Abstract
This chapter considers overall methods for pressure drop in gas liquid two-phase flow in pipes. The various elements of pressure drop are identified. Empirical methods are presented. The performance of these equations against available data are reported. Pressure drop in two-phase flow on the shell side of tube bundles is then considered. Geometries other than pipes are then considered. Firstly, pressure drop across fittings such and expansions and contractions are examined. Secondly, other aspects of two-phase flow at fittings are reviewed. Finally, the division of phase split at T-junctions is studied.
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References
Andeen, G.B., and Griffiths, P. (1968) Momentum flux in two-phase flow. Journal of Heat Transfer 90: 211–222.
Anderson, G.H., and Hills, P.D. (1974) Two-phase annular flow in tube bends. Symposium on. Multiphase Flow Systems, University of Strathclyde, paper J1, published in Instution of Chemical Engineers Symposium Series No. 38.
Archer, W.H. (1913) Experimental determination of loss of head due to sudden enlargement in circular pipes. Transactions of the Americaan Society of Civil Engineers 76: 999–1026.
Armand, A.A. (1946) The resistance during the movement of a two-phase system in horizontal pipes Izv. Vsesoyuznogo Tepl. Inst. 1:16–23.
Armand, A.A., and Treschev, G.G. (1947) Investigation of resistance during the movement of steam-water mixtures in heated boiler pipes at high pressures. Izv. Vsesoyuznogo Tepl. Inst 4: 1–5.
Arosio, S., Guglielmini, G., Lorenzi, A., Muzzio, A., and Sotgia, G. (1990) Two-phase pressure drop through sudden area contractions in horizontal flow. Heat Transfer 1990 (Proceedings of the 9th International Heat Transfer Conference, Jerusalem, 19–24 Aug. 1990), Hemisphere Publishing Corperation 6: 5964.
Attou, A., and Bolle, L. (1997a) Integral formulation of balance equations for two-phase flow through a sudden enlargement–part 1: basic approach. Proceedings of the Institution of Mechanical Engineers 211C: 387–397.
Attou, A., and Bolle, L. (1997b) Integral formulation of balance equations for two-phase flow through a sudden enlargement–part 2: a new interlocked volumes semi-empirical model. Proceedings of the Institution of Mechanical Engineers 211C: 399–408.
Attou, A., Giot, M., and Seynhaeve, J.M. (1997) Modelling of steady-state two-phase bubbly flow though a sudden enlargement. International Journal of Heat and Mass Transfer 40: 3375–3385.
Azzopardi, B.J. (1984) The effect of side arm diameter on two phase flow split at a T junction., International Journal of Multiphase Flow 10:509–512.
Azzopardi, B.J. (1985) Drop sizes in annular two-phase flow. Experiments in Fluids 3: 53–59.
Azzopardi, B.J. (1988) Measurements and observations of the split of annular flow at a vertical T junction. International Journal of Multiphase Flow 14: 701–710.
Azzopardi, B.J. (1989) The split of annular-mist flows at vertical and horizontal Ts. Proceedings of the Eighth International Conference on Offshore Mechanics and Arctic Engineering, The Hague, Netherlands, 19–23 March, ASME
Azzopardi, B.J. (1999) Phase split at T junctions. Multiphase Science and Technology 11:223–329. Azzopardi, B. J. and Whalley, P.B. (1982) The effect of flow pattern on two phase flow in a T junction. International Journal of Multiphase Flow 8: 481–507.
Azzopardi, B.J., Purvis, A., Govan, A.H. (1987) Annular two-phase flow split at an impacting T. International Journal of Multiphase Flow 13: 605–614.
Azzopardi, B.J., Wagstaff, D., Patrick, L., Memory, S.B., and Dowling, J. (1988) The split of two-phase flow at a horizontal T - annular and stratified flow. UKAEA Report AERE R13059.
Azzopardi B J and Memory, S.B. (1989) The split of two-phase flow at a horizontal T–annular and stratified flow. 4th International Conference on Multi phase Flow, Nice, France, 19–21 June (Pub. BHRA )
Azzopardi, B.J., and Smith, P.A. (1992) Flow split at a T junction: effect of side arm orientation and downstream geometry. International Journal of Multiphase Flow 18: 861–875.
