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16.13

Aerodynamics of Viscous Fluids

3-0-9 units · Graduate

Boundary layers as rational approximations to the solutions of exact equations of fluid motion. Physical parameters influencing laminar and turbulent aerodynamic flows and transition. Effects of compressibility, heat conduction, and frame rotation. Influence of boundary layers on outer potential flow and associated stall and drag mechanisms. Numerical solution techniques and exercises.

Fall 2003

Topics

  • Course Description. Fundamental Theorem of Kinematics - Convection, Vorticity, Strain.
  • Eulerian vs. Langrangian Description. Convection Relations.
  • Conservation of Mass. Conservation of Momentum. Stress Tensor.
  • Viscosity. Newtonian Fluids. Vorticity and Circulation
  • Navier-Stokes Equations. Physical Parameters. Dynamic Similarity.
  • Dimensional Analysis. Dominant Balance and Viscous Flow Classification.
  • Re →∞ Behavior. Thin Shear Layer Equations. TSL Coordinates.
  • TSL Coordinates. Boundary Conditions. Shear Layer Categories.
  • Local Scaling. Falkner-Skan Flows.
  • ODE’S, PDE’s, and Boundary Conditions. Well-posedness.
  • Numerical Methods for ODE’s. Discretization. Stability.
  • Finite Difference Methods. Newton-Raphson.
  • Integral Methods. Integral Momentum Equation. Thwaites’ Method.
  • Integral Kinetic Energy Equation. Dissipation Methods.
  • Integral Kinetic Energy Equation. Dissipation Methods. (cont.)
  • Asymptotic Perturbation Theory. Higher-Order Effects.
  • 2D Interaction Models: Displacement Body, Transpiration. Form Drag, Stall Mechanisms.
  • IBLT Solution Techniques. Iteration Stability.
  • Fully-coupled Iteration. 3-D IBLT.
  • Small-perturbation Theory. Orr-Sommerfeld Equation.
  • Small-perturbation Theory. Orr-Sommerfeld Equation. (cont.)
  • Boundary Conditions, Homogeneity, Solution Techniques.
  • Transition Mechanisms. Transition Prediction: Local Correlations, Amplification Methods.
  • Reynolds Averaging. Prandtl’s Analogy.
  • Turbulent BL Structure: Wake, Wall layers. Inner, Outer Variables. Effects of Roughness.
  • Turbulent BL Structure: Wake, Wall layers. Inner, Outer Variables. Effects of Roughness. (cont.)
  • Equilibrium BL’s: Clauser Hypothesis. Dissipation Formulas and Integral Closure.
  • Equilibrium BL’s: Clauser Hypothesis. Dissipation Formulas and Integral Closure. (cont.)
  • Turbulence Modeling and Closure. Algebraic Models. Transport Models.
  • Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy.
  • Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy. (cont.)
  • Approximate Temperature Profile. Reynolds Heat Flux.
  • New effects: Crossflow, Lateral Dilation, 3D Separation. Governing Equations.
  • Coordinate Systems. Characteristics, BC’s, and Well-posedness.
  • 3D Characteristics, BC’s. Quasi-3D: Constant-crossflow Approximation.
  • 3D Characteristics, BC’s. Quasi-3D: Constant-crossflow Approximation.(cont.)
  • 3D Stability Theory. 3D Transition Mechanisms.

