Cambridge University Press 978-1-107-15330-1 — Two-Phase Flow, Boiling, and Condensation 2Nd Edition Index More Information

Cambridge University Press 978-1-107-15330-1 — Two-Phase Flow, Boiling, and Condensation 2nd Edition Index More Information

Index

active impurities. See impurities, active nucleation nucleate boiling correlations, and, 392–396 sites; nucleation sites, active critical heat lux, and, 396–400 activity coeficient, 69 Fick’s law for, 14 adiabatic pipe low 136–143. See also near-azeotropic, 17 countercurrent low limitation phase diagrams for, 15–17, 391 for air–water, 140, 142 zeotropic, 15–17 bubbly low and, 136 binary systems CCFL in, 228, 285–305 phase diagrams for, 15–17, 391, 583 churn low and, 137 Biot number, 46 co-current horizontal low and, 139–143, Blasius’s correlation, 28 221–225 boiling. See boiling water reactors; ilm boiling; horizontal, low regimes, 139–143 low boiling; low boiling, size/; low boiling, horizontal, low regime maps, 143–144 subcooled; liquid-deicient ilm boiling; for bubbly low, 136 minimum ilm boiling; nucleate boiling; slug low and, 137 onset of nucleation boiling point; pool vertical upward, 136 boiling; pool boiling, hydrodynamic theory air–water low regimes of; stable ilm boiling regimes; transition adiabatic pipe low and, 140, 142 boiling regimes in minichannels, 316–319 boiling water reactors (BWRs), 210 in rectangular channels, 310, 311 choking and, 668 in triangular channels, 309 low boiling and, 444 annular-dispersed low regimes low regimes, and, 145 CCFL and, 300 nuclear reactor design and, 486 conservation equations in, 493 Bond number, 46 in dryout, 493–495 Bowring’s pumping parameter, 426 ideal, 176 bubble(s), 83. See also bubble ebullition; bubble in horizontal low, 139 nucleation; bubble point lines; bubble train in inclined tubes, 233 low regimes; capillary bubbly low; internal low condensation and, 603, conined bubbly low; heterogeneous 604–607 bubble nucleation; isolated bubbly low; two-phase mixtures, 137 plug-elongated bubbles low regimes annular low, wall friction, 616–617 coalescence and, 112–113 annular-slug low, 512 growth of, in superheated liquids, 87–89 Antoine’s equation, 58 Laplace–Kelvin relations and, 90 Archimedean spiral coil, 155 nucleation of, 87 Armand’s low parameter, 213 oscillation modes of, 84–87 averaging. See low area averaging; time averaging, Rayleigh equation for, 88–89 in two-phase mixtures Rayleigh equation, extended, for, 88, axisymmetric disturbances, 78–80 89 azeotrope, 17 shape regimes for, 83 azeotropic mixtures, 17 in turbulent eddies, 109 bubble ebullition, 362, 366–369 Bénard cellular low, 46–50 bubble departure in, 367–368 binary mixtures cavity nucleus and, 364, 416 azeotropic, 17 conigurations in OSV, 422 pool boiling, 389–400 growth period for, 367

759

760 Index

bubble ebullition (cont.) churn low, 137, 307 in micro/minichannels, 667–672 CISE correlation, 213, 314 waiting periods in, 368–369 CISE-4 correlation, 481 bubble nucleation, 27, 668 Clapeyron’s relations, 5 heterogeneous, 361–366 in bubbles, 88 bubble point lines, 16 closure relations, 7–10 bubble train low regimes, 335–346 constitutive relations and, 8 bubbly low transfer relations and, 8 adiabatic pipe low and, 136 coalescence, 112–113 capillary, 309 aerosol population models and, 113 conined, 512 bubbles and, 113 isolated, 512 CHF and, 473 minichannels, 307, 308 interfacial area transport equations and, 238 buoyancy forces, 49 co-current horizontal low BWRs. See boiling water reactors adiabatic pipe low and, 139–143 Colebrook–White correlation, 250, 328 capillary bubbly low, 309 computational luid dynamic (CFD) codes, 162 capillary waves, 74 condensation, 560–586. See also direct contact in Rayleigh–Taylor instability, 77 condensation; internal low condensation; cavity nucleus laminar ilm condensation angle deinitions for, 364 binary luids, 583–586, 634–638 bubble ebullition and, 364, 416 direct contact, 562–563, 609–614 CCFL. See countercurrent low limitation CFD dropwise, 562 codes; computational luid dynamic ilm, 562 codes fog formation and, 582–583 channels, conventional. See also luoropolymer heat transfer correlations for channels; microchannels; minichannels; pure saturated vapor, internal low, 596–608 polyethylene channels; polyurethane with noncondensables, 608–609 channels; Pyrex channels helical low passages, in, 631–634 critical low in, 667–672 heterogeneous, 561 microchannels v., differences between, 116–117 homogenous, 560–561 channels, rectangular, 319–324 on horizontal pipes, 574–577 air–water low regimes in, 308, 322, 323 as interfacial mass transfer, 53–57 DFM and, 321 interfacial shear and, 569–571 horizontal, 320–324 internal low, 590–638 inclined/vertical, 320–322 laminar ilm, 565–571 two-phase low in, 322, 323 in noncondensable presence, 566, 578–581, channels, triangular, 309 608–609 Chapman–Enskog model, 23–25 of pure vapors, 564 chemical species mass conservation, 10 small channels, in, 627–631 CHF. See critical heat lux regimes low regimes, 623–625 choking. See also RETRAN codes pressure drop, 625–627 bubble nucleation and, 668 heat transfer, 627–631 BWRs and, 668 subcooling effects of, 578 critical low models for, 649–656, 658–667 thermal resistances in, 563–565 delayed lashing and, 668 turbulent ilm, 571–573 homogeneous equilibrium isentropic model for, two-phase low regimes, 591–596 649–651, 668 wavy-laminar, 571–573 interphase slips in, 648–649 conined bubble low, 512 in micro/minichannels, 667–672 conservation equations. See also mass non-equilibrium mechanistic modeling for, conservation equations; ordinary 672–674 differential equations omega parameter method, 658–667 in Annular-Dispersed Flow regime, 494–495 physics of, 643–644 as ODEs, 188–195 PWRs and, 668 one-dimensional, numerical solutions of, 195 RETRAN codes in, 656–658 constants, physical, 700 sound velocity and, in single-phase luids, constitutive relations, 8 644–645 contact angles, 41–43 in two-phase low mixtures, 647–674 dynamic, 42–43 chugging, 447 hysteresis in, 42–43

