Top

Published in:

2017 | OriginalPaper | Chapter

2. Conversion and Transport of Mass, Energy, Momentum, and Materials

Authors : B. Epple, R. Leithner, H. Müller, K. Ponweiser, H. Walter, A. Werner

Published in: Numerical Simulation of Power Plants and Firing Systems

Publisher: Springer Vienna

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Before we go into the mathematical description of the balance equations for the conservation of mass, energy and momentum in more detail, a brief explanation concerning three types of time derivatives is given by way of introduction. A simple example is used, namely, the problem of determining the concentration of fish in a river (Bird et al. 2002). Clear descriptions of balance equations can be found in (Müller 2001), (Bird et al. 2002), (Baehr and Stephan 2008) and in many others.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Introduction

next chapter Numerical Methods

In the case of thin-walled tubes, the average area of the unfinned tube wall \(\overline{A}\) can be replaced by A _in, O for the sake of simplicity.

Friedel based the development of his equation on a database taken from the relevant literature—this gave him 25000 measured values of two-phase flow pressure drops with which to work.

Also referred to as Dufour’s energy flux density. It is based on the exchange of energy between the molecules of the individual components when compensating for differences in concentration—it also occurs in isothermal flows.

One exception is the condensation of metal vapors; due to the high thermal conductivity of the liquid metals, the heat transfer processes for film and drops of condensation differ only slightly (Tanaka 1981).

Flooding is the name given to the procedure that occurs during condensation: the condensate flows from the upper tube to the underlying tube, where it increases the average film thickness.

Akers WW, Deans HA, Crosser OK (1959) Condensation heat transfer within horizontal tubes. Chem Eng Prog Symp Ser 55:171–176

Alad’yev IG, Gorlov LD, Dodonov LD, Fedynskiy OS (1969) Heat Transfer to Boiling Potassium in Uniformly Heated Tubes. Heat Transfer Sov Res 1(4):14–26

Ames WF (1977) Numerical methods for partial differential equations, 2nd edn. Computer Science and Applied Mathematics. Academic Press, San DiegoMATH

Ananiev EP, Boyko LD, Kruzhilin GN (1961) Heat transfer in the presence of steam condensation in a horizontal tube. In: Proceedings of the 1^st Int. Heat Transfer Conf., Part II. Boulder, Colorado, pp 290–295

Auracher H, Drescher G, Hein D, Katsaounis A, Kefer V, Köhler W, Ulrych G (1996) kritische Siedezustände. In: VDI–Wärmeatlas – Berechnungsblätter für den Wärmeübergang, 10^th ed. S. Hbc1–Hbc32 VDI–Verlag GmbH, Düsseldorf

Azzi A, Friedel L, Belaadi S (2000) Two-phase gas/liquid flow pressure loss in bends. Forschung im Ingenieurwesen 65(10):309–318CrossRef

Azzi A, Friedel L, Kibboua R, Shannak B (2003) Reproductive accuracy of two-phase pressure loos correlations for vertical 90^∘ bends. Forschung im Ingenieurwesen 67(3):109–116CrossRef

Azzi A, Alger USTHB, Friedel L (2005) Two-phase upward flow 90^∘ bend pressure loss model. Forschung im Ingenieurwesen 69:120–130CrossRef

Azzopardi BJ, Purvis A, Govan AH (1987) Annular two-phase flow split at an Impacting T. Int J Multiphase Flow 13(5):605–614CrossRef

Baehr HD, Stephan K (1994) Wärme- und Stoffübertragung. Springer, Berlin, Heidelberg, New YorkCrossRef

Baehr HD, Stephan K (1998) Wärme- und Stoffübertragung, 2nd edn. Springer, Berlin, Heidelberg, New YorkCrossRef

Baehr HD, Stephan K (2004) Wärme- und Stoffübertragung, 4th edn. Springer, Berlin, Heidelberg, New YorkCrossRef

Baehr HD, Stephan K (2008) Wärme- und Stoffübertragung, 6th edn. Springer, Berlin, Heidelberg, New York

Baerns M, Hofmann H, Renken A (1987) Chemische Reaktionstechnik. Georg Thieme Verlag, Stuttgart, New York

Bankoff SG (1960) A variable density single-fluid model for two-phase flow with particular reference to steam-water flow. Trans ASME Ser C J Heat Transf 82(11):265–272CrossRef

Baroczy CJ (1966) A systematic correlation for two-phase pressure drop. Chem Eng Prog Symp Ser 62(64):232–249

Barrow GM (1983) Physikalische Chemie, Teil 3: Thermodynamische und kinetische Behandlung chemischer Reaktionen, 6th edn. Bohmann Verlag, Vieweg & Sohn Verlag, Wien Braunschweig

Biasi L, Clerici GC, Sala R, Tozzi A (1968) A theoretical approach to the analysis of an adiabatic two-phase annular dispersed flow. Energia Nucleare 15(6):394–405

Bier K, Goetz D, Gorenflo D (1981) Zum Einfluss des Umfangswinkels auf den Wärmeübergang beim Blasensieden an horizontalen Rohren. Wärme- und Stoffübertragung 15:159–169CrossRef

Bird BR, Stewart WE, Lightfoot EN (1960) Transport phenomena. Wiley, New York

Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena, 2nd edn. Wiley, London, Sydney

Bogdanoff FF (1955) Einfluss des Druckes auf die Wärmeübergangszahl in Siederohren. Brennstoff-Wärme-Kraft 7(3):130

Bouré JA, Delhaye JM (1982) General equations and two-phase flow modeling. In: Hetsroni G (ed) Handbook of multiphase systems, Hemisphere Publishing, Washington, New York, London

Boyko LD, Kruzhilin, GN (1967) Heat transfer and hydraulic resistance during condensation of steam in a horizontal tube and in a bundle of tubes. Int J Heat Mass Transf 10:361–373CrossRef

Brandt F (1995) Wärmeübertragung in Dampferzeugern und Wärmeaustauschern, 2nd edn. Bd. 2 of FDBR – Fachbuchreihe. Vulkan-Verlag, Essen

