Statistical Hydrodynamic Models for Developed Mixing Instability Flows

Analytical "0D" Evaluation Criteria, and Comparison of Single-and Two-Phase Flow Approaches

By: Antoine Llor

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Hardcover | 23 December 2005

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164 Pages

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23.5 x 15.88 x 1.27

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Part textbook, part exploratory work, this book aims to raise the awareness of students, physicists, and engineers in turbulence on the modeling of gravitationally induced turbulent mixing flows as produced, for instance, by Rayleigh-Taylor instabilities. The discussion is centered on the differences between single-fluid and two-fluid approaches, and it is illustrated with a 0D analysis of two specific elementary models in common use. Important deviations are shown to appear on many features, among others the prominence of directed energy, the simultaneous restitution of test cases, the responses to variable acceleration and shocks, and the behavior of various length scales.

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Introduction	p. 1
Short Primer on Basic Averaging and Modeling Approaches for Turbulent Mixing Instabilities
Single-Fluid Approach: Example of Dam's k-¿ Model	p. 7
Single-Fluid Statistical Equations	p. 7
An Elementary Single-Fluid Closure: The Incompressible k-¿ Model	p. 11
An Extension to Variable Densities: Dam's k-¿ Model	p. 13
Two-Fluid Approach: Example of Awe's Model	p. 17
Two-Fluid Statistical Equations	p. 17
An Elementary Two-Fluid Closure: Awe's Model	p. 23
Summary of Part I	p. 29
"OD" Reduction of Experiments and Models in Mixing Instabilities
Mixing Instabilities in Developed Regime: Phenomenology of Energy Balances	p. 33
Review of Different Instability Types and Regimes	p. 33
"OD" Energy Balance in Self-Similar, Incompressible, Developed Regime at Zero Atwood Number	p. 34
"OD" Turbulent Energy and Structure in Self-Similar, Incompressible, Developed Regime at Zero Atwood Number	p. 37
"OD" Reduction of Evolution Equations of Hydrodynamic Models	p. 43
Reconstruction by Dam's k-¿ Model of Developed Mixing Instabilities	p. 47
Comments on the "Richtmyer-Meshkov" Calibration of Coefficients C_¿O and <$>\sigma_{\varrho}<$>	p. 47
"OD" Reconstruction by Dam's k-¿ Model of Basic Self-Similar Instabilities	p. 49
General Remarks, Reconstruction of the Directed Kinetic Energy	p. 49
Construction and Resolution of the "OD" Differential System	p. 49
Realizability of Turbulent Closures	p. 54
Estimation of Errors Introduced by the "OD" Approach	p. 54
"OD Rayleigh-Taylor" Calibration of Coefficients C_¿O and <$>\sigma_{\varrho}<$>	p. 55
Discussion of the "OD" Results	p. 55
Stability and the RT Case with Self-Similar Variable Acceleration	p. 56
Conclusions on Dam's k-¿ Model	p. 60
Awe's Two-Fluid Model of Developed Mixing Instabilities	p. 63
"OD" Reconstruction by Awe's Two-Fluid Model of Basic Self-Similar Instabilities	p. 63
General Remarks, Drag Characteristic Length Scale	p. 63
Rayleigh-Taylor and Richtmyer-Meshkov Cases	p. 64
Kelvin-Helmholtz Case	p. 66
Calibration of Coefficients C_i and C_d of Awe's Two-Fluid Model	p. 70
Effect of the Coefficients on KH, RT, and RM Instabilities	p. 70
Stability and the RT Case with Self-Similar Variable Acceleration	p. 71
Summary of Part II	p. 75
Comparative Assessment of Models, New Development Approaches
Comparison of Single- and Two-Fluid Approaches	p. 79
Summary of "OD" Reconstructions of the Three Instabilities by the Single- and Two-Fluid Models	p. 79
About the "Rayleigh-Taylor" Source Term in Single-FluidModels	p. 81
Two-fluid Realizability of Single-Fluid Closures of Turbulent Fluxes	p. 84
The "Two-Fluid Extended" Single-Fluid Approach	p. 86
Specific Treatment of Shocks: Constraints on Models	p. 93
Qualitative Phenomenology of Interaction Between a Shock and Velocity or Density Heterogeneities	p. 93
Preliminary Comments on Modeling of Shock-Heterogeneity Interaction	p. 96
On Artificial Dissipation in a Two-Fluid Medium	p. 99
Basic Bias Estimates of Dam's k-¿ and Awe's Two-Fluid Models Applied to Shock-Turbulence Interaction	p. 102
Some Perspectives on Further Developments of Models	p. 107
About Second-Order Extensions of Single-Fluid Turbulent Mixing Models	p. 107
Molecular Interdiffusion, Demixing, and Separation of Geometric and Turbulent Scales	p. 109
Interdiffusion	p. 109
Geometric and Turbulent Scales	p. 112
<$$$> Self-Similar Variable Acceleration Rayleigh-Taylor Flows (SSVARTs)	p. 113
Extension of SSVARTs to n < -2	p. 113
Spectral Quasi-Equilibrium and Relevance of Models in SSVARTs	p. 115
Summary of Part III	p. 119
Conclusion, Future Modeling Trends	p. 121
Notations and Acronyms	p. 125
Modeling of Noise Term	p. 129
Correction of the Input Energy, K_I, of the Kelvin-Helmholtz Instability	p. 131
Turbulent Flux of k Expressed in Two-Fluid Terms	p. 133
About the Effects of Compressibility on Closures of Turbulent Fluxes	p. 135
References	p. 137
Index	p. 147
Table of Contents provided by Publisher. All Rights Reserved.

Statistical Hydrodynamic Models for Developed Mixing Instability Flows

Analytical "0D" Evaluation Criteria, and Comparison of Single-and Two-Phase Flow Approaches

At a Glance

Hardcover

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