High-fidelity simulations of bubble, droplet and spray formation in breaking waves. (English) Zbl 1381.76365
Summary: High-fidelity simulations of wave breaking processes are performed with a focus on the small-scale structures of breaking waves, such as bubble/droplet size distributions. Very large grids (up to 12 billion grid points) are used in order to resolve the bubbles/droplets in breaking waves at the scale of hundreds of micrometres. Wave breaking processes and spanwise three-dimensional interface structures are identified. It is speculated that the Görtler type centrifugal instability is likely more relevant to the plunging wave breaking instabilities. Detailed air entrainment and spray formation processes are shown. The bubble size distribution shows power-law scaling with two different slopes which are separated by the Hinze scale. The droplet size distribution also shows power-law scaling. The computational results compare well with the available experimental and computational data in the literature. Computational difficulties and challenges for large grid simulations are addressed.
MSC:
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
Software:
hypreReferences:
| [1] | Andreas, E. L.1998A new sea spray generation function for wind speeds up to 32 m s<![CDATA \([^{-1}]]\)>. J. Phys. Oceanogr.28, 2175-2184.10.1175/1520-0485(1998)028<2175:ANSSGF>2.0.CO;2 · doi:10.1175/1520-0485(1998)028<2175:ANSSGF>2.0.CO;2 |
| [2] | Aulisa, E., Manservisi, S., Scardovelli, R. & Zaleski, S.2003A geometrical area-preserving volume-of-fluid advection method. J. Comput. Phys.192, 355-364.10.1016/j.jcp.2003.07.003 · Zbl 1032.76632 · doi:10.1016/j.jcp.2003.07.003 |
| [3] | Brocchini, M. & Peregrine, D. H.2001The dynamics of strong turbulence at free surfaces. Part 1. Description. J. Fluid Mech.449, 225-254.10.1017/S00221120010060121871644 · Zbl 1007.76027 · doi:10.1017/S0022112001006012 |
| [4] | Brucker, K. A., O’Shea, T. T., Dommermuth, D. G. & Adams, P.2010Three-dimensional simulations of deep-water breaking waves. In 28th Symposium on Naval Hydrodynamics, Pasadena, CA, U.S. Office of Naval Research (ONR). |
| [5] | Cartmill, J. & Su, M.1993Bubble size distribution under saltwater and freshwater breaking waves. Dyn. Atmos. Oceans20, 25-31.10.1016/0377-0265(93)90046-A · doi:10.1016/0377-0265(93)90046-A |
| [6] | Chen, G., Kharif, C., Zaleski, S. & Li, J.1999Two-dimensional Navier-Stokes simulation of breaking waves. Phys. Fluids11, 121-133.10.1063/1.869907 · Zbl 1147.76356 · doi:10.1063/1.869907 |
| [7] | Choi, H. & Moin, P.1994Effects of the computational time step on numerical solutions of turbulent flow. J. Comput. Phys.113, 1-4.10.1006/jcph.1994.1112 · Zbl 0807.76051 · doi:10.1006/jcph.1994.1112 |
| [8] | Clift, R., Grace, J. R. & Webber, M. E.1978Bubbles, Drops, and Particles. Academic. |
| [9] | Deane, G. B. & Stokes, M. D.2002Scale dependency of bubble creation mechanisms in breaking waves. Nature418, 839-844.10.1038/nature00967 · doi:10.1038/nature00967 |
| [10] | Derakhti, M. & Kirby, J. T.2014Bubble entrainment and liquid – bubble interaction under unsteady breaking waves. J. Fluid Mech.761, 464-506.10.1017/jfm.2014.637 · Zbl 1306.76049 · doi:10.1017/jfm.2014.637 |
