good agreement with experiments. Periodic vortex shedding from a cylinder placed above a rigid bed is predicted in good agreement with laboratory experiments, provided that sufficiently detailed grids (~5,000 nodes) are used. Scour calculations are performed for a cylinder in a steady flow with its underside placed at the level of the original flat bed. Predicted scour at a pipeline in steady flow is in good agreement with laboratory measurements reported in the literature.
This review article focuses on the modeling of complex granular flows employing the discrete element method (DEM) approach. The specific topic discussed is the application of DEM models for the study of the flow behavior of nonspherical, flexible, or cohesive particles, including particle breakage. The major sources of particle cohesion-liquid induced, electrostatics, van der Waals forces-and their implementation into DEM simulations are covered. These aspects of particle flow are of great importance in practical applications and hence are the significant foci of research at the forefront of current DEM modeling efforts. For example, DEM simulations of nonspherical grains can provide particle stress information needed to develop constitutive models for continuum-based simulations of large-scale industrial processes.
This paper presents results of an experimental study on three-dimensional scour at submarine pipelines with uniform sediment under a unidirectional current in clear-water conditions. The data show that propagation of the scour hole in the transverse direction of flow may be divided into a rapid and a slack phase of development. The former is characterized by a higher and constant velocity, whereas the latter a lower and reducing propagation velocity. Four nondimensional parameters are identified and their effects examined experimentally. Pipeline embedment and water depth to pipeline diameter ratios, which represent the stability force, inhibit the scouring process, resulting in a reduced propagation velocity and a dominant slack phase of development. Conversely, Froude number and Shields parameters represent the environment force; they enhance the scouring process, causing a high propagation velocity and a dominant rapid phase of development. The experimental results reveal that the scour process is not sensitive to Shields parameter under clear-water conditions but is closely related to the other three parameters. The effect of all the parameters can be viewed in a balance between the environment and stability forces. DOI: 10.1061/(ASCE)HY.1943-7900.0000583. (C) 2012 American Society of Civil Engineers.
Supercritical water (SCW) fluidized bed is a new and promising reactor for gasification of wet biomass. In this paper, the particle distribution and fluid hydrodynamic characteristics in SCW fluidized bed were studied comprehensively by the discrete element method (DEM). The results from DEM simulation show that there exists a non-bubbling fluidization when superficial velocity is in the range of minimum fluidization velocity and minimum bubbling velocity although the particles are categorized as Geldart B. Particle circulation, including internal circulation and gross circulation are responsible for solids mixing in SCW fluidized bed. Particle circulation in SCW fluidized bed is not only induced by bubble motion, but also influenced by the vortices in bubbles. Other characteristics such as voidage distribution, particle and fluid velocity, granular temperature, and particle Reynolds number in SCW fluidized bed, are also discussed.
In this paper we study the effect of rolling friction on the dynamics in a single spout fluidized bed using Discrete Element Method (DEM) coupled to Computational Fluid Dynamics (CFD). In a first step we neglect rolling friction and show that the results delivered by the open source CFD–DEM framework applied in this study agree with previous simulations documented in literature. In a second step we include a rolling friction sub-model in order to investigate the effect of particle non-sphericity. The influence of particle–particle as well as particle–wall rolling friction on the flow in single spout fluidized bed is studied separately. Adequate rolling friction model parameters are obtained using first principle DEM simulations and data from literature. Finally, we demonstrate the importance of correct modelling of rolling friction for coupled CFD–DEM simulations of spout fluidized beds. We show that simulation results can be improved significantly when applying a rolling friction model, and that experimental data from literature obtained with Positron Emission Particle Tracking (PEPT) technique can be satisfactorily reproduced.
