mae 3241: aerodynamics and flight mechanics introduction to streamlines, stream functions, and...

MAE 3241: AERODYNAMICS ANDFLIGHT MECHANICS

Introduction to Streamlines, Stream Functions, and Velocity Potential

January 28, 2011

Mechanical and Aerospace Engineering DepartmentFlorida Institute of Technology

D. R. Kirk

2

HARRIER INSTANTANEOUS STREAMLINES• Streamline

– Set of points that form a line that is everywhere tangent to local velocity vector– No flow across streamlines– For a steady flow, moving fluid element traces out a fixed path in space

• Stream tube– A set of streamlines that intersect a closed loop in space

Water streamlines on F-16 modelhttp://www.aerolab.com/water.html

Harrier instantaneous streamlineshttp://ails.arc.nasa.gov/Images/InfoSys/AC91-0365-12.html

3

DIFFERENCES BETWEEN and 1. Flow field variables are found by:

– Differentiating in the same direction as velocities– Differentiating in direction normal to velocities

2. Potential function applies for irrotational flow only3. Stream function applies for rotational or irrotational flows

4. Potential function applies for 2D flows [(x,y) or (r,)] and 3D flows [(x,y,z) or (r,, )]

5. Stream function applies for 2D (x,y) or (r, ) flows only

6. Stream lines ( =constant) and equipotential lines ( =constant) are mutually perpendicular– Slope of a line with =constant is the negative reciprocal of the slope of a

line with =constant

4

STREAMLINE AND STREAM FUNCTION EXAMPLE

5

STREAMLINE AND STREAM FUNCTION EXAMPLE

02

22

waxyv

yxau

xyxa

yyxa

23

32

3

3

=0=1=2

=0=1=2

6

STREAMLINE PATTERN: MATLAB FUNCTION

• Physical interpretation of flow field1. Flow caused by three intersecting streams2. Flow against a 120º corner3. Flow around a 60º corner

• Patterns (2) and (3) would not be realistic for viscous flow, because the ‘walls’ are not no-slip lines of zero velocity

7

STREAMLINE PATTERN: MATLAB FUNCTION

8

STREAMLINE PATTERN: MATLAB FUNCTION

9

u AND v VELOCITY COMPONENTS

10

VELOCITY MAGNITUDE

11

STATIC PRESSURE FIELD

12

TOTAL PRESSURE FIELD: P + ½V2 = P + ½(u2 +v2)½

13

ASIDE: MATLAB CAPABILITY FOR STREAMLINE PLOTTING

Altitude 1

Altitude 2

Altitude 3

14

ASIDE: MATLAB CAPABILITY FOR STREAMLINE PLOTTING