ES 202Fluid and Thermal Systems

Lecture 29:Drag and Lift Coefficients

(2/18/2003)

Lecture 29 ES 202 Fluid & Thermal Systems 2

Assignments

• Homework:– 13-56C, 13-62, 13-63, 13-72C, 13-88

• Reading:– 13-7 to 13-8

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Announcements

• Guest speaker Dr. John Adams will talk 2 talks today:– “Hypersonic Systems, Technology, and Testing”, including

relevant remarks on the recent Columbia Space Shuttle tragedy in O259 at 4:20 pm

– “Flight Mechanics of a Spinning Dimpled Spheroid” in the Khan Room at 6:00 pm

• Homework assigned this week is just for your learning, no need to hand it in

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Road Map of Lecture 29• Finish up example on drag coefficient of cross-flow cylinder in a wind tunnel

• Give out answers to in-class drag analyses yesterday

• Introduce definition of drag coefficients

• (Combined) Drag coefficients for objects of various geometries– concept of streamlining

• Categorization of drag components– skin frictional drag versus pressure drag– effects of body shape on drag (blunt body versus slender body)– flow separation (an artifact of fluid viscosity)

• Exercise on qualitative description of flow acceleration and pressure variation over a blunt body

– notion of stagnation point (high pressure)

• Applications:– truck tipping problem– terminal velocity (balance between weight, drag and buoyancy)

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Answers to Drag Analyses

• Drag analysis on a flat plate:

• Drag analysis on a cross-flow cylinder in open air:

• Drag analysis on a cross-flow cylinder in a wind tunnel:

wUD 72

7 2

wdUD 2

1

3

4 2

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1

27

88 2

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Drag Coefficient

• From the results of drag analysis on a cross-flow cylinder in open air,

a non-dimensional group, the drag coefficient CD , can be defined:

• The definition of drag coefficient can also be arrived by means of dimensional analysis, similar to that on boundary layer thickness.

• Show drag coefficient tables for various geometries

flow by theseen area frontal

pressure dynamicstream-free

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3

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DC

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1

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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• dominant on slender bodies

Pressure (form) drag• indirectly related to fluid viscosity• due to momentum losses through viscosity• mostly involves flow separation• dominant on blunt bodies

• Relative importance between friction drag and pressure drag is strongly Reynolds number dependent and geometry dependent (slender versus blunt bodies).

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Fluid Acceleration and Pressure Variation

• Perform a qualitative assessment on the changes in a flow as it approaches a blunt object.

– speed decreases, pressure increases from free-stream to stagnation point– highest pressure at stagnation point– flow splits into upper and lower streams– speed increases, pressure decreases from stagnation point to edges– highest speed and lowest pressure at the edges– flow speed decreases and pressure recovers behind the object– too much momentum loss in boundary layer: not enough momentum to

negotiate pressure hill, flow separates– large pressure difference between front and back sides causes pressure drag

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Example Problem• Truck tipping problem:

– recognize blunt body geometry– pressure drag as dominant drag component– moment analysis about Point O to determine minimum wind speed to tip truck– assume drag coefficient is all attributed to pressure drag– assume line of action of pressure drag to be at the geometrical center of truck– at tipping position, R2 = 0– fine points:

• small frictional drag component in tabulated CD value• asymmetry in problem not accounted for in tabulated CD value

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R1R2U

O

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Terminal Speed of Falling Objects• Identify the major forces on a falling object

• As the falling object accelerates, the drag force increases rapidly (quadratic dependence on falling speed).

• At terminal speed, the net force on the falling object is zero, implying a perfect balance between body weight and drag.

• The force balance sets the condition to determine the terminal speed.

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1 2

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