Index 761

surface wettability and, 42 Tien–Kutateladze looding correlation in, 291 variations of, 43 vertical low passages in, correlations for, Young–Dupré equations and, 42 290–293 control volume zero liquid penetration point in, 289 energy terms homogeneous low, for, 172 critical discharge rates, 645–646 in homogenous mixture models, 170, 171 critical low, 643. See also choking; critical low liquid/vapor, 180 model (Henry/Fauske); critical low model for mass conservation equations, 170, 175 (Moody); critical low model, isenthalpic conventional channels. See channels, conventional models for, 649–656, 658–667 correlation of Akers, 599 pressure proiles in, 669 correlation of Bowring, 480–481 critical low model (Henry/Fauske), 653–655 correlation of Bromley, modiied, 384 extended, 656 correlation of Caira, 481–482 RETRAN codes and, 656–658 correlation of Chen, 433–434 temperature proiles in, 654 suppression factors in, 434 critical low model, omega parameter, 658–667 correlation of Chen, low condensation, 598 critical low model (Moody), 651–653 correlation of Cooper, 373 critical low model, isenthalpic, 656 correlation of Dobson and Chato, 599–600 critical heat lux (CHF) regimes, 358, 372. See also correlation of Forster and Zuber, 376 critical heat lux regimes, post correlation of Gorenlo, 373–374 binary liquid mixtures, in, 396–400, 504–505 correlation of Groeneveld, 503 CISE-4 correlation in, 481 correlation of Gungor and Winterton, 434–435 coalescence and, 474 correlation of Kandlikar, 434 correlation of Bowring and, 480–481 correlation of Liu and Winterton, 435 correlation of Caira and, 481–482 correlation of Marsh and Mudawar, 417 correlation of Shah and, 482–483 correlation of Rohsenow, 370–372 diameter effects in, 478, 545–546 correlation of Shah, CHF, 482–483 DNB and, 472 correlation of Shah, low condensation, 599, DNBR and, 488 600–602 dryout and, 405, 475 correlation of Soliman et al., condensation, 597 exit quality effects on, 477, 478 correlation of Steiner and Taborek, 435–436 low boiling and, maps for, 473 correlation of Unal, 419 low oscillations in, 548 correlation of Wallis, 290 global conditions correlations in, 479–480 correlations of Stephan and Abdelsalam, 372–373 hydrodynamic theory of boiling and, 71 Couette low ilm models, 32, 33–34 in inclined/horizontal systems, 495–497 in interfacial mass transfers, 62, 63 inlet conditions correlations in, 479 interfacial shear and, 573–574 KfK correlation and, 487 noncondensable presences and, 578–581 liquid superheat and, 473 countercurrent low limitation (CCFL), 228, local conditions correlations in, 479 285–305 mass lux effects on, 477 in adiabatic pipe low, 228, 285–305 mechanisms for, 472–475 annular, 300 MFB and, 502 correlation of Wallis in, 290, 297, 299 in minichannels, 545–556 delooding point in, 290 models for, 549–556 envelope method analysis in, 299, 300–302 in nonuniformly heated channels, 486–487, looding curve in, 287, 290. See looding line 498–500 looding line in, 287 in nuclear reactor design, 485–488 low reversal point in, 289 oscillation modes and, 522–525 hanging ilm phenomenon and, 303 parametric effects on, 377–379 in horizontal/inclined channels, 299–300 parametric trends for, 475–479 LB-LOCA and, 296 post-CHF regimes and, 500–501 patterns in, 289 PWRs and, 485 in perforated plates, 293–296 rising jets schematics in, 377 phase change effects on, 300 rod bundles and, 487–488 in porous media, 296 saturated low boiling and, 431–444 PWRs and, 298 shape/size corrections for, 377–379 in rectangular/vertical channels, 296 in slug/plug low, 475 relux phenomenon in, 285 in small channels, 515, 545–556 separated-low momentum equations and, subcooled liquid correlations in, 488–493 300–302 surface size effects on, 377–379