Brandt F (1999a) Brennstoffe und Verbrennungsrechnung, 3rd edn. Bd. 1 of FDBR – Fachbuchreihe. Vulkan-Verlag, Essen

Brauer H (1971) Stoffaustausch einschließlich chemischer Reaktionen. Verlag Sauerländer AG, Aarau, Schweiz

Breber G, Palen JW, Taborek J (1980) Prediction of horizontal tubeside condensation of pure components using flow regime criteria. J Heat Transf 102:471–476CrossRef

Bromley LA (1952) Effect of heat capacity of condensate. Ind Eng Chem 44:2966CrossRef

Bücker D, Span R, Wagner W (2003) Thermodynamic property models for moist air and combustion gases. Trans ASME J Eng Gas Turbines Power 125(1):374–384CrossRef

Butterworth D, Hewitt GF (1977) Two-phase flow and heat transfer. Harwell Series, Oxford University Press, Oxford

Cavallini A, Zecchin R (1974) A dimensionless correlation for heat transfer in forced convective condensation. In: Proceedings of the 5th Int Heat Transfer Conf, Vol 3, Tokyo, Japan, pp 309–313

Chato JC (1962) Laminar condensation inside horizontal and inclined tubes. ASHRAE J 4:52–60

Cherukat P, McLaughlin JB, Dandy DS (1999) A computational study of the inertial lift on a sphere in a linear shear flow flied. Int J Multiphase Flow 25(1):15–33MATHCrossRef

Chexal B, Merilo M, Maulbetsch J, Horowitz J, Harrison J, Westacott J, Peterson C, Kastner W, Schmidt H (1997) Void fraction technology for design and analysis. Technical Report TR-106326, EPRI

Chhabra RP, Agarwal L, Sinha NK (1999) Drag on non-spherical particles: an evaluation of available methods. Powder Technol 101:288–295CrossRef

Chisholm D (1967) A theoretical basis for the Lockhart-Martinelli correlation for two-phase flow. Int J Heat Mass Transf 10:1767–1778CrossRef

Chisholm D (1973) Pressure gradients due to friction during the flow of evaporating two-phase mixtures in smooth tubes and channels. Int J Heat Mass Transf 16:347–358CrossRef

Chisholm D (1980) Two-phase flow in bends. Int J Multiphase Flow 6(4):363–367CrossRef

Clift R, Grace JR, Weber ME (1978) Bubbles, drops and particles. Academic Press, New York

Collier JG (1972) Convective boiling and condensation. McGraw-Hill Book Company, London

Collier JG, Thome, JR (1994) Convective boiling and condensation, 3rd edn. The Oxford Engineering Science Series. Clarendon Press, Oxford

Crowe CT, Sommerfeld M, Tsuji Y (1998) Fundamentals of gas-particle and gas-droplet flows. CRC Press, Boca Raton, Florida

Dahmen W, Reusken, A (2006) Numerik für Ingenieure und Naturwissenschaftler. Springer, Berlin, HeidelbergMATH

Delhaye JM (1981a) Two-phase flow patterns. In: Delhaye JM, Giot M, Riethmuller ML (eds) Two-phase flow instabilities and propagation phenomena, pp 37–70. McGraw Hill Book, St. Louis, New York

Delhaye JM, Giot M, Riethmuller ML (1981b) Thermohydraulics of two-phase flow systems for industrial design and nuclear engineering. Series in Thermal and Fluids Engineering. Hemisphere Publishing, Washington, New York, London

Dickinson NL, Welch, CP (1958) Heat transfer to supercritical water. Trans ASME 80(3):746–752

Dobson MK (1994) Heat transfer and flow regimes during condensation in horizontal tubes. Dissertation, University of Illinois

Dobson MK, Chato JC (1998) Condensation in smooth horizontal tubes. J Heat Transf 120:193–213CrossRef

Dodemand E, Prud’homme R, Kuentzmann P (1995) Influence of unsteady forces acting on a particle in a suspension application to the sound propagation. Int J Multiphase Flow 21(1): 27–51MATHCrossRef

Domin G (1963) Wärmeübergang in kritischen und überkritischen Bereichen von Wasser in Rohren. BWK 15(11):527–532

Doroshchuk VE, Levitan LL, Lantsman FP (1975) Recommendations for calculating burnout in a round tube with uniform heat release. Teploenergetika 22(12):66–70

Drescher G, Köhler W (1981) Die Ermittlung kritischer Siedezustände im gesamten Dampfgehaltsbereich für innendurchströmte Rohre. Brennstoff-Wärme-Kraft 33(10):416–422

Durst F, Milojevic D, Schönung B (1984) Eulerian and lagrangian predictions of particulate two-phase flows: a numerical study. Appl Math Modell 8:101–115MathSciNetMATHCrossRef

El Hajal J, Thome JR, Cavallini A (2003) Condensation in horizontal tubes, part 1: two-phase flow pattern map. Int J Heat Mass Transf 46:3349–3363MATHCrossRef

Epple B, Schnell, U (1992a) Domain decomposition method for the simulation of fluid flow in coal combustion furnaces. In: Int. conf. of numerical methods in engineering and applied sciences, conception. VDI-Gesellschaft Energietechnik

Epple B (1993) Modellbildung und Simulation von Strömungs-, Reaktions- und NO _x-Bildungsvorgängen in technischen Feuerungen. Progress report VDI 295, VDI Verlag, Düsseldorf

Ertesvag IS (1996) The Eddy-Dissipation turbulence energy cascade model. Trondheim, Norwegen

Fischer KC (1999) Dreidimensionale Simulation der Gas-Feststoff-Strömung in kohlegefeuerten Dampferzeugern. Progress report VDI 415, VDI Verlag, Düsseldorf

Fraß F, Linzer W (1992) Wärmeübergangsprobleme an querangeströmten Rippenrohrbündel. Brennstoff-Wärme-Kraft 44(7/8):333–336

Fraß F, Hofmann R, Ponweiser K (2008) Principles of finned-tube heat exchangers design for enhanced heat transfer. WSEAS Press, Rhodes Island

