Arch dam–fluid interactions: By fem–bem and substructure concept

Arch dams can be conveniently analysed by the finite element method. For dam–fluid interaction problems, the fluid domain may be more conveniently handled by the boundary element method as a substructure first before connecting to the dam substructure. The added-mass matrix calculated from the fluid domain is symmetrized and lumped first so that the banded and symmetrical characteristics of the finite element method are retained. In the boundary element formulation, a mirror image method and quadratic elements are used for computational efficiency and accuracy. The strong singular terms are handled by using a solution which satisfies the governing equation and the free surface boundary condition. Infinite boundary conditions at the upstream of the reservoir can be reasonably approximated from the fundamental solution with accurate results, if the interior pressure distribution in the fluid domain is neglected. Numerical solutions on hydrodynamic pressure distribution and the natural frequencies of the dam–reservoir system with various water levels are obtained and compared with available analytical and experiment results.     

Coupling FEM and symmetric BEM for dynamic interaction of dam–reservoir systems

A numerical model coupling boundary and finite elements suitable for dynamic dam–reservoir interaction is presented herein. This model involves standard finite element idealization of the dam structure displacements and a new symmetric boundary element formulation of the unbounded reservoir domain leading to an equivalent symmetric stiffness matrix for the discretized pressure field. These two basic parts of the computation are directly coupled by imposing an equilibrium condition at the fluid–structure interface, then the resulting algebraic system is reduced by localizing the coupled terms in the global mass matrix such as usually achieved in the added-mass formulation. Finally, the performance and the accuracy of this model are examined by comparing its results to those obtained from three other numerical models.     

A coupled CFD-DEM analysis of granular flow impacting on a water reservoir

Massive debris flows or rock avalanches falling into a water reservoir may cause devastating hazards such as overtopping or dam breakage. This paper presents a coupled Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) analysis on the impacting behaviour of a granular flow falling from an inclined slope into a water reservoir. The coupling between CFD and DEM considers such important fluid–particle interaction forces as the buoyancy force, the drag force and the virtual mass force. It is found that the presence of water in the reservoir can generally help to reduce direct impact of granular flow on the check dam behind the reservoir, minimizes the intense collisions and bouncing among particles and helps form a more homogeneous final deposited heap as compared to the dry case. While the interparticle/particle–wall frictions and collisions dominate the energy dissipation in the dry granular flow, the majority of kinetic energy of the granular system in the wet case is first transferred to the water body, which leaves the granular flow itself to become a contact-shearing dominant one and causes impulse wave travelling between the check dam and the slope surface for a rather sustained period before settling down. A power law distribution is found for the velocity profile of the granular flow travelling on both the slope and the reservoir ground surfaces, and it may change temporarily to a linear distribution at the transition point of the slope toe where the Savage number depicts a peak. The consideration of rolling friction among particles may homogeneously reduce the travelling velocity of the granular flow and alleviate the overall impact on the check dam. The impact on the check dam depends on both the initial debris releasing height and the reservoir water level. Medium water levels in the reservoir have been found to be generally safer when the initial debris height is relatively high.     

Earthquake‐induced hydrodynamic pressures on a 3D rigid dam–reservoir system using DRBEM and a radiation matrix

The dual reciprocity method is applied to determine the hydrodynamic pressure distribution in a three‐dimensional dam–reservoir system subjected to earthquake excitation. The reservoir domain is idealized as a finite region of irregular geometry adjacent to the dam followed by an infinite domain of uniform cross‐section in the upstream direction. The reservoir hydrodynamic pressure response is governed by the Helmholtz equation subject to free surface, dam–reservoir interface, absorbing bottom/banks and radiation boundary conditions. A three‐dimensional (3D) dual reciprocity model is developed to determine the hydrodynamic pressure in the finite reservoir domain. A radiation matrix is developed and introduced to relate the hydrodynamic pressure and its normal derivative on the interface between the finite and infinite domains. The three‐dimensional radiation model used is developed by applying a two‐dimensional dual reciprocity formulation along the interface of the finite and infinite reservoirs together with a continuum solution in the upstream direction of the infinite domain. The model is compared for the hydrodynamic response of a three‐dimensional rectangular reservoir and found to be in excellent agreement with results obtained from a model based on the analytical formulation existing in the literature. Copyright © 2003 John Wiley & Sons, Ltd.     

Dynamic analysis of dam–reservoir-foundation interaction in time domain

In this paper, a time domain dynamic analysis of the dam–reservoir-foundation interaction problem is developed by coupling the dual reciprocity boundary element method (DRBEM) for the infinite reservoir and foundation domain and the finite element method for the finite dam domain. An efficient coupling procedure is formulated by using the substructuring method. Sharans boundary condition at the far end of the infinite fluid domain is implemented. To verify the proposed scheme, numerical examples are carried out and compared with available exact solutions and finite–finite element coupling results for the problem of the dam–reservoir interaction. Finally, a complete dam–reservoir-foundation interaction problem is solved and its solution is compared with previously published results.The author is thankful to the anonymous reviewer of this paper for his suggestions and comments, which improved considerably the present paper.     

