Peube J-L. Fundamentals of fluid mechanics and transport phenomena

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492 Fundamentals of Fluid Mechanics and Transport Phenomena

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Index

Actions

by contact, 18

volume, 18

Anemometry

Eulerian, 345

Lagrangian, 342

laser Doppler, 343

Archimedes’ theorem, 65

Balance equations, 54;

extensive quantity, 151

for sub-systems, 416

global, 151, 182

global for chemical species, 188

local, 151

local for chemical species, 177

Barotropic.fluid, 65

Bernoulli theorem

first, 166, 167

second, 269

Biot and Savart’s formula, 259

Boundary conditions, 178, 255, 322

Boundary layer, 319, 323

equations, 321

thermal, 437

Calorific coefficients, 27

Cauchy problem, 200, 202, 206,

207, 216, 235

Causal signal, 368

Causality, 3, 6, 406

Center of buoyancy, 65, 71

Cepstrum, 369

Characteristic curves, 205, 207, 209,

212, 214, 226, 240, 254

Characteristic determinant, 208, 213

Characteristic equation, 208, 222,

227

Circulation

creation of, 335

of the velocity, 258

Command model, 411, 473

Complex potential, 274

Compressibility coefficients, 27

Compression of data, 385

analytical methods, 387

arithmetic methods, 386

Concentration measurements, 347

Condition number, 353

Conditioning of a linear system, 353

Conjugated flows, 274

Conservation of volume, 160

Contact actions, 57, 58

Couette flow, 137

498 Fundamentals of Fluid Mechanics and Transport Phenomena

D’Alembert’s paradox, 281

Damköhler number, 197

Damping of oscillations, 294

Deformation rate tensors, 129

Determinism, 6, 13

Differential equations, 199

first order quasi-linear, 203

of order n, 218

quasi-linear partial, 220

reduced form, 229

second order partial, 225, 232

system of partial, 220

Diffusion, 73

coefficient, 61, 88, 93

equation, 97

in a closed container, 82

in a fixed component, 91

in a fluid at rest, 81, 90

in a moving medium, 83

in steady evaporation, 82

isothermal, 87

thermal, 58

velocities, 84, 89, 93

Dirac distribution, 418, 446

Discretization, 414, 472

schemes, 250

Discretized signals, 381

Dissipation function, 175, 176

Divariant fluid, 49, 162, 165, 167,

170

Drag, 280

coefficient, 195

Driving pressure, 66

Dynamic

moment, 108

resultant, 108

Eckert number, 192

Energy

internal, 21, 32, 40

mechanical, 44

Energy equation, 116, 172, 187

entropy form of, 117

Enthalpy, 24, 25, 26, 41, 164, 168,

174, 176, 188

generation, 167

total, 167, 168, 174, 187, 193

Entropy, 162, 164, 174, 211

balance equation, 175

source, 33, 43, 56, 118

Equations

elliptic, 227, 232, 234

equation of state, 190

hyperbolic, 227, 231, 235, 272

mixed, 238

parabolic, 227, 231, 312, 322

Equilibrium

local thermodynamic, 48

of the atmosphere, 67

stability of, 68

Errors

in measurements, 351

in numerical techniques, 384

Established regimes, 453, 474

for boundary layers, 461

harmonic, 456

in continuous media, 458

Euler equations, 163

Evaporation

steady, 82, 91

unsteady, 94

Extensive quantities, 16

Fick’s law, 61, 87

Floaters, 70

Flow

1D unsteady, 210, 239, 253

2D steady, 212, 213

2D unsteady, 221

around a circular cylinder, 279

compressible inviscid fluid, 270

in a nozzle, 244

in a pipe, 314

quasi-1D, 309

Index 499

steady, 327

unsteady, 327

Flux

mass, 125

thermal, 412

volume, 125

Flux density vector, 77, 124

diffusion, 84

extensive quantities, 50

mass, 78

molar, 52, 78

thermal, 52

Force

definition of, 104

deriving from a potential, 161

external, 108

internal, 109

power of, 107

power of external, 110

power of internal, 109

viscous volume, 148

Fourier

discrete transform of discretized

signal, 385

fast Fourier transform, 385

series, 362

short time transform, 370

transform, 364

transform of a discretized signal,

383

Fourier’s law, 59

Free surfaces, 180

Friction coefficient, 194

Froude number, 192

Fully immersed flows, 181

G, H

Gabor transform, 373

Galilean reference frame, 101, 123

Gibbs function, 25

Gibbs-Helmholtz relation, 25

Heat convection equation, 176

Heat engines, 45

Heat equation, 72

Heat-transfer coefficient, 73

