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Experimental data for solid–liquid flows at intermediate and high Stokes numbers

Published online by Cambridge University Press:  25 November 2019

Sarah E. Mena Open the ORCID record for Sarah E. Mena [Opens in a new window]  and
Jennifer Sinclair Curtis Open the ORCID record for Jennifer Sinclair Curtis [Opens in a new window]
Sarah E. Mena*
Affiliation:
Chemical Engineering Department, University of Florida, Gainesville, FL32611, USA
Jennifer Sinclair Curtis
Affiliation:
Chemical Engineering Department, University of Florida, Gainesville, FL32611, USA College of Engineering, University of California, Davis, CA95616, USA
*
†Email address for correspondence: sarah.mena@psri.org
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Abstract

Experimental data for turbulent solid–liquid flow in a vertical pipe were collected for glass beads with diameters from 0.5 mm to 5 mm, at concentrations up to 2 % v/v, and Reynolds numbers from 200 000 to 350 000. In addition, data for crushed glass, steel shot and two sizes of stainless-steel cylinders were also collected. The experiments span from the intermediate to the inertia-dominated regimes, and the results include direct measurements for the pressure drops, the solids concentration and the three velocity components for each of the phases using laser Doppler velocimetry and phase Doppler anemometry. In addition, the results include the Reynolds stresses, the granular temperature, the kinetic energy and calculations for the turbulence modulation. The results show augmentation of turbulence for all the conditions studied. The velocity fluctuations for the solid and the liquid are reduced with increasing Reynolds numbers at all conditions. The Reynolds number dictates the behaviour of the relative velocity with concentration: for the Reynolds number of 350 000, the relative velocity increases with increasing concentrations, which can be explained by a decrease in the solid shear and an increase in the solid-phase pressure with rising concentration. In contrast, for the Reynolds number of 200 000, the relative velocity decreases with increasing concentrations, which can be attributed to an increase in drag force at higher concentration. The unique dataset presented begins to close the gap in knowledge for two-phase flow experimentation at concentrations above 0.7 % v/v and Reynolds numbers above 30 000.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A24
Copyright
© 2019 Cambridge University Press

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References

Abbas, M. A. & Crowe, C. T. 1987 Experimental study of the flow properties of a homogenous slurry near transitional Reynolds numbers. Intl J. Multiphase Flow 13 (3), 357–364.CrossRefGoogle Scholar
Afzal, N. 1982 Fully-developed turbulent-flow in a pipe – an intermediate layer. Ing.-Arch. 52 (6), 355–377.CrossRefGoogle Scholar
Alajbegović, A., Assad, A., Bonetto, F. & Lahey, R. T. Jr 1994 Phase distribution and turbulence structure for solid/fluid upflow in a pipe. Intl J. Multiphase Flow 20 (3), 453–479.CrossRefGoogle Scholar
Albrecht, H., Borys, M., Damaschke, N. & Tropea, C. 2003 Laser Doppler and Phase Doppler Measurement Techniques. Springer.CrossRefGoogle Scholar
