A mass conserving level set method for detailed numerical simulation of liquid atomization. (English) Zbl 1349.76847
Summary: An improved mass conserving level set method for detailed numerical simulations of liquid atomization is developed to address the issue of mass loss in the existing level set method. This method introduces a mass remedy procedure based on the local curvature at the interface, and in principle, can ensure the absolute mass conservation of the liquid phase in the computational domain. Three benchmark cases, including Zalesak’s disk, a drop deforming in a vortex field, and the binary drop head-on collision, are simulated to validate the present method, and the excellent agreement with exact solutions or experimental results is achieved. It is shown that the present method is able to capture the complex interface with second-order accuracy and negligible additional computational cost. The present method is then applied to study more complex flows, such as a drop impacting on a liquid film and the swirling liquid sheet atomization, which again, demonstrates the advantages of mass conservation and the capability to represent the interface accurately.
MSC:
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
liquid atomization; interface capturing; level set method; mass conservation; swirl atomizationSoftware:
H-GTaRReferences:
| [1] | Harlow, F. H.; Welch, J. E., Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface, Phys. Fluids, 8, 2182-2189 (1965) · Zbl 1180.76043 |
| [2] | Daly, B. J., A numerical study of two-fluid Rayleigh-Taylor instability, Phys. Fluids, 10, 297-307 (1967) · Zbl 0147.45806 |
| [3] | Daly, B. J.; Pracht, W. E., Numerical study of density-current surges, Phys. Fluids, 11, 15-30 (1968) · Zbl 0153.57103 |
| [4] | Gorokhovski, M.; Herrmann, M., Modeling primary atomization, Annu. Rev. Fluid Mech., 40, 343-366 (2008) · Zbl 1232.76058 |
| [5] | Sethian, J. A.; Smereka, P., Level set methods for fluid interfaces, Annu. Rev. Fluid Mech., 35, 341-372 (2003) · Zbl 1041.76057 |
| [6] | Denner, F.; van der Heul, D. R.; Oud, G. T.; Villar, M. M.; Neto, A.d. S.; van Wachem, B. G.M., Comparative study of mass-conserving interface capturing frameworks for two-phase flows with surface tension, Int. J. Multiph. Flow, 61, 37-47 (2014) |
| [7] | Amiri, H. A.A.; Hamouda, A. A., Evaluation of level set and phase field methods in modeling two phase flow with viscosity contrast through dual-permeability porous medium, Int. J. Multiph. Flow, 52, 22-34 (2013) |
| [8] | Kim, J., Phase-field models for multi-component fluid flows, Commun. Comput. Phys., 12, 3, 613-661 (2012) · Zbl 1373.76030 |
| [9] | Sun, Y.; Beckermann, C., Sharp interface tracking using the phase-field equation, J. Comput. Phys., 200, 626-653 (2007) · Zbl 1228.76110 |
| [10] | Chiu, P. H.; Lin, Y. T., A conservative phase field method for solving incompressible two-phase flows, J. Comput. Phys., 230, 185-204 (2011) · Zbl 1427.76201 |
| [11] | Losasso, F.; Fedkiw, R.; Osher, S., Spatially adaptive techniques for level set methods and incompressible flow, Comput. Fluids, 35, 995-1010 (2006) · Zbl 1177.76295 |
| [12] | Nourgaliev, R. R.; Wiri, S.; Dinh, N. T.; Theofanous, T. G., On improving mass conservation of level set by reducing spatial discretization errors, Int. J. Multiph. Flow, 31, 1329-1336 (2005) · Zbl 1388.76149 |
| [13] | Salih, A.; Moulic, S. G., Some numerical studies of interface advection properties of level set method, Sadhana, 34, 271-298 (2009) · Zbl 1398.76156 |
| [14] | Sheu, T. W.H.; Yu, C. H.; Chiu, P. H., Development of a dispersively accurate conservative level set scheme for capturing interface in two-phase flows, J. Comput. Phys., 228, 661-686 (2009) · Zbl 1259.76054 |
| [15] | Sheu, T. W.H.; Yu, C. H.; Chiu, P. H., Development of level set method with good area preservation to predict interface in two-phase flows, Int. J. Numer. Methods Fluids, 67, 109-134 (2011) · Zbl 1303.76108 |
