Chapter
2.3 Coarse Grained Simulations
2.3.1 Determination of the Boundary between the Energy Containing and Inertial Ranges
2.3.2 Data Redundant in the Inertial Range
2.3.3 Local and Nonlocal Interactions in High Reynolds Number Flows
2.5.1 High Energy Density Physics Experiments
2.5.2 ILES Effective Reynolds Number
3 Finite Scale Theory: Compressible Hydrodynamics at Second Order
3.2 Hydrodynamics from Kinetic Theory
3.2.2 Brief Remarks on Chapman-Enskog Theory
3.2.3 Hydrodynamics at Second Order
3.3 Finite Scale Equations
3.3.2 Presenting the Finite Scale Equations
3.4 Properties of Finite Scale Equations
3.5 Numerical Considerations
3.5.1 Nonoscillatory Finite Volumes
3.5.2 An Early History and Rationalization of ILES
3.6 A Finite Scale Formulation at Molecular Length Scales
3.6.1 Eddy Diffusivity in Turbulence Models
3.6.2 An Alternate Perspective
3.7 Coarsening the Velocity Distribution
3.7.1 The Coarsening Process
3.7.2 Noninvariance of LTE
3.7.3 Invariance near Equilibrium
3.7.4 Unresolved Kinetic Energy and Pressure
3.8 Finite Scale Shock Width
4 Material Conservation of Passive Scalar Mixing in Finite Scale Navier Stokes Fluid Turbulence
4.2.1 FSNS and ILES Models
4.2.2 FSNS and LES Models
4.2.3 Nonlinear LES Model
4.3.1 The Reynolds Decomposition
4.3.2 Taylor’s Hypothesis
4.3.3 Energy Transfer Rates in FSNS
4.4 Passive Scalar Mixing in a Turbulent NS Fluid
4.4.1 Variance of the NS Scalar Field
4.4.2 Scalar Gradient Variance of a NS Scalar
4.5 Passive Scalar Mixing in a Turbulent FSNS Fluid
4.5.1 Variance of the FSNS Scalar Field
4.5.2 Scalar Gradient Variance of a FSNS Fluid
4.5.3 What Does This All Mean?
4.6 Passive Scalar Mixing in a Turbulent SMG Fluid
4.6.1 Variance of the SMG Scalar Field
4.7 Turbulent Mixing in NS, FSNS, and SMG Fluids
4.8 Summary and Conclusions
Appendix: Reynolds Averaging for FSNSFluid Turbulence
5 Subgrid and Supergrid Modeling
5.2.1 Finite Scale Navier Stokes
5.2.2 Coarse Grained Convergence
5.2.3 Transition to Turbulence
5.3 Supergrid Scale: Initial and Boundary Conditions
5.3.1 Characterizing Inflow
5.3.3 Initial Material Interface Characterization
6 Cloud Modeling: An Example of Why Small Scale Details Matter for Accurate Prediction
6.4 Implicit Large Eddy Simulations of Hurricane Guillermo
6.4.1 ECM Implicit Large Eddy Simulations
6.4.2 LCM Implicit Large Eddy Simulation
6.4.2.1 Model Description
7 Verification, Validation, and Uncertainty Quantification for Coarse Grained Simulation
7.2 The Scientific Simulation Context
7.3.1 Begin the Validation Process
7.3.2 Conduct Simulations
7.3.3 Determination of Simulation Uncertainty
7.3.4 Conduct Experiments
7.3.5 Determination of Experimental Uncertainty
7.3.6 Validation Comparison
7.3.7 Validation Assessment
7.4 Discussion of the Workflow in Practice
7.4.1 What Is Validation?
7.4.1.1 Validation’s Purpose
7.4.3 Role of Other Assessment Techniques in Validation
7.4.5 Distinguishing Calibration and Data Assimilation from Validation and Uncertainty Quantification
7.4.6 What Is Uncertainty Quantification and Its Purpose?
7.5 Conclusions and Recommendations
Part III Complex Mixing Consequences
8 Shock Driven Turbulence
8.2 Shocked Planar Interface
8.2.1 Initial Interface Modeling
8.2.2 Evolution of Mixing and Turbulence Characteristics
8.2.4 The Reshock Group of Instabilities
8.3.2 Initial Condition Parameterization and Data Reduction
9 Laser Driven Turbulence in High Energy Density Physics and Inertial Confinement Fusion Experiments
9.2.1 Description of Experiments
9.2.1.1 Reshock Experiment
9.2.2 Simulation Strategies
9.2.3 Interface Perturbation Spectra
9.2.4 Visualizations and Comparison with Experimental Data
9.2.5 Comparison with Results for Homogeneous Isotropic Turbulence
9.2.5.1 Integrated Flow Quantities
9.2.5.2 Vorticity Distributions
