Test Problem: Tilted Rayleigh-Taylor for 2-D Mixing Studies

Abstract

The 'tilted-rig' test problem originates from a series of experiments (Smeeton & Youngs, 1987, Youngs, 1989) performed at AWE in the late 1980's, that followed from the 'rocket-rig' experiments (Burrows et al., 1984; Read & Youngs, 1983), and exploratory experiments performed at Imperial College (Andrews, 1986; Andrews and Spalding, 1990). A schematic of the experiment is shown in Figure 1, and comprises a tank filled with light fluid above heavy, and then 'tilted' on one side of the apparatus, thus causing an 'angled interface' to the acceleration history due to rockets. Details of the configuration given in the next chapter include: fluids, dimensions, and other necessary details to simulate the experiment. Figure 2 shows results from two experiments, Case 110 (which is the source for this test problem) that has an Atwood number of 0.5, and Case 115 (a secondary source described in Appendix B), with Atwood of 0.9 Inspection of the photograph in Figure 2 (the main experimental diagnostic) for Case 110. reveals two main areas for mix development; 1) a large-scale overturning motion that produces a rising plume (spike) on the left, and falling plume (bubble) on the right, that are almost symmetric; and 2) a Rayleigh-Taylor drivenmore » mixing central mixing region that has a large-scale rotation associated with the rising and falling plumes, and also experiences lateral strain due to stretching of the interface by the plumes, and shear across the interface due to upper fluid moving downward and to the right, and lower fluid moving upward and to the left. Case 115 is similar but differs by a much larger Atwood of 0.9 that drives a strong asymmetry between a left side heavy spike penetration and a right side light bubble penetration. Case 110 is chosen as the source for the present test problem as the fluids have low surface tension (unlike Case 115) due the addition of a surfactant, the asymmetry small (no need to have fine grids for the spike), and there is extensive reasonable quality photographic data. The photographs in Figure 2 also reveal the appearance of a boundary layer at the left and right walls; this boundary layer has not been included in the test problem as preliminary calculations suggested it had a negligible effect on plume penetration and RT mixing. The significance of this test problem is that, unlike planar RT experiments such as the Rocket-Rig (Youngs, 1984), Linear Electric Motor - LEM (Dimonte, 1990), or the Water Tunnel (Andrews, 1992), the Tilted-Rig is a unique two-dimensional RT mixing experiment that has experimental data and now (in this TP) Direct Numerical Simulation data from Livescu and Wei. The availability of DNS data for the tilted-rig has made this TP viable as it provides detailed results for comparison purposes. The purpose of the test problem is to provide 3D simulation results, validated by comparison with experiment, which can be used for the development and validation of 2D RANS models. When such models are applied to 2D flows, various physics issues are raised such as double counting, combined buoyancy and shear, and 2-D strain, which have not yet been adequately addressed. The current objective of the test problem is to compare key results, which are needed for RANS model validation, obtained from high-Reynolds number DNS, high-resolution ILES or LES with explicit sub-grid-scale models. The experiment is incompressible and so is directly suitable for algorithms that are designed for incompressible flows (e.g. pressure correction algorithms with multi-grid); however, we have extended the TP so that compressible algorithms, run at low Mach number, may also be used if careful consideration is given to initial pressure fields. Thus, this TP serves as a useful tool for incompressible and compressible simulation codes, and mathematical models. In the remainder of this TP we provide a detailed specification; the next section provides the underlying assumptions for the TP, fluids, geometry details, boundary conditions (and alternative set-ups), initial conditions, and acceleration history (and ways to treat the acceleration ramp at the start of the experiment). This is followed by a section that defines data to be collected from the simulations, with results from the experiments and DNS from Livescu using the CFDNS code, and ILES simulations from Youngs using the compressible TURMOIL code and Andrews using the incompressible RTI3D code. We close the TP with concluding remarks, and Appendices that includes details of the sister Case 115, initial condition specifications for density and pressure fields. The Tilted-Rig Test Problem is intended to serve as a validation problem for RANS models, and as such we have provided ILES and DNS simulations in support of the test problem definition. The generally good agreement between experiment, ILES and DNS supports our assertion that the Tilted-Rig is useful, and the only 2-D TP that can be used to validate RANS models.« less