16.13 | Fall 2003 | Graduate

Aerodynamics of Viscous Fluids

Calendar

LEC # TOPICS KEY DATES
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

Course Info

As Taught In
Fall 2003
Level
Learning Resource Types
Lecture Notes
Problem Sets with Solutions