Averbakh, A., Shauly, A., Nir, A. & Semiat, R. 1997 Slow viscous flows of highly concentrated suspensions – Part I: laser-doppler velocimetry in rectangular ducts. Intl J. Multiphase Flow 23 (3), 409–424.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Bell, S. 1999 A Beginner’s Guide to Uncertainty of Measurement. Measurement Good Practice Guide, vol. 11, pp. 1–33. National Physical Laboratory.Google Scholar
Bellani, G., Byron, M. L., Collignon, A. G., Meyer, C. R. & Variano, E. A. 2012 Shape effects on turbulent modulation by large nearly neutrally buoyant particles. J. Fluid Mech. 712, 41–60.CrossRefGoogle Scholar
Boree, J. & Caraman, N. 2005 Dilute bidispersed tube flow: role of interclass collisions at increased loadings. Phys. Fluids 17 (5), 055108.CrossRefGoogle Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20 (1), 111–157.CrossRefGoogle Scholar
Brenn, G., Braeske, H. & Durst, F. 2002 Investigation of the unsteady two-phase flow with small bubbles in a model bubble column using phase-Doppler anemometry. Chem. Engng Sci. 57 (24), 5143–5159.CrossRefGoogle Scholar
Brennen, C. E. 2005 Fundamentals of Multiphase Flow. Cambridge University Press.CrossRefGoogle Scholar
Brucato, A., Grisafi, F. & Montante, G. 1998 Particle drag coefficient in turbulent fluids. Chem. Engng Sci. 53 (18), 3295–3314.CrossRefGoogle Scholar
Caraman, N., Boree, J. & Simonin, O. 2003 Effect of collisions on the dispersed phase fluctuation in a dilute tube flow: experimental and theoretical analysis. Phys. Fluids 15 (12), 3602–3612.CrossRefGoogle Scholar
Chemloul, N. S. & Benmedjedi, A. E. K. 2010 Particle velocity detection and measurement in two-phase flow using combined electronic logic system and LDA technique. Flow Meas. Instrum. 21 (3), 425–433.CrossRefGoogle Scholar
Chemloul, N. S. & Benrabah, O. 2008 Measurement of velocities in two-phase flow by laser velocimetry: interaction between solid particles’ motion and turbulence. J. Fluids Engng 130 (7), 071301.Google Scholar
Claudin, P., Duran, O. & Andreotti, B. 2017 Dissolution instability and roughening transition. J. Fluid Mech. 832, R2.CrossRefGoogle Scholar
Coleman, H. W. & Steele, W. G. 2009 Experimentation, Validation, and Uncertainty Analysis for Engineers, 3rd edn. Wiley.CrossRefGoogle Scholar
Compton, D. & Eaton, J. 1996 A high-resolution laser Doppler anemometer for three-dimensional turbulent boundary layers. Exp. Fluids 22 (2), 111–117.CrossRefGoogle Scholar
Crowe, C. T., Sommerfeld, M. & Tsuji, Y. 1998 Multiphase Flows with Droplets and Particles. CRC Press.Google Scholar
De Marchis, M. & Milici, B. 2016 Turbulence modulation by micro-particles in smooth and rough channels. Phys. Fluids 28 (11), 115101.CrossRefGoogle Scholar
Druzhinin, O. & Elghobashi, S. 1998 Direct numerical simulations of bubble-laden turbulent flows using the two-fluid formulation. Phys. Fluids 10 (3), 685–697.CrossRefGoogle Scholar
Durst, F., Muller, R. & Jovanovic, J. 1988 Determination of the measuring position in laser-Doppler anemometry. Exp. Fluids 6 (2), 105–110.CrossRefGoogle Scholar
Eaton, J. K. & Longmire, E. K. 2017 Turbulence interactions. In Multiphase Flow Handbook, 2nd edn. (ed. Michaelides, E., Crowe, C. T. & Schwarzkopf, J. D.), pp. 729–751. CRC Press, Taylor & Francis Group.Google Scholar
Elghobashi, S. 1994 On predicting particle-laden turbulent flows. Appl. Sci. Res. 52 (4), 309–329.CrossRefGoogle Scholar
Fairweather, M. & Hurn, J. 2008 Validation of an anisotropic model of turbulent flows containing dispersed solid particles applied to gas–solid jets. Comput. Chem. Engng 32 (3), 590–599.CrossRefGoogle Scholar
