Sharp interface Cartesian grid method. II: A technique for simulating droplet interactions with surfaces of arbitrary shape. (English) Zbl 1154.76358
Summary: A fixed-grid, sharp interface method is developed to simulate droplet impact and spreading on surfaces of arbitrary shape. A finite-difference technique is used to discretize the incompressible Navier-Stokes equations on a Cartesian grid. To compute flow around embedded solid boundaries, a previously developed sharp interface method for solid immersed boundaries is used [Part I, ibid. 210, No. 1, 1–31 (2005; Zbl 1154.76358)]. The ghost fluid method (GFM) is used for fluid-fluid interfaces. The model accounts for the effects of discontinuities such as density and viscosity jumps and singular sources such as surface tension in both bubble and droplet simulations. With a level-set representation of the propagating interface, large deformations of the boundary can be handled easily. The model successfully captures the essential features of interactions between fluid-fluid and solid-fluid phases during impact and spreading. Moving contact lines are modeled with contact angle hysteresis and contact line motion on non-planar surfaces is computed. Experimental observations and other simulation results are used to validate the calculations.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Citations:
Zbl 1154.76358Software:
RIPPLEReferences:
| [1] | Baer, T. A.; Cairncross, R. A.; Schunk, P. R.; Rao, R. R.; Sackinger, P. A., A finite element method for free surface flows of incompressible fluids in three dimensions. Part II: Dynamic wetting lines, International Journal for Numerical Methods in Fluids, 33, 3, 405 (2000) · Zbl 0989.76044 |
| [2] | Bussmann, M.; Mostaghimi, J.; Chandra, S., On a three-dimensional volume tracking model of droplet impact, Physics of Fluids, 11, 6, 1406-1417 (1999) · Zbl 1147.76344 |
| [3] | Dussan, E. B.; Rame, E.; Garoff, S., On identifying the appropriate boundary-conditions at a moving contact line - an experimental investigation, Journal of Fluid Mechanics, 230, 97-116 (1991) |
| [4] | Fedkiw, R.; Liu, X.-D., The ghost fluid method for viscous flows, (Hafez, M.; Chattot, J.-J., Innovative Methods for Numerical Solutions of Partial Differential Equations (2002), World Scientific Publishing: World Scientific Publishing New Jersey), 111-143 · Zbl 1078.76586 |
| [5] | Fukai, J.; Shiiba, Y.; Yamamoto, T.; Miyatake, O.; Poulikakos, D.; Megaridis, C. M.; Zhao, Z., Wetting effects on the spreading of a liquid droplet colliding with a flat surface - experiment and modeling, Physics of Fluids, 7, 2, 236-247 (1995) |
| [6] | Fukai, J.; Zhao, Z.; Poulikakos, D.; Megaridis, C. M.; Miyatake, O., Modeling of the deformation of a liquid droplet impinging upon a flat surface, Physics of Fluids A - Fluid Dynamics, 5, 11, 2588-2599 (1993) · Zbl 0807.76022 |
| [7] | Ghafouri-Azar, R.; Shakeri, S.; Chandra, S.; Mostaghimi, J., Interactions between molten metal droplets impinging on a solid surface, International Journal of Heat and Mass Transfer, 46, 8, 1395-1407 (2003) |
| [8] | Gutierrezmiravete, E.; Lavernia, E. J.; Trapaga, G. M.; Szekely, J.; Grant, N. J., A mathematical-model of the spray deposition process, Metallurgical Transactions A - Physical Metallurgy and Materials Science, 20, 1, 71-85 (1989) |
| [9] | Harlow, F. H.; Shannon, J. P., The splash of liquid droplet, Journal of Applied Physics, 38, 3885 (1967) |
| [10] | Hocking, L. M., Rival contact-angle models and the spreading of drops, Journal of Fluid Mechanics, 239, 671-681 (1992) · Zbl 0754.76022 |
| [11] | D. Jacqmin, An energy approach to the continuum surface method, in: 34th Aerospace Science Meeting, No. AIAA-96-0858, 1996; D. Jacqmin, An energy approach to the continuum surface method, in: 34th Aerospace Science Meeting, No. AIAA-96-0858, 1996 |
| [12] | Kang, M.; Fedkiw, R. P., A boundary condition capturing method for multiphase incompressible flow, Journal of Scientific Computing, 15, 323-360 (2002) · Zbl 1049.76046 |
| [13] | Kang, B. S.; Lee, D. H., On the dynamic behavior of a liquid droplet impacting upon an inclined heated surface, Experiments in Fluids, 29, 4, 380-387 (2000) |
| [14] | D.B. Kothe, R.C. Mjolsness, M.D. Torrey, Ripple: A computer program for incompressible flows with free surfaces, Technical Report LA-12007-MS, 1991; D.B. Kothe, R.C. Mjolsness, M.D. Torrey, Ripple: A computer program for incompressible flows with free surfaces, Technical Report LA-12007-MS, 1991 |
| [15] | Li, Z. L.; Lai, M. C., The immersed interface method for the Navier-Stokes equations with singular forces, Journal of Computational Physics, 171, 2, 822-842 (2001) · Zbl 1065.76568 |
| [16] | Liu, X. D.; Fedkiw, R. P.; Kang, M. J., A boundary condition capturing method for Poisson’s equation on irregular domains, Journal of Computational Physics, 160, 1, 151-178 (2000) · Zbl 0958.65105 |
