A Large Eddy Simulation Subgrid Model for Turbulent Phase Interface Dynamics

In this paper we report on the outline of a Large Eddy Simulation subgrid model for liquid/gas phase interface dynamics. A key feature of the proposed model is to take the subgrid phase interface dynamics fully into account by employing a dual-scale approach. Instead of modeling the LES subgrid phase interface geometry, we fully resolve it on an auxillary grid using the Refined Level Set Grid approach (Herrmann 2008). We then propose to model the LES subgrid velocity on the auxillary grid needed to move the fully resolved phase interface, by solving a dedicated PDE for its evolution near the phase interface. This PDE contains three different contributions. First, the subfilter turbulent eddies are taken into account by modeling the subfilter acceleration in lines of Oboukhovs log-normality conjecture on the stochastic field of ε. The second term, a velocity increment due to the relative motion between the two phases is modeled deriving renormalized velocity boundary condition at the phase interface. The final term, due to subfilter surface tension induced subfilter velocities is modeled following a Taylor analogy. Knowing the fully resolved phase interface geometry, all previously unclosed terms in the filtered Navier-Stokes equations can be directly closed using explicit filtering. Introduction Atomization processes are characterized by a vast range of length and time scales. Performing detailed simulations aiming to resolve all relevant scales is a daunting task even with today’s computational resources [1]. Detailed simulations are thus limited to research oriented tasks and not a viable approach for engineering design work. Models, simplifying the atomization process by pre-assuming certain types of atomization mechanisms, on the other hand, lack the ability to reliably predict atomization, especially in novel atomizer configurations. Simulation approaches in between detailed simulations and model simulations that do not presume the atomization mechanism are thus desirable. It has been shown in the past that for single phase flows involving mixing processes with complexity comparable to two-phase atomizing flows, Large Eddy Simulation (LES) approaches yield superior results as compared to RANS simulations [2]. However, introducing spatial filtering into the governing equations results in several unclosed terms. These include the subfilter contribution of the stress tensor, the subfilter surface tension term, and a subfilter transport term for liquid volume fraction. Previous LES approaches [3–8] have modeled the subfilter contribution of the stress tensor using a single phase formulation and have simply neglected the latter two terms on the faulty premise that they either cancel each other, or that they are not important on the subfilter scale. However, especially the subfilter surface tension term can be dominant and must not be neglected, since surface tension forces are inversely proportional to the length scales of local surface corrugations and topology changes always involve small scales. The purpose of this paper is to propose a novel LES modeling approach for phase interface dynamics that incorporates all the previously neglected terms. Governing equations The equations governing the fully resolved motion of an unsteady, incompressible, immiscible, two-fluid system are the Navier-Stokes equations ∗Corresponding Author: [email protected] ICLASS 2009 A Large Eddy Simulation Subgrid Model for Turbulent Phase Interface Dynamics