Tải bản đầy đủ

Cghemical engineering module

COMSOL

Multiphysics

Chemical Engineering
MODULE

MODEL LIBRARY
V ERSION

3.4


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Company home page
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Chemical Engineering Module Model Library
© COPYRIGHT 1994–2007 by COMSOL AB. All rights reserved
Patent pending
The software described in this document is furnished under a license agreement. The software may be used
or copied only under the terms of the license agreement. No part of this manual may be photocopied or
reproduced in any form without prior written consent from COMSOL AB.
COMSOL, COMSOL Multiphysics, COMSOL Reaction Engineering Lab, and FEMLAB are registered
trademarks of COMSOL AB. COMSOL Script is a trademark of COMSOL AB.
Other product or brand names are trademarks or registered trademarks of their respective holders.

Version:

October 2007

COMSOL 3.4


C O N T E N T S
Chapter 1: Introduction
Model Library Overview

2

Model Library Guide . . . . . . . . . . . . . . . . . . . . .

3

Typographical Conventions . . . . . . . . . . . . . . . . . . .

7

C h a p t e r 2 : F l u i d F l ow — Tu t o r i a l s a n d B e n c h m a r k s
Pressure Recovery in a Diverging Duct
Introduction

10

. . . . . . . . . . . . . . . . . . . . . . . . 10

Model Definition . . . . . . . . . . . . . . . . . . . . . . . 10
Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Modeling Using the Graphical User Interface . . . . . . . . . . . . 13
Flow in a Fuel Cell Stack
Introduction

18

. . . . . . . . . . . . . . . . . . . . . . . . 18

Model Definition . . . . . . . . . . . . . . . . . . . . . . . 18
Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Modeling Using the Graphical User Interface . . . . . . . . . . . . 23
Non-Newtonian Flow
Introduction

30

. . . . . . . . . . . . . . . . . . . . . . . . 30

Model Definition . . . . . . . . . . . . . . . . . . . . . . . 30
Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Reference . . . . . . . . . . . . . . . . . . . . . . . . . 34
Modeling Using the Graphical User Interface . . . . . . . . . . . . 34
Flow Between Two Parallel Plates
Introduction

39

. . . . . . . . . . . . . . . . . . . . . . . . 39

Model Definition . . . . . . . . . . . . . . . . . . . . . . . 40
Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Modeling Using the Graphical User Interface . . . . . . . . . . . . 42

CONTENTS

|i


Variations in Density in Porous Media Flow
Introduction

46

. . . . . . . . . . . . . . . . . . . . . . . . 46

Model Definition . . . . . . . . . . . . . . . . . . . . . . . 46
Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . . . 49
Modeling Using the Graphical User Interface . . . . . . . . . . . . 49
Coupled Free and Porous Media Flow
Introduction

57

. . . . . . . . . . . . . . . . . . . . . . . . 57

Model Definition . . . . . . . . . . . . . . . . . . . . . . . 58
Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Modeling Using the Graphical User Interface . . . . . . . . . . . . 61
Turbulent Flow Through a Bending Pipe
Introduction

65

. . . . . . . . . . . . . . . . . . . . . . . . 65

Model Definition . . . . . . . . . . . . . . . . . . . . . . . 65
Results and Discussion. . . . . . . . . . . . . . . . . . . . . 67
Reference . . . . . . . . . . . . . . . . . . . . . . . . . 69
Modeling Using the Graphical User Interface . . . . . . . . . . . . 69
Oscillating Liquid Cobalt Droplet
Introduction

75

. . . . . . . . . . . . . . . . . . . . . . . . 75

Model Definition . . . . . . . . . . . . . . . . . . . . . . . 75
Results and Discussion. . . . . . . . . . . . . . . . . . . . . 78
References . . . . . . . . . . . . . . . . . . . . . . . . . 81
Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . . . 81
Modeling Using the Graphical User Interface . . . . . . . . . . . . 82
Turbulent Flow over a Backward-Facing Step
Introduction

