High performance simulations of yield stress fluids in a structured adaptive mesh refinement framework with embedded boundaries

Viscoplastic fluids are a class of non-Newtonian liquids characterised by their yield stress. Unless an external stress is applied which is larger than this threshold value, the fluid does not flow, but exhibits rigid body behaviour. Above the yield stress, applied forces cause viscous deformation. Such fluids play important roles in a range of fields, notably in wellbore drilling, which is the application that motivated this project. One aspect of this operation requires displacement of drilling fluid by cement in the annulus between casing and geological surroundings, and both of these fluids are viscoplastics. Ensuring that this is done properly is of utmost importance to the overall safety of the drilling operation. Often, numerical simulations are the only viable way of experimenting with the effect of drilling parameters and fluid properties on the flow configuration and resulting behaviour. Unfortunately, the presence of a yield stress leads to a singularity in the apparent viscosity at zero strain. This causes substantial computational expense for the algorithms used to simulate fluid flow numerically, even when regularisation techniques are employed to alleviate the problem. Consequently, most published results in the literature on computational viscoplasticity has been restricted to two-dimensional and steady-state flows. In an attempt to address this, we have applied state-of-the-art techniques from high-performance computational fluid dynamics to the viscoplastic flow problem. Specifically, we utilise spatio-temporal adaptive mesh refinement on structured meshes in this context for the first time. This is achieved through the software framework AMReX, which includes state-of-the-art numerical tools for solving partial differential equations with optimal parallel scaling. The ability to rapidly simulate unsteady viscoplastic flow problems in three dimensions is demonstrated by novel numerical experiments in a lid-driven cavity. In order to investigate flows in more interesting domain geometries and around objects, an embedded boundary algorithm has been developed which works alongside the viscoplastic flow solver. We show how this methodology can be utilised to simulate flow inside non-rectangular objects, and investigate fully three-dimensional viscoplastic flow past several shapes of bodies for the first time.EPSRC Centre for Doctoral Training in Computational Methods for Materials Science grant number EP/L015552/1 BP International Centre for Advanced Materials (BP-ICAM) Extra support towards living expenses through the Aker Scholarshi

Drilling Foam Rheology and Hydraulics at High Pressure and Elevated Temperature

Foam has been successfully used as the motive fluid for different operations such as well stimulation, underbalanced drilling, enhanced oil recovery (EOR), cleanout, and acidizing operations in the oil and gas industry. Due to its low liquid content, it provides a distinct advantage with regards to less material requirements. However, due to its structure-driven viscosity, high compressibility, and complex flow behavior, accurate predictions of rheology and hydraulic parameters are essential for the success of field operations. This investigation focuses on rheological and hydraulic characteristics of foams, incorporating the effect of temperature on their flow behavior. In this investigation, polyanionic cellulose (PAC) polymer (0.25% by wt.) based foam was generated using nitrogen as the gas phase and its rheology was determined using a recirculating flow loop that has three pipe viscometers (3.05, 6.22, and 12.7 mm OD) and fully-eccentric annular section (3.05 mm OD × 12.57 mm ID, and 9.53 mm OD × 12.57 mm ID). Experiments were conducted within the temperature range of 24 to 149ºC and at various foam qualities (0%, 45%, 55%, 65%, and 75%). The foams displayed power-law fluid behavior in the shear rate range tested (100 to 5000 s-1), which is often experienced in the wellbore. Like its base liquid, polymer foam exhibited thermal thinning and a significant rheology change with temperature. Only high-quality foam (75%) at ambient temperature (24ºC) showed yielding behavior, which was measured in a pipe viscometer under static condition. The disappearance of yield stress at elevated temperature could be attributed to the thermal thinning of the liquid phase that weakens the strength of the bubble structure. Experimental data is used to develop new correlations to predict power-law fluid parameters as a function of temperature, base fluid properties, and foam quality. Moreover, the measurements are compared with the predictions of existing models, and discrepancies are observed, which could be attributed to the variation in foam generation technique, the nature and concentration of polymer, and the concentration of surfactant used in the experiments in which data was obtained to develop the models. Furthermore, annular pressure loss measurements obtained from fully eccentric annulus at low temperatures (24 and 79ºC) show predominantly good agreement with predictions of a hydraulic model that uses the new correlations. Discrepancies increased with temperature as the foam becomes unstable due to the thermal thinning of the liquid film and subsequent weakening of bubble structure and reduced stability of foam. A mathematical model has been developed by applying mechanical energy balance on small discretized control volume in the wellbore. The model combines the effect of hydrostatic, frictional and acceleration pressure loss components on the calculation of bottom hole pressure, and predicts foam quality, density, velocity, and pressure at different measured depths. A parametric study was performed to understand the effect of different variables on the foam drilling hydraulics

