Aerodynamics of Viscous Fluids

Readings

The course readings are described below. The key to the abbreviations in the Readings column is provided below.

Readings Legend

[W] White, F. _Viscous Fluid Flo_w. McGraw-Hill, 1991. ISBN:0-07-069712-4.

[B] Batchelor, G. K. An Introduction to Fluid Dynamics. Cambridge University Press, 2000. ISBN:0-521-66396-2.

[C&B] Cebeci, T., and P. Bradshaw. Momentum Transfer in Boundary Layers. McGraw-Hill, 1977. ISBN:0-07-010300-3.

[S] Schlichting, H et al. Boundary Layer Theory, 8th Ed. Springer Verlag, 1999. ISBN: 3540662707.

[R] Rosenhead, L. Laminar Boundary Layers. Dover Publications, 1988. ISBN:0-486-65646-2.

[B,C&W] Bradshaw, Cebeci, and Whitelaw. Engineering Calculation Methods for Turbulent Flow. Academic Press, 1981. ASIN:0121245500.

[K&C] Kuethe, A. and C-Y. Chow. Foundations of Aerodynamics, 4th Ed. John Wiley & Sons, 1986. ASIN:0471509531.

LEC #	TOPICS	READINGS
Underlying Physical Principles
1	Course Description. Fundamental Theorem of Kinematics - Convection, Vorticity, Strain.	[B] 78-87 [W] 16-22
2	Eulerian vs. Langrangian Description. Convection Relations.
Conservation Laws
3	Conservation of Mass. Conservation of Momentum. Stress Tensor.	[B] 73-75, 137-151 [S] 47-61 [W] 61-65
4	Viscosity. Newtonian Fluids. Vorticity and Circulation.	[W] 23-29, 59-69, 89-91 [K&C] 40-50 [B] 71-99
5	Navier-Stokes Equations. Physical Parameters. Dynamic Similarity.	[B] 164-173 [W] 81-94 [S] 15-23 [K&C] 461-462
Thin Shear Layer Approximation
6	Dimensional Analysis. Dominant Balance and Vscous Flow Classification.	[W] 81-88, 94, 104-107, 114-119, 132-141 [S] 13-18
7	_Re_→∞ Behavior. Thin Shear Layer Equations. TSL Coordinates.	[S] 96-99, 145-148 [W] 218-219, 227-233
8	TSL Coordinates. Boundary Conditions. Shear Layer Categories.
9	Local Scaling. Falkner-Skan Flows.	[B] 308-314 [S] 201-206 [W] 233-246
Solution Techniques
10	ODE’S, PDE’s, and Boundary Conditions. Well-Posedness.	[W] 77-78 Tannehill, Anderson and Pletcher. Computational Fluid Mechanics And Heat Transfer, 2nd Ed. Taylor and Francis, 1997. Pp. 19-31.
11	Numerical Methods for ODE’s. Discretization. Stability.	Hirsch, C. Numerical Computation of Internal and External Flows. Vol. 1. John Wiley & Sons, 1989. Pp. 267-290. Tannehill, Anderson and Pletcher. Pp. 76-83.
12	Finite Difference Methods. Newton-Raphson.
13	Integral Methods. Integral Momentum Equation. Thwaites’ Method.	[W] 264-274 [S] 191-202 (682-698 Optional) [C&B] 104-116
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.
18	IBLT Solution Techniques. Iteration Stability.
19	Fully-Coupled Iteration. 3-D IBLT.	[S] 449-483 [W] 335-355
Stability and Transition
20	Small-Perturbation Theory. Orr-Sommerfeld Equation.	[S] 449-483 [W] 335-355
21	Small-Perturbation Theory. Orr-Sommerfeld Equation. (cont.)
22	Boundary Conditions, Homogeneity, Solution Techniques.	[S] 434-473 [C&B] 290-301
23	Transition Mechanisms. Transition Prediction: Local Correlations, Amplification Methods.	[S] [W]
Turbulent Shear Layers
24	Reynolds Averaging. Prandtl’s Analogy.	[S] 496-538 [W] 394-463 [C&B]
25	Turbulent BL Structure: Wake, Wall Layers. Inner, Outer Variables. Effects of Roughness.	[S] 495-552 [C&B] 160-210 [W] 394-449
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.)
29	Turbulence Modeling and Closure. Algebraic Models. Transport Models.
Compressible Thin Shear Layers
30	Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy.	[S] 327-330, 340-352 [W] 184-200, 576-616
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.
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.	[W] 342-344 Reed, H.L. and W.S. Saric, “Stability of Three-Dimensional Boundary Layers”. Annual Review of Fluid Mechanics 21 (1989): 235 - 284. Mack, L.M. “Boundary-layer stability theory”, Special Course on Stability and Transition of Laminar Flow, AGARD R-709 (1984): 3-1 - 3-81.