2.5
Conclusions
In this work, a low-dissipation and low-dispersion discretization for the numerical simulation of turbulent interfacial flow is analyzed. The scheme is designed to minimize the amount of artificial dissipation introduced into the discrete system, while manages to limit the growth of spurious currents. In addition, as demonstrated in the series of tests performed, the hybrid convection scheme proposed can be coupled to different interface-capturing methods. The theoretical analysis presented in Secs. 2.2 and 2.3 demonstrates that the scheme is con- servative except for the subgroup of cells found in the vicinity of the interface, where a controlled amount of dissipation is introduced to diminish spurious flows. This feature is confirmed by the numerical results of a 3-D vortex presented in Sec. 2.4.1. The same test shows that the overall kinetic-energy dissipation is kept to a level well lower than classic dis- sipative schemes. The spatial accuracy of the method is numerically analyzed in Sec. 2.4.2, where it is shown to be second-order accurate on Cartesian grids and first-order on unstruc- tured 3-D meshes.
The localized injection of dissipation allows an effective control of the spurious currents growth, which provides enhanced stability to the numerical method. Indeed, as demonstrated in the spherical drop test in Sec. 2.4.3, spurious flows grow unbounded when using purely conservative discretizations, whereas remain contained to small values in the case of utilizing the hybrid convection scheme. This behavior is further corroborated by obtaining a proper interface advection when the sphere is placed in a swirling velocity field.
The performance of the numerical framework in a complete multiphase turbulent scenario has been tested by solving a liquid-gas atomizing jet. On the one hand, the test demonstrates that the controlled dissipation added to the interfacial region is sufficient to stabilize the numerical simulation. On the other hand, the results expose that, unlike pure dissipative schemes, the hybrid convection approach presented in this work is able to properly represent the underlying physics of turbulent flow. Consequently, the inability of a pure dissipative method to properly transport swirling structures is overcome.
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3
Adoption of AMR for
resource optimization in
two-phase flow
Main contents of this chapter are currently Under Review in:
E.Schillaci, O. Antepara, N. Balcázar, and A. Oliva. A dynamic mesh refinement strategy for the simulation of break-up phenomena in two-phase jets International Journal of Heat and Fluid Flow, Under Review.
Abstract.In this work we adopt an Adaptive Mesh Refinement (AMR) strategy to carry out the direct numerical simulation of complex multiphase flows by means of interface-capturing schemes. The model is globally addressed at improving the representation of interfacial and turbulent scales in the simulation of instability and break-up phenomena, while simultaneously reducing the computational requirements in comparison to static mesh computations. The refinement criteria are designed to ensure the proper representation of the characteristic lengths, by achieving the required mesh definition in each part of the domain. The discretization, built on a finite-volume basis, accounts for a divergence-free treatment of the refined/coarsened cells, that ensures the correct transport of mass, momentum and kinetic energy. Initially, we demonstrate the accuracy of the method and the benefits brought in contrast with static mesh for general multiphase cases, as vortex flow and rising bubbles. Next, we propose the analysis of various basic instability phenomena, including the capillary break-up of a liquid column, the injection of a liquid jet at different speeds, and the validation of a 2-D coaxial turbulent jet. In the last section, the simulation of a 3-D coaxial jet is presented and the physical features that we observed are validated by comparison to semi-empirical laws.
Additional contents have been published in:
E.Schillaci, O.Lehmkuhl, O.Antepara, and A.Oliva. Direct numerical simulation of multi- phase flows with unstable interfaces. Journal of Physics: Conference Series, (Vol. 745, No. 3, p. 032114). IOP Publishing.
E.Schillaci, O.Antepara, O.Lehmkuhl, N. Balcázar, and A. Oliva. Effectiveness of adaptive mesh refinement strategies in the DNS of multiphase flows. In: Proceedings of international symposium turbulent heat and mass transfer VIII; 2015 .