Evaluation of slip ratio correlations in two-phase flow
Main Article Content
Abstract
Critical flow is one of the essential parameters in LOCA accident analysis in which pressure difference is very high. Void fraction (α), in another term, slip ratio, s, is the key parameter that could affect critical flow prediction. Henry-Fauske (HF) model is the model for critical flow calculation existing in current computer codes such as MARS, RELAP, TRACE. However, the limitation of this model is slip ratio s=1. By modified the slip ratio correlation, the paper focuses on evaluating the HF model. Among the chosen correlations for slip ratio, Smith correlation is the best option for this purpose. The results in our paper showed that while the original Smith correlation with k=0.4 is suggested for horizontal tests, the modified one with k=0.2 could be applied for vertical tests.
Article Details
Keywords
Void fraction, slip ratio, critical flow
References
[1]. R. E. Henry, H. K. Fauske, “The two-phase critical flow of one-component mixtures in nozzles, orifices and short tubes”, Journal of heat transfer, 93, 179-187, 1971.
[2]. J. A. Trap and V. H. Ransom, “A choked-flow calculation criterion for nonhomogeneous, nonequilibrium, two-phase flows”, Int. J. Multiphase Flow, 8, 669-681, 1982.
[3]. B. D. Chung et al., MARS Code Manual Volume V: Models and Correlations, KAERI, 2006.
[4]. TRACE, V5.0, Theory manual, Field Equations, solution methods, and physical models, 2010.
[5]. T. T. Tran, Y.S. Kim, H.S. Park, Study on the most applicable critical flow models in the current system codes, KNS Conference 2017, Korea.
[6]. Y. S. Kim et al., “Overview of geometrical effects on the critical flow rate of sub-cooled and saturated water”, Annals of Nuclear Energy, 76, 12-18, 2015.
[7]. S. L. Smith, “Void fractions in two-phase flow: a correlation based upon an equal velocity head model”, Proc. Inst. Mech. Engrs, 184, 647-657, Part 1, 1969.
[8]. D. Butterworth, “A comparison of some void fraction relationships for co-current gas-liquid flow”, Int. J. Multiphase Flow, 1, 845-850, 1975.
[9]. M.A. Woldesemayat, A.J. Ghajar, “Comparison of void fraction correlations for different flow patterns in horizontal and upward vertical pipes”, International Journal of Multiphase Flow, 33, 347–370, 2007.
[10]. P. L. Spedding, J. J. J. Chen, “Holdup in two-phase flow”, Int. J. Multiphase Flow, 10, 307-339, 1984.
[11]. Marchettere, The effect of pressure on boiling density in multiple rectangular channels, Argonne National Laboratory, Illinois, United States, 1956.
[12]. Cook, Boiling density in vertical rectangular multichannel sections with natural circulation, Argonne National Laboratory, Illinois, United States, 1956.
[13]. Haywood, Experimental study on the flow conditions and pressure drop of steam-water mixture at high pressure in heated and unheated tubes, University of Cambridge, 1961.
[14]. E. S. Starkman et al., “Expansion of a very low-quality two-phase fluid through a convergent-divergent nozzle”, Journal of Basic Engineering, 86, 247-254, 1964.
[15]. H. K. Fauske, Contribution to the theory of two-phase, one-component critical flow, Argonne National Lab, United States, 1962.
[16]. S.M. Zivi, “Estimation of steady-state steam void fraction by means of the principle of minimum entropy production”. Trans. ASME, J. Heat Transfer, 86, 247–252, 1964.
[17]. D. Chisholm, “Pressure gradients due to friction during the flow of evaporating two-phase mixtures in smooth tubes and channels”, Int. J. Heat Mass Transfer, 16, 347-358, 1973.
[18]. P.J. Hamersma, J. Hart,. “A pressure drop correlation for gas/liquid pipe flow with a small liquid holdup”. Chem. Eng. Sci. 42,1187–1196, 1987.
[19]. J.M. Turner, G.B. Wallis, The separate-cylinders model of two-phase flow, Paper No. NYO-3114-6, Thayer’s School Eng., Dartmouth College, Hanover, NH, USA, 1965.
[20]. R.W. Lockhart, R.C. Martinelli, “Proposed correlation of data for isothermal two-phase, two-component flow in pipes”, Chem. Eng. Progr. 45, 39–48, 1949.
[21]. J.R.S. Thom, “Prediction of pressure drop during forced circulation boiling of water”, Int. J. Heat Mass Transfer 7, 709–724, 1964.
[22]. C.J. Baroczy, “A systemic correlation for two-phase pressure drop”, Chem. Eng. Progr. Symp. Ser. 62, 232–249, 1966.
[23]. A. Premoli, D. Francesco, A. Prima, An empirical correlation for evaluating two-phase mixture density under adiabatic conditions, European Two-Phase Flow Group Meeting, Milan, Italy, 1970.
[24]. N. Madsen, “A void fraction correlation for vertical and horizontal bulk-boiling of water”. AIChE J. 21, 607–608, 1975.
[25]. J.J.J. Chen, “A further examination of void-fraction in the annular two-phase flow”, Int. J. Heat Mass Transfer 29, 1760–1763, 1986.
[26]. N. Petalaz, K. Aziz, A mechanistic model for stabilized multiphase flow in pipes, a report for the members of Stanford reservoir simulation industrial affiliates and Stanford project on the productivity and injectivity of horizontal wells, Stanford University, Palo Alto, CA, 1997.
[27]. G. L. Sozzi, W. A. Sutherland, “Critical flow of saturated and subcooled water at high pressure”, Amer. Soc. Mech. Eng. Non-Equilibrium Two-Phase Flow Symp., 47, 1975.
