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Shahriar Amini - One of the best experts on this subject based on the ideXlab platform.
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on the choice of closure complexity in anisotropic drag closures for filtered Two Fluid Models
Chemical Engineering Science, 2019Co-Authors: Jan Hendrik Cloete, Shahriar Amini, Stefan Radl, Schalk CloeteAbstract:Abstract Filtered Two Fluid Models (fTFMs) aim to enable accurate industrial-scale simulations of Fluidized beds by means of closures accounting for the effects of bubbles and clusters. The present study aims to improve anisotropic closures for the drift velocity, which is the primary sub-grid effect altering the filtered drag force, by deriving increasingly complex closures by considering additional independent variables (markers). Three different anisotropic closures, as well as an isotropic closure, are evaluated. A priori tests revealed a significant increase in the predictive capability of the closures as the complexity, in terms of the number of markers considered, increases. However, this improvement is relatively small when compared to the effect of considering anisotropy. Next, a posteriori tests were completed by comparing coarse-grid simulations of bubbling, turbulent and core-annular Fluidization against benchmark resolved TFM simulations. This analysis shows good performance of all anisotropic closures, with negligible to minor effects of increasing the drag closure’s complexity by considering additional markers. On the other hand, the isotropic closure lacks generality and shows poor grid independence behaviour. It is therefore concluded that it is essential to include important physical effects, such as anisotropy, in fTFM closures, while complexity in terms of the number of markers considered is of lesser importance.
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Development and verification of anisotropic drag closures for filtered Two Fluid Models
Chemical Engineering Science, 2018Co-Authors: Jan Hendrik Cloete, Federico Municchi, Stefan Radl, Schalk Cloete, Shahriar AminiAbstract:Abstract Over the past decade, filtered Two Fluid Models (fTFMs) have emerged as a promising approach for enabling Fluidized bed simulations at industrially relevant scales. In these Models, the filtered drag force is considered to be the most important quantity that requires closure. To date, such closures have typically relied on an isotropic interphase momentum exchange coefficient by applying a drag correction factor to the microscopic drag closures commonly used in resolved simulations. In the present study, both isotropic and anisotropic closures are developed for predicting the filtered interphase forces. The relative performance of these Two approaches is then evaluated by means of an a priori assessment, considering data obtained from simulations in which all flow variables are resolved, which were also used for closure derivation. Also, an a posteriori assessment, which compares coarse grid simulation results to a benchmark resolved simulation of a bubbling Fluidized bed, is presented. The primary conclusion from the present study is that it is essential to account for the anisotropy of the filtered momentum exchange coefficient. It is shown that this can be done by employing a drift velocity formulation of the filtered drag force and by considering a gravitational contribution that only acts in the vertical direction. Furthermore, it is found that for the large computational grid sizes that are typically required in industrial scale Fluidized bed simulations, a closure for the meso-scale interphase force is essential. Finally, also for coarse grids, a non-linearity correction factor, which accounts for assumptions in deriving the drift velocity-based form of the filtered drag force, requires closure. The present study therefore highlights multiple avenues for improving drag closures used in fTFMs. Hence, these results may critically strengthen the predictive capabilities of fTFMs, as well as guide future modelling efforts.
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development and verification of anisotropic solids stress closures for filtered Two Fluid Models
Chemical Engineering Science, 2018Co-Authors: Jan Hendrik Cloete, Shahriar Amini, Stefan Radl, Schalk CloeteAbstract:Abstract Models for predicting flows in large scale Fluidized beds, such as filtered Two Fluid Models (fTFMs), must account for meso-scale phenomena that manifest spontaneously in sedimenting gas-particle suspensions. Next to the closures for interphase momentum exchange, the filtered solids stresses also require closure in such Models. A budget analysis reveals that, for large filter sizes, the meso-scale solids stresses, which arise due to the particles’ sub-grid velocity fluctuations, are the most important contribution to these stresses. Previously, closures for meso-scale stresses have commonly adopted a Boussinesq approach where (i) a filtered solids pressure is used to close the mean normal stress, and (ii) a filtered solids viscosity is modelled to close the deviatoric stress components. The present study highlights that such a Boussinesq approach fails to accurately predict the forces arising from the meso-scale stresses. This is primarily due to the fundamental inability of a viscosity-based formulation to approximate deviatoric stress components in sedimenting gas-particle suspensions. The present study proposes a novel anisotropic approach in which both normal (i.e., diagonal) and shear (i.e., off-diagonal) stress components are modelled individually. The proposed anisotropic closure explains resolved stress data significantly more reliably (i.e., with a correlation coefficient of R 2 ≈ 0.62 ) compared to a conventional Boussinesq-based approach ( R 2 ≈ - 0.65 ) using a single model equation. Finally, these findings are confirmed by evaluating different stress closures in fTFM simulations of bubbling and turbulent Fluidization. These simulations indicate that the novel anisotropic stress closure leads to improved model generality and better grid independence. Most important, it is found that a classical Boussinesq-based closure leads to worse predictions compared to a complete neglect of meso-scale solids stresses. Thereby, the present study underlines that it is essential to account for anisotropy when closing the meso-scale solids stress in fTFMs.