762 Index

critical heat lux (CHF) regimes (cont.) concentration parameters in, 200 table look-up method for, 503–504 concept of, 199–202 in uniformly heated channels, 476 countercurrent slug low in, 203 upward low correlations in, 479–488 distribution parameter, 200 vapor formation and, 473 gas, 200 critical heat lux (CHF) regimes, post, 500–501 gas drift velocity in, 200 ECCS and, 500 minichannels and, 212–213, 341 LB-LOCA and, 500 pipe low parameters in, 203–210 liquid-deicient ilm boiling as, 503 PWRs and, 210 stable ilm boiling as, 502 rod bundle parameters in, 210–212, 219 transition boiling as, 502 SB-LOCA and, 210 curved low Passages, 149–157 slip ratio in, 201 two-phase low, 149–157 slip velocity in, 201 bends, and 150–153 subcooled low boiling and, 424–425 low reversal, and, 152 2FM v., 202–203 helicoidally coiled passages, and, 154–157 two-phase distribution coeficient in, 200 two-phase low model equations and, 202–203 Dalton’s law, 12 in two-phase low regimes, 225–227 DC condensation. See direct contact condensation dropwise condensation, 562 delooding, 290 dryout Deissler eddy diffusivity model, 30 annular-dispersed low regimes in, 493–495 density-wave oscillations CHF and, 405, 475 dynamic instabilities and, 447 in low boiling, 405 velocity of, 448 mechanistic models for, 493–495 departure from nucleate boiling (DNB) in saturated low boiling, 442 CHF regimes and, 472 dynamic contact angles, 42–43 low boiling and, 473, 474 dynamic instabilities, 447 Helmholtz stability theory and, 491 density-wave oscillations and, 447 mechanistic models for, 490–493 model of Celata, 492–493 ECCS, 500. See emergency core cooling system model of Katto, 490–492 eddies; turbulence, in eddies emergency OSV correlations in, 492 core cooling system (ECCS) vapor blankets and, 473 energy conservation equations departure from nucleate boiling ratio (DNBR), in HEM models, 172–173 488 mixture, separated low, 180–183 dew point lines, 16 envelope method analysis, 299, 300–302 DFM. See drift lux model Eötvös numbers, 84 diffusion models, for two-phase mixtures, 167. See equilibrium states also drift lux model Clapeyron’s relations in, 5 DFM, 167, 199–213, 219 P–v–T surfaces and, 4 diffusivitiy. See also mass diffusivity phases in, 3–5 binary surface, 45 of single phase low, 3 direct contact (DC) condensation, 562–563, triple point as, 3 609–614 for vapors, 51–52 OC-OTEC and, 614, 641 Euler’s equations on subcooled liquid droplets, 610–611 in linear stability analysis models, integration of, on subcooled liquid jets, 611–614 71 disjoining pressure, 50–52 ODEs and, 195 in Lennard-Jones model, 50 evaporation, 53–57 dispersed-droplet low regimes, 138 dispersion equations, 76 falling ilms, 123–126 dissipation range, 107 on lat surfaces, 123 DNB. See departure from nucleate boiling heat transfers for, 127–128 DNB model of Celata, 492–493 Kapitza number and, 122, 125 DNB model of Katto, 490–492 linear stability analysis, 125 DNBR. See departure from nucleate boiling ratio mass transfer processes in, 124, 130 drift lux model (DFM), two-phase mixtures, 167, mechanistic modeling, 129–131 199–213 modeling of, mechanistic, 129–131 BWRs and, 210 Reynolds number in, 122, 124 co-current slug low in, 203 roll waves in, 125

Index 763

small-amplitude waves in, 125 NVG and, 413 thermally developed low for, 130 OSV and, 413 turbulence for, 127–128 pressure drops in, 429 turbulent eddies and, 130 pumping effect and, 426 liquid diffusion and, 25 2FM and, 424–425 ilm boiling, 379–386 void generation and, 426–427 on horizontal surfaces, 379–381 low regimes. See bubbly low; capillary bubbly on horizontal tubes, 385 low; churn low; frothy slug-annular; modiied Bromley correlation and, 384 laminar low; pseudo-slug low; slug low; thermal radiation effects in, 385–386 wavy-annular low on vertical surfaces, 382–384 low reversal point, 289 ilm condensation, 562 fog, 560, 582–583 inely dispersed bubbly low regime, 138, 139, form pressure drops, 246 223–224 Fourier’s law looding. See countercurrent low limitation in gas–liquid interfacial phenomena, 62 low area averaging, 100–101 heat transfers and, 31 low boiling, 404–471, 509–559. See also low in transport equations, 8 boiling, saturated; low boiling, subcooled; fugacity, 67, 68 two-phase low instability fugacity coeficient, 68 buoyancy effects on, 409–410 fractions. See phase volume fractions; void BWRs and, 444 fractions CHF and, maps for, 473 frothy slug-annular low, 308 curves in, 411 fundamental void–quality relation, 103 DNB and, 407, 408 dryout in, 405 gas drift velocity, 200 forced, regimes, 404–410 gaskinetic theory (GKT), 21–25 heat transfers in, 412–413, 449–453, 456–459, Chapman–Enskog model for, 24–25 531–544 Lennard- Jones model for, 24 in horizontal channels, 440–444 Maxwell–Boltzmann distribution in, 22 in microchannels, 509–511, 559 molecular effusion in, 23 in minichannels, 509–511, 559 gases. See also gas kinetic theory NVG and, 413 equilibrium states for, 3 ONB and, 404, 405, 408, 413–418 ideal, 690 OSV and, 413, 419–423 selected, binary diffusion coeficients of, 695 partial, 429–430 sparingly soluble, in interfacial mass transfers, saturated, 431–444 59–61 in small channels, 509–559 gas–liquid interfacial phenomena, 38–90. See also stratiied regimes for, deinitions of, 442 contact angles; Kelvin–Helmholtz subcooled, hydrodynamics of, 424–429 instability; mass transfers; mass transfers, two-phase low instability and, 444–449 interfacial; Rayleigh–Taylor instability; two-phase patterns for, 512–525 surface tension, in gas-liquid interfacial low boiling curves, 411 phenomena; thermocapillary; vapor–liquid low boiling, saturated, 431–444 systems correlation of Chen and, 433–434 contact angles in, 41–43 correlation of Gungor and Winterton and, disjoining pressure, 50–52 434–435 Fourier’s law in, 62 correlation of Kandlikar and, 434 Kelvin–Helmholtz instability, 75–80 correlation of Liu and Winterton and, 435 linear stability analysis models for, 125 correlation of Steiner and Taborek and, 435–436 mass transfers, 53–61 dryout in, 442 Rayleigh–Taylor instability, 77, 81–83 heat transfers and, 432–440 surface-active impurities’ effect on, 45 in horizontal channels, low regime dependent, surface tension in, 38–41 440–444 thermocapillary effects in, 46 low boiling, subcooled vapor–liquid interphase, 51–52, 53–61 Bowring’s pumping parameter and, 426 general dynamic equation. See population balance curves in, 411 equation DFM and, 424, 425 geysering, 447 luid-surface parameters and, 431 Gibbs free energy, 39 heat transfer, 430–431 in vapor–liquid systems, 51 hydrodynamics of, 424–429 Gibbs rule, 15