87

. . . . . . . . . . . . . . . . . . . . . . . . 87

Model Definition . . . . . . . . . . . . . . . . . . . . . . . 87
Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Reference . . . . . . . . . . . . . . . . . . . . . . . . . 92
Modeling Using the Graphical User Interface . . . . . . . . . . . . 93

ii | C O N T E N T S


C ha p ter 3: Hea t Tra ns fer a nd Non - Is ot her ma l
F low — Tut or i a l s a nd B e n c h m a r k s
Forced Turbulent Convection Cooling of a Hot Plate
Introduction

98

. . . . . . . . . . . . . . . . . . . . . . . . 98

Model Definition . . . . . . . . . . . . . . . . . . . . . . . 98
Results. . . . . . . . . . . . . . . . . . . . . . . . . .

101

References . . . . . . . . . . . . . . . . . . . . . . . .

106

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

107

Modeling Using the Graphical User Interface . . . . . . . . . . .

107

Heating of a Finite Slab

114

Introduction

114

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

114

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

115

Reference . . . . . . . . . . . . . . . . . . . . . . . .

115

Modeling Using the Graphical User Interface . . . . . . . . . . .

116

A 3D Model of a MEMS Heat Exchanger

119

Introduction

. . . . . . . . . . . . . . . . . . . . . . .

119

Model Definition . . . . . . . . . . . . . . . . . . . . . .

119

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

121

Reference . . . . . . . . . . . . . . . . . . . . . . . .

123

Modeling Using the Graphical User Interface . . . . . . . . . . .

123

Non-Isothermal Flow in a Cooling Process

129

Introduction

129

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

129

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

131

Modeling Using the Graphical User Interface . . . . . . . . . . .

133

MEMS Heat Exchanger

142

Introduction

142

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

142

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

144

Reference . . . . . . . . . . . . . . . . . . . . . . . .

145

CONTENTS

| iii


Modeling Using the Graphical User Interface . . . . . . . . . . .

145

C h a p t e r 4 : M u l t i c o m p o n e n t Tr a n s p o r t — Tu t o r i a l s
and Benchmarks
Separation through Dialysis

152

Introduction

152

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

153

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

158

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

159

References . . . . . . . . . . . . . . . . . . . . . . . .

159

Modeling Using the Graphical User Interface . . . . . . . . . . .

160

Stefan Tube

164

Introduction

. . . . . . . . . . . . . . . . . . . . . . .

164

Model Definition . . . . . . . . . . . . . . . . . . . . . .

164

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

166

References . . . . . . . . . . . . . . . . . . . . . . . .

168

Modeling Using the Graphical User Interface . . . . . . . . . . .

169

Maxwell-Stefan Diffusion in a Fuel Cell Unit Cell

173

Introduction

173

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

173

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

176

References . . . . . . . . . . . . . . . . . . . . . . . .

179

Modeling Using the Graphical User Interface . . . . . . . . . . .

180

C h a p t e r 5 : M i xe r s a n d S t i r r e d Ve s se l s

iv | C O N T E N T S

Laminar Static Mixer

186

Introduction

186

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

186

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

187

References . . . . . . . . . . . . . . . . . . . . . . . .

190


Modeling Using the Graphical User Interface . . . . . . . . . . .

191

Residence Time in a Turbulent Reactor

197

Introduction

197

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

198

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

200

Reference . . . . . . . . . . . . . . . . . . . . . . . .

205

Modeling Using the Graphical User Interface—2D Turbulent Reactor . .

205

Modeling Using the Graphical User Interface—3D Turbulent Reactor . .

211

Swirl Flow Around a Rotating Disk

216

Introduction

216

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

216

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

218

Reference . . . . . . . . . . . . . . . . . . . . . . . .

221

Modeling Using the Graphical User Interface . . . . . . . . . . .

222

Modeling of Rotating Parts

227

Introduction

227

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

228

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

229

Modeling Using the Graphical User Interface . . . . . . . . . . .