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hydrodynamic validation study of filtered Two Fluid Models
Chemical Engineering Science, 2018Co-Authors: Schalk Cloete, Jan Hendrik Cloete, Shahriar AminiAbstract:Abstract This work presents a validation study of new filtered Two Fluid Model closures for interphase momentum exchange and mesoscale solids stresses. Good quantitative comparisons to experimental data were achieved over a wide range of Fluidization velocities. The new Models also showed good grid independence behaviour compared to Two benchmark Models from literature. These encouraging results in realistic 3D flows were achieved even though the Models were derived from 2D resolved simulations. Comparisons to a benchmark model derived from 3D simulations suggests that it may be more accurate to derive filtered Models from resolved simulations conducted in a large 2D domain than from resolved simulations in a small 3D domain. Furthermore, the new model validated in this work could achieve good results in wall-dominated flows without the use of specialized wall corrections. Further work is therefore recommended to test these new filtered Models in more flow situations and to further assess the ability of filtered Models derived in 2D to predict real 3D flows.
Richard T. Lahey - One of the best experts on this subject based on the ideXlab platform.
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A characteristic analysis of void waves using Two-Fluid Models
Nuclear Engineering and Design, 2003Co-Authors: Thomas C. Haley, Richard T. Lahey, Donald A. DrewAbstract:Abstract This paper examines mathematical techniques for evaluating waves in systems of partial differential equations (PDEs), such as those found in the Two-Fluid modeling of Two-phase flows. In particular, this paper is concerned with a characteristic analysis of void waves for Two-Fluid Models of Two-phase flow. Such Models are comprised of the phasic conservation equations, the interfacial jump conditions and the associated closure laws. The well-posedness of such systems of PDEs is considered herein with respect to the morphology of the mathematical model. Closure involves balancing the number of equations and state variables, as well as specifying all the parameters, initial conditions, and boundary conditions needed in the Two-Fluid model. In order to avoid algebraic complexity, only fairly simple Two-Fluid Models will be considered in this paper. Nevertheless, the conclusions reached herein are also valid for much more detailed Two-Fluid Models.
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Analysis of phase distribution phenomena in microgravity environments
1994Co-Authors: Richard T. Lahey, Fabián J. BonettoAbstract:In the past one of NASA's primary emphasis has been on identifying single and multiphase flow experiments which can produce new discoveries that are not possible except in a microgravity environment. While such experiments are obviously of great scientific interest, they do not necessarily provide NASA with the ability to use multiphase processes for power production and/or utilization in space. The purpose of the research presented in this paper is to demonstrate the ability of multidimensional Two-Fluid Models for bubbly Two-phase flow to accurately predict lateral phase distribution phenomena in microgravity environments. If successful, this research should provide NASA with mechanistically-based analytical methods which can be used for multiphase space design and evaluation, and should be the basis for future shuttle experiments for model verification.
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Prediction of Two-phase sonic velocity using Two-Fluid Models
Transactions of the American Nuclear Society, 1993Co-Authors: C.j. Chang, Richard T. LaheyAbstract:Two-Fluid Models consist of six conservation equations and three interfacial jump conditions. In principle, they yield all conceivable evolutions when correctly formulated. In particular, such Models can be used to study sonic phenomena in Two-phase mixtures. The purpose of this study was to investigate Two-phase critical flow and sonic velocity by using a state-of-the-art Two-Fluid model. We consider here adiabatic air-water critical flow because such data are relatively easy to acquire, and it isolates the modeling of the virtual mass force.