| [16] | Reed, W. H.; Hill, T. R., Triangular mesh methods for the neutron transport equation (1973), Los Alamos Scientific Laboratory: Los Alamos Scientific Laboratory Los Alamos, NM, Tech. Report LA-UR-73-479 |
| [17] | Rasetarinera, P.; Hussaini, M. Y., An efficient implicit discontinuous spectral Galerkin method, J. Comput. Phys., 172, 718-738 (2001) · Zbl 0986.65093 |
| [18] | Remacle, J. F.; Chevaugeon, N.; Marchandise, A.; Geuzaine, C., Efficient visualization of high-order finite elements, Int. J. Numer. Methods Eng., 69, 750-771 (2007) · Zbl 1194.76226 |
| [19] | Enright, D.; Losasso, F.; Fedkiw, R., A fast and accurate semi-Lagrangian particle level set method, Comput. Struct., 83, 479-490 (2005) |
| [20] | Strain, J., Semi-Lagrangian methods for level set equations, J. Comput. Phys., 151, 498-533 (1999) · Zbl 0942.76060 |
| [21] | Xiu, D.; Karniadakis, G. E., A semi-Lagrangian high-order method for Navier-Stokes equations, J. Comput. Phys., 172, 658-684 (2001) · Zbl 1028.76026 |
| [22] | Adalsteinsson, D.; Sethian, J. A., The fast construction of extension velocities in level set methods, J. Comput. Phys., 148, 2-22 (1999) · Zbl 0919.65074 |
| [23] | Ovsyannikov, A.; Sabelnikov, V.; Gorokhovski, M., A new level set equation and its numerical assessments, (CTR Proceedings of the Summer Program (2012)) |
| [24] | Chopp, D. L., Another look at velocity extensions in the level set method, SIAM J. Sci. Comput., 31, 3255-3273 (2009) · Zbl 1204.65102 |
| [25] | Sabelnikov, V.; Ovsyannikov, A. Y.; Gorokhovski, M., Modified level set equation and its numerical assessment, J. Comput. Phys., 278, 1-30 (2014) · Zbl 1349.65331 |
| [26] | Olsson, E.; Kreiss, G., A conservative level set method for two phase flow, J. Comput. Phys., 210, 225-246 (2005) · Zbl 1154.76368 |
| [27] | Olsson, E.; Kreiss, G.; Zahedi, S., A conservative level set method for two phase flow II, J. Comput. Phys., 225, 785-807 (2007) · Zbl 1256.76052 |
| [28] | Xiao, F.; Honma, Y.; Kono, T., A simple algebraic interface capturing scheme using hyperbolic tangent function, Int. J. Numer. Methods Fluids, 48, 1023-1040 (2005) · Zbl 1072.76046 |
| [29] | Walker, C.; Muller, B., A conservative level set method for sharp interface multiphase flow simulation, (ECCOMAS CFD (2010)) |
| [30] | Desjardins, O.; Moureau, V.; Pitsch, H., An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys., 227, 8395-8416 (2008) · Zbl 1256.76051 |
| [31] | Owkes, M.; Desjardins, O., A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows, J. Comput. Phys., 249, 275-302 (2013) · Zbl 1427.76218 |
| [32] | Nonomura, T.; Kitamura, K.; Fujii, K., A simple interface sharpening technique with a hyperbolic tangent function applied to compressible two-fluid modeling, J. Comput. Phys., 258, 95-117 (2014) · Zbl 1349.76514 |
| [33] | Kohno, H.; Nave, J. C., A new method for the level set equation using a hierarchical-gradient truncation and remapping technique, Comput. Phys. Commun., 184, 1547-1554 (2013) · Zbl 1301.65100 |
| [34] | Sussman, M.; Smereka, P.; Osher, S., A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114, 146-159 (1994) · Zbl 0808.76077 |
| [35] | Sussman, M.; Fatemi, E.; Smereka, P.; Osher, S., An improved level set method for incompressible two-phase flows, Comput. Fluids, 27, 663-680 (1998) · Zbl 0967.76078 |
| [36] | Sussman, M.; Fatemi, E., An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow, SIAM J. Sci. Comput., 20, 1165-1191 (1999) · Zbl 0958.76070 |
| [37] | Russo, G.; Smereka, P., A remark on computing distance functions, J. Comput. Phys., 163, 51-67 (2000) · Zbl 0964.65089 |
| [38] | Hartmann, D.; Meinke, M.; Schröder, W., Differential equation based constrained reinitialization for level set methods, J. Comput. Phys., 227, 6821-6845 (2008) · Zbl 1189.76366 |
| [39] | Hartmann, D.; Meinke, M.; Schröder, W., The constrained reinitialization equation for level set methods, J. Comput. Phys., 229, 1514-1535 (2010) · Zbl 1329.76259 |
| [40] | Chang, Y. C.; Hou, T. Y.; Merriman, B.; Osher, S., A level set formulation of Eulerian interface capturing methods for incompressible fluid flows, J. Comput. Phys., 124, 449-464 (1996) · Zbl 0847.76048 |