拱坝地震动随机响应分析

将河谷地震动随机场半解析展开为正交函数随机过程及采用简化的地基模型,应用振型分解法可直接求得拱坝－地基－库水系统的各种随机响应及功率谱密度。本文方法不仅考虑地震动的空间随机性,山体放大作用及行波效应,而且考虑非比例阻尼的拱坝振型之间的相关性;地震动随机场只须分解一次,计算过程简单,是大型拱坝结构随机分析的一种有效方法。     

Effect of stratification on hydrodynamic pressures on dams

Summary The effect of stratification of the fluid in the reservoir on hydrodynamic pressures on dams due to horizontal, harmonic ground accelerations has been analyzed. It has been found that both the zeroth-order solution, which corresponds to the constant-density solution, and the first-order solution have two components in the hydrodynamic pressure distribution, an in-phase component and an out-of-phase component which is 90° lagging. The out-of-phase components vanish in the absence of surface waves, and they become dominant when the wave-effect parameter C becomes large. The wave-effect parameter C is defined as 49-1, where g is the gravitational constant, the oscillation frequency and h the height of the fluid in the reservoir. The total horizontal force on a dam due to harmonic ground excitations has also been presented.     

Dam break flood wave under different reservoir’s capacities and lengths

Dam failure has been the subject of many hydraulic engineering studies due to its complicated physics with many uncertainties involved and the potential to cause many losses of lives and economical losses. A primary source of uncertainties in many dam failure analyses refers to prediction of the reservoir’s outflow hydrograph, which is studied in the present investigation. This paper presents an experimental study on instantaneous dam failure flood under different reservoir’s capacities and lengths in which the side slopes change within a range of 30°–90°. Thus, several outflow hydrographs are calculated and compared. The results reveal the role of the side slopes on dam break flood wave, such that lower side slope creates more catastrophic outflow. The reservoir capacity and length are also recognized to be important factors, such that they do affect peak discharge and time to peak of the outflow hydrograph. Finally, the paper presents two simple relations for peak discharge and maximum water level estimation at any downstream location.     

Biomechanics of male erectile function.

Two major branches of engineering mechanics are fluid mechanics and structural mechanics, with many practical problems involving the effect of the first on the second. An example is the design of an aircraft's wings to bend within reasonable limits without breaking under the action of lift forces exerted by the air flowing over them; another is the maintenance of the structural integrity of a dam designed to hold back a water reservoir which would exert very large forces on it. Similarly, fluid and structural mechanics are involved in the engineering analysis of erectile function: it is the hydraulic action of increased blood flow into the corpora cavernosa that creates the structural rigidity necessary to prevent collapse of the penile column.     

Dynamics of submarine debris flow and tsunami

The general two-phase debris flow model proposed by Pudasaini (J. Geophys. Res. 117:F03010, 2012, doi:10.1029/2011JF002186) is employed to simulate subaerial and submarine two-phase debris flows and the mechanics of complex wave generation and interactions between the solid and the fluid phases. This includes the fluid waves or the tsunami generated by the debris impact at reservoirs, lakes, and oceans. The analysis describes the generation, amplification, and propagation of super tsunami waves and run-ups along coastlines, debris slide and deposition at the bottom floor, and debris shock waves. Accurate and advance knowledge of the arrival of tsunami waves in the coastal regions is very important for the design of early warning strategies. Here, we show that the amount of solid grain in the fluid reservoir plays a significant role in controlling the overall dynamics of the submarine debris flow and the tsunami. For very small solid particle concentrations in the reservoir, the submarine debris flow moves significantly faster than the surface tsunami wave. As the solid volume fraction in the reservoir increases, the submarine debris speed slows down. For relatively large solid volume fractions in the reservoir, the speed of the submarine debris becomes slower than the surface tsunami wave. This information can be useful for early warning strategies in the coastal regions. The fast or slow speed of the submarine wave can be attributed to several dynamical aspects of the model including the generalized drag, basal traction, pressure gradient, virtual mass force, the non-Newtonian viscous stress, and the strong phase interaction between the solid and the fluid as they enhance or diminish the motion of the solid phase. Solid particle concentration in the reservoir dam also substantially influences the interaction between the submarine debris flow and the frontal wall of the dam, and the interaction between the tsunami and the submarine debris wave. The tsunami wave impact generates a largely amplified fluid level at the dam wall. Submarine debris shock waves are observed for small solid volume fractions in the reservoir. Another important aspect of the simulation is to investigate the complex interactions between the internal submarine debris wave and the surface tsunami wave. Three complex waves occur simultaneously: the subaerial debris flow in the upstream region, submarine debris flow in the reservoir basin, and a super tsunami wave on the surface of the reservoir. This helps to develop insight into the basic features of the complex nonlinear solid and fluid waves and their interactions.     