Azzopardi, B.J., and Sudlow, C.A. (1993) The effect of pipe fittings on the structure of two-phase flow. XIth UIT National Heat Transfer Conference, Milan, Italy, 24–26 June.
Azzopardi, B.J., and Hervieu, E. (1994) Phase separation at junctions. Multiphase Science and Technology 8: 645–714.
Azzopardi, B.J., and Teixeira, J.C.F. (1994) Detailed measurements of vertical annular two phase flow–Part I: drop velocities and sizes. Journal of Fluids Engineering 116: 792–795.
Azzopardi, B.J., Colman, D.A., and Nicholson, D. (2002) Plant application of a T-junction as a partial phase separator. Transactions of the Institution of Chemical Engineers 80A: 87–96.
Ballyk, J.D., and Shoukri, M. (1990) On the development of a model for predicting phase separation phenomena in dividing two-phase flow. Nuclear Engineering and Design 123: 67–75.
Banerjee, S., Rhodes, E., and Scott, D.S. (1967) Film inversion of co-current two-phase flow in helical coils. American Institute of Chemical Engineers 13: 189–191.
Bankoff, S.G. (1960) A variable density single-fluid model for two-phase flow with particular reference to steam-water flow. Journal of Heat Transfer 82: 265–272.
Bao, Z.Y., Bosnich, M.G., and Haynes, B.S. (1994) Estimation of void fraction and pressure drop for twophase flow in fine passages. Transactions of the Institution of Chemical Engineers 72A: 625–632.
Baroczy, C.J. (1963) Correlation of liquid fraction in two-phase flow with application to liquid metals. 6 th National Heat Transfer Conference American Institute of Chemical Engineers, Preprint No 26.
Baroczy, C.J. (1966) A systematic correlation for two-phase pressure drop. Chemical Engineering Progress, Symposium Series, 62: 232–249.
Beattie, D.R.H., and Whalley, P.B. (1982) A simple two-phase frictional pressure drop calculation method. International Journal of Multiphase Flow 8: 83–87
Beggs, H.D., and Brill, J.P. (1973) A study of two-phase flow in inclined pipes. Journal of Petroleum Technology,25:607–617.
Benedict, R.P. (1980) Fundamentals of pipeflow. Wiley-Interscience, New York.Bhaga,D. and Weber, M.E., (1972) Holdup in vertical two-and three-phase flow. Canadian Journal of Chemical Engineering 50: 323–328.
Burkholz, A. (1989) Droplet Separation. VCH, Weinheim, Germany.
Cemak, J.O., Jicha, J.J., and Lightner, R.G. (1963) Two-phase pressure drop across vertically mounted thick plate restrictions. ASME paper 63-HT-11.
Chakbratai, P. (1976) Some aspects of annular two-phase flow in a horizontal tube PhD Thesis, Imperial College, London.
Charron, Y., and Whalley, P.B. (1995) Gas-liquid annular flow at a vertical tee junction–part I. Flow separation. International Journal of Multiphase Flow 21: 569–589.
Chisholm, D. (1967) A theoretical basis for the Lockhart-Martinelli correlation for two-phase flow. International Journal of Heat and Mass Transfer 10:1767–1778.
Chisholm, D. (1972) An equation for velocity ratio in two-phase flow. N.E.L., Report No 535.
Chisholm, D. (1983) Two-phase flow in pipelines and heat exchangers Pitman Press Ltd., Bath, England. Chisholm, D. (1985) Two-phase flow in heat exchangers and pipelines. Heat Transfer Engineering 6: 48–57.
Cicchitti, A., Lombardi, C., Silvestri, M., Soldani, G., and Zavatarelli, R. (1960) Two-phase cooling experiments–pressure drop, heat transfer and burnout experiments. Energia Nucleare 7: 407–425.
Clark, N.N., and Flemmer, R.L. (1985) Predicting the holdup in two-phase bubble upflow and downflow using the Zuber and Findlay drift-flux model. American Institute of Chemical Engineers Journal 31: 500–503.
Crane (1983) Flow offluids through valves, fittings and pipe. Crane Ltd., London.
Delhaye, J.M. (1981) Singular pressure drops. In Two-phase flow and heat transfer in the power and process industries. A.E. Bergles (Ed), Hemisphere Pub. Corp.