Friedel L (1978) Druckabfall bei der Strömung von Gas/Dampf-Flüssigkeits-Gemischen in Rohren. Chemie Ingenieur Technik 50(3):167–180CrossRef

Friedel L (1979) Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. European Two Phase Flow Group Meeting. Ispra, Italien, pp 1–25

Fujii T (1982) Condensation of steam and refrigerant vapors. In: The 7th int. heat transfer conference. München, Germany

Fujii T (1995) Enhancement to condensating heat transfer - new developments. J Enhanc Heat Transf 2:127–138CrossRef

Ganapathy V (2003) Industrial boilers and heat recovery steam generators: design, applications, and calculations. Marcel Dekker, New York

Gerlinger P (2005) Numerische Verbrennungssimulation. Springer, Berlin, Heidelberg, New YorkCrossRef

Gibson MM, Launder BE (1978) Ground effects on pressure fluctuations in the atmospheric boundary layer. J Fluid Mech 86:491–511MATHCrossRef

Gnielinski V (1975) Neue Gleichungen für den Wärme- und den Stoffübergang in turbulent durchströmten Rohren und Kanälen. Forschung im Ingenieurwesen 41(1):8–16CrossRef

Gnielinski V (1995) Ein neues Berechnungsverfahren für die Wärmeübertragung im Übergangsbereich zwischen laminarer und turbulenter Rohrströmung. Forschung im Ingenieurwesen 61(9):240–248CrossRef

Gnielinski V (2006) Wärmeübertragung bei der Strömung durch Rohre. In: VDI–Wärmeatlas – Berechnungsblätter für den Wärmeübergang, 10^th ed., Ga1–Ga9. VDI–Verlag GmbH, Düsseldorf

Görner K (1991) Technische Verbrennungssysteme: Grundlagen, Modellbildung, Simulation. Springer, Berlin, Heidelberg, New YorkCrossRef

Gran IR (1994) Mathematical modeling and numerical simulation of chemical kinematics in turbulent combustion. Dissertation, University of Trondheim

Griem H (1995) Untersuchungen zur Thermohydraulik innenberippter Verdampferrohre. Dissertation, Technical University of Munich

Griem H (1996) A new procedure for the prediction of forced convection heat transfer at near- and supercritical pressure. Int J Heat Mass Transf Wärme und Stoffübertragung 31:301–305CrossRef

Grigull U (1942) Wärmeübergang bei der Kondensation mit turbulenter Wasserhaut. Forschung im Ingenieurwesen 13:49–57CrossRef

Haar L, Gallagher JS, Kell GS (1988) NBS/NRC Wasserdampftafeln. Grigull U (Hrsg) Springer, Berlin

Haider A, Levenspiel O (1989) Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technol 58(1):63–70CrossRef

Hall WB, Jackson, JD (1978) Heat transfer near the critical point. In: Proceedings of the 6th Int. heat transfer conference, Vol. 6, 7.–11. August, Toronto, Canada, pp 377–392

Haßdenteufel W (1983) Wärmeübergang und Druckverlust bei Zweiphasenströmung. Dissertation, Technical University of Stuttgart

Hausen H (1959) Neue Gleichungen für die Wärmeübertragung bei freier und erzwungener Strömung. Allgemeine Wärmetechnik 9(4/5):75–79

Hausen H (1976) Wärmeübertragung im Gegenstrom, Gleichstrom und Kreuzstrom, 2nd edn. Springer, Berlin, Heidelberg, New YorkCrossRef

Hayduk W, Minhas BS (1982) Correlations for prediction of molecular diffusivities in liquids. Can J Chem Eng 60:295–299CrossRef

HDEH (1987) Heat exchanger design hand book, Vol. 5: Physical properties. VDI Verlag GmbH, Düsseldorf

HDEH (2002) HEDH heat exchanger design handbook: Heat exchanger theory. VDI Verlag GmbH, Düsseldorf

Hein D, Kastner W, Köhler W (1982) Einfluss der Rohrlage auf den Wärmeübergang in einem Verdampferrohr. Brennstoff-Wärme-Kraft 34(11):489–493

Hetsroni G (1995) Introduction and basics. Short courses on multiphase flow and heat transfer part A: bases. 20.-24. März, ETH Zürich, Schweiz, pp 1–43

Hewitt GF, Roberts, DN (1969) Studies of two-phase flow patterns by simultaneous X-ray and flash photography. Technical Report AERE-M2159

Hirschfelder JO, Curtiss CF, Bird RB (1954) Molecular theory of gases. Wiley, New YorkMATH

Hofmann R, Fraß F, Ponweiser K (2007) Heat transfer and pressure drop performance comparison of finned-tube bundles in forced convection. WSEAS Trans Heat Mass Transf 2(4):72–88

Hofmann R, Fraß F, Ponweiser K (2008) Performance evaluation of solid and serrated finned-tube bundles with different Fin geometries in forced convection. In: Proceedings of the 5^th European thermal-sciences conference. 18.–22. Mai Eindhoven, Holland, pp 1–8

Hofmann R (2009) Experimental and numerical air-side performance evaluation of finned tube heat exchangers. Dissertation, Vienna University of Technology

Hofmann R, Walter H, (2012a) Experimental and numerical investigation of the gas side heat transfer and pressure drop of finned tubes - Part 1: Experimental analysis. Trans ASME J Thermal Sci Eng Appl 4:041007-1–041007-11

Hofmann R, Walter H, (2012b) Experimental and numerical investigation of the gas side heat transfer and pressure drop of finned tubes - Part 2: Numerical analysis. Trans ASME J Thermal Sci Eng Appl 4:041008-1–041008-11

Hufschmidt W, Burck E (1968) Der Einfluss temperaturabhängiger Stoffwerte auf den Wärmeübergang bei turbulenter Strömung von Flüssigkeiten in Rohren bei hohen Wärmestromdichten und Prandtlzahlen. Int J Heat Mass Transf 11(6):1041–1048CrossRef

Huhn J, Wolf J (1975) Zweiphasenströmung gasförmig/flüssig. VEB Fachbuchverlag Leipzig, Leipzig

