1. DRAG on “Blunt” Bodies

2. FLUID FLOW ABOUT IMMERSED BODIES U p4p4 p1p1 p2p2 p3p3 p6p6 p5p5 p7p7 p8p8 p9p9 p 10 p 11 p 13 p…p… p 12  10 99 88 77 66 55 44 33 22 11 ………… Drag due to surface stresses composed of normal (pressure) and tangential (viscous) stresses. DRAG

3. “There is at present no satisfactory theory for the forces on an arbitrary body immersed in a stream flowing at an arbitrary Reynolds number.” White – Fluid Mechanics p = ? Boundary layer theory can usually predict separation point but not pressure distribution in separated region

4. DRAG Coefficient - C D C D = F D /( 1 / 2  U 2 A) EXPERIMENTALEXPERIMENTAL EXPERIMENTALEXPERIMENTAL C D = f(shape, Re, Ma, Fr,  /L)

5. F D =  surface pdA +  surface  wall dA =  surface pdA pressure in wake essentially constant pressure in wake can not be determined analytically C D = F D /( 1 / 2  U 2 A) A = usually frontal area for “stubby” bodies C D = 2 for Two-Dimensional and Re > 10,000 Flow over 2-D flat plate

6. b/h =1 square, C D = 1.18; (disk; C D = 1.17) C D independent of Re for Re > 1000 Question: C D = F D /( 1 / 2  U 2 A) What happens to C D if double area (b/h 2b/2h)? What happens to F D if double area (b/h 2b/2h)?

7. C D = F D /( 1 / 2  U 2 A) The area A is usually one of three types: Frontal area: the body area as seen from the stream – suitable for thick stubby bodies such as spheres, cylinders, cars, missiles, projectiles, torpedoes. Planform area: the body area as seen from above – suitable for wide flat bodies such as plates, wigs, hydrofoils Wetted area: total area – customary for surface ships and barges.

8. C D = F D /( 1 / 2  U 2 A) = C D,pressure + C D,friction t/c ~ 2-D flat plate 100% friction drag circular cylinder 3% friction drag Re c = 10 6 x ½ drag due to friction for t/c = 0.25

9. C dmin = 0.06 0.25 t c drag coefficient on a strut as a function of thickness/ chord

10. Mostly pressure drag, separation point fixed Friction drag Character of C D vs Re curves for different 2-D shapes press & fric

11. True or False: Sharp-edged bodies are relatively insensitive to Re because separation points are fixed. True or False: Smoothly-rounded bodies are relatively sensitive to Re because of laminar – turbulent transition /separation effects. True or False: Horizontal flat plates are relatively sensitive to Re because of laminar – turbulent transition effects.

12. sphere Character of C D vs Re curves for 3-D shape - sphere

13. Flow parallel to plate – viscous forces important and Re dependence Flow perpendicular to plate – pressure forces important and no strong Re dependence What about Re dependence for flow around sphere? Re CDCD ?

14. Drag Coefficient, C D, as a function of Re for a Smooth Sphere SMOOTH SPHERE C D = D/( ½  U 2 A) ? ? ? ?

15. Drag Coefficient, C D, as a function of Re for a Smooth Sphere SMOOTH SPHERE C D = D/( ½  U 2 A) ~ 1/5 th drag

16. ~82 o C D = 0.5 ~120 o C D = 0.2 PRESSURE DRAG on SMOOTH SPHERE inviscid theory laminar bdy layer turbulent bdy layer

17. Drag Coefficient, C D, as a function of Re for a Smooth Sphere SMOOTH SPHERE F D = 3  UD - theory C D = 3  UD/( 1 / 2  U 2 A) C D = 24/Re F D  U 2 F D  U

18. Laminar boundary layer Turbulent flow in wake Separation point moving forward Separation point fixed At Re ~ 1000 95% of drag due to pressure difference between front and back Turbulent boundary layer Laminar Flow * * F D  U 2

19. example

20. A small grain of sand is stirred 10 m from the bottom by the passage of an oil tanker. Assume a constant current of 1 m/s. There is a coral reef 1km downstream from where the sand was stirred up. Is it possible for the current to deposit the sand on the coral reef? Specific Gravity of sand = 2.3 Time for current to move sand 1 km = 1000m/(1m/s) = 1000s Time for sand to settle = 10m/U terminal velocity

21. weight buoyancy drag Terminal velocity so  F = 0 F weight = F buoyancy + F drag Drag Force = ½ SG  H2O U 2 C D Assume Re < 1 so C D = 24/Re Drag Force = 3  H2O UD Gravity Force = SG  H2O  D 3 /6  H2O =  g Buoyancy Force =  H2O  D 3 /6 U = (SG-1)  H2O gD 2 /(18  H2O ) = 0.00632 m/s Re = 0.564

22. A small grain of sand is stirred 10 m from the bottom by the passage of an oil tanker. Assume a constant current of 1 m/s. There is a coral reef 1km downstream from where the sand was stirred up. Is it possible for the current to deposit the sand on the coral reef? Specific Gravity of sand = 2.3 Time for current to move sand 1 km = 1000m/(1m/s) = 1000s Time for sand to settle = 10m/U terminal velocity = 10m/0.00632 m/s = 1582s

23. Roughness

24. Effect of surface roughness on the drag coefficient of a sphere in the Reynolds number range where laminar boundary layer becomes turbulent. Re critical ~ 400,000 Re critical ~ 50,000

25. Smooth Trip By roughening surface can “trip” boundary layer so turbulent which results in a favorable momentum exchange, pushing separation point further downstream, resulting in a smaller wake and reduced drag. 125 yd drive with smooth golf ball becomes 215 yds for dimpled* - Fox et al. From Van Dyke, Album of Fluid Motion Parabolic Press, 1982; Original photographs By Werle, ONERA, 1980 Re = 15000 Re = 30000

26. Picture of 8.5-in bowling ball entering water at 25 ft/sec. Why different flow patterns?

27. Dramatic differences in location of laminar and turbulent separation on an 8.5-in bowling ball entering water at 25 ft/sec. smooth rough

28. example

29. UCSD Sr. design team asks you whether they should dimple ping pong balls in an effort to make them go faster. Assume that the figure below shows the total range of Re that roughness can affect Re critical. What would you suggest?

