1. ES 202 Fluid and Thermal Systems Lecture 30: Lift and Drag Wrap-Up (2/20/2003)

2. Lecture 30ES 202 Fluid & Thermal Systems2 Assignments Study for your finals

3. Lecture 30ES 202 Fluid & Thermal Systems3 Announcements Problem session this evening at 7 pm –lift and drag –hydrostatics –Bernoulli’s equation –major and minor losses Time and date for final review session (need your input) What can you bring to the exam –textbook –3 sides of equation sheet –computer (cannot use EES) My advice for you on final exam –Study hard, see me if you have questions –Keep calm! You should have more than enough time!

4. Lecture 30ES 202 Fluid & Thermal Systems4 Road Map of Lecture 30 High-light from John Adams’ talk on golf ball aerodynamics –laminar-turbulent transition over curved surface Reynolds number dependency of drag coefficient –how it relates to terminal velocity calculation Common feature between internal and external flows –formation of boundary layer –inviscid core region –merging of boundary layers (disappearance of inviscid core) Visual learning: variation of lift and drag with angle of attack All about lift –origin of lift –definition of lift coefficient –conditions at take-off and cruise Course evaluation

5. Lecture 30ES 202 Fluid & Thermal Systems5 Drag on a Golf Ball Taken from John Adams’ ASME talk 2/3 of range at max. height (very different from simple projectile)

6. Lecture 30ES 202 Fluid & Thermal Systems6 Reynolds Number Dependency taken from Figure 8.2 in Fluid Mechanics by Kundu Determination of terminal velocity requires iteration

7. Lecture 30ES 202 Fluid & Thermal Systems7 Connection with Internal Flow Recall the drag analysis on a cross-flow cylinder in a wind tunnel –The blockage effect of the cylinder causes the flow to accelerate. As a result, pressure drops. This pressure drop is totally different from the pressure drop in pipe flow analysis during the 4 th week of this class. The pressure drop in pipe flow is due to frictional effect, not flow acceleration. In fact, the average flow speed in a constant cross-sectional pipe is constant as a result of mass conservation.

8. Lecture 30ES 202 Fluid & Thermal Systems8 Boundary Layer in a Pipe At the pipe entrance, the development of boundary layer is similar to that on a flat plate. As a result of fluid deceleration in the boundary layer, the flow accelerates within the inviscid core. Beyond the merging point of boundary layers, the fully viscous region is termed the fully developed flow. Within the fully developed flow, –averaged flow speed stays constant; –pressure drops as a response to fluid friction. inviscid core (flow acceleration) boundary layer merging of boundary layer (disappearance of inviscid core) fully viscous region

9. Lecture 30ES 202 Fluid & Thermal Systems9 Lift and Drag on an Airfoil Visual learning: –MMFM visualization of lift and drag variation as a function of angle of attack (serves as a motivation to lift analysis) –As the angle of attack is increased, the slender airfoil becomes more of a blunt body. Flow separation becomes more severe. The dominant drag component changes from frictional drag to pressure drag. Significant reduction in lift results. Notion of stall: large reduction in lift (highly unstable operating condition)

10. Lecture 30ES 202 Fluid & Thermal Systems10 All about Lift Generation of lift force –high pressure on bottom surface, low pressure on top surface –means of destroying flow symmetry non-zero angle of attack on symmetry airfoil asymmetric airfoil at zero angle of attack positive camber gives positive lift Design criterion of airfoil design –optimize the lift-to-drag ratio Lift coefficient –definition (similar to drag coefficient) –take-off condition (L > W) –cruise condition (L = W)