APPLICATION OF THE CONDITIONAL QUADRATURE METHOD OF MOMENTS FOR THE SIMULATION OF COALESCENCE, BREAKUP AND MASS TRANSFER IN GAS-LIQUID STIRRED TANKS
|
|
- Anna Eleanore Collins
- 6 years ago
- Views:
Transcription
1 14 th European Conference on Mixing Warszawa, Septemer 2012 APPLICATION OF THE CONDITIONAL QUADRATURE METHOD OF MOMENTS FOR THE SIMULATION OF COALESCENCE, BREAKUP AND MASS TRANSFER IN GAS-LIQUID STIRRED TANKS M. Petitti a, M. Vanni a, D.L. Marchisio a, A. Buffo a, F. Podenzani, a Politecnico di Torino, Dip. Scienza Applicata e Tecnologia, corso Duca degli Aruzzi 24, Torino, Italy ENI S.p.a., Divisione Refining and Marketing, via Felice Maritano 26, San Donato Milanese, Italy miriam.petitti@polito.it Astract. Mass transfer has een investigated in a gas-liquid stirred reactor y considering the asorption of oxygen in the liquid phase (water. A multivariate population alance model (PBM, coupled with an Eulerian multi-fluid approach, has een employed to descrie the spatial and temporal evolution of the ules size and composition distriutions. The PBM has een solved y adopting the Conditional Quadrature Method of Moments (CQMOM, that has een implemented through userdefined functions (UDF and scalars (UDS in the commercial Computational Fluid Dynamics code Ansys Fluent 12. Model predictions were compared with experimental data of ule size distriutions and then with oxygen accumulation in the liquid phase. The simulation results show that, although coalescence and reakup tend to homogenize ule composition, a multivariate PBM is necessary to properly descrie mass transfer. In fact, due to the fact that smaller ules, generally located in regions characterized y high turulent dissipation rates, exchange mass with a much faster rate than igger ules, oth ule size and ule composition should e included as internal coordinates. Keywords: Gas-liquid stirred tank, Population alance, Multiphase flow, Mass transfer, Bule size distriution, Conditional Quadrature Method of Moments (CQMOM. 1. INTRODUCTION An accurate description of fluid-dynamics and mass transfer in gas-liquid systems requires the evaluation of ule size and composition distriutions, oth varying in time and space, due to gas ule reakage, coalescence and mass exchange with the liquid phase. To this purpose a multivariate population alance model (PBM, coupled with an Eulerian multi-fluid approach, has een here employed to descrie the spatial and temporal evolution of ules size and composition distriutions in a gas-liquid system. The system examined is a 194 liter stirred-tank, previously studied y Laakkonen et al. [1] and then y Petitti et al. [2], agitated via a Rushton turine and operating with air and tap water. Gas-liquid mass transfer is investigated y considering the asorption of oxygen in the liquid phase, for which many experimental data are availale, in many different operating conditions (stirring speeds and gassing rates. 371
2 For the numerical solution of the multivariate PBM the Conditional Quadrature Method of Moments (CQMOM, the multivariate extension of the Quadrature Method of Moments (QMOM to two internal coordinates (ule size and composition, was implemented through user-defined functions (UDF in the commercial computational fluid dynamics (CFD code Ansys Fluent 12. The implemented algorithm was proven to e numerically stale in all the operating conditions examined. Validation was carried out y comparing first the model predictions with experimentally measured ule size distriutions and then with oxygen accumulation in the liquid phase, otaining satisfactory agreements. 2. REACTOR INVESTIGATED The stirred reactor investigated is a 194 liter four-affle reactor, agitated y a six-lade Rushton turine, previously investigated y Laakkonen et al. [1] and y Petitti et al. [2]. The gas is introduced through a metal porous sparger with pores of 15 µm in diameter. The asorption of oxygen in the liquid phase is examined and compared with experimental data in different operating conditions: the stirring speeds are in the range rpm while the gassing rates in the range vvm (vessel volumes per minute. 3. MODEL DESCRIPTION 3.1 Multiphase modeling The Eulerian multi-fluid approach (in this case two-fluid was adopted and oth phases (continuous and dispersed were considered incompressile. The drag force and the uoyancy force were the only forces taken into account for the dispersed phase; additional forces like lift and virtual mass were neglected ecause in stirred reactors the velocity field is dominated y the turine rotation (on the contrary of ule columns where these forces are usually accounted for. The drag coefficient for the gas-liquid interaction was evaluated from ule terminal velocity, y assuming a unique value for the terminal velocity of all the ules, equal to 12 cm/s, taking thus into account the damping effect of turulence on ule slip velocity (for details see [2]. Turulence was modeled with the k-ε standard mixture model since it represents a good trade-off etween accuracy and computational costs. 3.2 Population alance modeling The population of ules dispersed in a turulent liquid and characterized y different properties such as size (L and chemical composition (φ, representing the internal coordinates of the population, can e modeled through a smooth and differentiale Numer Density Function (NDF, as explained y Fox [3]. The NDF is defined in such a way that the following quantity: n( L, φ ;x, t dl dφ dx (1 represents the expected numer of ules in the physical volume dx=dx 1 dx 2 dx 3 around the physical point x = (x 1, x 2, x 3 and with ule size in the infinitesimal range etween L and L + dl and composition etween φ and φ + dφ. From the theoretical point of view, there is no limitation on the numer of internal coordinates (other possile coordinates might e temperature, velocity, etc. ut here only size and composition were examined. In fact, the system investigated is isothermal and, thanks to the low hold-up values, the effects of ules collision, reakage and coalescence on momentum exchange can e neglected. 372
