| Underlying Physical Principles |
| 1 |
Course Description. Fundamental Theorem of Kinematics - Convection, Vorticity, Strain. (PDF) |
Hierarchy of 3-D Configuration CFD Methods (PDF) |
| 2 |
Eulerian vs. Langrangian Description. Convection Relations. (PDF) |
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| Conservation Laws |
| 3 |
Conservation of Mass. Conservation of Momentum. Stress Tensor. (PDF) |
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| 4 |
Viscosity. Newtonian Fluids. Vorticity and Circulation. (PDF) |
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| 5 |
Navier-Stokes Equations. Physical Parameters. Dynamic Similarity. (PDF) |
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| Thin Shear Layer Approximation |
| 6 |
Dimensional Analysis. Dominant Balance and Viscous Flow Classification. (PDF) |
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| 7 |
Re→∞ Behavior. Thin Shear Layer Equations. TSL coordinates. (PDF) |
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| 8 |
TSL Coordinates. Boundary Conditions. Shear Layer Categories. (PDF) |
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| 9 |
Local Scaling. Falkner-Skan Flows. (PDF) |
Unsteady Local Scaling Transformation (PDF) |
| Solution Techniques |
| 10 |
ODE'S, PDE's, and Boundary Conditions. Well-Posedness. (PDF) |
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| 11 |
Numerical Methods for ODE's. Discretization. Stability. (PDF) |
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| 12 |
Finite Difference Methods. Newton-Raphson. (PDF) |
Solution of Falkner-Skan Equation by Finite Differences (PDF)
Finite Difference Solution of TSL Equations(PDF)
Basis for Integral BL Methods (PDF)
Thwaites' Method (PDF)
Integral Thicknesses (PDF)
Von-Karman Integral Momentum Equation (PDF)
Integral Kinetic Energy Equation (PDF) |
| 13 |
Integral Methods. Integral Momentum Equation. Thwaites' Method. (PDF) |
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| 14 |
Integral Kinetic Energy Equation. Dissipation Methods. (PDF) |
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| 15 |
Integral Kinetic Energy Equation. Dissipation Methods. (cont.) (PDF) |
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| Interacting Boundary Layer Theory |
| 16 |
Asymptotic Perturbation Theory - Higher-Order Effects. (PDF) |
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| 17 |
2D Interaction Models: Displacement Body, Transpiration. Form Drag, Stall Mechanisms. (PDF) |
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| 18 |
IBLT Solution Techniques. Iteration Stability. (PDF) |
Behavior of Separated Flow (PDF)
Displacement Effects of Boundary Layer on Potential Flow (PDF) |
| 19 |
Fully-Coupled Iteration. 3-D IBLT. (PDF) |
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| Stability and Transition |
| 20 |
Small-Perturbation Theory. Orr-Sommerfeld Equation. (PDF) |
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| 21 |
Small-Perturbation Theory. Orr-Sommerfeld Equation. (cont.) (PDF) |
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| 22 |
Boundary Conditions, Homogeneity, Solution Techniques. (PDF) |
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| 23 |
Transition Mechanisms. Transition Prediction: Local Correlations, Amplification Methods. (PDF) |
en Method (PDF) |
| Turbulent Shear Layers |
| 24 |
Reynolds Averaging. Prandtl's Analogy. (PDF) |
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| 25 |
Turbulent BL Structure: Wake, Wall Layers. Inner, Outer Variables. Effects of Roughness. (PDF) |
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| 26 |
Turbulent BL Structure: Wake, Wall Layers. Inner, Outer Variables. Effects of Roughness. (cont.) (PDF) |
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| 27 |
Equilibrium BL's: Clauser Hypothesis. Dissipation Formulas and Integral Closure. (PDF) |
G-Beta Locus Relations (PDF) |
| 28 |
Equilibrium BL's: Clauser Hypothesis. Dissipation Formulas and Integral Closure. (cont.) (PDF) |
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| 29 |
Turbulence Modeling and Closure. Algebraic Models. Transport Models. (PDF) |
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| Compressible Thin Shear Layers |
| 30 |
Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy. (PDF) |
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| 31a |
Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy. (cont.) (PDF) |
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| 31b |
Approximate Temperature Profile. Reynolds Heat Flux. (PDF) |
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| 3D Boundary Layer |
| 32 |
New Effects: Crossflow, Lateral Dilation, 3D Separation. Governing Equations. (PDF) |
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| 33 |
Coordinate Systems. Characteristics, BC's, and Well-Posedness. (PDF) |
Integral Boundary Layer Equations for Three-Dimensional Flows (PDF)
Closure for Three-Dimensional Boundary Layer Equations (PDF) |
| 34 |
3D Characteristics, BC's. Quasi-3D: Constant-Crossflow Approximation. (PDF) |
3D BL Equations - Sweep / Taper (PDF) |
| 35 |
3D Characteristics, BC's. Quasi-3D: Constant-Crossflow Approximation. (cont.) (PDF) |
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| 36 |
3D Stability Theory. 3D Transition Mechanisms. (PDF) |
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