Jiansheng Xiang

Modelling of fluid–solid interactions using an adaptive mesh fluid model coupled with a combined finite–discrete element model

Fluid–structure interactions are modelled by coupling the finite element fluid/ocean model ‘Fluidity-ICOM’ with a combined finite–discrete element solid model ‘Y3D’. Because separate meshes are used for the fluids and solids, the present method is flexible in terms of discretisation schemes used for each material. Also, it can tackle multiple solids impacting on one another, without having ill-posed problems in the resolution of the fluid’s equations. Importantly, the proposed approach ensures that Newton’s third law is satisfied at the discrete level. This is done by first computing the action–reaction force on a supermesh, i.e. a function superspace of the fluid and solid meshes, and then projecting it to both meshes to use it as a source term in the fluid and solid equations. This paper demonstrates the properties of spatial conservation and accuracy of the method for a sphere immersed in a fluid, with prescribed fluid and solid velocities. While spatial conservation is shown to be independent of the mesh resolutions, accuracy requires fine resolutions in both fluid and solid meshes. It is further highlighted that unstructured meshes adapted to the solid concentration field reduce the numerical errors, in comparison with uniformly structured meshes with the same number of elements. The method is verified on flow past a falling sphere. Its potential for ocean applications is further shown through the simulation of vortex-induced vibrations of two cylinders and the flow past two flexible fibres.

A new approach to upscaling fracture network models while preserving geostatistical and geomechanical characteristics

A new approach to upscaling two-dimensional fracture network models is proposed for preserving geostatistical and geomechanical characteristics of a smaller-scale “source” fracture pattern. First, the scaling properties of an outcrop system are examined in terms of spatial organization, lengths, connectivity, and normal/shear displacements using fractal geometry and power law relations. The fracture pattern is observed to be nonfractal with the fractal dimension D ≈ 2, while its length distribution tends to follow a power law with the exponent 2 < a < 3. To introduce a realistic distribution of fracture aperture and shear displacement, a geomechanical model using the combined finite-discrete element method captures the response of a fractured rock sample with a domain size L = 2 m under in situ stresses. Next, a novel scheme accommodating discrete-time random walks in recursive self-referencing lattices is developed to nucleate and propagate fractures together with their stress- and scale-dependent attributes into larger domains of up to 54 m × 54 m. The advantages of this approach include preserving the nonplanarity of natural cracks, capturing the existence of long fractures, retaining the realism of variable apertures, and respecting the stress dependency of displacement-length correlations. Hydraulic behavior of multiscale growth realizations is modeled by single-phase flow simulation, where distinct permeability scaling trends are observed for different geomechanical scenarios. A transition zone is identified where flow structure shifts from extremely channeled to distributed as the network scale increases. The results of this paper have implications for upscaling network characteristics for reservoir simulation.

Coupled FEMDEM/Fluids for coastal engineers with special reference to armour stability and breakage

Sea-level rise and increased storminess present huge challenges to coastal engineers worldwide. The seaward slope of many breakwaters and shoreline defence structures consists of thousands of interlocking units of concrete or rock making up a massive granular defence against wave attack. The units are placed freely to form an armour layer which is intended to both dissipate wave energy and remain structurally stable. Design guidance on the mass and shape of these units is based on empirical equations derived from Froude scale physical model tests. The two main failure modes for concrete armour layers are displacement (hydraulic instability) and breakage (structural instability) which are strongly coupled. Breakage mechanisms cannot all be faithfully reproduced under scaled physical models. Fundamental understanding of the forces governing such wave-structure interaction remains poor and unit breakages continue to baffle the designers of concrete armour units. This paper illustrates a range of DEM and FEMDEM methods being developed to model the granular solid skeleton of freely packed brittle units. Such discrete element methods are increasingly being used by engineers for solids modelling. They are especially powerful when coupled with a CFD model which can resolve ocean wave dynamics. The aim is to describe a framework for coupled modelling technologies applicable to coastal engineering problems. Preliminary simulation test cases, still at proof of concept stage, but based on a wealth of validation studies are presented. Thus, we report a snap-shot of progress towards a future where designers combine multi-physics numerical technology with knowledge from scaled physical models for a better understanding of wave energy turbulence, block movement, and internal stresses within armour units.

An immersed-shell method for modelling fluid-structure interactions.

The paper presents a novel method for numerically modelling fluid–structure interactions. The method consists of solving the fluid-dynamics equations on an extended domain, where the computational mesh covers both fluid and solid structures. The fluid and solid velocities are relaxed to one another through a penalty force. The latter acts on a thin shell surrounding the solid structures. Additionally, the shell is represented on the extended domain by a non-zero shell-concentration field, which is obtained by conservatively mapping the shell mesh onto the extended mesh. The paper outlines the theory underpinning this novel method, referred to as the immersed-shell approach. It also shows how the coupling between a fluid- and a structural-dynamics solver is achieved. At this stage, results are shown for cases of fundamental interest.

