Scott Wunsch

A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration

The turbulent Rayleigh–Taylor instability is investigated in the limit of strong mode-coupling using a variety of high-resolution, multimode, three dimensional numerical simulations (NS). The perturbations are initialized with only short wavelength modes so that the self-similar evolution (i.e., bubble diameter Db∝amplitude hb) occurs solely by the nonlinear coupling (merger) of saturated modes. After an initial transient, it is found that hb∼αbAgt2, where A=Atwood number, g=acceleration, and t=time. The NS yield Db∼hb/3 in agreement with experiment but the simulation value αb∼0.025±0.003 is smaller than the experimental value αb∼0.057±0.008. By analyzing the dominant bubbles, it is found that the small value of αb can be attributed to a density dilution due to fine-scale mixing in our NS without interface reconstruction (IR) or an equivalent entrainment in our NS with IR. This may be characteristic of the mode coupling limit studied here and the associated αb may represent a lower bound that is insensiti...

Carbon Ignition in Type Ia Supernovae: An Analytic Model

The observable properties of a Type Ia supernova are sensitive to how the nuclear runaway ignites in a Chandrasekhar-mass white dwarf: at a single point at its center, off-center, or at multiple points and times. We present a simple analytic model for the runaway guided by a combination of stellar mixing-length theory and analogy to Rayleigh-Benard convection. The convective flow just prior to runaway is likely to have a strong dipolar component, although this dipole may be unstable at the very high Rayleigh number (1025) appropriate to the white dwarf core. A likely outcome is multipoint ignition with an exponentially increasing number of ignition points during the few tenths of a second that it takes the runaway to develop. The first sparks ignite approximately 150-200 km off-center, followed by ignition at smaller radii. Rotation may be important to break the dipole asymmetry of the ignition and give a healthy explosion.

One-dimensional turbulence: vector formulation and application to free shear flows

One-dimensional turbulence is a stochastic simulation method representing the time evolution of the velocity profile along a notional line of sight through a turbulent flow. In this paper, the velocity is treated as a three-component vector, in contrast to previous formulations involving a single velocity component. This generalization allows the incorporation of pressure-scrambling effects and provides a framework for further extensions of the model. Computed results based on two alternative physical pictures of pressure scrambling are compared to direct numerical simulations of two time-developing planar free shear flows: a mixing layer and a wake. Scrambling based on equipartition of turbulent kinetic energy on an eddy-by-eddy basis yields less accurate results than a scheme that maximizes the intercomponent energy transfer during each eddy, subject to invariance constraints. The latter formulation captures many features of free shear flow structure, energetics, and fluctuation properties, including the spatial variation of the probability density function of a passive advected scalar. These results demonstrate the efficacy of the proposed representation of vector velocity evolution on a one-dimensional domain.

Near-wall LES closure based on one-dimensional turbulence modeling

A novel near-wall LES closure model is developed based on a revised form of the one-dimensional turbulence (ODT) model of Kerstein and is tested by performing LES calculations of turbulent channel flow at Reynolds numbers based on friction velocity ranging from 395 to 10,000. In contrast to previous models, which invoke Reynolds averaging, near-wall velocity fluctuations and turbulent transport are simulated down to the smallest scales, and can be compared directly to DNS data. Thus, the approach provides more than just a boundary condition. Rather, it is itself a complete (although simplified) model for the wall-normal profiles of velocity within the near-wall region. LES/ODT coupling is bi-directional and occurs both through the direct calculation of the subgrid turbulent stress by temporally and spatially filtering the ODT-resolved momentum fluxes (up-scale coupling), and through the LES-resolved pressure and velocities impacting the ODT behavior (down-scale coupling). The formulation involves finely resolved ODT lines that are embedded within each wall-adjacent LES cell - denoted the inner region. LES cells that are within approximately one LES filter width of the inner region belong to an overlap region where both ODT and LES modeling is active. All other cells are treated using a standard LES approach. Although more expensive than simpler models, the cost of the model relative to the LES portion of the simulation scales favorably with problem size, leading to computationally affordable simulations even at relatively high Reynolds numbers.

Convection and off-center ignition in type Ia supernovae

The turbulent convection that takes place in a Chandrasekhar-mass white dwarf during the final few minutes before it explodes determines where and how frequently it ignites. Numerical simulations have shown that the properties of the subsequent Type Ia supernova are sensitive to these ignition conditions. A heuristic model of the turbulent convection is explored. The results suggest that supernova ignition is likely to occur at a radius of order 100 km, rather than at the center of the star.

A stochastic model for high-Rayleigh-number convection

A stochastic one-dimensional model for thermal convection is formulated and applied to high-Rayleigh-number convection. Comparisons with experimental data for heat transfer in Rayleigh-Benard cells are used to estimate two model parameters. Using the model, the statistics of fluctuations in the core of the convection cell are studied

A model for layer formation in stably stratified turbulence

Stably stratified turbulent flows are common in geophysics and astrophysics, and frequently exhibit layered structures in which large regions of nearly constant fluid density are separated by sharp density gradients. Experiments have demonstrated that, under suitable conditions, the stirring of a stably stratified fluid generates these layer structures. In this paper, a stochastic one-dimensional model is used to study layer formation in stably stratified turbulence. The results support mixing length arguments previously proposed to describe layers in steady state.

Stochastic simulations of buoyancy-reversal experiments

Buoyancy reversal occurs when the mixing of two fluids, initially stably stratified, produces a mixture which is more dense than either pure fluid. The resulting instability generates turbulent mixing, and may play an important role in geophysical and astrophysical flows. In this work, a stochastic one-dimensional model is used to simulate these systems. Model validation is accomplished using experimental comparisons. Scalings inferred from the model simulations are used to suggest extrapolations from experimental results to natural systems.

Scaling laws for layer formation in stably-stratified turbulent flows

Experiments have demonstrated that the stirring of a stably-stratified fluid sometimes generates a series of layers of nearly constant density separated by steep density gradients. In this paper, mixing length arguments based on the Kolmogorov picture of turbulence are used to suggest scalings for the layer sizes, gradients, and buoyancy fluxes in the limit of strong turbulence. Experimentally observed layer sizes are consistent with the proposed scaling law.

On the Development of the Large Eddy Simulation Approach for Modeling Turbulent Flow: LDRD Final Report

This report describes research and development of the large eddy simulation (LES) turbulence modeling approach conducted as part of Sandias laboratory directed research and development (LDRD) program. The emphasis of the work described here has been toward developing the capability to perform accurate and computationally affordable LES calculations of engineering problems using unstructured-grid codes, in wall-bounded geometries and for problems with coupled physics. Specific contributions documented here include (1) the implementation and testing of LES models in Sandia codes, including tests of a new conserved scalar--laminar flamelet SGS combustion model that does not assume statistical independence between the mixture fraction and the scalar dissipation rate, (2) the development and testing of statistical analysis and visualization utility software developed for Exodus II unstructured grid LES, and (3) the development and testing of a novel new LES near-wall subgrid model based on the one-dimensional Turbulence (ODT) model.