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 |
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. |