Download ES 202 Lecture 27 - Rose

ES 202
Fluid and Thermal Systems
Lecture 27:
Drag on Cylinders and Spheres
(2/13/2003)
Assignments
• Homework:
– 13-12C, 13-13C, 13-33, 13-40E
– add the phrase “at high Reynolds numbers” to
13-13C
– only hand in Tuesday homework next Monday
• Reading:
– 13-7 to 13-8
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Announcements
• Problem session this evening at 7 pm
– hydrostatics
– Exam 2 solutions
– external flows
• Due date for Lab 3 write-up
• Undergraduate Research Awards
• Fluid mechanics made it to the news
– “snow-rollers” on the ground
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“Snow-Rollers”
(taken from www.wtwo.com)
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Road Map of Lecture 27
Knowledge items:
•
Drag on flat plates
– finish up control volume analysis of drag on a flat plate
– definition of friction coefficient for flat plates
•
Drag on cylinders
– categorization of drag components
– Reynolds number dependency of drag
– artifact of viscosity: flow separation
– drag coefficients for cylinders
– laminar versus turbulent boundary layers
•
Drag on spheres
– effects of a trip wire, dimples on a golf ball
Examples:
•
•
Dimensional analysis of skin friction over flat plate
Drag on a cylinder due to a cross-flow in open air
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Motivation: The Fun Side
• Dimples on golf ball
• Any cyclist here?
– concept of drafting in bike racing, formula 1 racing
– the V-shaped pattern in bird migration
• Design of aerodynamic helmet
• Design of sail and yacht
• Outfit on world record holding cyclists, swimmers, runners, etc.
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Motivation: The Commercial Side
• Drag optimization on airplanes and automobiles
upper surface
• Design for turbomachinery
(compressor and turbine)
lower surface
Pressure coefficient at Mach 2.2
Blade design in turbomachinery using computational
methods
Lecture 27
Images taken from Aerospace Computing Laboratory,
Stanford University
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Quiz on Lecture 26
• What does the boundary layer thickness at a particular streamwise
location on a flat plate depend on?
• At the same streamwise location, what is the qualitative change in the
boundary layer thickness if:
– the free-stream air speed doubles
– air is replaced by a less viscous fluid
• Again at the same streamwise location, what do you expect the
boundary layer thickness to behave if the flow speed is doubled?
– double/less than double/more than double
– half/less than half/more than half
– no change
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Comparison of Fluid Properties





air
 105 kg/m.s
 1 kg/m3
 105 m2/s
water
 103 kg/m.s  103 kg/m3
UL UL
Re 



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6
 10
2
m /s
At the same flow speed and object size, the
Reynolds number in water is 10 times larger
than that in air. This information is useful in
interpreting the difference in flow patterns
between air and water.
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Drag on a Flat Plate
• Due to viscous (fluid friction) effects, the flat plate will
experience a force in the downstream direction. The force is
termed “Drag”.
• Think of it as an action-reaction pair of force:
– the fluid experiences a force in the upstream direction to slow it down;
– the same force (in magnitude) acts on the flat plate in opposite direction.
• Exercise: Perform a control volume analysis on a flat plate to
find out its total drag
– choice of top boundary
– concept of momentum deficit
• Suggest another way to find the drag on a flat plate.
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Friction Coefficient on a Flat Plate
• As the boundary layer thickens in the streamwise direction, what
do you expect the local friction drag to behave?
• Exercise: Perform a dimensional analysis on the total drag force
on a flat plate of length L and width w.
• Definition of friction coefficient:
CD 
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D
1
2
 U LW
2
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Categorization of Drag Components
• The total drag force on an object can be broadly classified into two
categories:
Total drag force
Friction drag
• directly related to
skin friction on surfaces
Pressure (form) drag
• indirectly related to fluid viscosity
• due to momentum losses through viscosity
• mostly involves flow separation
• Relative importance between friction drag and pressure drag is
strongly Reynolds number dependent and geometry dependent
(slender versus blunt bodies).
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Pressure Drag
• The flat plate boundary layer illustrates the origin of friction drag
which is directly related to the viscosity of a fluid and the no-slip
boundary condition at a solid surface.
• Another drag component which is indirectly related to the viscosity of
a fluid is called the pressure drag, which is absent in the flat plate case.
• Pressure drag is due to the difference in pressure forces between the
front and back side of an object.
• The difference in pressure distribution is indirectly related to viscous
effects (phenomena of flow separation).
• Definition of pressure coefficient over a cylinder
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ES 202 Fluid & Thermal Systems
cp 
P  P
1
2
U 
2
13
Flow Separation
• Flow separation is an artifact of fluid friction
– think of blowing versus suction (application to pipe inlet and outlet)
• Show visualizations from MMFM:
–
–
–
–
–
–
Boundary layer transition
Conditions producing separation
Pressure losses and drag
Effects of boundary conditions on separation
Flow over cylinders: effect of Reynolds number
Flow over edges and blunt bodies
• Mechanism: The flow does not have enough momentum in the
boundary layer to negotiate the pressure hill it has to climb to remain
attached.
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Pressure Coefficient over a Cylinder
Taken from Figure 3.49 in “Fundamentals of Aerodynamics”
by John D. Anderson Jr.
5
Resup  6.7 10
Resub  1.9  105
q
P  P
1
 U 2
2
subcritical
supercritical
inviscid
q, degrees
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Example on Drag Coefficient of a cylinder
in cross-flow
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