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In this article, a finite volume formulation for solving the Navier-Stokes equations using unstructured hybrid grids and a staggered arrangement of variable pressure and velocity is presented. In t...

This paper presents the description of the experimental apparatus, instrumentation, and processing techniques developed for the study of quasi-real slug flow using Particle Image Velocimetry, High-Speed Camera and Laser Diode Photocell techniques. Most experimental studies of the flow fields around Taylor bubbles, aiming a deeper insight into slug flow pattern, analyze the situation of isolated Taylor bubbles rising in stagnant or co-current liquid flow. Furthermore, most of these studies, consider highly viscous fluids (or, in general, low values of the inverse viscosity number, N f = ρ 2 gD 3 / μ 2 ), to get “well behaved” Taylor bubbles, where flow fields are more easily measured. However, in most industrial situations slug flows are characterized by the presence of small dispersed bubbles in the liquid stream flowing together with large Taylor bubbles, and high values of the inverse viscosity number. On the other hand, the chaotic nature of a real slug flow would not allow an adequate characterization of the flow around single Taylor bubbles, mainly, due to the lack of the repeatability of the flow field measurement, making difficult the calculation of the averaged fields. Thus, in this work, a specific experimental apparatus and instrumentation were developed, which allows the study of the flow around Taylor bubbles with and without dispersed small bubbles in the liquid stream under controlled conditions. This allows the PIV measurements, around Taylor bubbles in flows with high N f numbers, be done under repeatable conditions and thus, the determination of the averaged flow fields. The laser diode photocell technique is used to synchronize the PIV system with the passage of Taylor bubbles at the test section as well as to measure the terminal velocity and length of Taylor bubbles. A dynamic masking procedure was developed to mask out the Taylor bubbles noses and tails in the PIV images, since, for high values of the inverse viscosity number ( N f ≈ 13 , 275 ) the interface fluctuations are strong and, therefore, no fixed masking can be used.

In this paper, the one-dimensional consolidation of a single-layered poroelastic column under the influence of a gravitational field is addressed. Analytical solutions of the model equations are provided for undrained and drained consolidation stages. Numerical simulations are also employed to confirm the results obtained. Two test cases are analyzed, where quite unexpected behaviors are observed. The results show that depending on the poromechanical properties, the poroelastic layer can expand when the top boundary is opened, thus causing an influx of fluid even in the presence of a compressive external load. In other situations, the fluid phase by itself is able to counteract the external load, thus allowing stress-free regions to be observed in the interior of the poroelastic layer. In this case, the maximum negative displacement is observed not at the top boundary, where the external load is applied, but somewhere below it. Physical interpretations for these phenomena are discussed in detail in accordance with the mathematical predictions. This paper also highlights the importance of having a clear understanding of the underlying physics of the problem, as well as a proper reference solution for assuring reliable numerical results.

This work presents an alternative to the discretization of the Navier–Stokes equations using a finite volume method for hybrid unstructured grids with a staggered grid arrangement of variables. It has developed a numerical scheme, analogous to the element-based finite volume method, for the solution of 2-D incompressible fluid flow problems using several coupling strategies. All velocity components are stored at each face of the elements (pressure control volumes), following the usual procedure of staggering velocity and pressure. With this staggered arrangement, the balance of mass and momentum is satisfied, simultaneously, for the same set of variables, rendering numerical stability when compared to the nonstaggered arrangement.

Biot’s equations of poroelasticity are numerically solved by an Element-based Finite Volume Method (EbFVM). A stabilization technique is advanced to avoid spurious pressure modes in the vicinity of undrained conditions. Classical benchmark problems and more realistic 3D test cases are addressed. The results show that the proposed stabilization is able to eliminate the pressure instabilities preserving the solution accuracy.

A major goal when using a horizontal well is to increase the productivity rate when compared to the vertical layout, due to a larger area of the reservoir exposed to the well. The coupled solution into the reservoir and through the well requires finding the answer to the Darcy equation in the reservoir and the Navier-Stokes equations in the well. Additionally, several types of completion, which introduce new flow resistances, such as completions with inflow control device (ICD), stinger completion, packed off, gravel pack, and slotted liner are considered. All these details are not available with the current reservoir simulators, since the level of local detail would require a very large computational time and a complex model. In this work, the coupling between the reservoir and the well is accomplished through a distributed system, where the flow, at various types of completion, is handled through correlations obtained analytically or provided by completion equipment manufacturers. The proposed procedure consists of a fast tool, accurate and easy to use for a petroleum engineer. The results of this work show that the distributed system allows a detailed view of the flow into the well and its completion, quantifying the flow rate and pressure over the annular and liner for different types of completion, adding more physics into these simulations.