IAPWS (1997) IAPWS Release: IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam. Technical Report, IAPWS Secretariat

Ishii M (1975) Thermo-fluid dynamic theory of two-phase flow. Scientific and Medical Publication of France, Eyrolles ParisMATH

Ishii M (1977) One dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes. Argonne National Laboratory USAEC Report ANL-7747

Ishii M, Mishima K (1984) Two-fluid model and hydrodynamic constitutive relations. Nucl Eng Des 82:107–126CrossRef

Jakovlev VV (1960) Örtlicher und mittlerer Wärmeübergang bei turbulenter Rohrsrömung nichtsiedenden Wassers und hohen Wärmebelastungen. Kernenergie 3(10/11):1098–1099

Jaster H, Kosky PG (1976) Condensation heat transfer in a mixed flow regime. Int J Heat Mass Transf 19:95–99CrossRef

Jens WH, Lottes PA (1951) Analysis of heat transfer, burnout, pressure drop and density data for high pressure water. Argonne national laboratory USAEC Report ANL-4627

Jischa M (1982) Konvektiver Impuls-, Wärme- und Stoffaustausch. Vieweg Verlag, Wien BraunschweigCrossRef

Johannessen T (1972) A theoretical solution of the Lockhart and Martinelli flow modell for calculating two-phase flow pressure drop and hold-up. Int J Heat Mass Transf 15(8):1443–1449CrossRef

Jones WP, Launder BE, Spalding DB (1972) The prediction of laminarization with a two equation model of turbulence. Int J Heat Mass Transf 15:301–314CrossRef

Kabelac S, Siemer M, Ahrendts J (2006) Thermodynamische Stoffdaten für Biogase. Forschung im Ingenieurwesen 70:46–55CrossRef

Kakaç S, Shah RK, Aung W (1987) Handbook of single-phase convective heat transfer. Wiley, New York

Kakarala ChR, Thomas LC (1974) A theoretical analysis of turbulent convective heat transfer for supercritical fluids. In: Proceedings of the 5th int. heat transfer conference, Vol 2, 3.–7. September Tokyo, Japan, pp 45–49

Kast W (1996) Druckverlust bei der Strömung durch Rohre. In: VDI–Wärmeatlas – Berechnungsblätter für den Wärmeübergang, 8th ed., Lb1–Lb7. VDI–Verlag GmbH, Düsseldorf

Katto Y (1979) Generalized correlations of critical heat flux for the forced convection boiling in vertical uniformly heated annuli. Int J Heat Mass Transf 22:575–584CrossRef

Katto Y (1980a) Critical heat flux of forced convection boiling in uniformly heated vertical tubes (correlation of CHF in HP-regime and determination of CHF-regime map). Int J Heat Mass Transf 23:1573–1580CrossRef

Katto Y (1980b) General features of CHF of forced convection boiling in uniformly heated vertical tubes with zero inlet subcooling. Int J Heat Mass Transf 23:493–504CrossRef

Katto Y (1981) General features of CHF of forced convection boiling in uniformly heated rectangular channels. Int J Heat Mass Transf 24(8):1413–1419CrossRef

Katto Y (1982) An analytical investigation on CHF of flow boiling in uniformly heated vertical tubes with special reference to governing dimensionless groups. Int J Heat Mass Transf 25(9):1353–1361CrossRef

Katto Y, Ohno H (1984) An improved version of the generalized correlation of critical heat flux for the forced convective boiling in uniformly heated vertical tubes. Int J Heat Mass Transf 27(9):1641–1648CrossRef

Kefer V (1989a) Strömungsformen und Wärmeübergang in Verdampferrohren unterschiedlicher Neigung. Dissertation, Technical University of Munich

Kefer V, Köhler W, Kastner W (1989b) Critical heat flux (CHF) and Post-CHF heat transfer in horizontal and inclined evaporator tubes. Int J Multiphase Flow 15(3):385–392CrossRef

Kern DQ (1958) Mathematical development of loading in horizontal condensers. AIChE J 4(2):157–160CrossRef

Keyes FG, Keenan JH, Hill PG, Moore JG (1968) In: A fundamental equation for liquid and vapor water. Report at the 7th Int. conference on the properties of steam. Tokyo

Kim NH, Youn B, Webb RL (1999) Air-side heat transfer and friction correlations for plain fin-and-tube heat exchangers with staggered tube arrangements. Trans ASME J Heat Transf 121:662–667CrossRef

Kleinstreuer C (2003) Two-phase flow: theory and applications. Taylor & Francis, New York, LondonMATH

Kocamustafaogullari G (1971) Thermo-fluid dynamics of separated two-phase flow. Dissertation, School of Mechanical Engineering, Georgia Institute of Technology, Atlanta

Köhler W (1984) Einfluss des Benetzungszustandes der Heizfläche auf Wärmeübergang und Druckverlust in einem Verdampferrohr. Dissertation, Technical University of Munich

Kolev NI (1986) Transiente Zweiphasenströmung. Springer, Berlin, Heidelberg, New YorkCrossRef

Konakov PK (1954) Eine neue Formel für den Reibungskoeffizienten glatter Rohre (Orig. russ.). Rep Acad Sci UDSSR 51(7):503–506

Kon’kov AS (1965) Experimental study of the conditions under which heat exchange deteriorates when a steam-water mixture flows in heated tubes. Teploenergetika 13(12):77

Krischer S, Grigull U (1971) Mikroskpische Untersuchung der Tropfenkondensation. Wärme- und Stoffübertragung 4:48–59CrossRef

Kühlert K (1998) Modellbildung und Berechnung der Wärmestrahlung in Gas- und Kohlenstaubfeuerungen. Peorts from the power engineering. Shaker Verlag, Aachen

Lahey Jr. RT (2005) The simulation of multidimensional multiphase flows. Nucl Eng Des 235:1043–1060CrossRef

Launder BE (1991) Current capabilities for modelling turbulence in industrial flows. Appl Sci Res 48:247–269MATHCrossRef

Launder BE, Spalding DB (1974) The numerical computation of turbulent flows. Comput Methods Appl Mech Eng 3:269–289MATHCrossRef

