1. ES 202 Fluid and Thermal Systems Lecture 29: Drag and Lift Coefficients (2/18/2003)

2. Lecture 29ES 202 Fluid & Thermal Systems2 Assignments Homework: –13-56C, 13-62, 13-63, 13-72C, 13-88 Reading: –13-7 to 13-8

3. Lecture 29ES 202 Fluid & Thermal Systems3 Announcements Guest speaker Dr. John Adams will talk 2 talks today: –“Hypersonic Systems, Technology, and Testing”, including relevant remarks on the recent Columbia Space Shuttle tragedy in O259 at 4:20 pm –“Flight Mechanics of a Spinning Dimpled Spheroid” in the Khan Room at 6:00 pm Homework assigned this week is just for your learning, no need to hand it in

4. Lecture 29ES 202 Fluid & Thermal Systems4 Road Map of Lecture 29 Finish up example on drag coefficient of cross-flow cylinder in a wind tunnel Give out answers to in-class drag analyses yesterday Introduce definition of drag coefficients (Combined) Drag coefficients for objects of various geometries –concept of streamlining Categorization of drag components –skin frictional drag versus pressure drag –effects of body shape on drag (blunt body versus slender body) –flow separation (an artifact of fluid viscosity) Exercise on qualitative description of flow acceleration and pressure variation over a blunt body –notion of stagnation point (high pressure) Applications: –truck tipping problem –terminal velocity (balance between weight, drag and buoyancy)

5. Lecture 29ES 202 Fluid & Thermal Systems5 Answers to Drag Analyses Drag analysis on a flat plate: Drag analysis on a cross-flow cylinder in open air: Drag analysis on a cross-flow cylinder in a wind tunnel:

6. Lecture 29ES 202 Fluid & Thermal Systems6 Drag Coefficient From the results of drag analysis on a cross-flow cylinder in open air, a non-dimensional group, the drag coefficient C D, can be defined: The definition of drag coefficient can also be arrived by means of dimensional analysis, similar to that on boundary layer thickness. Show drag coefficient tables for various geometries

7. Lecture 29ES 202 Fluid & Thermal Systems7 Categorization of Drag Components The total drag force on an object can be broadly classified into two categories: Total drag force Friction drag directly related to skin friction on surfaces dominant on slender bodies Pressure (form) drag indirectly related to fluid viscosity due to momentum losses through viscosity mostly involves flow separation dominant on blunt bodies Relative importance between friction drag and pressure drag is strongly Reynolds number dependent and geometry dependent (slender versus blunt bodies).

8. Lecture 29ES 202 Fluid & Thermal Systems8 Fluid Acceleration and Pressure Variation Perform a qualitative assessment on the changes in a flow as it approaches a blunt object. –speed decreases, pressure increases from free-stream to stagnation point –highest pressure at stagnation point –flow splits into upper and lower streams –speed increases, pressure decreases from stagnation point to edges –highest speed and lowest pressure at the edges –flow speed decreases and pressure recovers behind the object –too much momentum loss in boundary layer: not enough momentum to negotiate pressure hill, flow separates –large pressure difference between front and back sides causes pressure drag

9. Lecture 29ES 202 Fluid & Thermal Systems9 Example Problem Truck tipping problem: –recognize blunt body geometry –pressure drag as dominant drag component –moment analysis about Point O to determine minimum wind speed to tip truck –assume drag coefficient is all attributed to pressure drag –assume line of action of pressure drag to be at the geometrical center of truck –at tipping position, R 2 = 0 –fine points: small frictional drag component in tabulated C D value asymmetry in problem not accounted for in tabulated C D value W R1R1 R2R2 U O

10. Lecture 29ES 202 Fluid & Thermal Systems10 Terminal Speed of Falling Objects Identify the major forces on a falling object As the falling object accelerates, the drag force increases rapidly (quadratic dependence on falling speed). At terminal speed, the net force on the falling object is zero, implying a perfect balance between body weight and drag. The force balance sets the condition to determine the terminal speed. W