764 Index

GKT. See gaskinetic theory horizontal low gravity waves, 74 in adiabatic pipes, 139–143 CCFL and, 299–300 Hadamard–Rybczynski´ creep low solution, 49 in CHF, 495–497 hanging ilm phenomenon, 303 condensation in, 574–577 heat transfers, 31–36. See also heat transfers, low drainage during, 139 boiling low boiling and, 410 condensation correlations for, 596–608 internal low condensation correlations for, Couette low ilm model and, 32, 33–34 599–608, 627–631 in low boiling, 408, 409–410, 429–431, laminar ilm condensation and, 574–577 432–440 MFB and, 386–388 Fick’s law and, 31, 34 in rectangular channels, 310, 311 Fourier’s law and, 31, 34 saturated low boiling and, 432–440 in internal low condensation, 596–608, 614–631 horizontal surface, ilm boiling, 379–381 for laminar ilms, 127–128 hydrodynamic stability theory, 71 liquid-deicient regimes for, 503 hydrodynamic theory of boiling, 71, 306–354, mass transfer analogy and, 34–35 360. See also pool boiling, hydrodynamic molar lux-based formulation and, 33–34 theory of naphthalene and, 35 hysteresis, 42–43 in nucleate boiling, 370–375, 437 Ranz–Marshall correlation and, 35 impurities, active saturated low boiling and, 432–440 gas-liquid interfacial phenomena and, effect on, in single phase low, 115 44–46 subcooled low boiling and, 413, 430–431 surface tension and, 44–46 heat transfers, low boiling, 410, 411, 429–431, inertial size range, 107 432–444 instantaneous conservation equations, 7–15 binary liquid mixtures, in, 449–453 interfacial area transport equations, 235–236 in helicoidally coiled tubes, 456–459 coalescence and, 238 in minichannels, 531–544 one-group, 237 mechanisms for, in small low passages, 532–536 simpliication of, 236–238 helically coiled low passages, 453–459 two-group, 238–242 helical coil number, 271 interfacial mass transfers. See mass transfers, Helmholtz free energy, 39, 67 interfacial Helmholtz instability, 376 interfacial shear, 573–574 Helmholtz stability theory, 491 condensation and, 569–571 HEM. See homogenous-equilibrium mixture Couette low ilm models and, 573–574 model in internal low condensation, 616 Henry number, 59 internal low condensation, 590–638 Henry’s constant, 59, 696 annular low models for, 603, 614–619 Henry’s law, 59 annular low regimes and, 594, 596, 597, 603, heterogeneous bubble nucleation, 361–366 614–619, 624 active nucleation sites and, 361–366 correlation of Akers for, 599 heterogeneous condensation, 560–561 correlation of Dobson and Chato for, 599–600 HM. See homogeneous mixture models, for correlation of Shah for, 599, 600–602 two-phase mixtures horizontal low correlations for, 599–608 Homogeneous-equilibrium isentropic model, horizontal low regimes for, 592–596 649–651, 668 interfacial shear stress in, 616 homogeneous condensation, 560–561 method of Cavallini for, 604–606 homogeneous mixture (HM) models, for method of Kosky and Staub for, 603–604 two-phase mixtures, 167 method of Moser for, 606–607 control volume forces in, 171 in micro/minichannels, 619–631 HEM, 104, 167, 169 noncondensable effects on, 565, 578–581 pressure drops in, 247–250, 264 pressure drops in, 619–631 homogeneous-equilibrium mixture (HEM) model, semi-analytical models for, 603–608 104, 167, 169 in two-phase low regimes, 591–596 energy conservation equations in, 172–173 vertical low correlations for, 597–599 mass conservation in, 170 wall friction and, 616–617 momentum conservation in, 170–172 interphase balance equations, 163–166 pressure drops in, 247–250 jump conditions in, 165 thermal/mechanical energy equations in, 173 inverted-annular low regimes, 138