230

Chapter 6: Multiphase Flow
Rigid Body Motion

236

Introduction

236

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

236

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

237

Modeling Using the Graphical User Interface . . . . . . . . . . .

238

Rising Bubble Modeled with the Level Set Method

243

Introduction

243

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

244

Results and Discussion. . . . . . . . . . . . . . . . . . . .

246

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

248

CONTENTS

|v


Modeling Using the Graphical User Interface . . . . . . . . . . .

249

Boiling Flow

255

Model Definition . . . . . . . . . . . . . . . . . . . . . .

255

Results and Discussion. . . . . . . . . . . . . . . . . . . .

259

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

260

References . . . . . . . . . . . . . . . . . . . . . . . .

261

Modeling Using the Graphical User Interface . . . . . . . . . . .

261

Droplet Breakup in a T-Junction

270

Introduction

270

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

270

Results and Discussion. . . . . . . . . . . . . . . . . . . .

272

Reference . . . . . . . . . . . . . . . . . . . . . . . .

273

Modeling Using the Graphical User Interface . . . . . . . . . . .

273

Bubble Column Reactor

279

Introduction

279

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

279

Results and Discussion. . . . . . . . . . . . . . . . . . . .

283

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

286

Modeling Using the Graphical User Interface . . . . . . . . . . .

287

Contaminant-Removal from Wastewater in a Secondary Clarifier
294
Introduction

vi | C O N T E N T S

. . . . . . . . . . . . . . . . . . . . . . .

294

Model Definition . . . . . . . . . . . . . . . . . . . . . .

294

Results and Discussion. . . . . . . . . . . . . . . . . . . .

298

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

299

Modeling Using the Graphical User Interface . . . . . . . . . . .

300

Two-Phase Flow Modeling of a Dense Suspension

305

Introduction

305

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

305

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

309

References . . . . . . . . . . . . . . . . . . . . . . . .

311

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

312

Modeling Using the Graphical User Interface—Case 1 . . . . . . . .

312


Modeling Using the Graphical User Interface—Case 2 . . . . . . . .

316

Chapter 7: Microfluidics
Electrokinetic Flow in a DNA Chip

320

Introduction

320

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

321

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

324

References . . . . . . . . . . . . . . . . . . . . . . . .

328

Modeling Using the Graphical User Interface . . . . . . . . . . .

329

Filling of a Capillary Channel

334

Introduction

334

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

334

Results and Discussion. . . . . . . . . . . . . . . . . . . .

338

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

342

Modeling Using the Graphical User Interface . . . . . . . . . . .

342

Transport in an Electrokinetic Valve

348

Introduction

348

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

349

Results and Discussion. . . . . . . . . . . . . . . . . . . .

353

Reference . . . . . . . . . . . . . . . . . . . . . . . .

356

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

356

Modeling Using the Graphical User Interface . . . . . . . . . . .

356

Transport in an Electrokinetic Valve, 3D Model

365

Introduction

365

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

365

Results and Discussion. . . . . . . . . . . . . . . . . . . .

370

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

374

Reference . . . . . . . . . . . . . . . . . . . . . . . .

376

Modeling Using the Graphical User Interface . . . . . . . . . . .

376

Electroosmotic Flow in Porous Media

389

Introduction

389

. . . . . . . . . . . . . . . . . . . . . . .

CONTENTS

| vii


Model Definition . . . . . . . . . . . . . . . . . . . . . .

389

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

391

References . . . . . . . . . . . . . . . . . . . . . . . .

394

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

395

Modeling Using the Graphical User Interface . . . . . . . . . . .

395

Microchannel Cell

403

Introduction

403

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

404

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

407

Modeling Using the Graphical User Interface . . . . . . . . . . .

410

C ha p ter 8: Tra ns p or t, Reacti on s , a n d React ion
Engineering

viii | C O N T E N T S

Fixed-Bed Reactor for Catalytic Hydrocarbon Oxidation

418

Introduction

418

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

418

Results and Discussion. . . . . . . . . . . . . . . . . . . .

421

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

424

References . . . . . . . . . . . . . . . . . . . . . . . .

