Handbook of Turbulence: Volume 1 Fundamentals and Applications

ISBN-13: 9781468423242 / Angielski / Miękka / 2012 / 498 str.

Walter Frost

Opis

Turbulence takes place in practically all flow situations that occur naturally or in modern technological systems. Therefore, considerable effort is being expended in an attempt to understand this very complex physical phenome- non and to develop both empirical and mathematical models for its description. Such numerical and analytical computational schemes would allow the reliable prediction and design of turbulent flow processes to be carried out. The purpose of this book is to bring together, in a usable form, some of the fundamental concepts of turbulence along with turbulence models and experimental techniques. It is hoped that these have "general applicability" in current engineering design. The phrase "general applicabil- ity" is highlighted because the theory of turbulence is still so much in a formative stage that completely general analyses are not available now, nor will they be available in the immediate future. The concepts and models described herein represent the state-of-the- art methods that are now being used to give answers to turbulent flow problems. As in all turbulent flow analysis, the methods are a blend of analytical and empirical input, and the reader should be cognizant of the simplification and restrictions imposed upon the methods when applyingthem to physical situations different from those for which they have been developed.

Spis treści

1 The Complexity of Turbulent Fluid Motion.- 1.1. Introduction.- 1.2. On Continuum Fluid Motion.- 1.3. Further Remarks on Turbulence.- 1.4. Looking Onward.- References.- 2 An Introduction to Turbulence Phenomena.- 2.1. Introduction.- 2.2. On the Basic Equations of Motion.- 2.2.1. General Considerations.- 2.2.2. Detailed Development.- 2.3. Reynolds’ Decomposition.- 2.3.1. The Mean-Value Equations.- 2.3.2. Some Comments.- 2.3.3. On Pressure Fluctuations.- 2.3.4. Passage to Statistical Theory.- 2.4. Correlations and the Closure Condition.- 2.5. The Turbulent Boundary Layer.- 2.5.1. Preliminary Remarks.- 2.5.2. Comments.- 2.5.3. Further Developments.- 2.6. Final Remarks.- References.- 3 Statistical Concepts of Turbulence.- 3.1. Basic Physical Model of Turbulence.- 3.1.1. Vortex Stretching.- 3.1.2. Energy Cascade.- 3.2. Statistical Definitions.- 3.2.1. The Random Process.- 3.2.2. Stationarity and Ergodicity.- 3.2.3. Space-Dependent Random Variables.- 3.2.4. Homogeneous and Isotropic Turbulence.- 3.2.5. The Taylor Hypothesis.- 3.2.6. Random Field.- 3.2.7. Random Scalar and Vector Fields.- 3.3. Statistical Moments.- 3.3.1. Ordinary Moments.- 3.3.2. Central Moments.- 3.3.3. Joint Moments.- 3.3.4. Space-Time Moments.- 3.3.5. Other Terminology.- 3.3.6. Longitudinal and Lateral Correlations.- 3.3.7. Characteristics of Correlation Coefficients.- References.- 4 Spectral Theory of Turbulence.- 4.1. Introduction.- 4.2. Harmonic Analysis.- 4.2.1. Fourier Series.- 4.2.2. Fourier Integral.- 4.2.3. Stationary Random Process.- 4.2.4. Spectral Representation of a Stationary Random Process.- 4.2.5. Autocorrelation.- 4.3. Frequency Spectra.- 4.4. Wave-Number Spectra.- 4.4.1. From Taylor’s Hypothesis.- 4.4.2. Three-Dimensional Wave-Number Spectra.