3 The evolution of the NDF follows the Generalized Population Balance Equation (GPBE (for details see [4], [5]: ( n u + ( n G + ( n φ = H( L, φ ;x, t n + t x L φ (2 where u is the ule velocity; G represents the rate of continuous change of ule size generally, descriing ule continuous growth or shrinkage due to molecular phenomena, like the addition or the depletion of single molecules (evaporation, condensation, mass transfer processes; φ represents the rate of continuous change of ule composition (with respect to the different chemical components caused y chemical reactions and/or mass transfer processes etween the phases. The term appearing on the right hand side of the previous equation instead takes into account discontinuous events, accounting for instantaneous change of size and composition due to ule collisions, coalescence and reakage. The φ term is generally a vector ecause many chemical components may e considered, ut in the system here investigated the gas phase is made up of only two chemical components (nitrogen and oxygen, with only one active component (oxygen transferring etween the phases and thus φ is a scalar, representing the numer of moles of oxygen within one single ule; consequently in the following expressions it will e expressed as φ. In the present work all the ules of the distriution are assumed to have the same velocity. The local value of ules velocity (u is calculated from the momentum alance equation, using the local ule Sauter diameter (d 32 calculated from the multivariate PBM for the computation of drag and uoyancy forces. As regards the rates of continuous change of size and composition, the expressions for G and φ are calculated y considering only the effect of oxygen on mass transfer, through a simple mass alance on a single (spherical ule: 2kLM O φ 2 G = ψc HO 2 3 ρ kvl (3 2 φ φ = kl π L ψc H O (4 2 3 kvl where M O2 is the molecular weight of oxygen, ψ c is the concentration of oxygen in the continuous phase, H O2 is Henry constant and ρ is the density of the gas in the ule. The mass transfer coefficient k L has een evaluated with the expression used y Lamont and Scott [6], ased on the local value of the turulent dissipation rate: k L = c D 1 / 2 ερc μc 1 / 4 (5 where D is oxygen molecular diffusivity, ε the turulent dissipation rate, ρ c the density of the continuous phase and µ c the viscosity of the continuous phase. Different values were tested for the coefficient c appearing in Eq. (5 and the theoretical value of 1.13 proposed y Kawase et al. [7] gave promising results, as shown in section
4 By assuming that reakage and coalescence kernels depend only on ule size and y considering that in the present prolem φ is a scalar representing the numer of moles of oxygen within one single ule, the discontinuous event term can e expressed as follows: H( L, φ ; x,t = n( L, φ ; x,t L φ a ( L n( L, φ ; x,t a 3 3 ( 1 L λ, λ n( λ, φ ; x,t n ( L λ ,( φ φ ( L, λ n( λ, φ ; x,t dλ dφ + ( λ,λ,λ,λ L φ P( L, φ λ, φ,λ,λ, x,t dλ dφ n( λ, φ ; x,t +,λ,λ + (6 where the first two terms represent respectively the irth and death due to ules coalescence, whereas the last two terms the irth and death caused y ules reakage. The coalescence kernel (a, the reakage kernel ( and the daughter distriution function (P derive from turulence theory and were descried in detail in our previous work [2]. The prolem is here solved in terms of the moments of the NDF, expressed as: k l M k, l = n( L,φ L φdl dφ (7 ΩΩ L φ where Ω L and Ω φ are the phase spaces generated y the internal coordinates. By applying the moment transform to Eq. (2 the transport equation for a generic moment of the NDF can e otained. The population alance is solved y resorting to the Conditional Quadrature Method of Moments (CQMOM, where the closure is achieved y means of a quadrature approximation through which the NDF is represented as a weighted summation of Dirac delta functions centered on proper nodes: N1 φ = wiδ, i= 1 j= 1 N2 ( L Li wi jδ ( φ φ;i,j n( L, (8 The numer densities w i,j and the compositions φ ;i,j are conditioned on the value of the first internal coordinate L i with numer density w i.the total numer of nodes is given y N 1 N 2, where N 1 is the numer of nodes used for ule size and N 2 the numer of nodes used for ule composition. In other words each one of the N 1 groups of ules with size L i is sudivided into N 2 groups of ules characterized y different compositions φ,i,j.. In order to limit the computational costs in the present work the values adopted are N 1 =2; N 2 =1. This requires tracking the following six moments: M 0,0, M 1,0, M 2,0, M 3,0, M 0,1, M 1,1. The mean ule size (d 32 is then availale via the ratio of M 3,0 and M 2,0, whereas the mean oxygen concentration of the ules is calculated as the ratio etween M 0,1 and k v M 3,0, where k v is the volume shape factor of the ules (for details see [8]. 4. SIMULATION RESULTS The Multi Reference Frame method was adopted and the simulations were performed in non-stationary conditions on only one half of the reactor (485,974 cells including a region aove the liquid level occupied y the gas phase only. In fact, the use of a computational domain that extends eyond the initial liquid level turned out to e essential in simulating mass transfer. This is done y including a region aove the liquid in which there is only the gas phase; this is necessary in order to keep within the domain oundaries the whole liquid present in the system, whose level increases a little as a 374