425

Modeling Using the Graphical User Interface . . . . . . . . . . .

425

Absorption in a Falling Film

433

Introduction

433

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

434

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

438

Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . .

439

References . . . . . . . . . . . . . . . . . . . . . . . .

440

Modeling Using the Graphical User Interface . . . . . . . . . . .

440

Boat Reactor for Low Pressure Chemical Vapor Deposition

447

Introduction

447

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

448

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

451


References . . . . . . . . . . . . . . . . . . . . . . . .

454

Modeling Using the Graphical User Interface . . . . . . . . . . .

454

Monolithic Reactor

461

Introduction

461

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

462

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

464

Reference . . . . . . . . . . . . . . . . . . . . . . . .

466

Modeling Using the Graphical User Interface . . . . . . . . . . .

466

Selective Catalytic Reduction of NOx

470

Introduction

470

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

470

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

475

Reference . . . . . . . . . . . . . . . . . . . . . . . .

479

Modeling Using the COMSOL Reaction Engineering Lab . . . . . . .

480

Modeling Using COMSOL Multiphysics . . . . . . . . . . . . .

486

Porous Reactor with Injection Needle

494

Introduction

494

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

494

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

496

Modeling Using the Graphical User Interface . . . . . . . . . . .

499

Carbon Deposition in Heterogeneous Catalysis

506

Introduction

506

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

506

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

510

References . . . . . . . . . . . . . . . . . . . . . . . .

517

Modeling Using the COMSOL Reaction Engineering Lab . . . . . . .

517

Modeling Using COMSOL Multiphysics . . . . . . . . . . . . .

520

CONTENTS

| ix


Chapter 9: Electrochemical Cells and
Electrochemical Engineering
Current Distribution in a Chlor-Alkali Membrane Cell

530

Introduction

530

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

531

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

535

References . . . . . . . . . . . . . . . . . . . . . . . .

536

Modeling Using the Graphical User Interface . . . . . . . . . . .

536

Fuel Cell Cathode

541

Introduction

541

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

541

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

545

Reference . . . . . . . . . . . . . . . . . . . . . . . .

547

Modeling Using the Graphical User Interface . . . . . . . . . . .

547

Electrochemical Treatment of Tumors

552

Introduction

552

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

552

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

556

Reference . . . . . . . . . . . . . . . . . . . . . . . .

559

Modeling Using the Graphical User Interface . . . . . . . . . . .

560

Mass Transport and Electrochemical Reaction in a Fuel Cell Cathode
565
Introduction

x | CONTENTS

. . . . . . . . . . . . . . . . . . . . . . .

565

Model Definition . . . . . . . . . . . . . . . . . . . . . .

566

Results and Discussion. . . . . . . . . . . . . . . . . . . .

569

Modeling Using the Graphical User Interface . . . . . . . . . . .

573

Proton Exchange Membrane Fuel Cell

580

Introduction

580

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

581

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

587

References . . . . . . . . . . . . . . . . . . . . . . . .

591


Modeling Using the Graphical User Interface . . . . . . . . . . .

592

Serpentine Proton Exchange Membrane Fuel Cell Cathode

602

Introduction

602

. . . . . . . . . . . . . . . . . . . . . . .

Model Definition . . . . . . . . . . . . . . . . . . . . . .

602

Results. . . . . . . . . . . . . . . . . . . . . . . . . .

607

References . . . . . . . . . . . . . . . . . . . . . . . .

610

Modeling Using the Graphical User Interface . . . . . . . . . . .

611

Chapter 10: Electrophoresis and Chromatography
Electrophoresis—Transport in a Capillary Column

620

Introduction

620

. . . . . . . . . . . . . . . . . . . . . . .

Model Definitions . . . . . . . . . . . . . . . . . . . . .

621

Results and Discussion. . . . . . . . . . . . . . . . . . . .

624

References . . . . . . . . . . . . . . . . . . . . . . . .

627

Modeling Using the Graphical User Interface—Model 1 . . . . . . .