A new acoustic interface element for fluid-structure interaction problems

A new comprehensive acoustic 2-D interface element capable of coupling the boundary element (BE) and finite element (FE) discretizations has been formulated for fluid–structure interaction problems. The Helmholtz equation governing the acoustic pressure in a fluid is discretized using the BE method and coupled to the FE discretization of a vibrating structure that is in contact with the fluid. Since the BE method naturally maps the infinite fluid domain into finite node points on the fluid–structure interface, the formulation is especially useful for problems where the fluid domain extends to infinity. Details of the BE matrix computation process adapted to FE code architecture are included for easy incorporation of the interface element in FE codes. The interface element has been used to solve a few simple fluid–structure problems to demonstrate the validity of the formulation. Also, the vibration response of a submerged cylindrical shell has been computed and compared with the results from an entirely finite element formulation.     

Failure analysis of a cracked concrete gravity dam under earthquake

A dynamic contact model for simulating the interaction of two surfaces divided by a dam crack, and a simplified reinforcing steel constitutive model for simulating the effect of earthquake-resistant reinforcement on a cracked dam are developed in this study. After the verification of the dynamic contact model and the reinforcing steel constitutive model by illustrations, the JINANQIAO roller compacted concrete (RCC) gravity dam is investigated with two case scenarios: a straight crack case and a curving crack case scenarios, including their dam–foundation–reservoir interaction, respectively. Emphasis is paid to analysing the failure process of the cracked dam with and without reinforcement. Results show that the cracked dam maintains a large safety margin, and the curving crack is beneficial to the improvement of earthquake resistance. Commonly applied steel reinforcement measures can effectively decrease the sliding displacement and the joint opening of the cracked dam; however, the layout of the reinforcing steel and its quantity to be used needs particular consideration.     

The cool-down behaviour of a miniature Joule–Thomson (J–T) cryocooler with distributed J–T effect and finite reservoir capacity

The objective of this work is to study the effect of the reservoir pressure and volume on the cool-down behaviour of a miniature Joule–Thomson (J–T) cryocooler considering the distributed J–T effect. As the supply pressure to the J–T cooler reduces in case of a reservoir with finite capacity, the volume and the initial pressure of the reservoir are crucial for the operation of the cryocooler. These parameters affect the cool down time, cooling effect and the time for which the cooling effect is obtained at the required cryogenic temperature. A one dimensional transient model is formulated for the fluid streams and the solid elements of the recuperative heat exchanger of the cryocooler. Argon gas is used as the working fluid and its physical properties are evaluated at the local conditions of temperature and pressure. Cases with different reservoir capacities and pressures are worked out to study their effect on the transient behaviour of the cryocooler.     

The fractal finite element method for added‐mass‐type problems

The fractal finite element method (FFEM), originally developed for calculating stress intensity factors in fracture mechanics problems, has been extended to analyse fluid–structure interaction in the form of added‐mass‐type problems. These include the free vibration of a submerged spherical shell and the interaction between a dam and a reservoir. For the former problem, the numerical solution from the FFEM agrees well with the analytical solution, and the FFEM performed better than conventional finite elements and infinite elements in terms of efficiency. For the latter problem, the FFEM predicted an added mass profile that is different from that based on Westergaard's parabolic solution. Copyright © 2008 John Wiley & Sons, Ltd.     

Diagonalization procedure for scaled boundary finite element method in modeling semi‐infinite reservoir with uniform cross‐section

To improve the ability of the scaled boundary finite element method (SBFEM) in the dynamic analysis of dam–reservoir interaction problems in the time domain, a diagonalization procedure was proposed, in which the SBFEM was used to model the reservoir with uniform cross‐section. First, SBFEM formulations in the full matrix form in the frequency and time domains were outlined to describe the semi‐infinite reservoir. No sediments and the reservoir bottom absorption were considered. Second, a generalized eigenproblem consisting of coefficient matrices of the SBFEM was constructed and analyzed to obtain corresponding eigenvalues and eigenvectors. Finally, using these eigenvalues and eigenvectors to normalize the SBFEM formulations yielded diagonal SBFEM formulations. A diagonal dynamic stiffness matrix and a diagonal dynamic mass matrix were derived. An efficient method was presented to evaluate them. In this method, no Riccati equation and Lyapunov equations needed solving and no Schur decomposition was required, which resulted in great computational costs saving. The correctness and efficiency of the diagonalization procedure were verified by numerical examples in the frequency and time domains, but the diagonalization procedure is only applicable for the SBFEM formulation whose scaling center is located at infinity. Copyright © 2009 John Wiley & Sons, Ltd.     