[28]. M. H. Chun and C. K. Park, “An experimental investigation of critical flow rates of subcooled water through short pipes with small diameters”, Int. Comm. Heat Mass Transfer, 23 (No. 8), 1053-1064, 1996.
[29]. R. E. Henry, Pressure pulse propagation in two-phase one and two-component mixtures, ANL-7792, Argonne National Laboratory. Illinois, United States, 1971.
[2]. J. A. Trap and V. H. Ransom, “A choked-flow calculation criterion for nonhomogeneous, nonequilibrium, two-phase flows”, Int. J. Multiphase Flow, 8, 669-681, 1982.
[3]. B. D. Chung et al., MARS Code Manual Volume V: Models and Correlations, KAERI, 2006.
[4]. TRACE, V5.0, Theory manual, Field Equations, solution methods, and physical models, 2010.
[5]. T. T. Tran, Y.S. Kim, H.S. Park, Study on the most applicable critical flow models in the current system codes, KNS Conference 2017, Korea.
[6]. Y. S. Kim et al., “Overview of geometrical effects on the critical flow rate of sub-cooled and saturated water”, Annals of Nuclear Energy, 76, 12-18, 2015.
[7]. S. L. Smith, “Void fractions in two-phase flow: a correlation based upon an equal velocity head model”, Proc. Inst. Mech. Engrs, 184, 647-657, Part 1, 1969.
[8]. D. Butterworth, “A comparison of some void fraction relationships for co-current gas-liquid flow”, Int. J. Multiphase Flow, 1, 845-850, 1975.
[9]. M.A. Woldesemayat, A.J. Ghajar, “Comparison of void fraction correlations for different flow patterns in horizontal and upward vertical pipes”, International Journal of Multiphase Flow, 33, 347–370, 2007.
[10]. P. L. Spedding, J. J. J. Chen, “Holdup in two-phase flow”, Int. J. Multiphase Flow, 10, 307-339, 1984.
[11]. Marchettere, The effect of pressure on boiling density in multiple rectangular channels, Argonne National Laboratory, Illinois, United States, 1956.
[12]. Cook, Boiling density in vertical rectangular multichannel sections with natural circulation, Argonne National Laboratory, Illinois, United States, 1956.
[13]. Haywood, Experimental study on the flow conditions and pressure drop of steam-water mixture at high pressure in heated and unheated tubes, University of Cambridge, 1961.
[14]. E. S. Starkman et al., “Expansion of a very low-quality two-phase fluid through a convergent-divergent nozzle”, Journal of Basic Engineering, 86, 247-254, 1964.
[15]. H. K. Fauske, Contribution to the theory of two-phase, one-component critical flow, Argonne National Lab, United States, 1962.
[16]. S.M. Zivi, “Estimation of steady-state steam void fraction by means of the principle of minimum entropy production”. Trans. ASME, J. Heat Transfer, 86, 247–252, 1964.
[17]. D. Chisholm, “Pressure gradients due to friction during the flow of evaporating two-phase mixtures in smooth tubes and channels”, Int. J. Heat Mass Transfer, 16, 347-358, 1973.
[18]. P.J. Hamersma, J. Hart,. “A pressure drop correlation for gas/liquid pipe flow with a small liquid holdup”. Chem. Eng. Sci. 42,1187–1196, 1987.
[19]. J.M. Turner, G.B. Wallis, The separate-cylinders model of two-phase flow, Paper No. NYO-3114-6, Thayer’s School Eng., Dartmouth College, Hanover, NH, USA, 1965.
[20]. R.W. Lockhart, R.C. Martinelli, “Proposed correlation of data for isothermal two-phase, two-component flow in pipes”, Chem. Eng. Progr. 45, 39–48, 1949.
[21]. J.R.S. Thom, “Prediction of pressure drop during forced circulation boiling of water”, Int. J. Heat Mass Transfer 7, 709–724, 1964.
[22]. C.J. Baroczy, “A systemic correlation for two-phase pressure drop”, Chem. Eng. Progr. Symp. Ser. 62, 232–249, 1966.
[23]. A. Premoli, D. Francesco, A. Prima, An empirical correlation for evaluating two-phase mixture density under adiabatic conditions, European Two-Phase Flow Group Meeting, Milan, Italy, 1970.
[24]. N. Madsen, “A void fraction correlation for vertical and horizontal bulk-boiling of water”. AIChE J. 21, 607–608, 1975.
[25]. J.J.J. Chen, “A further examination of void-fraction in the annular two-phase flow”, Int. J. Heat Mass Transfer 29, 1760–1763, 1986.
[26]. N. Petalaz, K. Aziz, A mechanistic model for stabilized multiphase flow in pipes, a report for the members of Stanford reservoir simulation industrial affiliates and Stanford project on the productivity and injectivity of horizontal wells, Stanford University, Palo Alto, CA, 1997.
[27]. G. L. Sozzi, W. A. Sutherland, “Critical flow of saturated and subcooled water at high pressure”, Amer. Soc. Mech. Eng. Non-Equilibrium Two-Phase Flow Symp., 47, 1975.
[28]. M. H. Chun and C. K. Park, “An experimental investigation of critical flow rates of subcooled water through short pipes with small diameters”, Int. Comm. Heat Mass Transfer, 23 (No. 8), 1053-1064, 1996.
[29]. R. E. Henry, Pressure pulse propagation in two-phase one and two-component mixtures, ANL-7792, Argonne National Laboratory. Illinois, United States, 1971.