Readings

  • [W] White, F. _Viscous Fluid Flo_w. McGraw-Hill, 1991. ISBN:0-07-069712-4.
    Listed reading
  • [B] Batchelor, G. K. An Introduction to Fluid Dynamics . Cambridge University Press, 2000. ISBN:0-521-66396-2.
    Listed reading
  • [C&B] Cebeci, T., and P. Bradshaw. Momentum Transfer in Boundary Layers . McGraw-Hill, 1977. ISBN:0-07-010300-3.
    Listed reading
  • [S] Schlichting, H et al. Boundary Layer Theory, 8th Ed . Springer Verlag, 1999. ISBN: 3540662707.
    Listed reading
  • [R] Rosenhead, L. Laminar Boundary Layers . Dover Publications, 1988. ISBN:0-486-65646-2.
    Listed reading
  • [B,C&W] Bradshaw, Cebeci, and Whitelaw. Engineering Calculation Methods for Turbulent Flow . Academic Press, 1981. ASIN:0121245500.
    Listed reading
  • [K&C] Kuethe, A. and C-Y. Chow. Foundations of Aerodynamics, 4th Ed . John Wiley & Sons, 1986. ASIN:0471509531.
    Listed reading
  • LEC #: 1 · TOPICS: Course Description. Fundamental Theorem of Kinematics - Convection, Vorticity, Strain. · READINGS: [B] 78-87 [W] 16-22
    Reading assignment
  • LEC #: 3 · TOPICS: Conservation of Mass. Conservation of Momentum. Stress Tensor. · READINGS: [B] 73-75, 137-151 [S] 47-61 [W] 61-65
    Reading assignment
  • LEC #: 4 · TOPICS: Viscosity. Newtonian Fluids. Vorticity and Circulation. · READINGS: [W] 23-29, 59-69, 89-91 [K&C] 40-50 [B] 71-99
    Reading assignment
  • LEC #: 6 · TOPICS: Dimensional Analysis. Dominant Balance and Vscous Flow Classification. · READINGS: [W] 81-88, 94, 104-107, 114-119, 132-141 [S] 13-18
    Reading assignment
  • LEC #: 7 · TOPICS: Re →∞ Behavior. Thin Shear Layer Equations. TSL Coordinates. · READINGS: [S] 96-99, 145-148 [W] 218-219, 227-233
    Reading assignment
  • LEC #: 9 · TOPICS: Local Scaling. Falkner-Skan Flows. · READINGS: [B] 308-314 [S] 201-206 [W] 233-246
    Reading assignment
  • LEC #: 10 · TOPICS: ODE’S, PDE’s, and Boundary Conditions. Well-Posedness. · READINGS: [W] 77-78 Tannehill, Anderson and Pletcher. Computational Fluid Mechanics And Heat Transfer, 2nd Ed. Taylor and Francis, 1997. Pp. 19-31.
    Reading assignment
  • LEC #: 11 · TOPICS: Numerical Methods for ODE’s. Discretization. Stability. · READINGS: 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.
    Reading assignment
  • LEC #: 13 · TOPICS: Integral Methods. Integral Momentum Equation. Thwaites’ Method. · READINGS: [W] 264-274 [S] 191-202 (682-698 Optional) [C&B] 104-116
    Reading assignment
  • LEC #: 19 · TOPICS: Fully-Coupled Iteration. 3-D IBLT. · READINGS: [S] 449-483 [W] 335-355
    Reading assignment
  • LEC #: 20 · TOPICS: Small-Perturbation Theory. Orr-Sommerfeld Equation. · READINGS: [S] 449-483 [W] 335-355
    Reading assignment
  • LEC #: 22 · TOPICS: Boundary Conditions, Homogeneity, Solution Techniques. · READINGS: [S] 434-473 [C&B] 290-301
    Reading assignment
  • LEC #: 23 · TOPICS: Transition Mechanisms. Transition Prediction: Local Correlations, Amplification Methods. · READINGS: [S] [W]
    Reading assignment
  • LEC #: 24 · TOPICS: Reynolds Averaging. Prandtl’s Analogy. · READINGS: [S] 496-538 [W] 394-463 [C&B]
    Reading assignment
  • LEC #: 25 · TOPICS: Turbulent BL Structure: Wake, Wall Layers. Inner, Outer Variables. Effects of Roughness. · READINGS: [S] 495-552 [C&B] 160-210 [W] 394-449
    Reading assignment
  • LEC #: 30 · TOPICS: Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy. · READINGS: [S] 327-330, 340-352 [W] 184-200, 576-616
    Reading assignment
  • LEC #: 36 · TOPICS: 3D Stability Theory. 3D Transition Mechanisms. · READINGS: [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.
    Reading assignment
  • White, F. Viscous Fluid Flow . McGraw-Hill, 1991. ISBN:0-07-069712-4.
    Listed reading
  • Batchelor, G. K. An Introduction to Fluid Dynamics . Cambridge University Press, 2000. ISBN:0-521-66396-2.
    Listed reading
  • Cebeci, T., and P. Bradshaw. Momentum Transfer in Boundary Layers . McGraw-Hill, 1977. ISBN:0-07-010300-3.
    Listed reading
  • Schlichting, H et al. Boundary Layer Theory, 8th Ed. Springer Verlag, 1999. ISBN: 3540662707.
    Listed reading
  • Rosenhead, L. Laminar Boundary Layers . Dover Publications, 1988. ISBN:0-486-65646-2.
    Listed reading
  • Bradshaw, Cebeci, and Whitelaw. Engineering Calculation Methods for Turbulent Flow . Academic Press, 1981. ASIN:0121245500.
    Listed reading
  • Kuethe, A. and C-Y. Chow. Foundations of Aerodynamics, 4th Ed. John Wiley & Sons, 1986. ASIN:0471509531.
    Listed reading
  • Journals: American Institute of Aeronautics and Astronautics Journal , Journal of Fluid Mechanics
    Listed reading

Prerequisites & course information

Prereq: 16.100 , 16.110 , or permission of instructor Acad Year 2027-2028: Not offered Acad Year 2028-2029: G (Spring) 3-0-9 units

Sources