628

Modeling Using the Graphical User Interface—Model 2 . . . . . . .

631

Liquid Chromatography

635

Introduction

635

. . . . . . . . . . . . . . . . . . . . . . .

Model Definitions . . . . . . . . . . . . . . . . . . . . .

635

Results and Discussion. . . . . . . . . . . . . . . . . . . .

642

References . . . . . . . . . . . . . . . . . . . . . . . .

647

Modeling Using the Graphical User Interface—Model 1 . . . . . . .

647

Modeling Using the Graphical User Interface—Model 2 . . . . . . .

651

Modeling Using the Graphical User Interface—Model 3 . . . . . . .

655

INDEX

663

CONTENTS

| xi


xii | C O N T E N T S


1

Introduction
The Chemical Engineering Module Model Library consists of a large number of
models from various areas of chemical engineering. In particular, many of the
examples come from the fields of unit operations, chemical reaction engineering,
and transport phenomena.

1


M o de l L i b r a r y O v e rv i e w
The purpose of this Model Library is to assist you in learning, by example, how to
model sophisticated chemical-engineering units, processes, and phenomena. Through
them you can tap the expertise of top researchers in the field, examining how they
approach some of the most difficult modeling problems you might encounter. You can
thus get a feel for the power that COMSOL Multiphysics® offers as a modeling tool.
In addition to serving as a reference, the models can also give you a head start if you
are developing a model of a similar nature.
We have divided these models into nine chapters:
• Fluid Flow—Tutorials and Benchmarks
• Heat Transfer and Non-isothermal Flow—Tutorials and Benchmarks
• Multicomponent Transport—Tutorials and Benchmarks
• Mixers and Stirred Vessels
• Multiphase Flow
• Microfluidics
• Transport, Reactions, and Reaction Engineering
• Electrochemical Cells and Electrochemical Engineering
• Electrophoresis and chromatography
The first three chapters include tutorial and benchmark models that contain complete
descriptions of the main phenomena captured by the Chemical Engineering Module—
transport phenomena. The following chapters include examples from specific
application areas and models that are made up of coupled systems of the three
balances—multiphysics. In this Model Library you also find advanced models of, for
example, multiphase flow and reaction-engineering applications, including coupling
the Chemical Engineering Module to the COMSOL Reaction Engineering Lab®.
These models illustrate various chemical-engineering-specific application modes in the
Chemical Engineering Module. These specialized application modes are not available
in the base COMSOL Multiphysics package, and they come with their own user
interfaces that make it quick and easy to access their power.
Note that the model descriptions in this book do not contain every detail on how to
carry out every step in the modeling process. Before tackling these in-depth models,
we urge you to first read another book in the Chemical Engineering Module

2 |

CHAPTER 1: INTRODUCTION


documentation set. Titled the Chemical Engineering Module User’s Guide, it
introduces you to the basic functionality in the module, covers basic modeling
techniques, and includes reference material of interest to those working in chemical
engineering. The models that it presents are far simpler than those given in the Model
Library and might be more appropriate for your first introduction to COMSOL
Multiphysics.
Further information on how to work with the COMSOL Multiphysics graphical user
interface can be gained from the COMSOL Multiphysics User’s Guide or the
COMSOL Multiphysics Quick Start manual. An explanation on how to model with
a programming language is available in the COMSOL Multiphysics Scripting Guide.
This Chemical Engineering Module Model Library provides details about a large
number of ready-to-run models that illustrate real-world uses of the module. Each
entry comes with theoretical background as well as instructions that illustrate how to
set it up. The models are written by our staff engineers, who have years of experience
in chemical engineering. The terminology in the book should be familiar to you.
Finally, the software includes as loadable Model MPH-files (.mph) files all the examples
in the Chemical Engineering Module Model Library as well as the Chemical
Engineering Module User’s Guide. Click the Model Library tab in the Model Navigator
to find them under the chapter headings just listed. They are great to investigate if you
are familiar enough with the COMSOL Multiphysics structure and user interface but
still would like an idea on how to set up a certain model. You can even use them as a
starting point for models that are similar.