| [41] | McCaslin, L. O.; Desjardins, O., A localized re-initialization equation for the conservative level set method, J. Comput. Phys., 262, 408-426 (2014) · Zbl 1349.76506 |
| [42] | Sethian, J. A., Level Set Methods and Fast Marching Methods (1999), Cambridge University Press · Zbl 0929.65066 |
| [43] | Desjardins, O.; Pitsch, H., A spectrally refined interface approach for simulating multiphase flows, J. Comput. Phys., 228, 1658-1677 (2009) · Zbl 1409.76096 |
| [44] | Brackbill, J. U.; Kothe, D. B.; Zemach, C., A continuum method for modeling surface tension, J. Comput. Phys., 100, 335-354 (1992) · Zbl 0775.76110 |
| [45] | Ausas, R. F.; Dari, E. A.; Buscaglia, G. C., A geometric mass-preserving redistancing scheme for the level set function, Int. J. Numer. Methods Fluids, 65, 989-1010 (2011) · Zbl 1444.76084 |
| [46] | Salih, A.; Moulic, G., A mass conservation scheme for level set method applied to multiphase incompressible flows, Int. J. Comput. Methods Eng. Sci. Mech., 14, 271-289 (2013) · Zbl 07871349 |
| [47] | Sussman, M.; Puckett, E. G., A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows, J. Comput. Phys., 162, 301-337 (2000) · Zbl 0977.76071 |
| [48] | Sussman, M., A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles, J. Comput. Phys., 187, 110-136 (2003) · Zbl 1047.76085 |
| [49] | Son, G., Efficient implementation of a coupled level-set and volume-of-fluid method for three dimensional incompressible two-phase flows, Numer. Heat Transf., Part B, Fundam.: Int. J. Comput. Methodol., 43, 549-565 (2003) |
| [50] | Yang, X.; James, A. J.; Lowengrub, J.; Zheng, X.; Cristini, V., An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids, J. Comput. Phys., 217, 364-394 (2006) · Zbl 1160.76377 |
| [51] | Menard, T.; Tanguy, S.; Berlemont, A., Coupling level set/VOF/ghost fluid methods: validation and application to 3D simulation of the primary break-up of a liquid jet, Int. J. Multiph. Flow, 33, 510-524 (2007) |
| [52] | Lv, X.; Zou, Q.; Zhao, Y.; Reeve, D., A novel coupled level set and volume of fluid method for sharp interface capturing on 3D tetrahedral grids, J. Comput. Phys., 229, 2573-2604 (2010) · Zbl 1423.76303 |
| [53] | Wang, Z.; Yang, J.; Stern, F., A new volume-of-fluid method with a constructed distance function on general structured grids, J. Comput. Phys., 231, 3703-3722 (2012) · Zbl 1402.65091 |
| [54] | Wang, Z.; Tong, A. Y., A sharp surface tension modeling method for two-phase incompressible interfacial flows, Int. J. Numer. Methods Fluids, 64, 709-732 (2010) · Zbl 1426.76438 |
| [55] | Sun, D. L.; Tao, W. Q., A coupled volume-of-fluid and level set (VOSET) method for computing incompressible two-phase flows, Int. J. Heat Mass Transf., 53, 645-655 (2010) · Zbl 1303.76126 |
| [56] | Kees, C. E.; Akkerman, I.; Farthing, M. W.; Bazilevs, Y., A conservative level set method suitable for variable-order approximations and unstructured meshes, J. Comput. Phys., 230, 4536-4558 (2011) · Zbl 1416.76214 |
| [57] | Wang, Y.; Simakhina, S.; Sussman, M., A hybrid level set-volume constraint method for incompressible two-phase flow, J. Comput. Phys., 231, 6438-6471 (2012) |
| [58] | van der Pijl, S. P.; Segal, A.; Vuik, C.; Wesseling, P., A mass-conserving level-set method for modeling of multi-phase flows, Int. J. Numer. Methods Fluids, 47, 339-361 (2005) · Zbl 1065.76160 |
| [59] | van der Pijl, S. P.; Segal, A.; Vuik, C.; Wesseling, P., Computing three-dimensional two-phase flows with a mass-conserving level set method, Comput. Vis. Sci., 11, 221-235 (2008) · Zbl 1522.76101 |
| [60] | Enright, D.; Fedkiw, R.; Ferziger, J.; Mitchell, I., A hybrid particle level set method for improved interface capturing, J. Comput. Phys., 183, 83-116 (2002) · Zbl 1021.76044 |
| [61] | Hieber, S. E.; Koumoutsakos, P., A Lagrangian particle level set method, J. Comput. Phys., 210, 342-367 (2005) · Zbl 1076.65087 |
| [62] | Trontin, P.; Vincent, S.; Estivalezes, J. L.; Caltagirone, J. P., A subgrid computation of the curvature by a particle/level-set method. Application to a front-tracking/ghost-fluid method for incompressible flows, J. Comput. Phys., 231, 6990-7010 (2012) |
