Aerodynamics of Viscous Fluids

Lecture Notes

LEC #	TOPICS	SUPPORTING FILES
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)
Conservation Laws
3	Conservation of Mass. Conservation of Momentum. Stress Tensor. (PDF)
4	Viscosity. Newtonian Fluids. Vorticity and Circulation. (PDF)
5	Navier-Stokes Equations. Physical Parameters. Dynamic Similarity. (PDF)
Thin Shear Layer Approximation
6	Dimensional Analysis. Dominant Balance and Viscous Flow Classification. (PDF)
7	Re→∞ Behavior. Thin Shear Layer Equations. TSL coordinates. (PDF)
8	TSL Coordinates. Boundary Conditions. Shear Layer Categories. (PDF)
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)
11	Numerical Methods for ODE’s. Discretization. Stability. (PDF)
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)
14	Integral Kinetic Energy Equation. Dissipation Methods. (PDF)
15	Integral Kinetic Energy Equation. Dissipation Methods. (cont.) (PDF)
Interacting Boundary Layer Theory
16	Asymptotic Perturbation Theory - Higher-Order Effects. (PDF)
17	2D Interaction Models: Displacement Body, Transpiration. Form Drag, Stall Mechanisms. (PDF)
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)
Stability and Transition
20	Small-Perturbation Theory. Orr-Sommerfeld Equation. (PDF)
21	Small-Perturbation Theory. Orr-Sommerfeld Equation. (cont.) (PDF)
22	Boundary Conditions, Homogeneity, Solution Techniques. (PDF)
23	Transition Mechanisms. Transition Prediction: Local Correlations, Amplification Methods. (PDF)	en Method (PDF)
Turbulent Shear Layers
24	Reynolds Averaging. Prandtl’s Analogy. (PDF)
25	Turbulent BL Structure: Wake, Wall Layers. Inner, Outer Variables. Effects of Roughness. (PDF)
26	Turbulent BL Structure: Wake, Wall Layers. Inner, Outer Variables. Effects of Roughness. (cont.) (PDF)
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)
29	Turbulence Modeling and Closure. Algebraic Models. Transport Models. (PDF)
Compressible Thin Shear Layers
30	Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy. (PDF)
31a	Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy. (cont.) (PDF)
31b	Approximate Temperature Profile. Reynolds Heat Flux. (PDF)
3D Boundary Layer
32	New Effects: Crossflow, Lateral Dilation, 3D Separation. Governing Equations. (PDF)
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)
36	3D Stability Theory. 3D Transition Mechanisms. (PDF)