Part I . The results of previous experiments (Bagnold 1954) on the stresses set up in a uniform gravity-free dispersion of solid grains when uniformly sheared in a fluid are applied to the nonuniform case of grain flow over a gravity bed, assuming the results are quantitatively applicable to any sufficiently thin shear layer. It is found that if the bed is composed entirely of potentially mobile grains a stress-equilibrium relation at the bed surface can be defined whereby the magnitude of a certain ‘bed load’ of grains in transit over unit bed area is given in terms of the applied tangential stress. The bed load is independent both of the existence of any additional suspended load and of the degree of dispersion of the grains. The state of internal fluid motion enters as a single experimental constant. From a consideration of the stability of this equilibrium relation it is possible to predict the conditions under which an initially plane bed surface should become rippled; and general quantitative agreement is found with experimental data both for wind-blown and water-driven grains. Primary and secondary bed rippling are distinguished. The magnitude of the ‘form-drag’ due to primary bed ripples can be calculated. That due to secondary ripples is definable as an experimental constant. The gravity-free experiments disclosed that the shear resistance of a grain dispersion may vary as the square or the first power of the rate of shear, analogously to that of a true fluid, according to the value of a number G analogous to a Reynolds number. The square law is followed when the effects of grain inertia dominate over those of fluid viscosity. Assuming that the phenomenon of ‘saltation’ as observed over a gravity bed is an inertia effect, the conditions for saltation are predictable. The results again agree quantitatively with observation. Part II . The resistance offered by the grains to their displacement along the flow is shown to be proportional to their normal immersed weight component. And their measurable mass transport rate is hereby proportional to the rate of useful work done in transporting them. On this basis separate expressions are found for the transport rates of the bed load and suspended load, in terms of the applied tangential stress and of a tangential and a normal relative velocity respectively. When conditions are restricted to those of the ‘stream case’ these velocities become constant for any given system, being functions of an appropriate constant mean drag coefficient. The bed-load transport-rate expression found gives magnitudes, and variations of magnitude with grain size, in agreement with the experimental data for wind-blown sand. Agreement is also found for water-driven grains in open channels from the threshold of movement up to a certain value of the applied stress. The experimental rates are then found to increase suddenly. This increase is attributed to the development of an additional suspended load. The abrupt development of a suspended load may be explained as due to a change in the nature of the fluid turbulence when the stationary boundary becomes occluded from the fluid flow by a concentrated layer of moving bed-load grains. The assumption that under these new moving-boundary conditions the available fluid energy derived from shearing over the bed is equally apportioned between bed-load and suspended-load transport work leads to values for the suspended-load transport rate which agree closely with the experimental data. A critical relation emerges between the gravity slope of the bed, the fall velocity and the mean transport velocity of the suspended grains at which their transport may become very large. Conditions are examined under which the steady transport may be possible of grains of heterogeneous size or density. Part III . When the fluid flow is non-inertial (laminar) and the grain flow is also non-inertial the semi-empirical relations found previously for the internal stresses are such that both viscosity and shear rate can be eliminated, and a differential equation obtained whose solution gives the grain concentration in terms only of distance from the bed and of the applied tangential stress. It appears that with constant applied stress (unlimited flow depth) the degree of grain dispersion greatly exceeds that to be expected in turbulent fluid flow. But when the applied stress diminishes linearly with distance from the bed boundary a possible solution gives constant grain concentration throughout the flow. This appears to explain certain experimental results, including the behaviour of ‘slurries’. The effect is examined of a fixed or partially fixed bed on the grain flow in a turbulent fluid. The effect may be pronounced in the case of suspended grains. Under certain clearly definable conditions a loose grain bed must cease to remain stationary. And if the fluid flow above is turbulent the whole grain bed should flow at constant maximum concentration, underneath the flow proper and separated from it by a moving-bed surface interface at which the concentration is discontinuous. This explains phenomena sometimes found under river torrents. The factors giving rise to and limiting the development of bed features (dunes) on a bigger scale than ripples are examined. Dune formation appears as an inherent tendency of the grain flow alone, which may or may not be inhibited by the conditions of the fluid flow.