Ferre, A. & Shook, C. 1998 Coarse particle wall friction in vertical slurry flows. Particul. Sci. Technol. 16 (2), 125–133.CrossRefGoogle Scholar
Fevrier, P., Simonin, O. & Squires, K. 2005 Partitioning of particle velocities in gas–solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study. J. Fluid Mech. 533, 1–46.CrossRefGoogle Scholar
Frishman, F., Hussainov, M., Kartushinsky, A. & Rudi, Ü. 1999 Distribution characteristics of the mass concentration of coarse solid particles in a two-phase turbulent jet. J. Aerosol. Sci. 30 (1), 51–69.CrossRefGoogle Scholar
Ghatage, S. V., Sathe, M. J., Doroodchi, E., Joshi, J. B. & Evans, G. 2013 Effect of turbulence on particleand bubble slip velocity. Chem. Engng Sci. 100, 120–136.CrossRefGoogle Scholar
Gidaspow, D. 1994 Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic Press.Google Scholar
Gillandt, I., Fritsching, U. & Bauckhage, K. 2001 Measurement of phase interaction in dispersed gas/particle two-phase flow. Intl J. Multiphase Flow 27 (8), 1313–1332.CrossRefGoogle Scholar
Gore, R. A. & Crowe, C. T. 1989 Effect of particle-size on modulating turbulent intensity. Intl J. Multiphase Flow 15 (2), 279–285.CrossRefGoogle Scholar
Gorokhovski, M. & Herrmann, M. 2008 Modeling primary atomization. Annu. Rev. Fluid Mech. 40, 343–366.CrossRefGoogle Scholar
Guo, Y., Wassgren, C., Hancock, B., Ketterhagen, W. & Curtis, J. 2013 Granular shear flows of flat disks and elongated rods without and with friction. Phys. Fluids 25 (6), 063304.CrossRefGoogle Scholar
Hadinoto, K., Jones, E. N., Yurteri, C. & Curtis, J. S. 2005 Reynolds number dependence of gas-phase turbulence in gas–particle flows. Intl J. Multiphase Flow 31 (4), 416–434.CrossRefGoogle Scholar
Hanes, D. M. & Inman, D. L. 1985 Observations of rapidly flowing granular-fluid materials. J. Fluid Mech. 150, 357–380.CrossRefGoogle Scholar
Hardalupas, Y., Taylor, A. M. K. P. & Whitelaw, J. H. 1989 Velocity and particle-flux characteristics of trubulent particle-laden jets. Proc. R. Soc. Lond. A 426 (1870), 31–78.CrossRefGoogle Scholar
Hetsroni, G. 1989 Particles-turbulence interaction. Intl J. Multiphase Flow 15 (5), 735–746.CrossRefGoogle Scholar
Hosokawa, S. & Tomiyama, A. 2004 Turbulence modification in gas–liquid and solid–liquid dispersed two-phase pipe flows. Intl J. Heat Fluid Flow 25 (3), 489–498.CrossRefGoogle Scholar
Hutchinson, P., Hewitt, G. F. & Dukler, A. E. 1971 Deposition of liquid or solid dispersions from turbulent gas stream – stochastic model. Chem. Engng Sci. 26 (3), 419–439.CrossRefGoogle Scholar
Hwang, W. & Eaton, J. K. 2006 Homogeneous and isotropic turbulence modulation by small heavy (st similar to 50) particles. J. Fluid Mech. 564, 361–393.CrossRefGoogle Scholar
Johnson, P. C. & Jackson, R. 1987 Frictional-collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176, 67–93.CrossRefGoogle Scholar
Johnson, P. L. & Meneveau, C. 2017 Restricted euler dynamics along trajectories of small inertial particles in turbulence. J. Fluid Mech. 816, R2.CrossRefGoogle Scholar
Kays, W. M. & Crawford, M. E. 1980 Convective Heat and Mass Transfer, 2nd edn. McGraw-Hill.Google Scholar
Kliafas, Y. & Holt, M. 1987 LDV measurements of a turbulent air–solid two-phase flow in a 90 bend. Exp. Fluids 5 (2), 73–85.CrossRefGoogle Scholar
Koh, C. J., Hookham, P. & Leal, L. G. 1994 An experimental investigation of concentrated suspension flows in a rectangular channel. J. Fluid Mech. 266, 1–32.CrossRefGoogle Scholar