Spreading of viscous fluids and granular materials on slopes

Materials can flow down a slope in a wide range of geophysical and industrial contexts, including lava flows on volcanoes and thin films on coated surfaces. The aim of my research is to provide quantitative insight into these forms of motion and their dependence on effects of the topography, the volume and the rheology of the flowing structure. Numerous different problems are investigated through mathematical models, which are developed analytically and confirmed by laboratory experiments. The initial advance of long lava flows is studied by considering the flow of viscous fluid released on sloping channels. A scaling analysis, in agreement with analog experiments and field data, offers a practical tool for predicting the advance of lava flows and conducting hazard analysis. A simple and powerful theory predicts the structure of flows resulting from any time-dependent release of fluid down a slope. Results obtained by the method of characteristics reveal how the speed of the advancing front depends importantly on the rate of fluid supplied at an earlier time. Viscous flows on surfaces with different shapes are described by similarity solutions to address problems motivated by engineering as well as geophysical applications. Pouring viscous fluid out of a container can be a frustratingly slow process depending on the shape and the degree of tipping of the container. The discharge rate of the fluid is analysed in simple cases, shedding light on how containers can be emptied most quickly in cosmetic and food industries. In a separate study motivated by coating industries, thin films are shown to evolve with uniform thickness as they drain near the top of a horizontal cylinder or sphere. The leading edge eventually splits into rivulets as predicted theoretically and confirmed by experiments. Debris flows can develop levees and trigger avalanches which are studied by considering dense granular flows down a rough inclined plane. Granular materials released down a slope can produce a flowing structure confined by levees or trigger avalanches at regular intervals, depending on the steady rate of supply. The experimental results are discussed using theoretical ideas of shallow granular flows. Finally, materials flowing in long and slender ducts are investigated theoretically to better understand the digestive and urinary systems in biology. The materials are pumped in an elastic tube by translating waves of muscular contraction and relaxation. The deformation of the tube is predicted by solving a free-boundary problem, a similar mathematical exercise to predicting the moving boundaries of materials spreading on slopes

Computational and rheological studies for coating flows.

