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 Cylinder
Re=0.16
From Van Dyke (1982)
Visualization of Flow Around Smooth Circular Cylinder
Re=9.6
From Van Dyke (1982)
Visualization of Flow Around Smooth Circular Cylinder
Re=13.1
From Van Dyke (1982)
Visualization of Flow Around Smooth Circular Cylinder
Re=26
From Van Dyke (1982)
Visualization of Flow Around Smooth Circular Cylinder
Re=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
Boundary Layer is Laminar
Re=15,000
Boundary Layer is made Turbulent through tripping
Re=30,000
From Van Dyke (1982)
Visualization of Flow Structure Behind a Moving Disk
Re=6,200-4,200
t1
t2
t3
t4
Disk motion is from right to left
From Higuchi and Belligand (Physics of Fluids, 1992)
Drag and Lift Coefficient Definitions
Lift Coefficient:
CL =
r
L
1
2
ρU 2 A p
r
L = The Force due to the flow (aero - or hydro - dynamic)
perpendicular to the free - stream direction
Drag Coefficient:
CD =
r
D
1
2
ρU 2 A p
r
D = The Force due to the flow (aero - or hydro - dynamic)
parallel to the free - stream direction
A p = Area defined appropriately according to the geometry
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
Lift Coefficient:
CL =
r
L
1
2
ρU 2 A p
A p = planform area of the wing (maximum projected area)
Example of Airfoil Section Shape Designations
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
Cessna Citation VI
Wing Span 16.3 m
Wing Area 29m2
V=170 knots (313 km/hr)
Re=1.1x107 based on mean
aerodynamic chord of 2.1 m)
From Higuchi (Physics of Fluids, 1993)
Photograph by P. Bowen of Cessna Aircraft Co.
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.