Numerical validation of novel scaling laws for air–water flows including compressibility and heat transfer

References

• Ambrose, S., Hargreaves, D. M., & Lowndes, I. S. (2016). Numerical modeling of oscillating Taylor bubbles. Engineering Applications of Computational Fluid Mechanics, 10(1), 578–598. https://doi.org/10.1080/19942060.2016.1224737
   Web of Science ®Google Scholar
• Analytical Methods Committee AMCAN86 (2019). Revision of the international system of units (background paper). Royal Society of Chemistry, 11(12), 1577–1579. https://doi.org/10.1039/C9AY90028D
   Web of Science ®Google Scholar
• Bagnold, R. A. (1939). Interim report on wave-pressure research. Journal of the Institution of Civil Engineers, 12(7), 202–226. https://doi.org/10.1680/ijoti.1939.14539
   Google Scholar
• Barenblatt, G. I. (2003). Scaling (Vol. 34). Cambridge University Press.
   Google Scholar
• Brackbill, J. U., Kothe, D. B., & Zemach, C. (1992). A continuum method for modeling surface tension. Journal of Computational Physics, 100(2), 335–354. https://doi.org/10.1016/0021-9991(92)90240-Y
   Web of Science ®Google Scholar
• Bredmose, H., Bullock, G., & Hogg, A. (2015). Violent breaking wave impacts. Part 3. Effects of scale and aeration. Journal of Fluid Mechanics, 765, 82–113. https://doi.org/10.1017/jfm.2014.692
   Web of Science ®Google Scholar
• Carr, K. J., Ercan, A., & Kavvas, M. L. (2015). Scaling and self-similarity of one-dimensional unsteady suspended sediment transport with emphasis on unscaled sediment material properties. Journal of Hydraulic Engineering, 141(5), Article 04015003. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000994
   Web of Science ®Google Scholar
• Catucci, D., Briganti, R., & Heller, V. (2021). Numerical validation of novel scaling laws for air entrainment in water. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477(2255), Article 20210339. https://doi.org/10.1098/rspa.2021.0339
   Web of Science ®Google Scholar
• Catucci, D., Briganti, R., & Heller, V. (2022). Analytical and numerical study of novel scaling laws for air-water flows. In Proceeding of the 39th IAHR World Congress, 4551–4560.
   Google Scholar
• Chanson, H., Aoki, S., & Hoque, A. (2004). Physical modelling and similitude of air bubble entrainment at vertical circular plunging jets. Chemical Engineering Science, 59(4), 747–758. https://doi.org/10.1016/j.ces.2003.11.016
   Web of Science ®Google Scholar
• Chouet, B., Saccorotti, G., Martini, M., Dawson, P., De Luca, G., Milana, G., & Scarpa, R. (1997). Source and path effects in the wave fields of tremor and explosions at Stromboli volcano, Italy. Journal of Geophysical Research: Solid Earth, 102(B7), 15129–15150. https://doi.org/10.1029/97JB00953
   Web of Science ®Google Scholar
• Courant, R., Friedrichs, K., & Lewy, H. (1967). On the partial difference equations of mathematical physics. IBM Journal of Research and Development, 11(2), 215–234. https://doi.org/10.1147/rd.112.0215
   Web of Science ®Google Scholar
• Davies, R. M., & Taylor, G. I. (1950). The mechanics of large bubbles rising through extended liquids and through liquids in tubes. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 200(1062), 375–390. https://doi.org/10.1098/rspa.1950.0023
   Web of Science ®Google Scholar
• Ercan, A., & Kavvas, M. L. (2015). Self-similarity in incompressible Navier-Stokes equations. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), Article 123126. https://doi.org/10.1063/1.4938762
   Web of Science ®Google Scholar
• Ercan, A., & Kavvas, M. L. (2017). Scaling relations and self-similarity of 3-dimensional Reynolds-averaged Navier-Stokes equations. Scientific Reports, 7(1), Article 6416. https://doi.org/10.1038/s41598-017-06669-z
   PubMed Web of Science ®Google Scholar
• Felder, S., & Chanson, H. (2009). Turbulence, dynamic similarity and scale effects in high-velocity free-surface flows above a stepped chute. Experiments in Fluids, 47(1), 1–18. https://doi.org/10.1007/s00348-009-0628-3
   Web of Science ®Google Scholar
• Ferreira, J. P., Buttarazzi, N., Ferras, D., & Covas, D. I. (2021). Effect of an entrapped air pocket on hydraulic transients in pressurized pipes. Journal of Hydraulic Research, 59(6), 1018–1030. https://doi.org/10.1080/00221686.2020.1862323
   Web of Science ®Google Scholar
• Greenshields, C. J. (2019). The OpenFOAM foundation user guide 7.0. OpenFOAM Foundation Ltd.
   Google Scholar
• Heller, V. (2011). Scale effects in physical hydraulic engineering models. Journal of Hydraulic Research, 49(3), 293–306. https://doi.org/10.1080/00221686.2011.578914
   Web of Science ®Google Scholar
• Heller, V. (2017). Self-similarity and Reynolds number invariance in Froude modelling. Journal of Hydraulic Research, 55(3), 293–309. https://doi.org/10.1080/00221686.2016.1250832
   Web of Science ®Google Scholar
• Henriksen, R. N. (2015). Scale invariance: Self-similarity of the physical world. John Wiley & Sons.
