Turbulent Jets and Plumes A Lagrangian Approach

Jets and plumes are shear flows produced by momentum and buoyancy forces. Examples include smokestack emissions, fires and volcano eruptions, deep sea vents, thermals, sewage discharges, thermal effluents from power stations, and ocean dumping of sludge. Knowledge of turbulent mixing by jets and plumes is important for environmental control, impact and risk assessment.

Turbulent Jets and Plumes introduces the fundamental concepts and develops a Lagrangian approach to model these shear flows. This theme persists throughout the text, starting from simple cases and building towards the practically important case of a turbulent buoyant jet in a density-stratified crossflow. Basic ideas are illustrated by ample use of flow visualization using the laser-induced fluorescence technique. The text includes many illustrative worked examples, comparisons of model predictions with laboratory and field data, and classroom tested problems. An interactive PC-based virtual-reality modelling software (VISJET) is also provided. Engineering and science students, researchers and practitioners may use the book both as an introduction to the subject and as a reference in hydraulics and environmental fluid mechanics.

1. Introduction.- 2. Turbulent Jets.- 1. Plane Jet.- 1.1 Governing Equations.- 1.2 Integral Equations.- 1.3 Eulerian Integral Model.- 1.4 Entrainment Hypothesis.- 2. Round Jet.- 2.1 Mean Flow Structure.- 2.2 Additional Remarks on 3D Jet:.- 3. Theory vs Experiment.- 3.1 Mean Properties.- 3.2 Turbulence Properties.- 4. The Top-hat Profile.- 5. Prediction of Potential Core Length.- 6. Summary.- 3. Turbulent Buoyant Plumes.- 1. Buoyancy and Reduced Gravity.- 2. Turbulent Round Plume.- 2.1 Dimensional Considerations.- 2.2 Eulerian Integral Model.- 2.2.1 Governing Equations.- 2.2.2 Integral Model Equations.- 2.2.3 Entrainment Hypothesis.- 2.2.4 Asymptotic Solution.- 2.2.5 Densimetric Froude number.- 2.2.6 Experiments.- 2.3 Effect of Initial Momentum: Vertical Buoyant Jet.- 2.4 Buoyancy Reduction due to Density-temperature Nonlinearity.- 3. Lagrangian Approach for Plume Modelling.- 4. Negatively Buoyant Jets.- 5. Turbulent Line Plume.- 6. Summary.- 4. Inclined Buoyant Jet in Stagnant Environment.- 1. Lagrangian Model for Buoyant Jet in Stagnant Fluid.- 1.1 Zone of Established Flow (ZEF).- 1.2 The Potential Core (ZFE).- 2. Numerical Solution.- 2.1 Jet Trajectory and Potential Core Development.- 2.2 Dilution.- 2.3 Boundary effects.- 3. Application Examples.- 4. Summary.- 5. Density Stratification.- 1. Buoyancy Variation.- 1.1 Salinity Equation.- 1.2 Temperature Equation.- 1.3 Stratification Frequency.- 2. Thermals in Stratified Fluid.- 2.1 Round Thermals.- 2.2 Line Thermal.- 3. Plumes in Stratified Fluid.- 3.1 Round Plume in Linearly Stratified Environment.- 3.2 Plane Plume in Linearly Stratified Environment.- 3.3 Plumes in arbitrary density stratification.- 4. Plume in a Container.- 5. Summary.- 6. Turbulent Round Jet in Coflow.- 1. Summary of Experimental Observations.- 1.1 Cross-sectional Images.- 1.2 Gaussian Profiles.- 2. Integral Model.- 2.1 The Natural but Incorrect Formulation.- 2.2 Jet Spreading Hypothesis.- 2.3 Governing Equations.- 2.4 Approximate Initial Conditions.- 2.5 Prediction of Potential Core Length.- 2.6 Alternative Definition of Characteristic Velocity.- 3. Asymptotic Solutions: Strong and Weak-jet.- 4. Comparison of Theory with Experimental Data.- 4.1 Jet Spreading Rate.- 4.2 Centerline Dilution.- 4.3 Centerline Excess Velocity Decay.- 4.4 The Entrainment Coefficient.- 5. Correlation of Model Results with Experiments.- 5.1 Visual Boundary.- 5.1.1 Intermittency and top-hat edge.- 5.1.2 Visual boundary.- 5.2 Flow-weighted Average Dilution.- 5.3 Summary of Experimental Data.- 6. Summary.- 7. Jet in Crossflow: Advected Line Puffs.- 1. Length Scales and Regimes.- 1.1 Line Puff Analogy for MDFF.- 1.2 Similarity Variables for the Line Puff.- 2. 1D Model of Line Puff.- 3. 2D Model of Line Puff.- 3.1 Numerical Simulation of Line Puffs.- 4. 3D Model of Jet in Crossflow.- 4.1 The Advected Line Puff.- 4.2 3D Model of Advected Line Puff226.- 4.2.1 Characteristics of advected line puff.- 5. Measurements in Advected Line Puffs.- 5.1 Time-averaged properties.- 5.2 Turbulence properties.- 6. Practical Application.- 7. Summary.- 8. Plume in Crossflow: Advected Line Thermals.- 1. Length Scales and Regimes.- 1.1 Line-Thermal Analogy for BDFF.- 1.2 Similarity Variables for the Line Thermal.- 2. 1D Model of Line thermal.- 3. 2D Model of Line Thermal.- 3.1 Numerical Simulation of Line Thermals.- 4. 3D Model of Plume in Crossflow.- 4.1 The Advected Line Thermal.- 4.2 3D model of Advected Line Thermal.- 4.2.1 Characteristics of advected line thermal.- 5. Measurements in Line Thermals.- 5.1 Experiments on Advected Line Thermals.- 5.2 Concentration Measurements.- 5.3 Summary of Experimental Data.- 6. Buoyant Jet in Crossflow.- 6.1 Line Thermals and Puffs.- 6.2 Application Example.- 7. Summary.- 9. General Lagrangian Formulation.- 1. Elemental Volume.- 2. Method of Excesses.- 3. Spreading Hypothesis.- 3.1 Projected Area Entrainment.- 3.2 Surface Area Entrainment.- 3.3 Shear Entrainment.- 3.4 Summary.- 4. Puffs and Thermals.- 5. Buoyant Jet in Crossflow.- 5.1 Zone of Established Flow.- 5.2 Potential Core in the ZEF.- 6. Summary.- 10.Numerical Modelling and Field Application.- 1. Initial Dilution of Buoyant Plumes in a Current: the BDNF and BDFF.- 1.1 The BDNF-BDFF Transition.- 2. JETLAG — a Lagrangian buoyant jet model.- 2.1 Overview of Model.- 2.2 Basic Concepts of Lagrangian Model.- 2.3 Model Formulation.- 2.4 Shear and Vortex Entrainment.- 2.5 Formulation for Near-Far Field Transition.- 2.6 Comparison of Model Predictions with Laboratory Data.- 3. Field Application and Verification.- 3.1 Post-operation Monitoring of Sydney Outfall.- 3.2 Field Verification at North West New Territories outfall, Urmston Road, Hong Kong.- 3.3 Environmental Impact Assessment of the Hong Kong SSDS Ocean Outfall.- 3.4 VISJET — Interactive Virtual Reality Model.- Appendices.- A— Density of Seawater.- B— Notation.- References.