DIRECT NUMERICAL SIMULATION OF INCOMPRESSIBLE MULTIPHASE FLOW WITH PHASE CHANGE

Phase change problems arise in many practical applications such as air-conditioning and refrigeration, thermal energy storage systems and thermal management of electronic devices. The physical phenomenon in such applications are complex and are often difficult to be studied in detail with the help of only experimental techniques. The efforts to improve computational techniques for analyzing two-phase flow problems with phase change are therefore gaining momentum. The development of numerical methods for multiphase flow has been motivated generally by the need to account more accurately for (a) large topological changes such as phase breakup and merging, (b) sharp representation of the interface and its discontinuous properties and (c) accurate and mass conserving motion of the interface. In addition to these considerations, numerical simulation of multiphase flow with phase change introduces additional challenges related to discontinuities in the velocity and the temperature fields. Moreover, the velocity field is no longer divergence free. For phase change problems, the focus of developmental efforts has thus been on numerically attaining a proper conservation of energy across the interface in addition to the accurate treatment of fluxes of mass and momentum conservation as well as the associated interface advection. Among the initial efforts related to the simulation of bubble growth in film boiling applications the work in \cite{Welch1995} was based on the interface tracking method using a moving unstructured mesh. That study considered moderate interfacial deformations. A similar problem was subsequently studied using moving, boundary fitted grids \cite{Son1997}, again for regimes of relatively small topological changes. A hybrid interface tracking method with a moving interface grid overlapping a static Eulerian grid was developed \cite{Juric1998} for the computation of a range of phase change problems including, three-dimensional film boiling \cite{esmaeeli2004computations}, multimode two-dimensional pool boiling \cite{Esmaeeli2004} and film boiling on horizontal cylinders \cite{Esmaeeli2004a}. The handling of interface merging and pinch off however remains a challenge with methods that explicitly track the interface. As large topological changes are crucial for phase change problems, attention has turned in recent years to front capturing methods utilizing implicit interfaces that are more effective in treating complex interface deformations. The VOF (Volume of Fluid) method was adopted in \cite{Welch2000} to simulate the one-dimensional Stefan problem and the two-dimensional film boiling problem. The approach employed a specific model for mass transfer across the interface involving a mass source term within cells containing the interface. This VOF based approach was further coupled with the level set method in \cite{Son1998}, employing a smeared-out Heaviside function to avoid the numerical instability related to the source term. The coupled level set, volume of fluid method and the diffused interface approach was used for film boiling with water and R134a at the near critical pressure condition \cite{Tomar2005}. The effect of superheat and saturation pressure on the frequency of bubble formation were analyzed with this approach. The work in \cite{Gibou2007} used the ghost fluid and the level set methods for phase change simulations. A similar approach was adopted in \cite{Son2008} to study various boiling problems including three-dimensional film boiling on a horizontal cylinder, nucleate boiling in microcavity \cite{lee2010numerical} and flow boiling in a finned microchannel \cite{lee2012direct}. The work in \cite{tanguy2007level} also used the ghost fluid method and proposed an improved algorithm based on enforcing continuity and divergence-free condition for the extended velocity field. The work in \cite{sato2013sharp} employed a multiphase model based on volume fraction with interface sharpening scheme and derived a phase change model based on local interface area and mass flux. Among the front capturing methods, sharp interface methods have been found to be particularly effective both for implementing sharp jumps and for resolving the interfacial velocity field. However, sharp velocity jumps render the solution susceptible to erroneous oscillations in pressure and also lead to spurious interface velocities. To implement phase change, the work in \cite{Hardt2008} employed point mass source terms derived from a physical basis for the evaporating mass flux. To avoid numerical instability, the authors smeared the mass source by solving a pseudo time-step diffusion equation. This measure however led to mass conservation issues due to non-symmetric integration over the distributed mass source region. The problem of spurious pressure oscillations related to point mass sources was also investigated by \cite{Schlottke2008}. Although their method is based on the VOF, the large pressure peaks associated with sharp mass source was observed to be similar to that for the interface tracking method. Such spurious fluctuation in pressure are essentially undesirable because the effect is globally transmitted in incompressible flow. Hence, the pressure field formation due to phase change need to be implemented with greater accuracy than is reported in current literature. The accuracy of interface advection in the presence of interfacial mass flux (mass flux conservation) has been discussed in \cite{tanguy2007level,tanguy2014benchmarks}. The authors found that the method of extending one phase velocity to entire domain suggested by Nguyen et al. in \cite{nguyen2001boundary} suffers from a lack of mass flux conservation when the density difference is high. To improve the solution, the authors impose a divergence-free condition for the extended velocity field by solving a constant coefficient Poisson equation. The approach has shown good results with enclosed bubble or droplet but is not general for more complex flow and requires additional solution of the linear system of equations. In current thesis, an improved approach that addresses both the numerical oscillation of pressure and the spurious interface velocity field is presented by featuring (i) continuous velocity and density fields within a thin interfacial region and (ii) temporal velocity correction steps to avoid unphysical pressure source term. Also I propose a general (iii) mass flux projection correction for improved mass flux conservation. The pressure and the temperature gradient jump condition are treated sharply. A series of one-dimensional and two-dimensional problems are solved to verify the performance of the new algorithm. Two-dimensional and cylindrical film boiling problems are also demonstrated and show good qualitative agreement with the experimental observations and heat transfer correlations. Finally, a study on Taylor bubble flow with heat transfer and phase change in a small vertical tube in axisymmetric coordinates is carried out using the new multiphase, phase change method.