Corrected discrete least-squares meshless method for simulating free surface flows

In this paper, a modified version of discrete least-squares meshless (DLSM) method is used to simulate free surface flows with moving boundaries. DLSM is a newly developed meshless approach in which a least-squares functional of the residuals of the governing differential equations and its boundary conditions at the nodal points is minimized with respect to the unknown nodal parameters. The meshless shape functions are also derived using the Moving Least Squares (MLS) method of function approximation. The method is, therefore, a truly meshless method in which no integration is required in the computations. Since the second order derivative of the MLS shape function are known to contain higher errors compared to the first derivative, a modified version of DLSM method referred to as corrected discrete least-squares meshless (corrected DLSM) is proposed in which the second order derivatives are evaluated more accurately and efficiently by combining the first order derivatives of MLS shape functions with a finite difference approximation of the second derivatives. The governing equations of fluid flow (Navier–Stokes) are solved by the proposed method using a two-step pressure projection method in a Lagrangian form. Three benchmark problems namely; dam break, underwater rigid landslide and Scott Russell wave generator problems are used to test the accuracy of the proposed approach. The results show that proposed corrected DLSM can be employed to simulate complex free surface flows more accurately.     

Dynamic analysis of an inflatable dam subjected to a flood

A dynamic simulation of the response of an inflatable dam subjected to a flood is carried out to determine the survivability envelope of the dam where it can operate without rupture, or overflow. The free-surface flow problem is solved in two dimensions using a fully nonlinear mixed Eulerian-Lagrangian formulation. The dam is modeled as an elastic shell inflated with air and simply supported from two points. The finite element method is employed to determine the dynamic response of the structure using ABAQUS with a shell element. The problem is solved in the time domain which allows the prediction of a number of transient phenomena such as the generation of upstream advancing waves, the dynamic structural response and structural failure. Failure takes place when the dam either ruptures or overflows. Stresses in the dam material were monitored to determine when rupture occurs. An iterative study was performed to find the serviceability envelope of the dam in terms of the internal pressure and the flood Froude number for two flood depths. It was found that existing inflatable dams are quite effective in suppressing floods for a relatively wide range of flood velocities.     

深水锚泊线串联浮筒系统的动力特性分析

在时域范围内建立深水锚泊线串联浮筒系统的动力分析模型,考虑锚泊线和海床之间的接触作用,基于Morison公式计算锚泊线的惯性力和拖曳力荷载,并利用单根锚泊线由于上部浮体运动而吸收的能量来计算锚泊阻尼。分析串联浮筒系统对锚泊线张力和阻尼的影响特征,进而对串联浮筒的大小和所处位置进行参数敏感性分析。该结果对深水浮式平台锚泊系统设计中如何有效地减小锚泊张力具有实际意义。     

Updated Lagrangian free surface flow simulations with natural neighbour Galerkin methods

In this paper, a new method to simulate free surface fluid flows within an updated Lagrangian framework is described. It is based on the use of a meshless technique coined as natural element method (NEM) or, more recently, as natural neighbour Galerkin method. The position of the flow front or the geometry of the fluid domain is handled by invoking the geometrical concept of α‐shape of the cloud of points, thus avoiding the explicit definition of the boundary of the domain as it evolves. This method also avoids the traditional need of remeshing typical in finite element simulations of this kind of processes. Three types of fluid behaviour have been considered, namely a purely Newtonian fluid, a non‐Newtonian short fibre‐reinforced thermoplastic, and finally a Norton–Hoff viscoplastic behaviour. Benchmark examples showing the performance of the technique are included in the paper. Copyright © 2004 John Wiley & Sons, Ltd.     

Updated Lagrangian/Arbitrary Lagrangian–Eulerian framework for interaction between a compressible neo‐Hookean structure and an incompressible fluid

We propose a numerical method for a fluid–structure interaction problem. The material of the structure is homogeneous, isotropic, and it can be described by the compressible neo‐Hookean constitutive equation, while the fluid is governed by the Navier–Stokes equations. Our study does not use turbulence model. Updated Lagrangian method is used for the structure and fluid equations are written in Arbitrary Lagrangian–Eulerian coordinates. One global moving mesh is employed for the fluid–structure domain, where the fluid–structure interface is an ‘interior boundary’ of the global mesh. At each time step, we solve a monolithic system of unknown velocity and pressure defined on the global mesh. The continuity of velocity at the interface is automatically satisfied, while the continuity of stress does not appear explicitly in the monolithic fluid–structure system. This method is very fast because at each time step, we solve only one linear system. This linear system was obtained by the linearization of the structure around the previous position in the updated Lagrangian formulation and by the employment of a linear convection term for the fluid. Numerical results are presented. Copyright © 2016 John Wiley & Sons, Ltd.