Kulick, J., Fessler, J. & Eaton, J. 1994 Particle response and turbulence modification in fully-developed channel flow. J. Fluid Mech. 277, 109–134.CrossRefGoogle Scholar
Kussin, J. & Sommerfeld, M. 2002 Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness. Exp. Fluids 33 (1), 143–159.CrossRefGoogle Scholar
LaMarche, C. Q., Morán, A. B., van Wachem, B. & Curtis, J. S. 2017 Two-fluid modeling of cratering in a particle bed by a subsonic turbulent jet. Powder Technol. 318, 68–82.CrossRefGoogle Scholar
Langsholt, M. & Zarruk, G. A. 2015 Particle transport in semi-dilute turbulent pipe flow. J. Dispersion Sci. Technol. 36 (10), 1513–1526.CrossRefGoogle Scholar
Lau, T. C. W. & Nathan, G. J. 2016 The effect of stokes number on particle velocity and concentration distributions in a well-characterised, turbulent, co-flowing two-phase jet. J. Fluid Mech. 809, 72–110.CrossRefGoogle Scholar
Lau, T. C. W. & Nathan, G. J. 2014 Influence of stokes number on the velocity and concentration distributions in particle-laden jets. J. Fluid Mech. 757, 432–457.CrossRefGoogle Scholar
Laufer, J.1954. The structure of turbulence in fully developed pipe flow. NACA Tech. Rep. No. 1174, pp. 1–18.Google Scholar
Lee, S. L. & Durst, F. 1982 On the motion of particles in turbulent duct flows. Intl J. Multiphase Flow 8 (2), 125–146.CrossRefGoogle Scholar
Lucci, F., Ferrante, A. & Elghobashi, S. 2011 Is Stokes number an appropriate indicator for turbulence modulation by particles of Taylor-length-scale size? Phys. Fluids 23 (2), 025101.CrossRefGoogle Scholar
Lun, C. K. K. 1991 Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres. J. Fluid Mech. 233, 539–559.CrossRefGoogle Scholar
Lun, C. K. K., Savage, S. B., Jeffrey, D. J. & Chepurniy, N. 1984 Kinetic theories for granular flow: inelastic particles in couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 140, 223–256.CrossRefGoogle Scholar
Lyon, M. & Leal, L. 1998 An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 1. Monodisperse systems. J. Fluid Mech. 363, 25–56.CrossRefGoogle Scholar
MacKenzie, J., Soderberg, D., Swerin, A. & Lundell, F. 2018 Turbulent stress measurements of fibre suspensions in a straight pipe. Phys. Fluids 30 (2), 025104.CrossRefGoogle Scholar
Marchisio, D. L. & Fox, R. O. 2013 Computational Models for Polydisperse Particulate and Multiphase Systems. Cambridge University Press.CrossRefGoogle Scholar
Matousek, V. 2009 Pipe-wall friction in vertical sand-slurry flows. Particul. Sci. Technol. 27 (5), 456–468.CrossRefGoogle Scholar
Maxey, M. R. 1987 The gravitational settling of aerosol-particles in homogeneous turbulence and random flow-fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
Mena, S. E. 2016 Experimental Studies of Fluid-solid Flows in Turbulent Dilute and Laminar Concentrated Regimes. University of Florida.Google Scholar
Michaelides, E. 2006 Particles, Bubbles & Drops: Their Motion, Heat and Mass Transfer. World Scientific.CrossRefGoogle Scholar
Michaelides, E., Crowe, C. T. & Schwarzkopf, J. D. 2017 Multiphase Flow Handbook, 2nd edn. CRC Press, Taylor & Francis Group.Google Scholar
Modarress, D., Tan, H. & Elghobashi, S. 1983 Two-component LDA measurement in a two-phase turbulent jet. AIAA J. 22 (5), 624–630.CrossRefGoogle Scholar
Mostafa, A., Mongia, H., Mcdonell, V. & Samuelsen, G. 1989 Evolution of particle-laden jet flows - a theoretical and experimental-study. AIAA J. 27 (2), 167–183.CrossRefGoogle Scholar
