59th Annual Report on Research 2014

Figure 1: Interface-refined mesh (bottom) for initial condition and DNS mesh (top).

A second consideration is viscous length scales in wall boundary layers. Resolving these near the wall increases the overall mesh count significantly due to the required simulated length of the pipe for spatially developing flow. To reduce computational cost, a multi-mesh approach is taken in which a mesh without wall-refinement is used to drive the two-phase flow to a statistically steady state that is used as an initial condition for a then fully-refined simulation, see Fig. 1, resolving the wall boundary layer.    

Inflow Boundary Conditions To correctly predict the phase interface dynamics, physically meaningful inflow boundary conditions must be prescribed. In preliminary simulations it was found that either time averaged velocity profiles or fluctuating turbulent velocity profiles using artificial turbulence were inadequate to produce accurate interface dynamics in the development region of the flow. Thus, in order to properly include inflow turbulence for each flow-phase, a transient database is generated for each flow condition necessary to study all flow regimes. Using periodic half-pipe DNS/LES simulations that account for viscous dissipation and volumetric flow, see Fig. 2, a transient boundary condition for each phase can be generated at time intervals such that the relevant time scales are resolved. The time-length and size of each database can vary, but the objective is to obtain enough data for the multi-phase simulations using these inflow databases to reach statistically steady state. Once generated, the databases can be used interchangeably for each of the cases outlined in the proposal.

Figure 2: Example of velocity magnitude profiles, two phases, single time instance.

Multi-phase Outlet Treatment One of the most challenging aspects of the simulation of spatially developing multiphase pipe flows is the development of a technique to model a multi-phase outlet boundary. In principle, outlet boundary corrections only take into consideration system-wide mass conservation, which tends to yield non-physical results in instances where multi-phase flow is present. For the proposed simulations, it is thus necessary to consider each phase separately at the outlet such that the system maintains stability (divergence condition). A method is currently in development that employs a multi-fluid outlet correction, which has shown improved numerical stability in current simulations. Using the case in Fig. 3 as an example, with initial condition of 50% liquid phase and 50% gas phase, a conventional outlet correction yields a system mass of 70% liquid phase and 30% gas phase after five flow-through times. The newly developed method, on the other hand, yields +/- 0.01% deviation from the initial condition in terms of mass percent ratio.

Figure 3: Mesh layout SS to SW transition regime simulation, phase-interface after five flow-through times.

Progress and Cost Turbulent inflow boundary databases are currently being generated, starting with the SS-SW regime, in conjunction with the development of the multi-phase outlet boundary correction. To estimate final simulation cost, preliminary simulation results for a condition in the SS-SW regime can be used: to achieve a statistically-steady state, it is estimated that at least 10 flow-through times are required, for which each simulation requires a run-time of 16 days on 128 processors, thus approximately 5e4 compute-hours. These simulations will be performed in the final period of this project.