| [17] | Liu; Huimin; Lavernia, Enrique J.; Rangel, Roger H., Numerical simulation of substrate impact and freezing of droplets in plasma spray processes, Journal of Physics D: Applied Physics, 26, 11, 1900-1908 (1993) |
| [18] | S. Marella, S. Krishnan, H. Liu, H.S. Udaykumar, Sharp interface Cartesian grid method I: an easily implemented technique for 3D moving boundary computations, Journal of Computational Physics (accepted); S. Marella, S. Krishnan, H. Liu, H.S. Udaykumar, Sharp interface Cartesian grid method I: an easily implemented technique for 3D moving boundary computations, Journal of Computational Physics (accepted) · Zbl 1154.76359 |
| [19] | Mostaghimi, J.; Pasandideh-Fard, M.; Chandra, S., Dynamics of splat formation in plasma spray coating process, Plasma Chemistry and Plasma Processing, 22, 1, 59-84 (2002) |
| [20] | D.R. Noble, T.A. Baer, R.R. Rao, Contact angle specification in level-set simulations, Sandia National Laboratories Internal Report, 1994; Obtained by private communication with D.R. Noble; D.R. Noble, T.A. Baer, R.R. Rao, Contact angle specification in level-set simulations, Sandia National Laboratories Internal Report, 1994; Obtained by private communication with D.R. Noble |
| [21] | M. Pasandideh-Fard, Y.M. Qiao, S. Chandra, J. Mostaghimi, Effect of surface tension and contact angle on the spreading of a droplet impacting on a substrate, American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED, Experimental and Numerical Flow Visualization 218 (1995) 53-61; M. Pasandideh-Fard, Y.M. Qiao, S. Chandra, J. Mostaghimi, Effect of surface tension and contact angle on the spreading of a droplet impacting on a substrate, American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED, Experimental and Numerical Flow Visualization 218 (1995) 53-61 |
| [22] | Pasandideh-Fard, M.; Bhola, R.; Chandra, S.; Mostaghimi, J., Deposition of till droplets on a steel plate: simulations and experiments, International Journal of Heat and Mass Transfer, 41, 19, 2929-2945 (1998) |
| [23] | Pasandideh-Fard, M.; Bussmann, M.; Chandra, S.; Mostaghimi, J., Simulating droplet impact on a substrate of arbitrary shape, Atomization and Sprays, 11, 4, 397-414 (2001) |
| [24] | Renardy, M.; Renardy, Y.; Li, J., Numerical simulation of moving contact line problems using a volume-of-fluid method, Journal of Computational Physics, 171, 1, 243-263 (2001) · Zbl 1044.76051 |
| [25] | P. Savic, G.T. Boult, The fluid flow associated with the impact of liquid drops with solid surfaces, in: Proceedings of the Heat Transfer Fluid Mechanics Institute, 1957; P. Savic, G.T. Boult, The fluid flow associated with the impact of liquid drops with solid surfaces, in: Proceedings of the Heat Transfer Fluid Mechanics Institute, 1957 |
| [26] | Smith, K. A.; Solis, F. J.; Chopp, D. L., A projection method for motion of triple junctions by level sets, Interfaces and Free Boundaries, 4, 3, 263-276 (2002) · Zbl 1112.76437 |
| [27] | Sussman, M., An adaptive mesh algorithm for free surface flows in general geometries, (Adaptive Method of Lines (2001), Chapman-Hill/CRC Press: Chapman-Hill/CRC Press Boca Raton, FL), 207-227 |
| [28] | Trapaga, G.; Matthys, E. F.; Valencia, J. J.; Szekely, J., Fluid-flow, heat-transfer, and solidification of molten-metal droplets impinging on substrates - comparison of numerical and experimental results, Metallurgical Transactions B - Process Metallurgy, 23, 6, 701-718 (1992) |
| [29] | Trapaga, G.; Szekely, J., Mathematical-modeling of the isothermal impingement of liquid droplets in spraying processes, Metallurgical Transactions B - Process Metallurgy, 22, 6, 901-914 (1991) |
| [30] | Tsurutani, K.; Yao, M.; Senda, J.; Fujimoto, H., Numerical-analysis of the deformation process of a droplet impinging upon a wall, JSME International Journal Series II - Fluids Engineering Heat Transfer Power Combustion Thermophysical Properties, 33, 3, 555-561 (1990) |
| [31] | Ye, T.; Mittal, R.; Udaykumar, H. S.; Shyy, W., An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries, Journal of Computational Physics, 156, 2, 209-240 (1999) · Zbl 0957.76043 |
| [32] | Zhao, H. K.; Merriman, B.; Osher, S.; Wang, L., Capturing the behavior of bubbles and drops using the variational level set approach, Journal of Computational Physics, 143, 2, 495-518 (1998) · Zbl 0936.76065 |
| [33] | Zheng, L. L.; Zhang, H., An adaptive levelset method for moving-boundary problems: application to droplet spreading and solidification, Numerical Heat Transfer Part B - Fundamentals, 37, 437-454 (2000) |
| [34] | Zoltowski, P., Les couches en alumine effectuees au pistolet a plasma (Plasma gun spraying of aluminum oxide - 1), Revue Internationale des Hautes Temperatures et des Refractaires, 5, 4, 253-265 (1968), (in French) |
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.