5 consequence of the gas fed into the tank. In this way any loss of liquid, where the oxygen accumulates, is avoided and any liquid ackflow with unknown concentration is prevented. The ules entering the reactor were modeled with fixed oxygen concentration (saturation value and with a lognormal size distriution, with a mean ule size (d 32 calculated with Kazakis s correlation for porous spargers [9]. The PBM was solved only where the local gas volume fraction was in the range , elsewhere the local d 32 was set equal to the inlet value. Oxygen adsorption in the liquid was monitored and its temporal evolution was compared with the experiments y Laakkonen conducted under different operating conditions. Different values were tested for the coefficient c appearing in Lamont and Scott s correlation. The more promising results were otained with the values reported in Fig. 1. Figure 1. Comparison of the predicted temporal evolution of the dimensionless oxygen concentration in the liquid with the experimental data, in the monitor point, for the operating conditions investigated. The theoretical value of 1.13, proposed y Kawase et al. [7] gives the est agreement with the experimental data, especially at the lowest stirring speed and gassing rate. The stirring speeds investigated guarantee a good mixing in the reactor and a rather uniform concentration of oxygen in the liquid is oserved at the end of the simulations. The predictions for k L a reported in Fig. 2 highlight that the highest values are reached near the impeller where the ules are smaller due to significant reakage. A satisfactory agreement is then otained for the comparison of the predicted d 32 with the experimental data, in selected points on the planes at 45 etween the affles, as shown in Fig
6 Figure 2. Contours of the local kla predicted for the case at 250 rpm and vvm. Figure 3. Comparison of the predicted d32 (mm with the experimental data (in green, 250 rpm and vvm. The value zero is plotted for the d32 where the PBM is not solved. 5. REFERENCES [1] Laakkonen M., Alopaeus V., Aittamaa J., Validation of ule reakage, coalescence and mass transfer models for gas-liquid dispersion in agitated vessel, Chem. Eng. Sci., 61, [2] Petitti M., Nasuti A., Marchisio D.L., Vanni M., Baldi G., Podenzani F., Mancini N., Bule size distriution modelling in stirred gas-liquid reactors with QMOM augmented y a new correction, AIChE J., 56, [3] Fox R.O., Introduction and fundamentals of modeling approaches for polydisperse multiphase flows, in: Multiphase Reacting Flows, (D.L. Marchisio, R.O. Fox, eds, vol. 492 of CISM International Centre for Mechanical Sciences, Springer, Wien, pp [4] Ramkrishna D., Population Balances, Academic Press, New York. [5] Marchisio D.L., Quadrature method of moments for poly-disperse flows, in: Multiphase Reacting Flows, (D.L. Marchisio, R.O. Fox, eds, vol. 492 of CISM International Centre for Mechanical Sciences, Springer, Wien, pp [6] Lamont J.C., Scott D.S., An eddy cell model of mass transfer into the surface of a turulent liquid, AIChE J., 16, [7] Kawase Y., Halard B., Moo-Young M., Theoretical prediction of volumetric mass transfer coefficients in ule columns for Newtonian and non-newtonian fluids, Chem. Eng. Sci., 42, [8] Buffo A., Vanni M., Marchisio D.L., Fox R.O., Comparison etween different methods for turulent gas-liquid systems y using multivariate population alances, Proc. 8th Int. Conf. on CFD in Oil and Gas, Metallurgical Process Industries (Trondheim, June, pp. 10. [9] Kazakis N.A., Mouza A.A., Paras S.V., Experimental study of ule formation at metal porous spargers: Effect of liquid properties and sparger characteristics on the initial ule size distriution, Chem. Eng. J., 137,
Prediction of Minimum Fluidisation Velocity Using a CFD-PBM Coupled Model in an Industrial Gas Phase Polymerisation Reactor
Journal of Engineering Science, Vol. 10, 95 105, 2014 Prediction of Minimum Fluidisation Velocity Using a CFD-PBM Coupled Model in an Industrial Gas Phase Polymerisation Reactor Vahid Akbari and Mohd.
More informationAggregation and Breakage of Nanoparticle Dispersions in Heterogeneous Turbulent Flows
ggregation and reakage of Nanoparticle Dispersions in Heterogeneous Turbulent Flows M. Soos,, D. Marchisio*, J. Sefcik, M. Morbidelli Swiss Federal Institute of Technology Zürich, Z CH *Politecnico di
More informationSTUDY OF AGGREGATION IN BARIUM SULPHATE PRECIPITATION
15 th International Symposium on Industrial Crystallization Sorrento, Italy, 15-18 September 2002 paper 171 STUDY OF AGGREGATION IN BARIUM SULPHATE PRECIPITATION D. L. Marchisio 1, A. A. Barresi, M. Garbero,
More informationFlow Generated by Fractal Impeller in Stirred Tank: CFD Simulations
Flow Generated by Fractal Impeller in Stirred Tank: CFD Simulations Gunwant M. Mule and Amol A. Kulkarni* Chem. Eng. & Proc. Dev. Division, CSIR-National Chemical Laboratory, Pune 411008, INDIA *Corresponding
More informationEffect of Uniform Horizontal Magnetic Field on Thermal Instability in A Rotating Micropolar Fluid Saturating A Porous Medium
IOSR Journal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume, Issue Ver. III (Jan. - Fe. 06), 5-65 www.iosrjournals.org Effect of Uniform Horizontal Magnetic Field on Thermal Instaility
More informationCFD ANALYSIS OF TURBULENCE EFFECT ON REACTION IN STIRRED TANK REACTORS
CFD ANALYSIS OF TURBULENCE EFFECT ON REACTION IN STIRRED TANK REACTORS Udaya Bhaskar Reddy R*, Gopalakrishnan S, Ramasamy E Department of Chemical Engineering, Coimbatore Institute of Technology, Coimbatore-
More informationPolitecnico di Torino. Porto Institutional Repository
Politecnico di Torino Porto Institutional Repository [Proceeding] Simulation of macromolecule self-assembly in solution: multiscale approach a Original Citation: Lavino, A; Di Pasquale, N; Carbone, P;
More informationDEVELOPMENT OF A NUMERICAL APPROACH FOR SIMULATION OF SAND BLOWING AND CORE FORMATION
TMS (The Minerals, Metals & Materials Society), DEVELOPMENT OF A NUMERICAL APPROACH FOR SIMULATION OF SAND BLOWING AND CORE FORMATION G.F. Yao, C. W. Hirt, and
More informationMASS TRANSFER EFFICIENCY IN SX MIXERS
MASS TRANSFER EFFICIENCY IN SX MIXERS By R. Sheinman, Y. Kootov, L. Braginsy, J. Riordan, M. Vancas Turbulent Technologies Ltd. Israel Tenova Bateman Advanced Technologies Ltd. Israel, Australia ABSTRACT
More informationCFD modelling of multiphase flows
1 Lecture CFD-3 CFD modelling of multiphase flows Simon Lo CD-adapco Trident House, Basil Hill Road Didcot, OX11 7HJ, UK simon.lo@cd-adapco.com 2 VOF Free surface flows LMP Droplet flows Liquid film DEM
More informationAvailable online at Energy Procedia 100 (2009) (2008) GHGT-9
Availale online at www.sciencedirect.com Energy Procedia (29) (28) 655 66 Energy Procedia www.elsevier.com/locate/procedia www.elsevier.com/locate/xxx GHGT-9 Pre-comustion CO 2 capture for IGCC plants
More informationModelling of Break-up and Coalescence in Bubbly Two-Phase Flows