Lee RA, Haller, KH (1974) Supercritical water heat transfer developments and applications. In: Proceedings of the 5th int. heat transfer conference, Vol 4. Tokyo, Japan, pp 335–339

Leithner R (1984) Vorlesung Wärme- und Stoffübertragung. Technical University of Braunschweig

Lendt B (1991) Numerische Berechnung der Stickoxidkonzentration in Kohlenstaubflammen - Ein Vergleich unterschiedlicher Reaktionsmodelle. Progress report VDI 254, VDI Verlag, Düsseldorf

Leschziner MA (1989) Modeling turbulent recirculating flows by finite-volume methods - current status and future directions. Int J Heat Fluid Flow 10(3):186–202CrossRef

Levy S (1966) Prediction of two-phase annular flow with liquid entrainment. Int J Heat Mass Transf 9:171–188CrossRef

Levy S (1999) Two-phase flow in complex systems. Wiley, New York, Chichester, Weinheim

Lockhart RW, Martinelli RC (1949) Proposed correlation of data for isothermal two-phase, two component flow in pipes. Chem Eng Progress 45(1):39–48

Lombardi E, Pedrocchi E (1972) A pressure drop correlation in two-phase flow. Energia Nucleare 19(2):91–99

Lun CKK, Liu HS (1997) Numerical simulation of dilute turbulent gas-solid flows in horizontal channels. Int J Multiphase Flow 23(3):575–605MATHCrossRef

Magel HC (1997) Simulation chemischer Reaktionskinetik in turbulenten Flammen mit detaillierten und globalen Mechanismen. Progress report VDI 377, VDI Verlag, Düsseldorf

Magnussen BF (1989) The eddy dissipation concept. In: Proceedings of 11th task leaders meeting, IEA working party on energy conservation in combustion. O”renäs, Glumslöv, Sweden, pp 248–268

Martin H (1988) Wärmeübertrager. Thieme-Verlag, Stuttgart, New York

Martinelli RC, Nelson DB, Schenectady NY (1948) Prediction of pressure drops during forced circulation boiling of water. Trans ASME 70(8):695–702

Marto PJ (1998) Condensation. In: Rohsenow WM, Hartnett JP, Cho YI (eds) Handbook of heat transfer, 3rd edn. McGraw Hill, New York, San Francisco, Washington, pp 14.1–14.63

Mayinger F (1982) Strömung und Wärmeübergang in Gas-Flüssigkeits-Gemischen. Springer, Vienna, New YorkCrossRef

McAdams WH, Kennel WE, Addoms JN (1950) Heat transfer of superheated steam at high pressures. Trans Am Soc Mech Eng 72:421–428

McBride BJ, Heimel S, Ehlers JG, Gordon G (1963) Thermodynamic properties to 6000 K for 210 substances involving the first 18 elements. Technical Report NASA SP-3001, N63-23715, Office of Scientific and Technical Information, National Aeronautics and Space Administration, Washington, D.C.

Mei R (1992) An approximate expression for the shear lift force on a spherical particle at finite reynolds number. Int J Multiphase Flow 18:145–147MATHCrossRef

Menter FR (2002) Methoden, Möglichkeiten, Grenzen numerischer Strömungsberechnungen. Kurzlehrgang NUMET 2002: Numerische Methoden zur Berechnung von Strömungs- und Wärmeübertragungsproblemen. Erlangen, Germany

Michejew MA (1961) Grundlagen der Wärmeübertragung, 2nd edn. VEB Verlag Technik, Berlin

Modest MF (1993) Radiative heat transfer. McGraw-Hill Verlag, New York

Müller H (1992) Numerische Berechnung dreidimensionaler turbulenter Strömungen in Dampferzeugern mit Wärmeübergang und chemischen Reaktionen am Beispiel des SNCR-Verfahrens und der Kohleverbrennung. Progress report VDI 268, VDI Verlag, Düsseldorf

Müller H, Heitmüller RJ (1997) Untersuchung der Brennkammerverschmutzung mit einem mathematischen Modell. VGB Fachtagung “Feuerungen 1997”. Essen, Germany

Müller I (2001) Grundzüge der Thermodynamik: mit historischen Anmerkungen, 3rd edn. Springer, BerlinCrossRef

Muschelknautz S, Wellenhofer A (2006) Druckverlust von Gas- Flüssigkeitsströmungen in Rohren, Leitungselementen und Armaturen: In VDI-Wärmeatlas – Berechnungsblätter für den Wärmeübergang, 10^th ed., Lbb1–Lbb15. VDI–Verlag GmbH., Düsseldorf

Nafe J, Schmidt D, Maas U (2002) Reduzierte kinetische Modelle für die Beschreibung turbulenter Verbrennungsprozesse. VDI-GET Fachtagung “Modellierung und Simulation von Dampferzeugern und Feuerungen” 5.–6. März. VDI-Report Nr. 1664, Braunschweig, Germany

Nakanishi K (1978) Predictions of diffusion coefficient of nonelectrolytes in dilute solution based on generalized Hammond-Stokes plot. Ind Eng Chem Fundam 17(4):253CrossRef

Nallasamy M (1987) Turbulence models and their aplications to the prediction of internal flows. Comput Fluids 15(2):151–194MATHCrossRef

Nau M, Wölfert W, Maas U, Warnatz J (1995) A reduction scheme for chemical kinetics based on manifold anaysis in conjunction with pdf modelling, Vol 2, S 19.25–19.30

Nusselt W (1915) Das Grundgesetz des Wärmeübergangs. Der Gesundheits-Ingenieur 38(42):477–482

Nusselt W (1916) Die Oberflächenkondensation des Wasserdampfes. VDI-Zeitschrift 60:541–546 und 569–575

Odar F, Hamilton WS (1964) Forces on a sphere accelerating in a viscous fluid. J Fluid Mech 18:302–314MATHCrossRef

Perry RH (1984) Perry’s chemical engineers’ handbook, 6th edn. McGraw Hill Book Company, St. Louis, New York

