2145-213 - 2008 - Review Sheet - Figures of External …fmeabj.lecturer.eng.chula.ac.th/2103-351 HP/351 Course Materials... · 9. Abbott, I. H., von Doenhoff, A. E., and Stivers,

2103-Fluid Mechanics Review Period: Figures of External Flow, and Lift and Drag Coefficients for Various Bodies, with Brief Descriptions ABJ

Fluid Mechanics Review Period: Figures of External Flow, and Lift and Drag Coefficients for Various Bodies,

with Brief Descriptions References The figures and data below are from

1. Munson B. R., Young, D. F., and Okiishi, T. H., 2002, Fundamentals of Fluid Mechanics, Fourth Edition, Wiley, New York.

Some of these are after 2. Blevins, R. D., 1984, Applied Fluid Dynamics Handbook, Van Nostrand Reinhold, New York. 3. Schlichting, H., 1979, Boundary Layer Theory, Seventh Edition, McGraw-Hill, New York. 4. White, F. M., 1986, Fluid Mechanics, McGraw-Hill, New York. 5. Vennard, J. K., and Street, R. L., 1982, Elementary Fluid Mechanics, Sixth Edition, Wiley, New York. 6. Hoerner, S. F., 1965, Fluid-Dynamic Drag, published by the author, Library of Congress No. 64, 19666. 7. Vogel, J., 1994, Life in Moving Fluids, Second Edition, Willard Grant Press, Boston. 8. Gross, A. C., Kyle, C. R., and Malewicki, D. J., 1983, The Aerodynamics of Human Powered Land Vehicles,

Scientific American, Vol. 29, No. 6. 9. Abbott, I. H., von Doenhoff, A. E., and Stivers, L. S., 1945, Summary of Airfoil Data, NACA Report No. 824,

Langley Field, Va. 10. Abbott, I. H., and von Doenhoff, A. E., 1959, Theory of Wing Sections, Dover Publications, New York. 11. Goldstein, S., 1938, Modern Developments in Fluid Dynamics, Oxford Press, London.


Approximate boundary layer profiles

Fig. 9.12 Typical approximate boundary layer profiles used in the momentum integral equation. From Ref. 1.

Laminar, transitional, and turbulent boundary layer profiles

Fig. 9.14 Typical boundary layer profiles on a flat plate for laminar, transitional, and turbulent flow. From Ref. 1,

after Ref. 3.

• Various simple analytic functions are used to appropriately approximate the more complicated, analytically exact or actual profiles.

• Turbulent BL has a ‘fuller’ profile (i.e., less mass flux deficit as measured by δδ /* ) than the laminar one.

• This can be seen more clearly in Uu / VS δ/y plot.


Drag coefficients for a flat plate as a function of Reynolds number

Fig. 9.15 Friction drag coefficient for a flat plate parallel to the upstream flow. From Ref. 1, after Ref. 4.

Boundary layer characteristics and pressure coefficient on a circular cylinder

Fig. 9.17 Boundary layer characteristics on a circular cylinder:

(a) boundary layer separation location, (b) typical boundary layer velocity profiles at various locations on the cylinder, (c) surface pressure distributions for inviscid flow and boundary layer flow.

From Ref. 1.

• Drag coefficient, DC , is a function of Reynolds number, Re. • For low Re, the normalized/nondimensionalized drag as

measured with the drag coefficient, DC , tends to be a strong function of Re.

• At higher Re, however, DC tends to be a weak function of Re.

• Subcritical flow (laminar BL separation, ~ at θ = 70o-80o).

• Supercritical flow (turbulent BL separation, ~ at θ = 120o).

• Pressure at the leeward region of LBL

separation is relatively lower than the case of TBL separation, which is also lower than the inviscid counterpart.

• This results in the drag force in the LBL separation being greater than the case of TBL separation.


Flow visualization photographs of flow past an airfoil

Fig. 9.18 Flow visualization photographs of flow past an airfoil (the boundary layer velocity profiles for the points

indicated are similar to those indicated in Fig. 9.17b): (a) zero angle of attack, no separation, (b) 5o angle of attack, flow separation.

From Ref. 1, Photograph of ONERA, France.

Drag coefficient for an ellipse at various thicknesses (or aspect ratios Dl / )

Fig. 9.19 Drag coefficient for an ellipse with the characteristic area either the frontal area, bDA = , or the planform

area, blA = . From Ref. 1, after Ref 2.

Separation bubble

• Two possible choices of characteristic area for the non-dimensionalization of the drag force, which results in two possible definitions of DC .

• Large Dl / - streamlined body • Large lD / - blunt body • Streamlined body tends to have lower drag than blunt body.


