1. ES 202 Fluid and Thermal Systems Lecture 27: Drag on Cylinders and Spheres (2/13/2003)

2. ES 202 Fluid & Thermal Systems
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
Lecture 27
ES 202 Fluid & Thermal Systems

3. ES 202 Fluid & Thermal Systems
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
Lecture 27
ES 202 Fluid & Thermal Systems

4. ES 202 Fluid & Thermal Systems
“Snow-Rollers”
(taken from
Lecture 27
ES 202 Fluid & Thermal Systems

5. ES 202 Fluid & Thermal Systems
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
Lecture 27
ES 202 Fluid & Thermal Systems

6. 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.
Lecture 27
ES 202 Fluid & Thermal Systems

7. Motivation: The Commercial Side
Drag optimization on airplanes and automobiles
Design for turbomachinery
(compressor and turbine)
lower surface
upper surface
Pressure coefficient at Mach 2.2
Blade design in turbomachinery using computational
methods
Images taken from Aerospace Computing Laboratory,
Stanford University
Lecture 27
ES 202 Fluid & Thermal Systems

8. ES 202 Fluid & Thermal Systems
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
Lecture 27
ES 202 Fluid & Thermal Systems

9. Comparison of Fluid Properties
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.
Lecture 27
ES 202 Fluid & Thermal Systems

10. ES 202 Fluid & Thermal Systems
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.
Lecture 27
ES 202 Fluid & Thermal Systems

11. 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:
Lecture 27
ES 202 Fluid & Thermal Systems

12. 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).
Lecture 27
ES 202 Fluid & Thermal Systems

13. ES 202 Fluid & Thermal Systems
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
Lecture 27
ES 202 Fluid & Thermal Systems

14. ES 202 Fluid & Thermal Systems
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.
Lecture 27
ES 202 Fluid & Thermal Systems

15. Pressure Coefficient over a Cylinder
Taken from Figure 3.49 in “Fundamentals of Aerodynamics”
by John D. Anderson Jr. q
subcritical
supercritical
inviscid
q, degrees
Lecture 27
ES 202 Fluid & Thermal Systems

16. Example on Drag Coefficient of a cylinder in cross-flow
Lecture 27
ES 202 Fluid & Thermal Systems