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Table of Contents
Intro
Preface
Contents
Editors and Contributors
Part I Theoretical Foundation and Applications for Turbulence and Transition Research
1 Liutex and Third Generation of Vortex Definition and Identification
1.1 Introduction
1.2 Three Generations of Vortex Definition and Identification
1.2.1 First Generation of Vortex Identification Methods (Vorticity-Based Methods)
1.2.2 Second Generation of Vortex Identification
1.2.3 Limitations of Existing Vortex Identification Methods
1.2.4 Mathematical Misunderstandings of the First and Second Generation of Vortex Identification Methods
1.2.5 Contaminations of First and Second Generations of Vortex Identification Methods
1.2.6 Liutex
1.3 Future Research Plan
1.3.1 Develop Unique, Accurate, and Threshold-Free Vortex Identification Methods
1.3.2 Characterize Vortex Structure
1.3.3 Liutex Similarity
1.3.4 Correlation Analysis of Pressure Fluctuation (Noise Generation) and Liutex Spectrum by Mathematical Analysis and Experimental Modeling
1.4 Conclusions and Future Work
References
2 Galilean Variance of Streamline in Vortex/Liutex Visualization
2.1 Introduction
2.2 Galilean Invariance
2.3 Galilean Variance of Streamline
2.4 Galilean Invariance of Liutex
2.5 Numerical Example
2.6 Conclusion
References
3 Rules of Tensor and Matrix Operation for Liutex Calculation
3.1 Introduction
3.2 Express Tensor and Its Operation by Matrix
3.3 Matrix Form of Velocity Gradient Tensor
3.4 Some Calculation Examples Using Matrix Expressions
3.5 Conclusion
References
4 Liutex Core Tube for Vortex Visualization and Structure
4.1 Introduction
4.2 Data
4.3 Liutex Core Tube
4.3.1 Constructing the Liutex Core Tube
4.3.2 Liutex Core Tube Versus Iso-Surface
4.4 Conclusion
References
5 Study of Vortex and Vorticity in a Laminar Flow
5.1 Introduction
5.2 Vortex Identification Methods
5.2.1 Vorticity-Based Method
5.2.2 Second-Generation Vortex Identification Method
5.2.3 Third-Generation Vortex Identification Method
5.3 Vortex Versus Vorticity
5.3.1 Vorticity Meter and Long Channel Device
5.3.2 Reynolds Number and Laminar Flow
5.3.3 Modified Shapiro's Experiment
5.3.4 Mathematical Analysis
5.3.5 Vorticity and Liutex
5.4 Conclusion and Discussion
References
6 POD Analysis on Losing Symmetry of Vortex Structure in the Flow Transition by Liutex Method
6.1 Introduction
6.2 Numerical Setup
6.3 Proper Orthogonal Decomposition (POD)
6.4 POD Analysis Inflow Transition by Modified Liutex Omega Method
6.5 POD Analysis on Losing Symmetry of Vortex Structure
6.6 Conclusion
References
7 The Liutex Shear Interaction in Boundary Layer Transition
7.1 Introduction
7.2 Vortex Identification Method
7.2.1 Vortex, Vorticity, Velocity Gradient Tensor
Preface
Contents
Editors and Contributors
Part I Theoretical Foundation and Applications for Turbulence and Transition Research
1 Liutex and Third Generation of Vortex Definition and Identification
1.1 Introduction
1.2 Three Generations of Vortex Definition and Identification
1.2.1 First Generation of Vortex Identification Methods (Vorticity-Based Methods)
1.2.2 Second Generation of Vortex Identification
1.2.3 Limitations of Existing Vortex Identification Methods
1.2.4 Mathematical Misunderstandings of the First and Second Generation of Vortex Identification Methods
1.2.5 Contaminations of First and Second Generations of Vortex Identification Methods
1.2.6 Liutex
1.3 Future Research Plan
1.3.1 Develop Unique, Accurate, and Threshold-Free Vortex Identification Methods
1.3.2 Characterize Vortex Structure
1.3.3 Liutex Similarity
1.3.4 Correlation Analysis of Pressure Fluctuation (Noise Generation) and Liutex Spectrum by Mathematical Analysis and Experimental Modeling
1.4 Conclusions and Future Work
References
2 Galilean Variance of Streamline in Vortex/Liutex Visualization
2.1 Introduction
2.2 Galilean Invariance
2.3 Galilean Variance of Streamline
2.4 Galilean Invariance of Liutex
2.5 Numerical Example
2.6 Conclusion
References
3 Rules of Tensor and Matrix Operation for Liutex Calculation
3.1 Introduction
3.2 Express Tensor and Its Operation by Matrix
3.3 Matrix Form of Velocity Gradient Tensor
3.4 Some Calculation Examples Using Matrix Expressions
3.5 Conclusion
References
4 Liutex Core Tube for Vortex Visualization and Structure
4.1 Introduction
4.2 Data
4.3 Liutex Core Tube
4.3.1 Constructing the Liutex Core Tube
4.3.2 Liutex Core Tube Versus Iso-Surface
4.4 Conclusion
References
5 Study of Vortex and Vorticity in a Laminar Flow
5.1 Introduction
5.2 Vortex Identification Methods
5.2.1 Vorticity-Based Method
5.2.2 Second-Generation Vortex Identification Method
5.2.3 Third-Generation Vortex Identification Method
5.3 Vortex Versus Vorticity
5.3.1 Vorticity Meter and Long Channel Device
5.3.2 Reynolds Number and Laminar Flow
5.3.3 Modified Shapiro's Experiment
5.3.4 Mathematical Analysis
5.3.5 Vorticity and Liutex
5.4 Conclusion and Discussion
References
6 POD Analysis on Losing Symmetry of Vortex Structure in the Flow Transition by Liutex Method
6.1 Introduction
6.2 Numerical Setup
6.3 Proper Orthogonal Decomposition (POD)
6.4 POD Analysis Inflow Transition by Modified Liutex Omega Method
6.5 POD Analysis on Losing Symmetry of Vortex Structure
6.6 Conclusion
References
7 The Liutex Shear Interaction in Boundary Layer Transition
7.1 Introduction
7.2 Vortex Identification Method
7.2.1 Vortex, Vorticity, Velocity Gradient Tensor