This paper reviews the results of an experimental investigation of the interaction between an erodible bed and a pipeline vibrating in the transverse direction to a current. A spring-supported rigid cylinder is used as a model pipe. First, the influence of pipe vibration on the scour process is studied. The experiments show that pipe vibration induces extra erosion, resulting in relatively larger scour depths and scour widths than when the pipe is held fixed. The effect is most pronounced for pipes elevated slightly above the static bed, and ceases to exist for gaps of one pipe diameter or larger. Second, the influence of scour on pipe vibration is studied. A scour hole is produced on a loose sand bed. The model pipe is placed above (as well as in) the scour hole. The amplitude and frequency responses of cylinder vibration are obtained. Experiments show that the effect of scour on the pipe response can be significant; the vibrations are found to be dominated by vortex shedding even if the pipe is placed very close to the original undisturbed bed.
This paper summarizes the results of an experimental study on the onset of scour below and self-burial of pipelines in currents/waves. Pressure was measured on the surface of a slightly buried pipe at two points, one at the upstream side and the other at the downstream side of the pipe, both in the sand bed. The latter enabled the pressure gradient (which drives a seepage flow underneath the pipe) to be calculated. The results indicated that the excessive seepage flow and the resulting piping are the major factor to cause the onset of scour below the pipeline. The onset of scour occurred always locally (but not along the length of the pipeline as a two-dimensional process). The critical condition corresponding to the onset of scour was determined both in the case of currents and in the case of waves. Once the scour breaks out, it will propagate along the length of the pipeline, scour holes being interrupted with stretches of soil (span shoulders) supporting the pipeline. As the span shoulder gets shorter and shorter, more and more weight of the pipeline is exerted on the soil. In this process, a critical point is reached where the bearing capacity of the soil is exceeded (general shear failure). At this point, the pipe begins to sink at the span shoulder (self-burial). It was found that the self-burial depth is governed mainly by the Keulegan–Carpenter number. The time scale of the self-burial process, on the other hand, is governed by the Keulegan–Carpenter number and the Shields parameter. Diagrams are given for the self-burial depth and the time scale of the self-burial process.
Understanding and modelling the dynamic behaviour of particulate systems has been a major research focus worldwide for many years. Discrete particle simulation plays an important role in this area. This technique can provide dynamic information, such as the trajectories of and transient forces acting on individual particles, which is difficult to obtain by the conventional experimental techniques. Consequently, it has been increasingly used by various investigators for different particulate processes. In spite of the large bulk volume, little effort has been made to comprehensively review and summarize the progress made in the past. To overcome this gap, we have recently completed a review of the major work in this area in two separate parts. The first part has been published [Zhu, H.P., Zhou, Z.Y., Yang, R.Y., Yu, A.B., 2007. Discrete particle simulation of particulate systems: theoretical developments. Chemical Engineering Science 62, 3378–3392.], which reviews the major theoretical developments. This paper is the second one, aiming to provide a summary of the studies based on discrete particle simulation in the past two decades or so. The studies are categorized into three subject areas: particle packing, particle flow, and particle–fluid flow. The major findings are discussed, with emphasis on the microdynamics including packing/flow structure and particle–particle, particle–fluid and particle–wall interaction forces. It is concluded that discrete particle simulation is an effective method for particle scale research of particulate matter. The needs for future research are also discussed.
The statistical particle stress (SPS) is a result of group particle movement, which is not referred directly from E–L (Euler–Lagrange) calculations. This paper derives SPS in Eulerian regime and proves that in aeolian sand movement, as the height increases the gas stress also increases while the SPS decreases; however, the sum of gas stress and SPS keeps to be a constant value, which equals to the gas stress in particle absent region. This paper also suggests that SPS predominates in the momentum transportation of particle phase.
This paper presents the results of an experimental investigation on scour below pipelines exposed to waves. The effect of lee-wake of the pipe is the key element in the scour process, and it is demonstrated that the Keulegan-Carpenter number is the main parameter that governs the equilibrium scour depth. Based on the presently available data, a design equation is established, relating the equilibrium scour depth to the Keulegan-Carpenter number for the live-bed situation and for a pipe in contact with the bed. The latter equation indicates that the equilibrium scour depth normalized with the pipe diameter is proportional to the square root of the Keulegan-Carpenter number, the proportionality constant being 0.1. The effect of Shields parameter on the final scour depth is found to be quite weak. It is also found that the surface roughness of the pipe imposes practically no influence on the scour process. The pipe position with respect to the bed appears to be an important parameter in determining the equilibrium scour depth.
