This book presents the fundamentals and advanced research on the global stability analysis of the shear flows. The contents investigate the results of global stability analysis for different configurations of internal and external shear flows. The topics covered are global stability analysis of converging-diverging channel flows, axisymmetric boundary layer developed on a circular cylinder, cone and inclined flat-plate boundary layer, and wall jets. It further explains the effect of divergence, convergence, transverse curvature, and pressure gradients on the global stability of the different configurations of shear flows. The book is a valuable reference for beginners, researchers, and professionals working in the field of aerodynamics and marine hydrodynamics.
Author(s): Rameshkumar Bhoraniya, Gayathri Swaminathan, Vinod Narayanan
Series: Springer Tracts in Mechanical Engineering
Publisher: Springer
Year: 2023
Language: English
Pages: 231
City: Singapore
Preface
Contents
About the Authors
1 Introduction to Flow Instabilities
1.1 Introduction
1.2 Physics of Flow Stability and Transition
1.3 Flow Transition Stages in Boundary Layer
1.4 Methods of Instability Investigation
1.5 Overview of the Present Work
References
2 Global Stability Approach
2.1 Introduction
2.2 Linear Stability Theory
2.3 Stability of Parallel Flows
2.4 Stability of Weakly Non-parallel Flows
2.5 Global Stability Analysis
2.6 Discretization
2.6.1 1D Discretization
2.6.2 2D Discretization-Y
2.6.3 2D Discretization-X
2.6.4 Coordinate Transformation and Grid Stretching
2.6.5 Domain Transformation
2.7 Baseflow Calculation and Boundary Conditions
2.8 Boundary Conditions
2.9 Numerical Method
2.10 Issues with Global Stability Computations
2.11 Grid Sensitivity
2.12 Validation
References
3 Diverging Channel
3.1 Introduction
3.2 Diverging Channel
3.3 Base Flow
3.3.1 JH Base Flow
3.3.2 SDS Base Flow
3.4 Comparison of Base Flow—JH and SDS
3.5 Sensitivity of the Critical Reynolds Number to Divergence
3.6 Global Stability Analysis
3.6.1 Boundary Conditions
3.6.2 Validation
3.6.3 Sensitivity Study
3.6.4 Comparison of JH and SDS Spectra
3.6.5 JH Results
3.6.6 SDS Results
3.7 Upstream Propagation
3.8 Summary
References
4 Converging-Diverging Channel
4.1 Introduction
4.2 Base Flow
4.2.1 Parameters
4.2.2 Numerical Scheme
4.3 Global Stability Analysis
4.4 Results
4.4.1 The Standard Geometry
4.4.2 The Instability Ratchet
4.4.3 Spatio-Temporal Interplay
4.4.4 Numerical Floquet Study and Its Limitations
4.4.5 Reverse Geometry
4.4.6 Symmetric Geometry
4.4.7 Comparison of Forward, Reverse and Symmetric Geometries
4.4.8 Effect of Amplitude of Wall Waviness
4.4.9 Eigenvalue Sensitivity and Pockets of Transient Growth
4.4.10 Other Parameters
4.5 Summary
References
5 Axisymmetric Boundary Layer on a Cylinder
5.1 Introduction
5.2 Mathematical Modelling
5.2.1 Boundary Conditions
5.2.2 Solution of General Eigenvalues Problem
5.3 Base Flow Solution
5.4 Validation of Global Approach
5.4.1 Axisymmetric Mode (N = 0)
5.4.2 Helical Mode, N = 1
5.5 Comparison with the Local Stability Analysis
5.6 Global Stability Results
5.6.1 Grid Convergence Study
5.6.2 Effect of Wall-Normal Domain Size
5.6.3 Effect of Streamwise Domain Size
5.6.4 Sponging
5.6.5 Effect of Outflow Boundary Conditions
5.6.6 Axisymmetric Mode
5.6.7 Effect of Transverse Curvature
5.6.8 Helical Mode N=1
5.6.9 Helical Mode N=2
5.6.10 Helical Mode N = 3
5.7 Temporal Growth Rate
5.8 Spatial Amplification Rate
5.9 Summary
References
6 Axisymmetric Boundary Layer on a Circular Cone
6.1 Introduction
6.2 Problem Formulation
6.2.1 Boundary Conditions
6.2.2 Solution of General Eigenvalues Problem
6.3 Base Flow Solution
6.4 Code Validation
6.5 Boundary Conditions Evaluation
6.6 Influence of the Domain Length
6.7 Global Stability Results
6.7.1 Semi-cone Angle α=2°
6.7.2 Semi-cone Angle α= 4°
6.7.3 Semi-cone Angle α=6°
6.8 Temporal Growth Rate
6.9 Spatial Amplification Rate
6.10 Summary
References
7 Boundary Layer on an Inclined Flat Plate
7.1 Introduction
7.2 Problem Formulation
7.2.1 Boundary Conditions
7.3 Base Flow Solution
7.3.1 Code Validation
7.3.2 Grid Convergence Study
7.3.3 Effect of Streamwise Domain Length
7.4 Global Stability Results
7.4.1 Favourable Pressure Gradient
7.4.2 Adverse Pressure Gradient
7.5 Summary
References
8 Wall Jet
8.1 Introduction
8.2 Base Flow
8.3 Local Stability Analysis of Wall Jets
8.4 Global Stability Analysis of Wall Jets
8.4.1 Numerical Method
8.4.2 Validation
8.4.3 Sensitivity
8.4.4 Main Results
References