Implementation of an Empirical Joint Constitutive Model into Finite-Discrete Element Analysis of the Geomechanical Behaviour of Fractured Rocks

An empirical joint constitutive model (JCM) that captures the rough wall interaction behaviour of individual fractures associated with roughness characteristics observed in laboratory experiments is combined with the solid mechanical model of the finite-discrete element method (FEMDEM). The combined JCM-FEMDEM formulation gives realistic fracture behaviour with respect to shear strength, normal closure, and shear dilatancy and includes the recognition of fracture length influence as seen in experiments. The validity of the numerical model is demonstrated by a comparison with the experimentally established empirical solutions. A 2D plane strain geomechanical simulation is conducted using an outcrop-based naturally fractured rock model with far-field stresses loaded in two consecutive phases, i.e. take-up of isotropic stresses and imposition of two deviatoric stress conditions. The modelled behaviour of natural fractures in response to various stress conditions illustrates a range of realistic behaviour including closure, opening, shearing, dilatancy, and new crack propagation. With the increase in stress ratio, significant deformation enhancement occurs in the vicinity of fracture tips, intersections, and bends, where large apertures can be generated. The JCM-FEMDEM model is also compared with conventional approaches that neglect the scale dependency of joint properties or the roughness-induced additional frictional resistance. The results of this paper have important implications for understanding the geomechanical behaviour of fractured rocks in various engineering activities.

Modelling of fluid-structure interaction with multiphase viscous flows using an immersed-body method

An immersed-body method is developed here to model fluid-structure interaction for multiphase viscous flows. It does this by coupling a finite element multiphase fluid model and a combined finite-discrete element solid model. A coupling term containing the fluid stresses is introduced within a thin shell mesh surrounding the solid surface. The thin shell mesh acts as a numerical delta function in order to help apply the solid-fluid boundary conditions. When used with an advanced interface capturing method, the immersed-body method has the capability to solve problems with fluid-solid interfaces in the presence of multiphase fluid-fluid interfaces. Importantly, the solid-fluid coupling terms are treated implicitly to enable larger time steps to be used. This two-way coupling method has been validated by three numerical test cases: a free falling cylinder in a fluid at rest, elastic membrane and a collapsing column of water moving an initially stationary solid square. A fourth simulation example is of a water-air interface with a floating solid square being moved around by complex hydrodynamic flows including wave breaking. The results show that the immersed-body method is an effective approach for two-way solid-fluid coupling in multiphase viscous flows.

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

This work presents the first application of a non-intrusive reduced order method to model solid interacting with compressible fluid flows to simulate crack initiation and propagation. In the high fidelity model, the coupling process is achieved by introducing a source term into the momentum equation, which represents the effects of forces of the solid on the fluid. A combined single and smeared crack model with the Mohr-Coulomb failure criterion is used to simulate crack initiation and propagation. The non-intrusive reduced order method is then applied to compressible fluid and fractured solid coupled modelling where the computational cost involved in the full high fidelity simulation is high. The non-intrusive reduced order model (NIROM) developed here is constructed through proper orthogonal decomposition (POD) and a radial basis function (RBF) multi-dimensional interpolation method.The performance of the NIROM for solid interacting with compressible fluid flows, in the presence of fracture models, is illustrated by two complex test cases: an immersed wall in a fluid and a blasting test case. The numerical simulation results show that the NIROM is capable of capturing the details of compressible fluids and fractured solids while the CPU time is reduced by several orders of magnitude. In addition, the issue of whether or not to subtract the mean from the snapshots before applying POD is discussed in this paper. It is shown that solutions of the NIROM, without mean subtracted before constructing the POD basis, captured more details than the NIROM with mean subtracted from snapshots.