Petukhov BS, Polyskov AF, Kuleshov VA, Sheckter YuL (1974) Turbulent flow and heat transfer in horizontal tubes with substantial influence of thermogravitational forces. In: 4th int. heat transfer conference, Vol 3. Tokyo, Japan, pp 164–168

Polifke W, Kopitz J (2005) Wärmeübertragung. Pearson Verlag, München

Poling BE, Prausnitz JM, O’Connell JP (2001) The properties of gases and liquids. 5th edn. McGraw Hill Book Companies, Boston, New York

Pollak R (1975) Eine neue Fundamentalgleichung zur konsistenten Darstellung der thermodynamischen Eigenschaften von Wasser. Brennstoff-Wärme-Kraft 27(5):210–215

Ponweiser K, Walter H (1993) Erweiterung der NBS/NRC Wasserdampftafeln um die Umkehrfunktionen und deren Ableitungen. Progress report VDI 291, VDI Verlag, Düsseldorf

Ponweiser K, Walter H (1994) Die thermodynamischen Zustandsgrößen von Wasser und Wasserdampf und deren partielle Ableitungen in unterschiedlichen Darstellungsformen. Brennstoff-Wärme-Kraft 46(1/2):53–55

Pope SB (1975) A more general effective-viscosity hypothesis. J Fluid Mech 72(2):331–340MATHCrossRef

Pope SB (1990a) Computations of turbulent combustion. In: Progress and challenges, 23th (int.) on combustion, The Combustion Institute, Pittsburgh, S 591–611

Pope SB (1990b) PDF methods for turbulent reactive flows. Prog Energy Combust Sci 11:119–192CrossRef

Prandtl L, Oswatitsch K, Wieghardt K (1990) Führer durch die Strömungslehre, 9th edn. Vieweg & Sohn Verlagsges. m. b. H., Braunschweig/WiesbadenMATHCrossRef

Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in FORTRAN, 2th edn. Cambridge University Press, New YorkMATH

Rahman MM, Fathi AM, Soliman HM (1985) Flow pattern boundaries during condensation: new experimental data. Can J Chem Eng 63:547–552CrossRef

Reid DR, Taborek J (1994) Selection criteria for plain and segmented finned tubes for heat recovery systems. Trans ASME J Eng Gas Turbines Power 116(2):406–410CrossRef

Reimann M, Meyer-Pittroff R, Grigull U (1970) Berechnung von Zustandsgrößen aus thermodynamisch konsistenten Zustandsgleichungen und Vergleich der Ergebnisse verschiedener Gleichungssysteme für Wasser und Wasserdampf. Brennstoff-Wärme-Kraft 22(8):373–378

Richter H (1962) Rohrhydraulik, 4th edn. Springer, Berlin, HeidelbergMATHCrossRef

Richter F (1983) Physikalische Eigenschaften von Stählen und ihre Temperaturabhängigkeit. MANNESMANN Researchreport 10, Verlag Stahleisen m. b. H., Düsseldorf

Rifert VG, Smirnov HF (2004) Condensation heat transfer enhancement. In: Sunden B (ed). WIT Press, Southampton, Boston

Ro S (1992) Numerische Berechnung der NO_x-Bildung in Kohlenstaubflammen – Einfluss des Dralls und des Brennstoffstickstoffgehaltes. Progress report VDI 271, VDI Verlag, Düsseldorf

Rohsenow WM, Webber JH, Ling AT (1956) Effect of vapor velocity on laminar and turbulent film condensation. Trans ASME 78:1637–1643

Rosner N (1986) Thermische Zustandsgleichung für Wasser im Bereich vom Tripelpunkt bis 10000 bar erstellt durch multiple Regressionsanalyse. Dissertation, Technical University of Munich

Saffman PG (1965) The lift on a small sphere in a slow shear flow. J Fluid Mech 22:385–400MATHCrossRef

Saffman PG (1968) Corrigendum to “The Lift on a Small Sphere in a Slow Shear Flow”. J Fluid Mech 31:624CrossRef

Schiebener P (1989) Schnelle Berechnungsverfahren für Zustandseigenschaften am Beispiel Wasser. Dissertation, Technical University of Munich

Schiller L, Naumann A (1933) Über die grundlegende Berechnung bei der Schwerkraftaufbereitung. Zeitschrift Verein Deutscher Ingenieure 44:318–320

Schiller A (1999) Optimierung der Simulation von Kohlenstaubfeuerungen. Progress report VDI 416, VDI Verlag, Düsseldorf

Schlichting H (1965) Grenzschicht-Theorie, 5th edn. G. Braun Verlag, KarlsruheMATH

Schmidt ThE (1963a) Der Wärmeübergang an Rippenrohren und die Berechnung von Rohrbündel-Wärmetauschern. Kältetechnik 15(4):98–102

Schmidt ThE (1963b) Der Wärmeübergang an Rippenrohren und die Berechnung von Rohrbündel-Wärmetauschern. Kältetechnik 15(12):370–378

Schmidt E (1967b) International vereinbarte Gleichungen für die Eigenschaften von Wasser und Wasserdampf zum Gebrauch der Industrie in Rechenanlagen. Brennstoff-Wärme-Kraft 19(2):69–70

Schmidt J, Friedel L (1997) Two-phase pressure drop across sudden contractions in duct areas. Int J Multiphase Flow 23(2):283–299MATHCrossRef

Schnell U (1990) Berechnung der Stickoxidemission von Kohlestaubfeuerungen. Progress report VDI 250, VDI Verlag, Düsseldorf

Schulz A (1994) Numerische Simulation einer hochbeladenen Gas-Feststoffströmung am Beispiel einer zirkulierenden atmospherischen Wirbelschicht. Dissertation, Technical University of Braunschweig

Shah MM (1979a) A generalized correlation for heat transfer during film condensation inside of pipes. Int J Heat Mass Transf 22:547–556CrossRef

Shah MM (1979b) A generalized graphical method for predicting CHF in uniformly heated vertical tubes. Int J Heat Mass Transf 22:557–568CrossRef

Shah MM (1980) A general correlation for critical heat flux in annuli. Int J Heat Mass Transf 23:225–234CrossRef