Dowlati, R., Kawaji, M., and Chan A.M.C. (1988) Void fraction and friction pressure drop in two-phase flow across a horizontal tube bundle. American Institute of Chemical Engineers Symposium Series 84: 126–132.
Dowlati, R., Kawaji, M., and Chan A.M.C. (1990) Pitch-to diameter effect on two-phase flow across an in-line tube bundle. American Institute of Chemical Engineers Journal 36: 765–772
Dukler, A.E., Moye Wicks III, and Cleveland, R.G. (1965) Frictional pressure drop in two-phase flow–B: an approach through similarity analysis. American Institute of Chemical Engineers Journal 10: 44–51.
El-Shaboury, A.M.F., Soliman, H,M., and Sims, G.E. (2001) Current state of knowledge on two-phase flow in horizontal impacting tee junctions. Multiphase Science and Technology 13:139–178.
Engineering Science Data Unit (ESDU) (1989) Two-phase flow pressure losses in pipeline fittings. ESDU Item No. 89012.
Fairhurst, C.P. (1983) Component pressure loss during two-phase flow. International Conference on the Physical Modelling of Multiphase Flow, Coventry, England, Paper Al, 1–24.
Ferrell, J.K., and McGee, J.W. (1964) Two-phase flow through abrupt expansions and contractions. TID 23394.
Fitzsimmons, D.E. (1964) Two-phase pressure drop in piping components. HW 80970 Rev. 1
Friedel, L. (1979) Improved friction pressure drop calculations for horizontal and vertical two-phase pipe flow. European Two-phase Flow Group Meeting.
Friedel, L., and Kissner, H.M. (1985) Pressure loss in safety valves during two-phase gas/vapour-liquid flow. Proceedings of the 2nd International Conference on Multiphase Flow, London, June (BHRA), 39–66.
Fruendt, J., Steiff, A., and Weinspach, P.-M. (1997) Pressure relief with highly viscous fluids. Process Safety Progress 16: 57–59.
Fryer, P.J., and Whalley, P.B. (1982) The effect of swirl on the liquid distribution in annular two-phase flow. International Journal of Multiphase Flow 8: 285–289.
Fukano, T., and Ousaka, A. (1989) Prediction of the circumferential distribution of film thickness in horizontal and near-horizontal gas-liquid annular flow. International Journal of Multiphase Flow 15: 403419.
Gardel, A. (1957) Les pertes de charge dans les ecoulementes au travers de branchements en te. Bulletin Technique de la Suisse Romande 9:122–130 and 10: 143–148.
Gardner, G.C., and Neller, P.H. (1969) Phase distributions in flow of an air-water mixture round bends and past obstructions at the wall of a 76 mm boil tube. Proceedings of the Institution of Mechanical Engineers 184: 36.
Geiger, G.E., and Rohrer, W.M. (1966) Sudden contraction losses in two-phase flow. Journal of Heat Transfer:1–9.
Guglielmini, G., Lorenzi, A., Muzzio, A., and Sotgia, G. (1986) Two-phase pressure drops across sudden area contractions - pressure and void fraction profiles. Heat Transfer 86, (Proceedings of the 8th International Heat Transfer Conference, San Francisco, 17–22 Aug., C.L. Tien et al. Ed. ), Hemisphere 5: 2361–2366.
Guglielmini, G., Muzzio, A., and Sotgia, G. (1997) The structure of two-phase flow in ducts with sudden contractions and its effect on the pressure drop. Proceedings of the Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics:1023–1036..
Haaland, S.E. (1983) Simple and explicit formulas for the friction factor in turbulent pipe flow. Journal of Fluids Engineering 105:89-
Harmathy, T.Z. (1960) Velocity of large drops and bubbles in media of infinite or restricted extent. American Institute of Chemical Engineers Journal 6: 281–288.
Harris, D.M. (1967) Calibration of a steam-quality-meter for channel power measurement in the prototype SGHW Reactor. European Two-Phase Flow Group Meeting, Bournemouth.
Harris, D.M., and Shires, G.L. (1972) Two-phase pressure drop in a Venturi. National Engineering Laboratory UK, Report No. 549, pp. 18–33.
Harshe, B., Hussain, A., and Weisman, J. (1976) Two-phase pressure drop across restrictions and other abrupt area changes. Cincinnati University Ohio, Report NUREG 0062.