Modelling of Break-up and Coalescence in Bubbly Two-Phase Flows Simon Lo and Dongsheng Zhang CD-adapco, Trident Park, Didcot OX 7HJ, UK e-mail: simon.lo@uk.cd-adapco.com Abstract Numerical simulations
More informationAdvective and Diffusive Turbulent Mixing
Advective and Diffusive Turulent Mixing J. J. Monaghan School of Mathematical Sciences Monash University, Clayton Melourne, Australia joe.monaghan@monash.edu J. B. Kajtar School of Mathematical Sciences
More informationCFD Models for Polydisperse Solids Based on the Direct Quadrature Method of Moments
CFD Models for Polydisperse Solids Based on the Direct Quadrature Method of Moments Rodney O. Fox H. L. Stiles Professor Department of Chemical Engineering Iowa State University Acknowledgements: US National
More informationStudy on residence time distribution of CSTR using CFD
Indian Journal of Chemical Technology Vol. 3, March 16, pp. 114-1 Study on residence time distribution of CSTR using CFD Akhilesh Khapre*, Divya Rajavathsavai & Basudeb Munshi Department of Chemical Engineering,
More informationThe Use of COMSOL for Integrated Hydrological Modeling
The Use of for Integrated Hydrological Modeling Ting Fong May Chui *, David L. Freyerg Department of Civil and Environmental Engineering, Stanford University *Corresponding author: 380 Panama Mall, Terman
More informationMODELLING PARTICLE DEPOSITION ON GAS TURBINE BLADE SURFACES
MODELLING PARTICLE DEPOSITION ON GAS TURBINE BLADE SURFACES MS. Hesham El-Batsh Institute of Thermal Turbomachines and Power Plants Vienna University of Technology Getreidemarkt 9/313, A-1060 Wien Tel:
More informationSTUDY ON BUBBLE BEHAVIOR OF INERT GASES AT ENTRANCE NOZZLE IN SODIUM-COOLED FAST REACTOR
NTHAS8: The Eighth Japan-Korea Symposium on Nuclear Thermal Hydraulics and Safety Beppu, Japan, Decemer 9-12, 2012 Paper Numer N8P1081 STUDY ON BUBBLE BEHAVIOR OF INERT GASES AT ENTRANCE NOZZLE IN SODIUM-COOLED
More informationRELATION BETWEEN PARTICLE RISING BEHAVIOR AND LIQUID FLOW AROUND THE BOTTOM OF A STIRRED VESSEL
14 th European Conference on Mixing Warszawa, 10-13 September 2012 RELATION BETWEEN PARTICLE RISING BEHAVIOR AND LIQUID FLOW AROUND THE BOTTOM OF A STIRRED VESSEL Ryuta Misumi a, Takuji Sasaki b, Hayato
More informationA generalized approach to model oxygen transfer in bioreactors using population balances and computational fluid dynamics
Chemical Engineering Science 60 (2005) 213 218 www.elsevier.com/locate/ces A generalized approach to model oxygen transfer in bioreactors using population balances and computational fluid dynamics Kumar
More informationCFD SIMULATIONS OF SINGLE AND TWO-PHASE MIXING PROESSES IN STIRRED TANK REACTORS
CFD SIMULATIONS OF SINGLE AND TWO-PHASE MIXING PROESSES IN STIRRED TANK REACTORS Hristo Vesselinov Hristov, Stephan Boden, Günther Hessel, Holger Kryk, Horst-Michael Prasser, and Wilfried Schmitt. Introduction
More informationOn the Comparison between Population Balance Models for CFD Simulation of Bubble Columns
Chemical and Biological Engineering Publications Chemical and Biological Engineering 2005 On the Comparison between Population Balance Models for CFD Simulation of Bubble Columns Jay Sanyal Fluent Inc.
More informationAGITATION AND AERATION
AGITATION AND AERATION Although in many aerobic cultures, gas sparging provides the method for both mixing and aeration - it is important that these two aspects of fermenter design be considered separately.
More informationDetailed 3D modelling of mass transfer processes in two phase flows with dynamic interfaces
Detailed 3D modelling of mass transfer processes in two phase flows with dynamic interfaces D. Darmana, N.G. Deen, J.A.M. Kuipers Fundamentals of Chemical Reaction Engineering, Faculty of Science and Technology,
More informationA Stable and Convergent Finite Difference Scheme for 2D Incompressible Nonlinear Viscoelastic Fluid Dynamics Problem
Applied and Computational Mathematics 2018; (1): 11-18 http://www.sciencepulishinggroup.com/j/acm doi: 10.11648/j.acm.2018001.12 ISSN: 2328-5605 (Print); ISSN: 2328-5613 (Online) A Stale and Convergent
More informationModeling Industrial Crystallizers
Modeling Industrial Crystallizers Kumar Dhanasekharan, Ph.D. Fluent Inc., 10 Cavendish Court, Lebanon, NH 03766 Phone: (603) 643-2600 x323; Email: kd@fluent.com One of the main challenges in industrial
More informationTravel Grouping of Evaporating Polydisperse Droplets in Oscillating Flow- Theoretical Analysis
Travel Grouping of Evaporating Polydisperse Droplets in Oscillating Flow- Theoretical Analysis DAVID KATOSHEVSKI Department of Biotechnology and Environmental Engineering Ben-Gurion niversity of the Negev
More informationMODENA. Deliverable 3.2. WP s leader: TU/e. Simulations for foams, dispersion and mixing and developed SW. Principal investigator:
Delivery date: 11-4-2015 MODENA Authors: Patrick Anderson, Martien Hulsen, Christos Mitrias TU/e E-mail : pda@tue.nl Deliverable 3.2 Simulations for foams, dispersion and mixing and developed SW Daniele
More informationCFD SIMULATION OF SOLID-LIQUID STIRRED TANKS
CFD SIMULATION OF SOLID-LIQUID STIRRED TANKS Divyamaan Wadnerkar 1, Ranjeet P. Utikar 1, Moses O. Tade 1, Vishnu K. Pareek 1 Department of Chemical Engineering, Curtin University Perth, WA 6102 r.utikar@curtin.edu.au
More informationENGG 199 Reacting Flows Spring Lecture 4 Gas-Liquid Mixing Reactor Selection Agitator Design
ENGG 199 Reacting Flows Spring 2006 Lecture 4 Gas-Liquid Mixing Reactor Selection gitator Design Copyright 2000,.W. Etchells, R.K.Grenville & R.D. LaRoche ll rights reserved. Background Roughly 25 % of
More informationSoot formation in turbulent non premixed flames
Soot formation in turbulent non premixed flames A. Cuoci 1, A. Frassoldati 1, D. Patriarca 1, T. Faravelli 1, E. Ranzi 1, H. Bockhorn 2 1 Dipartimento di Chimica, Materiali e Ing. Chimica, Politecnico
More informationMULTIPHASE FLOW MODELLING
MULTIPHASE FLOW MODELLING 1 Introduction 2 Outline Multiphase Flow Modeling Discrete phase model Eulerian model Mixture model Volume-of-fluid model Reacting Flow Modeling Eddy dissipation model Non-premixed,
More informationModeling Complex Flows! Direct Numerical Simulations! Computational Fluid Dynamics!