- 4.5. Characteristics of Energy Spectra.- 4.5.1. Three-Dimensional Energy Spectra.- 4.5.2. One-Dimensional Energy Spectra.- References.- 5 Turbulence: Diffusion, Statistics, Spectral Dynamics.- 5.1. Introduction.- 5.2. Turbulent Diffusion.- 5.3. Fourier Transforms.- 5.4. Particle Diffusion.- 5.5. Another Look at Fourier Transforms.- 5.6. On the Interpretation of Frequency.- 5.7. Strong Interactions.- 5.8. Vorticity and Velocity.- 5.9. The “First Law” of Turbulence.- 5.10. The Energy Cascade.- 5.11. Some Enlightening Errors.- 5.12. Other Inertial Ranges.- 5.13. Turbulent Diffusion Revisited.- 5.14. Conclusions.- References.- 6 Transition.- 6.1. Introduction.- 6.2. Weak Oscillations of Simple Flow.- 6.3. Multiple Perturbations of Laminar Flow.- 6.4. Amplification of Initial Perturbations.- 6.5. Strong Disturbances of Simple Flows.- 6.6. Statistical Models.- 6.7. Comment.- References.- 7 Turbulence Processes and Simple Closure Schemes.- 7.1. Introduction.- 7.2. Theoretical Development.- 7.3. Final Remarks.- References.- 8 Kinetic Energy Methods.- 8.1. Introduction.- 8.2. Eddy Viscosity Transport Models.- 8.3. Turbulent Kinetic Energy Models.- 8.3.1. ND Models I: Bradshaw etal.- 8.3.2. ND Models II: Morel etal.- 8.3.3. ND Models III: Lee and Harsha.- 8.3.4. PK Models I: Ng and Spalding; Rodi and Spalding.- 8.3.5. PK Models II: Launder etal.- 8.3.6. Three-Equation Model: Hanjalic and Launder.- 8.3.7. Comparison of Turbulence-Model Predictions with Free Shear Layer Data.- 8.4. Summary and Conclusions.- References.- 9 Use of Invariant Modeling.- 9.1. Introduction.- 9.2. Model Development.- 9.2.1. Closure Requirements.- 9.2.2. Dissipation Terms.- 9.2.3. Pressure Correlations.- 9.2.4. Third-Order Velocity Correlations.- 9.2.5. Modeled Equations.- 9.2.6. Scale Determination.- 9.3. Evaluation of Model Coefficients.- 9.3.1. Dissipation Coefficient b.- 9.3.2. Diffusion Coefficient vc.- 9.3.3. Scale Determination.- 9.3.4. Low-Reynolds-Number Dependence.- 9.3.5. Additional Coefficients Required to Compute Temperature Fluctuations A, s, and s5.- 9.4. Model Verification.- 9.4.1. Axisymmetric Free Jet.- 9.4.2. Free Shear Layer.- 9.4.3. Two-Dimensional Wake.- 9.4.4. Axisymmetric Wake.- 9.4.5. Flat-Plate Boundary Layer.- 9.4.6. Flow over an Abrupt Change in Surface Roughness.- 9.4.7. Temperature Fluctuations in the Plane Turbulent Wake.- 9.4.8. Stability Influence in the Atmospheric Surface Layer.- 9.4.9. Shear Layer Entrainment in a Stratified Fluid.- 9.4.10. Free Convection.- 9.4.11. Planetary Boundary Layer for Neutral Steady State.- 9.5. Local Equilibrium Approximations.- 9.6. Applications.- 9.6.1. Diurnal Variations in the Planetary Boundary Layer.- 9.6.2. Stratified Wake.- 9.6.3. Pollutant Dispersal.- 9.7. Concluding Remarks.- References.- 10 Numerical Simulation of Turbulent Flows.- 10.1. Introduction.- 10.2. Methods.- 10.3. Problems.- 10.4. Survey of Applications.- 10.5. Comparison with Other Methods.- 10.6. Prospects.- References.- 11 Laboratory Instrumentation in Turbulence Measurements.- 11.1. Introduction.- 11.2. Measurement of Velocity Fluctuations.- 11.2.1. Heat-Transfer Techniques.- 11.2.2. Tracer Techniques.- 11.2.3. Electrochemical Techniques.- 11.2.4. Sonic Anemometer.- 11.2.5. Lift and Drag Sensors.- 11.2.6. Corona-Discharge Anemometer.- 11.3. Measurement of Temperature Fluctuations.