Model Library Guide
The following table summarizes key information about the entries in the Chemical
Engineering Module Model Library as well as the Chemical Engineering Module
User’s Guide. The solution time is the elapsed time measured on a machine running
Windows Vista with a 2.6 GHz AMD Athlon X2 Dual Core 500 CPU and 2 GB of

MODEL LIBRARY OVERVIEW

|

3


RAM. For models with a sequential solution strategy, the Solution Time column shows
the elapsed time for the longest solution step.

NONLINEAR

TIME DEPENDENT

STATIONARY

3D

2D

APPLICATION MODES

1D

PAGE

SOLUTION TIME

MODEL

PARAMETRIC STUDY

TABLE 1-1: CHEMICAL ENGINEERING MODULE MODEL LIBRARY

FLUID FLOW—TUTORIALS AND BENCHMARKS

thermal decomposition

UG16

Navier-Stokes

35 s



gravity tutorial

UG48

Weakly Compressible
Navier-Stokes

3s









diverging duct

10

Navier-Stokes

5s

√axi





fuel cell stack*

18

Navier-Stokes

124
min





non-newtonian flow

30

Non-Newt Flow

12 s

√axi

parallel plates

39

Navier-Stokes

3s



darcy 3d

46

Darcy’s Law

4s

porous free

57

Brinkman,
Navier-Stokes

4s

bending pipe

65

k-ε Turbulence Model

7 min

oscillating droplet

75

Navier-Stokes,
Conv&Conduction

86 min

√axi

turbulent backstep

87

k-ε Turbulence Model

5 min










































HEAT TRANSFER AND NON-ISOTHERMAL FLOW—TUTORIALS AND BENCHMARKS

forced turbulent
convection

98

Turbulent FluidThermal

7 min

slab

114

Conduction

1s

mems heat
exchanger 3d

119

Conv&Conduction

9s

non-isothermal flow

129

Non-Isothermal Flow

16 s

sinusoidal heat
exchanger

142

Conv&Conduction,
Navier-Stokes

2 min

MULTICOMPONENT TRANSPORT—TUTORIALS AND BENCHMARKS

4 |

CHAPTER 1: INTRODUCTION

























stefan tube

164

Maxwell-Stefan

1s

maxwell stefan diffusion

173

Maxwell-Stefan

14 s

laminar static mixer

186

Conv&Diffusion,
Navier-Stokes

28 min

turbulent residence
time 2d

197

k-ε Turbulence Model,
Conv&Diffusion

49 s

turbulent residence
time 3d

197

k-ε Turbulence Model,
Conv&Diffusion

34 min

rotating disk

216

Swirl Flow

38 s

√axi



schematic pump

227

Rotating
Navier-Stokes

10 min





rigid body motion

236

Level Set

7s







rising bubble

243

Navier-Stokes,
Conv&Diffusion

7s







boiling flow

255

Level Set Two-Phase
Flow, Laminar,
Conv&Conduction

36 min







droplet breakup

270

Level Set Two-Phase
Flow, Laminar

13 min







bubble column

279

Bubbly Flow,
Conv&Diffusion

3 min







sedimentation

294

Mixture Model,
k-ε Turbulence Model

6 min







dense suspension

305

Mixture Model,
Laminar
PDE, General Form

7 min












NONLINEAR

1s

TIME DEPENDENT

Conv&Diffusion,
Navier-Stokes,
Diffusion

STATIONARY

152

3D

dialysis

2D

APPLICATION MODES

1D

PAGE

SOLUTION TIME

MODEL

















PARAMETRIC STUDY

TABLE 1-1: CHEMICAL ENGINEERING MODULE MODEL LIBRARY

MIXERS AND STIRRED VESSELS


















MULTIPHASE FLOW

MODEL LIBRARY OVERVIEW

|

5




capillary filling

334

Level Set Two-Phase
Flow, Laminar

149
min

√axi



electrokinetic valve 2d

348

Electrokinetic Flow,
Navier-Stokes,
Conductive DC

6s





electrokinetic valve 3d

365

Electrokinetic Flow,
Navier-Stokes,
Conductive DC

9 min

electroosmotic flow

389

Electrokinetic Flow,
PDE General Form

10 s

h cell

403

Navier-Stokes,
Conv&Diffusion

58 s

PARAMETRIC STUDY

4s

TIME DEPENDENT

Navier-Stokes,
Conductive DC

STATIONARY

320

3D

biochip

2D

APPLICATION MODES

1D

PAGE

SOLUTION TIME

MODEL

NONLINEAR

TABLE 1-1: CHEMICAL ENGINEERING MODULE MODEL LIBRARY

MICROFLUIDICS






























TRANSPORT, REACTIONS, AND REACTION ENGINEERING

√axi