Heisenberg-Gabor inequality, 372

Hilbert transform, 368

Homoentropic fluid, 65, 67, 164

Homogenity, 19

Hugoniot relation, 169

Hydrostatics, 69

center of buoyancy, 71

center of pressure, 69

equations, 66

thrust, 69

Hysteresis, 407

Impulse, 105

input, 418

response, 447

Initial conditions, 181, 418

Integral transforms, 363

Intermittency, 379

Internal energy equation, 174

Inviscid fluid, 163, 166, 172, 187

Irreversibility, 3

Irreversible phenomena, 49, 58

Irrotational flows, 273

Isolated systems, 2

K, L

Kinetic energy, 106

balance, 115

coefficient, 318

enthalpic form of theorem, 165

theorem, 107, 109, 164, 186

Lagrange’s theorem, 267

Laplace transform, 368, 450

Laplace’s law, 66, 181, 287

Laws for viscous fluids, 139

Bingham, 142

Newtonian, 141

Ostwald-de Waele, 141

purely viscous, 138, 141

time-dependent, 140

500 Fundamentals of Fluid Mechanics and Transport Phenomena

Lewis number, 88

Lift, 280

Mach lines, 215

Mach number, 160, 169, 192, 215

Mass

average velocity, 79

concentration, 76

conservation, 154, 160, 170, 184,

190

enthalpy, 65

fraction, 76

Matched asymptotic expansions, 437

Material derivative, 122

of a flux integral, 128

of a volume integral, 125

Modal reduction, 465

continuous media, 469

discrete models, 471

discrete systems, 466

Model reduction

input-output, 473

Modulation

amplitude, 378

frequency, 378

Molar

average velocity, 79

concentration, 76

fraction, 76

molarity, 76

momentum, 102, 103

angular, 107

balance, 113, 160

coefficient, 317

conservation of, 103

flux, 114

flux theorem, 184

linear, 107

MP3 encoding, 388

N, O

Navier-Stokes equations, 161, 190

Newtonian fluid, 163, 176, 407

Non-dimensional parameters, 189

Non-isothermal mixtures, 97

Numerical solutions, 250

Nusselt number, 194

Ohm’s law, 61

Onsager relations, 42, 59

P, Q

Parametric models, 451

Parseval’s theorem, 362

Particle Image Velocimetry, 349

Péclet diffusion number, 192, 197

Perfect gas, 23, 28, 39

Perturbation, 296

parameter, 300

regular, 296

singular, 305

Poiseuille flow, 142

Potential

equation, 271

flows, 269, 282

lines, 276

Power

mechanical, 173

thermal, 173

Prandtl number, 192

Pressure

center of, 70

driving, 162, 170, 180, 181, 194

forces, 63, 68

mean driving, 318

measurement of, 341

partial, 76

total, 166

total driving, 166

Process, 13

natural, 15, 16

possible, 15

quasi-static, 15

reversible, 15

Index 501

Progressive wave, 241

Propeller thrust, 185

Q, R

Quantity of acceleration

Rabinowitsch-Mooney relation, 144

Rayleigh criterion, 371

Reconstruction of a signal, 363

Reduced extensive quantities, 47

Representation

analytical, 448

by differential equations, 455

external, 410, 446, 456

internal, 408

mixed, 438

modal, 445, 471

state, 408

Representation of signals, 357

analytical, 360

on basis of functions, 361

Reynolds number, 146, 193, 195

Rotation vector, 123, 257

material derivative, 260

Saint-Venant relation, 167

Sampling of signals, 382

Schmidt number, 197

Separation

steady flow, 325

unsteady flow, 334

Shannon’s theorem, 384

Shock waves, 239, 247, 248

Sound analysis, 390

musical signals, 393

Source, 275

Sources of entropy, 35

Specific heats, 27

Spectrogram

sonagram, 376

Speed of sound, 28

Spring-mass oscillator, 288

State, 11

equation, 19, 23

general equation, 19, 20

internal, 9

of equilibrium, 12, 15, 19

representation, 412, 453

variables, 9

vector, 408

Statics of fluids, 63

Stefan’s law, 45

Streakline, 121

Stream function, 155, 273

Streamline, 121, 155, 166, 276

Strouhal number, 195

Superposed flows, 277

Supersonic flow, 244

Surface

tension, 287

waves in shallow water, 284

Synthesis of musical signals, 397

MIDI system, 397

musical instruments, 399

System, 13

closed, 14

insulated thermal, 32

isolated mechanical, 102

open, 14, 112

out-of-equilibrium, 30, 37

rigid, 111

Temperature

mean mixing, 415

measurements, 346

Thermal

conduction, 59, 62, 72

conductivity, 60

diffusion, 62

diffusion coefficient 98

diffusivity, 60, 72, 88

radiation, 45

Thermal system

2 components, 423, 449

3 components (series), 425