Multi-phase modelling

Multiphase flows with sharp interfaces are found in many industrial applications and fundamental physics problems. For example, the study of fluid-fuel interactions, bubbles and droplets, designing of sprays, boiling flows among others. This type of flows are usually referred as free surface and interfacial flows, since the contact of immiscible fluids or phases in motion produces a thin region that separates them called interface. In detail, interfacial flows are governed by the unsteady Navier-Stokes equations in the variable-density incompressibility limit, additionally, they require the solution of a set of equations that describes the interface topology as it moves due to the velocity field.

In order to accurately solve multiphase flows, the Navier-Stokes equations are fully-conservative discretized in terms of mass, momentum and kinetic energy. In detail, finite-volume numerical schemes, suitable for 3D unstructured meshes, are used to solve the momentum equations. Moreover, different interface-capturing methods, such as: level-set, volume-of-fluid and coupled level-set/volume-of-fluid, are implemented to capture the topology of the phase interface as it evolves in time.

Direct Numerical Simulation of Gravity-Driven Bubbly flows

Gravity-driven bubbly flows play an important role in many natural and industrial processes. Steam generators in nuclear plants, unit operations in chemical engineering such as distillation, absorption, extraction, heterogeneous catalysis and bubble reactors are only a few among a multitude of applications that involve the motion of fluid particles (bubbles or droplets). These applications have motivated a large number of experimental investigations on bubble dynamics, moreover, the development of computers has promoted Direct Numerical Simulation (DNS) of the Navier-Stokes equations as another means of performing controlled experiments, providing a good way to non-invasive measure of bubble flows. Figure (1) illustrates some DNS examples of the rising motion of a swarm of bubbles in a vertical channel, carried out by means of a multiple marker level-set methodology introduced in [1, 2]. Simulations illustrated in Fig. (1) are performed as part of the 10th-call PRACE supercomputing project: “Direct Numerical Simulation of Gravity Driven Bubbly Flows” (see http://www.prace-ri.eu/prace-10th-project-call/ ).

Fig. 1:  Direct numerical simulation of gravity-driven bubbly flows.
(a) Spherical bubbles (b) Deformable bubbles

Interface-capturing methods and two-phase flows

There are multiple methods for DNS of two-phase flows with sharp interfaces, for instance level-set and volume-of-fluid methods. Although the idea behind these methods is similar, their numerical implementation may differ greatly, moreover, each method has advantages and disadvantages, therefore the development and improvement of interface capturing methodologies, and its application to the direct computation of two-phase flows is an intense field of investigation over the last years. Regarding the aforementioned applications, some numerical methods, including their validation and verification, have been reported by the group in [1-4].

 

 
Fig. 2:  Multiple marker level-set method. Droplet collision with a fluid-fluid interface without coalescence. Detailed simulations have been reported in [1].

 

Fig. 3:  Multiple marker level-set method. Binary droplet collision with bouncing outcome. Detailed simulations have been reported in [1].
Fig. 4:  Interfacial flow with topology changes. Oblique coalescence of two deformable bubbles, computed by means of the finite-volume/level-set method introduced in [2]. (a) Time evolution of the bubble shape, (b) Velocity field
 

 

Figure 5: Interfacial flow with topology changes. Impact of a drop (water) fallen down into a liquid film (air as environment fluid). This simulation has been performed by means of the finite-volume/level-set method introduced in [2].
   
 
Fig. 6: Free surface flow. Collapse of a liquid column (water) in a rectangular container (air as environment fluid), computed by means of the finite-volume/level-set method introduced in [2].

Fig. 7: Free surface flow. Oscillating water column (OWC) system (air as environment fluid), computed by means of the finite-volume/level-set method introduced in [2]. (a) Unstructured mesh adapted to the complex domain, (b) Snapshot of the free surface/OCW interaction.