Hart, J., Hamersma, P.J., and Fortuin, J.M.H. (1989) Correlations predicting frictional pressure drop and liquid holdup during horizontal gas-liquid pipe flow with a small liquid holdup, International Journal of Multiphase Flow 15: 947–964.
Hart, J., Hamersma, P.J., and Fortuin, J.M.H. (1991) A model for predicting liquid route preference during gas-liquid flow through horizontal branched pipelines. Chemical Engineering Science 46: 1609–1622.
Hervieu, E. (1988) Ecoulement monophasique et diphasique a bulles dans un branchement en T: étude théorique et expérimentale. Thèse de Doctorat de l’Institut National Polytechnique de Grenoble, France.
Hewitt, G.F., and Dell, F.R. (1968) Two-phase flow of air-water mixtures in horizontal coiled tubes. Private communication.
Hewitt, G.F. (1978), Measurement of two phase flow parameters. Academic Press, London
Hewitt, G.F. (1984) Two-phase flow through orifices, valves, bends and other singularities. 8th Lecture Series on Two-Phase Flow, Trondheim.
Hewitt, G.F., Gill, L.E., Roberts, D.N., and Azzopardi, B.J. (1990) The split of low inlet quality gas/liquid
flow at a vertical T - Experimental data. UKAEA Report AERE M3801. Report AERE M2459.
Hewitt, G.F., and Govan, A.H. (1990) Phenomenological modelling of non-equilibrium flow with phase
change. International Journal of Heat and Mass Transfer 32:229–242.
Hills, J.H., Azzopardi, B.J., and Barhey, A.S. (1996) Spatial unsteadiness–a way towards intensive gasliquid reactors Transactions of the Institution of Chemical Engineers 74A: 567–574.
Holt, A.J., Azzopardi, B.J., and Biddulph, M.W. (1995) The effect of density ratio on two-phase frictional pressure drop. International Symposium on Two-Phase Flow Modelling and Experimentation, Rome, 9–11 October.
Holt, A.J., Azzopardi, B.J., and Biddulph, M.W. (1997) Two-phase pressure drop and void fraction in narrow channels. 5th U.K. National Heat Transfer Conference, London.
Holt, A.J., Azzopardi, B.J., and Biddulph, M.W. (1999) Calculation of two-phase pressure drop for vertical upflow in narrow passages by means of a flow pattern specific model. Transactions of the Institution of Chemical Engineers 77A: 7–15.
Honan, T.J., and Lahey, R.T. (1981) Measurement of phase separation in wyes and tees. Nuclear Engineering and Design 64: 93–102.
Hoogerndoorn, C.J., and Welling, W.A. (1965) Experimental studies on the character of annular-mist flow in horizontal pipes. Symposium on Two-phase Flow, Exeter, 21–23 June, Paper C3.
Hughmark, G.A. (1962) Hold-up in gas-liquid flow. Chemical Engineering Progress 58: 62–65.
Isbin, H.S., Moen, R.H., Wickey, R.O., Mosher, D.R., and Larson, H.C. (1958) Two-phase steam-water pressure drops. Nuclear Science and Engineering Conference, Chicago.
Issa, R.I., and Oliveira, P.J. (1994) Numerical prediction of phase separation in two-phase flow through T-junctions. Computers Fluids 23: 347–372.
Issa, R.I, and Adechy, D. (2002) Modelling of annular flow through pipes and t-junctions. Submitted.
James, P.W. Azzopardi, B.J. Graham, D.I., and Sudlow, C.A. (2000) The effect of a bend on droplet size distribution in two-phase flow. 7 th International Conference on Multiphase Flow in Industrial Plants, Bologna, 13–15 September.
Janssen, E., and Kervinen, J.A. (1964) Two-phase pressure losses - final report. US Atomic Energy Comm., Report No. GEAP 4634.
Kirillov, P.R., Smogalev, I.P., Doroshenko, V.A. (1982) A graphical method of predicting the losses of pressure due to friction with a rising steam-water flow in round tubes. Thermal Engineering 29: 171172
Kooijman, J.M., and Lacey, P.M.C. (1968) Unpublished experiments. University of Exeter.
Lahey, R.T., and Moody, F.J. (1977) The Thermal Hydraulics of a Boiling Water Nuclear Reactor, American Nuclear Society.