Polyaxial stress-dependent permeability of a three-dimensional fractured rock layer

A study about the influence of polyaxial (true-triaxial) stresses on the permeability of a three-dimensional (3D) fractured rock layer is presented. The 3D fracture system is constructed by extruding a two-dimensional (2D) outcrop pattern of a limestone bed that exhibits a ladder structure consisting of a “through-going” joint set abutted by later-stage short fractures. Geomechanical behaviour of the 3D fractured rock in response to in-situ stresses is modelled by the finite-discrete element method, which can capture the deformation of matrix blocks, variation of stress fields, reactivation of pre-existing rough fractures and propagation of new cracks. A series of numerical simulations is designed to load the fractured rock using various polyaxial in-situ stresses and the stress-dependent flow properties are further calculated. The fractured layer tends to exhibit stronger flow localisation and higher equivalent permeability as the far-field stress ratio is increased and the stress field is rotated such that fractures are preferentially oriented for shearing. The shear dilation of pre-existing fractures has dominant effects on flow localisation in the system, while the propagation of new fractures has minor impacts. The role of the overburden stress suggests that the conventional 2D analysis that neglects the effect of the out-of-plane stress (perpendicular to the bedding interface) may provide indicative approximations but not fully capture the polyaxial stress-dependent fracture network behaviour. The results of this study have important implications for understanding the heterogeneous flow of geological fluids (e.g. groundwater, petroleum) in subsurface and upscaling permeability for large-scale assessments.RésuméUne étude sur l’influence des tensions polyaxiales (triaxiales véritables) sur la perméabilité d’une couche de roche fracturée en 3D est. présentée. Le système de fractures 3D est. construit en extrayant le motif d’affleurement 2D d’un niveau calcaire qui présente une structure en échelle consistant en un ensemble de joints parallèles contigu à des fractures courtes d’un stade ultérieur. Le comportement géomécanique de la roche fracturée en 3D en réponse aux contraintes in-situ est. modélisé par la méthode des éléments finis discrets, qui peut saisir la déformation des blocs de matrice, les variations du champ de contraintes, la réactivation de fractures préexistantes rugueuses et la propagation de nouvelles fissures. Une série de simulations numériques est. conçue pour imposer des contraintes à une roche fracturée en utilisant différentes tensions in situ polyaxiales et les propriétés d’écoulement dépendantes des tensions sont ensuite calculées. La couche fracturée a tendance à présenter une localisation plus forte des flux et une perméabilité équivalente supérieure lorsque le rapport des contraintes du champ éloigné augmente et que le champ de contraintes pivote de telle manière que les fractures sont orientées préférentiellement en faveur du cisaillement. La dilatation par cisaillement de fractures préexistantes a des effets dominants sur la localisation du flux dans le système, tandis que la propagation de nouvelles fractures a des impacts mineurs. Le rôle de la contrainte liée à la surcharge suggère que l’analyse conventionnelle 2D qui néglige l’effet de la contrainte hors plan (perpendiculaire à l’interface de stratification) peut fournir des approximations indicatives mais ne traduit pas entièrement le comportement du réseau de fractures soumis à des tensions polyaxiales. Les résultats de cette étude ont d’importantes implications pour comprendre l’écoulement hétérogène de fluides géologiques (par ex. eau souterraine, pétrole) en milieu souterrain et pour améliorer la perméabilité pour des évaluations à grande échelle.ResumenSe presenta un estudio sobre la influencia de los esfuerzos poliaxiales (triaxiales verdaderas) sobre la permeabilidad de una capa tridimensional (3D) de rocas fracturadas. El sistema de fractura en 3D se construye mediante la extrusión de un patrón de afloramiento 2D de un lecho de caliza que exhibe una estructura de escalera que consiste en un conjunto articulado limitado por fracturas cortas de una etapa posterior. El comportamiento geomecánico de la roca fracturada en 3D en respuesta a los esfuerzos in situ es modelado por el método de elementos finitos y discretos, que puede capturar la deformación de bloques de matriz, la variación de campos de esfuerzos, la reactivación de fracturas irregulares preexistentes y la propagación de nuevas grietas. Una serie de simulaciones numéricas está diseñada para cargar la roca fracturada utilizando diferentes esfuerzos poliaxiales in situ y se calculan además las propiedades de flujo dependientes del esfuerzo. La capa fracturada tiende a exhibir una localización de flujo más fuerte y una permeabilidad equivalente más alta a medida que se incrementa la relación del esfuerzo en el campo lejano y se hace girar el campo de esfuerzo de tal manera que las fracturas se orientan preferentemente para el cizallamiento. La dilatación por cizalladura de fracturas preexistentes tiene efectos dominantes sobre la localización del flujo en el sistema, mientras que la propagación de nuevas fracturas tiene impactos menores. El papel del esfuerzo de la sobrecarga sugiere que el análisis 2D convencional que descuida el efecto del esfuerzo fuera del plano (perpendicular a la interfase del lecho) puede proporcionar aproximaciones indicativas pero no capturar completamente el comportamiento de la red de fractura dependiente del esfuerzo poliaxial. Los resultados de este estudio tienen importantes implicancias para la comprensión del flujo heterogéneo de fluidos geológicos (por ejemplo, aguas subterráneas, petróleo) en el subsuelo y en el escalado de la permeabilidad para evaluaciones a gran escala.摘要本文论述了多轴(真三轴)应力对三维裂隙岩层渗透率影响的研究成果。该石灰岩层具有阶梯结构,早期裂缝贯穿整个系统,后期较短的裂缝毗连早期裂缝。通过对两维露头 的几何沿岩层方向进行延申,建立了三维裂隙系统的几何模型。通过有限-离散元方法模拟了现场应力作用下三维裂隙岩体的力学特性,该方法能捕获岩块变形、应力场变化、自然裂缝的变形以及新裂隙的扩展。本文 设计了一系列的数值模拟实验,模拟加载多种多轴现场应力,进一步分析了渗透率对应力场的依赖性。随着远场应力比的 增加以及应力场的旋转,有些裂缝表现出很强的滑移,岩层也因此表现出很强的局部流动及很高的渗透率。研究表明,已有裂缝的滑移及剪涨效应对渗透率有非常重要的影响,而新裂缝的扩展影响较小。本文中发现的纵向应力效应表明,忽略平面外应力(垂直于层理界面)影响的传统二维分析可能提供了象征性的近似值,但无法完全捕获取决于多轴应力的裂缝网络的特性。本研究的结果对于了解地质流体(如地下水、石油)的不均匀流动、预测大尺度渗透率等具有重要的意义。ResumoUm estudo é apresentado sobre a influência de esforço poliaxial (verdadeiramente triaxial) sobre a permeabilidade de uma camada de rocha fraturada tridimensional. O sistema fraturado 3D é construído extraindo-se um padrão de afloramento 2D de uma camada de calcário que exibe uma estrutura de escada consistindo de um conjunto de juntas interceptadas posteriormente por fraturas pequenas. O comportamento geomecânico 3D da rocha fraturada em resposta aos esforços locais é modelado pelo método de elementos discretos finitos, que pode capturar a deformação da matriz dos blocos, variação do campo de esforços, reativação de fraturas pré-existentes e propagação de novas rachaduras. Uma serie de simulações numéricas é desenvolvida para sobrecarregar a rocha fraturada usando diversos esforços poliaxiais locais e as propriedades de fluxo dependente dos esforços são posteriormente calculadas. A camada fraturada tende a mostrar forte fluxo localizado e maior permeabilidade equivalente assim que a taxa de esforço do campo externo é aumentada e o campo de esforço é rotacionado de forma que as fraturas são preferencialmente orientadas para cisalhamento. A dilatação por cisalhamento de fraturas pré-existentes tem efeitos dominantes no sistema de fluxo localizado, enquanto que a propagação de novas fraturas tem um impacto menor. O efeito do esforço do sobrecarregamento sugere que a análise 2D convencional que negligencia os efeitos dos esforços de fora do plano (perpendicular à interface do acamamento) pode fornecer indicações aproximadas, porém não captar integralmente o comportamento a rede de fraturas dependente do esforço poliaxial. Os resultados deste estudo possuem importantes implicações para entender o fluxo heterogêneo de fluidos geológicos (ex. águas subterrâneas e petróleo) em subsuperfície e aumentar a escala da avaliação da permeabilidade em grande escala.