fixed bed reactor

418

Conv&Conduction,
Conv&Diffusion

8s

falling film

433

Conv&Diffusion

2 min

boat reactor

447

Navier-Stokes,
Conv&Diffusion

5s

√axi

monolithic reactor

461

Conv&Diffusion

2s

√ps

nox reduction

470

Navier-Stokes,
Darcy’s Law,
Conv&Diffusion

7s

√axi

porous reactor

494

Navier-Stokes,
Conv&Diffusion,
Brinkman

45 s



√ps



















ELECTROCHEMICAL CELLS AND ELECTROCHEMICAL ENGINEERING

chlor alkali

6 |

530

CHAPTER 1: INTRODUCTION

Conductive DC

1s




tumor

552

Nernst-Planck

14 s

fc cathode

565

Conductive DC,
Maxwell-Stefan,
Darcy’s Law

30 s

pemfc

580

Conductive DC,
Maxwell-Stefan,
Darcy’s Law

16 s

serpentine

602

Navier-Stokes,
Maxwell-Stefan

5 min







PARAMETRIC STUDY

3s

NONLINEAR

Conductive DC,
Diffusion

TIME DEPENDENT

541

STATIONARY

mcfc

3D

APPLICATION MODES

2D

PAGE

SOLUTION TIME

MODEL

1D

TABLE 1-1: CHEMICAL ENGINEERING MODULE MODEL LIBRARY






















ELECTROPHORESIS AND CHROMATOGRAPHY

capillary
electrophoresis 1

620

Electrokinetic Flow,
PDE General Form

11 s





capillary
electrophoresis 2

620

Electrokinetic Flow,
PDE General Form,
Conv&Diffusion

2 min





liquid chromatography 1

635

Conv&Diffusion

42 s





liquid chromatography 2

635

Conv&Diffusion

4 min





liquid chromatography 3

635

Conv&Diffusion

5 min





*This model has been solved on a machine running Linux with an AMD64 processor
and 12 GB of RAM.

Typographical Conventions
All COMSOL manuals use a set of consistent typographical conventions that should
make it easy for you to follow the discussion, realize what you can expect to see on the
screen, and know which data you must enter into various data-entry fields. In
particular, you should be aware of these conventions:
• A boldface font of the shown size and style indicates that the given word(s) appear
exactly that way on the COMSOL graphical user interface (for toolbar buttons in

MODEL LIBRARY OVERVIEW

|

7


the corresponding tooltip). For instance, we often refer to the Model Navigator,
which is the window that appears when you start a new modeling session in
COMSOL; the corresponding window on the screen has the title Model Navigator.
As another example, the instructions might say to click the Multiphysics button, and
the boldface font indicates that you can expect to see a button with that exact label
on the COMSOL user interface.
• The names of other items on the graphical user interface that do not have direct
labels contain a leading uppercase letter. For instance, we often refer to the Draw
toolbar; this vertical bar containing many icons appears on the left side of the user
interface during geometry modeling. However, nowhere on the screen will you see
the term “Draw” referring to this toolbar (if it were on the screen, we would print
it in this manual as the Draw menu).
• The symbol > indicates a menu item or an item in a folder in the Model Navigator.
For example, Physics>Equation System>Subdomain Settings is equivalent to: On the
Physics menu, point to Equation System and then click Subdomain Settings.
COMSOL Multiphysics>Heat Transfer>Conduction means: Open the COMSOL
Multiphysics folder, open the Heat Transfer folder, and select Conduction.
• A Code (monospace) font indicates keyboard entries in the user interface. You might
see an instruction such as “Type 1.25 in the Current density edit field.” The
monospace font also indicates COMSOL Script codes.
• An italic font indicates the introduction of important terminology. Expect to find
an explanation in the same paragraph or in the Glossary. The names of books in the
COMSOL documentation set also appear using an italic font.