| [63] | Chiu, P. H.; Lin, Y. T., A conservative phase field method for solving incompressible two-phase flows, J. Comput. Phys., 230, 185-204 (2011) · Zbl 1427.76201 |
| [64] | Sussman, M.; Almgren, A. S.; Bell, J. B.; Colella, P.; Howell, L. H.; Welcome, M. L., An adaptive level set approach for incompressible two-phase flows, J. Comput. Phys., 148, 81-124 (1999) · Zbl 0930.76068 |
| [65] | Fuster, D.; Bague, A.; Boeck, T.; Moyne, L. L.; Leboissetier, A.; Popinet, S.; Ray, P.; Scardovelli, R.; Zaleski, S., Simulation of primary atomization with an octree adaptive mesh refinement and VOF method, Int. J. Multiph. Flow, 35, 550-565 (2009) |
| [66] | Herrmann, M., A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids, J. Comput. Phys., 227, 2674-2706 (2008) · Zbl 1388.76252 |
| [67] | Kim, H.; Liou, M. S., Accurate adaptive level set method and sharpening technique for three dimensional deforming interfaces, Comput. Fluids, 44, 111-129 (2011) · Zbl 1271.76244 |
| [68] | Pai, M. G.; Pitsch, H.; Desjardins, O., Detailed numerical simulations of primary atomization of liquid jets in crossflow, (47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida (2009)) |
| [69] | Pierce, C. D.; Moin, P., Progress-variable approach for large eddy simulation of turbulent combustion (2001), Flow Physics and Computation Division, Dept. Mech. Eng., Standford University, Technical Report TF80 |
| [70] | Zalesak, S. T., Fully multidimensional flux-corrected transport algorithms for fluids, J. Comput. Phys., 31, 335-362 (1979) · Zbl 0416.76002 |
| [71] | Bell, J. B.; Colella, P.; Glaz, H. M., A second order projection method for the incompressible Navier Stokes equations, J. Comput. Phys., 85, 257-283 (1989) · Zbl 0681.76030 |
| [72] | Ashgriz, N.; Poo, J. Y., Coalescence and separation in binary collisions of liquid drops, J. Fluid Mech., 221, 183-204 (1990) |
| [73] | Tanguy, S.; Berlemont, A., Application of a level set method for simulation of droplet collisions, Int. J. Multiph. Flow, 31, 1015-1035 (2005) · Zbl 1135.76560 |
| [74] | Cossali, G. E.; Marengo, M.; Coghe, A.; Zhdanov, S., The role of time in single drop splash on thin film, Exp. Fluids, 36, 888-900 (2004) |
| [75] | Lee, S. H.; Hur, N.; Kang, S., A numerical analysis of drop impact on liquid film by using a level set method, J. Mech. Sci. Technol., 25, 2567-2572 (2011) |
| [76] | Desjardins, O.; Pitsch, H., Detailed numerical investigation of turbulent atomization of liquid jets, At. Sprays, 20, 311-336 (2010) |
| [77] | Shinjo, J.; Umemura, A., Simulation of liquid jet primary breakup: dynamics of ligament and droplet formation, Int. J. Multiph. Flow, 36, 513-532 (2010) |
| [78] | Herrmann, M., On simulating primary atomization using the refined level set grid method, (21st ILASS. 21st ILASS, Orlando (2008)) |
| [79] | Herrmann, M., Detailed numerical simulations of the primary atomization of a turbulent liquid jet in crossflow, (Proceedings of ASME Turbo Expo. Proceedings of ASME Turbo Expo, Orlando (2009)) |
| [80] | Pai, M. G.; Pitsch, H.; Desjardins, O., Detailed numerical simulations of primary atomization of liquid jets in crossflow, (47th AIAA Aerospace Sciences Meeting. 47th AIAA Aerospace Sciences Meeting, Orlando (2009)) |
| [81] | Muppidi, S.; Mahesh, K., Direct numerical simulation of round turbulent jets in crossflow, J. Fluid Mech., 574, 59-84 (2007) · Zbl 1133.76323 |
| [82] | Desjardins, O.; McCaslin, J. O.; Owkes, M.; Brady, P., Direct numerical and large-eddy simulation of primary atomization in complex geometries, At. Sprays, 23, 1001-1048 (2013) |
| [83] | Osher, S.; Fedkiw, R., Motion involving mean curvature, (Level Set Methods and Dynamics Implicit Surfaces (2002), Springer-Verlag), 41-46 |
| [84] | LeVeque, R. J., High-resolution conservative algorithms for advection in incompressible flow, SIAM J. Numer. Anal., 33, 627-665 (1996) · Zbl 0852.76057 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