Coating flows can be defined as a laminar free surface flows, whereby a liquid layer is applied onto a solid substrate. A typical industrial application consists of co-rotating cylindrical rollers, which are used to apply a liquid coating (paint) onto a moving substrate, and depending on the direction of the rollers, can be configured in either forward or reverse mode. These types of coating solution flows are industrially important applications, and convey viscoelastic aspects due to their polymeric content and unsteady polymeric behaviour. The process often possesses localized regions of high shear and extension rates (narrow nip and wetting-line zones), which may cause instabilities on the coated substrate (ribbing, leveling, striping). These non-Newtonian and viscoelastic studies for industrial reverse roll coating focus on the use of computational techniques to model these types of coating flows, alongside the analysis of the fluid flow behaviour and under varied rheological properties. Two flow problem configurations have been considered, a model benchmark problem of mixed combined-separating flow, and the industrial application of reverse roll coating flow. Predictions and corresponding solutions are reported for viscous, inelastic and complex viscoelastic fluid properties. The numerical formulation adopts a Taylor-Galerkin pressure-correction (TGPC) scheme, using a finite element method for viscous, inelastic flows and a hybrid finite element/finite volume method for their viscoelastic counterparts. The research plan is centered around computational fluid dynamics and rheological studies, with the main target focused on industrial roll-coating operations. From simple theory, Newtonian and non-Newtonian coating flows possess specific, yet disparate characteristics. This may lead to distinct and significant differences in their detailed flow behaviour, and in the stressing levels generated, dependent upon the nature of the flow configuration. The study is segmented into several stages: initially, solution was sought for a benchmark flow problem, where a semi- implicit time stepping finite element procedure was employed to simulate a mixed combined- separating flow. Here, both viscous and viscoplastic material approximations have been introduced. Secondly, the industrial application of reverse roll coating flow was addressed for viscous inelastic coating fluids. This incorporated scenarios of inclusion and not of a dynamic wetting line and consideration of the effects of a rubber elastomer-cover upon the applicator roll. Thirdly, viscoelastic paint coatings were addressed for the industrial reverse roll coating flow. Here, a hybrid finite element/finite volume sub-cell method was utilized, and with inclusion of a dynamic wetting line. Of the various viscoelastic material models available, use has been made of the Phan-Thien Taimer (PTT) network class of models, in both linear and exponential variety, and of the FENE class of models, with FENE-CR and FENE-P versions. This has offered a richness in capacity over variation of rheological properties. The choice of computational methods has been justified and the TGPC algorithm was deemed suitable for problem solution. The methodology tested on combined-separating flow provided high-quality numerical results, which compare favorably against experiments, literature and theory. When applied to the reverse roll coating problem, the TGPC algorithm has been coupled to a time-dependent free-surface update procedure, to determine the dynamic movement of the meniscus and the wetting line. Around the nip-region, the flow problem manifests strong flow features, which have been investigated for a range of rheological properties of varying shear and extensional response. The direct impact these have on localized peak nip-pressures and distributional lift levels has been observed, where several relief mechanisms have been successfully identified (important to optimize process control). The influence of solvent fraction, extensional viscosity and increasing elasticity, up to critical stress states have been analysed in considerable detail. In summary, the success of this work indicates optimal flow process settings and preferential Theological coating properties to employ, with respect to this industrial coating process. As such, it lays the foundation and guide towards achieving a stable and consistent coating application - specifically, as high-speed high-gain production is of current demanded

Flow of bubbles and foams in narrow microfluidic geometries

The movement of gas-liquid foams through narrow channels of various complex geometries is commercially challenging and technically important. This thesis investigates the dynamics of bubbles and foams in microfluidic channels with constrictions, expansions and obstacles. The flow of single bubbles in a sudden contraction, followed by a sudden expansion was studied. Effect of the capillary number was investigated, showing that bubbles deformation increased with it. Larger bubbles were also investigated in different constrictions with the emphasis on the snap-off break-up. Effect of thin liquid films is shown experimentally to be the main contribution. Furthermore, inertial effects are found to be influential during the final neck collapse. Foams in microfluidic channels with constrictions were investigated with regards to topological changes, including bubble re-arrangements and various break-ups caused by higher shear stresses. Effects of the geometry, including, constriction width and length, are highlighted. The neck collapse also gives different scalings for various break-ups, suggesting different dynamics and forces driving the break-ups. Furthermore, foams in suddenly and gradually expanding channels were analysed with regards to velocity, elasticity and plasticity. Foams flowing in channels with spherical obstacles were studied. Dynamics of different foam regimes are presented as they flow around centrally located obstacle. The bamboo foam was found to generate two bubbles via lamella division mechanism. The sizes of the daughter bubbles are correlated with the capillary number, liquid fraction and initial bubble size. Additionally, shifting the location induced only size dependence. A more complicated structure consisting of four obstacles was studied experimentally and analysed with regards to the new number of bubbles generated. All the data is shown to collapse on a single line and to be in agreement with the numerical results

