| 1 |
Introduction to 16.100 |
Homework #1 Out |
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Project Lab 1:
Lift and Drag Estimation
Drag Breakdown: Skin Friction, Pressure, Wave, and Induced Drag
Example: L/D Estimation for U2 Spy-plane in Cruise |
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| 2 |
Lift Generation on an Airfoil Focusing on Conservation of Momentum and Flow Turning
In-class Demo of Flow Turning with Water Stream Impinging on a Spoon
Concept Questions: Flow Turning on Spoon and for an Airfoil in a Wind Tunnel |
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| 3 |
Last Lift Concept Question: Reaction of Tunnel to Airfoil (Lightweight Tunnel)
Begin Discussion of Kinematics Focusing on Rotationality
Concept Question: Determining Rotationality from Streamlines |
Homework #1 Due
Homework #2 Out
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| 4 |
Kinematics of a Fluid Element: Convection, Strain Rates, Vorticity and Rotationality, Divergence, Substantial Derivative
Example: Irrotational and Zero Strain Swirling Flows, Relationship to Physical Vortices |
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Project Lab 2:
Overview of Project
Discuss Current Requirements for Interim Report
Distribute Team Assignments
Collect Wind Tunnel Testing Times |
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| 5 |
Finish Discussion of Strain, Divergence, and Rotationality
Concept Question: Incompressible Fluid Element Motion
Begin Discussion of Newtonian Stress-strain Relationship including Sign Convention and Need for Symmetric Stresses (tau_xy = tau_yx)
Concept Question on Correct Expression for Net Viscous Forces on the Fluid in a Channel |
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| 6 |
Finish Discussion of Stress-strain Relationship |
Homework #2 Due
Homework #3 Out
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| 7 |
Discussion of Stokes Hypothesis and Molecular Source of Momentum Transport
Play Diffusion Game |
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Project Lab 3:
Introduce Vortex Lattice Methods and Begin Demonstration of AVL |
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| 8 |
Discussion of Compressible Navier-Stokes Equations in Integral and Differential Form
Concept Questions: Magnitude of Acceleration vs Net Pressure Force vs Net Viscous Force on a Fluid Element |
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| 9 |
Guest Lecture by Bob Liebeck, Boeing Company/MIT, on "BWB Design Challenges" |
Homework #3 Due
Homework #4 Out
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Project Lab 4:
Finish Demonstration of AVL
Group Work Session During Last Hour |
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| 10 |
Discussion of Incompressible Viscous Flow Solutions Giving Specific Example of Between Two Rotating Cylinders
Presentation of Hierarchy of Governing Equations |
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| 11 |
Two Lectures Scheduled Today:
Discussion of Basic Assumptions and Concepts in Incompressible Potential Flow: Irrotationality, Conservation of Mass, Linearity with Respect to Velocity and Conservation of Mass, d'Alemberts Paradox, Kutta Joukowsky Theorem, and the Kutta Condition
Concept Questions: Irrotationality versus Conservation of Mass for a Potential Flow, Linearity of Velocity versus Static Pressure, d'Alembert's Paradox for Cylinder and Airfoil, Kutta-Joukowsky vs Kutta Condition |
Homework #4 Due
Homework #5 Out
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Project Lab 5:
Group Work Session |
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| 12 |
No lecture today since two lectures were held on Lec #11 |
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| 13 |
Discussion of Vortex Panel Method |
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| 14 |
Introduction to Thin Airfoil Theory |
Homework #5 Due
Homework #6 Out |
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Project Lab 6:
Introduction to CFD
Short Demo on the Use of Fluent |
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| 15 |
Application of Thin Airfoil Theory to Leading-edge and Trailing-edge Flaps
Purpose of Leading-edge and Trailing-edge Flaps
Leading-edge Suction Peak and Relation to Thin Airfoils and Incidence |
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| 16 |
Application of Thin Airfoil Theory to Improving Static Stability
Reflex Trailing Edges |
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Project Lab 7:
Group Work Session |
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| 17 |
Finish Discussion of Designing Airfoils for Static Stability and Reflexed Trailing Edges
Introduction to Lifting Line
Concept Questions: Relationship Between Lift, Lift Distribution, and Induced Drag |
Homework #6 Due |
| 18 |
Discussion of Lifting Line Results
Impact of Aspect Ratio on Induced Drag and Lift
Impact of Geometry on Span Efficiency
Trefftz Plane Analysis of Induced Drag |
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| 19 |
Finish Discussion of Lifting Line
Impact of Twist
Achieving Elliptic Lift Distribution without Elliptic Planform |
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Project Lab 8:
Group Work Time |
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| 20 |
Summarize Lifting Line Main Conclusions
Begin Discussion of Wind Tunnel Testing and Flow Similarity |
Homework #7 Out |
| 21 |
Finish Discussion of Flow Similarity and Application to Wind Tunnel Testing
