External Flows

Figure 8.2 – Examples of complicated immersed flows: (a) flow near a solid boundary; (b) flow between two turbine blades; (c) flow around an automobile; (d) flow near a free surface.

Figure 8.3 –Flow around a blunt body and a streamlined body.

Figure 8.4 – Streamlined body that is stalled.

Figure 8.5 – Separation due to abrupt geometry changes.

Figure 8.6 – Flow separation on a flat surface due to an adverse pressure gradient.

Visualization of Flow Around Smooth Circular CylinderRe=0.16

From Van Dyke (1982)

Visualization of Flow Around Smooth Circular CylinderRe=9.6

From Van Dyke (1982)

Visualization of Flow Around Smooth Circular CylinderRe=13.1

From Van Dyke (1982)

Visualization of Flow Around Smooth Circular CylinderRe=26

From Van Dyke (1982)

Visualization of Flow Around Smooth Circular CylinderRe=2,000

From Van Dyke (1982)

Pressure Distribution Around Smooth Sphere

From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.

Figure 8.7 – Comparison of laminar and turbulent velocity profiles.

Figure 8. 8 –Effect of boundary layer transition on separation: (a) laminar boundary layer before separation; (b) turbulent boundary layer before separation. (U.S.Navy photographs.)

Visualization of Flow Around Smooth Circular Cylinder Re=10,000

From Van Dyke (1982)

Boundary Layer is made Turbulent through tripping

Boundary Layer is Laminar

Re=15,000

Re=30,000

Visualization of Flow Structure Behind a Moving DiskRe=6,200-4,200

From Higuchi and Belligand (Physics of Fluids, 1992)

t1

t2 t3 t4

Disk motion is from right to left

Drag and Lift Coefficient Definitions

p2

21L AU

LC

ρ=

rLift Coefficient:

geometry the toaccordingely appropriat defined AreaAp =

p2

21D AU

DC

ρ=

r

Drag Coefficient:

direction stream-free thelar toperpendicu dynamic)-hydroor -(aero flow the todue Force The L =

r

direction stream-free the toparallel dynamic)-hydroor -(aero flow the todue Force The D =

r

Figure 8.9 – Drag coefficients for flow around a long cylinder and a sphere. (See E. Achenbach, J. Fluid Mech., Vol. 46, 1971, and Vol. 54, 1972.)

Figure 8.10 –Vortex shedding from a cylinder: (a) vortex shedding; (b) Strouhal number versus Reynolds number. (From NACA Rep. 1191, by A. Roshko, 1954.)

Figure 8.11 – Vortex shedding at high and low Reynolds numbers: (a) Re = 10.000 (photograph by Thomas Corke and Hassan Nagib); (b) Re = 140 (photograph by Sadatoshi Taneda.)

Effect of Streamlining on Drag Coefficient

From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.

Airfoils: Geometrical Aspects

α: Angle of Attack

Airfoils: Terminology

p2

21L AU

LC

ρ=

r

Lift Coefficient:

Example of Airfoil Section Shape Designations

area) projected (maximum wing theof area planformAp =

Conventional: 23015 Laminar Flow: 662-215

Figure 8.12 – Flow around an airfoil at an angle of attack

Drag Breakdown on Non-Lifting and Lifting Bodies

From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.

Pressure Distribution Around Airfoils

From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.

Figure 8.13 – Lift and drag coefficients for airfoils with Re = V c/v = 9x106

Airfoil Lift and Drag Coefficients

From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.

Figure 8.14 – Flapped airfoil with slot for separation control.

Effect of Flaps

From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.

Figure 8.15 – Drag coefficient as a function of Mach number (speed) for a typical unswept airfoil.

Figure 8.16 – Trailing vortex.

Figure 8.17 – Trailing vortices from a rectangular wing. The flow remains attached over the entire wing surface. The centers of the vortex cores leave the trailing edge at the tips. The model is tested in a smoke tunnel at Reynolds number 100 000. (Courtesy of The Parabolic Press, Stanford, California. Reprinted with permission.)

Trailing Vortices in the Wake of an Aircraft

From Higuchi (Physics of Fluids, 1993)Photograph by P. Bowen of Cessna Aircraft Co.

Cessna Citation VIWing Span 16.3 mWing Area 29m2

V=170 knots (313 km/hr)Re=1.1x107 based on meanaerodynamic chord of 2.1 m)

Drag and Lift on Smooth Spinning Sphere

From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.

Lift and Drag Coefficients of Golf Balls

From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.

Figure 8.21 – Boundary layer on a curved surface.

Figure 8.22 – Boundary layer with transition.

Figure 8.23 –Turbulent boundary layer: (a) nomenclature sketch; (b) streamwise slice of the boundary layer. (Photograph by R.E. Falco.)

Figure 8.24 – Boundary layer in air with Recrit = 3 x 105.

Figure 8.25 – Control volume for a boundary layer with variable U(x).

Figure E8.14

Figure 8.26 – Velocity profile in a turbulent boundary layer.

Figure 8.27 –Influence of a strong pressure gradient on a turbulent flow: (a) a strong negative pressure gradient may relaminarize a flow; (b) a strong positive pressure gradient causes a strong boundary layer top thicken. (Photograph by R.E. Falco)

Figure 8.28 –Influence of the pressure gradient.