Determination of minimum fluidization velocity for gas-solid beds by experimental data and numerical simulations

The purpose of this work is to predict the minimum fluidization velocity Umf in a gas-solid fluidized bed. The study was carried out with an experimental apparatus for sand particles with diameters between 310μm and 590μm, and density of 2,590kg/m3. The experimental results were compared with numerical simulations developed in MFIX (Multiphase Flow with Interphase eXchange) open source code [1], for three different sizes of particles: 310mum, 450μm and 590μm. A homogeneous mixture with the three kinds of particles was also studied. The influence of the particle diameter was presented and discussed. The Ergun equation was also used to describe the minimum fluidization velocity. The experimental data presented a good agreement with Ergun equation and numerical simulations. Copyright © 2011 by ASME.

Simulação numérica de escoamentos gás-sólido em leito fluidizado borbulhante utilizando a teoria cinética dos escoamentos granulares

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Efeitos numéricos na simulação de escoamentos gás-sólido em leito fuidizado borbulhante utilizando a teoria cinética dos escoamentos granulares

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Report on the multiphase flow of gas, oil, and water through vertical flow strings with application to the design of gas lift installations,

Cover title.

Influence of impact angles on penetration rates of CRAs exposed to a high velocity multiphase flow

A combined flow loop - jet impingement pilot plant has been used to determine mass loss rates in a mixed gas - saltwater - sand multiphase flow at impact velocities up to 70 m/s. Artificial brine with a salt content of 27 g/1 was used as liquid phase. Sand content, with grain size below 150 µ, was 2.7 g/l brine. CO at a pressure of 15 bar was used as gas phase. The impact angle between jet stream (nozzle) and sample surface was varied between 30 and 90°. Rectangular stainless steel disc samples with a size of 20 × 15 × 5 mm were used. They were mechanically ground and polished prior to testing. Damaged surfaces of specimens exposed to the high velocity multiphase flow were investigated by stereo microscopy, scanning electron microscopy (SEM) and an optical device for 3D surface measurements. Furthermore, samples were investigated by applying atomic force microscopy (AFM), magnetic force microscopy (MFM) and nanoindentation. Influence of impact velocity and impact angle on penetration rates (mass loss rates) of two CRAs (UNS S30400 and N08028) are presented. Moreover effects of chemical composition and mechanical properties are critically discussed. © 2008 by NACE International.

Volume averaging of multiphase flows with hydrate formation in subsea pipelines

In oil and gas pipeline operations, the gas, oil, and water phases simultaneously move through pipe systems. The mixture cools as it flows through subsea pipelines, and forms a hydrate formation region, where the hydrate crystals start to grow and may eventually block the pipeline. The potential of pipe blockage due to hydrate formation is one of the most significant flow-assurance problems in deep-water subsea operations. Due to the catastrophic safety and economic implications of hydrate blockage, it is important to accurately predict the simultaneous flow of gas, water, and hydrate particles in flowlines. Currently, there are few or no studies that account for the simultaneous effects of hydrate growth and heat transfer on flow characteristics within pipelines. This thesis presents new and more accurate predictive models of multiphase flows in undersea pipelines to describe the simultaneous flow of gas, water, and hydrate particles through a pipeline. A growth rate model for the hydrate phase is presented and then used in the development of a new three-phase model. The conservation equations of mass, momentum, and energy are formulated to describe the physical phenomena of momentum and heat transfer between the fluid and the wall. The governing equations are solved based on an analytical-numerical approach using a Newton-Raphson method for the nonlinear equations. An algorithm was developed in Matlab software to solve the equations from the inlet to the outlet of the pipeline. The developed models are validated against a single-phase model with mixture properties, and the results of comparative studies show close agreement. The new model predicts the volume fraction and velocity of each phase, as well as the mixture pressure and temperature profiles along the length of the pipeline. The results from the hydrate growth model reveal the growth rate and location where the initial hydrates start to form. Finally, to assess the impact of certain parameters on the flow characteristics, parametric studies have been conducted. The results show the effect of a variation in the pipe diameter, mass flow rate, inlet pressure, and inlet temperature on the flow characteristics and hydrate growth rates.