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ON THE DEVELOPMENT OF MULTIDIMENSIONAL Two-Fluid Models FOR VAPOR/LIQUID Two-PHASE FLOWS
Chemical Engineering Communications, 1992Co-Authors: Richard T. Lahey, Donald A. DrewAbstract:Abstract The status of multidimensional Two-Fluid modeling of vapor/liquid Two-phase flows is reviewed. In particular, a three dimensional Two-Fluid model is derived using ensemble averaging. It is proposed that realistic interfacial closure laws should: • Be mathematically objective • Lead to well-posed Models • Satisfy the second law of thermodynamics • Agree with all relevant experimental data. Unfortunately, most Two-Fluid Models in use today do not satisfy these fundamental constraints.
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Void wave propagation phenomena in Two-phase flow (Kern award lecture)
AIChE Journal, 1991Co-Authors: Richard T. LaheyAbstract:This paper presents a detailed linear and nonlinear analysis of void wave phenomena in Two-phase flow. A state-of-the-art, one-dimensional Two-Fluid model was used as the basis for this analysis. It is shown that void wave dispersion is strongly influenced by phasic slip. In particular, the smaller the slip the more dispersion occurs. It has also been found that nonlinear wave forms, such as shocks and solitons, may occur. Moreover, the virtual mass force was found to be an important parameter in the modeling of void waves. It is shown that void wave analysis is an excellent means of assessing the closure assumptions used in Two-Fluid Models. It is also implied that carefully taken void wave data are needed for this purpose.
Sankaran Sundaresan - One of the best experts on this subject based on the ideXlab platform.
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validation of filtered Two Fluid Models for gas particle flows against experimental data from bubbling Fluidized bed
Powder Technology, 2015Co-Authors: Shailesh S Ozarkar, Fernando Eduardo Milioli, Christian C Milioli, Shuyan Wang, Sankaran SundaresanAbstract:Abstract Predictions of simulations based on filtered Two-Fluid Models (TFMs) with constitutive relations for filtered Fluid–particle drag coefficient and filtered stresses proposed by Igci and Sundaresan [Ind. Eng. Chem. Res. 50 (2011) 13190–13201] and Milioli et al. [AIChE J. 59 (2013) 3265–3275] were compared against experimental data from a bubbling Fluidized bed challenge problem put forward by the National Energy Technology Laboratory and Particulate Solids Research Inc. It is found that the most important correction to filtered Models is a modification to the drag, and filtered stresses play a secondary role at best. As expected, coarse grid simulations using the kinetic-theory based TFM over-predicted the gas–particle drag force, yielding unphysical bed expansion. The filtered Fluid–particle drag model proposed by Igci and Sundaresan that classifies the inhomogeneity in sub-filter scale flow structures using filter size and filtered particle volume fraction as markers also predicted unphysical bed expansion. Refined filtered drag Models proposed by Milioli et al. based on filtered Fluid–particle slip velocity as an additional marker led to good agreement with experimental data on bed expansion and the time-averaged gas pressure gradient. It was also observed that inadequate grid resolution in the region between gas distributor and the adjacent cylindrical wall of the test unit could lead to spurious asymmetric gas–particle flow predictions. With the inclusion of adequate inflation layer elements in that region, flow predictions became nearly symmetric with little to no effect on bed expansion predictions. However, it dramatically and qualitatively altered the details of gas–particle structures in the bed.