Lahey, R.T., Azzopardi, B.J., and Cox, M. (1985) Modelling two-phase flow division at T-junctions. 2nd International Conference on Multiphase Flows, London, 19–21 June (ed. BHRA ).
Lahey, R.T. (1990) The analysis of phase separation and phase distribution phenomena using two-fluid models. Nuclear Engineering and Design 122: 17–40.
Lemonnier, H., and Hervieu, E. (1991) Theoretical modelling and experimental investigation of singlephase and two-phase division at a tee junction. Nuclear Engineering and Design 125: 201–213.
Levy, S. (1960) Steam-slip–theoretical prediction from momentum model. Journal of Heat Transfer 82: 113–124.
Lin, Z.H. (1985) Two-phase flow measurements with orifices. In Encyclopedia of Fluid Mechanics (Ed. N. Cherenmisinoff) Gulf Publishing Co. Houston.
Lockhart, R.W., and Martinelli, R.C. (1949) Proposed correlation of data for isothermal, two-phase, two-component flow in pipes. Chemical Engineering Progress 45: 39–48.
McNown, J.S. (1954) Mechanics of manifold flow. ASCE Transactions 119: 1103–1142.
McQuillan, K.W., and Whalley, P.B. (1984) The effect of orifices on the liquid distribution in annular two-phase flow. International Journal of Multiphase Flow 10: 721–73.
Maddock, C., Lacey, P.M.C., and Patrick, M.A. (1974) The structure of two-phase flow in a curved pipe. Symposium on. Multiphase Flow Systems, University of Strathclyde, paper J2, published in Instution of Chemical Engineers Symposium Series No. 38.
Marchaterre, J.F., and Hoglund, B.M. (1962) Correlation for two-phase flow. Nucleonics 8:142-
Martinelli, R.C., and Nelson, D.B. (1948) Prediction of pressure drop during forced circulation boiling of water“, Transaction of the American Society of Mechanical Engineers 70: 695–702.
Massena, W.A. (1960) Steam-water pressure drop. Hanford report H.W. 65706.
Mishima, K., And Hibiki, T. (1996) Some characteristics of air-water two-phase flow in small diameter vertical tubes. International Journal of Multiphase Flow 22: 703–712.
Morris, S.D. (1984) A simple model for estimating two-phase momentum flux. Institution of Chemical Engineers Symposium Series No. 86, 2: 773–784.
Morris, S.D (1985) Two-phase pressure drop across valves and orifice plates. European Two-phase Flow Group Meeting, Marchwood Engineering Laboratory, Southampton, England.
Muller-Steinhagen, H., and Heck, K. (1986), A Simple Friction Pressure Drop Correlation for Two-Phase Flow in Pipes, Chemical Engineering Process 20: 297–308.
Norstebo, A. (1985) Pressure drop in bends and valves in two-phase refrigerant flows. 2nd International Conference on Multiphase Flows, London, 19–21 June (ed. BHRA ).
Oshinowo, T., and Charles, M.E. (1974) Vertical two-phase flow. Canadian Journal of Chemical Engineering 52: 438–448.
Owens, W.L. (1961) Two-phase pressure gradient. International Heat Transfer Conference, Boulder, Colorado.
Patrick, M., and Swanson, B.S. (1959) Expansion and contraction of an air-water mixture in vertical flow. American Institute of Chemical Engineers 5: 440–445.
Popp, M., and Sallet, D.W. (1983) Experimental investigation of one and two-phase flow through a tee-junction. Paper B3, International Conference on the Physical Modelling of Multiphase Flows, Coventry, England, April 19–21.
Premoli, A., Francesco, D., and Prina, A. (1970) An empirical correlation for evaluating two-phase mixture density under adiabatic conditions. European Two-Phase Flow Group Meeting.
Ribeiro, A.M., Bott, T.R., and Jepson, D.M. (2001) The influence of a bend on drop sizes in horizontal annular two-phase flow. International Journal of Multiphase Flow 27: 721–728.
Richardson, B.E. (1959) Some problems in horizontal two-phase two component flows. ANL 5949.
Romie, F. (1958) Unpublished information.
Rooney, D.H. (1968) Void fraction prediction under saturated conditions. N.E.L. Report No 386.
Rose, S. (1964) Some hydrodynamic Characteristics of bubbly mixtures flowing vertically upwards in tubes. ScD Thesis, Massachusetts Institute of Technology.