http://www.nd.edu/~gtryggva/cfd-course/! Modeling Complex Flows! Grétar Tryggvason! Spring 2011! Direct Numerical Simulations! In direct numerical simulations the full unsteady Navier-Stokes equations
More informationApplication of the CFD method for modelling of floating particles suspension
Application of the CFD method for modelling of floating particles suspension Joanna Karcz, Lukasz Kacperski, Marcelina Bitenc Szczecin University of Technology, Dept. of Chem. Eng. al. Piastow 42, PL-7-65
More informationMinimum fluidization velocity, bubble behaviour and pressure drop in fluidized beds with a range of particle sizes
Computational Methods in Multiphase Flow V 227 Minimum fluidization velocity, bubble behaviour and pressure drop in fluidized beds with a range of particle sizes B. M. Halvorsen 1,2 & B. Arvoh 1 1 Institute
More informationHybrid CFD-Multizonal Modelling of Polymorphs and Agglomeration Phenomena in Crystallisation Processes
Hybrid CFD-Multizonal Modelling of Polymorphs and Agglomeration Phenomena in Crystallisation Processes Sean K. Bermingham 1, Stefania Trivellato 1,2, Maddalena Vernier 1,2, Fabrizio Bezzo 2,* 1 Process
More information2. Modeling of shrinkage during first drying period
2. Modeling of shrinkage during first drying period In this chapter we propose and develop a mathematical model of to describe nonuniform shrinkage of porous medium during drying starting with several
More informationModeling of Water Flows around a Circular Cylinder with the SPH Method
Archives of Hydro-Engineering and Environmental Mechanics Vol. 61 (2014), No. 1 2, pp. 39 60 DOI: 10.1515/heem-2015-0003 IBW PAN, ISSN 1231 3726 Modeling of Water Flows around a Circular Cylinder with
More informationSimulation of mixing and precipitation of nanoparticles for pharmaceutical applications with CFD and MD
14th European Conference on Mixing Warszawa, 10-13 September 2012 Simulation of mixing and precipitation of nanoparticles for pharmaceutical applications with CFD and MD N. Di Pasquale 1, P. Carbone 2,
More informationPredicting Size Distribution of Dispersed Phase Systems
Predicting Size Distribution of Dispersed Phase Systems Evren Bayraktar Supervisors: Prof. S.Turek (Dortmund), Dr. Ing. Otto Mierka, Dr. Ing. Frank Platte 28.11.2008, Sulzer Page 1 Outline Introduction
More informationEuler-Euler Modeling of Mass-Transfer in Bubbly Flows
Euler-Euler Modeling of Mass-Transfer in Bubbly Flows Roland Rzehak Eckhard Krepper Text optional: Institutsname Prof. Dr. Hans Mustermann www.fzd.de Mitglied der Leibniz-Gemeinschaft Overview Motivation
More informationA PRAGMATIC APPROACH TO CFD MODELLING OF SEPARATION PROCESSES
10th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries SINTEF, Trondheim, NORWAY 17-19th June 2014 CFD 2014 A PRAGMATIC APPROACH TO CFD MODELLING OF SEPARATION PROCESSES
More informationEFFECTS OF STRONG TEMPERATURE GRADIENT ON A COMPRESSIBLE TURBULENT CHANNEL FLOW
th International Symposium on Turulence and Shear Flo Phenomena (TSFP, Chicago, USA, July, 7 EFFECTS OF STRONG TEMPERATURE GRADIENT ON A COMPRESSIBLE TURBULENT CHANNEL FLOW Mitsuhiro Nagata Mechanical
More informationHigh-order approximations for unsteady-state diffusion and reaction in slab, cylinder and sphere catalyst
Korean J. Chem. Eng., 9(, 4-48 (0 DOI: 0.007/s84-0-00-7 INVITED REVIEW PPER High-order approximations for unsteady-state diffusion and reaction in sla, cylinder and sphere catalyst Dong Hyun Kim and Jitae
More informationApplications of Computational Fluid Dynamics in the Process Industries. Ahmad Haidari & Peter Spicka Fluent Inc.
Applications of Computational Fluid Dynamics in the Process Industries Ahmad Haidari & Peter Spicka Fluent Inc. 1 Outline Overview of CFD s growth in the process Industry Overview of modeling multiphase
More informationCFD MODEL FOR DETERMINING LOCAL PHASE FRACTION OIL-WATER DISPERSION IN TURBULENT FLOW
CFD MODEL FOR DETERMINING LOCAL PHASE FRACTION OIL-WATER DISPERSION IN TURBULENT FLOW Siti Aslina Hussain 1* and Soo Mee Khuan 1 1 Department of Chemical and Environment Engineering, Faculty of Engineering,
More informationNATURAL CONVECTION IN HEAT EXCHANGERS - A NEW INCENTIVE FOR MORE COMPACT HEAT EXCHANGERS?