Simulation and Characterisation of Packed Columns for Cylindrical Catalyst Supports and Other Complex-Shaped Bodies

Catalyst pellets are packed in reactor beds and the shape and mechanical properties have a major influence on the reactor performance by virtue of (i) the detailed topology of the void space and grain surface area and (ii) the fragility of the pack to withstand in-service stresses within the solid skeleton—often through thermal and cyclic stressing. The paper highlights the features of the FEMDEM code used to simulate these performance-related properties of the pack. The local porosity, packing structure, bulk porosity and orientation distributions of the resulting bodies making up the pack of pellets will be presented. The generic methodology illustrated is shown to be suitable for shape optimisation of industrial packing processes.

A New Finite Discrete Element Approach for Heat Transfer in Complex Shaped Multi Bodied Contact Problems

This work presents a new approach for the modelling of the heat transfer of 3D discrete particle systems. Using a finite-discrete element (FEMDEM) method, the surface of contact is numerically computed when two discrete meshes of contacting solids are overlapping. Incoming heat flux and heat conduction inside and between solid bodies is linked. In traditional FEM approaches to model heat transfer across contacting bodies, the surface of contact is not directly reconstructed. The approach adopted here uses the number of surface elements from the penetrating boundary meshes to form a polygon of the intersection. This results in a significant decrease in the mesh dependency of the method. Moreover, this new method is suited to any shape of particle and heat distribution across particles is an inherent feature of the model.