8 |

CHAPTER 1: INTRODUCTION


2

Fluid Flow—Tutorials and Benchmarks
This chapter contains a selection of fluid flow models. Among the examples you
find models of laminar and turbulent flow, non-newtonian flow and porous media
flow. There is also a two-phase flow example that accounts for surface tension. All
models within this chapter are simple and instructive, demonstrating how you can
use the fluid flow application modes to model different kinds of isothermal fluid
flow.

9


Pressure Recovery in a Diverging
D uc t
Introduction
When the diameter of a pipe suddenly increases, as shown in Figure 2-1, the area
available for flow increases. A fluid with relatively high velocity decelerates into a
relatively slow moving fluid. Depending on the Reynolds number, this can cause
turbulence, and much of the excess kinetic energy converts into heat and is therefore
wasted. If the change of the cross section is gradual, it is possible to recover the kinetic
energy as pressure energy.
This example presents a qualitative study of the pressure-recovery phenomenon in a
uniformly diverging duct. It also shows the implementation of the Navier-Stokes
equations in cylindrical coordinates.

Figure 2-1: Geometrical representation of the modeling geometry.

Model Definition
The inlet condition is described by water flowing in a pipe with a diameter of 1 cm.
The flow is laminar and has a fully developed laminar velocity profile, a so-called
Hagen-Poiseuille profile. After 2 cm the water enters a uniformly diverging duct whose
length is 5 cm and whose outlet diameter is 2 cm.
Because water is a Newtonian fluid and its density is constant at isothermal conditions,
the Navier-Stokes equations combined with a continuity equation characterize the
flow:

10 |

C H A P T E R 2 : F L U I D F L O W — TU T O R I A L S A N D B E N C H M A R K S


η ∇2u + ρ ( u ⋅ ∇ )u + ∇p = 0
∇⋅u = 0

(2-1)

Here η denotes the dynamic viscosity (Pa·s), u represents the velocity (m/s), ρ gives
the fluid density (kg/m3), and p denotes the pressure (Pa). The model becomes
axisymmetrical and can be described in the r and z coordinates.

Figure 2-2: Simplification of the modeling geometry showing the symmetry axis and
boundary labels.
The following equations describe the relevant boundary conditions at the symmetry
axis, the outlet, the inlet, and the edge (wall) respectively:
n⋅u= 0

at ∂Ω symmetry

T

η ( ∇u + ( ∇u ) )n = 0, p = 0
2

at ∂Ω outlet

r
u = ⎛⎝ 0, vmax ⎛⎝ 1 – ⎛⎝ ----⎞⎠ ⎞⎠ ⎞⎠
R

at ∂Ω inlet

u = ( 0, 0 )

at ∂Ω edge

(2-2)

In these equations, for each boundary point n is the normal vector and t is any
tangential vector, Furthermore, vmax is the maximum flow speed in the axial direction
and R is the pipe radius at the inlet. The analytical expression above provides the
velocity distribution at the inlet, a parabolic Hagen-Poiseuille profile.

Results
Figure 2-3 clearly shows that the velocity vector magnitude decreases as the
cross-sectional area for the flow increases. You can additionally see the velocity vector
itself by introducing arrows. The arrow plot also shows how a small radial velocity

PRESSURE RECOVERY IN A DIVERGING DUCT

|

11


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