Proceedings of Fifth International Conference on Enhanced, Compact and Ultra-Compact Heat Exchangers: Science, Engineering and Technology, Eds. R.K. Shah, M. Ishizuka, T.M. Rudy, and V.V. Wadekar, Engineering
More informationHydrodynamics of Bubble Columns: Turbulence and Population Balance Model
Article Hydrodynamics of Bubble Columns: Turbulence and Population Balance Model Camila Braga Vieira *, and Pierre Proulx ID ID, Giuliana Litrico, Ehsan Askari ID, Gabriel Lemieux ID Chemical Engineering
More informationCFD Analysis and Experimental Evaluation of the Effective Parameters on Paint Homogeneity in Mixing Tanks
ISTP-16, 2005, PRAGUE 16 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA CFD Analysis and Experimental Evaluation of the Effective Parameters on Paint Homogeneity in Mixing Tanks N. K. Mohtaram*, M.
More informationInternational Journal of Thermal Sciences
International Journal of Thermal Sciences 50 (2011) 2430e2442 Contents lists availale at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts Development
More informationGas Film Liquid Film Bulk Gas
Diagram of Two Film Theory showing gas adsorption (solid arrows) and gas stripping (dashed arrows). Dissolved gas is rought to interfacial film surface y mixing (convection) and diffuses to interface where
More informationPrinciples of Convection
Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid
More informationExperimental and Numerical Investigation of Two- Phase Flow through Enlarging Singularity
Purdue University Purdue e-pubs International Refrigeration and Air Conditioning Conference School of Mechanical Engineering 212 Experimental and Numerical Investigation of Two- Phase Flow through Enlarging
More informationNumerical Simulation of Gas-Liquid-Reactors with Bubbly Flows using a Hybrid Multiphase-CFD Approach
Numerical Simulation of Gas-Liquid-Reactors with Bubbly Flows using a Hybrid Multiphase-CFD Approach TFM Hybrid Interface Resolving Two-Fluid Model (HIRES-TFM) by Coupling of the Volume-of-Fluid (VOF)
More informationEffect of Carrier Gas Flow Behavior on Performance of Separation by Using Ultrasonic Atomization
Effect of Carrier Gas Flow Behavior on Performance of Separation by Using Ultrasonic Atomization Yoshiyuki Bando 1, Keiji Yasuda 1, Akira Matsuoka 1 and Yasuhito Kawase 2 1. Department of Chemical Engineering,
More informationNUMERICAL AND EXPERIMENTAL STUDIES OF LIQUID-LIQUID MIXING IN A KENICS STATIC MIXER
14 th European Conference on Mixing Warszawa, 10-13 September 2012 NUMERICAL AND EXPERIMENTAL STUDIES OF LIQUID-LIQUID MIXING IN A KENICS STATIC MIXER Zdzislaw Jaworski a, Halina Murasiewicz a, a Institute
More informationCOMPUTATIONAL STUDY OF PARTICLE/LIQUID FLOWS IN CURVED/COILED MEMBRANE SYSTEMS
COMPUTATIONAL STUDY OF PARTICLE/LIQUID FLOWS IN CURVED/COILED MEMBRANE SYSTEMS Prashant Tiwari 1, Steven P. Antal 1,2, Michael Z. Podowski 1,2 * 1 Department of Mechanical, Aerospace and Nuclear Engineering,
More informationThe effect of momentum flux ratio and turbulence model on the numerical prediction of atomization characteristics of air assisted liquid jets
ILASS Americas, 26 th Annual Conference on Liquid Atomization and Spray Systems, Portland, OR, May 204 The effect of momentum flux ratio and turbulence model on the numerical prediction of atomization
More informationcen29305_ch08.qxd 11/30/05 3:05 PM Page 451 INTERNAL FORCED CONVECTION CHAPTER 8 Liquid or gas flow through pipes or ducts is commonly used in heating
cen29305_ch08.qxd 11/30/05 3:05 PM Page 451 INTERNAL FORCED CONVECTION CHAPTER 8 Liquid or gas flow through pipes or ducts is commonly used in heating and cooling applications. The fluid in such applications
More informationStudies on flow through and around a porous permeable sphere: II. Heat Transfer
Studies on flow through and around a porous permeable sphere: II. Heat Transfer A. K. Jain and S. Basu 1 Department of Chemical Engineering Indian Institute of Technology Delhi New Delhi 110016, India
More informationModelling and Simulation of a Batch Poly(Vinyl Chloride) Reactor
769 A publication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 32, 23 Chief Editors: Sauro Pierucci, Jiří J. Klemeš Copyright 23, AIDIC Servizi S.r.l., ISBN 978-88-968-23-; ISSN 974-979 The Italian Association
More informationCFD in COMSOL Multiphysics
CFD in COMSOL Multiphysics Mats Nigam Copyright 2016 COMSOL. Any of the images, text, and equations here may be copied and modified for your own internal use. All trademarks are the property of their respective
More informationMath background. Physics. Simulation. Related phenomena. Frontiers in graphics. Rigid fluids
Fluid dynamics Math background Physics Simulation Related phenomena Frontiers in graphics Rigid fluids Fields Domain Ω R2 Scalar field f :Ω R Vector field f : Ω R2 Types of derivatives Derivatives measure
More informationLuis Manuel Santana Gallego 100 Investigation and simulation of the clock skew in modern integrated circuits. Clock Skew Model
Luis Manuel Santana Gallego 100 Appendix 3 Clock Skew Model Xiaohong Jiang and Susumu Horiguchi [JIA-01] 1. Introduction The evolution of VLSI chips toward larger die sizes and faster clock speeds makes
More information3. FORMS OF GOVERNING EQUATIONS IN CFD
3. FORMS OF GOVERNING EQUATIONS IN CFD 3.1. Governing and model equations in CFD Fluid flows are governed by the Navier-Stokes equations (N-S), which simpler, inviscid, form is the Euler equations. For
More informationCFD Simulation of Flashing and Boiling Flows Using FLUENT
CFD Simulation of Flashing and Boiling Flows Using FLUENT Hua Bai and Paul Gillis The Dow Chemical Company FLUENT UGM 2004 Liquid/Gas Phase Change found in many industrial chemical processes involves complex
More informationCFD analysis of the transient flow in a low-oil concentration hydrocyclone
CFD analysis of the transient flow in a low-oil concentration hydrocyclone Paladino, E. E. (1), Nunes, G. C. () and Schwenk, L. (1) (1) ESSS Engineering Simulation and Scientific Software CELTA - Rod SC-41,
More informationBest Practice Guidelines for Computational Turbulent Dispersed Multiphase Flows. René V.A. Oliemans
Best Practice Guidelines for Computational Turbulent Dispersed Multiphase Flows René V.A. Oliemans ERCOFTAC Seminar, Innventia, Stockholm, June 7-8, 2011 1 Vermelding onderdeel organisatie Department of
More informationDEVELOPMENT OF A MULTIPLE VELOCITY MULTIPLE SIZE GROUP MODEL FOR POLY-DISPERSED MULTIPHASE FLOWS
DEVELOPMENT OF A MULTIPLE VELOCITY MULTIPLE SIZE GROUP MODEL FOR POLY-DISPERSED MULTIPHASE FLOWS Jun-Mei Shi, Phil Zwart 1, Thomas Frank 2, Ulrich Rohde, and Horst-Michael Prasser 1. Introduction Poly-dispersed
More informationModeling of dispersed phase by Lagrangian approach in Fluent
Lappeenranta University of Technology From the SelectedWorks of Kari Myöhänen 2008 Modeling of dispersed phase by Lagrangian approach in Fluent Kari Myöhänen Available at: https://works.bepress.com/kari_myohanen/5/
More informationSection 8.5. z(t) = be ix(t). (8.5.1) Figure A pendulum. ż = ibẋe ix (8.5.2) (8.5.3) = ( bẋ 2 cos(x) bẍ sin(x)) + i( bẋ 2 sin(x) + bẍ cos(x)).