Shah RK, Sekulić DP (1998) Heat exchangers. In: Rohsenow WM, Hartnett JP Cho YI (eds) Handbook of heat transfer, 3rd edn. McGraw Hill Book Company, New York, San Francisco, Washington pp 17.1–17.169

Shah RK, Sekulić DP (2003) Fundamentals of heat exchanger design. Wiley Verlag, HobokenCrossRef

Siegel R, Howell JR, Lohrengel J (1991a) Wärmeübertragung durch Strahlung, Vol 2, Strahlungsaustausch zwischen Oberflächen und in Umhüllungen der Wärme und Stoffübertragung. Springer, Berlin, Heidelberg, New York

Siegel R, Howell JR, Lohrengel J (1991b) Wärmeübertragung durch Strahlung, Vol 3, Strahlungsübergang in absorbierenden, emitierenden und streuenden Medien der Wärme und Stoffübertragung. Springer, Berlin, Heidelberg, New York

Siegel R, Howell, JR (1992) Thermal radiation heat transfer, 3rd edn. Hemisphere Publishing Corp., Washington, Philadelphia, London

Sloan DG, Smith PJ, Smoot LD (1986) Modeling of swirl in turbulent flow systems. Prog Energy Combust Sci 12:163–250CrossRef

Smoot LD, Pratt, DT (1979) Pulverized-coal combustion and gasification. Plenum Press, New YorkCrossRef

Soliman M, Shuster JR, Berenson PJ (1968) A general heat transfer correlation for annular flow condensation. Trans ASME C J Heat Transf 90(2):267–276CrossRef

Sommerfeld M (1993a) Review on numerical modelling of dispersed two-phase flows. In: Proceedings of the 5th int. symposium on refined flow modelling and turbulence measurements. Paris, France

Sommerfeld M, Kohnen G, Rüger M (1993b) Some open questions and inconsistencies of lagrangian particle dispersion models. In: Proceedings of the 9th symposium on turbulent shear flows. Kyoto, Japan

Sommerfeld M, Huber N (1999) Experimental analysis and modelling of particle-wall collisions. Int J Multiphase Flow 25:1457–1489MATHCrossRef

Sommerfeld M (2006) Bewegung fester Partikel in Gasen und Flüssigkeiten. In: VDI–Wärmeatlas – Berechnungsblätter für den Wärmeübergang, 10th edn., Lca1–Lca9. VDI–Verlag GmbH, Düsseldorf

Sonar T (2009) Turbulenzen um die Fluidmechanik. Spektrum der Wissenschaften (4):78–87

Soo SL (1990) Multiphase fluid dynamics. Science Press, Beijing

Stasiulevičius J, Skrinska A (1988) Heat transfer of finned tube bundles in crossflow. Hemisphere Publ. Corp., Washington, New York, London

Stephan K (1988) Wärmeübergang beim Kondensieren und beim Sieden. Springer, Berlin, Heidelberg, New York, LondonCrossRef

Stiefel E (1970) Einführung in die numerische Mathematik. B. G. Teubner Verlag, StuttgartMATH

Stokes GG (1851) On the effect of the internal frictions of fluids on the motion of pendulums. Trans Cambr Phil Soc 9:8–106

Strelets M (2000) Detached eddy simulation of massively separated flows. AIAA-00-2306

Styrikowitsch MA, Miropolsky SL, Schitzman ME (1959) Wärmeübergang im kritischen Druckgebiet bei erzwungener Strömung des Arbeitsmediums. VGB Kraftwerkstechnik 61:288–294

Swenson HS, Carver JR, Kakarala CR (1965) Heat transfer to supercritical water in Smooth-Bore tubes. Trans ASME, Ser C J Heat Transf 87:477–484CrossRef

Taitel Y, Dukler AE (1976) A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow. AIChE J 22(1):47–55CrossRef

Tanaka H (1981) Effect of knudsen number on dropwise condensation. Trans ASME Ser A J Heat Transf 103(3):606–607CrossRef

Tandon TN, Varma HK, Gupta CP (1982) A new flow regime map for condensation inside horizontal tubes. J Heat Transf 104:763–768CrossRef

Techo R, Tickner RR, James RE (1965) An accurate equation for the computation of the friction factor for smooth pipes from the Reynolds number. J Appl Mech 32(2):443CrossRef

Teichel H (1978) Druckabfall, Dampfgehalt und turbulenter Queraustausch in Wasser- und Wasserdampfströmungen. Brennstoff-Wärme-Kraft 30(8):334–340

Thom JRS (1964) Prediction of pressure drop during forced circulation boiling of water. Int J Heat Mass Transf 7:709–724CrossRef

Thom JRS, Walker WM, Fallon TA, Reising GFS (1965) Boiling in subcooled water during flow up heated tubes or annuli. Symp. Inst. Mech. Eng., London

Thomas PJ (1992) On the influence of the Bassest history force on the motion of a particle through a fluid. Phys Fluids A 4(9):2090–2093CrossRef

Thompson B, Macbeth R (1964) Boiling water heat transfer burnout in uniformly heated round tubes. Technical Report AAEW-R 356

Thompson TL, Clark NN (1991) A holistic approach to particle drag prediction. Powder Technol 67(1):57–66CrossRef

Tong LS, Tang YS (1997) Boiling heat transfer and two-phase flow, 2nd edn. Taylor & Francis, New York

Traviss DP, Rohsenow WM, Baron AB (1972) Forced convection condensation inside tubes: a heat transfer equation for condenser design. ASHRAE Trans 79:157–165

Truckenbrodt E (1983) Lehrbuch der angewandten Fluidmechanik. Springer, Berlin, Heidelberg, New York, TokyoCrossRef

Tyn C, Calus W (1975) Diffusion coefficients in dilute binary liquid mixtures. J Chem Eng Data 20:106 ff

van Kan JJ, Segal A (1995) Numerik Partieller Differentialgleichungen für Ingenieure. B. G. Teubner Verlag, StuttgartMATHCrossRef