Index 765

isolated bubbly low, 512 in separated low models, for two-phase isotropic turbulence, 106 mixtures, 175–177 three-dimensional spectrum in, 107 mass diffusivity, for species, 9 mass lux in, 9 Kapitza number, 122 molar lux in, 9, 14–15 Kelvin–Helmholtz instability, 75–80 transfers for, 9 dispersion equations in, 76 transport properties and, 21 neutral conditions in, 77 mass lux in two-phase low regimes, 229 CHF and, effects on, 477 KfK correlation, 487 for critical low model (Moody), 653 Knudsen numbers 114 Fick’s law for, 14 Knudsen rates, 54 in mass species diffusivity, 9 Kolmogorov’s theory, 106, 107, 108 in momentum conservation equations, 9 Kutateladze number, 291 phasic, 101 two-phase mixtures, 101 laminar ilm condensation, 565–571 mass fractions, 11 on horizontal tubes, 574–577 proiles, 60 Nusselt’s integral analysis on, 566–569 mass transfer, 9, 31–36. See also mass transfers, laminar low interfacial in microchannels/minichannels, 325, 334–335 analogy, heat and, 34–35 Laplace length scales, 77 heat transfers and, 31–36 Laplace–Kelvin relations, 52 interfacial, 53–61 large-break loss of coolant accident (LB-LOCA), naphthalene and, 35 500 Ranz–Marshall correlation and, 35, 36 countercurrent low limitation and, 296 mass transfers, interfacial, 53–61 LB-LOCA. See large-break loss of coolant condensation as, 53–57 accident in Couette low ilm models, 62, 63 Ledinegg instability, 445 evaporation as, 53–57 Lennard-Jones potential model, 24, 50 Henry number in, 59 collision diameter, for diffusion in liquids 26 Henry’s law for, 59 collision integrals for, 699 Knudsen rates in, 54 model constants for, 698 oscillation modes and, 86 linear stability analysis models, 125 Maxwell–Boltzmann distribution, 22 Euler’s equation integration in, 71 metastable states, 5–7 hydrodynamic stability theory, 71 spinodal lines in, 6 for laminar ilms, 125 spontaneous phase change within, 6–7 two-dimensional surface waves in, 45, 71–72 statistical thermodynamic predictions within, 5 liquid diffusion, 25 method of Cavallini, 604–606 Fick’s law and, 25 method of Chisholm, 625 Stokes–Einstein expression and, 26 method of Kosky and Staub, 603–604 liquid ilms. See laminar ilms MFB. See minimum ilm boiling liquid slugs microchannels, 114 adiabatic pipe low for, 137 bubble ebullition in, 509 liquid-deicient ilm boiling regimes, 500 choking in, 667–672 liquid-deicient heat transfer regimes, 503 conventional channels v., differences between, LOCA. See loss of coolant accident 116–117 local instantaneous equations, 163–166 low boiling in, 509–511, 559 Lockhart–Martinelli method, 250–251 internal low condensation in, 619–631 Martinelli parameter in, 250, 251 laminar low in, 325 loop seal effect, 151 single-phase low regimes in, 115–117, 325 loss of coolant accident (LOCA), 388 surface wettability in, 311, 317 thin annuli, 323–324 Marangoni effect, 44 two-phase low regimes in, 316–319 thermocapillary effects and, 46 minichannels, 114 Marangoni number, 46 air–water low regimes in, 316–319 Martinelli parameter, 250, 251 bubble ebullition in, 509 Martinelli–Nelson method, 255 bubble train regimes in, 335–346 mass conservation equations, 9 bubbly low in, 307 control volumes for, 170, 175 Chisholm method for, 328 in HEM model, 170 choking in, 667–672

766 Index

minichannels (cont.) naphthalene churn low, 307 heat/mass transfers and, 35 DFM and, 314 Navier–Stokes equations low boiling heat transfers in, 509–544 for two-phase mixtures, 162 low boiling in, 509–511, 559 near-azeotropic mixtures, 17 frothy slug-annular low in, 308 net vapor generation (NVG), 413 geometry of, as factor for, 325 noncondensable presences, 565, 578–581 with hard inlet conditions, low regimes for, Couette low ilm models and, 53–57 526–528 internal low condensation and, effects on, homogeneous low models in, 327–328 608–609, 619 ideal annular low in, 334–335 nonlinear chaos dynamics, 369 internal low condensation in, 619–631 nucleate boiling, 361–366, 370–375. See also isolated bubble low in, 512 bubble ebullition; departure from nucleate laminar low in, 325, 335 boiling; onset of nucleation boiling point parallel channel instability in, 524–525 inary liquid mixtures, and, 392–396 pressure drop oscillations in, 522–524 bubble ebullition and, 366–369 pressure drops in, 324–331, 342–343 correlation of Cooper and, 373 pseudo-slug low in, 307 correlation of Forster and Zuber and, 372 schematics for, 510, 511, 523 correlation of Gorenlo and, 373–374 slug low in, 307, 335 correlation of Rohsenow and, 370–372 Taylor low regimes in, 335–346 correlations of Stephan and Abdelsalam and, two-phase low regimes in, 307–314 372–373 vapor backlow in, 549 gravity and, 360 void fractions in, 314–316 heat transfer mechanisms in, 369–375 wavy-annular low in, 308 nonlinear chaos dynamics and, 369 minimum ilm boiling (MFB), 359, 386–388, 502 ONB and, 357, 413–418 on horizontal surfaces, 386–388 surface roughness and, 359 TMFB correlations and, 386–388 nucleation sites, active, 366 mixture energy conservation equations, heterogeneous bubble nucleation and, 366 homogeneous two-component, 175 Nukiyama’s experiment, 357 mixture mass conservation equations, Numerical Recipes, 195 homogeneous two-component, 175 Nusselt’s integral analysis, 566–569 mixture momentum conservation equations, improvements to, 569–571 homogeneous two-component, 175 on laminar condensation, 574–577 mixtures. See azeotropic mixtures; binary NVG. See net vapor generation mixtures; near-azeotropic mixtures; single-phase multi-component mixtures; OC-OTEC. See open-cycle ocean thermal energy vapor-noncondensable gas mixtures; conversion zeotropic mixtures ODEs. See ordinary differential equations modiied Bromley correlation. See correlation of OFI. See onset of low instability Bromley, modiied ONB. See onset of nucleation boiling point molar concentrations, 11 onset of low instability (OFI), 446 molar lux, 14–15 OSV and, 528 heat transfers and, 33–34 onset of nucleate boiling point (ONB), 404, mole fractions, 11 408 molecular effusion, 23 correlation of Marsh and Mudawar and, 417 momentum conservation equations, 9 low boiling and, 404, 408, 526–531 in HEM models, 170–172 hard inlet conditions and, 526–528 mass lux in, 9 models for, 413–418 in separated low models, for two-phase in parallel channels, 528–531 mixtures, 175–184 pool boiling and, 357 in transport equations, 10 low boiling and, 413–418 momentum density, 264 tangency in, 414 Morton numbers, 84 onset of signiicant void (OSV), 413 multi-luid models, for two-phase mixtures, 167. empirical correlations for, 419–423 See also two-luid model low boiling and, 526–531 low ield in, 167 hard inlet conditions and, 526–528 2FM, 167 models for, 419–422 multiphase low conservation equations, OFI and, 528 simpliied, 166 Small passages, and 526–531

