Geometry dynamics of compressible turbulence structures
Abstract
A characterization of the time-evolution of the geometry of finite-sized structures educed from turbulent flows will be pursued in this research. The objective is to provide a systematic, quantitative description of turbulence dynamics that relates geometry and physics carried by structures found at different scales, as evolved by the underlying turbulent flow. Numerical simulation (DNS and LES) datasets of four canonical compressible turbulent flow types will be considered: homogeneous isotropic turbulence, shear mixing layer, shearless mixing layer, and shock-turbulence interaction. While simple in their configuration, these flow types are chosen as they cleanly isolate several building blocks of turbulence (convective nonlinearities, shear and acoustic-vorticity coupling, anisotropy, and rapid compression/distortion). To carry out this research, we introduce novel methodologies to analyze time series of volumetric datasets, comprising: 1) multi-scale decomposition based on the curvelet transform; 2) structure identification and extraction; 3) discrete differential geometry characterization combined with integration of physical quantities conditioned onto area-based probability density functions; 4) unsupervised learning for clustering and classification of common geometric patterns; 5) time-tracking of collections of individual structures through constrained correspondence searches between consecutive time snapshots, 6) encoding structure evolution into graphs that represent the life of each structure and its interactions with others, and, 7) search for common dynamical patterns of ensembles of structures in suitable state spaces that combine geometry and physics. The proposed research addresses the study of turbulence dynamics from the standpoint of collections of individual, finite-sized structures evolving in time and being characterized in physical space. For each flow type here considered, the proposed methodology will be applied to study structures of key scalar physical fields derived from the velocity gradient tensor, such as enstrophy, dissipation-rate, and dilatation. In addition to the time evolution of the structures of each field, we will also analyze the interplay between groups of structures with common geometries and dynamical patterns educed from different fields and scales. Such analyses will help answer long-lasting fundamental questions in turbulence research, such as: are vortex tubes in the inertial range generated by the roll-up of surrounding sheets of dissipation? Does the the signature cascade of kinetic energy present in Fourier space (scale) have a counterpart in physical space (turbulent eddy size), as hypothesized by Richardson? The time-evolution analysis of collections of structures with common geometries could then elucidate the mechanisms enabling such cascade dynamics in physical space and link with established Fourier-based statistical theories to justify of models of turbulence fine scales. Expected outcomes of this research include, first, an understanding of the structure dynamics of each of the compressible turbulent flow types under consideration, specifically regarding dominant geometries and their evolution for each field and scale, and possible universal features across flow types at the small scales. Second, the resulting quantitative data from the proposed analyses will be paramount to inform the development of reduced order models (such as structure-based SGS models) for improved predictive simulation of compressible turbulent flows, relevant in applications in high-speed flight and propulsion, noise reduction in rockets and supersonic combustion jet engines, inertial confinement fusion, and multiphase flows (e.g., sprays, droplet collision, etc). The proposed methodologies are also applicable in scientific fields that benefit from tracking the evolution in time of geometric and physical quantities on 3D structures extracted from 3D, volumetric datasets.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 09, 2020
- Source ID
- W911NF2010096
Entities
People
- Iván Bermejo-Moreno
Organizations
- Army Contracting Command
- United States Army
- University of Southern California