In this paper, the interfacial heat transfer in spherical and distorted fluid particles, flowing at Re numbers up to 80.0, is studied through the Volume-of-Fluid approach, aiming the development of closure relations for the interfacial heat and mass transfer, in the context of the Two-Fluid model. The Nusselt numbers of spherical particles are compared with the usual correlations presented in the literature to validate the numerical model. From the approach adopted in this work, based on the detailed modeling of the interfacial heat transfer process, it is possible to analyze the local flow structure and thermal field around the fluid particles, providing a better understanding of the effect of the particle deformation on the global heat transfer coefficients. It is shown that the interfacial heat flux distribution is affected by the particles shape, which substantially affects the flow and thermal fields around the fluid particles and, consequently, the total heat transfer rate. In addition, the effect of the increase of the interfacial area density, due to the particle deformation, on the total interfacial heat transfer is analysed. New correlations are proposed for the interfacial Nu or Sh numbers, in single rising fluid particles, which become dependent on the Eotvos ( Eo ) number, and for the correction of the interfacial area density, which should be included in the closure of the interfacial heat or mass transfer terms in the Two-Fluid model equations. It is shown that, as the particles become distorted, the transfer coefficient decreases, but the interfacial area increases, compensating the effect on the total interfacial flow. Nonetheless, for highly distorted particles, the effect of the interfacial area increase becomes dominant and the resulting total interfacial transfer is higher than the case of spherical particles.

The finite volume techniques for solving fluid flow problems can be broadly classified in cell center and cell vertex methodologies. The conventional finite volume techniques belong to the former class, since the elements coming from the grid generator are used as control volumes for performing the balances of the physical quantities, like mass, momentum and energy. The majority of the available methods in the literature uses this type of approach for solving multiphase flows of oil, water and gas in porous media. In petroleum reservoir simulation it is common for the conventional finite volume method to be linked to corner-point grids. This paper presents an Element-based Finite Volume Method (EbFVM), whereby the control volumes are constructed using parts of the elements, generating polygonal meshes in which mass, momentum and energy conservation are enforced. Polygonal meshes considerably reduce the number of unknowns of the linear system when compared with conventional finite volume methods. Three-dimensional hybrid grids are employed for the solution of oil-water flows in a porous media resembling a petroleum reservoir using the IMPES, sequential and fully implicit approaches. The analytical solution of the 1D Buckley-Leverett problem is used for evaluation purposes, and numerical solutions for 2D and 3D problems using unstructured grids are carried out to demonstrate the generality of the method and for comparing the robustness, convergence rate and CPU time of the IMPES and Fully Implicit solutions. Memory usage and convergence rate are also presented for the solution of 3D problems using tetrahedral grids in a cell-center and cell-vertex methodologies.

This work presents an element based finite volume methodology (EbFVM) [11] for solving two-dimensional viscoelastic fluid flows. The method can easily deal with hybrid unstructured meshes consisting of both triangular and quadrilateral elements, which allows the discretization of complex geometries. To overcome the problem of partial decoupling of pressure and velocity fields due to the use of a collocated arrangement of variables, it is used a interpolation function of the FIELDS type. Such a function also promoted the inclusion of pressure and stresses in the mass conservation equation improving conditioning of the coefficient matrix of the system of discretized equations. The advection terms in the constitutive equations are approximated using the single point upwind scheme. For testing different aspects of the numerical solution two classic benchmark problems were solved: flow between fixed parallel plates, and 4:1 planar contraction flow.

SUMMARY The literature shows an increasing number of works focused on investigating the behaviour of methods that uses concepts of control volumes in the solution of structural problems. In recent years, new approaches using unstructured meshes have been proposed, most of which addressing new applications and, to a lesser extent, the underling physical perspective. This paper presents a unified approach to the element-based finite volume method and FEM-Galerkin within the framework of the finite element space. Numerical examples highlight some accuracy issues associated with the element-based finite volume method developed in this work. Copyright © 2014 John Wiley & Sons, Ltd.

A mathematical model for pulverized wet coal combustion is presented. A new detailed kinetic mechanism composed of 500 reactions an 88 species was established. The mass transfer in reacting flow was simulated by including reactions in the kinetic mechanism. The results obtained were compared to numerical and experimental published data and demonstrated a good performance of large mechanisms, in which the model detected the presence of great amounts of the sulfuric species. As for moisture, it always should be treated as an uncoupled phenomenon from devolatilization. Tests were carried out to determine the release of moisture together with volatile matter and demonstrated great changes in the energy and kinetics of the system. The presence of moisture favors the overlapping between devolatilization and heterogeneous combustion. Emissions of SO2, CO and NO are significantly reduced with the increase of moisture in the coal particle, but the H2SO molar fraction is increased.