Index 767

subcooled low boiling and, 424 Nukiyama’s experiment and, 357 two-phase low instability and, 447 ONB and, 357, 413–418 onset of signiicant void (OSV), models for, surface wettability and, 359 419–422 table look-up method for, 503–504 model of Levy, 420–421 transition regimes and, 359, 388–389, 423–424 model of Rogers, 421–422 vapor structures in, 370 Open-cycle ocean thermal energy conversion pool boiling, hydrodynamic theory of, 376–379 (OC-OTEC), 641 CHF and, 376–379 ordinary differential equations (ODEs), 189–195 Helmholtz instability and, 376 Euler equations and, 195 Taylor instability, MFB and, 387 numerical solutions of, 189–195 population balance equation (PBE), 111–112 Runge–Kutta method and, 195 simpliied forms of, 111 state variables for, 189 Prandtl number, 28 stiffness in, 195 pressure drop-low rate oscillations, 447 ordinary diffusion, 9 in helically coiled low passages, 270–277 oscillation modes in minichannels, 522–525 of bubbles, 84–87 pressure drops, in intermittent-low regimes, CHF and, 548 331–334 density-wave, 447 pressure drops, in single-phase low regimes, interfacial transfer processes and, 84 258 pressure drop-low rate, 447 from low disturbances, 258–263 schematics for, 85 loss coeficients in, 263 OSV. See onset of signiicant void reversible, 259 sudden contractions and, 261–263, 265–266 P–v–T surfaces, 4 sudden expansions and, 260–261, 263–265 P–T phase diagrams, 5 pressure drops, in two-phase low, 246–258, partial density, for species, 12 262–269, 274–284 PBE. See population balance equation acceleration in, 246 perforated plates, 293–296 bend conigurations in, 264 phase diagrams, 3–5. See also vapor-liquid systems empirical methods for, 250–256 azeotropic mixtures in, 17 form, 246 for binary mixtures, 15–17 in HEM models, 247–250 for binary systems, 15–17 in HM models, 247–250, 281 Gibbs rule in, 15 in internal low condensation, 625–627 for P–v–T surfaces, 4 local, 257, 262–269 for pure substances, 3–5 Lockhart–Martinelli method for, 250–251 for T–v,5 Martinelli–Nelson method for, 255 for zeotropic mixtures, 15–17 in minichannels, 324–331, 342–343, 347–348 phase volume fractions, 97–99 momentum density in, 264 void fractions and, 98 one-dimensional system schematics for, physical constants. See constants, physical 247 plug low in oriices, 266 CHF in, 475 in spacer grids in rod bundles, 266 Plug-elongated bubbles low regimes, 139 sudden contraction and, 265–266, 347–348 polyethylene channels, 311 sudden expansion and, 263–265, 347–348 polyurethane channels, 311 two-phase multipliers and, 247–250, 262, pool boiling, 357–403. See also ilm boiling; 326 minimum ilm boiling; nucleate boiling; pressurized water reactors (PWRs), 210 onset of nucleation boiling point; pool CCFL and, 293 boiling, hydrodynamic theory of CHF and, 485 binary liquid mixtures, and, 389–400 core schematic for, 298 CHF and, 376–379 low regimes, and, 145 curve for, 357–361, 390 pseudo-slug low, 307 ilm boiling and, 379–386 PWRs. See pressurized water reactors in fully developed boiling region, 358 heterogeneous bubble nucleation and, 361–366 quality proile it, 425, 492 hydrodynamic theory of, 376–379 liquid subcooling and, 306–354, 360 Ranz–Marshall correlation MFB and, 359, 386–388 heat/mass transfers and, 35, 36 nucleate boiling and, 359–361, 369–375 Rayleigh equations, 88–89

