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