| [11] | Drazen, D. A., Melville, W. K. & Lenain, L.2008Inertial scaling of dissipation in unsteady breaking waves. J. Fluid Mech.611, 307-332.10.1017/S00221120080028262456767 · Zbl 1151.76387 · doi:10.1017/S0022112008002826 |
| [12] | Duncan, J. H.1981An experimental investigation of breaking waves produced by a towed hydrofoil. Proc. R. Soc. Lond. A377 (1770), 331-348.10.1098/rspa.1981.0127 · doi:10.1098/rspa.1981.0127 |
| [13] | Falgout, R. D., Jones, J. E. & Yang, U. M.2006The design and implementation of hypre, a library of parallel high performance preconditioners. In Numerical Solution of Partial Differential Equations on Parallel Computers (ed. A.Bruaset & A.Tveito), Lecture Notes in Computational Science and Engineering, vol. 51, pp. 267-294. Springer.10.1007/3-540-31619-1_8 · Zbl 1097.65059 |
| [14] | Garrett, C., Li, M. & Farmer, D.2000The connection between bubble size spectra and energy dissipation rates in the upper ocean. J. Phys. Oceanogr.30, 2163-2171.10.1175/1520-0485(2000)030<2163:TCBBSS>2.0.CO;2 · doi:10.1175/1520-0485(2000)030<2163:TCBBSS>2.0.CO;2 |
| [15] | Gui, L., Yoon, H. & Stern, F.2014a Experimental and theoretical investigation of instabilities for flow over a bump in a shallow water flume with steady downstream wave train. Tech. Rep. 487. IIHR, The University of Iowa. |
| [16] | Gui, L., Yoon, H. & Stern, F.2014bTechniques for measuring bulge-car pattern of free surface deformation and related velocity distribution in shallow water flow over a bump. Exp. Fluids55 (4), 1721.10.1007/s00348-014-1721-9 · doi:10.1007/s00348-014-1721-9 |
| [17] | Herrmann, M.2010A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure. J. Comput. Phys.229 (3), 745-759.10.1016/j.jcp.2009.10.009 · Zbl 1253.76126 · doi:10.1016/j.jcp.2009.10.009 |
| [18] | Hinze, J. O.1955Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J.1 (3), 289-295.10.1002/aic.690010303 · doi:10.1002/aic.690010303 |
| [19] | Iafrati, A.2009Numerical study of the effects of the breaking intensity on wave breaking flows. J. Fluid Mech.622, 371-411.10.1017/S0022112008005302 · Zbl 1165.76327 · doi:10.1017/S0022112008005302 |
| [20] | Iafrati, A.2010Air – water interaction in breaking wave events: quantitative estimates of drops and bubbles. In 28th Symposium on Naval Hydrodynamics, Pasadena, CA, U.S. Office of Naval Research (ONR). |
| [21] | Jeong, J. & Hussain, F.1995On the identification of a vortex. J. Fluid Mech.285, 69-94.10.1017/S00221120950004621317900 · Zbl 0847.76007 · doi:10.1017/S0022112095000462 |
| [22] | Jiang, G.-S. & Shu, C.-W.1996Efficient implementation of weighted {ENO} schemes. J. Comput. Phys.126 (1), 202-228.10.1006/jcph.1996.01301391627 · Zbl 0877.65065 · doi:10.1006/jcph.1996.0130 |
| [23] | Kang, D., Ghosh, S., Reins, G., Koo, B., Wang, Z. & Stern, F.2012Impulsive plunging wave breaking downstream of a bump in a shallow water flume. Part I. Experimental observations. J. Fluids Struct.32, 104-120.10.1016/j.jfluidstructs.2011.10.010 · doi:10.1016/j.jfluidstructs.2011.10.010 |