   Google Scholar
• Hughes, S. A. (1993). Physical models and laboratory techniques in coastal engineering (Vol. 7). World Scientific.
   Google Scholar
• James, M. R., Lane, S. J., Chouet, B., & Gilbert, J. S. (2004). Pressure changes associated with the ascent and bursting of gas slugs in liquid-filled vertical and inclined conduits. Journal of Volcanology and Geothermal Research, 129(1-3), 61–82. https://doi.org/10.1016/S0377-0273(03)00232-4
   Web of Science ®Google Scholar
• Kiger, K. T., & Duncan, J. H. (2012). Air-entrainment mechanisms in plunging jets and breaking waves. Annual Review of Fluid Mechanics, 44, 563–596. https://doi.org/10.1146/fluid.2012.44.issue-1
   Web of Science ®Google Scholar
• Kline, S. J. (1965). Similitude and approximation theory. McGraw-Hill.
   Google Scholar
• Launder, B. E., & Spalding, D. B. (1974). The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 3(2), 269–289. https://doi.org/10.1016/0045-7825(74)90029-2
   Google Scholar
• Lie, S. (1880). Theorie der Transformationsgruppen I. Mathematische Annalen, 16(4), 441–528. https://doi.org/10.1007/BF01446218
   Google Scholar
• Lin, P., Xiong, Y.-Y., Zuo, C., & Shi, J.-K. (2021). Verification of similarity of scaling laws in tunnel fires with natural ventilation. Fire Technology, 57(4), 1611–1635. https://doi.org/10.1007/s10694-020-01084-9
   Web of Science ®Google Scholar
• Llewellin, E. W., Del Bello, E., Taddeucci, J., Scarlato, P., & Lane, S. J. (2012). The thickness of the falling film of liquid around a Taylor bubble. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468(2140), 1041–1064. https://doi.org/10.1098/rspa.2011.0476
   Web of Science ®Google Scholar
• Müller, G. (2019). Energy dissipation through entrained air compression in plunging jets. Journal of Hydraulic Research, 58(3), 541–547. https://doi.org/10.1080/00221686.2019.1609105
   Web of Science ®Google Scholar
• Peregrine, D. H., & Thais, L. (1996). The effect of entrained air in violent water wave impacts. Journal of Fluid Mechanics, 325, 377–397. https://doi.org/10.1017/S0022112096008166
   Web of Science ®Google Scholar
• Pfister, M., & Chanson, H. (2014). Two-phase air-water flows: Scale effects in physical modeling. Journal of Hydrodynamics, 26(2), 291–298. https://doi.org/10.1016/S1001-6058(14)60032-9
   Web of Science ®Google Scholar
• Polyanin, A. D., & Manzhirov, A. V. (2008). Handbook of integral equations. Chapman and Hall/CRC.
   Google Scholar
• Pope, S. B. (2000). Turbulent flow. Cambridge University Press.
   Google Scholar
• Pringle, C. C. T., Ambrose, S., Azzopardi, B. J., & Rust, A. C. (2015). The existence and behaviour of large diameter Taylor bubbles. International Journal of Multiphase Flow, 72, 318–323. https://doi.org/10.1016/j.ijmultiphaseflow.2014.04.006
   Web of Science ®Google Scholar
• Roenby, J., Bredmose, H., & Jasak, H. (2016). A computational method for sharp interface advection. Royal Society Open Science, 3(11), Article 160405. https://doi.org/10.1098/rsos.160405
   Web of Science ®Google Scholar
• Shin, S. C., Lee, G. N., Jung, K. H., Park, H. J., Park, I. R., & Suh, S. B. (2021). Numerical study on Taylor bubble rising in pipes. Journal of Ocean Engineering and Technology, 35(1), 38–49. https://doi.org/10.26748/KSOE.2020.045
   Google Scholar
• Stagonas, D., Warbrick, D., Muller, G., & Magagna, D. (2011). Surface tension effects on energy dissipation by small scale, experimental breaking waves. Coastal Engineering, 58(9), 826–836. https://doi.org/10.1016/j.coastaleng.2011.05.009
   Web of Science ®Google Scholar
• Van Wylen, G. J., & Sonntag, R. E. (1985). Fundamentals of classical thermodynamics (Vol. 3). John Wiley & Son.
   Google Scholar
• Vereide, K., Lia, L., & Nielsen, T. K. (2015). Hydraulic scale modelling and thermodynamics of mass oscillations in closed surge tanks. Journal of Hydraulic Research, 53(4), 519–524. https://doi.org/10.1080/00221686.2015.1050077
   Web of Science ®Google Scholar
• Zhang, X. Y., Leung, C. F., & Lee, F. H. (2009). Centrifuge modelling of caisson breakwater subject to wave-breaking impacts. Ocean Engineering, 36(12-13), 914–929. https://doi.org/10.1016/j.oceaneng.2009.06.006
   Web of Science ®Google Scholar
• Zhou, L., Liu, D., & Karney, B. (2013). Investigation of hydraulic transients of two entrapped air pockets in a water pipeline. Journal of Hydraulic Engineering, 139(9), 949–959. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000750
   Web of Science ®Google Scholar
• Zohuri, B. (2015). Dimensional analysis and self-similarity methods for engineers and scientists. Springer.
   Google Scholar