This paper addresses bubbly flow modeling within Venturi tubes and nozzles using the two-fluid model. The effects of non-drag forces as virtual mass and the so-called “transversal forces” such as lift and wall lubrication are investigated in the context of the two-fluid model. As expected, the transversal forces have an important influence on void distribution as long as the virtual mass affects the pressure drop along the contraction, which is the main parameter for the flow rate measurement. Models for the virtual mass and lift forces were implemented via user routines in commercial computational fluid dynamics (CFD) software, as the models embedded within these packages, specifically for virtual mass, were found not to be adequate for the purpose of this study. The models are validated against results from the literature and pressure drop measurements along a Venturi tube, developed in this work. Additionally, some experimental visualizations were used to make a qualitative comparison with predicted void distribution.

This paper addresses the key issue of calculating fluxes at the control-volume interfaces when finite-volumes are employed for the solution of partial differential equations. This calculation becomes even more significant when unstructured grids are used, since the flux approximation involving only two grid points is no longer correct. Two finite volume methods with the ability in dealing with unstructured grids, the EbFVM-Element-based Finite Volume Method and the MPFA-Multi-Point Flux Approximation are presented, pointing out the way the fluxes are numerically evaluated. The methods are applied to a porous media flow with full permeability tensors and non-orthogonal grids and the results are compared with analytical solutions. The results can be extended to any diffusion operator, like heat and mass diffusion, in anisotropic media.

This work presents a theoretical and experimental study of nickel deposition on iron samples at relatively high pressure using a pulsed DC glow discharge. The deposition process was conducted in conditions similar to that used for plasma sintering, using the confined anode-cathode configuration. The cathode was made from nickel commercially pure and the samples were made from interstitial free steel and sintered pure iron. The samples were characterized by mass weight gain, scanning electron microscopy and energy-dispersive X-ray microanalysis. The deposition process was mathematically modeled and the model was numerically solved using a conservative finite-volume method. The experiments demonstrated that the deposition occurs at a constant rate, with the mass flux changing linearly with the cathode voltage in the range of parameters considered. The results obtained from the diffusion model applied to the sample presented good agreement with the experimental values. Concerning the gas phase, the proposed model helped us to clarify some phenomenological aspects of the process. However, further studies, principally in the area of electrical discharges, are needed to permit a complete comprehension of this process.

The near-well regions require special attention in reservoir simulation due to the pronounced pressure gradients in those regions. Hence, the large pressure variation near the wells are rarely well captured with the commonly employed grid refinement. One of the leading goals of adopting hybrid grids is to capture the flow behavior in those regions with more ac- curacy. This paper presents two different approaches to deal with that situation. The first one treats the well-reservoir interface as a grid boundary. Then, as the grid gets closer to the well, it is demanded a severe refinement in the radial direction. The second approach employs a well model with the purpose of avoiding extremely refined grid. A single phase flow problem with a known well pressure value was solved in order to test the feasibility of these two approaches with several two-dimensional hybrid grids. The results are compared with a reference solution, which, regardless of also being numerical, was solved in a highly refined grid, especially in the near-well area.

The correct prediction of moving fronts is of utmost importance in mold injection. Due to the complexity of the computational domains encountered in this engineering application, finite element methods (FEM) are widely used for predicting the fluid flow. The prediction of the position of the front are, however, usually done using finite differences because of local mass conservation requirements. This paper presents a finite volume method for simulating flows with moving fronts using Voronoi discretization, where the conservation principles are obeyed in solving the flow variables inside the domain as well as in the moving front. The method extends the knowledge of the classical finite volume method for structured grids to unstructured grids.

A non isotropic turbulence model is extended and applied to three dimensional stably stratified flows and dispersion calculations. The model is derived from the algebraic stress model (including wall proximity effects), but it retains the simplicity of the "eddy viscosity" concept of first order models. The "modified k-epsilon" is implemented in a three dimensional numerical code. Once the flow is resolved, the predicted velocity and turbulence fields are interpolated into a second grid and used to solve the concentration equation. To evaluate the model, various steady state numerical solutions are compared with small scale dispersion experiments which were conducted at the wind tunnel of Mitsubishi Heavy Industries, in Japan. Stably stratified flows and plume dispersion over three distinct idealized complex topographies (flat and hilly terrain) are studied. Vertical profiles of velocity and pollutant concentration are shown and discussed. Also, comparisons are made against the results obtained with the standard k-epsilon model.