Multiphase flow in porous media: meta-modeling techniques for sensitivity analysis and risk assessment

One of the biggest challenges that contaminant hydrogeology is facing, is how to adequately address the uncertainty associated with model predictions. Uncertainty arise from multiple sources, such as: interpretative error, calibration accuracy, parameter sensitivity and variability. This critical issue needs to be properly addressed in order to support environmental decision-making processes. In this study, we perform Global Sensitivity Analysis (GSA) on a contaminant transport model for the assessment of hydrocarbon concentration in groundwater. We provide a quantification of the environmental impact and, given the incomplete knowledge of hydrogeological parameters, we evaluate which are the most influential, requiring greater accuracy in the calibration process. Parameters are treated as random variables and a variance-based GSA is performed in a optimized numerical Monte Carlo framework. The Sobol indices are adopted as sensitivity measures and they are computed by employing meta-models to characterize the migration process, while reducing the computational cost of the analysis. The proposed methodology allows us to: extend the number of Monte Carlo iterations, identify the influence of uncertain parameters and lead to considerable saving computational time obtaining an acceptable accuracy.

Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

Natural convection flow with combined buoyancy effects due to thermal and mass diffusion in a thermally stratified media

We present here a numerical study of laminar doubly diffusive free convection flows adjacent to a vertical surface in a stable thermally stratified medium. The governing equations of mass, momentum, energy and species are non-dimensionalized. These equations have been solved by using an implicit finite difference method and local non-similarity method. The results show many interesting aspects of complex interaction of the two buoyant mechanisms that have been shown in both the tabular as well as graphical form.

Natural convection flow with surface radiation along a vertical wavy surface

In this study, natural convection boundary layer flow of thermally radiating fluid along a heated vertical wavy surface is analyzed. Here, the radiative component of heat flux emulates the surface temperature. Governing equations are reduced to dimensionless form, subject to the appropriate transformation. Resulting dimensionless equations are transformed to a set of parabolic partial differential equations by using primitive variable formulation, which are then integrated numerically via iterative finite difference scheme. Emphasis has been given to low Prandtl number fluid. The numerical results obtained for the physical parameters, such as, surface radiation parameter, R, and radiative length parameter, ξ, are discussed in terms of local skin friction and Nusselt number coefficients. Comprehensive interpretation of velocity distribution is also given in the form of streamlines.

Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularisation

We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.

Multiphase experiments with at least one later laboratory phase. I. orthogonal designs

The paper provides a systematic approach to designing the laboratory phase of a multiphase experiment, taking into account previous phases. General principles are outlined for experiments in which orthogonal designs can be employed. Multiphase experiments occur widely, although their multiphase nature is often not recognized. The need to randomize the material produced from the first phase in the laboratory phase is emphasized. Factor-allocation diagrams are used to depict the randomizations in a design and the use of skeleton analysis-of-variance (ANOVA) tables to evaluate their properties discussed. The methods are illustrated using a scenario and a case study. A basis for categorizing designs is suggested. This article has supplementary material online.

Corner and finger formation in Hele-Shaw flow with kinetic undercooling regularisation

We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele--Shaw flow, in both bubble and channel geometries. We present analytical and numerical evidence that the bubble boundary is unstable and may develop one or more corners in finite time, for both expansion and contraction cases. This loss of regularity is interesting because it occurs regardless of whether the less viscous fluid is displacing the more viscous fluid, or vice versa. We show that small contracting bubbles are described to leading order by a well-studied geometric flow rule. Exact solutions to this asymptotic problem continue past the corner formation until the bubble contracts to a point as a slit in the limit. Lastly, we consider the evolving boundary with kinetic undercooling in a Saffman--Taylor channel geometry. The boundary may either form corners in finite time, or evolve to a single long finger travelling at constant speed, depending on the strength of kinetic undercooling. We demonstrate these two different behaviours numerically. For the travelling finger, we present results of a numerical solution method similar to that used to demonstrate the selection of discrete fingers by surface tension. With kinetic undercooling, a continuum of corner-free travelling fingers exists for any finger width above a critical value, which goes to zero as the kinetic undercooling vanishes. We have not been able to compute the discrete family of analytic solutions, predicted by previous asymptotic analysis, because the numerical scheme cannot distinguish between solutions characterised by analytic fingers and those which are corner-free but non-analytic.