VDI 3930 VDI 3930, Abgaskühlung und -erwärmung. Release 1998

VDI-Wärmeatlas (2002) VDI–Wärmeatlas – Berechnungsblätter for the Wärmeübergang, 9th edn. VDI-Verlag GmbH., Düsseldorf

VDI-Wärmeatlas (2006) VDI–Wärmeatlas – Berechnungsblätter für den Wärmeübergang, 10th edn. VDI-Verlag GmbH., Düsseldorf

Wagner W, Rukes B (1995) Die Entwicklung einer neuen Industrie-Formulation für die Zustandseigenschaften von Wasser und Wasserdampf. Brennstoff-Wärme-Kraft 47(7/8):312–316

Wagner W, Kruse A (1998a) Zustandsgrößen von Wasser und Wasserdampf: Der Industrie-Standard IAPWS-IF97 für die thermodynamischen Zustandsgrößen und ergänzende Gleichungen für andere Eigenschaften. Springer, Berlin, Heidelberg, New YorkCrossRef

Wagner W, Cooper JR, Dittmann A, Kijima J, Kretzschmar HJ, Kruse A, Mares R, Oguchi K, Sato H, Stöcker I, Šnifer O, Takaishi Y, Tanishita I, Trübenbach J, Willkommen Th (2000) The IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam. Trans ASME Ser D J Eng Gas Turbines Power 122(1):150–182CrossRef

Wagner W, Rukes B (1998b) IAPWS-IF97: Die neue Industrie-Formulation. Brennstoff-Wärme-Kraft 50(3):42–47

Wallis GB (1969) One-dimensional two-phase-flow. McGraw-Hill Book Company, St. Louis, New York, San Francisco, London

Walter H (2001) Modellbildung und numerische Simulation von Naturumlaufdampferzeugern. Progress report VDI 457, VDI Verlag, Düsseldorf

Wang Y, Mason MT (1992) Two-dimensional rigid-body collisions with friction. J Appl Mech 59:635–642MATHCrossRef

Wang ChCh, Lee WS, Sheu WJ (2001) A comparative study of compact enhanced fin-and-tube heat exchangers. Int J Heat Mass Transf 44(18):3565–3573CrossRef

Warnatz J, Maas U, Dibble RW (1996) Combustion Springer, New YorkMATHCrossRef

Wassen E, Frank Th (2001) Simulation of cluster formation in gas-solid flow induced by particle-particle collision. Int J Multiphase Flow 27:437–458MATHCrossRef

Watson GB, Lee RA, Wiener M (1974) Critical heat flux in inclined and vertical smooth and ribbed tubes. In: Proceedings of the 5^th int. heat transfer conference, Vol 4. Tokyo, Japan, pp 275–279

Webb RL (1994) Principles of enhanced heat transfer. Wiley, New York

Weber R, Visser BM, Boysan F (1990) Assessment of turbulence modeling for engineering prediction of swirling vortices in the near burner zone. Int J Heat Fluid Flow 11(3):225–235CrossRef

Weierman Ch (1975) Finned tubes can lower heat-transfer costs. Oil Gas J 73:64–72

Weierman Ch (1976) Correlations ease the selection of finned tubes. Oil Gas J 74(36):94–100

Weierman Ch, Taborek J, Marner WJ (1978) Comparison of performance of inline and staggered banks of tubes with segmented fins. AIChE Symp Ser 74(174):39–46

Whalley PB (1996) Two-phase flow and heat transfer, Vol. 42 der Oxford Chemistry Primers. Oxford University Press, New York

Wheeler A, Hart RD (1951) Reaction rates and selectivity in catalyst pores. Adv Catal 3:249–327

Wilke CR, Chang P (1955) Correlation of diffusion coefficients in dilute solutions. AIChE J 1:264–270CrossRef

Wölfert A (1997) Verwendung von PDF-Methoden zur Modellierung turbulenter reaktiver Strömungen. Dissertation, Technical University of Stuttgart

Yadigaroglu G, Lahey Jr. RT (1987) On the various forms of the conservation equations in two-phase flow. Int J Multiphase Flow 2:477–494MATHCrossRef

Yadigaroglu G (1995) Closure relationships. In: Short courses on multiphase flow and heat transfer Part A: bases. ETH Zürich, Schweiz, pp 1–33

Yamagata K, Nishikawa K, Hasegawa S, Fuji T, Yoshida S (1972) Forced convective heat transfer to supercritical water flowing in tubes. Int J Heat Mass Transf 15:2575–2593CrossRef

Zhang X, Zhou L (2005) A second order momentum particle-wall collision model accounting for the wall roughness. Powder Technol 159:111–120CrossRef

Zheng Q (1991a) Reibungsdruckverlust von Gas/Flüssigkeitsströmungen in glatten und innenberippten Rohren. Dissertation, Technical University of Erlangen-Nürnberg

Zheng Q, Köhler W, Kastner W, Riedle K (1991b) Druckverlust in glatten und innenberippten Verdampferrohren. Wärme- und Stoffübertragung 26:323–330CrossRef

Zivi SM (1964) Estimation of steady-state steam void-fraction by means of the principle of minimum entropy production. Trans ASME Ser C J Heat Transf 86:247–252CrossRef

Zoebl H, Kruschik J (1982) Strömung durch Rohre und Ventile, 2nd edn. Springer, Wien, New YorkCrossRef

Zuber N, Findlay JA (1965) Average volumetric concentration in two-phase flow systems. Trans ASME Ser C J Heat Transf 87:453–468CrossRef

Žukauskas A, Ulinskas R (1988) Heat transfer in tube banks in crossflow Series in Experimental and Applied Heat Transfer Guide Books. Hemisphere Publ. Corp., New York, London

Žukauskas A (1989) High-performance single-phase heat exchangers. Hemisphere Publ. Corp., New York, London

Title: Conversion and Transport of Mass, Energy, Momentum, and Materials
Authors: B. Epple
R. Leithner
H. Müller
K. Ponweiser
H. Walter
A. Werner
Publisher: Springer Vienna
Book: Numerical Simulation of Power Plants and Firing Systems
Print ISBN: 978-3-7091-4853-2

Electronic ISBN: 978-3-7091-4855-6

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-7091-4855-6_2