The drag force on a particle in a fluid—multiparticle interaction system may be expressed as the product of the drag force on an unhindered particle, subject to the same volumetric flux of fluid, and a voidage function. It is demonstrated that for a wide varicty of both fixed-bed and.suspended-particle systems, file voidage function may be expressed as ϵ−β, where the exponent β is dependent on the particle Reynolds number but independent of other system variables.
Particle science and technology is a rapidly developing interdisciplinary research area with its core being the understanding of the relationships between micro-and macroscopic properties of particulate/granular matter—a state of matter that is widely encountered but poorly understood. The macroscopic behaviour of particulate matter is controlled by the interactions between individual particles as well as interactions with surrounding fluids. Understanding the microscopic mechanisms in terms of these interaction forces is therefore key to leading to truly interdisciplinary research into particulate matter and producing results that can be generally used. This aim can be effectively achieved via particle scale research based on detailed microdynamic information such as the forces acting on and trajectories of individual particles in a considered system. In recent years, such research has been rapidly developed worldwide, mainly as a result of the rapid development of discrete particle simulation technique and computer technology. This paper reviews the work in this area with special reference to the discrete element method and associated theoretical developments. It covers three important aspects: models for the calculation of the particle–particle and particle–fluid interaction forces, coupling of discrete element method with computational fluid dynamics to describe particle–fluid flow, and the theories for linking discrete to continuum modelling. Needs for future development are also discussed.
The scour around a long fixed pipeline placed just above a non-cohesive sandy bed is numerically simulated using an Eulerian
two-phase model that implements Euler–Euler coupled governing equations for fluid and solid phases and a modified k−ɛ turbulence closure for the fluid phase, the modeling system being a part of the CFD software package FLUENT. Both flow–particle
and particle–particle interactions are considered in the model. During the simulations, the interface between sand and water
is specified using a threshold volume fraction of sand, and the evolution of the bedforms is studied in detail. The predictions
of bedform evolution are in good agreement with previous laboratory measurements. Investigations into the mechanisms of scour
reveal that three sediment transport modes (bed-load, suspended-load and laminated-load) are associated with the scour development.
While some previously proposed scour development formulae for cylindrical objects are in good general agreement with the simulations,
scour prediction based on a commonly used operational mine-burial model (DRAMBUIE) shows disparities with present simulations.
A vertical two-dimensional (2D) numerical model for time dependent local scour below offshore pipelines subject to unidirectional steady flow is developed. The governing equations for the flow and sediment transport are solved by using finite difference method in a general curvilinear coordinate system. The performance of two turbulence models, the standard k–ɛ model and Smagorinsky subgrid scale (SGS) model, on modeling time dependent scour processes is examined. Both suspended load and bed load are considered in the scour model. The suspended-load model is verified against two channel sediment transport cases. The change of bed level is calculated from the continuity equation of total sediment transport. A new time marching scheme and a sand slide scheme are proposed for the scour calculation. It is found that the proposed time marching scheme and sand slide model work well for both clear-water and live-bed scour situations and the standard k–ɛ turbulence closure is more preferable than the SGS model in the 2D scour model developed in this study.
Pirker, Models, algorithms and validation for opensource
- C Kloss
- C Goniva
- A Hager
- S Amberger
- S Dem
- Cfd-Dem Prog
C. Kloss, C. Goniva, A. Hager, S. Amberger, S. Pirker, Models, algorithms and
validation for opensource DEM and CFD-DEM, Prog. Comput. Fluid Dyn., 12 (2012) 140152.
Fluid hydrodynamic characteristics in supercritical
- Y J Lu
- J K Huang
- P F Zheng
Y.J. Lu, J.K. Huang, P.F. Zheng, Fluid hydrodynamic characteristics in supercritical
- C Kloss
- C Goniva
- A Hager
- S Amberger
- S Pirker
C. Kloss, C. Goniva, A. Hager, S. Amberger, S. Pirker, Models, algorithms and
validation for opensource DEM and CFD-DEM, Prog. Comput. Fluid Dyn., 12 (2012) 140-152.