# NERSC Initiative for Scientific Exploration (NISE) 2011 Awards

## Surface Instabilities and Subgrid Scale Models in Computational Fluid Dynamics

### James Glimm, Stony Brook University

**NISE project m1289**

NISE Award: | 500,000 Hours |

Award Date: | March 2011 |

Turbulent mixing and sub grid scale models (SGS) for large eddy simulation remain as a major challenge for computational fluid dynamics. Building on prior success with front tracking and use of SGS models, we propose to conduct validation and verification simulations for a new Front Tracking incompressible flow solver with dynamic SGS turbulence models. Two flow regimes are proposed for these tests, chosen because of (a) prior experience of the proposers, (b) intrinsic importance of the problems to DOE, and (c) availability of experimental data. The flow regimes are (1) high speed two phase Couette flow, as arises in a contactor used for reprocessing of spent nuclear fuel from nuclear power reactors and (2) Rayleigh-Taylor mixing problems, of importance as a test bed for ICF capable simulation codes.

Preliminary simulations for the Couette flow problem have been completed, and here we propose to study properties of the mixing regime as a function of the volume fractions of the two fluids, a test for which there is experimental data.

A series of Rayleigh-Taylor simulations have been completed, using a related compressible code. These have given successful comparison to experiment in the overall growth of the mixing layer (the famous "alpha" problem). Uncertainties associated with unmeasured initial conditions have been largely eliminated by use of early time experimental data, and remaining uncertainties have been quantified and the effect on the growth rate for the mixing zone has also been quantified, showing agreement with experimental data. Here we propose to study molecular mixing properties. For this purpose a more efficient incompressible code will be used, to facilitate increased resolution. Good comparison to experiment was achieved for experiments of M. Andrews at early time, but improved resolution appears to be needed to go to later time in this comparison.

We emphasize the fundamental scientific issues at play in this investigation. Validated and verified simulations of chaotic flow regimes are important to a number of DOE problems, and methodologies to achieve this goal will have significance beyond the present investigation.

This proposal will allow improved fidelity in the study of microscopic mixing in a commonly considered test problem of Rayleigh-Taylor instability. We will be able to improve on the mesh resolution due to the incompressible nature of the simulation, and we hope thereby to improve on the match to experiment. The incompressible simulation will also improve on the accuracy of the physical modeling by allowing removal of some modifications to the physical parameters that were needed for a compressible simulation.

It will allow study of the majority vs. minority phase in a turbulent two phase Couette flow, as a function of the volume fraction of the two fluids and as a function of the radius. We will also conduct a separate study of a gas-liquid two phase Couette flow to determine the proper rotation speed at the air gap - liquid boundary for three phase mixing.

The flows studied are important for DOE missions (nuclear fuel reprocessing and ICF). The problems studied occur in a number of DOE problems, and the solutions proposed will be helpful outside of the specific context studied. While turbulent and chaotic flow fields are generally understood to be statistical in nature, an accepted methodology for statistical convergence of random fields does not appear to be a well established part of the numerical analysis culture. The proposed simulations will serve to contribute to an understanding of the proper nature of statistical convergence as it is to be verified and validated in a simulation study.