DNS of Wall-Bounded Turbulent Flows. A First Principle Approach

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Preface References Contents Symbols Description List of Figures List of Tables 1 DNS of Wall-Bounded Turbulent Flow: An Introduction 1.1 Introduction 1.2 Why Deterministic Study Is More Relevant than Stochastic Approaches? 1.2.1 Historic Developments 1.3 Present State of Art in the Field 1.4 Different Transition Routes 1.5 Role of Equilibrium Flow in DNS 1.6 What Is Instability? 1.7 Temporal and Spatial Instability 1.8 Some Instability Mechanisms 1.8.1 Kelvin–Helmholtz Instability References 2 DNS of Navier–Stokes Equation 2.1 Fluid Dynamical Equations 2.1.1 Equation of Continuity 2.1.2 Momentum Conservation Equation 2.1.3 Energy Conservation Equation 2.1.4 Alternate Forms of the Energy Equation 2.1.5 Vorticity Transport Equation for Incompressible Flows 2.1.6 Derived Variable Formulation for 2D Incompressible Navier–Stokes Equation 2.2 Spatial and Temporal Scales for Transitional and Turbulent Flows 2.3 Numerical Methods for Developing DNS/LES 2.3.1 Waves – Building Blocks of a Disturbance Field 2.3.2 Resolution of Spatial Discretization 2.3.3 High-Accuracy Compact Schemes for Evaluation of First Derivatives 2.3.4 Boundary Closure Schemes for Compact Schemes to Evaluate First Derivative 2.3.5 Compact Schemes for Second Derivative Evaluation 2.3.6 Compact Schemes for Interpolation and First Derivative Evaluation in Staggered Grids 2.3.7 Discretization of Self-Adjoint Terms 2.3.8 Computing Methods for Unsteady Flows: Dispersion Relation Preserving (DRP) Methods 2.3.9 Numerical Amplification Factor for 1D Convection Equation 2.3.10 Quantification of Dispersion Error and Error Propagation Equation 2.3.11 Dispersion Relation Preserving Schemes 2.4 Design of DRP Schemes for DNS/LES 2.5 Numerical Filtering: Error Control via Stabilization and Dealiasing 2.5.1 Use of Filters for DNS and LES 2.5.2 Use of 1D Filters at the Outflow 2.5.3 Two-Dimensional Higher Order Filters 2.5.4 Adaptive 2D Filter 2.6 Role of Solenoidality Errors in Velocity-Vorticity Formulations 2.6.1 Computation of Physically Unstable Flows in Square Lid Driven Cavity 2.6.2 Solution of 3D Cubic Lid Driven Cavity Using Velocity-Vorticity Formulation and Role of Solenoidality Error for Vorticity References 3 Receptivity and Instability 3.1 Linear Stability/Receptivity Theories: Classical Approaches and Signal Problem 3.1.1 The Equilibrium Flow Equation 3.2 Linear Stability Equation 3.3 Linear Receptivity Analysis of Parallel Boundary Layer 3.3.1 Receptivity of Blasius Boundary Layer 3.3.2 Near-Field of the Localized Excitation: The Local Solution 3.3.3 The Spatio-Temporal Wave-Front (STWF) 3.4 Stability and Transition of Mixed Convection Flows 3.5 Governing Equations 3.6 Equilibrium Boundary Layer Flows 3.6.1 Schneider's Similarity Solution 3.6.2 Ambiguities of Spatial and Temporal Linear Theories: Example of Mixed Convection Problem 3.7 Equilibrium Solution for Mixed Convection Flows: Isothermal Wall Case 3.7.1 Governing Equation for Flow over Isothermal Wall 3.7.2 Mixed Convection Governing Equations and Boundary Conditions for DNS 3.7.3 Linear Viscous Instability: Spatial and Temporal Routes 3.7.4 Linear Spatial Viscous Theory for Mixed Convection Flows 3.7.5 Linear Temporal Viscous Theory for Mixed Convection Flows 3.8 Receptivity of Mixed Convection Flows 3.8.1 Receptivity of Cold Adiabatic Flat Plate Cases 3.8.2 Receptivity of Hot Isothermal Wedge Case 3.8.3 DNS of Instability of Mixed Convection Flows: New Theorems of Instability 3.9 Nonlinear and Nonparallel Effects: Receptivity by DNS 3.9.1 Computational Domain and Grid Resolution 3.9.2 The Equilibrium Flow 3.9.3 Typical Morphology of the Disturbance Field 3.9.4 Receptivity to SBS Excitation: Nonlinear and Nonparallel Effects 3.9.5 Effects of Nonlinearity: Role of Amplitude of Excitation 3.9.6 Comparison of Results for α1= 0.002, 0.005 and 0.01 3.9.7 Results for α1=0.1 3.9.8 Wall-Normal Variation of ud and vd 3.9.9 Further Evidences of Nonparallel, Nonlinear Effects and Bypass Transition 3.9.10 Effects of the Location of Exciter 3.9.11 Effects of Frequency of Excitation References 4 Nonlinear Theoretical and Computational Analysis of Fluid Flows 4.1 Nonlinear Instability Theory Based on Mechanical Energy 4.2 Vortex-Induced Instability: Application of a Nonlinear Theory for Total Mechanical Energy 4.2.1 An Experimental Observation of Vortex-Induced Instability 4.3 Numerical Simulation of Vortex-Induced Instability 4.3.1 Velocity-Vorticity Formulations for 2D Flows 4.3.2 Boundary Conditions 4.3.3 Numerical Methods and Grids 4.3.4 Grid Generation 4.3.5 Numerical Results and Discussion 4.3.6 The Instability Mechanism 4.4 Enstrophy Transport Equation: A New Approach to Nonlinear Receptivity Theory 4.4.1 Enstrophy Transport Equation 4.4.2 Enstrophy Cascade for General Inhomogeneous Flows 4.5 Theory of Instability for Enstrophy: Creation of Rotationality 4.6 Proper Orthogonal Decomposition 4.6.1 Some Useful Mathematical Relations 4.6.2 Method of Snapshots 4.6.3 TS Wave Instability over Zero-Pressure Gradient Boundary Layer References 5 Dynamics of the Spatio-Temporal Wave-Front in 2D Framework 5.1 Introduction 5.2 From Linear Theory to Turbulence via Deterministic Routes 5.2.1 Governing Equations, Numerical Schemes and Simulation Parameters 5.3 Small Amplitude Disturbance at Moderate Frequency 5.3.1 Growth and Speed of STWF 5.3.2 Spatial Spectrum and Scale Selection of STWF 5.3.3 Wall-Normal Variation of the Disturbance Velocity 5.4 Dynamics of STWF for High Amplitude Wall-Excitation … 5.5 Low Frequency Excitation: Interaction of Near-Field … 5.5.1 Low Frequency Excitation: Dominant Role of the Near-Field Solution 5.6 Dynamics of the STWF for Excited Flow Over an Airfoil References 6 3D Routes of Transition to Turbulence by STWF 6.1 Introduction 6.1.1 Governing Equations and Numerical Methods 6.1.2 Boundary Conditions 6.1.3 Initial Condition 6.1.4 Grid Generation 6.1.5 Numerical Method and Solution Technique 6.2 Gaussian Circular Patch (GCP) Excitation 6.3 Spanwise Modulated (SM) Excitation 6.4 Routes of Flow Transition: K- and H-Type Routes 6.5 Formation of Turbulent Spots and Fully Developed Turbulent Flow References A A.1 Boundary Layer Equation for Mixed Convention Problem A.2 Similarity Transformation Index