VOF/FVM prediction and experimental validation for shear-thinning fluid column collapse. (English) Zbl 1360.76202
Summary: Dam break problems for non-Newtonian fluids can be found in sudden collapse of mine tailings, snow avalanches, debris and lava flows, and casting solidification. A numerical simulation and experimental validation of collapse of a shear-thinning fluid column with a high viscosity is presented. The 2D fluid mechanics, described in terms of the non-linear coupled continuity and momentum equations, was solved by the finite volume method (FVM) with the Pressure Implicit with Splitting of Operators (PISO) coupling algorithm and the volume of fluid method (VOF). The shear-thinning fluid column that collapses was described by the rheological model of Carreau-Yasuda. The numerical results obtained for the instantaneous position of the free surface were validated with 7% accuracy in comparison with experimental measurements, determining that when a small container is used the walls affect the transport of fluid, causing a creeping flow.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76T99 | Multiphase and multicomponent flows |
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 76M28 | Particle methods and lattice-gas methods |
References:
| [1] | Topin, V.; Dubois, F.; Monerie, Y.; Perales, F.; Wachs, A., Micro-rheology of dense particulate flows: application to immersed avalanches, J. Non-Newton. Fluid Mech., 166, 63-72 (2011) · Zbl 1281.76047 |
| [2] | Kohno, H.; Tanahashi, T., Numerical analysis of moving interfaces using a level set method coupled with adaptive mesh refinement, Internat. J. Numer. Methods Fluids, 45, 921-944 (2004) · Zbl 1085.76056 |
| [3] | Hu, C.; Sueyoshi, M., Numerical simulation and experiment on dam break problem, J. Mar. Sci. Appl., 9, 109-114 (2010) |
| [5] | Ancey, Ch.; Cochard, S., The dam-break problem for Herschel-Bulkley viscoplastic fluids down steep flumes, J. Non-Newton. Fluid Mech., 158, 18-35 (2009) · Zbl 1274.76008 |
| [6] | Cruchaga, M.; Celentano, D.; Tezduyar, T., Collapse of a liquid column: numerical simulation and experimental validation, Comput. Mech., 39, 453-476 (2007) · Zbl 1160.76013 |
| [7] | Cruchaga, M.; Celentano, D.; Tezduyar, T., Moving-interface computations with the edge-tracked interface locator technique (ETILT), Internat. J. Numer. Methods Fluids, 15, 65-75 (2005) · Zbl 1134.76382 |
| [8] | Steffe, J., Rheological Methods in Food Process Engineering (1996), Freeman Press: Freeman Press Michigan, USA |
| [9] | Shamekhi, A.; Sadeghy, K., Cavity flow simulation of Carreau-Yasuda non-Newtonian fluids using PIM mesh free method, Appl. Math. Model., 33, 4131-4145 (2009) · Zbl 1205.76163 |
| [10] | Balan, C.; Broboana, D.; Balan, C., Mixing process of immiscible fluids in micro channels, Int. J. Heat Fluid Flow, 31, 1125-1133 (2010) |
| [11] | Janßen, C.; Grilli, S.; Krafczyk, M., On enhanced non-linear free surface flow simulations with a hybrid LBM-VOF model, Comput. Math. Appl., 65, 211-229 (2013) · Zbl 1268.76046 |
| [12] | Tezduyar, T.; Behr, M.; Liu, J., A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests, Comput. Methods Appl. Mech. Engrg., 94, 339-351 (1992) · Zbl 0745.76044 |
| [13] | Oñate, E.; García, J.; Idelsohn, S. R.; Del Pin, F., Finite calculus formulations for finite element analysis of imcompressible flows. Eulerian, ALE and Lagrangian approaches, Comput. Methods Appl. Mech. Engrg., 195, 3001-3037 (2006) · Zbl 1115.76051 |
| [14] | Wang, J. P.; Borthwick, A.; Taylor, R., Finite-volume VOF method on dynamically adaptative quadtree grids, Internat. J. Numer. Methods Fluids, 00, 1-22 (2003) |
| [15] | Sethian, J. A., Evaluation, implementation, and application of level set and fast marching methods for advancing fronts, J. Comput. Phys., 169, 503-555 (2001) · Zbl 0988.65095 |
| [16] | Kim, M.; Lee, W., A new VOF-based numerical scheme for the simulation of fluid flow with free surface. Part I: new free surface-tracking algorithm and its verification, Internat. J. Numer. Methods Fluids, 42, 765-790 (2003) · Zbl 1143.76536 |
| [17] | Wacławczyk, T.; Koronowicz, T., Modelling of the free surface flows with high resolution schemes, Chem. Proc. Eng., 27, 3/1, 783-802 (2006) |
| [18] | Ubbink, O.; Issa, R. I., Method for capturing sharp fluid interfaces on arbitrary meshes, J. Comput. Phys., 153, 26-50 (1999) · Zbl 0955.76058 |
| [19] | Wacławczyk, T.; Koronowicz, T., Comparison of CICSAM and HRIC high-resolution schemes for interface capturing, J. Theoret. Appl. Mech., 46, 325-345 (2008) |
| [20] | Rico, M.; Benito, G.; Díez-Herrero, A., Floods from tailings dam failures, J. Hazard. Mater., 154, 79-87 (2008) |
| [21] | Stefanescu, D., Science and Engineering of Casting Solidification, 380 (2009), Springer Editorial |
| [22] | Leonard, B. P., The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection, Comput. Methods Appl. Mech. Engrg., 88, 17-74 (1991) · Zbl 0746.76067 |
| [23] | Martin, J. C.; Moyce, W. J., An experimental study of collapse of liquid columns on a rigid horizontal plane, Philos. Trans. R. Soc. Lond. Ser. A, 244, 312-324 (1952) |
| [24] | Koshizuka, S.; Tamako, H.; Oka, Y., A particle method for incompressible viscous flow with fluid fragmentation, Comput. Fluid Dyn. J., 4, 29-46 (1995) |
| [25] | Kačeniauskas, A.; Pacevič, R.; Katkevičius, T., Dam break flow simulation on grid, Mater. Phys. Mech., 9, 96-104 (2010) |
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.