30. UCSD Sr. design team asks you whether they should dimple ping pong balls in an effort to make them go faster. Assume that the figure below shows the total range of Re that roughness can affect Re critical. What would you suggest? Determine Re numbers of interest – turns out that highest ping pong ball speeds correspond to Re < 400,000 so probably will not work.

31. Sphere vs Cylinder

32. Drag coefficient as a function of Reynolds number for smooth circular cylinders and smooth spheres. From Munson, Young, & Okiishi, Fundamentals of Fluid Mechanics, John Wiley & Sons, 1998 ASIDE: At low very low Reynolds numbers Drag   UL C D = D / ( 1 / 2  U 2 A f ) D ~ U C D = constant D ~ U 2

33. Drag coefficient as a function of Reynolds number for smooth circular cylinders and smooth spheres. From Munson, Young, & Okiishi, Fundamentals of Fluid Mechanics, John Wiley & Sons, 1998 C D = D / ( 1 / 2  U 2 A f ) D ~ U C D = constant D ~ U 2

34. A B C D E FLOW AROUND A SMOOTH CYLINDER ~82 o ~120 o Smooth Cylinder

35. vortex shedding

36. for 250 < Re < 2 x 10 5 – smooth circular cylinder f = 0.198(U/d)(1-19.7/Re) [ G.I. Taylor (1886-1975)] St = fD/U = 0.198 (1.19.7/Re) ~ 0.2 [Strouhal (1850-1922)]

37. for 250 < Re < 2 x 10 5 smooth circular cylinder f = 0.198(U/d)(1-19.7/Re) [ G.I. Taylor (1886-1975)] St = fD/U = 0.198 (1.19.7/Re) ~ 0.2 [Strouhal (1850-1922)]

38. Re = 6.5 x 10 5 M = 0.61 Schlicting Boundary-Layer Theory

39. Spiral blades used for break up of span wise coherence of vortex shedding from a cylindrical rod. from Kundu & Cohen – FLUID MECHANICS

40. Flow Separation

41. FLOW SEPARATION

42. Fig. 9.6 U upstream = 3 cm/sec; divergent angle = 20 o ; Re= 900; hydrogen bubbles Unfavorable pressure gradient necessary for flow separation to be “possible” but separation not guaranteed.

43. Water, velocity = 2 cm/s, cylinder diameter = 7 cm, Re = 1200 Photographed 2 s after start of motion; hydrogen bubble technique Back flow 0 velocity at y = dy

44. Favorable Pressure Gradient  p/  x < 0; U increasing with x Unfavorable Pressure Gradient  p/  x > 0; U decreasing with x When velocity just above surface = 0, then flow will separate; causes wake. Gravity “working”against friction Gravity “working” with friction

45. Favorable Pressure Gradient  p/  x < 0; U increasing with x Unfavorable Pressure Gradient  p/  x > 0; U decreasing with x When velocity just above surface = 0, then flow will separate; causes wake. Gravity “working”against friction Gravity “working” with friction

46. Streamlining

47. STREAMLINING First employed by Leonardo da Vinci – First coined by d’Arcy Thompson – On Growth and Form (1917) C D ~ 0.06C D ~ 2 for flat plate

48. “In general, we can not overstress the importance of streamlining to reduce drag at Re numbers above about 100.” – White, Fluid Mechanics (b) has ? % of drag as (a) (c) has ? % of drag as (b) 2-D rectangular cylinder

49. (b) has 1 – C D(b) /C D(a) x 100% = 45% (c) has 1 – C D(b) /C D(a) x 100% = 86% 2-D rectangular cylinder C D = F D /( 1 / 2  U 2 A) [F D(a) -F D(b) ] /F D(a) x 100%

50. (d) has 1/8 th the thickness and 1/300 th the cross section of (c), yet same drag

51. STREAMLINING

52. 2 cm ~ same drag AND wake

53. (a)Because the Re numbers of most familiar flows over blunt bodies are large, the per cent of drag caused directly by shear stresses (friction drag) is often quite small. (b) For low Re flows most of the drag is due to shear stresses (friction drag). (c) For streamlined bodies most of the drag may be due to Shear stresses (friction drag). Which of the following statements is most true: (1)Only statements (a) and (b) are true (2) Only statements (a) and (c) are true (3) Only statements (b) and (c) are true (4) All statements are true

54. C D = F D /( 1 / 2  U 2 A) F D = C D ( 1 / 2  U 2 A) C D = 2.0 C D = 1.2 C D = 0.12 C D = 1.2 C D = 0.6 d = d/10 d = As C D decreases, what is happening to wake? Is there a wake associated with pipe flow? If C D decreases does that necessarily imply that the drag decreases? 2 - D

55. (note that frictional force increased from (b) to (c) but net force decreased) (note that although C D decreased from (d) to (e) that the Drag force did not. C D = 2.0 C D = 1.2 C D = 0.12 C D = 1.2 C D = 0.6 * * * *

56. First flight of a powered aircraft 12/17/03 120ft in 12 seconds Orville Wright at the controls Same drag at 210 mph

57. The End