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