Difference Equations to Differential Equations Section 8.5 Applications: Pendulums Mass-Spring Systems In this section we will investigate two applications of our work in Section 8.4. First, we will consider
More informationEXPERIMENTAL INVESTIGATION AND CFD MODELING OF MICROMIXING OF A SINGLE-FEED SEMI-BATCH PRECIPITATION PROCESS IN A LIQUID-LIQUID STIRRED REACTOR
14 th European onference on Mixing Warszawa, 10-13 September 2012 EXPERIMENTAL INVESTIGATION AND FD MODELING OF MIROMIXING OF A SINGLE-FEED SEMI-BATH PREIPITATION PROESS IN A LIQUID-LIQUID STIRRED REATOR
More informationprecipitation in a Confined Impinging Jets Reactor by means of
Modeling of nanoparticles precipitation in a Confined Impinging Jets Reactor by means of Computational Fluid Dynamics E. Gavi, D.L. Marchisio, A.A. Barresi Politecnico di Torino, Department of Material
More informationCHAPTER 3. Mathematical Models and Numerical Methods Involving First-Order Equations
CHAPTER 3 Mathematical Models and Numerical Methods Involving First-Order Equations 2. Compartmental Analysis The asic one-compartment system consists of a function x(t) that represents the amount of a
More informationFormation of binary ion clusters from polar vapours: effect of the dipole-charge interaction
Atmos. Chem. Phys., 4, 385 389, 24 SRef-ID: 68-7324/acp/24-4-385 Atmospheric Chemistry and Physics Formation of inary ion clusters from polar vapours: effect of the dipole-charge interaction A. B. Nadykto
More informationUNSTEADY POISEUILLE FLOW OF SECOND GRADE FLUID IN A TUBE OF ELLIPTICAL CROSS SECTION
THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume, Numer 4/0, pp. 9 95 UNSTEADY POISEUILLE FLOW OF SECOND GRADE FLUID IN A TUBE OF ELLIPTICAL CROSS SECTION
More informationCOMPARTMENTAL MODELLING OF AN INDUSTRIAL BUBBLE COLUMN
COMPARTMENTAL MODELLING OF AN INDUSTRIAL BUBBLE COLUMN Christophe Wylock 1, Aurélie Larcy 1, Thierry Cartage 2, Benoît Haut 1 1 Transfers, Interfaces and Processes (TIPs) Chemical Engineering Unit, Université
More informationM Manuela R da Fonseca, DEQB. Mixing
Mixing Mixing time and degree of mixing: A) reactor without recirculation Mixing time and degree of mixing: B) reactor with recirculation van t Riet and van der Lans, in Comprehensive Biotechnol, 2nd ed.