 

 

Figure 8: Richtmyer-Meshkov instability: Images of the experimental (top) and numerical simulation (bottom) of the 2D Richtmyer-Meshkov instability. These simulations have been performed by means of the volume-of-fluid method introduced in [3].
 
 
Fig. 9: Richtmyer-Meshkov instability: Images of the experimental (top) and numerical simulation (bottom) of the 3D Richtmyer-Meshkov instability. These simulations have been performed by means of the volume-of-fluid method introduced in [3].

Publications

On International Journals:

[1] Balcázar, N., Jofre, L., Lehmkuhl, O., Castro, J., Rigola, J., A finite-volume/level-set method for simulating two-phase flows on unstructured grids. International Journal of Multiphase Flow 64, September 2014, pp. 55-72. https://doi.org/10.1016/j.ijmultiphaseflow.2014.04.008

[2] Balcázar, N., Lehmkuhl, O., Rigola, J., Oliva, A., A multiple marker level-set method for simulation of deformable fluid particles, International Journal of Multiphase Flow 74, September 2015, pp. 125-142. https://doi.org/10.1016/j.ijmultiphaseflow.2015.04.009

[3] Balcázar, N., Lehmkuhl, O., Jofre, L., Oliva, A., Level-set simulations of buoyancy-driven motion of single and multiple bubbles. International Journal of Heat and Fluid Flow, 56:91-107, 2015. http://dx.doi.org/10.1016/j.ijheatfluidflow.2015.07.004

[4] Balcázar, N., Lehmkhul, O., Jofre, L., Rigola, J., Oliva, A. A coupled volume-of-fluid/level-set method for simulation of two-phase flows on unstructured meshes. Computers and Fluids 124, 12-29, 2016. http://dx.doi.org/10.1016/j.compfluid.2015.10.005

[5] Balcázar, N., Rigola, J., Castro, J., Oliva, A., A level-set model for thermocapillary motion of deformable fluid particles, International Journal of Heat and Fluid Flow, Volume 62, Part B, 2016, pp 324-343. http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.09.015

[6] Jofre, L., Borrell, R., Lehmkuhl, O., Oliva, A., Parallel load balancing strategy for Volume-of-Fluid methods on 3-D unstructured meshes. Journal of Computational Physics 282, 2015, pp. 269-288
https://doi.org/10.1016/j.jcp.2014.11.009

[7] Jofre, L., Lehmkuhl, O., Castro, J., Lluís Jofre, Oliva, A., A 3-D Volume-of-Fluid advection method based on cell-vertex velocities for unstructured meshes. Computers & Fluids 94. 2014, pp. 14-29.
https://doi.org/10.1016/j.compfluid.2014.02.001

[8] Schillaci, E., Jofre, L., Balcázar, N., Lehmkuhl, O., Oliva, A. A level-set aided single-phase model for the numerical simulation of free-surface flow on unstructured meshes, Computers & Fluids 140, 2016, 97-110. http://dx.doi.org/10.1016/j.compfluid.2016.09.014

[9] Schillaci, E., Jofre, L., Balcázar, N., Antepara, O., Oliva, A. A low-dissipation convection scheme for the stable discretization of turbulent interfacial flow. Computers & Fluids 15. 2017, 102-117. https://doi.org/10.1016/j.compfluid.2017.05.009

[10] E. Gutiérrez, N. Balcázar, E. Bartrons, J. Rigola. Numerical study of Taylor bubbles rising in a stagnant liquid using a level-set/moving-mesh method. Chemical Engineering Science 164. 2017, 158-177. https://doi.org/10.1016/j.ces.2017.02.018

 

On International Conference Proceedings:

[11] Balcázar, N., Castro, J., Rigola, J., Oliva, A., DNS of the wall effect on the motion of bubble swarms. Procedia Computer Science 108, 2017, Pages 2008-2017. https://doi.org/10.1016/j.procs.2017.05.076