Begin Discussion of Wind Tunnel Wall Effects |
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| 22 |
Finish Discussion of Image Analysis for Ground Effect and Tunnel Wall Effects
Begin Discussion of Results from Oral Exam |
Homework #7 Due |
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Project Lab 9:
Group Work Time |
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| 23 |
Discussion of the Effect of Camber and Thickness on Pressure Distribution Over an Airfoil Using Normal Momentum Equation (i.e. dp/dr = rho V^2/R) |
Homework #8 Out |
| 24 |
Begin discussion of boundary layer concept using several concept questions on the behavior of pressure through boundary layer, the effect of the boundary layer on the pressure, and the behavior of the skin friction vs chord-wise distance on a laminar airfoil |
Project Report Due |
| 25 |
Introduction of order of magnitude scaling analysis for boundary layers
Derivation of boundary layer equations using scaling analysis |
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| 26 |
Introduction of control volume analysis of a boundary layer to discuss basic mechanisms involved: specifically, wall friction and pressure gradients resulting in momentum changes
Discussion of need for adverse pressure gradient for flow reversal/separation to occur |
Homework #9 Out
Homework #8 Due |
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Project Lab 10:
Group Work Time |
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| 27 |
Introduction of integral boundary layer parameters and equations including displacement and momentum thickness
Demonstration of pressure drag source due to boundary layer thickness |
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| 28 |
Basic behavior of skin friction and friction drag with respect to Reynolds number
Concept question: behavior of drag due to changes in freestream velocity and streamwise orientation (i.e. chord length) |
Homework #9 Due |
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Project Lab 11 |
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| 29 |
Discussion of the behavior of turbulent flows using flow visualizations from experiments and simulations
Demonstration of the difference between laminar, laminar unsteady, transitional, and turbulent flow stressing laminar (i.e. microscopic) mixing versus turbulent (i.e. macroscopic) mixing |
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| 30 |
Discussion of the behavior of the boundary layer on airfoils as Reynolds number increases
Laminar, transition, and turbulent flows: behavior of skin friction in transition
Transition modeling through e^N method (only basic idea of linearly unstable boundary layers and amplification of disturbances leading to transition) |
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| 31 |
Derivation of compressible 1-D channel flow equations using a control volume analysis and reduction to isentropic form of equations |
Homework #10 Out |
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Project Lab 12 |
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| 32 |
Demonstration of the evolution of a shock wave as the downstream pressure is lowered for a converging-diverging nozzle using a quasi-1D Euler solver
Discussion of different behaviors of this flow: isentropic subsonic, transonic with shock inside nozzle, transonic with shock at exit plane, isentropic subsonic-to-supersonic with shocks or expansion fans outside of nozzle |
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| 33 |
Introduction to waves in 1-D compressible flow (acoustic and entropy waves)
Derivation of nonlinear shock jump relationships
Behavior of properties (Mach number, pressure, total pressure, enthalpy, entropy) across a shock |
Homework #10 Due
Homework #11 Out
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| 34 |
Derivation of speed of sound using linearized control volume analysis
Manipulation of the conservation of mass, with students placed into teams to complete the derivation themselves
Presentation of isentropic condition and final results |
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Project Lab 13 |
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| 35 |
Behavior of waves in two-dimensional compressible flows: subsonic vs. supersonic
Mach angle |
Homework #11 Due |
| 36 |
Subsonic compressible flow
Prandtl-Glauert scaling and behavior of pressure coefficient, lift coefficient, and drag coefficient in subsonic flow
Discussion of d'Alembert's paradox for subsonic inviscid flows (various concept questions on these topics will be used) |
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Project Lab 14 |
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| 37 |
Discussion of supersonic linearized potential flow
Discussion on ramp problem given in homework; application to airfoil lift and drag |
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| 38 |
Finish discussion of airfoil lift and drag in linearized supersonic flow
Demonstration of dependence of lift only on angle of attack (not on camber)
Critical Mach number
Drag divergence at transonic conditions
Breakdown of friction, wave, and pressure drag through transonic speeds |
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| 39 |
Discussion of sweep theory and delay of the critical Mach number
Comments on preparing for final exam |
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Project Lab 15 |
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