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filtered Two Fluid Models of Fluidized gas particle flows new constitutive relations
Aiche Journal, 2013Co-Authors: Christian C Milioli, William Holloway, Fernando Eduardo Milioli, Kapil Agrawal, Sankaran SundaresanAbstract:New constitutive relations for filtered Two-Fluid Models (TFM) of gas-particle flows are obtained by systematically filtering results generated through highly resolved simulations of a kinetic theory-based TFM. It was found in our earlier studies that the residual correlations appearing in the filtered TFM equations depended principally on the filter size and filtered particle volume fraction. Closer inspection of a large amount of computational data gathered in this study reveals an additional, systematic dependence of the correction to the drag coefficient on the filtered slip velocity, which serves as a marker for the extent of subfilter-scale inhomogeneity. Furthermore, the residual correlations for the momentum fluxes in the gas and particle phases arising from the subfilter-scale fluctuations are found to be modeled nicely using constitutive relations of the form used in large-eddy simulations of single-phase turbulent flows. V C 2013 American
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Filtered Models for reacting gas–particle flows
Chemical Engineering Science, 2012Co-Authors: William Holloway, Sankaran SundaresanAbstract:Using the kinetic-theory-based Two-Fluid Models as a starting point, we develop filtered Two-Fluid Models for a gas–particle flow in the presence of an isothermal, first-order, solid-catalyzed reaction of a gaseous species. As a consequence of the filtering procedure, terms describing the filtered reaction rate and filtered reactant dispersion need to be constituted in order to close the filtered species balance equation. In this work, a constitutive relation for filtered reaction rate is developed by performing fine-grid, Two-Fluid model simulations of an isothermal, solid-catalyzed, first-order reaction in a periodic domain. It is observed that the cluster-scale effectiveness factor, defined as the ratio between the reaction rate observed in a fine-grid simulation to that observed in a coarse-grid simulation, can be substantially smaller than unity, and it manifests an inverted bell shape dependence on filtered particle volume fraction in all simulation cases. Moreover, the magnitude of the deviation in the cluster-scale effectiveness factor from unity is a strong function of the meso-scale Thiele modulus and dimensionless filter size. Thus coarse-grid simulations of a reacting gas–particle flow will over-estimate the reaction rate if the cluster-scale effectiveness factor is not accounted for.
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Filtered Models for reacting gas-particle flows
arXiv: Other Condensed Matter, 2012Co-Authors: William Holloway, Sankaran SundaresanAbstract:Using the kinetic-theory-based Two-Fluid Models as a starting point, we develop filtered Two-Fluid Models for a gas-particle flow in the presence of an isothermal, first-order, solid-catalyzed reaction of a gaseous species. As a consequence of the filtering procedure, terms describing the filtered reaction rate and filtered reactant dispersion need to be constituted in order to close the filtered species balance equation. In this work, a constitutive relation for filtered reaction rate is developed by performing fine-grid, Two-Fluid model simulations of an isothermal, solid-catalyzed, first-order reaction in a periodic domain. It is observed that the cluster-scale effectiveness factor, defined as the ratio between the reaction rate observed in a fine-grid simulation to that observed in a coarse-grid simulation, can be substantially smaller than unity, and it manifests an inverted bell shape dependence on filtered particle volume fraction in all simulation cases. Moreover, the magnitude of the deviation in the cluster-scale effectiveness factor from unity is a strong function of the meso-scale Thiele modulus and dimensionless filter size. Thus coarse-grid simulations of a reacting gas-particle flow will overestimate the reaction rate if the cluster-scale effectiveness factor is not accounted for.
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Constitutive Models for Filtered Two-Fluid Models of Fluidized Gas–Particle Flows
Industrial & Engineering Chemistry Research, 2011Co-Authors: Yesim Igci, Sankaran SundaresanAbstract:Our prior study [Igci et al., AIChE J., 2008, 54, 1431–1448] presented a methodology where computational results obtained through highly resolved simulations of a given microscopic Two-Fluid model (TFM) for gas-particle flows are filtered to deduce Models for the residual correlations appearing in the corresponding filtered TFM equations that are appropriate for coarse-grid simulations of gas-particle flows. In the present study, we have performed a large number of highly resolved simulations of a kinetic theory based TFM in Two- and three-dimensional periodic domains using this methodology and filtered the results to generate computational data on the filtered drag coefficient, the filtered particle phase pressure, and the filtered particle phase viscosity. These results have been captured in the form of correlations that can readily be employed in coarse-grid simulations of gas-particle flows.
Iztok Tiselj - One of the best experts on this subject based on the ideXlab platform.