Drag coefficient as a function of Reynolds number for a smooth circular cylinder and a smooth sphere

Fig. 9.21 (a) Drag coefficient as a function of Reynolds number for a smooth circular cylinder and a smooth sphere.

(b) Typical flow patterns for flow past a circular cylinder at various Reynolds numbers as indicate in (a). From Ref. 1.

• Drag crisis for blunt bodies: sharp drop in DC . • At low Re, LBL is separated early ~ at θ = 70o-

80o. • As Re increases, the BL transitions to TBL early,

before separation. • Since TBL is less susceptible to separation, this

results in the delay of separation, from ~ at θ = 70o-80o in LBL separation case to ~ at θ = 120o in TBL separation case.

• [See also Figs. 9.17 and 9.21 D and E below.] • This further results in

o smaller low pressure region at the leeward side, i.e.,

TBL over, o2401200 << θ

( o120~θΔ )

VS LBL over o290700 << θ

( o220~θΔ ), o less drag, for the case of TBL separation than the case of LBL separation.


Character of the drag coefficient as a function of Reynolds number for objects with various degrees of streamlining:

Blunt body VS Streamlined Body

Fig. 9.22 Character of the drag coefficient as a function of Reynolds number for objects with various degrees of

streamlining, from a flat plate normal to the upstream flow to a flat plate parallel to the flow (two-dimensional flow). From Ref. 1, after Ref. 2.


Compressibility Effect: Drag coefficient as a function of Mach number

Fig. 9.23 Drag coefficient as a function of Mach number for two-dimensional objects in subsonic flow. From Ref.

1, after Ref. 2.

Fig. 9.24 Drag coefficient as a function of Mach number for supersonic flow. From Ref. 1, after Ref 5.


Effect of surface roughness on the drag coefficient of a blunt body

Fig. 9.25 The effect of surface roughness on the drag coefficient of a sphere in the Reynolds number range for

which the laminar boundary layer becomes turbulent. From Ref. 1, after Ref. 2. Historical trend of the drag coefficient of automobiles

Fig. 9.27 The historical trend of streamlining automobiles to reduce their aerodynamic drag and increase their miles

per gallon. From Ref. 1, after Ref. 2.

• Surface roughness has an effect of promoting turbulence and transition to turbulent flow.

• This causes early transition of LBL to TBL.

• This causes early drag crisis. (Drag crisis occurs at lower Re.)

• See also Figs. 9.17 and 9.21.

• Not taking into account various types of automobiles for various purposes (truck VS passenger cars),

~ reduction of 0.5 over 80 years 0.00625 / year, or 0.0625 / 10 years.


Typical drag coefficients for regular two-dimensional objects

Fig. 9.28 Typical drag coefficients for regular two-dimensional objects. From Ref. 1, after Refs. 2 and 6.


Typical drag coefficients for regular three-dimensional objects

Fig. 9.29 Typical drag coefficients for regular three-dimensional objects.

From Ref. 1, after Ref. 2.

Interesting. • Why do you think that is? • What do they imply?


Typical drag coefficients for objects of interests

Fig. 9.30 Typical drag coefficients for objects of interests.

From Ref. 1, after Refs. 2, 6, 7, and 8.

Interesting. Maybe we can learn a thing or two.


Typical lift and drag coefficient data of an airfoil/wing as a function of angle of attack and the aspect ratio

Fig. 9.33 Typical lift and drag coefficient data as a function of angle of attack and the aspect ratio of the airfoil:

(a) lift coefficient, (b) drag coefficient.

From Ref. 1.

Effect of aspect ratio (aspect ratio = span/chord) • If we want to design a glider, should the wings have low or high

aspect ratio?


Lift-to-drag ratio and lift-and-drag polar diagram

Fig. 9.34 Two representations of the same lift and drag data for a typical airfoil:

(a) lift-to-drag ratio as a function of angle of attack, with the onset of boundary layer separation on the upper surface indicated by the occurrence of stall,

(b) the lift and drag polar diagram with the angle of attack indicated. From Ref. 1, after Ref. 9.

Flow control device: Flaps

Fig. 9.35 Typical lift and drag alterations possible with the use of various types of flap designs.

From Ref. 1, after Ref. 10.

• Asymetric airfoil has lift even at zero angle of attack.

• Can you find – by

geometrical means - the direction of the resultant aerodynamic force from the polar plot?


Lift and drag coefficients for a spinning sphere

Fig. 9.39 Lift and drag coefficients for a spinning smooth sphere. From Ref. 1, after Ref. 11.

• Spinning creates circulation around the body, resulting in lift force.

Documents

2145-213 - 2008 - Review Sheet - Figures of External …fmeabj.lecturer.eng.chula.ac.th/2103-351 HP/351 Course Materials... · 9. Abbott, I. H., von Doenhoff, A. E., and Stivers,