Subject Index

Added mass, see virtual mass Agitated reactors, see stirred reactors

Algebraic stress models 76, 77 Algorithms for treating pressure-velocity coupling 167

Algorithms for treating pressure-velocity coupling, co-located grid 171 Algorithms for treating pressure-velocity coupling, PISO 170 Algorithms for treating pressure-velocity coupling, SIMPLE 168 Algorithms for treating pressure-velocity coupling, SIMPLEC 169 Algorithms for treating pressure-velocity coupling, SIMPLER 169 Application of CFM, stirred reactors 318 Application of finite volume method, example 175 Application to reactor engineering, bubble columns 355 Application to reactor engineering, fluidized bed reactors 394 Approximation, of time integrals 173 Assessing convergence 179 Assessing influence of numerical issues 429

Auxiliary equations 44 Averaging, favre 67 Averaging, reynolds 66

Basic governing equations 35 Batchelor length scales 126 Beta PDF 139

Block correction methods 165 Boundary conditions 45 Boundary conditions, bubble column reactors 343 Boundary conditions, cyclic 51 Boundary conditions, free stream turbulence 75 Boundary conditions, inlet 48 Boundary conditions, numerical implementation 171 Boundary conditions, outlet 49 Boundary conditions, periodic 51

Boundary conditions, symmetry 51

Boundary conditions, turbulence near wall 73 Boundary conditions, wall 50 Boundedness, discretization method 157 Breakage probability 365 Brief review of modeling of fixed bed reactors 413 Bubble column reactor 264 Bubble column reactor, coalescence-breakup 364 Bubble column reactor, methanol synthesis 359

Bubble column reactor, multi-scale modeling 265 Bubble column reactor, typical wish list 331 Bubble column reactors 327 Bubble column reactors, boundary conditions 343 Bubble column reactors, CFD

modeling 332 Bubble column reactors, control volume for governing equations 334 Bubble column reactors, engineering 331 Bubble column reactors, equations of two-fluid model 334 Bubble column reactors, Eulerian-Eulerian approach 333 Bubble column reactors, Eulerian-Lagrangian approach 353 Bubble column reactors, flow regimes 329 Bubble column reactors, industrial applications 329

Bubble column reactors, k—s model of turbulence 341 Bubble column reactors, long time averaged flow 336 Bubble column reactors, modeling of gas—liquid interface 343 Bubble column reactors, modeling of sparger 343

Bubble column reactors, multi-group model 363 Bubble column reactors, ozonation reactor 358 Bubble column reactors, rectangular 2D 335 Bubble column reactors, review of recent simulations 346 Bubble column reactors, simulation of mixing for different spargers 356 Bubble column reactors, simulation of unsteady flows 347 Bubble column reactors, solution domain 342 Bubble column reactors, three-phase model 351 Bubble column reactors, turbulence models 339 Bubble column reactors, two bubble class model 351 Bubble column reactors, types 328

Bubble column reactors, VOF

approach 353 Bubble columns, slurry reactors 352

Bubble population, multi-group model 364 Bubble size distribution, influence of energy dissipation rate 349 Bubble size distribution, influence of energy dissipation rate 365 Bubble, bursting at interface 343

Bubble, rise velocity 338

Capacity enhancement of existing OXY reactor 256 Catalytic convertors, CFD

model 421 Central differencing scheme 159

CFD based modeling of bubble column reactors 332 CFD based modeling of stirred reactors 290 CFD codes, general purpose 233

CFD Modeling of gas-solid reactors 376 CFD solver, see solver CFM for CRE 26 CFM for CRE, key issues 428 Chemical kinetics 8, 9 Chemical reactor engineering

(CRE) 4, 7 Chemical vapor deposition reactor 419

Closure models / PDF based models 137 Collision time scale 119 Co-located grid 166 Complex geometry 219 Complex geometry, measures of grid quality 220 Computational flow modeling

(CFM) 19 Computational flow modeling, areas requiring further work 430 Computational flow modeling, future trends 432 Computational fluid dynamics

(CFD) 5, 19 Computational fluid dynamics, advantages 20 Computational molecule 163 Computational snapshot approach 292 Computational tools for simulating flow processes 229

Concentration spectra, isotropic turbulence 127 Conservation of energy 40 Conservation of mass 36 Conservation of momentum 38 Conservativeness, discretization method 157 Consistency, numerical method 152

Continuous fluid 36 Continuous random walk (CRW) method 100 Continuous surface force (CSF), for VOF 92 Continuous surface force, for

VOF 201 Control volume 153 Convergence and error analysis 179

Convergence, assessment 179 Convergence, numerical method 152

Correlations, drag coefficient 119

Correlations, heat transfer coefficient 121 Correlations, mass transfer coefficient 121 Cyclic boundary 51

Damkohler number 43 Daughter bubble size distribution 366 Density, mixture 44 Design models 245 Diffusion coefficient, binary 46 Diffusion coefficient, mixture 45

Diffusive flux 38 Dimensionless equations 41 Dimensionless numbers 43 Direct numerical simulations

