Entropy Based Design and Analysis of Fluids Engineering Systems

Entropy-Based Design and Analysis of Fluids Engineering Systems......Page 1
Contents......Page 4
Foreword......Page 8
Preface......Page 9
Acknowledgments......Page 11
Authors......Page 12
1.1 Background......Page 13
1.2.1 Vector and Tensor Notations......Page 16
1.2.2 Mass and Momentum Equations......Page 17
1.2.3 Energy Transport Equations......Page 19
1.3 Mathematical Properties of Entropy and Exergy......Page 20
1.3.1 Concavity Property of Entropy......Page 21
1.3.2 Distance Functional with Respect to Equilibrium Conditions......Page 26
1.4.1 Closed System......Page 29
1.4.2 Open System......Page 32
1.5.1 Closed System......Page 34
1.5.2 Linear Advection Equation (without Diffusion)......Page 35
1.5.3 Linear Advection Equation (with Diffusion)......Page 36
1.5.4 Navier–Stokes Equations......Page 37
References......Page 41
2.1 Introduction......Page 44
2.2 Conservation Laws as Moments of the Boltzmann Equation......Page 45
2.3 Extended Probability Distributions......Page 47
2.4 Selected Multivariate Probability Distribution Functions......Page 49
2.4.2 Central Distribution Probability Distribution Function......Page 50
2.4.3 Chapman–Enskog Probability Distribution Function......Page 51
2.4.4 Skew-Normal Probability Distribution Function......Page 52
2.5 Concave Entropy Functions......Page 54
2.6 Statistical Formulation of the Second Law......Page 57
2.7.1 Discretization of the Problem Domain......Page 59
2.7.2 Discretization of the Conservation Equations......Page 62
2.7.3 Discretization of the Second Law......Page 64
References......Page 66
3.1 Introduction......Page 68
3.2 Entropy Transport Equation for Incompressible Flows......Page 69
3.3.1 Entropy Production in Bernoulli’s Equation......Page 72
3.3.2 Loss Coefficients in a Plane Diffuser......Page 74
3.3.3 Case Study of Channel and Diffuser Design......Page 75
3.4 Upper Entropy Bounds in Closed Systems......Page 81
3.4.1 Upper Bounds of Thermal Irreversibility......Page 82
3.4.2 Optimal Aspect Ratio of Upper Entropy Bounds......Page 86
3.4.3 Case Study of Mixing Tank Design......Page 87
3.5.1 Electrochemical Irreversibilities in a Porous Electrode......Page 90
3.5.2 Formulation of Channel Flow Irreversibilities......Page 93
3.5.3 Proton Exchange Membrane Fuel Cell (PEMFC) and Solid Oxide Fuel Cell (SOFC) Design......Page 96
3.6 Case Study of Fluid Machinery Design......Page 101
References......Page 103
4.2.1 Velocity Field Measurement......Page 105
4.2.2 Temperature Field Measurement......Page 107
4.2.3 Postprocessing for Entropy Production Measurement......Page 109
4.3 Case Study of Magnetic Stirring Tank Design......Page 110
4.4 Case Study of Natural Convection in Cavities......Page 113
4.5.1 Bias and Precision Errors......Page 115
4.5.2 Velocity Field Uncertainties in Channel Flow......Page 116
4.5.3 Measurement Uncertainties of Entropy Production......Page 118
References......Page 119
5.1 Introduction......Page 121
5.2.1 Continuum Equations and Slip Boundary Conditions......Page 122
5.2.2 Case Study of Exergy Losses in Channel Design......Page 123
5.3.1 Irreversibilities with a Constant Magnetic Field......Page 127
5.3.2 Case Study of Channel Design at Varying Hartmann Numbers......Page 132
5.4.1 Fluid Flow Formulation......Page 136
5.4.2 Heat Transfer Formulation......Page 141
5.4.3 Formulation of Entropy Production......Page 142
Case (ii): Unspecified (Exponential) Profile, Laminar Flow, Uniform Wall Heat Flux......Page 143
Case (iii): Unspecified Cross-Stream Profile Variation, Laminar Flow, Uniform Wall Heat Flux......Page 145
5.4.4 Case Studies of Surface Micropattern Design......Page 146
References......Page 151
6.1 Introduction......Page 153
6.2.1 Finite Volume Formulation......Page 155
6.2.2 Central, Upwind, and Exponential Differencing Schemes......Page 157
6.2.3 Case Study of Nozzle Flow Analysis and Design......Page 162
6.3.1 Entropy Correction of Numerical Diffusion......Page 167
6.3.2 Case Study of Shock Capturing in a Shock Tube......Page 171
6.4.1 Formulation of Average Entropy Difference......Page 173
6.4.2 Case Study of Error Indicators in Supersonic Flow......Page 175
References......Page 183
7.1 Introduction......Page 185
7.2 Stability Norms......Page 186
7.3.1 Linear Scalar Advection......Page 190
7.3.2 Nonlinear Scalar Advection......Page 199
7.3.3 Coupled Nonlinear Equations......Page 207
7.4 Stability of Shock Capturing Methods......Page 212
References......Page 220
8.1 Introduction......Page 222
8.2 Entropy Transport Equations for Solidification and Melting......Page 224
8.3.1 Irreversibility of Interdendritic Permeability......Page 229
8.3.2 Thermal Recalescence and Dimensionless Entropy Ratio......Page 231
8.4.1 Modeling of Two-Phase Entropy Production......Page 236
8.4.2 Iterative Phase Rules and the Second Law......Page 239
8.4.3 Entropy Correction of Numerical Conductivity......Page 241
8.4.4 Entropy Condition for Temporal Stability......Page 243
8.4.5 Case Study of Melting in an Enclosure......Page 246
8.4.6 Case Study of Free Convection and Solidification......Page 249
8.5.1 Formulation of an Inverse Method......Page 251
8.5.2 Entropy Correction for Numerical Stability......Page 253
8.5.3 Case Study with Solidification of a Pure Material......Page 255
8.6.1 Formulation of Heat Transfer and Irreversibility Distribution......Page 259
8.6.2 Case Study of Flat Plate Condensation......Page 265
References......Page 267
9.1 Introduction......Page 270
9.2 Reynolds Averaged Entropy Transport Equations......Page 271
9.3 Eddy Viscosity Models of Mean Entropy Production......Page 274
9.4 Turbulence Modeling with the Second Law......Page 275
9.5.1 Formulation of Dissipation Rate......Page 277
9.5.2 Large Eddy Particle Image Velocimetry......Page 280
9.5.3 Case Study of Turbulent Channel Flow......Page 282
References......Page 293
Table A.1: Conversion of Units and Constants......Page 295
Table A.2: Properties of Metals at STP......Page 296
Table A.3: Properties of Nonmetals......Page 297
Table A.4: Properties of Air at Atmospheric Pressure......Page 298
Table A.5: Properties of Other Gases (1 atm, 298 K)......Page 299
Table A.6: Properties of Other Gases (Effects of Temperature)......Page 301
Table A.7: Properties of Liquids (300 K, 1 atm)......Page 303
Table A.8: Properties of Saturated Water......Page 304
References......Page 305
Nomenclature......Page 306
Subscripts and Superscripts......Page 307
Greek Symbols......Page 308