| [24] | Kiger, K. T. & Duncan, J. H.2012Air entrainment mechanisms in plunging jets and breaking waves. Annu. Rev. Fluid Mech.44, 563-596.10.1146/annurev-fluid-122109-1607242882609 · Zbl 1352.76026 · doi:10.1146/annurev-fluid-122109-160724 |
| [25] | Koo, B., Wang, Z., Yang, J. & Stern, F.2012Impulsive plunging wave breaking downstream of a bump in a shallow water flume. Part II. Numerical simulations. J. Fluids Struct.32, 121-134.10.1016/j.jfluidstructs.2011.10.011 · doi:10.1016/j.jfluidstructs.2011.10.011 |
| [26] | Leonard, B. P.1979A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Meth. Appl. Mech. Engng19 (1), 59-98.10.1016/0045-7825(79)90034-3 · Zbl 0423.76070 · doi:10.1016/0045-7825(79)90034-3 |
| [27] | Lhuissier, H. & Villermaux, E.2012Bursting bubble aerosols. J. Fluid Mech.696, 5-44.10.1017/jfm.2011.418 · Zbl 1250.76166 · doi:10.1017/jfm.2011.418 |
| [28] | Li, X., Arienti, M., Soteriou, M. C. & Sussman, M. M.2010 Towards an efficient, high-fidelity methodology for liquid jet atomization computations. AIAA Paper 2010-210. |
| [29] | Loewen, M. R., ODor, M. A. & Skafel, M. G.1996Bubbles entrained by mechanically generated breaking waves. J. Geophys. Res.101, 20759-20820.10.1029/96JC01919 · doi:10.1029/96JC01919 |
| [30] | Longuet-Higgins, M.1995On the disintegration of the jet in a plunging breaker. J. Phys. Oceanogr.25, 2458-2462.10.1175/1520-0485(1995)025<2458:OTDOTJ>2.0.CO;2 · doi:10.1175/1520-0485(1995)025<2458:OTDOTJ>2.0.CO;2 |
| [31] | Lubin, P. & Glockner, S.2015Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments. J. Fluid Mech.767, 364-393.10.1017/jfm.2015.623378291 · doi:10.1017/jfm.2015.62 |
| [32] | Lubin, P., Vincent, S., Abadie, S. & Caltagirone, J. P.2006Three-dimensional large eddy simulation of air entrainment under plunging breaking waves. Coast. Engng53, 631-655.10.1016/j.coastaleng.2006.01.001 · doi:10.1016/j.coastaleng.2006.01.001 |
| [33] | Mori, N. & Kakuno, S.2008Aeration and bubble measurements of coastal breaking waves. Fluid Dyn. Res.40 (7-8), 616-626.10.1016/j.fluiddyn.2007.12.013 · Zbl 1186.76005 · doi:10.1016/j.fluiddyn.2007.12.013 |
| [34] | Saric, W. S.1994Görtler vortices. Annu. Rev. Fluid Mech.26, 379-409.10.1146/annurev.fl.26.010194.002115 · Zbl 0802.76027 · doi:10.1146/annurev.fl.26.010194.002115 |
| [35] | Saruwatari, A., Watanabe, Y. & Ingram, D. M.2009Scarifying and fingering surfaces of plunging jets. Coast. Engng56 (1112), 1109-1122.10.1016/j.coastaleng.2009.08.007 · doi:10.1016/j.coastaleng.2009.08.007 |
| [36] | Scardovelli, R. & Zaleski, S.2003Interface reconstruction with least-square fit and split Eulerian-Lagrangian advection. Intl J. Numer. Meth. Fluids41, 251-274.10.1002/fld.431 · Zbl 1047.76080 · doi:10.1002/fld.431 |
| [37] | Soloviev, A. & Lukas, R.2006The Near-Surface Layer of the Ocean: Structure, Dynamics and Applications. Springer. |
| [38] | Suh, J., Yang, J. & Stern, F.2011The effect of air – water interface on the vortex shedding from a vertical circular cylinder. J. Fluids Struct.27, 1-22.10.1016/j.jfluidstructs.2010.09.001 · doi:10.1016/j.jfluidstructs.2010.09.001 |