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First and second-order accurate schemes for Two-Fluid Models
Journal of fluids engineering, 2017Co-Authors: Stojan Petelin, Iztok TiseljAbstract:The six-equation Two-Fluid model of Two-phase flow taken from the RELAP5/MOD3 computer code has been used to simulate three simple transients: a Two-phase shock tube problem, the Edwards Pipe experiment, and water hammer due to rapid valve closure. These transients can be characterized as fast transients, since their characteristic time-scales are determined by the sonic velocity. First and second-order accurate numerical methods have been applied both based on the well-known, Godunov-type numerical schemes. Regarding the uncertainty of the Two-Fluid Models in today's large computer codes for the nuclear thermal-hydraulics, use of second-order schemes is not always justified. While this paper shows the obvious advantage of second-order schemes in the area of fast transients, first-order accurate schemes may still be sufficient for a wide range of Two-phase flow transients where the convection terms play a minor role compared to the source terms.
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Slug modeling with 1D Two-Fluid model
Kerntechnik, 2012Co-Authors: Iztok Tiselj, C. Samuel MartinAbstract:Abstract Simulations of condensation-induced water hammer with one-dimensional Two-Fluid model requires explicit modeling of slug formation, slug propagation, and in some cases slug decay. Stratified flow correlations that are more or less well known in 1D Two-Fluid Models, are crucial for accurate description of the initial phase of the slug formation and slug propagation. Slug formation means transition to other flow regime that requires different set of correlations. To use such Two-Fluid model for condensation induced water hammer simulations, a single slug must be explicitly recognized and captured. In the present work Two cases of condensation-induced water hammer simulations performed with WAHA code, are described and discussed: injection of cold liquid into horizontal pipe filled with steam and injection of hot steam into horizontal pipe partially filled with cold liquid.
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Two-Fluid model with interface sharpening
International Journal for Numerical Methods in Engineering, 2010Co-Authors: Luka Štrubelj, Iztok TiseljAbstract:Two-Fluid Models are applicable for simulations of all types of Two-phase flows ranging from separated flows with large characteristic interfacial length scales to highly dispersed flows with very small characteristic interfacial length scales. The main drawback of the Two-Fluid model, when used for simulations of stratified flows, is the numerical diffusion of the interface. Stratified flows can be easily and more accurately solved with interface tracking methods; however, these methods are limited to the flows, that do not develop into dispersed types of flows. The present paper describes a new approach, where the advantage of the Two-Fluid model is combined with the conservative level set method for interface tracking. The advection step of the volume fraction transport equation is followed by the interface sharpening, which preserves the thickness of the interface during the simulation. The proposed Two-Fluid model with interface sharpening was found to be more accurate than the existing Two-Fluid Models. The mixed flow with both: stratified and dispersed flow, is simulated with the coupled model in this paper. In the coupled model, the dispersed Two-Fluid model and Two-Fluid model with interface sharpening are used locally, depending on the parameter which recognizes the flow regime. Copyright © 2010 John Wiley & Sons, Ltd.
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Coupling of the interface tracking and the Two-Fluid Models for the simulation of incompressible Two-phase flow
Journal of Computational Physics, 2001Co-Authors: Gregor Černe, Stojan Petelin, Iztok TiseljAbstract:Abstract The volume of Fluid (VOF) method, which uses an interface tracking algorithm for the simulation of the Two-phase flow, is coupled with the “Two-Fluid” model, which is based on time and space averaged equations and cannot track the interface explicitly. The idea of the present work is to use the VOF method in the parts of the computational domain where the grid density allows surface tracking. In the parts of the domain where the flow is too dispersed to be described by the interface tracking algorithms, the Two-Fluid model is used. The equations of the Two-Fluid model are less accurate than the VOF model due to the empirical closures required in the averaged equations. However, in the case of the sufficiently dispersed flow, the Two-Fluid model results are still much closer to the real world than the results of the VOF method, which do not have any physical meaning when the grid becomes too coarse. Each model in the present work uses a separate set of equations suitable for description of Two-dimensional, incompressible, viscous Two-phase flow. Similar discretization techniques are used for both sets of equations and solved with the same numerical method. Coupling of both Models is achieved via the volume fraction of one of the Fluids, which is used in both Models. A special criterion for the transition between the Models is derived from the interface reconstruction function in the VOF method. An idealized vortical flow and the Rayleigh–Taylor instability are used as tests of the coupling. In both cases the time development causes mixing of the Fluids and dispersion of the interface that is beyond the capabilities of the model based on the VOF method. Therefore the Two-Fluid model gradually replaces the interface tracking model. In the final stages of the Rayleigh–Taylor instability, when both Fluids are approaching their final positions and the tractable interface appears again, the Two-Fluid model is gradually replaced by the VOF method.