(DNS) 63 Discrete particle models (DPM), fluidized bed reactors 377 Discrete random walk (DRW)

method 100 Discretization method, boundedness 157 Discretization method, conservativeness 157 Discretization method, desired properties 157 Discretization method, transportiveness 157 Discretization methods 23, 159 Discretization of governing model equations 154 Dispersed multiphase flows, areas requiring further work 431 Dispersed multiphase flows, coupling between phases 91

Dispersed multiphase flows, Eulerian-Eulerian approach 102 Dispersed multiphase flows, time scales 118 Dispersed phase particles, enthalpy conservation 101 Dispersed phase particles, hard sphere approach 99 Dispersed phase particles, Monte Carlo techniques 99

Dispersed phase particles, soft sphere approach 99 Dispersed phase particles, species conservation 101 Dispersed phase particles, wall boundary conditions 98 Dissipation of energy due to inelastic collisions 107 Donor-acceptor method 200 Double delta PDF 139 Drag coefficient 95, 338 Drag coefficient, influence of other bubbles 338 Drag coefficient, multi-particle systems 120 Drag coefficient, single particle 119

Drag coefficient, swarm of bubbles 338 Drag force 94 Drag force, influence of other particles 104 Drop breakage 248 Dual impellers, interaction 310

Dual rushton turbine, flow simulation 305

Eddy breakup model 137 Eddy life time 118 Eddy life time, seen by a perticle 118 Eddy viscosity models 69 Effective particle diameter 111 Effective thermal conductivity 113

Effective viscosity 69

Eigenvalues 47

Energy exchange, between fluid and solids phase 107 Engineering of fubble column reactors 328 Engineering of fluidized bed reactors 368 Engineering of stirred reactors 286

Engulfment model 131 Engulfment, deformation, diffusion model 131 Enhancing convergence performance 222 Enhancing performance of semi-batch reactor 320 Enthalpy conservation equation, multiphase flows 107 Eotvos number 95 Equation of motion of a particle 94

Ergun equation 113 Ergun equation, for representing resistance of fixed bed 407

Error analysis 179 Error analysis of complex simulations 224 Errors in numerical simulations, origin 20 ESCIMO model 141 Euler method, explicit 173 Euler method, implicit 174 Euler number 43 Eulerian approach 36, 37 Eulerian-Eulerian approach 90 Eulerian-Eulerian approach, bubble column reactors 333

Eulerian-Eulerian approach, dispersed multiphase flows 102

Eulerian-Eulerian approach, interphase coupling terms 103

Eulerian-Eulerian approach, interphase drag force 103 Eulerian-Eulerian approach, numerical aspects 209 Eulerian-Eulerian approach, overall procedure 214

Eulerian-Eulerian approach, phase continuity equation 211

Eulerian-Eulerian approach, pressure correction equation 214 Eulerian-Eulerian approach, simulation example 215 Eulerian-Eulerian approach, solution of momentum equations 213 Eulerian-Eulerian approach, solution of volume fraction equations 212 Eulerian-Lagrangian approach 89, 94

Eulerian-Lagrangian approach, calculation of volume fraction 206 Eulerian-Lagrangian approach, interphase momentum transfer 207 Eulerian-Lagrangian approach, interpolation at the center of mass 205 Eulerian-Lagrangian approach, numerical aspects 204 Eulerian-Lagrangian approach, overall procedure 206 Eulerian-Lagrangian approach, simulation example 208 Eulerian-Lagrangian approach, time steps 204

Face velocity, interpolation 156

Favre averaging 67

FCC Regenerator 271

FCC regenerator, bubble-bubble interaction model 277 FCC regenerator, CFD model 278

FCC regenerator, mixing cell model 276 FCC regenerator, schematic 274

FCC regenerator, spent catalyst entry configuration 281 FCC regenrator, oxygen break-through 280 FCC riser reactor 397 FCC riser reactor, enhancing yield of gasoline 399 Finite difference method 23 Finite element method 23 Finite volume method 23 Finite volume method 153 Finite volume method for calculation of flow field 165

Finite volume method for unsteady flows 173

Fixed bed reactor, modeling of microscopic flow 414 Fixed bed reactors 403 Fixed bed reactors, gas-liquid flow 415 Fixed bed reactors, industrial applications 404 Fixed bed reactors, structure of bed porosity 416 Fixed bed reactors, types 404 Flamelet models 142 Flow modeling for reactor engineering 243 Flow modeling project, steps 21

Flow processes in porous media 112

Flow regime map, gas-solid flow 372 Flow regimes, bubble column reactor 329 Flow regimes, gas-liquid stirred reactor 16 Flow regimes, granular flows 104

Flow regimes, multiphase reactors 17 Flow simulation, basic elements 231

Flow, classification 21 Fluid dynamics of OXY reactor 260

Fluidized bed reactor for ethylene di-chloride (EDC) 254

Fluidized bed reactors 368 Fluidized bed reactors, discrete particle models 377 Fluidized bed reactors, granular flow models 381 Fluidized bed reactors, hierarchy of models 376 Fluidized bed reactors, industrial applications

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