| [39] | Tavakolinejad, M.2010 Air bubble entrainment by breaking bow waves simulated by a <![CDATA \([2d+t]]\)> technique. PhD thesis, University of Maryland. |
| [40] | Towle, D. M.2014 Spray droplet generation by breaking water waves. Master’s thesis, University of Maryland. |
| [41] | Veron, F., Hopkins, C., Harrison, E. L. & Mueller, J. A.2012Sea spray spume droplet production in high wind speeds. Geophys. Res. Lett.39 (16), l16602.10.1029/2012GL052603 · doi:10.1029/2012GL052603 |
| [42] | Wang, Z., Suh, J., Yang, J. & Stern, F.2012b Sharp interface LES of breaking waves by an interface piercing body in orthogonal curvilinear coordinates. AIAA Paper 2012-1111. |
| [43] | Wang, Z., Yang, J., Koo, B. & Stern, F.2009aA coupled level set and volume-of-fluid method for sharp interface simulation of plunging breaking waves. Intl J. Multiphase Flow35, 227-246.10.1016/j.ijmultiphaseflow.2008.11.004 · doi:10.1016/j.ijmultiphaseflow.2008.11.004 |
| [44] | Wang, Z., Yang, J. & Stern, F.2009bAn improved particle correction procedure for the particle level set method. J. Comput. Phys.228 (16), 5819-5837.10.1016/j.jcp.2009.04.0452542917 · Zbl 1177.76333 · doi:10.1016/j.jcp.2009.04.045 |
| [45] | Wang, Z., Yang, J. & Stern, F.2012a High-fidelity simulations of bubble, droplet, and spray formation in breaking waves. HPC Insights, Fall Issue, 5-7. |
| [46] | Wang, Z., Yang, J. & Stern, F.2012cA new volume-of-fluid method with a constructed distance function on general structured grids. J. Comput. Phys.231, 3703-3722.10.1016/j.jcp.2012.01.0222902415 · Zbl 1402.65091 · doi:10.1016/j.jcp.2012.01.022 |
| [47] | Wang, Z., Yang, J. & Stern, F.2012dA simple and conservative operator-splitting semi-Lagrangian volume-of-fluid advection scheme. J. Comput. Phys.231, 4981-4992.10.1016/j.jcp.2012.04.0292929929 · Zbl 1351.76192 · doi:10.1016/j.jcp.2012.04.029 |
| [48] | Watanabe, Y. & Saeki, H.2002Velocity field after wave breaking. Intl J. Numer. Meth. Fluids39, 607-637.10.1002/fld.345 · Zbl 1048.76042 · doi:10.1002/fld.345 |
| [49] | Watanabe, Y., Saeki, H. & Hosking, R.2005Three-dimensional vortex structures under breaking waves. J. Fluid Mech.545, 291-328.10.1017/S00221120050067742263818 · Zbl 1085.76511 · doi:10.1017/S0022112005006774 |
| [50] | Yang, J., Bhushan, S., Suh, J., Wang, Z., Koo, B., Sakamoto, N. & Xing, T.2008Large-eddy simulation of ship flows with wall-layer models on cartesian grids. In 27th Symposium on Naval Hydrodynamics, Seoul, Korea, U.S. Office of Naval Research (ONR). |
| [51] | Yang, J. & Stern, F.2007 A sharp interface method for two-phase flows interacting with moving bodies. AIAA Paper 2007-4578. |
| [52] | Yang, J. & Stern, F.2009Sharp interface immersed-boundary/level-set method for wave – body interactions. J. Comput. Phys.228, 6590-6616.10.1016/j.jcp.2009.05.0472549857 · Zbl 1261.76040 · doi:10.1016/j.jcp.2009.05.047 |
| [53] | Zhou, Z., Sangermano, J., Hsu, T.-J. & Ting, F. C. K.2014A numerical investigation of wave-breaking-induced turbulent coherent structure under a solitary wave. J. Geophys. Res.119 (10), 6952-6973.10.1002/2014JC009854 · doi:10.1002/2014JC009854 |
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