More informationCFD Simulation of Binary Fluidized Mixtures: Effects of Restitution Coefficient and Spatial Discretization Methods
Engineering Conferences International ECI Digital Archives The 14th International Conference on Fluidization From Fundamentals to Products Refereed Proceedings 2013 CFD Simulation of Binary Fluidized Mixtures:
More informationOn the Comparison between Presumed and Full PDF Methods for Turbulent Precipitation
Chemical and Biological Engineering Publications Chemical and Biological Engineering 2001 On the Comparison between Presumed and Full PDF Methods for Turbulent Precipitation Daniele L. Marchisio Politecnico
More informationAn initiation to SPH
An initiation to SPH Lucas Braune, Thomas Lewiner Department of Mathematics, PUC Rio Rio de Janeiro, Brazil Figure 1. An SPH simulation of a dam reak. Astract The recent expansion of particle-ased methods
More informationBOUSSINESQ-TYPE MOMENTUM EQUATIONS SOLUTIONS FOR STEADY RAPIDLY VARIED FLOWS. Yebegaeshet T. Zerihun 1 and John D. Fenton 2
ADVANCES IN YDRO-SCIENCE AND ENGINEERING, VOLUME VI BOUSSINESQ-TYPE MOMENTUM EQUATIONS SOLUTIONS FOR STEADY RAPIDLY VARIED FLOWS Yeegaeshet T. Zerihun and John D. Fenton ABSTRACT The depth averaged Saint-Venant
More informationCFD Simulation of Sodium Boiling in Heated Pipe using RPI Model
Proceedings of the 2 nd World Congress on Momentum, Heat and Mass Transfer (MHMT 17) Barcelona, Spain April 6 8, 2017 Paper No. ICMFHT 114 ISSN: 2371-5316 DOI: 10.11159/icmfht17.114 CFD Simulation of Sodium
More informationThe CMFD code TransAT
TransAT Report Series Presentations The CMFD code TransAT Multiphase Flow Modelling ASCOMP Switzerland Edited by: Damel Lakehal Release date: Sep, 2014 References: TRS-P/ 05-2014 www.ascomp.ch - info@ascomp.ch
More informationCAV2001:SESSIONA
CAV001:SESSIONA1.004 1 Effects of model size and free stream nuclei on tip vortex cavitation inception scaling Young Shen*, Georges Chahine**, Chao-Tsung Hsiao**, and Stuart Jessup* *NSWCCD, West Bethesda,
More informationOn Temporal Instability of Electrically Forced Axisymmetric Jets with Variable Applied Field and Nonzero Basic State Velocity
Availale at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 19-966 Vol. 6, Issue 1 (June 11) pp. 7 (Previously, Vol. 6, Issue 11, pp. 1767 178) Applications and Applied Mathematics: An International Journal
More informationOPTIMAL WAVELENGTH SELECTION ALGORITHM OF NON-SPHERICAL PARTICLE SIZE DISTRIBUTION BASED ON THE LIGHT EXTINCTION DATA
THERMAL SCIENCE, Year 202, Vol. 6, No. 5, pp. 353-357 353 OPTIMAL WAVELENGTH SELECTION ALGORITHM OF NON-SPHERICAL PARTICLE SIZE ISTRIBUTION BASE ON THE LIGHT EXTINCTION ATA y Hong TANG * College of Metrology
More informationNumerical investigation of solid-liquid two phase flow in a non-clogging centrifugal pump at offdesign
IOP Conference Series: Earth and Environmental Science Numerical investigation of solid-liquid two phase flow in a non-clogging centrifugal pump at offdesign conditions To cite this article: B J Zhao et
More informationBASIC DESIGN EQUATIONS FOR MULTIPHASE REACTORS
BASIC DESIGN EQUATIONS FOR MULTIPHASE REACTORS Starting Reference 1. P. A. Ramachandran and R. V. Chaudhari, Three-Phase Catalytic Reactors, Gordon and Breach Publishers, New York, (1983). 2. Nigam, K.D.P.
More informationCharacteristics of flow over the free overfall of triangular channel
MATEC We of Conferences 16, 03006 (018) BCEE3-017 https://doi.org/10.101/matecconf/0181603006 Characteristics of flow over the free overfall of triangular channel Raad Irzooki 1,*, Safa Hasan 1 Environmental
More informationPARTICLE DISPERSION IN ENCLOSED SPACES USING A LAGRANGIAN MODEL
IV Journeys in Multiphase Flows (JEM 217) March 27-31, 217, São Paulo, SP, Brazil Copyright 217 by ABCM Paper ID: JEM-217-4 PARTICLE DISPERSION IN ENCLOSED SPACES USING A LAGRANGIAN MODEL Ana María Mosquera
More informationSIEVE TRAY EFFICIENCY USING CFD MODELING AND SIMULATION
SIEVE TRAY EFFICIENCY USING CFD MODELING AND SIMULATION Getye Gesit* School of Chemical and Bio Engineering Addis Ababa Institute of Technology, Addis Ababa University ABSTRACT In this work, computational
More informationMASS TRANSFER COEFFICIENTS DURING AERATION BY A SELF-ASPIRATING IMPELLER
th European Conference on Mixing Warszawa, - September MASS TRANSFER COEFFICIENTS DURING AERATION BY A SELF-ASPIRATING IMPELLER Czesław Kuncewicz, Jacek Stelmach Lodz University of Technology, Department
More informationMass transfer coefficient for drying of moist particulate in a bubbling fluidized bed
Mass transfer coefficient for drying of moist particulate in a uling fluidized ed Dr. Yassir T. Makkawi 1, and Prof. Raffaella Ocone 2 1 Chemical Engineering & Applied Chemistry, Aston University, Birmingham
More informationComputer Life (CPL) ISSN: The Numerical Simulation on Internal Gas-liquid Two Phase Flow Field of. Three Layers of Air Stirred Reactor
Computer Life (CPL) ISSN: 1819-4818 DELIVERING QUALITY SCIENCE TO THE WORLD The Numerical Simulation on Internal Gas-liquid Two Phase Flow Field of Three Layers of Air Stirred Reactor Haiyue Wang*, Zhixi
More informationSupporting Information. Dynamics of the Dissociating Uracil Anion. Following Resonant Electron Attachment
Supporting Information Dynamics of the Dissociating Uracil Anion Following Resonant Electron Attachment Y. Kawarai,, Th. Weer, Y. Azuma, C. Winstead, V. McKoy, A. Belkacem, and D.S. Slaughter, Department
More information2014 International Conference on Computer Science and Electronic Technology (ICCSET 2014)
04 International Conference on Computer Science and Electronic Technology (ICCSET 04) Lateral Load-carrying Capacity Research of Steel Plate Bearing in Space Frame Structure Menghong Wang,a, Xueting Yang,,
More informationLIQUID VELOCITY CONTROL IN EXTERNAL - LOOP AIRLIFT BY MEANS OF MAGNETIZABLE PARTICLES
Hristov J.Y., Liquid velocity control in an external loop airlift by means of magnetizable particles, In: Proc. Of 3 rd Int. Workshop on Transport Phenomena in Two-phase Flow, (Chr. Boyadjiev, Ed.), pp.
More informationNatural Convection in a Trapezoidal Enclosure Heated from the Side with a Baffle Mounted on Its Upper Inclined Surface
Heat Transfer Engineering ISSN: 0145-7632 Print) 1521-0537 Online) Journal homepage: http://www.tandfonline.com/loi/uhte20 Natural Convection in a Trapezoidal Enclosure Heated from the Side with a Baffle
More informationModelling wind speed parameters for computer generation of wind speed in Flanders
Modelling wind speed parameters for computer generation of wind speed in Flanders A case study using small wind turines in an uran environment Michaël Gay, Michel Van Dessel Dept. of Applied Engineering
More information