In this paper, an Artificial Neural Network soft matrix correlation to estimate the pressure drop of air-water two-phase flow is developed. The applicability of the model is extended by using dimensionless physical numbers as inputs (Air-Reynolds number, Water-Reynolds number, and the ratio of Air Inertial Forces to Water Inertial Forces), so the model can be implemented for vertical pipes with the proper combination of diameter-velocity-density-viscosity allowing estimations of dimensional numbers within the range of: Air-Reynolds numbers (430–6100), Water-Reynolds number (2400–7200), and Air-Water-Inertial forces ratio (1.6–1834), including the diameter range from 3 to 28 mm. Experimental measurements of frictional pressure drop of water-air mixtures are determined at different conditions. A search of the most suitable density, viscosity, and friction models was conducted and used in the model. The performance of the proposed ANN correlation is compared against published expressions showing good approximation to experimental data; results indicate that the most used correlations are within a mean relative error (mre) of 23.9–30.7%, while the proposed ANN has a mre = 0.9%. Two additional features are discussed: i) the applicability and generality of the ANN using untrained data, ii) the applicability in laminar, transitional, and turbulent flow regimen. To take the approach beyond a robust performance mapping, the methodology to translate the ANN into a programmable equation is presented.
WallisGB.One-dimensional two-phase flow.
New York:
McGraw-Hill Book Company, 1991.
2.
DongWVetschBT.Numerical simulation of air–water two-phase flow on stepped spillways behind X-shaped flaring gate piers under very high unit discharge. Water2019;
11: 1956.
3.
OliemansR. Two phase flow in gas-transmissions pipelines. ASME paper 76-Pet-25, presented at Pet. Div. ASME Meeting, Mexico, 1976.
4.
OuyangL.Single phase and multiphase fluid flow in horizontal wells. PhD Thesis, Satnford University. USA, 1998.
CicchittiALombardiCSilvestriM, et al. Two-phase cooling experiments: pressure drop, heat transfer and burnout measurements.
Centro Informazioni Studi Esperienze,
Milan, 1959.
8.
XuYFangXSuX, et al.
Evaluation of frictional pressure drop correlations for two-phase flow in pipes. Nucl Eng Des2012;
253: 86–97.
9.
DuklerAEWicksMClevelandRG.Frictional pressure drop in two-phase flow: B. An approach through similarity analysis. AIChE J1964;
10: 44–51.
10.
BeattieDRHWhalleyPB.A simple two-phase frictional pressure drop calculation method. Int J Multiphase Flow1982;
8: 83–87.
11.
LinSKwokCCKLiR-Y, et al.
Local frictional pressure drop during vaporization of R-12 through capillary tubes. Int J Multiphase Flow1991;
17: 95–102.
12.
ChenIYYangK-SChangY-J, et al.
Two-phase pressure drop of air–water and R-410A in small horizontal tubes. Int J Multiphase Flow2001;
27: 1293–1299.
13.
AwadMM andMuzychkaYS. Review and modeling of two-phase frictional pressure gradient at microgravity conditions. In: ASME 2010 3rd joint US-European fluids engineering summer meeting: volume 1, Symposia – Parts A, B, and C, 2010, pp. 987–1002.
14.
AwadMMMuzychkaYS.Two-phase flow modeling in microchannels and minichannels. Heat Transf Eng2010;
31: 1023–1033.
15.
LuCKongRQiaoS, et al.
Frictional pressure drop analysis for horizontal and vertical air-water two-phase flows in different pipe sizes. Nucl Eng Des2018;
332: 147–161.
16.
FourarMBoriesS.Experimental study of air-water two-phase flow through a fracture (narrow channel). Int J Multiphase Flow1995;
21: 621–637.
17.
YaoCLiHXueY, et al.
Investigation on the frictional pressure drop of gas liquid two-phase flows in vertical downward tubes. Int Commun Heat Mass Transf2018;
91: 138–149.
18.
MoraRJPérezTCGonzálezNFF, et al.
Thermodynamic properties of refrigerants using artificial neural networks. Int J Refrig2014;
46: 9–16.
19.
Barroso-MaldonadoJMBelman-FloresJMLedesmaS, et al.
Prediction of heat transfer coefficients for forced convective boiling of N2-hydrocarbon mixtures at cryogenic conditions using artificial neural networks. Cryogenics (Guildf)2018;
92: 60–70.
20.
Barroso-MaldonadoJMMontañez-BarreraJABelman-FloresJM, et al.
ANN-based correlation for frictional pressure drop of non-azeotropic mixtures during cryogenic forced boiling. Appl Therm Eng2019;
149: 492–501.
21.
SwainADasMK.Artificial intelligence approach for the prediction of heat transfer coefficient in boiling over tube bundles. Proc IMechE, Part C: J Mechanical Engineering Science2014;
228: 1680–1688.
22.
Shervani-TabarMTEttefaghMMLotfanS, et al.
Cavitation intensity monitoring in an axial flow pump based on vibration signals using multi-class support vector machine. Proc IMechE, Part C: J Mechanical Engineering Science2018;
232: 3013–3026.
23.
Al-NaserMElshafeiMAl-SarkhiA.Artificial neural network application for multiphase flow patterns detection: a new approach. J Pet Sci Eng2016;
145: 548–564.
24.
AlizadehdakhelARahimiMSanjariJ, et al.
