external flows ch8
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External Flows
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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.
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Figure 8.3 –Flow around a blunt body and a streamlined body.
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Figure 8.4 – Streamlined body that is stalled.
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Figure 8.5 – Separation due to abrupt geometry changes.
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Figure 8.6 – Flow separation on a flat surface due to an adverse pressure gradient.
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Visualization of Flow Around Smooth Circular CylinderRe=0.16
From Van Dyke (1982)
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Visualization of Flow Around Smooth Circular CylinderRe=9.6
From Van Dyke (1982)
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Visualization of Flow Around Smooth Circular CylinderRe=13.1
From Van Dyke (1982)
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Visualization of Flow Around Smooth Circular CylinderRe=26
From Van Dyke (1982)
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Visualization of Flow Around Smooth Circular CylinderRe=2,000
From Van Dyke (1982)
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Pressure Distribution Around Smooth Sphere
From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.
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Figure 8.7 – Comparison of laminar and turbulent velocity profiles.
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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.)
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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
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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
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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
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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.)
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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.)
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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.)
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Effect of Streamlining on Drag Coefficient
From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.
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Airfoils: Geometrical Aspects
α: Angle of Attack
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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
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Figure 8.12 – Flow around an airfoil at an angle of attack
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Drag Breakdown on Non-Lifting and Lifting Bodies
From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.
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Pressure Distribution Around Airfoils
From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.
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Figure 8.13 – Lift and drag coefficients for airfoils with Re = V c/v = 9x106
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Airfoil Lift and Drag Coefficients
From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.
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Figure 8.14 – Flapped airfoil with slot for separation control.
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Effect of Flaps
From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.
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Figure 8.15 – Drag coefficient as a function of Mach number (speed) for a typical unswept airfoil.
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Figure 8.16 – Trailing vortex.
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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.)
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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)
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Drag and Lift on Smooth Spinning Sphere
From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.
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Lift and Drag Coefficients of Golf Balls
From Fox and McDonald, “Introduction to Fluid Mechanics”, 3d ed.
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Figure 8.21 – Boundary layer on a curved surface.
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Figure 8.22 – Boundary layer with transition.
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Figure 8.23 –Turbulent boundary layer: (a) nomenclature sketch; (b) streamwise slice of the boundary layer. (Photograph by R.E. Falco.)
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Figure 8.24 – Boundary layer in air with Recrit = 3 x 105.
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Figure 8.25 – Control volume for a boundary layer with variable U(x).
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Figure E8.14
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Figure 8.26 – Velocity profile in a turbulent boundary layer.
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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)
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Figure 8.28 –Influence of the pressure gradient.