[12] Balcázar, N., Rigola, J., Oliva, A., A level-set method for thermal motion of bubbles and droplets. 7th European Thermal-Sciences Conference (Eurotherm2016). Journal of Physics: Conference Series 745 (2016) 032113. doi:10.1088/1742-6596/745/3/032113

[13] E. Gutiérrez, N. Balcázar, O. Lehmkuhl, A. Oliva., On the solution of the full three-dimensional Taylor bubble problem by using a coupled Conservative Level Set - Moving Mesh method. 7th European Thermal-Sciences Conference (Eurotherm2016). Journal of Physics: Conference Series 745 (2016) 032116. doi: 10.1088/1742-6596/745/3/032116

[14] Balcázar, N., Lehmkuhl, O., Castro, J., Rigola, J., Oliva, A., GRAVITY-DRIVEN MOTION OF A SWARM OF BUBBLES IN A VERTICAL PIPE. 27th International Conference on Parallel Computational Fluid Dynamics, Parallel CFD2015. 2015.

[15] Balcázar, N.; Jofre, L.; Lehmkuhl, O.; Castro, J.; Oliva, A., A multiple marker level-set method for simulation of bubbly flows. Proceedings of the jointly organized WCCM XI, ECCM V, ECFD VI. July 20-25, 2014, Barcelona, Spain., pp. 5298-5309.

[16] Jofre, L.; Balcázar, N.; Lehmkuhl, O.; Borrell, R.; Castro, J., Direct numerical simulation of the flow over a spherical bubble in a turbulent pipe flow. Proceedings of the jointly organized WCCM XI, ECCM V, ECFD VI., July 20-25, 2014, Barcelona, Spain. pp. 5333-5343.

[17] Schillaci, E.; Balcázar, N.; Lehmkuhl, O.; Jofre, L.; Oliva, A."A free surface model for the numerical simulation of oscillating water column systems".En: Proceedings of the jointly organized WCCM XI, ECCM V, ECFD VI. pp. 5286-5297. 2014.

[18] Balcázar, N.; Jofre, L.; Lehmkuhl, O.; Rigola, J.; Castro, J.; Oliva, A., A finitevolume/level-set interface capturing method for unstructured grids: Simulations of bubbles rising through viscous liquids. Advances in Fluid Mechanics X, WIT Transactions on Engineering Sciences. pp. 239-252. 2014.

[19] Jofre, L.; Lehmkuhl, O.; Balcázar, N.; Castro, J.; Rigola, J.; Oliva, A, Conservative discretization of multiphase flow with high density ratios. Advances in Fluid Mechanics X, WIT Transactions on Engineering Sciences. pp. 153 – 164. 2014.

[20] R. Borrell, L. Jofre, O. Lehmkuhl and J. Castro. Parallelization strategy for the volume-of-fluid method on unstructured meshes. In Proceedings of the 25th International Conference on Parallel Computational Fluid Dynamics, 2013.

[21] L. Jofre, N. Balcázar, O. Lehmkuhl, J. Castro and A. Oliva. Numerical study of the incompressible Richtmyer-Meshkov instability. Interface tracking methods on general meshes. In Proceedings of the 15th International Conference on Fluid Flow Technologies, 2012.

[22] N. Balcázar, L. Jofre, O. Lehmkuhl, J. Castro and A. Oliva. Numerical simulation of incompressible two-phase flows by conservative level-set method. In Proceedings of the 15th International Conference on Fluid Flow Technologies, 2012.

[23] L. Jofre, O. Lehmkuhl, J. Castro and A. Oliva. Vof/Navier-Stokes implementation on 3D unstructured staggered meshes. Application to the Richtmyer-Meshkov instability. In Proceedings of the 7th International Conference on Computational Heat and Mass Transfer, 2011.

[24] L. Jofre, O. Lehmkuhl, J. Castro and A. Oliva. A Plic-Vof implementation on parallel 3D unstructured meshes. In Proceedings of the 5th European Conference on Computational Fluid Dynamics, 2010.