Saba, N., and Lahey, R.T. (1984) The analysis of phase separation phenomena in branched conduits. International Journal of Multiphase Flow 10:1–20.
Salcudean, M., Chun, C.H., and Groenveld, D.C. (1983) Effect of flow obstructions on void distribution in horizontal air-water flow. International Journal of Multiphase Flow 9: 91–96.
Schadel, S.A., Leman, G.W., Binder, J.L., and Hanratty, T.J. (1990) Rates of atomisation in vertical annular flow. International Journal of Multiphase Flow 16: 363–374.
Schmidt, J., and Friedel, L. (1997) Two-phase pressure drop across sudden contractions in duct area. International Journal of Multiphase Flow 23: 283–299.
Schrage, D.S., Hau, J.T., and Jensen, M.K. (1987) Void fractions and two-phase multipliers in a horizontal tube bundle. American Institute of Chemical Engineers Symposium Series No 257.
Shoham, O., Brill, J.P., and Taitel,Y. (1987) Two-phase flow splitting in a Tee junction–experiment and modelling. Chemical Engineering Science 42: 2667–2676.
Simpson, H.C., Rooney, D.H., and Gratton, E. (1983) Two-phase flow through gate valves and orifice plates. International Conference on the Physical Modelling of Multiphase Flow, Coventry, England, Paper A2,: 25–40.
Simpson, H.C., Rooney, D.H., and Callender, T.M. (1985) Pressure loss through gate valves with liquid-vapour flows. 2nd International Conference on Multiphase Flows, London, 19–21 June (ed. BHRA):67–80.
Smith, S.L. (1971) Void fraction in two-phase flow–a correlation based upon equal velocity head model. Heat and Fluid Flow 1: 22–39
Taitel, Y., and Dukler, A.E. (1976) A model for predicting flow regime transitions in horizontal and near-horizontal gas-liquid flow. American Institute of Chemical Engineers Journal 22: 47–55.
Thom, J.R.S. (1964) Prediction of pressure drop during forced circulation boiling of water. International Journal of Heat and Mass Transfer 7: 709–624.
Ulbrich, R., and Mewes, D. (1995) Experiemtnal study of gas void fraction for two-phase flow across tube bundles. Proceedings of the International Symposium on Two-Phase Flow Modelling and Experimentation, Rome, 9–11 October, 1211–1218.
Wallis, G.B. (1961) Flooding velocities for air and water in vertical tubes. UKAEA Report AEEW R123.
Wallis, G.B. (1969) One-dimensional Two-phase Flow.,McGraw-Hill.
Ward Smith, A.J. (1971) Pressure losses in ducted flows. Butterworth, London.
Weisman, J. (1974) Two-phase pressure drop studies. Second Water Reactor Information Meeting, Washington, October.
Whalley, P.B. (1980) Air-water two-phase flow in a helically coiled tube. International Journal of Multiphase Flow 6: 345–356.
Wiafe, F.K. (1970) Two-phase flow through rough tubes. PhD Thesis, University of Strathclyde.
Williams, L.R., Dykhno, L.A., and Hanratty, T.J., (1996) Droplet flux distributions and entrainment in horizontal gas-liquid flows. International Journal of Multiphase Flow 22: 1–18.
Wooley, D.M., and Muller-Steinhagen, H. (1989) Prediction of frictional pressure drop for two phase flow in horizontal pipes. Proceedings of the Seventeenth Australian Chemical Engineering Conference, 184190.
Zivi, S.M. (1964) Estimation of steady state steam void fraction by means of the principle of minimum entropy production. Journal of Heat Transfer 86: 247–252.
Zuber, N., and Findlay, J.A. (1965) Average volumetric concentration in two-phase flow systems. Journal of Heat Transfer 87: 453–468.
Zuber, N., and Hench, J. (1962) Steady state and transient void fraction of bubbling systems and their operating limits, Part I: Steady state operation. General Electric Report 62GL100.
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Azzopardi, B., Hills, J. (2003). One Dimensional Models for Pressure Drop, Empirical Equations for Void Fraction and Frictional Pressure Drop and Pressure Drop and other Effects in Fittings. In: Bertola, V. (eds) Modelling and Experimentation in Two-Phase Flow. International Centre for Mechanical Sciences, vol 450. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2538-0_4
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