CFD and artificial neural network modeling of two-phase flow pressure drop. Int Commun Heat Mass Transf2009;
36: 850–856.
25.
BarNDasSKBiswasMN.Prediction of frictional pressure drop using artificial neural network for air-water flow through U-bends. Procedia Technol2013;
10: 813–821.
26.
CengelYACimbalaJM.Fluid mechanics: fundamentals and applications.
New York:
McGraw-Hill, 2006.
27.
ShahRKLondonAL.Laminar flow forced convection in ducts.
New York:
Elsevier, 1978.
28.
BlasiusH. Das Ahnlickkeitsgesetz bei Reibungsvorgangen in Flussigkeiten Forshungheft 131, 1913.
29.
DrewTBKooECMcAdamsWH.The friction factor for clean round pipe. Trans AIChE1932;
28: 56–72.
30.
PetukhovBS. Heat Transfer and Friction in Turbulent Pipe Flow with Variable Physical Properties. Advances in Heat Transfer, 1970; 6: 503–564.
31.
GnielinskiV.New equations for heat and mass transfer in turbulent pipe and channel flow. Int Chem Eng1976;
16: 359–368.
ZigrangDJSylvesterND.Explicit approximations to the solution of Colebrook’s friction factor equation. AIChE J1982;
28: 514–515.
34.
PhillipsRJ.Forced convection, liquid cooled, microchannel heat sinks. Master’s Thesis, Massachusetts Institute of Technology, USA, 1987.
35.
FangXXuYZhouZ.New correlations of single-phase friction factor for turbulent pipe flow and evaluation of existing single-phase friction factor correlations. Nucl Eng Des2011;
241: 897–902.
Garcı́aFGarcı́aRPadrinoJ, et al.
Power law and composite power law friction factor correlations for laminar and turbulent gas–liquid flow in horizontal pipelines. Int J Multiphase Flow2003;
29: 1605–1624.
38.
ArrheniusS.On the internal friction of solution in water. Zeitschrift Physikalische Chemie (Leipzig)1887;
1: 285–298.
39.
BinghamEC.Viscosity and fluidity. Am Chem J1906;
3: 195–217.
40.
EinsteinA.A new definition of molecular dimensions. Ann Physik1909;
19: 289–306.
41.
HatschekE.The viscosity of liquids.
London:
Bell & Sons Ltd, 1928.
42.
TaylorGI.The viscosity of a fluid containing small drops of another fluid.Proc R Soc Lond Ser A1932;
138: 41–48.
43.
RichardsonEG.On the viscosity of emulsions. Kolloid Zeitschrift1933;
65: 32–37.
44.
BrinkmanHC.The viscosity of concentrated suspensions and solutions. J Chem Phys1952;
20: 571–571.
45.
VermeulenTWilliamsGMLangloisGE.Interfacial area in liquid-liquid and gas-liquid agitation. Chem Eng Prog1952;
51: 85–94.
46.
FinniganJW.Pressure losses and heat transfer for the flow of mixtures of immiscibles liquids in circular tubes. PhD Thesis, Oregon State College, USA, 1958.
47.
HoogendoornCJ.Gas-liquid flow in horizontal pipes. Chem Eng Sci1959;
9: 205–217.
48.
AkersWWDeansHACrosserOK.Condensation heat transfer within horizontal tubes. Chem Eng Prog Symp Ser1959;
55: 171–176.
49.
BankoffSG.A variable density single-fluid model for two-phase flow with particular reference to steam-water flow. J Heat Transfer1960;
82: 265–272.
50.
OwensWL.Two-phase pressure gradient. ASME Int Dev Heat Transfer1961;
2: 363–368.
51.
CengelYA.Viscosity of liquid-liquid dispersions in laminar and turbulent flow. PhD Thesis, Oregon State University, USA, 1967.
52.
OglesbyKD.An experimental study on the effects of oil viscosity, mixture velocity and water fraction on horizontal oil-water flow. Master Thesis, U. of Tulsa, Tulsa, OK, USA, 1979.
53.
TodaKFuruseH.Extension of Einstein’s viscosity equation to that for concentrated dispersions of solutes and particles. J Biosci Bioeng2006;
102: 524–528.
54.
MuzychkaYSWalshEWalshP, et al. Non-boiling two phase flow in microchannels. In: Microfluidics and nanofluidics handbook: chemistry, physics, and life science principles. Boca Raton, FL: CRC Press Taylor & Francis Group, 2011.
RusselSJNorvigP.Artificial intelligence: a modern approach.
Upper Saddle River, NJ:
Prentice Hall, 2009.
57.
JonesMT.Artificial intelligence: a systems approach.
Hingham, MA:
Infinity Science Press LLC, 2008.
58.
LedesmaSIbarra-ManzanoM-AGarcia-HernandezM-G, et al. Neural lab a simulator for artificial neural networks. In: 2017 computing conference, 2017, pp. 716–721. New York: IEEE.
59.
PressWHTeukolskySVetterlingWT.Numerical recipes: the art of scientific computing.
Cambridge:
Cambridge University Press, 2007.
60.
ShadlooMSRahmatAKarimipourA, et al.
Estimation of pressure drop of Two-Phase flow in horizontal long pipes using artificial neural networks. J Energy Resour Technol2020;
142.
61.
ShibaMYamazakiYA.Comparative study on the pressure drop of air-water flow. Bull JSME1967;
10: 290–298.