768 Index

Rayleigh–Taylor instability, 77 phase diagrams for, 3–5 axisymmetric disturbances in, 78–80 single-phase multicomponent mixtures in, 10–15 capillary waves in, 74 size classiication for, 114 dispersion equations in, 76 sound velocity in, 647–674 Laplace length scales in, 77 temperature proiles in, 28–29 neutral conditions in, 77 transport equations with, 7–15 in two-phase mixtures, 119 transport properties for, 21–26 unstable wavelengths and, 80 turbulent boundary layer velocity and, 27–30 for viscous liquids, 80 single-phase multicomponent mixtures, 10 rectangular channels. See channels, rectangular Dalton’s law in, 12 relux phenomenon, 285 partial density in, for species, 11 RELAP5–3D code, 147–149 relative humidity deinitions in, 12 relative humidity, 12, 561 slip ratios, 103, 201 deinitions for, 12 slip velocity, 101, 201 relaxation instability, 447 slug low,. See also slug low regimes RETRAN codes, 656–658 adiabatic pipe low and, 137 critical low model (Henry/Fauski) and, 657–658 CHF in, 475 critical low model (Moody) and, 656 frothy-annular, 308 isoenthalpic low models and, 656 unit cells in, 332 RETRAN-03, 656 slug low regimes, 139 RETRAN-3D, 656 small break loss of coolant accident (SB-LOCA), Reynolds numbers, 28, 84 210 in falling ilm hydrodynamics, 124, 131 small low passages. See microchannels; ripples, 77. See capillary waves minichannels rod bundles small-amplitude waves, 125 CHF and, 487–488 Soret effect, 9 in DFM, 210–212 species spacer grids in, 266 chemical mass conservation for, 10 vertical, 145–148 mass diffusivity for, 9, 21 roll waves, 125 mass fraction of, 11 Runge–Kutta method, 195 molar concentration of, 11 mole fraction of, 11 saturated low boiling. See low boiling, saturated noncondensable, 174 saturated steam. See steam, saturated partial density of, 11 saturated water. See water, saturated partial pressure of, 12 SB-LOCA. See small break loss of coolant spinodal lines, 6 accident spontaneous phase change, 6–7 separated low models, for two-phase mixtures, stable ilm boiling regimes, 502 175–184 steam, saturated. See also low boiling, saturated CCFL and, 300–302 thermodynamic properties of, 678 energy conservation equations in, 180–183 transport properties of, 680 energy transfers at interphase, in, 182–183 Stokes–Einstein expression, 25 mass conservation equations in, 175–177 stratiied-smooth low regimes, 139 momentum conservation equations, in, 177–180 stratiied-wavy low regimes, 139 virtual mass force terms in, 177, 180 subcooled low boiling. See low boiling, subcooled simpliied multiphase low conservation equations. subcooled liquid jets, 611–614 See multiphase low conservation surface tension, in gas–liquid interfacial equations, simpliied phenomena, 38–41. See also thermocapillary single phase low, 7–15. See also equilibrium states; active impurities and, 44–46 heat transfers; metastable states; pressure Bénard cellular low in, 46–50 drops, in single-phase low regimes; Gibbs free energy and, 39 single-phase multicomponent mixtures; Helmholtz free energy and, 38, 39 turbulent boundary layer velocity interfacial pressure in, 41 closure relations with, 7–10 Marangoni effect in, 44 continuum regime in, 115 nonuniformity, 43–44 critical discharge rates in, 647–656, 674 for pure liquids, 38–40 equilibrium states of, 3 thermocapillary effects and, 46–50 heat transfers in, 31–36 thermodynamic deinition of, 38–39 metastable states for, 5–7 velocity of interphase, 45 microchannels in, 115–117 Young–Laplace equation in, 40

Index 769

surface wettability species mass diffusivity for, 21 contact angles and, 42 triangular channel, 309 in microchannels, 311, 317 triple point, 3 pool boiling and, 359 turbulence, in eddies, 106–110 breakup and, 113–114 T–v phase diagrams, 5 bubbles in, 109 Taylor low regimes, 335–346 coalescence and, 112–113 rise velocity, and, 345 energy spectrums in, 107 unit cell deinitions in, 340 falling ilms and, 129–131 temperature glides, 16, 17 in equilibrium, 106 “temperature law of the wall”, 28–29 homogenous, 106 thermal radiation inertial, 108 in ilm boiling, 385–386 as isotropic, 106 thermal/mechanical energy equations, 173 in Kolmogorov’s theory, 106 thermocapillary effects, 46–50 particle-eddy collision frequency in, 112 buoyancy forces and, 49 PBE in, 111–112 Hadamard–Rybczynski creep low solution and, stationary, 106 49 in universal equilibrium range, 107 linear stability analysis within, 125 turbulent boundary layer velocity, 27–30 Marangoni effect and, 46 Blasius’s correlation in, 28 thermodynamics bubble nucleation, 27 statistical predictions for, 5 Deissler correlation in, 30 tie lines, 17 Karman’s constant in, 30 Tien–Kutateladze looding correlation, 291 Prandtl number in, 28 time averaging, in two phase mixtures, 97–99 Reynolds number in, 28 double, 98 “temperature law of the wall” and, 28–29 properties in, 99–100 Van Driest model, 30 TMFB correlations, 386–388 turbulent ilm condensation, 571–573 transfer(s). See also heat transfers; mass transfers; two-dimensional surface waves, 72–74 mass transfers, interfacial; transfer relations capillary, 74 in Fick’s law, 31 gravity, 74 in Fourier’s law, 31 two-luid model (2FM), 167 in GKT, 54, 55 conservation equations in, 234 interfacial mass, 61–66 DFM v., 202–203 mass, 31–36 generalized drag forces in, 187–188 molar lux and, 33–34 interfacial transport terms in, 186 naphthalene and, 35 material derivatives for, 188 in separated low models, for two-phase multi-dimensional, 185–188 mixtures, 182–183 subcooled low boiling and, 424–425 in single phase low, 31–36, 115 virtual mass terms in, 187–188 transfer relations, 8 two-phase low instability transition boiling regimes, 359, 388–389, 502 chugging and, 447 LOCA and, 500 dynamic, 447–449 as post CHF regime, 500–501 low boiling and, 444–449 transport equations, 7–15. See also mass diffusivity, low excursions, 445 for species geysering in, 447 chemical species mass conservation in, 10 Ledinegg instability and, 445 Fick’s law in, 8 mal-distribution, 447 Fourier’s law in, 8 OFI and, 446 mass conservation in, 9 OSV and, 447 momentum conservation, 10 relaxation instability and, 447 ordinary diffusion in, 9 static, 445–447 Soret effect in, 9 two-phase mixtures, 96, 135, 159. See also laminar species mass diffusivity in, 9 ilms; turbulence, in eddies; two-phase thermal energy in, 10 mixtures, low regimes for; two-phase transport properties, for single phase low, 21–26. mixtures, modeling for See also gaskinetic theory; liquid diffusion CFD codes for, 162 gaskinetic theory GKT and, 21–25 conservation equations for, 162 liquid diffusion and, 25 deinitions in, 101–104 mixture rules within, 21 density in, 102

