Simple rules are developed for obtaining rational bounds for two-phase frictional pressure gradient. Both the lower and upper bounds are based on the separate cylinders formulation. The lower bound is based on turbulent-turbulent flow that uses the Blasius equation to represent the Fanning friction factor. The upper bound is based on an equation that represents well the Lockhart-Martinelli correlation for turbulent-turbulent flow. The model is verified using published experimental data of two-phase frictional pressure gradient versus mass flux at constant mass quality. The published data include different working fluids such as R-12 and R-22 at different mass qualities, different pipe diameters, and different saturation temperatures. It is shown that the published data can be well bounded for a wide range of mass fluxes, mass qualities, pipe diameters and saturation temperatures. The bounds models are also presented in a dimensionless form as two-phase frictional multiplier (φl and φg) versus Lockhart-Martinelli parameter (X) for different working fluids such as R-12, R-22, air-oil and air-water mixtures.

Volume Subject Area:
Fluids Engineering
Topics:
Pipes, Pressure gradient, Two-phase flow, Turbulence, Flow (Dynamics), Fluids, Temperature, Cylinders, Flux (Metallurgy), Friction, Water
1.
ASHRAE, 1993, Handbook of Fundamentals, ASHRAE, Atlanta, GA, Chap. 4.
2.
Lockhart
R. W.
, and
Martinelli
R. C.
,
1949
, “
Proposed Correlation of Data for Isothermal Two-Phase, Two-Component Flow in Pipes
,”
Chemical Engineering Progress Symposium Series
,
45
(
1
), pp.
39
–
48
.
3.
Martinelli
R. C.
, and
Nelson
D. B.
,
1948
, “
Prediction of Pressure Drop during Forced-Circulation Boiling of Water
,”
Trans. ASME
,
70
(
6
), pp.
695
–
702
.
4.
Tong, L. S., 1967, Boiling Heat Transfer and Two-Phase Flow, John Wiley & Sons, Inc., New York.
5.
Wallis, G. B., 1969, One-Dimensional Two-Phase Flow, McGraw-Hill Book Company, New York.
6.
Chisholm, D., 1983, Two-Phase Flow in Pipelines and Heat Exchangers, George Godwin in Association with Institution of Chemical Engineers, London.
7.
Awad, M. M., and Muzychka, Y. S., 2004, “A Simple Two Phase Frictional Multiplier Calculation Method,” Proceedings of IPC2004, International Pipeline Conference, Track: 3. Design & Construction, Session: System Design/Hydraulics, IPC04-0721, Vol. 1, pp. 475–483, Calgary, Alberta.
8.
Awad, M. M., and Muzychka, Y. S., 2004, “A Simple Asymptotic Compact Model for Two-Phase Frictional Pressure Gradient in Horizontal Pipes,” Proceedings of IMECE 2004, Fluids Engineering, General Papers, FE-8 A Gen. Pap.: Multiphase Flows, IMECE2004-61410, Vol. 1, Anaheim, California.
9.
Carey, V. P., 1992, Liquid-Vapor Phase-Change Phenomena: An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment, Hemisphere Pub. Corp., Washington, D.C, Chap. 10, pp. 423.
10.
Turner, J. M., 1966, “Annular Two -Phase Flow,” Ph.D. Thesis, Dartmouth College, Hanover, NH.
11.
Blasius, H., 1913, “Das A¨hnlichkeitsgesetz bei Reibungsvorga¨ngen in Flu¨ssikeiten,” Forsch. Gebiete Ingenieurw., 131.
12.
Collier, J. G., 1981, Convective Boiling and Condensation (2nd Edn), McGraw-Hill Book Company, New York.
13.
Chisholm
D.
,
1967
, “
Theoretical Basis for the Lockhart-Martinelli Correlation for Two-Phase Flow
,”
Int. J. Heat Mass Transfer
,
10
(
12
), pp.
1767
–
1778
.
14.
Powley, M. B., 1965, “Two -Phase Flow,” 15th Canadian Chemical Engineering Conference, Chemical Institute of Canada, Universite´ Laval, Quebec City.
15.
Chisholm, D., 1970, “Pressure Gradients during the Flow of Evaporating Two-Phase Mixtures,” NEL Report No. 470, National Engineering Laboratory, East Kilbride, Glasgow.
16.
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 Transfer
,
16
(
2
), pp.
347
–
358
.
17.
Baroczy
C. J.
,
1966
, “
A Systematic Correlation for Two - Phase Pressure Drop
,”
Chemical Engineering Progress Symposium Series
,
62
(
44
), pp.
232
–
249
.
18.
Chisholm
D.
,
1978
, “
Influence of Pipe Surface Roughness on Friction Pressure Gradient during Two-Phase Flow
,”
J. Mechanical Engineering Science
,
20
(
6
), pp.
353
–
354
.
19.
Friedel, L., 1979, “Improved Fiction Pressure Drop Correlations for Horizontal and Vertical Two Phase Pipe Flow,” paper E2, European Two Phase Flow Group Meeting, Ispra, Italy.
20.
Whalley, P. B., 1987, Boiling, Condensation, and Gas-Liquid Flow, Clarendon Press, Oxford.
21.
Mu¨ller-Steinhagen
H.
, and
Heck
K.
,
1986
, “
A Simple Friction Pressure Drop Correlation for Two-Phase Flow in Pipes
,”
Chemical Engineering Process
,
20
, pp.
297
–
308
.
22.
Bandel, J., 1973, “Druckverlust u¨nd Wa¨rmeu¨bergang bei der Verdampfung siedender Ka¨ltemittel im durchstro¨mten waagerechten Rohr,” Doctoral Dissertation, Universita¨t Karlsruhe.
23.
Churchill
S. W.
,
1977
, “
Friction Factor Equation Spans all Fluid Flow Regimes
,”
Chemical Engineering
,
84
(
24
), pp.
91
–
92
.
24.
Souza, A. L., and Pimenta, M. M., 1995, “Prediction of Pressure Drop During Horizontal Two-Phase Flow of Pure and Mixed Refrigerants,” ASME Conference Cavitation and Multi-Phase Flow, HTD, Vol. 210, pp. 161–171, South Carolina, U. S. A.
25.
Hashizume
K.
,
1983
, “
Flow Pattern, Void Fraction and Pressure Drop of Refrigerant Two-Phase Flow in a Horizontal Pipe. Part I: Experimental Data
,”
Int. J. Multiphase Flow
,
9
(
4
), pp.
399
–
410
.
26.
Govier
G. W.
and
Omer
M. M.
,
1962
, “
Horizontal Pipeline Flow of Air-Water Mixtures
,”
The Canadian Journal of Chemical Engineering
,
40
(
3
), pp.
93
–
104
.
27.
Hoogendoorn
C. J.
,
1959
, “
Gas-Liquid Flow in Horizontal Pipes
,”
Chemical Engineering Science
,
9
, pp.
205
–
217
.
28.
Cheremisinoff
N. P.
and
Davis
E. J.
,
1979
, “
Stratified Turbulent-Turbulent Gas-Liquid Flow
,”
AIChE J.
,
25
(
1
), pp.
48
–
56
.
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