Submission Title
Matryoshka Inspired Statistical Surrogate for Turbulent Mixing
Presentation Type
Poster
Start Date
18-12-2018 1:00 PM
Abstract
Thermalhydraulics of reactor plena is often the most challenging problem due to turbulent mixing, role of jets and stratified flows. Due to which, the safety analysis of the overall reactor vessel or reactor system become complex. Inability of the system level analysis codes to accurately model the role of tur- bulent mixing in scalar transport leads to a major source of uncertainties. The computational cost of accurate CFD models renders the sensitivity studies using those for reactor safety ineffective. Reduced order models are needed which can effectively capture the effects of turbulent mixing and can be used for parametric studies important for safety analysis.
Turbulent flows compose of many energetic scales which are hidden inside one another in a ‘Matryoshka’ like fashion and exhibit non-trivial interactions. These multi-scale interactions can be accurately captured by Direct Numerical Simulations (DNS) of Navier Stokes equations or high fidelity experimental data. Hence, if a data learning model can be trained to capture the energetic interactions it can serve as a statistical surrogate. For this study, DNS data for a channel flow problem is used to obtain statistical surrogates. A lagrangian description of the field is developed by removing the long time correlations or the fine scale structures of the turbulent system. To obtain this, Kramers-Moyal analysis [1, 2] of the measured time series was performed and parameters of the Itô’s equation (or the Eulerian Fokker-Planck equation) were calculated directly from the data. This data driven coarse-grained stochastic differential equation surrogate of the turbulent system which can be coupled to the Lagrangian- Lagrangian type of simulations for the transport of passive scalar quantity.
References
[1] R. Friedrich and J. Peinke, “Description of a turbulent cascade by a fokker- planck equation,” Physical Review Letters, vol. 78, no. 5, p. 863, 1997.
[2] H. Risken, “Fokker-planck equation,” in The Fokker-Planck Equation, pp. 63–95, Springer, 1996.
Recommended Citation
Gairola, Abhinav and Bindra, Hitesh (2018). "Matryoshka Inspired Statistical Surrogate for Turbulent Mixing," Symposium on Advanced Sensors and Modeling Techniques for Nuclear Reactor Safety. https://newprairiepress.org/asemot/2018/fullprogram/11
Matryoshka Inspired Statistical Surrogate for Turbulent Mixing
Thermalhydraulics of reactor plena is often the most challenging problem due to turbulent mixing, role of jets and stratified flows. Due to which, the safety analysis of the overall reactor vessel or reactor system become complex. Inability of the system level analysis codes to accurately model the role of tur- bulent mixing in scalar transport leads to a major source of uncertainties. The computational cost of accurate CFD models renders the sensitivity studies using those for reactor safety ineffective. Reduced order models are needed which can effectively capture the effects of turbulent mixing and can be used for parametric studies important for safety analysis.
Turbulent flows compose of many energetic scales which are hidden inside one another in a ‘Matryoshka’ like fashion and exhibit non-trivial interactions. These multi-scale interactions can be accurately captured by Direct Numerical Simulations (DNS) of Navier Stokes equations or high fidelity experimental data. Hence, if a data learning model can be trained to capture the energetic interactions it can serve as a statistical surrogate. For this study, DNS data for a channel flow problem is used to obtain statistical surrogates. A lagrangian description of the field is developed by removing the long time correlations or the fine scale structures of the turbulent system. To obtain this, Kramers-Moyal analysis [1, 2] of the measured time series was performed and parameters of the Itô’s equation (or the Eulerian Fokker-Planck equation) were calculated directly from the data. This data driven coarse-grained stochastic differential equation surrogate of the turbulent system which can be coupled to the Lagrangian- Lagrangian type of simulations for the transport of passive scalar quantity.
References
[1] R. Friedrich and J. Peinke, “Description of a turbulent cascade by a fokker- planck equation,” Physical Review Letters, vol. 78, no. 5, p. 863, 1997.
[2] H. Risken, “Fokker-planck equation,” in The Fokker-Planck Equation, pp. 63–95, Springer, 1996.
