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Introduction to Streamlines and Velocity Potentials in Aerodynamics

Learn about streamlines, stream functions, and velocity potentials in aerodynamics, with examples and patterns illustrated using MATLAB functions. Explore instantaneous streamlines and key concepts in fluid mechanics.

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Introduction to Streamlines and Velocity Potentials in Aerodynamics

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  1. MAE 3241: AERODYNAMICS ANDFLIGHT MECHANICS Introduction to Streamlines, Stream Functions, and Velocity Potential January 28, 2011 Mechanical and Aerospace Engineering Department Florida 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 model http://www.aerolab.com/water.html Harrier instantaneous streamlines http://ails.arc.nasa.gov/Images/InfoSys/AC91-0365-12.html

  3. DIFFERENCES BETWEEN f and y • Flow field variables are found by: • Differentiating f in the same direction as velocities • Differentiating y in direction normal to velocities • Potential function f applies for irrotational flow only • Stream function y applies for rotational or irrotational flows • Potential function f applies for 2D flows [f(x,y) or f(r,q)] and 3D flows [f(x,y,z) or f(r,q, f)] • Stream function y applies for 2D y(x,y) or y(r, q) flows only • Stream lines (y =constant) and equipotential lines (f =constant) are mutually perpendicular • Slope of a line with y =constant is the negative reciprocal of the slope of a line with f =constant

  4. STREAMLINE AND STREAM FUNCTION EXAMPLE

  5. STREAMLINE AND STREAM FUNCTION EXAMPLE y=0 y=1 y=2 f=0 f=1 f=2

  6. STREAMLINE PATTERN: MATLAB FUNCTION • Physical interpretation of flow field • Flow caused by three intersecting streams • Flow against a 120º corner • 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 + ½rV2 = P + ½r(u2 +v2)½

  13. ASIDE: MATLAB CAPABILITY FOR STREAMLINE PLOTTING Altitude 1 Altitude 2 Altitude 3

  14. ASIDE: MATLAB CAPABILITY FOR STREAMLINE PLOTTING

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