Mychkovsky, A., Rangarajan, D. & Ceccio, S. 2012 LDV measurements and analysis of gas and particulate phase velocity profiles in a vertical jet plume in a 2D bubbling fluidized bed: Part I: a two-phase LDV measurement technique. Powder Technol. 220, 55–62.CrossRefGoogle Scholar
Nouri, J. M., Whitelaw, J. H. & Yianneskis, M. 1987 Particle motion and turbulence in dense two-phase flows. Intl J. Multiphase Flow 13 (6), 729–739.CrossRefGoogle Scholar
Oliveira, J. L. G., van der Geld, C. W. M. & Kuerten, J. G. M. 2017 Concentration and velocity statistics of inertial particles in upward and downward pipe flow. J. Fluid Mech. 822, 640–663.CrossRefGoogle Scholar
Pepple, M. A.2010 Benchmark data and analysis of dilute turbulent fluid–particle flow in viscous and transitional regimes. Gainesville, FL: University of Florida.Google Scholar
Pepple, M. A., Curtis, J. S. & Yurteri, C. U. 2010 Variation in measurements of turbulence intensity in pipe flow. I. Re. Ch. E. 2 (3), 337–342.Google Scholar
Portela, L. M. & Oliemans, R. V. A. 2002 Direct and large eddy simulation of particle-laden flows using the point-particle approach. In Direct and Large Eddy Simulations IV (ed. Geurts, B., Friedrich, R. & Metais, O.), pp. 453–460. Springer.Google Scholar
Ristroph, L. 2018 Sculpting with flow. J. Fluid Mech. 838, 1–4.CrossRefGoogle Scholar
Rowe, P. N. 1961 Drag forces in a hydraulic model of a fluidized bed: II. Trans. Inst. Chem. Engng 39, 175–180.Google Scholar
Savage, S. B. & Sayed, M. 1984 Stresses developed by dry cohesionless granular materials sheared in an annular shear cell. J. Fluid Mech. 142, 391–430.CrossRefGoogle Scholar
Sharp, B. B. & O’Neill, I. C. 1971 Lateral diffusion of large particles in turbulent pipe flow. J. Fluid Mech. 45, 575–584.CrossRefGoogle Scholar
Sheen, H., Jou, B. & Lee, Y. 1994 Effect of particle-size on a 2-phase turbulent jet. Exp. Therm. Fluid Sci. 8 (4), 315–327.CrossRefGoogle Scholar
Shokri, R., Ghaemi, S., Nobes, D. S. & Sanders, R. S. 2017 Investigation of particle-laden turbulent pipe flow at high-Reynolds-number using particle image/tracking velocimetry (PIV/PTV). Intl J. Multiphase Flow 89, 136–149.CrossRefGoogle Scholar
Shuen, J., Solomon, A. S. P., Zhang, Q. F. & Faeth, G. M.1983 A theoretical and experimental study of turbulent particle-laden jets. NASA Tech. Rep. No. CR-168293, pp. 1–102.Google Scholar
Squires, K. & Eaton, J. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3 (5), 1169–1179.CrossRefGoogle Scholar
Stone, H. A. 2017 Seeking simplicity for the understanding of multiphase flows. Phys. Rev. Fluids. 2 (10), 100507.CrossRefGoogle Scholar
Subramaniam, S. & Balachandar, S. 2018 Towards combined deterministic and statistical approaches to modeling dispersed multiphase flows. In Droplets and Sprays: Applications for Combustion and Propulsion (ed. Basu, S., Agarwal, A. K., Mukhopadhyay, A. et al. ), pp. 7–42. Springer.CrossRefGoogle Scholar
Sundaresan, S. 2000 Modeling the hydrodynamics of multiphase flow reactors: current status and challenges. AIChE J. 46 (6), 1102–1105.CrossRefGoogle Scholar
Talmon, A. M. 2013 Analytical model for pipe wall friction of pseudo-homogenous sand slurries. Particul. Sci. Technol. 31 (3), 264–270.CrossRefGoogle Scholar
Tanaka, T. & Eaton, J. K. 2010 Sub-Kolmogorov resolution partical image velocimetry measurements of particle-laden forced turbulence. J. Fluid Mech. 643, 177–206.CrossRefGoogle Scholar