- 11.3.1. Resistance Thermometer.- 11.3.2. Measurement of Temperature-Velocity Correlations.- 11.4. Measurement of Density and Pressure Fluctuations.- 11.5. Measurement of Concentration Fluctuations.- 11.5.1. Heat-Transfer Techniques.- 11.5.2. Light Scattering.- 11.6. Measurement of Surface Shear Fluctuations.- References.- 12 Techniques for Measuring Atmospheric Turbulence.- 12.1. Introduction.- 12.2. Measurements: Background, Instruments, Platforms, and Techniques.- 12.2.1. Instrument Response.- 12.2.2. Tower-Based Cup Anemometers.- 12.2.3. Wave Propagation Methods.- 12.2.4. Other Measurement Techniques.- 12.3. Measurements from Aircraft.- 12.3.1. Introduction.- 12.3.2. Simple Techniques of Lower Accuracy.- 12.3.3. Higher-Accuracy Methods.- 12.3.4. Data Processing and Analysis of Errors.- 12.4. Aircraft Measurement of Turbulent Airflow Downwind of a Mountain Range.- 12.5. Elk Mountain PBL Profiles.- 12.6. Suppression of Mixing Coefficient by Forced Boundary-Layer Upward Curvature.- 12.7. Turbulent Airflow across a Building.- 12.8. Concluding Remarks.- References.- 13 Optical and Acoustical Measuring Techniques.- 13.1. Introduction.- 13.2. Background and Basic Principles.- 13.3. Laser Doppler.- 13.3.1. General Types of Laser Doppler Systems.- 13.3.2. Typical Wavelengths and Common Uses of Lasers Presently in Use in LD V Systems.- 13.3.3. Conclusions and Recommendations Concerning Laser Doppler Systems.- 13.4. Acoustic Doppler.- 13.4.1. Types.- 13.4.2. Conclusions and Recommendations Concerning Acoustic Doppler Systems.- References.- 14 Monte Carlo Turbulence Simulation.- 14.1. Introduction.- 14.2. Control-System Simulation.- 14.3. Use of Standard System Function Elements.- 14.3.1. Fitting the Empirical Autocorrelation.- 14.3.2. The System Function.- 14.3.3. The State Space System.- 14.3.4. The Discrete State Space System.- 14.3.5. Effect of Digitizing on the Autocorrelation.- 14.3.6. Discrete Autocorrelations.- 14.3.7. Computer Signal Output.- 14.4. Digital Filter Simulation.- 14.4.1. Discretizing the Convolution Integral.- 14.4.2. Theoretical Correlation for the Control-System Simulation.- 14.5. Discrete Fourier Series.- 14.5.1. Discrete Fourier Transform.- 14.5.2. Discrete Fourier Series Using Randomly Chosen Coefficients.- 14.5.3. Relationship of the Fourier Spectrum to the Power Spectrum.- 14.5.4. Discrete Fourier Series Simulation.- 14.5.5. Theoretical Statistical Moments for Discrete Fourier Series Simulation.- 14.6. Non-Gaussian Simulation.- 14.7. Multidimensional Simulation.- 14.8. Nonhomogeneous Atmospheric Boundary-Layer Simulation.- 14.8.1. Definition of the Problem.- 14.8.2. Filter Synthesis.- 14.8.3. Coherence Matching.- 14.8.4. Autospectral Density Matching.- 14.8.5. Phase Angle Matching.- 14.8.6. Longitudinal Gust Statistics.- 14.8.7. Longitudinal Autospectra.- 14.8.8. Standard Deviation and Integral Scale of Turbulence.- 14.8.9. Coherence and Phase.- 14.8.10. Longitudinal Gust Simulation and Application...- 14.8.11. Coherence Determination.- 14.8.12. Autospectra Factorization.- 14.8.13. Phase Angle Determination.- 14.9. Self-Similar Simulation.- 14.9.1. Inverse Fourier Transformation.- 14.9.2 Transformation to Vehicle time Domain.- 114.10. Conclusions.- References.- 15 Wind, Turbulence, and Buildings.- Author Index.