Type
Text
Type
Dissertation
Advisor
Glimm, James G | Jiao, Xiangmin | Li, Xiaolin | McGuigan, Michael.
Date
2016-12-01
Keywords
Hydrodynamical instabilities, Large eddy simulations, Predictive simulations, Richtmyer-Meshkov, Turbulence modeling, Turbulent transport | Applied mathematics
Department
Department of Applied Mathematics and Statistics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/77288
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Turbulent mixing from hydrodynamical instabilities, such as Richtmyer-Meshkov (RMI) and Rayleigh-Taylor (RTI) instabilities, plays a critical role in numerous applications ranging from performance degradation in inertial confinement capsules to supernova explosions. At high Reynolds numbers (Re), for which experimental data is not available, numerical simulations are paramount in studying these instabilities. However, the algorithmic differences due to differences in numerical modeling often give solutions that are converged but not unique, that is, different codes converge to different solutions. Thus, to establish the credibility of the simulation in an objective manner, it is necessary to fulfill three main requirements: (1) verification (2) validation and (3) uncertainty quantification. In this dissertation, we present a “validation by extrapolation" strategy accompanied with appropriate interface and subgrid modeling. Instead of using the traditional pointwise convergence, we use Youngs' measure, which is stochastic in nature and is more appropriate for studying turbulent properties. We also analyze the stochastic properties of turbulence using exponential distribution across Re and mesh. The highlight of our numerical algorithm is use of front-tracking in conjunction with dynamic subgrid scale models. This unique combination has been successfully verified for RMI and validated for RTI. The use of front-tracking and a calibration-free SGS model facilitates the smooth extrapolation of LES simulations from experimentally validated regime to higher Re. This seamless extrapolation is important in designing simulations that are truly predictive in nature. Motivated by the Richtmyer-Meshkov instability in inertial confinement fusion, we carry out a parameter study on a simplified hydrodynamical version of the ICF problem in 2D. In this parameter study, we vary the Reynolds number starting from the experimentally achieved highest Re for RTI (35,000) to Re=infinity (Euler's equation/no physical viscosity). At such high Re, turbulent transport is the dominant mode of transport. We analyze the sensitivity of the turbulent transport coefficients (calculated via the dynamic SGS) to the Reynolds number. These coefficients vary little in the high Re range. However, they are observed to be very sensitive to the changes in subgrid model, thus emphasizing the importance of using the parameter-free subgrid models for turbulent mixing problems. We find that in high Re limit, the turbulent transport coefficients are converged under mesh refinement and have a Kolmogorov-type scaling. We also draw quantitative comparisons between the single-shocked incipiently turbulent regime and the reshocked regime with fully developed turbulence. | Turbulent mixing from hydrodynamical instabilities, such as Richtmyer-Meshkov (RMI) and Rayleigh-Taylor (RTI) instabilities, plays a critical role in numerous applications ranging from performance degradation in inertial confinement capsules to supernova explosions. At high Reynolds numbers (Re), for which experimental data is not available, numerical simulations are paramount in studying these instabilities. However, the algorithmic differences due to differences in numerical modeling often give solutions that are converged but not unique, that is, different codes converge to different solutions. Thus, to establish the credibility of the simulation in an objective manner, it is necessary to fulfill three main requirements: (1) verification (2) validation and (3) uncertainty quantification. In this dissertation, we present a “validation by extrapolation" strategy accompanied with appropriate interface and subgrid modeling. Instead of using the traditional pointwise convergence, we use Youngs' measure, which is stochastic in nature and is more appropriate for studying turbulent properties. We also analyze the stochastic properties of turbulence using exponential distribution across Re and mesh. The highlight of our numerical algorithm is use of front-tracking in conjunction with dynamic subgrid scale models. This unique combination has been successfully verified for RMI and validated for RTI. The use of front-tracking and a calibration-free SGS model facilitates the smooth extrapolation of LES simulations from experimentally validated regime to higher Re. This seamless extrapolation is important in designing simulations that are truly predictive in nature. Motivated by the Richtmyer-Meshkov instability in inertial confinement fusion, we carry out a parameter study on a simplified hydrodynamical version of the ICF problem in 2D. In this parameter study, we vary the Reynolds number starting from the experimentally achieved highest Re for RTI (35,000) to Re=infinity (Euler's equation/no physical viscosity). At such high Re, turbulent transport is the dominant mode of transport. We analyze the sensitivity of the turbulent transport coefficients (calculated via the dynamic SGS) to the Reynolds number. These coefficients vary little in the high Re range. However, they are observed to be very sensitive to the changes in subgrid model, thus emphasizing the importance of using the parameter-free subgrid models for turbulent mixing problems. We find that in high Re limit, the turbulent transport coefficients are converged under mesh refinement and have a Kolmogorov-type scaling. We also draw quantitative comparisons between the single-shocked incipiently turbulent regime and the reshocked regime with fully developed turbulence. | 88 pages
Recommended Citation
Rao, Pooja, "Turbulent Mixing in Richtmyer-Meshkov Instability Using Front-Tracking" (2016). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 3109.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/3109