Tanaka, T. & Eaton, J. K. 2008 Classification of turbulence modification by dispersed spheres using a novel dimensionless number. Phys. Rev. Lett. 101 (11), 114502.CrossRefGoogle ScholarPubMed
Tenneti, S. & Subramaniam, S. 2014 Particle-resolved direct numerical simulation for gas–solid flow model development. Annu. Rev. Fluid Mech. 46, 199–230.CrossRefGoogle Scholar
Theofanous, T. G. & Sullivan, J. 1982 Turbulence in two-phase dispersed flows. J. Fluid Mech. 116, 343–362.CrossRefGoogle Scholar
Tropea, C. 2011 Optical particle characterization in flows. Annu. Rev. Fluid Mech. 43 (1), 399–426.CrossRefGoogle Scholar
Troutt, T. R.2006 Particle and droplet dispersion in turbulent flows. In Multiphase Flow Handbook (ed. C. T. Crowe), pp. 12-81–12-86. CRC Press.Google Scholar
TSI2005. Phase Doppler particle analyzer (PDPA)/laser Doppler velocimeter (LDV). Operations manual. Report no. P/N 1990048, Revision D.Google Scholar
Tsuji, Y., Morikawa, Y. & Shiomi, H. 1984 LDV measurements of an air–solid two-phase flow in a vertical pipe. J. Fluid Mech. (139), 417–434.CrossRefGoogle Scholar
Tsuji, Y. & Morikawa, Y. 1982 LDV measurements of an air–solid two-phase flow in a horizontal pipe. J. Fluid Mech. 120 (1), 385–409.CrossRefGoogle Scholar
Uhlmann, M. 2008 Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20 (5), 053305.CrossRefGoogle Scholar
Varaksin, A., Polezhaev, Y. & Polyakov, A. 2000 Effect of particle concentration on fluctuating velocity of the disperse phase for turbulent pipe flow. Intl J. Heat Fluid Flow 21 (5), 562–567.CrossRefGoogle Scholar
Wen, C. & Yu, Y. 1966 A generalized method for predicting minimum fluidization velocity. AIChE J. 12 (3), 610–612.CrossRefGoogle Scholar
Westerweel, J., Elsinga, G. E. & Adrian, R. J. 2013 Particle image velocimetry for complex and turbulent flows. Annu. Rev. Fluid Mech. 45, 409–436.CrossRefGoogle Scholar
Whitaker, S. 1968 Introduction to Fluid Mechanics. Prentice-Hall.Google Scholar
Wylie, J., Koch, D. & Ladd, A. 2003 Rheology of suspensions with high particle inertia and moderate fluid inertia. J. Fluid Mech. 480, 95–118.CrossRefGoogle Scholar
Yamamoto, Y., Potthoff, M., Tanaka, T., Kajishima, T. & Tsuji, Y. 2001 Large-eddy simulation of turbulent gas–particle flow in a vertical channel: effect of considering inter-particle collisions. J. Fluid Mech. 442, 303–334.CrossRefGoogle Scholar
Yang, T. & Shy, S. 2005 Two-way interaction between solid particles and homogeneous air turbulence: particle settling rate and turbulence modification measurements. J. Fluid Mech. 526, 171–216.CrossRefGoogle Scholar
Yanta, W. & Smith, R. 1973 Measurements of turbulence-transport properties with a laser Doppler velocimeter. In 11th Aerospace Sciences Meeting, Washington, DC, pp. 1–9. American Institute of Aeronautics and Astronautics.Google Scholar
Young, J. & Hanratty, T. 1991 Optical studies on the turbulent motion of solid particles in a pipe-flow. J. Fluid Mech. 231, 665–688.CrossRefGoogle Scholar
Zeng, L., Balachandar, S., Fischer, P. & Najjar, F. 2008 Interactions of a stationary finite-sized particle with wall turbulence. J. Fluid Mech. 594, 271–305.CrossRefGoogle Scholar
Zisselmar, R. & Molerus, O. 1979 Investigation of solid–liquid pipe flow with regard to turbulence modification. Chem. Engng J. 18 (3), 233–239.Google Scholar
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