770 Index

two-phase mixtures (cont.) model; separated low models, for ield schematic for, 97, 98 two-phase mixtures low area-averaging in, 100–101 for diffusion models, 167 low quality in, 103 Fick’s law in, 164 fundamental void–quality relations in, 103 low area averaging for, 167–169 HEM in, 104 gas–liquid interphase schematic in, 164 Knudsen numbers in, 114 for homogenous mixtures, 167 laminar ilm hydrodynamics in, 123–126 interphase balance equations in, 163–166 mass lux in, 103 local instantaneous equations in, 163–166 modeling for, 162–198 for multi-luid models, 167 Navier–Stokes equations for, 162 with separated low, 175–184 particle dispersion in, 111–114 two-phase multipliers, 247–250, 262, 326 phase volume fractions in, 97–99 Rayleigh–Taylor instability in, 119 unit conversions, 701–703 in situ properties for, 102 universal equilibrium range, 107 size classiication for, 118–121 dissipation range within, 107 slip ratio in, 103 inertial size range within, 107 slip velocity in, 101 small low passage in, 120 Van Driest eddy diffusivity model, 30 time averaging in, 97–100 vapor(s). See also fog turbulence in, 106–110 backlow for, in minichannels, 549 two-phase mixtures, low regimes for, 135, 159, of laminar ilm condensation, 574–577 221–242. See also adiabatic pipe low; thermodynamic properties of, for selected annular-dispersed low regimes; choking; refrigerants, 681–689 minichannels; pressure drops, in vapor–liquid systems single-phase low regimes; pressure drops, binary systems, of, 15–17 in two-phase low regimes bubble point lines in, 16 in adiabatic pipe low, 136–143 disturbed interphases in, 72 annular-dispersed, 137 dew point lines in, 16 annular-mist 137 as gas-liquid interfacial phenomena, 5–7 bends, and, 150–153 Gibbs free energy in, 51, 52 choking in, 644–646 Laplace-Kelvin relations and, 52 curved low passages, and, 149–157 mass fraction proiles in, 60 DFM and, 225–227 temperature glides in, 16, 17 dispersed-droplet, 138 tie lines in, 17 dynamic models for, 234–242 vapor-partial pressure in, 52 empirical maps, comments on, 158–159 Young–Laplace equations and, 51 inely dispersed bubbly low, 138, 139, 223–224 vapor–noncondensable gas mixtures, 17–21 helicoidally coiled tubes, and, 154–157 Clapeyron’s relations in, 5 in inclined tubes, 232–234 velocity interfacial area transport equations in, 234–242 choking and, in single-phase luids, internal low condensation in, 591–596 645–646 inverted-annular, 138 in interfacial mass transfers, 54 Kelvin–Helmholtz instability in, 229 surface tension and, as factor in, 44, 45 maps of, pipe low, 143–144 supericial in one-dimensional two-phase in microchannels, 314–316 mixtures, 102 in minichannels, 307–314 vertical low plug-elongated bubbles, 139, 141 in adiabatic pipes, 136–143 pressure drops in, 246–258, 262–269, CCFL and, 285–290, 301 274–284 correlations for, 290–293 in rectangular channels, 310, 311 ilm boiling and, 382–384 RELAP5–3D code schematics, 147–149 internal low condensation and, correlations for, slug low, 137, 139 597–599 in small low passages, 306–354, 360 in rectangular channels, 320–322 stratiied-smooth low, 139 vertical rod bundles, 145–149 stratiied-wavy low, 139 vertical surface, ilm boiling, 379–381 in vertical rod bundles, 145–149 void fractions, 98 void fractions in minichannels and, 314–316 minichannels, in, 314–316 two-phase mixtures, modeling for, 162–198. See microchannels, in, 316–319 also homogenous-equilibrium mixture void-quality correlations, 213–218

Index 771

Armand’s low parameter in, 213 Eötvös numbers and, 84 CISE correlation in, 213, 314 Morton numbers and, 84 von Kármán’s constant, 30 Reynolds numbers and, 84 wavy-annular low, 308 wall friction, annular low, 616–617 wavy-laminar condensation, 571–573 water, saturated. See also low boiling, saturated diffusion coeficients for, at ininite dilution, 697 Young–Dupreé equations, 42 thermodynamic properties of, 678 Young–Laplace equations, 40 transport properties of, 680 vapor–liquid systems and, 51 waves, 83. See also bubbles; capillary waves; gravity waves; roll waves; small-amplitude zeotropic mixtures, 15–17 waves; two-dimensional surface waves phase diagrams for, 16 bubbles and, 84 zero liquid penetration point, 289