The present work deals with the numerical solution of elliptic flows encountered in open-ended channels. The important question of applying boundary conditions for pressure and velocity for these flows is considered and a new method for the application of boundary conditions at the channel inlet is proposed. It is shown that the flow reversal at the channel outlet, which appears when nonsymmetric flow conditions are present, is strongly dependent on the entrance boundary conditions for pressure. Results for the straight channel in situations where flow reversal is present are reported for a wide range of Rayleigh numbers. Solutions for L-shaped channels are also reported with the aim of demonstrating the application of the model to arbitrary channels. It is shown that for certain flow situations the use of an elliptic formulation is imperative in order to predict correctly the flow behavior in open-ended channels.

The development of an all-speed Euler and/or Navier-Stokes flow simulation code that uses a segregated finite volume algorithm for three-dimensional body-conforming curvilinear coordinates with a collocated variable arrangement is described. The efforts towards the physical validation of this code are the major contribution of the present work. The details of an experimental wind-tunnel investigation for pressure distribution and force measurements for the Brazilian Satellite Launch Vehicle (VLS) are also described. The computational results obtained for subsonic and supersonic flow conditions are in very good agreement with the experimental data. Transonic calculations, however, show poorer agreement with the available data for equivalent and even more refined meshes. The computational results produced by the present codes are already supplying aerodynamic information that is currently being used in the VLS design process.

A Finite Volume Method is employed for solving the coupled fluid/structure problem encountered in porous deformable media, namely the flow in the porous rock of a petroleum reservoir coupled with the stress field in the porous matrix. As oil is produced, the porous pressure diminishes changing the porosity of the structure, requiring careful monitoring of the structure of the matrix to avoid rock collapse. This coupled problem is normally solved using two different methodologies, finite volume, or finite-differences, for the flow in the porous media, and finite element for the rock mechanics. The reason for this approach is the belief that finite volume methods are suitable only for fluid flow problems. In fact, the momentum conservation equation is, obviously, the same for both problems, allowing the proposition of a single method, using a single grid for solving the coupled problem. As a consequence, it is not required grid interpolation to transfer results from one problem to another and, even more att...

The use of the segregated finite-volume method requires special procedures for handling the pressure-velocity coupling. It is a normal practice to employ staggered grids to promote the adequate coupling between pressure and velocity. However, this alternative becomes unfeasible for three-dimensional problems, especially if boundary-fitted grids are employed. In this work a numerical model employing co-located variables is developed. The model uses nonorthogonal boundary-fitted meshes and is therefore suitable for the solution of all speed flows, considering the extra coupling between pressure and density. Results are obtained for selected test cases, including incompressible as well as supersonic flows, which are compared with experimental ones.

This work presents a comparative study among three linearization schemes widely used in petroleum reservoir simulation, namely the Implicit Pressure Explicit Saturation (IMPES), Fully Implicit (FI) and Adaptive Implicit Method (AIM). Attention is given to the criterion used for switching from IMPES to FI and vice-versa. The black-oil model considering the oil-water flow is employed. The equations are discretized using an unstructured Voronoi mesh in a finite-volume framework. The numerical results are analyzed based on the number of iterations in the Newton and solver procedures, number of implicit volumes, and mass balance error of components. The effect of the stopping criterion on Newton's iterations is also investigated. The outcome of the study reveals that adaptive implicit methodologies can be a good choice when unstructured grids are present, allowing the use of time steps with the same order of magnitude as the ones used in FI procedures, but with reduction in the computational effort.

Pioneer methods for simulating petroleum reservoirs were developed in the framework of finite difference methods with Cartesian grids. Therefore, the concept of transmissibility was readily applied for calculating the fluxes at the control volume interfaces. With the advent of new methods using curvilinear non-orthogonal and unstructured grids, the concept of transmissibility was maintained, probably for taking advantage of the simplicity in the programming. However, it is well known that for non-orthogonal grids, unstructured or not, the fluxes can not be exactly calculated using only two grid points, what precludes the use of the transmissibility for the flux calculation in such situations. On the other hand, it is common to find in the literature a recommendation that triangles, as used in unstructured grids should not have internal angles greater than 90 in order to avoid the appearance of a negative transmissibility. It is shown that this is a misinterpretation of the transmissibility concept, since transmissibility is always a positive quantity.