Numerical Modelling of Mixing and Separating of Fluid Flows through Porous Media

In present finite element study, the dynamics of incompressible isothermal flows of Newtonian and two generalised non–Newtonian models through complex mixing–separating planar channel and circular pipe filled with and without porous media, including Darcy’s term in momentum equation, is presented. Whilst, in literature this problem is solved only for planar channel flows of Newtonian and viscoelastic fluids. The primary aim of this study is to examine the laminar flow behaviour of Newtonian and inelastic non–Newtonian fluids, and investigate the robustness of the numerical algorithm. The rheological properties of non–Newtonian fluids are defined utilising a range of constitutive equations, for inelastic non–Newtonian fluids non–linear viscous models, such as Power Law and Bird–Carreau models are used to capture the shear thinning behaviour of fluids. To simulate such complex flows, steady–state solutions are sought employing time–dependent finite element algorithm. Temporal derivatives are discretised using second order Taylor series expansion, while, spatial discretisation is achieved through Galerkin approximation in combination to deal with incompressibility a pressure–correction scheme adopted. In order to achieve the algorithm of semi-implicit form Darcy’s–Brinkman equation is utilized for the conversion in Darcy’s terms and diffusion, while Crank–Nicolson approach is adopted for stability and acceleration. Simple and complex flows for various complex flow bifurcations of the combined mixing–separating geometries, for both two–dimensional planar channel in Cartesian coordinates, as well as axisymmetric circular tube in cylindrical polar coordinates system are investigated. These geometries consist of a two-inverted channel and pipe flows connected through a gap in common partitions, initially filled with non-porous materials and later with homogeneous porous materials. Computational domain is having variety it has been investigated with many configurations. These computational domains have been appeared in industrial applications of combined mixing and separating of fluid flows both for porous and non-porous materials. Fully developed velocity profile is applied on both inlets of the domain by imposing analytical solutions found during current study for porous materials. Numerical study has been conducted by varying flow rates and flow direction due to a variety in the domain. The influence of varying flow rates and flow directions are analysed on flow structure. Also the impact of increasing inertia, permeability and power law index on flow behaviour and pressure difference are investigated. From predicted solution of present numerical study, for Newtonian fluids a close agreement is realised between numerical solutions and experimental data. During simulations, it has been noticed that enhancing fluid inertia (flow rates), and permeability has visible effects on the flow domains. When the Reynolds number value increases the size and power of the vortex for recirculation increases. Under varying flow rates an early activity of vortex development was observed. During change in flow directions reversed flow showed more inertial effects as compared with unidirectional flows. Less significant influence of inertia has been observed in domains filled with porous media as compared with non-porous. The power law model has more effects on inertia and pressure as compared with Bird Carreau model. Change in the value of permeability gave significant impact on pressure difference. Numerical simulations for the domain and fluids flow investigated in this study are encountered in the real life of mixing and separating applications in the industry. Especially this purely quantitative numerical investigation of flows through porous medium will open more avenues for future researchers and scientists

Bibliography of Lewis Research Center technical publications announced in 1987

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1987. All the publications were announced in the 1987 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

Bibliography of Lewis Research Center technical publications announced in 1985

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1985. All the publications were announced in the 1985 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

Coupled and multiphysics phenomena

The contributions assembled in the present volume proceed from the lectures of the 2015 ALERT Geomaterials Doctoral School devoted to Coupled and Multiphysics Phenomena. The school has been organized and coordinated by Bernhard Schrefler (Universit\ue0 degli Studi di Padova), Lorenzo Sanavia (Universit\ue0 degli Studi di Padova) and Fr\ue9d\ue9ric Collin (Universit\ue9 de Liege). When dealing with the behaviour of multiphase porous systems, e.g. geomaterials, instances of complexity and interaction are numerous, mainly because of the coexistence of several constituents and phases, their physical and mechanical interactions, their reactivity and their often non-linear behaviour. The study of these coupled processes deals with a large number of applications, e.g. in geomechanics: underground structures (storage, tunnelling), surface structures (earth and concrete dams, embankments) as well as the exploitation of geo-resources (petroleum and gas extraction, mines and quarries). This volume contains nine chapters in which emphasis is given to the presentation of the fundamental and new concepts that help understanding coupled and multiphysics phenomena in porous systems. The contributions cover experimental, theoretical, as well as numerical aspects. The school is divided into three main parts: the description of the couplings in multiphysics phenomena, including the experimental developments; the mathematical modelling of all these coupled processes, with an introduction to the constitutive modelling taking into account the dilatancy, which characterizes the mechanical behaviour of geomaterials; the numerical implementation of the mathematical models, comprising constitutive equations as well as balance equations and finally numerical modelling through advanced applications