ES 202 Fluid and Thermal Systems

Lecture 29: Drag and Lift Coefficients (2/18/2003)

Assignments • Homework: – 13-56C, 13-62, 13-63, 13-72C, 13-88 • Reading: – 13-7 to 13-8

Lecture 29 ES 202 Fluid & Thermal Systems 2

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 Lecture 29 ES 202 Fluid & Thermal Systems 3

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 blunt body – notion of stagnation point (high pressure) and pressure variation over a Applications: – truck tipping problem – terminal velocity (balance between weight, drag and buoyancy) Lecture 29 ES 202 Fluid & Thermal Systems 4

Answers to Drag Analyses

• Drag analysis on a flat plate:

D

 7 72 

U

2 

w

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

D

 4 3   1 2 

U

2  

d w

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

D

 88 27   1 2 

U

2  

d w

Lecture 29 ES 202 Fluid & Thermal Systems 5

Drag Coefficient

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

D

 4 3   1 

U

2   frontal area free stream dynamic pressure seen by the flow a non-dimensional group, the drag coefficient

C D ,

can be defined:

C D



D

1 2 

U

2

A f

• 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 Lecture 29 ES 202 Fluid & Thermal Systems 6

Categorization of Drag Components

• The total drag force categories: on an object can be broadly classified into two 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 strongly Reynolds number dependent and (slender versus blunt bodies).

friction drag and pressure geometry drag is dependent Lecture 29 ES 202 Fluid & Thermal Systems 7

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 – highest pressure at stagnation point from free-stream to stagnation point – flow splits into upper and lower streams – speed increases, pressure decreases from stagnation point to edges – highest speed and lowest pressure – flow speed decreases and at the edges 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 Lecture 29 ES 202 Fluid & Thermal Systems 8

Example Problem

• Truck tipping problem:

U R 2 R 1 O

– recognize blunt body – pressure drag geometry as dominant drag component

W

– 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 – at tipping position,

R 2

– fine points: • small frictional drag of pressure drag to be at the geometrical center of truck

= 0

component in tabulated

C D

value • asymmetry in problem not accounted for in tabulated

C D

value Lecture 29 ES 202 Fluid & Thermal Systems 9

Terminal Speed of Falling Objects

• Identify the major forces on a falling object

D



C D

  1 2 

U

2  

A f W

• As the falling object accelerates, dependence on falling speed).

the drag force increases rapidly ( quadratic • At terminal speed, the net force perfect balance between on the falling object is body weight and drag.

zero, implying a • The force balance sets the condition to determine the terminal speed.

Lecture 29 ES 202 Fluid & Thermal Systems 10