9.2.5.3 Autocorrelation Analysis
9.2.5.4 Velocity Structure Functions
9.2.5.5 Velocity Variances
9.2.5.6 Effective Reynolds Number Analyses
9.3 Inertial Confinement Fusion Simulations
9.3.1 Simulation Strategies
9.3.2 Testing and Validating the 2D-3D Strategy: Reshock Experiment
9.3.2.1 2D-3D Mapping and Flow Initialization Strategies
9.3.2.2 Hydrodynamic Instability Growth in the Reshock Experiment
9.3.2.3 Augmenting Initial Perturbation Level in 2D-3D Pure Rotation Context
9.3.2.4 Generalized 2D-3D Mapping with Perturbations
9.3.2.5 Effects of Simulating a Quadrant of the Reshock Problem
9.3.2.6 Summary of Results for the Reshock Problem
9.3.3.1 Initial Material Interface Conditions and Drive Asymmetries
9.3.3.2 Hydrodynamic Instability Growth in an ICF Capsule
9.3.3.3 2D-3D Mapping for ICF Capsule Simulations
9.3.3.5 Capsule Performance and Comparison to Experiment
10 Drive Asymmetry, Convergence, and the Origin of Turbulence in Inertial Confinement Fusion Implosions
10.2 RAGE Simulations of an ICF Capsule with an Imposed Asymmetry
10.2.1 2D RAGE Simulations of the Capsule Implosion
10.2.1.1 Effect of Varying the Mode Number of the Imposed Asymmetry
10.2.1.2 Growth and Scaling in the rhoR Asymmetries of the CH Shell
10.2.1.3 Effect of Varying the Initial Gas Fill Density and Increasing Convergence Ratio
10.2.1.4 Summary of 2D RAGE Simulation Results for the Idealized OMEGA Capsule
10.2.2 Linked 3D RAGE Simulations of the Late Time Implosion
10.2.2.1 Spatial Resolution Study of 3D RAGE Simulations
10.2.2.2 Enstrophy Production in the 3D RAGE Simulations
10.2.2.3 3D RAGE Simulations of the 5% Amplitude Case
10.2.3 Advantages and Limitations of RAGE for ICF Implosions
10.3 Implications for NIF Ignition
11 Rayleigh-Taylor Driven Turbulence
11.2 Modeling and Computational Approach
11.2.1 Details about the Codes Used for the Study
11.2.2 BHR-2 Governing Equations and Modeling Rationale
11.3 Tilted Rig Test Problem
11.3.1 Initial Conditions and Postprocessing Analysis
11.3.2 Simulation Results
11.3.2.1 Contour Comparisons
11.3.2.2 Time Evolution of Integral Quantities
12 Spray Combustion in Swirling Flow
12.2 General Features of Swirling Flows
12.2.1 Generation Mechanisms
12.2.2 Definitions and Features
12.3 Swirling Spray Combustion
12.3.1 Experimental Approaches
12.3.2 Computational Approaches
12.3.2.1.1 Eulerian Gas Phase
12.3.2.1.2 Lagrangian Liquid Phase
12.3.2.1.3 Eulerian Liquid Phase
12.3.2.2 Coupling Between the Phases
12.3.2.3 Subgrid Terms and Closure
12.4.1 Instantaneous Features
12.4.3 Multiple Injectors
12.5 Summary and Future Prospects
13 Combustion in Afterburning Behind Explosive Blasts
13.2 CGS Modeling of Heterogeneous Afterburning
13.2.1 Governing Equations
13.2.2.1 Functional Models
13.2.2.2 Hyperviscosity Models
13.2.2.3 Implicit Large Eddy Simulation Models
13.2.3 Thermal Equation of State
13.2.4 Combustion Modeling
13.2.4.1 Infinite Chemistry Approximation
13.2.4.2 Partially Stirred Reaction TCI Model
13.2.5 Interphase Coupling Terms
13.2.6 Dispersed Phase Modeling
13.3 Afterburning behind Heterogeneous Nitromethane Charges
13.3.1 Setup, Initial Conditions, and Grid Resolution
13.3.2 Mixing Layer Characteristics
13.3.2.1 Chronology of the Postdetonation Flow
13.3.2.2 Turbulent Kinetic Energy and Baroclinic Torque
13.3.3 Comparison to a Homogeneous Explosive Charge
13.4 TNT Afterburning at Different Heights of Blast
13.4.1 Effect of HoB on Afterburning
13.4.2 Characteristics of the Mixing Layer at Different HoB
13.5.1 Aluminium Combustion
13.5.2 Effect of Aluminium on Afterburning
Epilogue: Vision for Coarse Grained Simulation
E.2 Fundamental Challenges
E.3 Complex Mixing Consequences
Coarse Grained Simulation and Turbulent Mixing
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