Jean-marc Hérard - One of the best experts on this subject based on the ideXlab platform.
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Comparison of Two-Fluid Models on steam-water transients
ESAIM: Mathematical Modelling and Numerical Analysis, 2016Co-Authors: Hippolyte Lochon, Frédéric Daude, Pascal Galon, Jean-marc HérardAbstract:This paper is devoted to the comparison of three Two-Fluid Models in steam-water applications involving phase transition and shock waves. The three Models are presented in a common formalism that helps to underline their shared properties. A numerical method based on previous work is extended to all Models and to more complex Equations Of State. Particular attention is paid to the verification of every step of the method so that convergence studies can be carried out. Afterwards, Models are compared with each other and with experimental data in Two different cases of steam-water transients. The first one is Simpson water-hammer experiment and the second one is a rapid depressurization with flashing studied in Canon experiment.
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A class of Two-Fluid Two-phase flow Models
2012Co-Authors: Frédéric Coquel, Jean-marc Hérard, Khaled Saleh, Nicolas SeguinAbstract:We introduce a class of Two-Fluid Models that complies with a few theoretical requirements that include: (i) hyperbolicity of the convective subset, (ii) entropy inequality, (iii) uniqueness of jump conditions for non-viscous flows. These specifications are necessary in order to compute relevant approximations of unsteady flow patterns. It is shown that the Baer-Nunziato model belongs to this class of Two-phase flow Models, and the main properties of the model are given, before showing a few numerical experiments.
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a fractional step method to compute a class of compressible gas liquid flows
Computers & Fluids, 2012Co-Authors: Jean-marc Hérard, Olivier HurisseAbstract:Abstract We present in this paper some algorithms dedicated to the computation of numerical approximations of a class of Two-Fluid Two-phase flow Models. Governing equations for the statistical void fraction, partial mass, momentum, energy are presented first, and meaningful closure laws are given. Then we may give the main properties of the class of Two-Fluid Models. The whole algorithm that relies on the fractional step method and complies with the entropy inequality is presented afterwards. Emphasis is given on the computation of pressure–velocity–temperature relaxation source terms. Conditions pertaining to the existence and uniqueness of discrete solutions of the relaxation step are given. While focusing on some one-dimensional test cases, the true rates of convergence may be obtained within the evolution step and the relaxation step. Eventually, some Two-dimensional numerical simulations of a heated wall are shown and are briefly discussed. Some advantages and weaknesses of algorithms are also discussed.
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A fractional step method to compute a class of compressible gas–liquid flows
Computers and Fluids, 2012Co-Authors: Jean-marc Hérard, Olivier HurisseAbstract:We present in this paper some algorithms dedicated to the computation of numerical approximations of a class of Two-Fluid Two-phase flow Models. Governing equations for the statistical void fraction, partial mass, momentum, energy are presented first, and meaningful closure laws are given. Then we may give the main properties of the class of Two-Fluid Models. The whole algorithm that relies on the fractional step method and complies with the entropy inequality is presented afterwards. Emphasis is given on the computation of pressure-velocity-temperature relaxation source terms. Conditions pertaining to the existence and uniqueness of discrete solutions of the relaxation step are given. While focusing on some one-dimensional test cases, the true rates of convergence may be obtained within the evolution step and the relaxation step. Eventually, some Two-dimensional numerical simulations of a heated wall are shown and are briefly discussed. Some advantages and weaknesses of algorithms are also discussed.
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a simple method to compute standard Two Fluid Models
International Journal of Computational Fluid Dynamics, 2005Co-Authors: Jean-marc Hérard, Olivier HurisseAbstract:We describe in this paper, a tool to compute approximate solutions of standard Two-Fluid Models with an equilibrium pressure assumption. The basic approach takes its grounds in the Two-Fluid Two-pressure formalism, and takes advantage of the relaxation techniques. The method may be used to compute either the single- or the Two-pressure model, depending on the size of mesh, which is used. It is also shown on the basis of a simple numerical experiment that the local equilibrium assumption may lead to a blow-up of the numerical solution on fine meshes, even if one accounts for drag stabilizing effects.
